by Golam Mohammed Ashique Habib - University of Toronto

Three Essays in Macroeconomics

by

Golam Mohammed Ashique Habib

A thesis submitted in conformity with the requirementsfor the degree of Doctor of PhilosophyGraduate Department of Economics

University of Toronto

c© Copyright 2018 by Golam Mohammed Ashique Habib

Abstract

Three Essays in Macroeconomics

Golam Mohammed Ashique HabibDoctor of Philosophy

Graduate Department of EconomicsUniversity of Toronto

2018

This thesis collects three papers studying topics related to financial frictions and macroeconomics.

In Chapter 1, I study how rating agencies affect liquidity and welfare in over-the-counter (OTC) asset

markets. My main finding is that when assets are rated matters for welfare and liquidity: When sellers

rate the asset prior to matching, then ratings can improve liquidity but their use is fragile. However,

a better arrangement is to rate the asset after buyers and sellers meet. Although this arrangement

eliminates liquidity distortions and improves welfare, it is difficult to sustain if buyers are not incentivized

to follow through with rating the asset. Buyers can overcome this commitment problem by constructing

a semi-pooling equilibrium. I use my framework to show that policies that support buyers purchasing

ratings can substantially improve market liquidity.

In Chapter 2, I propose that an important channel through which financial frictions adversely impact

aggregate productivity is by hindering the discovery of productive entrepreneurs. I develop a model

where households have imperfect information about the quality of their business idea and show how

financial frictions arising from weak contract enforcement systematically reduce access to capital for

poor households with good ideas, which undermines their incentive to learn. After calibrating the model

to US data, I find that with imperfect information, total factor productivity (TFP) falls by 23% when

contract enforcement is lowered to developing country levels, compared to 12% with perfect information.

Half of the productivity loss in the economy with imperfect information is due to financial frictions

hindering the discovery of good ideas by poor households. I find that these losses can be substantially

mitigated by subsidizing young entrepreneurs.

In Chapter 3, I present ongoing work with Chaoran Chen and Xiaodong Zhu examining the joint

role of financial and managerial frictions in explaining factor misallocation and lower productivity in

developing countries. We present a model where weak contract enforcement prevents productive firms

from hiring outside managers and expanding production in developing countries, and show that its key

features are consistent with cross-country evidence from the IPUMS-International dataset.

ii

Acknowledgements

I am deeply indebted to the members of my supervisory committee. I thank Diego Restuccia, RonaldWolthoff and Xiaodong Zhu for their patience and guidance. I am grateful for everything I have learnedfrom them.

I have also greatly benefitted from insightful discussions with many faculty members at the Universityof Toronto. In particular, I would like to mention Rahul Deb, Burhan Kuruscu and Joseph Steinberg. Ialso want to thank Stephen Ayerst, Chaoran Chen, Kevin Devereux, Adam Lavecchia, Mathieu Marcouxand Nicolas Saldias for their help and support, which contributed greatly to the completion of this thesis.I owe a lot to my parents and my sisters for their continuing encouragement.

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Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Contents iv

List of Tables vi

List of Figures vii

1 Rating Agencies, Liquidity and Adverse Selection in Decentralized Asset Markets 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Complete Information Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4 Information asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4.1 Equilibrium without rating agencies . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.2 Allowing Agents to Rate their Assets . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.5 Analyzing the Financial Crisis and Policy Intervention . . . . . . . . . . . . . . . . . . . . 251.5.1 Policy Intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Imperfect Information about Entrepreneurial Productivity, Financial Frictions, andAggregate Productivity 362.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.2.1 Stylized Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2.2 Main Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.2.3 Properties of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.3 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562.3.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562.3.2 Weakening Contract Enforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582.3.3 Increasing Imperfect Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632.3.4 Policy Intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

2.5.1 Modified Environment Where Wealth Smoothing is Optimal . . . . . . . . . . . . . 71

iv

3 Contracting Frictions with Managers, Financial Frictions, and Misallocation 773.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.2 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

3.2.1 Firm-Level Evidence from China and India . . . . . . . . . . . . . . . . . . . . . . 793.2.2 Cross-Country Differences in Contracting Frictions . . . . . . . . . . . . . . . . . . 82

3.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.3.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.3.3 Contracting Frictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.3.4 Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.3.5 Entrepreneur’s Problem and Characterization . . . . . . . . . . . . . . . . . . . . . 883.3.6 Recursive Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923.3.7 Aggregation and Stationary Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 923.3.8 Model Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.4 Preliminary Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943.4.1 Calibration Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943.4.2 Contracting Frictions and Aggregate Productivity . . . . . . . . . . . . . . . . . . 953.4.3 Cross-Sectional Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 973.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.6.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993.6.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Bibliography 102

v

List of Tables

2.1 Calibrated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.2 Benchmark and Calibrated (US) Economies . . . . . . . . . . . . . . . . . . . . . . . . . . 582.3 Decomposing TFP Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.1 Calibrated Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

vi

List of Figures

1.1 Timeline of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.2 Equilibrium for Different Values of Rating Accuracy and Rating Fee . . . . . . . . . . . . 161.3 Liquidity, High-quality Seller’s Payoff, and Adverse Selection Penalty when Sellers are

Allowed to Buy Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.4 Equilibrium Rating Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231.5 Equilibrium Liquidity, Pooling, and Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . 251.6 Analyzing the Financial Crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.1 Timeline for Stylized Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.2 Expected Benefit and Cost of Operating in First Period . . . . . . . . . . . . . . . . . . . 412.3 Threshold Belief for Operating First Period . . . . . . . . . . . . . . . . . . . . . . . . . . 422.4 Timeline for an Entrepreneur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472.5 Credit Limit with Age for a High-Quality Entrepreneur . . . . . . . . . . . . . . . . . . . 542.6 Access to Credit with Age for a High-Quality Entrepreneur . . . . . . . . . . . . . . . . . 552.7 Disciplining Imperfect Information Parameters . . . . . . . . . . . . . . . . . . . . . . . . 572.8 TFP and GDP per Capita for Different Levels of φ . . . . . . . . . . . . . . . . . . . . . . 582.9 Decomposing TFP Losses from Weaker Contract Enforcement . . . . . . . . . . . . . . . . 602.10 Access to Credit by Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622.11 Exit Rate with Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622.12 TFP as Imperfect Information Increases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632.13 TFP and GDP per Capita with Subsidy Size . . . . . . . . . . . . . . . . . . . . . . . . . 662.14 Decomposing TFP Gains from Subsidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.15 Timeline for Entrepreneurs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712.16 Timeline for Workers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.1 Average Product of Capital of Indian Firms . . . . . . . . . . . . . . . . . . . . . . . . . . 803.2 Decomposition of Wedges of Indian Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.3 Average Product of Capital of Chinese Firms . . . . . . . . . . . . . . . . . . . . . . . . . 813.4 Decomposition of Wedges of Chinese Firms . . . . . . . . . . . . . . . . . . . . . . . . . . 823.5 Decomposition of Wedges of Chinese Firms: Alternative Size Measure . . . . . . . . . . . 833.6 Fraction of Individuals Working as Managers . . . . . . . . . . . . . . . . . . . . . . . . . 843.7 Income Premium of Managers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.8 Entrepreneur’s Timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883.9 TFP and Contracting Frictions with Managers . . . . . . . . . . . . . . . . . . . . . . . . 95

vii

3.10 Fraction Employed as Outside Managers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963.11 TFP and Financial Frictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 973.12 Number of Managerial Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.13 Marginal Product of Capital and Firm Size . . . . . . . . . . . . . . . . . . . . . . . . . . 98

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Chapter 1

Rating Agencies, Liquidity andAdverse Selection in DecentralizedAsset Markets

1.1 Introduction

I study the role of credit rating agencies in the market for asset backed securities (ABS). These securitiescomprise a large portion of US assets, and are traded bilaterally in over-the-counter (OTC) markets.In these markets, adverse selection is a potential problem since the seller is often the originator of theunderlying assets and therefore is better informed about its payoffs.1 Rating agencies can act as aneutral third party inspector who publicly releases information about the assets and therefore mitigatesthe lemons problem. Indeed, rating agencies do rate ABS before sale and the ABS market was a largesource of revenue for the three major rating agencies before the crisis [Gorton and Metrick, 2011].

Yet, during the financial crisis of 2007-2009, buyers lost confidence in credit ratings [Brunnermeier,2009].2 Simultaneously, there was a sharp decline in the prices, liquidity and new issuances of securitizedproducts. Market participants believed that the rating agencies statistical models were under-estimatingthe riskiness of securitized assets. Furthermore, they started questioning the incentive of rating agenciesand issuers to report ratings honestly.

I present a model in which a relationship naturally arises between the quality of credit ratings andliquidity. The over-the-counter market is described using a competitive search model. The existing lit-erature finds that in a competitive search environment with information asymmetry, illiquidity emergesas a means of screening sellers [Chang, 2017]. In these models, introduction of adverse selection leads todiscontinuous drops in liquidity and the resulting equilibrium is generally inefficient. I find that whenratings are introduced as a substitute method of screening, the liquidity distortions can be eliminated.When I restrict sellers to rate assets prior to meeting buyers, I find that if the rating technology issufficiently accurate, information asymmetry has no effect on liquidity. However, when the rating tech-nology’s effectiveness drops below a certain threshold, buyers switch to using only liquidity distortions

1For example, the asset might be a mortgage-backed security and the seller could be the bank issuing the underlyingmortgages.

2Also see Gorton and Metrick [2011].

1

Chapter 1. Rating Agencies, Liquidity, and OTC Markets 2

as a screening device and there is a large drop in liquidity. I also show that buyers buying ratings aftermeeting with sellers is generally a better rating arrangement, but may not obtain because of endoge-nous commitment problems. I provide a rationale for why multiple screening mechanisms are used bymarket participants, and help explain how the declines in the CRA’s ability to screen and liquidity canbe connected.

One motivation for my paper is the empirical literature, which suggests that asymmetric informationexisted in the OTC markets prior to the crisis. For example, Downing et al. [2008] show that securitizedmortgage loans faced higher pre-payment risk than the loans banks keep on their books. Keys et al.[2012] found that banks screen mortgage borrowers less rigorously when the mortgage can be securitizedand sold off. Since low-quality assets always existed in these markets, these models would predict thatliquidity should always be low. I show that the crisis can be interpreted as a switch between screeningschemes, from ratings to liquidity distortions.

Let me briefly outline the key features of my model: Buyers and sellers are both risk-neutral, and tryto bilaterally trade indivisible assets. These assets are either high- or low-quality. Only an asset’s ownerknows its quality, which creates the potential for adverse selection. As in Chang [2017] and Guerrieri et al.[2010], buyers organize trade by posting contracts. Each type of posted contract constitutes a submarket,and sellers choose which submarket to enter to sell their asset.3 When choosing the submarket to enter,sellers take into account the probability of meeting a buyer in that submarket. The probability ofmeeting buyers is the relevant notion of market liquidity in my model, and it varies endogenously acrosssubmarkets. Finally, the economy also contains rating agencies, who sell noisy assessments of assetquality for a fee. Either buyers or sellers can purchase a rating from a rating agency.

As in Chang [2017], buyers can separate low- and high-quality sellers by exploiting differences insellers’ preferences of price and liquidity. Since high-quality sellers receive a higher payoff than low-quality sellers from holding onto their asset, they are more willing to risk not meeting a buyer for ahigher price. In equilibrium, low-quality sellers are sorted into a high-liquidity, low-price submarket andhigh-quality sellers are sorted into a high-price, low-liquidity submarket.

This equilibrium has several notable properties relevant to my analysis: It is unique, generally notconstrained efficient, and the cost of adverse selection is fully borne by high-quality sellers.4 The marketis fragile, because even a tiny fraction of low-quality sellers results in a sharp drop in liquidity. Finally,both liquidity and welfare falls as the gap in quality between the two types of assets increases.

I introduce the option to rate assets in two steps, to highlight how the time when assets are ratedaffect outcomes. First, I only allow assets to be rated by sellers prior to meeting buyers. I find that assetsare rated only if doing so improves high-quality sellers’ welfare. High-quality sellers’ welfare improvesif the benefit of rating the asset (i.e. more liquid market) outweighs the cost of purchasing the rating.One might expect that ratings are used to create a better quality pool of assets, as in Chiu and Koeppl[2016]. However, I show that liquidity for rated assets is higher only if low-quality sellers can be inducedto not rate their assets. If some low-quality sellers were to rate their assets then buyers would fullyreduce liquidity to induce separation, negating any gains from the rating.

3Since the uninformed side (buyers) post contracts, this is a screening problem. Screening is the common approach inthe literature studying adverse selection in competitive search models. See Delacroix and Shi [2013] and Williams [2016]for studies of signalling (informed party posts contracts) in a competitive search framework.

4For example, if there were only few low-quality sellers, a social planner constrained by the same frictions would poolthe two types. However, in the competitive economy, pooling is undermined by individual buyers who try to separateout the high-quality sellers. Davoodalhosseini [2017] discusses the efficiency properties of competitive search models underadverse selection.


The relationship between liquidity and the quality gap is no longer monotonic, and ratings are usedonly for intermediate levels of information asymmetry (i.e. gap in asset quality). For small gaps inquality, ratings are not used because the rating fee is too high compared to the small welfare cost oflower liquidity. For high quality gaps, the low-quality sellers’ incentive to mimic high-quality sellers istoo high and liquidity would not increase sufficiently with ratings to justify paying the fee.

I then introduce the option to rate assets after buyers and sellers meet. This turns out to be the betterrating arrangement, but the market’s ability to sustain it depends on whether buyers can commit tofollow through with rating the asset. This rating arrangement allows buyers to offer contracts with ratingcontingent prices, which yields low- and high- quality sellers different expected payments. Liquidity isnever distorted because buyers are always able to set the expected payment for low-quality sellers suchthat they prefer their own submarket.

When buyers buy ratings and sellers are fully separated, there is no need for liquidity distortionsin equilibrium. Low-quality assets are sold unrated, while high quality assets are rated by buyers.The welfare cost of adverse selection is bounded by the rating fee, no matter how large is the qualitygap between the two types of assets. Furthermore, the equilibrium is robust to either an increase ininformation asymmetry or a decrease in rating accuracy. I find that an equilibrium where buyers ratethe assets and fully separate the two types dominates sellers buying ratings.

However, full separation is not sustainable if buyers cannot commit to rate the asset. The intuitionis as follows: If sellers are fully separated, then buyers know the asset quality from the submarketthey enter, and are better off just paying the high price and saving on the rating fee. Since it is therating-contingent payments that keeps low types out of the submarket, the arrangement unravels.

I show that if the quality gap is high enough, then a semi-pooling equilibrium exists. Buyers maketheir promise to rate credible by including low-quality sellers. With enough low-quality sellers in thesubmarket, buyers find it optimal to follow through with their promise to rate in order avoid overpayingfor low-quality assets. High-quality sellers’ welfare is lower than under full separation, as they must bearthe cost of rating the low-quality assets. However, as the cost of overpayment increases with the qualitygap, fewer low-quality sellers are needed to solve the commitment problem. Interestingly, high-qualitysellers’ welfare actually increases with the level of information asymmetry.

Finally, I show how subsidizing highly-rated assets can improve welfare by helping buyers overcometheir commitment constraint. The reason is that in the decentralized market, buyers and sellers maynot be using ratings optimally. Thus, my analysis illustrates the potential importance of accounting forthe downstream market structure when evaluating interventions in the rating market.

1.1.1 Literature Review

This paper contributes to the literature on adverse selection in decentralized markets, and the literatureon rating agencies. Because of the decentralized and bilateral nature of the market for asset backedsecurities, a recent literature has studied these markets using search models. In a perfect informationsetting, Duffie et al. [2005] show how the degree of search frictions can affect liquidity and prices. Lesterand Camargo [2014] study adverse selection in this market using a random search environment. Chang[2017], Guerrieri and Shimer [2011], and Guerrieri et al. [2010] consider competitive search, which allowsfor multiple trading prices. They find that when the information asymmetry is only about the commonvalue of the asset, the sellers are fully separated by quality in equilibrium, but liquidity is distorteddownward. Williams [2016] considers retaining a fraction of the asset as an alternate screening device,


but finds that liquidity distortion is generally the better option. I show that ratings can be a betterscreening option. Furthermore, I find that the standard relationship between adverse selection andliquidity is obtained only when ratings are not sufficiently accurate to use as an alternative instrument,and when buyers have difficulty committing to rate the asset.

To my knowledge, Chiu and Koeppl [2016] is the only other paper to study the role of credit ratingagencies in OTC markets. In their paper, ratings are the only tool for inducing separation betweenlow- and high-quality sellers. They emphasize buyers’ market power resulting from bilateral trade indecentralized markets. Since future buyers capture all the gains from improving rating accuracy, dealerschoose rating accuracy that is just high enough for the market to exist. Furthermore, dealers have anincentive to profit from intermediating lemons between sellers and secondary market buyers.

In my environment, buyers endogenously sort sellers into different submarkets and separate low- andhigh-quality assets. It is not possible to pass off lemons to future buyers as liquidity distortions canalways separate assets by quality (e.g. Guerrieri and Shimer [2011]). Instead, this paper’s highlights theinterplay between liquidity variation and ratings to sort sellers into separate submarkets.

The central role of the credit rating agencies (CRAs) in the financial crisis has encouraged a growingcorporate finance literature on the incentives of these institutions, and how their behaviour affectsinvestors and market efficiency. For example, Mathis et al. [2009] examine the role that reputationalconcerns play in disciplining credit rating agencies. Skreta and Veldkamp [2009] study the incentive ofissuers to shop around for favourable ratings. They show that shopping around is related to increasingcomplexity of assets. Pagano and Volpin [2012] show one channel through which CRA behaviour canlead to illiquidity. In their model, releasing (concealing) information generates illiquidity in the primary(secondary) market for the asset. Their finding relies on differences in investor’s ability to processinformation. Kashyap and Kovrijnykh [2015] consider optimal payment schemes for CRAs. My papercontributes to this branch of the finance literature, by identifying a new channel through which creditrating agencies affect the market. My results are also potentially helpful for thinking about policyinterventions.

The rest of the paper is organized as follows: In section 1.2, I describe the model. In section 1.3 Ipresent the complete information benchmark and in section 1.4, I analyze the equilibrium under imperfectinformation. In section 1.5 I map my model to the 2007 financial crisis and present a welfare-improvingpolicy intervention. Finally, section 1.6 concludes.

1.2 Model

I construct a static model of bilateral trade in an OTC market, building on the competitive searchframeworks developed by Chang [2017] and Guerrieri et al. [2010]. I abstract from matching frictions toobtain closed-form solutions for prices and liquidity. Although this substantially simplifies the exposition,it is without loss of generality as the results hold in an economy with matching frictions.

Sellers. There is a measure 1 of risk-neutral sellers, each of whom have one indivisible asset of qualitys. The asset quality s is either high (sH) or low (sL). A fraction α of all assets are high-quality, andthis fraction is public information. Define ∆ ≡ sH − sL as the quality gap between the two asset types.


This quality gap is the relevant measure of information asymmetry in my model.5

Sellers face a holding cost c > 0, which reduces the value of the asset to s− c > 0. This holding costrepresents, for example, a need for liquidity.

Buyers. There is a large measure of risk-neutral buyers. Buyers do not face a holding cost, whichcreates a difference in the value of holding the asset between buyers and sellers, and thus potential gainsfrom trade.

Ratings. There are a number of rating agencies who can evaluate the quality of assets at a priceF > 0. I abstract from rating agency market structure and treat these institutions as technologies. Anasset can receive either an A or a B rating. A high-quality asset receives an A rating with certainty. Alow-quality asset receives an A rating with probability π and a B rating with probability 1 − π.6 Theprobability π is the accuracy or quality of the rating technology. The higher is π, the better is the ratingtechnology at identifying low-quality assets.

The rating agency issues a report stating the asset’s rating R, which is A or B. I treat unrated assetsas having an NR rating. Therefore, an asset can have one of three possible ratings: R ∈ NR,B,A.In assumption 1, I assume that the purchaser of the rating can hide the rating from other marketparticipants if they wish.7

Assumption 1. Agents can hide their asset’s rating from other buyers and sellers.

In assumption 2, I restrict the number of times an asset can be rated by an agent to one. Thisassumption means we do not need to consider how buyers evaluate assets with multiple ratings, andtherefore simplifies the exposition. Although it rules out shopping around for good ratings by sellers,the results of this paper would be qualitatively similar if this assumption was relaxed and agents wereable to rate assets multiple times.8

Assumption 2. An agent may rate an asset at most once.

Markets. Trading is decentralized, bilateral, and is organized as follows: Each buyer who wants totrade posts a contract specifying the terms of trade they wish to offer. Posting the contract coststhe buyer k > 0. At a minimum, these contracts state a trading price. However, buyers can includeadditional terms such as a transaction fee, a requirement that the asset have a particular rating, or theoption to rate the asset and offer rating-contingent prices. I will describe the potential contracts in detailshortly. Following the literature, each type of posted contracts defines a submarket.

Assumption 3 ensures that both types of assets give buyers and sellers a positive payoff, and thatthere are sufficient gains from trading both types of assets.

5As I will make clear later on, the equilibrium is invariant to the the fraction of low-quality sellers 1− α, as long as itis not zero. Therefore, α is not a useful measure of information asymmetry.

6An interpretation of this rating technology is that low-quality assets are just like high-quality assets, except with somehidden defects which are detected with probability π. Since high-quality assets do not have these defects, they are neverwrongly assigned a B rating. The results of this model are robust to high-quality assets receiving a B rating with someprobability.

7This assumption gives low-quality sellers the option to try rating their asset, and if they fail, sell their asset as anunrated one. This option is never exercised in equilibrium.

8To clarify, assumptions 1 and 2 together leave open the possibility that a seller might rate an asset, hide it, and thenthe buyer can rate it again.


Assumption 3. The asset qualities (sL, sH), the holding cost (c) and the posting cost (k) satisfy thefollowing inequalities:

sH > sL > c > k

After buyers set up submarkets by posting contracts, each seller decides which submarket to enter.As is standard in the literature, a seller can search in only one submarket.

Matching technology. If a submarket has a buyer-to-seller ratio of θ, then the probabilities of buyersand sellers finding a trading partner are q(θ) and m(θ) respectively. These matching probabilities are:

m(θ) =min θ, 1 (1.1)

q(θ) =min

1,1

θ

(1.2)

These matching probabilities simply state that agents on the short-side in a submarket always getsto trade. If there are fewer buyers than sellers in a submarket (θ < 1), then since matching is bilateral,only a fraction θ of sellers can trade (m(θ) = θ) while all buyers can (q(θ) = 1). In contrast, if θ ≥ 1,then all sellers (m(θ) = 1) and a fraction 1

θ of buyers trade (q(θ) = 1θ ).

9

Buyers will always match in equilibrium, but sellers may not. Therefore, in my framework, sellers’matching probability is the relevant notion of liquidity (definition 1).

Definition 1. Liquidity in a submarket is defined as the matching probability for sellers, m(θ).

Rating arrangements. Buyers specify in contracts conditions for rating the asset. An asset can berated either before or after its seller meets a buyer. If it is rated before the meeting, the rating must bepurchased by the seller. Prior to matching, an asset can be unrated (NR), or, if the seller decides torate the asset, have either an A or B rating. If an asset is unrated when buyers and sellers meet, thenthe buyer can rate the asset himself.10

There are four rating arrangements buyers can specify: they can ask for unrated assets (NR), askfor assets of a particular rating (A and B), or rated the asset themselves (BR). Although I refer to thelast arrangement as buyers rating the asset, I would like to emphasize that, in equilibrium, sellers payfor the rating. In total, the possible rating arrangements are:

R ∈ R ≡ NR,BR,A,B (1.3)

Buyers specify when posting contracts the rating arrangement they want. In assumption 4, I restrictbuyers to choosing exactly one rating arrangement from the set R.

Assumption 4. Buyers can choose exactly one rating arrangement R from the set of rating arrange-ments R.

9As previously stated, I abstract from frictions in the matching technology to simplify the presentation of my analysis.My results are robust to frictions in the matching process (i.e. maxm(θ), q(θ) < θ).

10An asset may be unrated when buyers and sellers meet because it was never rated, or because the seller hid the rating.


Buyers are not allowed to post contracts specifying multiple rating arrangements. For example, theycannot post contracts open to both unrated and A-rated assets. This assumption is without loss ofgenerality, and it greatly simplifies the exposition. This assumption is not restrictive for the followingreasons: If buyers were able to post contracts with multiple rating arrangements, they will weakly prefernot to do so in equilibrium. Further, the possibility of deviant buyers to post contracts with multiplerating arrangements will also not change the equilibrium contracts.

Contracts. A contract ω has three elements: a price function P , a transaction fee f , and a ratingarrangement R. The price function specifies a price for each rating that assets in the submarket mayhave. If the rating arrangement states that the asset will be bought unrated, or must already have an Aor B rating, then the pricing function specifies just one price. For example, in a submarket for A-ratedassets, contracts specify just a price for A-rated assets as B-rated and unrated assets are excluded fromthe submarket. If the buyer intends to rate the asset themselves, then they need to specify a price foreach rating. In this case, the pricing function specifies a price for an A-rating and a B-rating.

Formally, a contract is ω = (P (R), f,R) and Ω is the set of all possible contracts. Let Ω be the set ofall posted contracts and ΩR be the set of posted contracts that specify the rating arrangement R. If nocontracts with rating arrangement R is posted, then ΩR = ∅. Because assumption 4 restricts contractsto exactly one rating arrangement, the sets ΩR are mutually exclusive. The union of the sets ΩR is theset of all posted contracts.

ΩA ∪ ΩB ∪ ΩNR ∪ ΩBR = Ω

ΩR ∩ ΩR′ = ∅, where R,R′ ∈ R, R′ 6= R

Expected payments. Each contract’s terms imply an expected payment for each type of seller uponmatching. In submarkets with only one price, the expected payments are VH = VL = P − f . Insubmarkets with rating contingent prices, the expected payments are:

VH = PA − f (1.4)

VL = (1− π)PA + πPB − f (1.5)

A high-quality seller receives an A-rating for sure and therefore receives price PA. A low-quality sellerreceives price PA only if they receive an A-rating, which happens with probability 1−π. Otherwise theyreceive PB . Both sellers pay the upfront transaction fee f .

Alternative contracts. It is useful to replace the price function P (R) and the transaction fee f withthe expected payment given to each type of seller conditional on matching, VL and VH . With some abuseof notation, I will also express the contracts as ω = (VL, VH ,R). Although I will characterize equilibriain terms of expected payments, I will also show the corresponding prices and transaction fees that yieldthose expected payments.

Rating commitment. After matching, buyers decide whether to follow through with rating the asset.I capture exogenous commitment by introducing a cost, χ ≥ 0, of reneging on rating the asset. If a


buyer does not rate the asset after promising to do so, they pay the seller the higher price PA.Buyers and sellers have rational expectations regarding whether buyers will renege on rating the

asset. Let Vj be the actual expected payment the seller with asset quality sj gets (as opposed Vj , whichis the expected payment implied by the posted contract). If sellers know that the buyer will renege, thentheir expected payments are VL = VH = PA − f .

Timeline of events. Figure 1.1 outlines the sequence of events.

1 3

2 4

Buyer decideswhether to rate

asset

Sellersdecide

whether torate

assets to maximizeJ

Sellersenter

submarkets tomaximize W.

Buyers/sellersmatch

Trade takesplace

5

Buyerspost

contractsto maximize U

Figure 1.1: Timeline of Events

Buyer to seller ratio and asset quality distribution. Let µ(ω) be the fraction of high-qualitysellers and θ(ω) be the buyer-to-seller ratio in active submarket ω.

Buyers’ payoff. A buyer’s expected payoff, U , from posting a contract ω depends on the actualexpected payment they will make (VL, VH), the probability that they will match with a seller (q(θ)),whether they will rate the asset (Irate ∈ 0, 1), the distribution of sellers in their submarket (µ), andwhether they will renege on the promise to rate the asset (Irenege ∈ 0, 1). Their payoff is:

U(ω) = U(VL, VH , θ, µ, Irate, Irenege)

= −k − F Irate − χIrenege + q(θ)[µsH + (1− µ)sL − µVH − (1− µ)VL] (1.6)

In the right-hand side of equation (1.6), I suppress reference to the submarket ω although all variables


are submarket-specific. The buyer incurs the cost k from posting the contract. If they rate the asset(Irate = 1), then they incur the rating fee F . If they had promised to rate the asset (i.e. had posted acontract with the rating arrangement BR), then they incur χ if they renege on their promise.11 Theymatch with a seller with probability q(θ). If they match with a high-quality seller, which happens withprobability µ, then they get the asset sH and pay the seller VH . If they match with a low-quality seller,then they get the asset sL and pay the seller VL.

Sellers’ payoff in a submarket. Let W (ω; sj , R) denote the expected payoff of a seller who has anasset with quality sj and rating R, and has entered submarket ω. Sellers can only enter a submarket iftheir asset’s rating is consistent with the submarket’s rating arrangement: Sellers with an asset ratedA (rated B) can only enter the submarket if ω ∈ ΩA (ω ∈ ΩB). Sellers with unrated assets can entersubmarkets where buyers want unrated assets or want to rate the assets themselves (i.e. ω ∈ ΩNR∪ΩBR).

Sellers care only about the expected payment Vj and the likelihood of matching with a buyer (m(θ)).Conditional on having the required rating to enter the submarket, their payoff is:

W (ω; sj , R) = W (θ, Vj ; sj , R) = (1−m(θ))(sj − c) +m(θ)Vj (1.7)

On the right-hand side of the first equality in equation (1.7), I have again suppressed ω. Withprobability 1 − m(θ), the seller does not find a buyer and is left holding the asset. With probabilitym(θ), they meet a buyer and receive the expected payment Vj .

Define W (sj , R) as the maximum expected payoff a seller with asset quality sj and asset rating Rcan receive, given the set of active submarkets. If a seller has an unrated asset, then they can try to sellit in a market for unrated assets (NR), in a submarket where buyers rate the assets (BR), or hold onto the asset. The maximum expected payoff W for these sellers is:

W (sj , NR) = maxsj − c, max

ω∈ΩNR∪ΩBRW (ω; sj , R)

(1.8)

If a seller has a rated asset (R ∈ A,B), then they can hold on to their asset, or try to sell it in asubmarket with a rating arrangement matching their asset’s rating (R = R), or hide their asset’s ratingand try to sell it as an unrated asset. The maximum expected payoff W for these sellers is:

W (sj , R) = maxsj − c, max

ω∈ΩRW (ω; sj , R) ,W (sj , NR)

, where R = R (1.9)

Seller’s payoff when deciding whether to rate. Let J(ISR, sj) be the expected payoff of a sellerwith asset quality sj as a function of their decision to rate their asset prior to entering a submarket.The variable ISR equals 0 if the seller does not rate their asset and 1 if they do.

To characterize J , I use the fact that sellers will subsequently choose which submarket to enteroptimally.12. If a seller does not rate their asset, then they can only enter submarkets open to unratedassets (i.e. ω ∈ ΩNR ∪ ΩBR). Therefore, their expected payoff J(0; sj) is:

11This formulation of the buyers’ payoff captures all rating arrangements. Buyers who never promised to rate the asset(i.e. buyers who posted contracts specifying NR, B, or A) can not rate the asset (i.e. set Irate = 0) without incurring thecost χ, since Irenege = 0 for them.

12They can also choose not enter any submarket


J(0; sj) = W (sj , NR) (1.10)

If a seller rates their asset, then their expected payoff takes into account that they may receive eitheran A or a B-rating. Their expected payoff J(1; sj) is:

J(1; sj) = P(A|sj)W (sj , A) + P(B|sj)W (sj , B)− F (1.11)

As discussed previously, a high-quality seller gets an A rating for sure (P(A|sH) = 1), while a low-quality seller gets an A rating with probability P(A|sL) = 1 − π. The terms W (sj ;A) and W (sj ;B)

accounts for the possibility that the seller will, upon receiving the rating, decide to hide their rating andsell their asset as an unrated one (see equation (1.9)).

Equilibrium definition. In equilibrium buyers earn zero profits in every active submarket. Given theactive set of submarkets Ω, sellers optimally choose whether to rate their assets and which submarketsto enter. Before we can formally define the equilibrium, we need describe what happens if a buyer postsa contract outside the active set, that is, if they post a contract ω ∈ Ω/Ω.

A buyer’s payoff from posting ω will depend on both the number of sellers (i.e. the market tightnessθ) as well as the composition of sellers (i.e. proportion of high-quality sellers µ) the new submarketattracts. Sellers of type sj will enter this submarket as long as doing so yields a higher utility than theirmarket utility J . When posting deviating contracts, buyers believe the two variables (ω, µ) will takevalues such that no additional sellers want to deviate to this submarket. The condition that µ and θ

must satisfy depends on whether the deviant contract requires the asset to be rated by the seller. I willtherefore, present the derivation for both when the asset does not (does) need to be rated by the seller.

If the deviant buyer’s contract ω specifies either NR or BR as the rating arrangement, then a sellerwith asset quality sj is better of switching to this submarket if:

W (ω; sj , NR) ≥ J(sj)

The pair (θ, µ) is pinned down by the condition that it is not profitable for additional sellers of eithertype to enter:

W (θ,˜Vj ; sj , NR) ≤ J(sj), for j ∈ L,H (1.12)

For any seller type that actually enters this submarket, the inequality in equation (1.12) binds.

Similarly, if ω is open only to assets with rating R ∈ A,B, then a seller with asset quality sj isbetter off switching if:

P(R|sj)W (ω; sj , R) + P(R′|sj)W (sj , R′)− F ≥ J(sj), where R,R′ ∈ A,B and R 6= R′

The seller can only enter the deviant submarket if he receives the required rating R. If he insteadreceives R′, then he does the best that he can given that rating (i.e. W (sj ;R

′)). Sellers will deviate tothis submarket as long as it is profitable for them to do so. As above, the pair (θ, µ) is pinned down bythe condition that it is not profitable for any additional sellers to try and enter:


P(R|sj)W (θ,˜Vj ; sj , R) + P(R′|sj)W (sj ;R

′)− F ≤ J(sj), for j ∈ L,H (1.13)

The inequality in equation (1.13) binds for any seller type that actually wants to try to enter thissubmarket.

The pair (θ, µ) may not be uniquely determined. In such cases, I assume buyers are optimistic andexpect the pair (θ, µ) to take the values that gives them the highest profit. This is a common assumptionin the literature (for example, see McAfee [1993] and Cai et al. [2017]). When posting contract ω ∈ Ω/Ω,a buyer’s expected profit is:

U(ω) = maxθ,µ

U(

˜VL,

˜VH , θ, µ, Irate, Irenege)

subject to (1.12) and (1.13) (1.14)

Definition 2 presents the equilibrium concept, and is consistent with both contracts defined overprices, transaction fees and rating arrangements and with contracts defined over expected payments toeach type and rating arrangements.

Definition 2. An equilibrium consists of a set of active submarkets Ω ⊂ Ω, the proportion of high-qualitysellers in each active submarket (µ(ω)), and the ratio of buyers-to-sellers in each active submarket (θ(ω))that satisfy the following conditions:

i) In each active submarket ω ∈ Ω, buyers earn zero profits, i.e. U(ω) = 0

ii) Sellers optimally choose whether to rate their asset and whether to enter a submarket.

iii) There are no profitable deviations for buyers. For all ω ∈ Ω/Ω, U(ω) ≤ 0

1.3 Complete Information Benchmark

If buyers can observe asset quality, then they will refuse to trade with any seller that misrepresentstheir asset’s quality. In proposition 1, I characterize the unique equilibrium with contracts defined overexpected payments.

Proposition 1 (Complete information equilibrium). High- and low-quality assets trade in separatesubmarkets. The set of posted contracts (Ω), and the associated market tightnesses (θ(ω)) and thefraction of high-quality sellers (µ(ω)) are:

• For low-quality sellers: ωL = (VL,L, VL,H ,NR) = (sL − k, sL − k,NR),θ(ωL) = 1, µ(ωL) = 0

• For high-quality sellers: ωH = (VH,L, VH,H ,NR) = (sH − k, sH − k,NR),θ(ωH) = 1, µ(ωH) = 1

Vi,j denotes the expected payment a seller with asset quality sj receives in submarket ωi.

Buyers can offer the expected payments in proposition 1 by many combination of prices and transac-tion fees. One particular solution is to pay PL = sL − k in the low-type’s submarket, pay PH = sH − kin the high-type’s submarket, and not charge a transaction fee in either submarket.


The complete information equilibrium corresponds to the social planner’s solution (first-best). In thisequilibrium, all potential gains from trade are being realized. Furthermore, unlike in Chiu and Koeppl[2016], the sellers capture all the gains from trade. For future reference, the payoff for the high-qualitysellers is:

WFBH = sH − k (1.15)

1.4 Information asymmetry

If buyers cannot directly observe asset quality, then the complete information equilibrium characterizedin proposition 1 cannot be sustained: At the complete information matching probabilities, low-qualitysellers are strictly better off moving into the high-quality asset market because the price is higher by ∆

and the matching probability is the same. Their entry would lower the expected asset quality in thatsubmarket and give buyers a negative expected payoff.

I analyze the equilibrium with information asymmetry in three steps: First, I highlight how liquiditycan be used as a screening mechanism by removing the option to rate assets. Next, I study what happenswhen buyers can ask sellers to first rate their assets prior to entering the submarket, and finally whenbuyers can also rate the assets themselves after matching.

1.4.1 Equilibrium without rating agencies

When no rating agencies are available, the market does not break down. Instead, buyers respond to theinformation asymmetry by lowering liquidity in the high-quality sellers’ market, as in Chang [2017].13

Buyers can induce separation by lowering liquidity because sellers with high-quality assets are morewilling to go without trading than sellers with low-quality assets, as they get a higher payoff fromholding on to their assets. Technically, the indifference curves of the two types of sellers, defined overexpected payment V and liquidity θ, exhibit a single-crossing property.

Lemma 1 states that there is no pooling in equilibrium, which is a consequence of the single crossingproperty. Pooling cannot be sustained because deviant buyers can always make a profit by posting acontract offering a slightly higher expected payment that attracts only high-quality sellers.

Lemma 1 (No pooling). In equilibrium, there are no submarkets with both types of sellers.

In proposition 2, I characterize the unique equilibrium in terms of expected payments.

Proposition 2 (Equilibrium without ratings). An unique equilibrium exists and it features full separa-tion of the two types of sellers. The set of posted contracts Ω, and the associated market liquidity (θ(ω))and fraction of high quality sellers (µ(ω)) are:

• For low-quality sellers: ωL = (VL,L, VL,H ,NR) = (sL − k, sL − k,NR),θ(ωL) = 1, µ(ωL) = 0

• For high-quality sellers: ωH = (VH,L, VH,H ,NR) = (sH − k, sH − k,NR),θ(ωH) = θNRH , µ(ωH) = 1

13The lower liquidity in the high-quality asset submarket is achieved by fewer buyers entering that market. All high-quality sellers are strictly better off entering that market and attempting to trade.


Vi,j denotes the expected payment a seller with asset quality sj receives in submarket ωi. The buyer-to-seller ratio in the high-quality sellers’ submarket is:

θNRH =c− k

c− k + ∆(1.16)

Buyers can offer the expected payments in proposition 2 by offering price PL = sL − k in the low-quality sellers’ submarket, offering PH = sH − k in the high-quality sellers’ submarket, and chargingtransaction fee f = 0 in both submarkets.

The liquidity in the high-quality seller’s submarket, which is equal to the buyer-to-seller ratio θNRH ,is less than 1.14 Buyers reduce liquidity in the high-quality sellers’ submarket just enough so that low-quality sellers do not want to go there. The low-quality sellers’ submarket remains undistorted and fullyliquid.15

The welfare cost of information asymmetry is borne entirely by high-quality sellers. Because Iabstracted from matching frictions, I am able to present a closed-form expression for this cost in termsof parameters. Definition 3 defines this cost, which I call the adverse selection penalty without ratings. Itequals the probability of not being able to trade (1− θNRH ) times the gains from trade that are foregone(c− k).

Definition 3 (Adverse selection penalty, no rating). The cost of information asymmetry to high-qualitysellers when assets are not rated is:

δNR(∆) ≡ (c− k)(1− θNRH ) = (c− k)

[∆

(c− k) + ∆

](1.17)

The high-quality sellers’ payoff with incomplete information and no ratings is:

WNRH (∆) = WFB

H − δNR(∆) (1.18)

The adverse selection penalty δNR depends on the quality gap ∆ between the two assets, and not onthe levels. As the quality gap increases, the price difference between the two submarkets increases. Inorder to keep low quality sellers out, liquidity in the high-quality sellers’ market must fall. Therefore,the adverse selection penalty increases as the quality gap increases.

Corollary 1 highlights an important implication of full-separation: the equilibrium outcomes do notdepend on the fraction of low-quality sellers (1 − α). Even a small number of low-quality assets wouldinduce a sharp decline in liquidity and welfare for high-quality sellers.

Corollary 1 (High-quality sellers’ outcome does not depend on distribution.). Liquidity in the high-quality sellers’ submarket and high-quality sellers’ welfare do not depend on the fraction of high-qualitysellers in the economy (α), for α ∈ (0, 1).

1.4.2 Allowing Agents to Rate their Assets

In reality, buyers do not rely solely on liquidity distortions to separate low- and high-quality sellers. Inow consider how they can use ratings as another instrument for overcoming information asymmetry.

14I will refer to θ as liquidity, since m(θ) = min 1, θ = θ for θ < 1.15It is easy to check that, with the equilibrium submarkets, high-quality sellers do not want to deviate to the low-quality

sellers’ submarket. Even if they did, buyers in that submarket would make a positive profit and therefore would not wantto separate them. Therefore, there is no need to distort that submarket.


I will study the use of ratings as an alternate instrument in two steps. First, buyers will be able toask sellers to rate their asset before they enter the market. Second, buyer will be able to rate the assetthemselves after meeting with a seller. Of course, buyers can still try to separate sellers into differentsubmarkets by manipulating liquidity.

Sellers can Rate Assets Prior to Matching

In the first case, buyers can post contracts that require the sellers’ assets to have a particular ratingin order for the seller to participate in that sub-market. For example, buyers can state they will onlyconsider sellers with an A-rated asset. The allowed rating arrangements are R ∈ NR,B,A.

I will show that there is an unique equilibrium, and it features full separation of the two types ofassets. In propositions 3 and 4, I present the necessary and sufficient conditions for using ratings andthen characterize the equilibrium respectively.

Proposition 3 (Conditions for sellers rating assets). In equilibrium, high-quality sellers will rate theirassets prior to meeting buyers if and only if the rating fee (F ) and the rating accuracy (π) satisfy thefollowing conditions:

i) The rating fee is not too expensiveF ≤ δNR(∆) (1.19)

ii) The rating accuracy is sufficiently high:

π ≥ 1− θNRH (∆) (1.20)

Proposition 4 (Sellers buy ratings, equilibrium). If the rating fee (F ) and accuracy (π) satisfy the con-ditions in proposition 3, then high-quality sellers buy ratings in equilibrium. The set of active submarketsΩ, and the associated market liquidity (θ(ω)) and fraction of high-quality sellers (µ(ω)) are:

• For low-quality sellers: ωL = (VL,L, VL,H ,NR) = (sL − k, sL − k,NR),θ(ωL) = θFBL = 1, µ(ωL) = 0

• For high-quality sellers: ωH = (VH,L, VH,H ,A) = (sH − k, sH − k,A),θ(ωH) = θA, µ(ωH) = 1

Vi,j denotes the expected payment a seller with asset quality sj receives in submarket ωi. The buyer-to-seller ratio in the high-quality sellers’ submarket is:

θA = min

1,

(c− k) + F1−π

∆ + (c− k)

(1.21)

If the rating fee (F ) and accuracy (π) do not satisfy the conditions in proposition 3, then sellers donot buy ratings and the equilibrium is as characterized in proposition 2.

Notice how the equilibrium when sellers can buy ratings builds on the equilibrium without ratings.When the rating technology is not used, the obtained equilibrium looks exactly like the equilibriumwithout ratings.


For ratings to be used in equilibrium, there are two conditions that must be satisfied: First, thehigh-quality sellers’ payoff from rating their asset must be higher than their payoff from selling the assetunrated. In other words, there is a participation constraint for high-quality sellers:

WAH − F = sH − c+ θA(V A − (sH − c))− F ≥WNR

H (1.22)

The second condition for ratings to be used is that low-quality sellers must be induced to not rate theirassets, i.e. all rated assets must be high-quality ones. This second condition requires some consideration,as the literature typically states that ratings can be useful as long as they improve the pool of assets.However, in a competitive search environment, ratings are useful only if they eliminate all low-qualitysellers from the pool. The reason is as follows: if there are a mixture of high- and low-quality assetswith an A rating, then buyers will separate them into two submarkets by varying liquidity. The liquidityreduction necessary to fully separate the two types is the same as in the equilibrium with unrated assets(characterized in proposition 2), thus negating any benefits from rating the assets in the first place.

In order to keep low-quality sellers from rating their asset, the expected payoff these sellers receivefrom trying to enter the A-rated submarket must be less than their payoff in their own submarket. Theirpayoff from rating the asset and trying to enter the high-quality submarket is calculated as follows:First, they must pay the rating fee F . With probability π they will receive a B-rating, in which casethe best they can do is hide the rating and sell their asset in the unrated submarket.16 With probability1− π, they will receive an A-rating and then can try to find a buyer in the A-rated submarket. In orderfor them to be better off not rating their asset, the following incentive compatibility constraint must besatisfied:

WFBL = sL − k ≥ π

[sL − c+ θA

(V A − (sL − c)

)]+ (1− π)WFB

L − F

This incentive compatibility constraint can be re-written as an upper bound on liquidity in thesubmarket for A-rated assets:

θA ≤c− k + F

1−πV A − (sL − c)

(1.23)

In equilibrium, the two conditions on the rating technology in proposition 3 are implied by the high-quality sellers’ participation constraint and the low-quality sellers’ incentive compatibility constraint.Figure 1.2 illustrates, for a given quality gap ∆, the values of π and F for which sellers buy ratings inequilibrium. Sellers buy ratings only in the bottom-right region, where the two conditions in proposition3 are satisfied.

Role of rating fee F . In this economy with endogenous market segmentation, buyers do not asksellers to rate their assets for the informational content. Instead, buyers use ratings as an additionalinstrument to sort sellers into different sub-markets. Ratings effectively impose different costs of entryinto the A-rated submarket for low- and high-quality sellers. We see this by comparing the conditionsfor high- and low-quality sellers to participate in the A-rated submarket.

16Here is where I make use of the option to hide ratings. If this option were taken away, sellers who received a B-ratingwould not be able to trade and receive their outside option sL − k. The incentive compatibility constraint would be easierto satisfy, but the analysis would remain qualitatively unchanged.


Rating accuracy (π)0 1

Ra

tin

g f

ee

(F

)

θA

=1

F = δNR

(∆)

π = 1 - θNR

(∆)

Sellers do not buy rating(fee too high)

Sellers buyrating:

(θA

<1)

Sellers do not buy rating(accuracy too low)

Sellers do not buy rating(accuracy too low,

fee too high)

Sellers do not buy rating(accuracy too low,

fee too high)

Sellers buyrating:

(θA

=1)

Figure 1.2: Equilibrium for Different Values of Rating Accuracy and Rating Fee

[sH − c+ θA (V − (sH − c))

]− F ≥WNR

H[sL − c+ θA (V − (sL − c))

]− F

1− π≥WFB

L

The first inequality is the high-quality sellers’ participation constraint (equation (1.22)). The secondinequality is the low-quality sellers’ (violated) incentive compatibility constraint (equation (1.23)). Thehigh-quality sellers pay F to enter the A-rated submarket, while the low-quality sellers pay an expectedcost of F

1−π to do the same.

If the ratings were free (F = 0), then the difference in the cost of entry for the two types disappears.Low-quality sellers face no cost at all from trying to rate their assets. If they succeed at getting anA-rating, then they can mimic high quality sellers and receive a higher payoff. If they do not get anA-rating, then they simply sell their asset in their own submarket. Lemma 2 states that to keep the low-quality sellers out with a free rating, liquidity in the high-quality sellers’ market must be fully distortedto θNRH . In other words, even if buyers have access to a free, highly accurate rating technology, theymust still rely on liquidity distortions.

Lemma 2 (Free ratings are useless). If the rating fee F is zero and ratings are not perfectly accurate(π < 1), then liquidity for A-rated assets must be fully distorted to θNR(∆) to induce separation.


Adverse selection penalty when sellers buy ratings. Just as in the equilibrium without ratings,high-quality sellers bear the full-cost of adverse selection. We can characterize an adverse selectionpenalty δSR similarly to δNR. Towards that end, I define the following function:

Definition 4. Define δSR(∆) as follows:

δSR(∆) = maxF, δNR(∆) +

F

1− π[(1− π)− θNR(∆)

](1.24)

=

δNR(∆) + F1−π

[(1− π)− θNR(∆)

]if F

1−π ≤ ∆

F if F1−π ≥ ∆

Proposition 5 characterizes the adverse selection penalty.

Proposition 5 (Adverse selection penalty, sellers buy ratings.). If the rating fee F and accuracy π

satisfy the conditions in proposition 3, then ratings are used in equilibrium and the adverse selectionpenalty is δSR(∆). Otherwise, the equilibrium adverse selection penalty is δNR(∆).

δSR(∆) =

δSR(∆) if F ≤ δNR(∆) and π ≥ 1− θNR(∆)

δNR(∆) if otherwise

Where δSR(∆) is as defined in Definition 4.

Choice of screening mechanism and the quality gap. So far, I have characterized and analyzedthe equilibrium taking the quality gap ∆ as given. Now I show how the choice of screening mechanismdepends on the quality gap ∆. This exercise highlights how the economy might respond during a crisis,if the gap between the two types of assets goes up.

Lemma 3 provides the condition the rating technology must satisfy in order for ratings to be usedfor any quality gap.

Lemma 3. If the rating fee F is greater than the gains from trade c− k, then sellers never buy ratings.If the rating fee F is less than the gains from trade c− k, then there exists some accuracy π and qualitygap ∆ such that sellers buy ratings.

The intuition behind lemma 3 is simple: Ratings help recover some of the gains from trade. If thecost of ratings is greater than the gains from trade, then they are never worth using.

Lemma 4 shows, for a technology that satisfies the condition in lemma 3 for ratings to be used, thatthere is an interval within which ratings are bought by sellers. If the quality gap is less than the lowerbound of this interval, then the adverse selection penalty without ratings is too low to justify paying therating fee. In this region, liquidity and welfare strictly decreases as the quality gap increases.

Lemma 4. High-quality sellers buy ratings in equilibrium if the rating technology satisfies lemma 3,and the quality gap ∆ is in the interval

[F

1− Fc−k

, (c− k) π1−π

]. If the quality gap ∆ is in

[F

1− Fc−k

, F1−π

],

then only ratings are used to separate sellers by asset quality (the A-rated submarket is fully liquid).If ∆ ∈

(F

1−π , (c− k) π1−π

]then both ratings and liquidity reduction is used to separate sellers by asset

quality.


Lemma 4 further partitions the interval where ratings are bought into two parts: In the left subinter-val, low-quality sellers will not try to purchase a rating to mimic high-quality sellers even if the A-ratedsubmarket is fully liquid. Therefore, buyers use only ratings to separate sellers by asset quality. In theright sub-interval, the price difference between the two submarkets is large enough that, if the A-ratedsubmarket were fully liquid, low-quality sellers would try to rate their assets and enter. To keep themout, buyers use both ratings and liquidity reduction. Finally, when the quality gap exceeds the upperbound of the interval in lemma 4, the liquidity gain from rating the asset is not large enough to justifypaying the rating fee. In this case, buyers revert to relying only on liquidity reduction to separate low-and high-quality sellers. Figure 1.3 is an illustration of lemma 4, and shows how liquidity, high-qualitysellers’ payoff, and the adverse selection penalty varies with the quality gap.

Asset quality gap (∆)

Liq

uid

ity

(θ

)

0

1


Pay

off

(W

)


Pen

alty

(δ

)

Equilibrium

Buy ratings (off-equilibrium)

No ratings (off-equilibrium)

Figure 1.3: Liquidity, High-quality Seller’s Payoff, and Adverse Selection Penalty when Sellers are Al-lowed to Buy Ratings

Unlike in Chang [2017] and other papers that abstract from ratings, figure 1.3 shows that the re-lationship between liquidity and the quality gap is non-monotonic. Liquidity jumps discretely at thequality gap where high-quality sellers are indifferent between using ratings or relying solely on liquidityreduction. However, the relationship between the quality gap and high-quality sellers’ welfare remainsmonotonic.

Buyers Rate Assets

I now allow agents to rate the asset after buyers and sellers meet. As mentioned previously, I will callthis arrangement buyers rating assets though ultimately the fee is borne by sellers. The feasible ratingarrangements are R ∈ NR,B,A,BR. Buyers can condition payments on the rating, and therefore


offer different expected payments to low- and high-quality sellers. The ability to offer different expectedpayments to the two types of sellers opens a new way to overcome adverse selection: In the market forhigh quality assets, buyers could set the expected payment for low-quality sellers so low that these sellersprefer going to their own submarket even if the high-quality sellers’ submarket is fully liquid.

However, full separation using different expected payments may not be sustainable in equilibrium.If sellers are completely sorted into two submarkets, then buyers in the high-quality submarket knowthat any seller they meet must have a high-quality asset even before rating it. Individual buyers in thissubmarket may be better off foregoing rating the asset. Low-quality sellers, anticipating that buyers willnot follow through with rating the asset, will deviate to the high-quality submarket. Therefore, buyersmust ensure that their promise to rate the asset is credible.17

Buyers can commit to rate assets. To make these ideas concrete, I characterize in proposition 6the equilibrium when χ, which is the cost the buyer incurs when they renege on the promise to rate theasset, is greater than the rating fee F . In this case, buyers will never forego rating the asset.

Proposition 6 (Equilibrium, buyers rate assets, full commitment). Suppose the adjustment cost χ isgreater than the rating fee F . If F ≤ δSR(∆), then buyers buy ratings in equilibrium and the two typesof assets are fully separated. The set of active submarkets Ω and the associated market liquidity (θ(ω))and fraction of high-quality sellers (µ(ω)) are:


• For high-quality sellers: ωH = (VH,L, VH,H ,BR) = (sL − k, sH − k − F,BR),θ(ωH) = 1, µ(ωH) = 1

Vi,j denotes the expected payment a seller with asset quality sj receives in submarket ωi. If the ratingfee F is greater than δSR(∆), then the equilibrium is as characterized in proposition 4.

If buyers buy ratings then the two types are fully separated, the high-quality sellers’ submarket isfully liquid, and the welfare cost of information asymmetry is the rating fee F .

The welfare cost to high-quality sellers does not increase with the quality gap ∆. Buyers respondto an increase in ∆ by adjusting the transaction fee f and the two rating contingent prices to keeplow-quality sellers out. They can do this without affecting the expected payment to high-quality sellers.The relationships between the expected payments and prices are:

VH,H = sH − k − F = PA − f

VH,L = sL − k = πPB + (1− π)PA − f

As an example, one particular solution is to set PB = sL − k. Then the two types of sellers receivethe required expected payments if PA = 1

π [∆− F + π (sL − k)] and f = 1−ππ (∆− F ). Sellers with an

A-rated asset effectively get the transaction fee back through PA, whereas sellers with a B-rated asset do

17The same problem would arise if the seller was responsible for rating the asset after meeting. Having already revealedtheir type to the buyer from their presence in the market, they have an incentive to propose to the buyer that they foregorating the asset and divide up the savings from the rating fee.


not. If the quality gap ∆ increases, buyers increase the transaction fee f and the price PA appropriatelyto maintain the required expected payments to both types of sellers.

We can formally check that if χ ≥ F , then the buyers in the high-quality submarket do not want toforego rating assets, as their payoff from not reneging (sH − VH − F ) is greater than their payoff fromdoing so (sH − VH − χ).

Buyers cannot commit to rate assets. If the cost χ equals 0, then the equilibrium in proposition6 cannot be sustained. Upon meeting a seller in the high-quality seller submarket, buyers are strictlybetter off not rating the asset as their payoff from reneging (sH − VH) is greater than their payoff fromhonoring their promise (sH − VH − F ).

Low-quality sellers, anticipating that buyers will not rate the assets, are strictly better off deviatingto the high-quality submarket. Therefore this submarket cannot be part of an equilibrium.

Buyers make their promise to rate the asset credible by including some low-quality sellers in thesubmarket. Buyers who forego rating the asset then run the risk of overpaying if the seller they meethappen to have a low-quality asset. If the expected cost of overpayment is sufficiently large, then buyers’promise to rate the asset is credible.

I will first describe the set of conditions that a submarket must satisfy in order to attract both typesof sellers, and to ensure buyers rate the assets. Second, I will identify the set of parameter values forwhich such a submarket can be active in equilibrium.

Submarket with high-quality sellers. The submarket is characterized by four variables: VH , VL,µ, and θ. Buyers participating in this sub-market must credibly commit to rate the asset (commitmentconstraint):

µ(sH − VH) + (1− µ)(sL − VL)− F ≥ µsH + (1− µ)sL − VH (1.25)

Denote by WH and WL the high- and low-types’ outside options respectively. Both types of sellersmust receive at least as much as their outside options:

WBRH =sH − c+ θ (VH − (sH − c)) ≥WH

WBRL =sL − c+ θ(VL − (sL − c)) ≥WL

Characterizing the active pooling submarket. Now I turn to solving for the values of the fourendogenous variables (VL, VH , µ, and θ) such that the pooling submarket can be sustained in equilibrium.First, buyers must earn zero profit:

0 = −k − F + µ(sH − VH) + (1− µ)(sL − VL)

Lemma 5 states that a pooling submarket that is active in equilibrium must maximize the high-qualitysellers’ payoff WBR

H , subject to the various constraints.

Lemma 5. If a pooling submarket exists in equilibrium, it maximizes WBRH while satisfying the buy-

ers’ zero-profit condition and commitment constraint, and low-quality sellers’ (binding) participation


constraint.

Lemma 5 implies that an active pooling submarket must be part of the solution to the followingmaximization problem:

maxµ,VL

WBRH (µ, VL;WL)

= max

µ,VL

sH − c+ θ(VL;WL) (VH(µ, VL)− (sH − c))

(1.26)

subject to

θ(VL;WL) = WL−(sL−c)

VL−(sL−c)

VH(µ, VL) = sH − k − F + 1−µµ (sL − k − F − VL)

(1− µ) (VH(µ, VL)− VL) ≥ F

A solution to to the maximization problem is not necessarily an equilibrium outcome if sellers can dobetter under another rating arrangement, for example selling the asset unrated. I identify the conditionfor a pooling submarket to be active when characterizing the equilibrium.

Lemma 6 states that an equilibrium pooling submarket must be completely liquid. Buyers insteadrely on different expected payments to each type to control entry into the submarket. Technically, thehigh quality sellers’ payoff is strictly increasing in θ.18 The matching probability does not affect thebuyers’ commitment constraint, as it applies only after buyers and sellers meet.

The low-quality sellers’ binding participation constraint can be satisfied with perfect liquidity onlyif their expected payment is set equal to their outside option WL. Furthermore, setting the low-qualitysellers’ expected payoff to its lowest value makes it easier to satisfy the buyers’ commitment constraint,as the overpayment [VH − VL] is maximized.

Lemma 6 (No liquidity reduction). If a pooling submarket is active in equilibrium, then it must becompletely liquid (θ = 1).

After setting θ = 1 and VL = WL, the optimization problem simplifies to:

maxµ

WBRH (µ;WL)

= max

µ

sH − k − F −

(1− µ)

µ

(WL + F − (sL − k)

)subject to: ∆µ2 −

(∆ +WL − (sL − k)

)µ+

(F +WL − (sL − k)

)≤ 0

Buyers make losses on their trade with low-quality sellers.19 To break even, buyers pass these losses tothe high-quality sellers. The term (1−µ)

µ

(WL + F − (sL − k)

)in the high-quality sellers’ payoff captures

this cost.Therefore, high-quality sellers are better off when their submarket contains as few low-quality sellers

as possible. The solution to the maximization problem is to set the fraction of high-quality sellers µto the highest value that satisfies the buyers’ commitment constraint. The commitment constraint is aquadratic function in µ, and it is possible that there may not be any value of µ that satisfies it. Lemma7 states that, if a solution to commitment constraint exists, then it must be greater than 1

2 .

Lemma 7. The proportion of high-quality sellers in a pooling submarket must be greater than 12 .

18I restrict attention to the relevant case of VH > sH − c, as otherwise high-types will not trade.19The low-quality sellers’ outside option WL must be greater than sL − k in equilibrium, as otherwise deviant buyers

can make positive profits by offering them sL − k. Therefore, the term WL − (sL − k) + F must be strictly positive.


In my analysis of the pooled sub-market so far, I have treated the low-quality seller’s outside optionWL as a parameter. For ease of exposition, I assume that the fraction of low-quality sellers in thepopulation is greater than the fraction of high-quality sellers (assumption 5). Lemma 8 is impliedby lemma 7 and assumption 5, and states that some low-quality sellers must be fully separated. Forlow-quality sellers to be indifferent between full separation and pooling, WL must be sL − k.

Assumption 5. The fraction of high-quality sellers α is less than 12 .

Lemma 8. Some strictly positive mass of low-quality sellers must be fully separated into their ownsubmarket.

In lemma 9, I solve for the fraction of high-quality sellers in the pooled submarket (µ∗(∆)) andidentify the condition for when it exists.

Lemma 9. If in the high type’s submarket VL = sL − k and θ = 1, then the highest proportion ofhigh-quality sellers (µ∗) that satisfies the buyers’ commitment constraint is:

µ∗(∆) =

does not exist if ∆ < 4F

12

[1 +

√1− 4F

∆

]if ∆ ≥ 4F

If the rating fee is not too large relative to the quality gap, then the commitment constraint can besatisfied with some pooling. If the rating fee is too large, then no amount of pooling can satisfy thecommitment constraint.

Where µ∗ is defined, the high-quality sellers’ payoff is:

WBRH (∆) = sH − k −

F

µ∗(∆)(1.27)

For the cases where µ∗ is defined, I define the adverse selection penalty:

Definition 5. If µ∗(∆) exists, then define δBR(∆) as follows:

δBR(∆) =F

µ∗(∆)(1.28)

In proposition 7, I characterize the equilibrium when buyers can rate the assets.

Proposition 7 (Equilibrium if buyers can buy ratings). If ∆ ≥ 4F and δBR(∆) ≤ δSR(∆), then asemi-pooling equilibrium exists where buyers buy ratings after matching with sellers. The set of activecontracts Ω, and the associated market liquidity (θ(ω)), and fraction of high-quality sellers (µ(ω)) are:


• For high-quality sellers: ωH = (VH,L, VH,H ,BR) =(sL − k, sH − k − F

µ∗(∆) ,BR),

θ(ωH) = 1, µ(ωH) = µ∗(∆)

Vi,j denotes the expected payment a seller with asset quality sj receives in submarket ωi. The fractionof high-quality sellers µ∗(∆) in submarket ωH is given by lemma 9.

If ∆ ≥ 4F and δBR(∆) > δSR(∆), or if ∆ < 4F then an equilibrium with buyers buying ratings isnot feasible. The equilibrium is as characterized in proposition 4.


Comparative Statics Without Commitment

In this section, I illustrate how the equilibrium rating arrangement and other variables responds tochanges in parameters when all three rating arrangements are available but buyers cannot exogenouslycommit to follow through with rating the asset.

The model has four parameters that affect equilibrium outcomes: the quality gap between assets(∆ = sH − sL), the gains from trade (c − k), the rating accuracy (π), and the rating fee (F ). I willillustrate how equilibrium outcomes respond to changes in π and ∆, while holding the gains from tradeand the rating fee constant.20 In figure 1.4, I show how the equilibrium rating arrangement varies withπ and ∆. For ease of exposition, I present in the left panel the case where only sellers can buy ratings,then use the analysis in that panel to characterize the case when all rating arrangements are available(right panel).

Quality gap (∆)

Ra

tin

g a

ccu

racy (π

)

NR or SR

Quality gap (∆)

NR, SR, or BR

F = δNR(∆)

π = 1-θNR(∆)

θA=1

(BR = NR)(BR = SR)

NR

NR

NR

SR

(θA

< 1)

NR

SR

(θA

< 1)

SR

(θA

= 1)

SR

(θA

< 1)

BR

BRNR

NR

SR

(θA

= 1)

(III)

(II)

(I)

Figure 1.4: Equilibrium Rating Regimes

NR or SR (left panel). In this panel, I restrict the rating arrangements to either sellers buyingratings or selling assets unrated. Therefore, the relevant equilibrium characterization is in proposition4. In proposition 3, I identified two conditions that the rating technology must satisfy for sellers to ratetheir assets. The first condition is that the rating fee must be less than the adverse selection penaltywithout ratings (F ≤ δNR(∆)). This condition is satisfied to the right of the line labeled F = δNR(∆).The second condition is that the rating accuracy must be sufficiently high (π ≥ 1 − θNR(∆)). Thiscondition is satisfied above the increasing line labeled π = 1 − θNR(∆). Sellers buy ratings only in the

20I restrict the rating fee F to the interesting case of F < c− k. Otherwise, ratings will never be bought.


top-right region of the panel.Lemma 4 states that ratings are sufficient to separate sellers if the rating accuracy π is greater than

1− F∆ . The line labeled θA = 1 maps π = 1− F

∆ , and partitions the region where sellers buy ratings intoareas where the market is perfectly liquid and where the market is illiquid.

NR, SR, or BR (right panel). In this panel I allow for all three rating arrangements. Therefore, therelevant equilibrium characterization is proposition 7. The panel builds on the left panel, by demarcatingthe regions where buyers prefer buying the ratings after meeting.

First, consider the region (I) in the left panel. The quality gap at which buyers rating the asset ispreferred to selling the asset unrated must be in this region, as to the left of this region the rating feeF is greater than the adverse selection penalty δNR(∆). Lemma 10 states that there exists a qualitygap ∆BR=NR above which buyers rating assets is preferred to selling assets unrated. The vertical linelabeled BR = NR in the right panel corresponds to this threshold.

Lemma 10. There exists ∆BR=NR such that:

δNR(∆BR=NR

)= δBR

(∆BR=NR

)For ∆ > ∆BR=NR (∆ < ∆BR=NR), buyers buying ratings is preferred to selling assets unrated

(selling assets unrated is preferred to buyers buying ratings).

Next, consider region (III) in the left panel: In this region when sellers buy ratings, the adverseselection penalty δSR = F since π ≥ 1 − F

∆ and no liquidity distortions are necessary. Even if buyersbuying ratings was feasible, the penalty would be δBR = F

µ∗(∆) . Since the penalty with sellers buyingratings is strictly less than the penalty when buyers buy ratings, sellers buying ratings is still strictlypreferred.

Finally, in region (II), when sellers buy ratings the A-rated submarket is illiquid, and the adverseselection penalty δSR increases as accuracy falls. If pooling is possible, then buyers buying ratingsmight yield a lower penalty than sellers buying ratings. Lemma 11 partitions this region into two parts,by characterizing a level of rating accuracy π above (below) which sellers (buyers) buying ratings ispreferred.

Lemma 11. For ∆ ≥ ∆BR=NR, there exists πBR=SR ∈[

∆∆+(c−k) , 1−

F∆

]such that:

δBR(∆;πBR=SR

)= δSR

(∆;πBR=SR

)Furthermore, πBR=SR is increasing in ∆.

Liquidity, pooling, and welfare. In figure 1.5, I plot liquidity, fraction of high-quality sellers, andwelfare for a low-accuracy rating technology (π < F

c−k ) and for a high-accuracy rating technology(π > F

c−k ). In the first case, sellers never buy ratings in equilibrium. In the second case, sellers buyratings for intermediate values of the quality gap.

The relationship between the quality gap and liquidity is non-monotonic: Liquidity is strictly de-creasing in the quality gap when assets are sold unrated, as in Chang [2017]. However, when assets


Quality gap (∆)

Liq

uid

ity (θ)

an

d

fra

ctio

n o

f s

H (µ

)

1

Low accuracy (πL)

θµ

Quality gap (∆)

Liq

uid

ity (θ)

an

d

fra

ctio

n o

f s

H (µ

)

1

High accuracy (πH)

θµ

Quality gap (∆)

Eq

uili

briu

m p

en

alty (δ)

Quality gap (∆)

Eq

uili

briu

m p

en

alty (δ)

NR

NR

NR

BR

BRNR

BR

BR

SR

SR

Figure 1.5: Equilibrium Liquidity, Pooling, and Penalty

start being rated, liquidity jumps back to the undistorted level. If buyers are buying the ratings, thenliquidity remains undistorted even as the quality gap increases. If sellers are buying the ratings, thenliquidity starts falling again once ratings alone cannot keep low-quality sellers out of the high-qualitysellers’ submarket.

The equilibrium penalty is also non-monotonic in the quality gap. If in equilibrium the high-qualityassets are sold unrated or rated by the sellers, then the penalty is weakly increasing in the quality gap.However, if buyers are rating the assets then the equilibrium penalty is decreasing in the quality gap. Inother words, the welfare cost of adverse selection decreases with information asymmetry if buyers ratethe assets.

The reason is that as the quality gap increases it becomes possible to satisfy the buyers’ commitmentconstraint with fewer low-quality sellers. As the quality-gap goes up, so does the cost of overpayment.Therefore, the probability of meeting a low-quality sellers (1−µ∗(∆)) can be reduced while still satisfyingthe buyers’ commitment constraint.

1.5 Analyzing the Financial Crisis and Policy Intervention

Brunnermeier [2009] documents that prior to the crisis, sellers rated their assets and the over-the-countermarket for asset backed securities was relatively liquid. During the crisis, market participants lost faithin the quality of ratings, liquidity fell, and market participants were worse off. I use my model to studyhow an increase in adverse selection or a fall in rating accuracy can explain these outcomes.

In figure 1.6, the area outlined in red is where the market must be prior to the crisis, otherwise an


increase in the quality gap or a fall in accuracy would move the market towards buyers buying ratings.From the outlined area, either an increase in the quality gap (∆ ↑) or a decrease in the rating accuracy(π ↓) can push the market into a region where ratings are no longer used. In either case, the conditionthat is violated in proposition 3 is π ≥ 1 − θNR(∆): the accuracy is no longer high enough to justifyusing ratings. Because sellers are no longer buying ratings, liquidity falls sharply as it becomes the onlyinstrument for separating low- and high-quality sellers. Finally, the high-quality sellers’ welfare alsodecreases.

A key difference between my model and the literature is that the quality gap cannot increase toomuch, as that would push the market into the region where buyers can commit to rate the assets andit is optimal for them to do so. Not only will the change in the rating arrangement be counterfactual,liquidity would also increase as it is no longer used as an instrument. High-quality sellers’ welfarecould also potentially increase. These more complicated relationships between information asymmetryand outcomes during the financial crisis are absent in models without endogenous choice of ratingarrangements.

Quality gap (∆)

Ra

tin

g a

ccu

racy (π

)

F = δNR

(∆)

π = 1-θNR

(∆)

θSR

=1(BR = NR)(BR = SR)

BR

NR

NR

NR

SR

(θA

= 1)SR

(θA

< 1)

BR

SR

(θA

= 1)

SR

(θA

< 1)

NR

1. MarketBefore

the crisis

2. Ratingaccuracy falls

(π ↓)

3. Quality gapincreases

(∆ ↑)

Figure 1.6: Analyzing the Financial Crisis

1.5.1 Policy Intervention

I show that subsidizing the purchase of ratings can improve welfare, by helping to overcome buyers’commitment problem and ensuring ratings are used to separate assets by quality. Suppose a policymaker understands the market structure, and knows the fraction of high-quality assets α, the ratingaccuracy π, the rating fee F , the gains from trade c− k, and the quality gap ∆. The policy maker does


not observe individual asset’s quality, but does observe individual ratings. Suppose this policy makercan impose a lump-sum tax τ on all sellers and providing a lump-sum subsidy σ for A-rated assets. Irestrict the policy maker to choose taxes and subsidies such that they break even.

Lemma 12. The policy maker chooses the following subsidy for A-rated assets:

σ =

0 if F < δNR(∆)

F if F ≥ δNR(∆)

The policy maker sets the lump sum tax τ = ασ to satisfy their budget constraint.

If the rating fee F is less than δNR(∆), then the cost of rating is less than the adverse selection penaltyand it is better to sell assets unrated. If the fee is greater than the adverse selection penalty, then becauseof buyers’ commitment problem, ratings are either not being used or used sub-optimally. Proposition 8states that the equilibrium with subsidies features buyers rating the asset and full separation.

Proposition 8 (Equilibrium, subsidy σ = F ). Buyers buy ratings in equilibrium and the two types ofassets are fully separated. The set of active submarkets Ω and the associated market liquidity (θ(ω)) andfraction of high-quality sellers (µ(ω)) are:


• For high-quality sellers: ωH = (VH,L, VH,H ,BR) = (sL − k, sH − k − F + σ,BR),θ(ωH) = 1, µ(ωH) = 1

Vi,j denotes the expected payment a seller with asset quality sj receives in submarket ωi.

In this equilibrium, buyers’ commitment problem is solved, low-quality sellers do not want to ratetheir asset, and all sellers want to sell their assets despite being taxed. For buyers to earn zero profits inthe submarket for high-quality assets, they must pass the subsidy onto sellers. Therefore, the expectedpayment to high-quality sellers is VH,H = sH − k − F + σ.

If the buyers rate the asset, then their payoff is sH−VH,H−F+σ = sH−(sH − k − F + σ)−F+σ = k.If they do not rate the asset, they receive sH − VH,H = sH − (sH − k − F + σ) = k. Therefore, buyers’promise to rate is credible even with full separation.

Low-quality sellers (or buyers of low-quality assets) do not attempt to get the subsidy by rating theirasset. A low-quality seller who rated their asset would get (1− π)σ − F , which is less than zero.

Finally, sellers do not avoid trading in order to avoid the tax, since the gains from trade c−k outweighthe tax τ = αF , as F ≤ c− k.

Social welfare in subsidized economy. In a risk-neutral economy, the taxes and subsidies have nodirect effect on social welfare. Also, buyers earn zero profits in equilibrium. Therefore, social welfare isis the sum of the two types of sellers’ payoffs:

Wsubsidies = (1− α)(sL − k) + α (sH − k)− αF


With subsidies, social welfare is lower than the first-best by the aggregate cost of ratings, αF . Asthe adverse selection penalty is absent the subsidy is greater than the rating fee, welfare improves.

Unlike in Cole and Cooley [2014], ‘subsidizing’ high-quality ratings can improve welfare in my econ-omy. Because of endogenous sorting of sellers and lack of commitment, buyers and sellers may not beusing ratings optimally. Thus, my analysis illustrates the potential importance of accounting for thedownstream market structure when evaluating interventions in the rating market.

1.6 Conclusion

I use a parsimonious, static model to analyze the role of rating agencies in a competitive search envi-ronment. I show that rating agencies can improve liquidity in this environment, by offering an alternatescreening mechanism. I also find that it is generally better if buyers rate assets after matching than sell-ers rating assets prior to matching, but that buyers’ inability to commit may undermine their ability todo so. Subsidizing highly rated assets can overcome buyers’ commitment problem and improve welfare.

I conjecture that it would be worthwhile to extend the framework to a dynamic setting with assetresale, though I expect that many of the results would carry over. Guerrieri and Shimer [2011] showsthat because there is no way to record that an asset had previously been revealed to be of high-quality, itsfuture sellers continue to face illiquidity. Ratings, in conjunction with a fully separating equilibrium, maybe one way to record the asset’s history. However, this may count against semi-pooling equilibria, whichis obtained when buyers rate assets after matching, as that involves rating both low- and high-qualityassets. I leave a study of the dynamic setting with resale as future work.


Appendix

Proof of proposition 1. The conjectured posted contracts maximize seller welfare while giving buyerszero expected profit. We can use the zero profit condition for buyers’ expected profit to express V interms of θ:

U = −k + q(θ)[s− V ]

U=0=⇒ V = s− k

q(θ)

The sellers’ expected payoff is:

W = s− c+m(θ)[V − s+ c]

= s− c+m(θ)

[c− k

q(θ)

]= s− c+ minθ, 1c− kθ

Since assumption 3 states that c > k, it follows that θ = 1 is the unique maximizer. ThereforeV = s − k. The only way to give sellers a higher payoff is to offer them a higher expected paymentV , but that would leave buyers with a negative payoff. Pooling types is also not feasible, as either thehigh-quality seller will receive a lower expected payment or buyers will earn negative expected profit.

Proof of lemma 1. I prove this by showing that if there was pooling in a submarket, then buyers canpost a contract to to attract away only high-quality sellers and make a positive profit.

Suppose a fraction µ ∈ (0, 1) of sellers in an active submarket are high-quality. If both types arepresent in the pooled submarket, then the submarket must give each type their market utilities, WL

and WH . The indifference curve of type sj , defined over (V, θ) passing through this submarket is:

W j = (1− θ)(sj − c) + θV

= sj − c+ θ(V − (sj − c))

The slope of the indifference curve evaluated at the pooled submarket is:

dθ

dV= − θp

V p − (sj − c)< 0

The change in the slope with respect to the asset quality is:

∂

∂sj

(dθ

dV

)= − θ

(V − (sj − c))2< 0

The slope of the indifference curve is steeper for high-quality sellers than for low-quality sellers. Inother words, high-quality sellers will accept a lower liquidity for a higher payment than low-quality


sellers. Therefore if some deviant buyers post a contract with slightly higher expected payment, thenthey will only attract high-quality sellers. By offering an arbitrary small improvement in the expectedpayment, these buyers can avoid low-quality sellers altogether and earn a positive profit. Formally,

U = −k + sH − (V p + ε) > −k + sL + µ(sH − sL)− V p = 0, for small ε > 0

Proof of proposition 2. The proposition makes two claims: First, the set of active submarkets is anequilibrium. Second, that this equilibrium is unique. I prove the two claims in order.

First, it is easy to check that buyers earn zero profits in each of the two active submarkets, andthat high- and low-quality sellers find it optimal to enter submarket respectively. Therefore, conditions(i) and (ii) of the equilibrium definition are satisfied. We need to check that there are no profitabledeviations by buyers (condition (iii)).

Suppose buyers offer V ′. Low-quality sellers will come as long as θ′ ≥ VH−(sL−c)V ′−(sL−c) θ

NRH . Similarly, high-

quality sellers will want to enter this submarket as long as θ′ ≥ VH−(sH−c)V ′−(sH−c) θ

NRH . If V ′ > sH − k, then at

the value of θ′ at which high-quality sellers are indifference, low-quality sellers will strictly prefer theiroriginal submarket. Therefore only high-quality sellers will come. However, buyers will earn negativeprofits as U ′ = −k + q(θ′)(sH − V ′) = sH − k − V ′ < sH − k − VH,H = 0. If V ′ < sH − k, then at thevalue of θ′ at which high-quality sellers are indifferent to deviating to this submarket, low-quality sellerswill still strictly prefer deviating. Therefore, only low-quality sellers will come. Again, buyers will earnnegative expected profits as U ′ = −k + q(θ′)(sL − V ′) = sL − k − V ′ < sL − k − VL,L = 0. Therefore,there are no profitable deviations.

Now I prove uniqueness. Lemma 1 rules out pooling submarkets in equilibrium, therefore I focuson fully separating candidate equilibria. Consider an alternate separating arrangement that satisfiesconditions (i) and (ii). If it offers low-quality sellers any other contract other than ωL, then low-qualitysellers’ market utility is less than what they would receive from ωL. Therefore, deviant buyers can postωL and earn positive profits. A similar argument applies for ωH and high-quality sellers.

Proof of proposition 3. Note: This proposition and 4 together characterize the equilibrium whensellers have the option to rate their asset prior to meeting buyers. I break the characterization into twoparts for ease of reference.

This proposition applies in equilibrium, therefore I rely on the buyers’ zero profit condition and low-quality sellers’ IC constraint being satisfied. In particular, these two conditions imply that VH,H = sH−kand θA = min

1,

c−k+ F1−π

c−k+∆

. High-quality rate in equilibrium if and only if it offers them a higher payoff

than relying on liquidity distortions (i.e. WAH ≥ WNR

H ). I will first show that WAH ≥ WNR

H implies thatF ≤ δNR and π ≥ 1− θNR. I will then show that if F ≤ δNR and π ≥ 1− θNR, then WA

H ≥WNRH .

WAH ≥WNR

H =⇒ F ≤ δNR follows from rewriting WNRH in terms of δNR, and some algebra.


WAH −WNR

H ≥ 0

sH − k − (1− θA)(c− k)− F − (sH − k − δNR) ≥ 0

=⇒ δNR − (1− θA)(c− k) ≥ F

=⇒ δNR ≥ F

To prove that WAH > WNR

H =⇒ π > 1− θNR, I will consider three mutually exclusive intervals for∆. First, I will consider ∆ > F

1−π , second I will consider ∆ = F1−π , and third ∆ ∈

[0, F

1−π

).

i) ∆ > F1−π : In this case, θA =

c−k+ F1−π

c−k+∆ = θNR +F

1−π∆+c−k . Simplify WA

H ≥ WNRH to show that the

property holds.

ii) ∆ = ∆ = F1−π : In this case, WA(∆) −WNR(∆) = F

1−π(θNR(∆)− (1− π)

). Therefore if WA ≥

WNR, then it must be that π ≥ 1− θNR(∆)

iii) ∆ ∈[0,∆

): In this case, θA(∆) = 1 and WA(∆) = WA(∆). Since WNR = sH −k− (c−k) ∆

∆+c−kis decreasing in ∆, it must be that WNR(∆) < WNR(∆). Therefore, if WA(∆) ≥WNR(∆), thenWA(∆) > WNR(∆). Using part (ii), we have that π > 1− θNR(∆). Since θNR(∆) > θNR(∆), wehave π > 1− θNR(∆) as required.

To prove F ≤ δNR and π > 1 − θNR =⇒ WA > WNR, I write the difference between WA andWNR (with some simplification):

WA −WNR = max

0,minδNR − F, F

1− π[π −

(1− θNR

)]It is now easy to see that if F ≤ δNR and π ≥ 1− θNR, then WA ≥WNR.

Proof of proposition 4. In order for only high-quality sellers to buy ratings, the following two condi-tions must be satisfied:

(PC) WAH − F ≥WNR

H

(IC) WAH (sL) ≤WFB

L +F

π

The zero-profit condition implies that the price of the high-quality rated asset is sH − k. We can usethis to re-write the (PC) and (IC) constraints as constraints on market liquidity.

(PC) θAH ≥ θNRH + F

(1

c− k

)(IC) θAH ≤ θNRH +

F

π

(1

∆ + (c− k)

)


The IC constraint implies:

θAH = min

1, θNRH +F

π

[1

∆ + (c− k)

]If θAH = 1, then to satisfy the PC constraint, we must have:

F ≤ δNR(∆)

If θAH = Fπ

(1

∆+(c−k)

)+ θNRH , then to satisfy the PC constraint, we need:

π ≥ 1− θNRH

Given ∆, we can check whether (F, π) satisfy the above two conditions. If either condition is violated,then the rating technology is either too expensive or too weak (or both) to justify sellers buying ratings. Ifboth conditions are satisfied, then sellers will use ratings to separate themselves for low-quality sellers.

Proof of lemma 2. The proof of the lemma is straight-forward. Supposed the conditions in proposition3 are satisfied and ratings are used in equilibrium. According to equation (1.21), liquidity in the A-ratedsubmarket is θA = c−k

c−k+∆ = θNRH .

Proof of proposition 5. If F > δNR(∆) or π < 1− θNR(∆), then according to proposition 4, ratingsare not used and only liquidity distortions are used to separate low- and high-quality sellers. Therefore,the penalty for high-quality sellers is δNR(∆).

If F ≤ δNR(∆) and π ≥ 1 − θNR(∆), then sellers buy ratings and in equilibrium the liquidity inthe A-rated submarket is θA = min

1,

c−k+ F1−π

c−k+∆

. If ∆ ≤ F

1−π , then θA = 1, and the penalty is F .Otherwise, some liquidity distortions are necessary and with some algebra, the required expression forthe penalty is obtained.

Proof of proposition 6. The two submarkets are constructed such that conditions (i) and (ii) of theequilibrium definition are satisfied. We need to check whether there are any profitable deviations thatattracts high-quality sellers, when F ≤ δSR(∆). As submarket ωH is offering the high-quality sellers thehighest payoff they can get amongst submarkets where buyers rate, we can restrict attention to deviantcontracts offering SR or NR. In order for such a deviant contract to not attract low-types, the ICconstraint must be satisfied. For example, for deviations offering NR:

sL − k ≥ sL − c+ θ′(∆ + c− k) =⇒ θ′ ≤ θNR(∆)

However, if F ≤ δSR(∆) = minδSR(∆), δNR(∆)

then such a deviant submarket will offer high-

quality sellers less than ωH , and no high-quality sellers will go there.On the other hand, if F > δSR(∆), then deviant buyers can create submarkets that offer a higher

payoff to high-quality sellers and make positive profit (e.g. by creating submarket ωH from proposition4). Therefore, the equilibrium cannot feature buyers buying ratings.


Proof of lemma 3. If F > c−k, high-quality sellers are never better off rating their asset than sellingtheir asset unrated. If the market for rated assets was perfectly liquid, then high-quality sellers who ratewould get a payoff of sH − k − F . If they sold their asset unrated, they would get sH − k − δNR(∆).However, δNR(∆) = (1 − θNR(∆))(c − k) < c − k for all ∆. Therefore, the sellers are better off notrating the asset.

If F < c − k, I will find one pair (∆, π) such that rating is optimal. In particular, I will choose thepair such that:

sL − k = (1− π)(sH − k) + π(sL − k)− F =⇒ π(∆) = 1− F

∆

That is, I choose π such that at the given ∆, low-quality sellers’ IC constraint binds when the A-ratedsubmarket is fully liquid. To satisfy the high-quality sellers’ participation constraint, pick a value of ∆

large enough such that δNR(∆) > F .

Proof of lemma 4. We can confirm that in the interval[

F1− F

c−k, F

1−π

], the low-quality sellers’ IC and

the high-quality sellers’ PC are satisfied with θA = 1. Therefore, rating is preferable to not rating inthis interval. We need to confirm that for ∆ < F

1− Fc−k

, it is better to not rate. To do this, I show that

the participation constraint binds at ∆ = F1− F

c−k:

WNRH = sH − k − δNR = sH − k − (c− k)

F1− F

c−k

c− k + F1− F

c−k

= sH − k − F = WAH

For ∆ < F1− F

c−k, WNR

H is smaller than WAH and therefore the participation constraint is violated.

We can similarly confirm that for the interval[F

1−π , (c− k) π1−π

]the PC and IC constraints are satis-

fied with θA =c−k+ F

1−πc−k+∆ , and therefore ratings are used. At ∆ = π

1−π (c−k), the participation constraintbinds. As ∆ increases further, WA

H falls faster than WNRH , and therefore not rating is preferable.

Proof of lemma 5. I will prove this lemma by contradiction: I will suppose that a submarket violatingthis lemma exists, and then construct a profitable deviation for buyers. Let VL, VH , θ and µ characterizethis submarket. Then since this submarket is active in equilibrium, the following conditions must besatisfied:

(ICL) : WL = sL − k = sL − c+ θ (VL − (sL − c))

=⇒ θ =c− k

VL − (sL − c)(ZPC) : U = 0 = −k − F + µ(sH − VH) + (1− µ)(sL − VL)

=⇒ VH = sH +(1− µ)(sL − VL)− k − F

µ

(CC) : µ(sH − VH) + (1− µ)(sL − VL)− F ≥ µsH + (1− µ)sL − VH

=⇒ F

1− µ≤ (VH − VL)


Notice that the incentive compatibility constraint allows us to express θ in terms of VL. We capturethe idea that VL ≥WL = sL−k in order to attract any low-types by defining VL(φ) = sL−k+φ, whereφ ≥ 0. We can now re-write θ, VH and WH in terms of φ as well:

θ(φ) =c− k

c− k + φ(θ(φ) < 1 if φ > 0)

VH(φ) = sH − k + φ− F + φ

µ

WH(φ) = sH − k −(

c− kc− k + φ

)(φ+ F

µ

)

Constructing a profitable deviation with pooling A profitable deviation with pooling must beable to attract both types and satisfy the buyer’s commitment constraint. Consider the following:

VL = sL − k

VH = WH(φ)

Both types will be indifferent between this deviation and the original submarket if θ = 1. Themaximum µ that satisfies the commitment constraint is greater than µ since:

F

1− µ=[VH − VL

]> [VH(φ)− VL(φ)] =

F

1− µ

Now I show that the buyers earn positive profit, using the facts µ > µ, sH − VH > sL − VL,sH − VH > sH − VH(φ), and sL − VL > sL − VL(φ),

U = −k − F + µ(sH − VH

)+ (1− µ)

(sL − VL

)> −k − F + µ

(sH − VH

)+ (1− µ)

(sL − VL

)> −k − F + µ (sH − VH) + (1− µ) (sL − VL)

= U = 0

Proof of lemma 7. Let n be the fraction of low-quality sellers who enter the pooled submarket. Then

µ∗(∆) =α

α+ (1− α)n

n must be between [0, 1]. To check whether this holds, we rearrange:

n =

(α

1− α

)(1− µ∗(∆)

µ∗(∆)

)From assumption 5, we have α < 1

2 and from lemma 9 we have that µ∗(∆) > 12 when it exists.

Therefore, n ∈ [0, 1] as required.


Proof of lemma 8. I prove the lemma by contradiction. Suppose all low-quality sellers were pooledwith high-quality sellers over N ≥ 1 submarkets. Let λn be the mass of sellers in submarket n. Sincethe total mass of sellers is 1, it follows that

∑Nn=1 λn = 1.

Lemma 7 tells us that in a pooling submarket, the fraction of high-quality sellers must be at least 12 .

Otherwise, buyers will forego rating the assets. I now show that this implies that the mass of high-qualitysellers must be greater than 1

2 , violated assumption 5.

α =

N∑n=1

µnλn ≥N∑n=1

1

2λn ≥

1

2

But in assumption 5, we assumed that α < 12 .

Proof of lemma 10. The adverse selection penalty without rating δNR(∆) is increasing in the qualitygap and in the limit, approaches (c− k). The penalty δBR(∆) is decreasing in the quality gap and in inthe limit, approaches F . Since, c−k > F , there exists an unique ∆BR=NR ∈ [4F,∞) where δNR = δBR.

Proof of lemma 11. The proof is an application of the intermediate value theorem. Given ∆ ≥∆BR=NR, the penalty function δSR(∆;π) is a continuous decreasing function, taking the value δNR(∆)

when π = ∆∆+c−k and taking the value F when π = 1− F

∆ . The penalty δBR(∆) is between (F, δNR(∆)).Therefore, there exists an unique π where the two penalties are equal.

Chapter 2

Imperfect Information aboutEntrepreneurial Productivity, FinancialFrictions, and Aggregate Productivity

2.1 Introduction

Underdeveloped financial markets misallocate resources and distort entry by productive entrepreneurs. Alarge literature has tried to understand how such misallocation hinders economic development by loweringaggregate productivity.1 I argue that an important negative impact of financial underdevelopment is thatit impedes the discovery of productive entrepreneurs. To evaluate this hypothesis, I consider a model of amarket economy where implementing high-quality entrepreneurial ideas and allocating capital efficientlyacross operating firms are the critical determinants of productivity. Entrepreneurs with new ideas canonly discover its productivity by operating a firm. I find that financial frictions systematically distortthe incentives of households with potentially good ideas to learn about its quality, which substantiallylower productivity.

My study is motivated by recent evidence that entry by new entrepreneurs is a key driver of economicgrowth. For example, Haltiwanger et al. [2013a] document that in the US, new firms account for adisproportionate share of employment growth. However, young firms face greater uncertainty about theviability of their idea. They gradually learn about their idea’s productivity by actually observing itsperformance in the market [Kerr et al., 2014]. The literature also documents that young firms havedifficulty accessing credit because of their project’s uncertainty [Lerner, 2009]. The relationship betweenthe financing environment and experimentation by young entrepreneurs is further emphasized by Kerrand Nanda [2009], Calvino et al. [2016] and others who find that financing conditions have a stronginfluence on the entry, growth and survival of young firms.

In this paper, I study the joint impact of financial and information frictions using a general equi-librium model with heterogenous production units. My model builds on Buera et al. [2011a], whichis a standard model to study how financial frictions impact the aggregate economy by distorting both

1See Restuccia and Rogerson [2013] and Buera et al. [2015] for surveys of the misallocation and financial frictionliteratures respectively.

36

Chapter 2. Imperfect information, Financial frictions and TFP 37

capital allocation and the selection of households into entrepreneurship, as in Lucas [1978]. I introduceimperfect information about productivity following Jovanovic [1982]. In this framework, highly produc-tive entrepreneurs initially have low expected productivity but gradually discover their high productivityover time. Conversely, low productivity entrepreneurs learn their firms’ productivity is low and exit.This learning mechanism is an empirically relevant channel for explaining age-dependent patterns in firmdynamics (e.g. Arkolakis et al. [2014]).

Let me review the critical features of my model and how they relate to aggregate productivity:All households are equally productive as workers but differ in the productivity of their entrepreneurialideas, as in Lucas [1978]. Therefore aggregate productivity is maximized if the households with highentrepreneurial productivity sort into entrepreneurship.2 The productivity of a household’s idea changesfrom time to time, and therefore re-sorting is necessary. Households with new ideas need to actuallyimplement their idea to learn something about its productivity, which I consider a form of experimen-tation. They have an incentive to experiment because households with very good ideas can earn largeincomes. The allocation of capital across the operating entrepreneurs is also important for productivity.

I introduce financial frictions by assuming contracts are not perfectly enforced and there is a fixedcost of intermediation. Lenders in countries with weak legal systems have difficulty enforcing contracts,and this is an often cited form of financial underdevelopment. The fixed intermediation cost capturesscreening and administrative costs. My paper is the first to investigate how these frictions impact thediscovery of productive entrepreneurs.

When contracts cannot be perfectly enforced, lenders are willing to lend only to entrepreneurs whocan credibly promise to repay. Lenders seize a defaulting entrepreneur’s assets and recoup whateverincome they can through the legal system. Households with little assets and low-expected productivityeither face tight credit limits or, if their assets and expected productivity are very low, cannot accesscredit markets at all.

I show that households with new ideas are systematically more likely to face tight financing conditions.First, these households are likely to have been workers in the recent past and therefore have few assets tocollateralize loans. Second, their expected productivity is lower than its true value because of imperfectinformation.3 Because they have low assets and low expected productivity, young entrepreneurs infinancially underdeveloped economies face an increased probability that they will not have access toexternal credit at all. If they do have access, they are likely to face tight credit limits.

These tight financing conditions reduce the scale at which households with new ideas can operate,lowering the net benefit of learning about their idea. As a result, many poor households with new ideasforgo experimentation altogether. In contrast, if highly productive households had perfect informationabout their productivity, these same tight financing conditions would have little impact on their decisionto operate. Knowing they can earn very high incomes, these households would undo credit constraintsby accumulating assets (Moll [2014b], Midrigan and Xu [2014]). Therefore imperfect information limitsthe ability of high-productivity households with new ideas to overcome credit constraints through saving.

This paper contributes to a recent literature on the importance of imperfect information on produc-tivity. Greenwood et al. [2010] and Steinberg [2013] highlight the importance of cross-country differencesin lenders’ ability to learn about borrowers. David et al. [2016] shows that imperfect information about

2I assume households are equally productive as workers for simplicity. One consequence is that households cannotuse their worker productivity to infer their entrepreneurial productivity. Furthermore, this assumption eliminates en-trepreneurship by households with low labor productivity, an important feature of developing economies [Poschke, 2013].

3Highly productive ideas are rare, and therefore households with new ideas rationally discount very high initial signalsas possibly due to noise.


transitory shocks increase static misallocation and lower TFP.4 To my knowledge, my paper is the firstto study the impact of financial frictions on the discovery of entrepreneurial talent.5

I quantify the impact of financial and information frictions on TFP by calibrating the model to USdata, assuming the US has imperfect information and perfect contract enforcement. My calibrationstrategy uses data on exit rates of firms with age to infer the amount of imperfect information in the USeconomy. In the model, all entrepreneurs face the same probability that their ideas die. Old firms havea very accurate assessment of their productivity and therefore exit only when their idea dies. Youngfirms are less informed about their productivity, and exit either if their idea dies or if they learn theiridea is not worth implementing any further. I use the difference between the exit rates of young and oldfirms to identify the amount of imperfect information in the US economy.

I then use the calibrated model to evaluate the extent to which differences in imperfect informationand contract enforcement can explain cross-country TFP differences. I benchmark my results to aneconomy with both perfect enforcement and perfect information, because this economy not only has thehighest productivity but is also the standard benchmark used in the literature. I find that my calibratedUS economy, which has imperfect information and perfect enforcement, has a TFP about 3% lower thanthe benchmark, suggesting that imperfect information alone lowers TFP.

In my first counterfactual experiment, I hold imperfect information to US levels and weaken contractenforcement to developing country levels. I find that both TFP and GDP per capita fall monotonicallyas financing conditions worsen, and at the lowest level of contract enforcement, TFP is 23% lower thanthe benchmark economy. To understand whether interaction between financial frictions and imperfectinformation play any role, I repeat the same experiment of weakening contract enforcement, assuminghouseholds have perfect information about their productivity. I find that TFP falls by 12% in theworst case scenario. Taking into account that imperfect information directly lowers TFP by 3%, theseexercises suggest that about 7% of the TFP loss in the economy with imperfect information and lowcontract enforcement is due to the interaction between financial and information frictions.

In order to further understand the interaction of the two frictions, I decompose the total TFP lossinto several components including the portions due to capital misallocation and to the distorted selectionof entrepreneurs. I find that the importance of distorted selection differs markedly between the perfectinformation and imperfect information cases. In the economy with imperfect information when contractenforcement is at its lowest level, distorted selection accounts for about half of the total productivityloss of 23%. In contrast, in the economy with perfect information when contract enforcement is at itslowest, distorted selection lowers TFP by about 2% (out of a total loss of 12%).

To provide further support of the importance of my mechanism, I also investigate how weak contractenforcement impacts the exit rate of firms and young firms’ access to credit. I find that my model’spredictions are consistent with cross-country differences in young firm exit rates and access to credit, asrecently documented by Hsieh and Klenow [2014a] and Chavis et al. [2011] respectively. In economieswith weak contract enforcement, I find that the exit rate of young firms is lower than in the US, consistentwith Hsieh and Klenow [2014a]’s finding for India. Access to credit for young firms also falls substantially.Weak contract enforcement alone is unable to generate these facts.

Having identified a novel channel through which financial frictions can reduce TFP, I investigate

4This paper focuses on learning from stock prices and abstracts from financial frictions.5Learning about productivity or demand is an empirically relevant explanation for age-dependent firm life-cycle dy-

namics (e.g. Arkolakis et al. [2014], Eaton et al. [2014], and Foster et al. [2016]). This literature abstracts from financialfrictions and the implications for aggregate productivity.


whether a government policy to subsidize young entrepreneurs can correct some of the distortions. I findthat a relatively simple subsidy scheme financed by lump-sum taxes can go a long way to correcting theselection of entrepreneurs and increasing TFP.

Finally, I explore whether higher levels of imperfect information about entrepreneurial productivitymight be an independent cause for productivity differences across countries. My model allows meto evaluate the full range of information regimes, from perfect information to an environment withno learning. While holding contract enforcement at the US level, I increase the amount of imperfectinformation. I find that TFP monotonically decreases as the ability to learn declines. Relative to thefull information economy, TFP in the economy with no learning is 56% lower. Although we do not havedata on how imperfect information about entrepreneurial productivity and the learning process variesacross countries, the literature does document that other forms of uncertainty are generally higher indeveloping countries. My experiment suggests that further exploring differences in imperfect informationacross countries is a fruitful channel for explaining cross country income differences.

The rest of the paper is organized as follows: Section 2.2 presents the model, section 2.3 presents thecalibration strategy and quantitative exercises. Section 2.4 concludes.

2.2 Model

I will use a simple, stylized model to illustrate how financial frictions reduce a household’s incentive tolearn about their idea. I will then present a framework where households will face the same tradeoffs asin the simple model, but that is more appropriate for quantitative assessment.

2.2.1 Stylized Model

In this simple model, households are risk-neutral and live for two periods. Each household has an idea,but they do not initially know its productivity. The idea’s productivity (x) takes either a high or a lowvalue (i.e. x ∈ xL, xH). A fraction p of households have high-quality ideas. In order to use their ideato produce output, households must first implement it at an implementation cost w ≥ 0 and also usecapital as an input.

The low productivity ideas produce no output (xL = 0), and therefore are never worth implementing.If a household has productivity x and uses k units of capital, then their net output is xk−w. There is amaximum scale kuc above which employing additional capital produces no additional output. I capturethe scale reducing effects of financial frictions by assuming that each household draws the amount ofcapital they own from a distribution at birth, and cannot adjust it afterwards.

New households observe a noisy signal which they use to update the probability that their idea’sproductivity is high. The updated probability is p. If a household implements their idea, then they learnthe exact productivity by observing the output.

In order to make experimentation both costly and potentially worthwhile, I assume that if a highproductivity idea is operated at the unconstrained scale, then the realized output is strictly greater thanthe implementation cost. However, high productivity households are relatively rare: If a household’sexpected probability their productivity is high is the same as the population probability (p = p), thenthe expected income from implementing the project is negative. In particular, the assumptions are:


xHkUC − w > 0 (High quality ideas should be implemented)

pxHkUC − w < 0 (High quality ideas are rare)

In each period, households only implement their ideas if doing so maximizes their expected lifetimeincome. Figure 2.1 presents the timeline of events and decisions each household faces. Let me workbackwards to characterize the implementation decisions.

operate

do not operate

draw (x,k)

observe

signal,

update phat

operate/

do not operate

operate/

do not operate

period 2

period 2

no additional

information

discover idea

quality

Figure 2.1: Timeline for Stylized Model

Second period, perfect information. A household that implemented their idea in the first periodknows their productivity exactly. They will never implement the idea in the second period if theirproductivity is xL. If their productivity is xH then they will only implement their idea if they canoperate it at a sufficiently large scale. The threshold scale (k2) above which households with productivityxH implement their idea is:

k2 =w

xH

Second period, imperfect information. If the household did not implement the project in the firstperiod, then they still face imperfect information in the second period. They will implement the projectonly if their expected output is greater than the implementation cost (pxHk ≥ w). For households withcapital k, there is a threshold expected probability p2(k) above which they will implement their idea.

p2(k) =w

kxH


First period, imperfect information. In addition to the expected income in the first period, thereis a real option value of implementing the project because it reveals the idea’s productivity and allowsthe household to implement it in the second period only if it is high-productivity. A household withcapital k implements the project if and only their expected probability of having a high productivity isabove a threshold p1(k).

p1(k) =w

2xHk − w

Because of the value of learning about the idea’s quality, the threshold expected probability in period1 is strictly less than the threshold expected probability in period 2 (i.e. p1(k) < p2(k)).

Define the expected benefit of experimentation as B(p, k) = p(xHk − w) and the expected cost asC(p, k) = w − pxHk. The expected benefit is the net income in the second period if the productivity ishigh, multiplied by the probability that it might be so. The cost is the first period net income, accountingfor the probability that output might be zero. In figure 2.2 I plot the cost and benefit functions for ahousehold with low capital and a household with high capital. Higher capital allows the household tooperate at a higher scale, reducing the expected cost and increasing the expected benefit of operatingin the first period. Therefore, households with more capital have a lower threshold expected probabilityp1(k) above which they will experiment.

Probability that productivity is high

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ben

efi

t an

d c

ost

of

imp

lem

en

tin

g i

n t

he f

irst

peri

od

Cost, kUC

Benefit, kUC

Cost, k<kUC

Benefit, k<kUC

cost ↑

as k ↓

benefit ↓

as k ↓

threshold

probability

↑

as k ↓

Figure 2.2: Expected Benefit and Cost of Operating in First Period

In figure 2.3, I plot the threshold p1 as a function of capital k. The left panel illustrates two key ideas.First, even if a household has perfect information and is certain they have high productivity (p = 1),they will not operate if their capital k is below a certain threshold (labeled ‘do not operate (perfect)’).This is the standard way financial frictions distort entry into entrepreneurship. Second, if householdsare uncertain about their productivity (p < 1), they require a higher minimum scale to operate (labeled‘threshold (imperfect)’). Hence, imperfect information amplifies the distortion to entry from financialfrictions.


Scale (k)

Expecte

d p

robabil

ity o

f x

H (

phat )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Threshold for operating

do not operate (perfect info)

operate (perfect info)

threshold (imperfect info)

Scale (k)0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Change in implementation cost (w)

operatedo not

operatew ↓ w ↑

Figure 2.3: Threshold Belief for Operating First Period

Implementation cost. I illustrate the impact of the implementation cost w in the right panel. Theimplementation cost w plays an important role in determining the threshold p2(k): In the right panelof figure 2.3 I show that the threshold for implementing the project in period 1 is increasing in theimplementation cost w. A higher implementation cost increases both the cost of experimentationC(p, k) = w − pxHk and lowers the benefit B(p, k) = p (xH − w).

I now present the main model, which endogenizes the scale of operations and the implementationcost, and allows long-lived households to increase the scale of operation over time by accumulating assets.

2.2.2 Main Model

There is a measure 1 of infinitely-lived households. Each household has an idea, the productivity ofwhich varies across the population. Households implement their ideas by setting up and running a firm,and the quality of the idea determines the firm’s average productivity.

Let me begin by describing the distribution of ideas and how households learn about the quality oftheir ideas.

Distribution of ideas and learning process. Each household has an entrepreneurial idea. Thequality of the idea, X, is log-normally distributed across the population, i.e. x = log(X) ∼ N (µx, σ

2x).

Each period, the household’s current idea dies with probability 1−ρ,6 in which case the household drawsa new idea from the population distribution. The probability of carrying over the same idea into the

6We can think of the “death” of an idea as a permanent adverse shift in the demand for the good the firm was producing.The firm only continues to operate if its next product is sufficiently profitable.


next period is ρ ∈ (0, 1).7 Households know when their idea has died, but do not directly observe thequality of their next draw.

i) Initial signal about new idea. Immediately after losing an idea and drawing a new one, householdsobserve a noisy signal s. This signal is normally distributed, with mean equal to the idea’s quality (i.e.E(s|x) = x) and variance σ2

s , that is s ∼ N (x, σ2s). Since all households draw ideas from the same

population distribution, their prior about their new idea’s quality is the population distribution for ideasN (µx, σ

2x). The household uses the signal to update their beliefs and form their posterior distribution

x1 ∼ N (µ1, σ21). The mean and variance µ1 and σ2

1 of the posterior distribution are given by equations(2.1) and (2.2).

µ1 =σ2xs+ σ2

sµxσ2x + σ2

s

(2.1)

σ21 =

σ2sσ

2x

σ2s + σ2

x

(2.2)

I include this initial signal to encapsulate the perfect information economy as a special case of mygeneral model. In particular, if σ2

s = 0 then the signal immediately reveals the new idea’s type. I willuse this feature of the model to conduct counterfactual exercises.

ii) Subsequent learning. I capture the idea that discovering a business idea’s quality requires ob-serving its performance [Kerr et al., 2014] by assuming that households can only learn more abouttheir idea’s quality by setting up a firm and observing its total productivity. Households that do notimplement their idea in a given period do not learn anything new. Operating the firm requires all ofthe household’s time, and as a result it precludes working in the labor market. Therefore, the cost oflearning is the foregone wage minus any income from actually operating the firm.

A household implementing a new idea does not immediately learn its quality from the firm’s pro-ductivity because operating firms experience idiosyncratic, transitory productivity shocks each period.8

I think of these shocks as transitory changes in market conditions. The transitory shocks are also log-normally distributed with mean 0 and variance σ2

e , i.e. e ∼ N (0, σ2e). The total productivity of a firm

with idea quality X hit by transitory shock E is Z = XE = exp x+ e.If a household begins the period having observed j signals and their prior distribution based on these

signals has mean µ and variance σ2j , then after observing z and updating, the mean and variance of their

posterior distribution are given in equations (2.3) and (2.4).

µ+1 =σ2j z + σ2

eµ

σ2j + σ2

e

(2.3)

σ2j+1 =

σ2jσ

2e

σ2e + σ2

j

(2.4)

7Since households are infinitely-lived, each one will shift into and out of entrepreneurship over time based on the qualityof their ideas.

8There is a large literature documenting firm-level idiosyncratic, transitory shocks, e.g. Castro et al. [2009]


Terminology. I will refer to x as an idea’s quality and the first moment of the posterior distributionµ as the idea’s expected quality. I call E(Z) the expected productivity of an operating firm. Of course,with imperfect information, the expected productivity of a firm depends on the expected quality of theunderlying idea.

This completes the description of the learning process. I assume the amount firms learn from oper-ating for a period does not depend on the scale of their operation. If learning depended on the scale ofoperation, then financial frictions could have a larger impact by distorting the speed of learning. I leaveexploring this channel for future work. I will now describe the rest of the environment.

Preferences. All households have identical preferences, which are defined over a homogenous con-sumption good. Their period utility function is u(c) and their discount rate is β. They maximize theirlifetime expected utility by choosing among the sequences of consumption ct∞t=0 that satisfy theirbudget constraints, i.e.,

E∞∑s=0

βtu(ct), u(c) =c1−γ

1− γ, γ > 1, β ∈ (0, 1) (2.5)

Production technology. Goods are produced by competitive firms, each run by an entrepreneurialhousehold. Each firm operates a technology that is specific to the entrepreneurial household.9 Thetechnology takes the entrepreneur’s time as a fixed input, and capital (k) and labor (l) as variableinputs. The output of a firm with log-total productivity z as a function of capital k and labor l is:

ω(k, l; z) = ezkαlθ, α+ θ < 1 (2.6)

Since the above production function has decreasing returns to scale in the variable inputs, the mostproductive entrepreneur does not completely dominate production. Instead, a distribution of firmsoperate in equilibrium. As alluded to earlier, the main contribution of this study is to show howfinancial and information frictions distort the distribution of operating firms.

Markets. Factors of production are traded in competitive markets. The labor market is frictionless.The wage W equates labor supplied by worker households to labor demanded by entrepreneurial ones.

The credit market consists of lenders, owned by the households, who intermediate funds within theperiod. Near the beginning of the period, they take deposits from households and lend to entrepreneursat rental rate R. Near the end of the period, they collect payments from entrepreneurs and repayhouseholds their deposits with interest r.

Financial frictions. This intermediation process is affected by two sources of financial frictions: alump-sum intermediation cost per loan and imperfect contract enforcement.

9The assumption that the technology requires the particular household’s managerial time as an input is a standard wayto rule out poor households selling their ideas to rich ones. In this environment, if a poor household sells their good idea toa rich household, the poor household remains the monopoly seller of a necessary input (his managerial effort) and wouldextract all the rents.


i) Intermediation cost. For every loan issued, lenders incur a fixed cost ψ ≥ 0. Following Dabla-Norris et al. [2015] and Arellano et al. [2012], this fixed cost is a reduced form way to capture theadministrative costs of intermediation, such as screening borrowers and operating bank branches. Thelenders pass this cost on to the borrowers. Borrowers can either pay the cost up front if they havesufficient wealth at the beginning of the period, or at the end of the period from their wealth afterproduction. Borrowers who cannot pay the cost up front must credibly commit to pay the cost at theend of the period.

I include this cost to introduce the possibility that some entrepreneurs will not be able to accessexternal credit. In particular, borrowers who cannot pay the cost up front or credibly commit to pay atthe end of the period will not be able to access credit markets. Instead, they must completely self-financetheir project using their own assets.10 I will show that young firms will be more likely to not have access.

ii) Imperfect enforcement. Borrowers can default and refuse to give the lender the contractedpayment if it is optimal for them to do so. Lenders will therefore offer loans they know the borrower willactually honor. In this economy, all loan contracts are short-term, and defaulting borrowers have fullaccess to capital markets in subsequent periods despite their default history. Therefore, lenders cannotimpose any dynamic penalties. Instead, they will seize any assets the borrower puts up as collateral,and take the borrower to court to recoup as much of the borrower’s post-production wealth as possible.

Lenders can seize a fraction φ ∈ [0, 1] of the end of period wealth. The parameter φ captures thefull range of legal enforcement institutions.11 On one hand, contract enforcement is perfect if φ = 1.In this case, borrowers have no incentive to default since lenders can seize everything. On the otherhand, if φ = 0 then lenders cannot seize anything other than assets. In this case, loans must be fullycollateralized by assets.

I will defer the formulation and solution to the contracting problem momentarily, and instead firstpresent the recursive formulation of the household’s problem.

Recursive formulation of household’s problem. At the beginning of each period, households’state variables are assets (a), and their beliefs about their entrepreneurial idea which is summarized bythe expected quality µ and the variance σ2

j . To emphasize the connection between learning and theentrepreneurs’ age, I will replace σ2

j with j which is the number of periods the agent has ran a firmbased on this idea.

Each period, households first decide whether to be a worker or an entrepreneur. Then they dividetheir wealth between consumption (c) and savings (a′). Entrepreneurial households make additionaldecisions, which I describe momentarily. Let VW (a, µ, j), V E(a, µ, j) and V (a, µ, j) be the household’sexpected payoff from working, from entrepreneurship, and from optimally choosing their occupationrespectively.

If a household works, then their wealth after production is yW (a) = (1 + r)a + W . Their expectedpayoff is:

10I prove this in proposition 11.11In practice, lenders utilize both formal and informal methods to collect payments. Allen et al. [2012] documents in

their study of firm financing in India that lenders also use social pressure and arbitration by business partners.


VW (a, µ, j) = maxc,a′≥0

u(c) + β

[ρV (a′, µ, j) + (1− ρ) E

x,sV (a′, µ1(s), 1)

](2.7)

subject to: c+ a′ ≤ yW (a) = (1 + r)a+W

The worker’s value function VW depends on their beliefs about their entrepreneurial productivity(µ, j) because they might choose to implement their idea in the future. Since workers learn nothingnew about their productivity this period, conditional on keeping their current idea, their beliefs are stillsummarized by (µ, j) in the next period. With probability ρ they keep their idea, in which case theirexpected payoff from taking a′ assets to the next period is V (a′, µ, j). However, with probability 1−ρ thehousehold will lose their current idea, draw a new one from the population distribution, and observe anoisy signal s. The expected value of having a new idea and assets a′ is summarized by E

x,sV (a′, µ1(s), 1).

An entrepreneur’s value function is:

V E(a, µ, j) = maxc,a′≥0

u(c) + β

[ρEzV (a′, µ+1, j + 1) + (1− ρ) E

x,sV (a′, µ1(s), 1)

](2.8)

subject to: c+ a′ ≤ yE(a, µ, j)

An entrepreneur’s value function is similar to the worker’s, with two key differences. First, byoperating this period they learn something more about their idea’s quality. If they get to keep theircurrent idea next period, then their belief about its quality will be (µ+1, j+1). Second, their end of periodwealth after production is yE(a, µ, j). I will characterize this variable when I solve the entrepreneurs’problem.12

Remark. I assume the households choose their saving a′ prior to production. This assumption onlymatters for entrepreneurs13, since they must choose a′ prior to observing their current productivityand income. Entrepreneurs can choose a′ without worrying about potentially violating their budgetconstraint because they will find it optimal to insure their output against the transitory shock, andtherefore will be able to characterize their deterministic post-production wealth as a function of statevariables. I will discuss the insurance mechanism and what it buys me later.

Households choose the occupation that gives them the highest payoff. Let o(a, µ, j) equal 1 if thehousehold chooses to be an entrepreneur and 0 if they choose to be a worker. Their occupational choicemaximizes:

V (a, µ, j) = maxo(a,µ,j)∈0,1

(1− o(a, µ, j))VW (a, µ, j) + o(a, µ, j)V E(a, µ, j)

(2.9)

I now describe the contracting problem between lenders and entrepreneurs, which will determine theincome of entrepreneurs yE(a, µ, j).

12The interested reader can refer to proposition 13.13Since workers’ income is deterministic and their beliefs are the same before and after production, when they choose a′

does not matter.


Entrepreneurs’ and Lenders’ Problems

Entrepreneurs make financing, input and default choices based on the set of loan contracts offered tothem by lenders. On the other hand, lenders anticipate entrepreneurs’ behaviour when determiningthe set of contracts to offer each type of entrepreneur. Therefore, the entrepreneur’s and the lender’sproblems must be solved jointly. Figure 2.4 presents the timeline of events and decisions faced by anentrepreneur.

z realized.

production

lenders

enforce

contracts

purchase

insurance

insurance

pays out

choose

default (d)

choose

labor (l)

2

3

4

5

6

71

choose

deposits,

capital (k),

access (f)

Figure 2.4: Timeline for an Entrepreneur

Entrepreneurs make all choices before observing their total productivity (z). They first choosewhether to access external finance (f) and the amount of capital to use. If the entrepreneur accessescredit markets, then they deposit assets as interest-bearing collateral, and choose the optimal quantityof capital given credit limits. If they do not access external finance, then their capital choice is restrictedby their assets. These decisions are made at point (1) in figure 2.4.

Their remaining tasks are to decide whether to default (d), how many workers to hire (l), andwhether to insure their output against the transitory shock. Next, the transitory shock e is realized andproduction takes place. Insurance contracts pay out and workers are paid.

Finally, lenders enforce their contracts. Non-defaulting entrepreneurs make the required paymentsand receive back their collateral with interest. Defaulting entrepreneurs lose their collateral, and thelender seizes a fraction φ of their remaining end of period wealth.

All of the entrepreneur’s choices after choosing capital (points (2) onward in figure 2.4) can beperfectly anticipated based on financing choices (f, k) and state variables (a, µ, j). I will therefore solvethe entrepreneur’s and lender’s problems in three steps: first, I will solve the entrepreneur’s insuranc,elabor demand, and default decision taking financing decisions (f, k) as given. Second, I will solve forthe set of contracts lenders are willing to offer this entrepreneur. Third, I will solve the entrepreneurs’


choice of capital and accessing credit markets.

Insurance against the transitory shock. Since entrepreneurs choose inputs prior to observing z,their realized resources might be less than their obligations to lenders and workers and they might beforced to default. I abstract from equilibrium default by assuming entrepreneurial households have ac-cess to a competitive insurance market that opens after the decision to default has been made but priorto the realization of the transitory shock.14 As proposition 9 shows, they choose an insurance contractthat gives them the expected output for all realizations of total productivity z.

Proposition 9 (Optimal insurance). An entrepreneur with inputs (k, l) and beliefs (µ, j) finds it optimalto purchase an insurance contract that pays their expected output:

Ez

(ω(k, l; z)|µ, j) = exp

µ+

σ2j + σ2

e

2

kαlθ (2.10)

for all realizations of total productivity z.

Optimal labor demand. The optimal choice does not depend on the decision to default. Givencapital k, the optimal choice of labor and the output remaining after labor is compensated is:

l(k;µ, j) =

[exp

µ+

σ2j + σ2

e

2

kα(θ

W

)] 11−θ

(2.11)

π(k;µ, j) = (1− θ)

[exp

µ+

σ2j + σ2

e

2

kα(θ

W

)θ] 11−θ

(2.12)

Default decision. An entrepreneur’s end of period wealth if they do not default (yND) and if theydo default (yD) are:

yND(k; a, µ, j) = π(k;µ, j) + (1− δ)k + (1 + r)a− (1 + r)(k + ψ) (2.13)

yD(k; a, µ, j) = (1− φ) [π(k;µ, j) + (1− δ)k] (2.14)

If the entrepreneur does not default, they get the output after labor is paid (π(k;µ, j)), the depreciatedcapital ((1− δ)k), their assets plus interest ((1+ r)a), minus the payments to the lender ((1+ r)(k+ψ)).

14I abstract from lenders providing the insurance because if they could, they would condition payments on the defaultdecision and relax credit constraints. Furthermore, I assume the entrepreneur cannot pre-commit to not insure himself ifhe defaults in order to reduce his expected payoff of doing so.


If they do default, they get a fraction (1 − φ) of their output after labor is paid and the depreciatedcapital.

Because there are no dynamic penalties, the entrepreneur defaults if it maximizes expected end-of-period wealth. Proposition 10 characterizes the default decision.

Proposition 10 (Optimal default decision). An entrepreneur with capital k and state variables (a, µ, j)

defaults if and only if it maximizes their end-of-period wealth. Their default decision is:

d(k; a, µ, j) =

1 if yD(k; a, µ, j) > yND(k; a, µ, j)

0 if otherwise(2.15)

The lender’s problem. Lenders take into account an entrepreneur’s default decision (proposition10) when determining the set of contracts to offer. When an entrepreneur defaults, their lender earnsnegative profit. Therefore, lenders will only offer contracts which the entrepreneurs will honor. Thecapital lent must satisfy the following incentive-compatibility constraint:

π(k;µ, j) + (1− δ)k + (1 + r)(a− ψ)− (1 + r)k ≥ (1− φ)(π(k;µ, j) + (1− δ)k) (2.16)

We can re-arrange the IC constraint to isolate the role of assets on the left-hand side (LHS) and therole of beliefs about productivity and the loan size on the right-hand size (RHS).

(1 + r)(a− ψ) ≥ −φπ(k;µ, t) + (1 + r − φ(1− δ))k (2.17)

The entrepreneur will not be able to borrow if the incentive-compatibility constraint (2.17) cannotbe satisfied for any value of k. Proposition 11 shows that entrepreneurs with assets less than ψ andexpected productivity below a certain level will not be able to borrow.

Proposition 11 (Access to external finance). Entrepreneurs who cannot afford to pay the access costup front (a < ψ) can only access credit if the expected quality of their idea is above a threshold µ(a, j).Entrepreneurs who can afford to pay the access cost up front can access credit for all expected productivity.Define the constant C1:

C1 = −σ2e

2+

[α logα+ θ log

(θ

W

)− (1− α− θ) log(1 + r)

]The threshold µ(a, j) is:

µ(a, j) =

C1 + (1− θ) log φ+ α log(1 + r − φ(1− δ))

+(1− α− θ) log(ψ − a)− σ2j

2 if a < ψ

−∞ if a ≥ ψ


Let me now characterize the effective credit limits faced by entrepreneurs with state variables (a, µ, j).

Definition 6. Let k∗ be the values of k for which the incentive-compatibility constraint (equation (2.16))binds.

k∗(a, µ, j) = k : (1 + r)(a− ψ) + φπ(k;µ, j)− (1 + r − φ(1− δ))k = 0

If there are two solutions, then let kL(a, µ, j) and kU (a, µ, j) be the lower and upper ones.

Proposition 12 characterizes the incentive-compatible loan contracts that lenders offer to entrepreneursbased on their state variables (a, µ, j).

Proposition 12 (Incentive-compatible loan contracts). The set of loans that lenders are willing to extendto an entrepreneur with state variables (a, µ, j) is given by the interval K(a, µ, j) ≡ [k(a, µ, j), k(a, µ, j)].

The lower limit and upper limits k(a, µ, j) and k(a, µ, j) are:

k(a, µ, j) =

0 if a < ψ, µ < µ(a, j)

kL(a, µ, j) if a < ψ, µ ≥ µ(a, j)

0 if a ≥ ψ

k(a, µ, j) =

0 if a < ψ, µ < µ(a, j)

kU (a, µ, j) if a < ψ, µ ≥ µ(a, j)

k∗(a, µ, j) if a ≥ ψ

The entrepreneur’s wealth maximization problem. I can now solve for the entrepreneur’s wealthyE(a, µ, j). They choose whether to access external finance (f ∈ 0, 1) and how much capital to use inproduction to maximize their expected wealth:

Proposition 13 (Entrepreneur’s wealth maximization problem). An entrepreneur with state variables(a, µ, j) maximizes wealth by choosing whether to access external finance: f ∈ 0, 1, and how muchcapital to use given feasible sets. The problem is:

yE(a, µ, j) = maxf,k

π(k;µ, j) + (1− δ)k + (1 + r)a− (1 + r)k − fψ

Subject to:

k ∈ K(a, µ, j) if f = 1

k ≤ a if f = 0


Where π(k;µ, j) is the expected output net of the wage bill as defined in equation (2.12). K(a, µ, j)

is the set of loan contracts lenders are willing to offer this entrepreneur, as characterized in proposition12.

Definition of Stationary Equilibrium

The stationary equilibrium consists of three prices r, R and W , household policy functions for savinga′(a, µ, j) and occupational choice o(a, µ, j), entrepreneur’s policy functions for accessing external creditf(a, µ, j), capital demand kd(a, µ, j) and labor demand ld(a, µ, j), lower and upper bounds of feasiblecontracts k(a, µ, j) and k(a, µ, j), and the stationary distribution of the population over the state-spaceG(a, x, µ, j). These satisfy the following properties:

i) Given prices, o(a, µ, j) and a′(a, µ, j) solve the household’s problem.

ii) Given prices, f(a, µ, j), kd(a, µ, j) and ld(a, µ, j) solves the entrepreneur’s problem.

iii) Given prices, k(a, µ, j) and k(a, µ, j) solve the lender’s problem.

iv) Labor market clears:

Ls =

∞∑j=1

∫(1− o(a, µ, j))G(da, dx, dµ, j)

=

∞∑j=1

∫ld(a, µ, j)o(a, µ, j)G(da, dx, dµ, j) = Ld (2.18)

v) Capital market clears:

Ks =

∞∑j=1

∫aG(da, dx, dµ, j)

=

∞∑j=1

∫kd(a, µ, j)o(a, µ, j)G(da, dx, dµ, j) = Kd (2.19)

iv) Intermediaries make zero profit: R = r + δ

vi) Distribution G(a, x, µ, j) is the fixed point given the transition rules for a, x, µ and j.

2.2.3 Properties of the Model

Before turning to the quantitative analysis, I will highlight some important properties of the learningprocess and how they interact with financial frictions. I will also describe some properties of the modelthat will help us to discipline the learning process and decompose the role of imperfect information andfinancial frictions.


Properties of the Learning Process

Although there is a stationary distribution of households’ beliefs over the state variables (x, µ, j), thisdistribution does not have an analytical characterization because of selection.15 I will therefore shutdown selection to characterize the evolution of beliefs for different types of entrepreneurs.

I can characterize the distribution of beliefs of households with new ideas after they observe the firstsignal. The key takeaway is that households with high-quality new ideas on average have an expectedquality (µ) that is lower than the true quality, and their expected quality gradually increases towardsits true value as they observe more signals. They also on average have an expected productivity lessthan their true productivity, which is relevant for accessing capital, credit limits, and income fromentrepreneurship.

Consider a household with a new idea of quality x. This household uses the initial signal s to updatetheir expected quality µ1 (calculated according to equation (2.1)). Given an underlying type x, the

distribution of µ1 is normal with mean E (µ1|x) =σ2xx+σ2

sµxσ2x+σ2

sand variance V (µ1|x) =

(σ2x

σ2x+σ2

s

)2

σ2s . The

term E(µ1|x) is the average expected quality of households with idea of quality x.Property 1 expresses the average expected quality as a deviation from the true quality. Households

with ideas above (below) the population average (µx) have an average expected quality below (above)the true quality.

Property 1. The average expected quality of a new idea with underlying quality x is:

E (µ1|x) = x−(

σ2s

σ2x + σ2

s

)[x− µx] (2.20)

Households with idea quality x, above the population mean µx, on average have an expected quality µ1

below the true value. Households with idea quality below the population average have an expected qualityabove the true value.

Property 1 is intuitive. Households account for the possibility of noise when updating their expectedquality. If the signal s = x is greater than the prior expected quality µx, then they consider the possibilitythat the signal is upward biased by noise by partially adjusting their expected quality. If the signal wasprecise (σ2

s = 0), then the household’s expected quality immediately jumps to equal their true qualityx. If the signal is completely noisy (σ2

s = ∞), then their expected quality does not change at all andremains µx.

If the household with the average expected quality (µ1 = E(µ1|x)) implements their idea and operatesa firm, then their firm’s expected productivity is:

E(Z|E(µ1|x), σ2

1

)= exp

E(µ1|x) +

σ21 + σ2

e

2

(2.21)

Although I can characterize the distribution of expected productivity, a more informative exercise isto compare the average expected productivity (equation (2.21)) with the expected productivity underperfect information. The expected productivity under perfect information is:

E (Z|x) = exp

x+

σ2e

2

(2.22)

15As discussed in section 2.2.2, all households with new ideas observe an initial signal. They learn more only if theyoperate a firm, and therefore the distribution is affected by selection.


Property 2 compares the expected productivity of the household with the median signal, underimperfect and perfect information.

Property 2. The difference in the log-expected productivity under imperfect and perfect information,for an entrepreneur with new idea of quality x that has the average expected quality E (µ1|x) is:

log(E(Z|E (µ1|x) , σ2

1

)))− log (E (Z|x)) = −

(σ2s

σ2x + σ2

s

)[x−

(µx +

σ2x

2

)](2.23)

Households with an idea quality x above µx +σ2x

2 have a lower average expected productivity underimperfect information.

Property 2 shows that households takes into account that uncertainty raises expected productivityby increasing the possibility of a high x. However, for households whose quality x is actually high, theoverall effect is to drive down their expected productivity.

In lemma 13, I extend property 2 to households with additional signals. Households receiving signalscorresponding to their true quality each period gradually update their expected quality toward thetrue value. For ideas with quality x > µx +

σ2x

2 , the expected productivity is less than the expectedproductivity with perfect information.

Lemma 13. The difference in log-expected productivity under imperfect and perfect information, for anentrepreneur who in the j+1 period of operation and has observed the mean signal (s = z1 = · · · = zj = x)so far is: [

E(µj+1|x) +σ2j+1

2− x

]=

(σ2j

σ2j + σ2

e

)[E(µj |x) +

σ2j

2− x

](2.24)

I will show next that imperfect information, by lowering expected productivity makes financingconditions tighter and decreases the net benefit of experimentation.

Interaction between Financial Frictions and Imperfect Information

In lemma 14, I show that conditional on having access to external credit, an entrepreneur’s credit limitsrelax with higher expected quality µ and higher assets a. The reason is that an entrepreneur with eitherhigher assets or higher expected quality loses more if they default. Therefore, more capital can be lentto them while ensuring repayment.

Lemma 14. [Relaxing credit limits] For entrepreneurs who can access credit, (i.e. µ ≥ µ(a, j)), theircredit limits relax if either their assets or their expected quality increase.

∂k

∂µ≤ 0,

∂k

∂µ> 0

∂k

∂a≤ 0,

∂k

∂a> 0

For a highly productive entrepreneur, lemmas 13 and 14 imply that if they repeatedly receive themedian signal, then their credit limit relaxes over time. In figure 2.5 I illustrate this by taking a highlyproductive entrepreneur and evaluate their credit limit if they receive the mean signal (s = z1 = x) for


the first two periods. I also plot what their credit limit would be if they had perfect information, andshow that it is higher for all asset levels.

Assets

0

Cre

dit

lim

it

0

1

2

3

4

5

6

7

Age = 1, Imperfect information


Age 1, Quality known

For those with

access,

limit increases

with

more information

Figure 2.5: Credit Limit with Age for a High-Quality Entrepreneur

Access to finance. In proposition 11, I defined a threshold expected quality µ(a, j) that entrepreneurswho cannot pay the intermediation cost up front must have to access credit. Proposition 14 shows theminimum expected productivity necessary to access credit, and how this threshold expected productivitychanges with the contract enforcement parameter φ. This threshold depends on an entrepreneur’s assetsbut not their beliefs, and is therefore a common threshold faced by all entrepreneurs.

Proposition 14. An entrepreneur with assets less than the intermediation cost has access to credit iftheir expected productivity µ+

σ2j

2 is greater than χ(a). χ(a) solves:

χ(a) = C1 − (1− θ) log φ+ α log (1 + r − φ(1− δ)) + (1− α− θ) log (ψ − a) , ∀a < ψ

Where C1 is a constant defined in proposition 11. For assets a < ψ, the threshold χ(a) → ∞ asφ→ 0+.16

Lemma 13 and proposition 14 suggest that for a highly productive entrepreneur who is asset poor, theprobability of having access increases with age. I illustrate this by taking a high-productive entrepreneurand calculating their probability of having access by integrating over all realizations of the initial signals and the first period productivity z1. I also plot their probability of having access if their productivitywas known.

These results suggest that imperfect information tightens financing conditions for young firms whencontract enforcement is weak. However, if high-productivity households operate, they gradually discover

16The prices r and W depend on φ but are bounded (W ≥ 0, r ≥ −δ). The direct effect on χ(a) of small values of φdominates any indirect effect through the prices.


Assets

0

Pro

bab

ilit

y o

f h

av

ing

access

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1



Age = 1, Quality known

Probability of

having

access increases

with more

information

Figure 2.6: Access to Credit with Age for a High-Quality Entrepreneur

their idea’s quality and their financing conditions relax.17 These tight financing conditions have a muchbigger impact by reducing the scale of operations, reduce the net expected benefit of learning about theidea’s quality and leading some households to forego learning altogether. The stylized model in section2.2.1 illustrates the intuition.

Other Model Properties

Capital allocation with perfect enforcement. Households have no incentive to default since theylose all their output to the lender. As a result, they are able to borrow the amount that maximizes theirprofit, and is independent of wealth.

kuc(µ, j) = arg maxk

π(k;µ, j)−Rk (2.25)

The associated profit is πuc(µ, j). In this economy, expected marginal product of capital is equatedacross operating units.

All entrepreneurs have access with zero intermediation cost. Weak contract enforcement alonedoes not affect access rates.

Lemma 15 (Zero intermediation cost). If the fixed intermediation cost ψ = 0, then all entrepreneurshave access to credit.

Occupation choice under perfect information and enforcement. Households have perfect in-formation if the variance of the initial signal σ2

s = 0 and s perfectly reveals their type. Proposition 15

17They also accumulate assets, which helps relax credit limits further. The speed of accumulation is lowered by imperfectinformation, since expected productivity is lower.


shows that the household’s occupational choice does not depend on the number of signals j or theirassets a.

Proposition 15 (Occupational choice with perfect information and enforcement). If households haveperfect information, their beliefs are (µ, σ2

j ) = (x, 0). With perfect enforcement, the household’s occupa-tional choice is determined by static income maximization. Households are entrepreneurs if:

πuc(x, 0) ≥W (2.26)

Isolating the role of imperfect information. The initial signal and the insurance scheme means Ican eliminate any direct impact of the transitory shocks. This is a useful tool, because it will allow usto isolate the impact of imperfect information.18

Proposition 16 (Transitory shocks have no direct effects). If σ2s = 0 and µx = −σ

2e

2 , then the transitoryshocks have no impact on household decisions or aggregates.

2.3 Quantitative Analysis

I calibrate the stationary equilibrium of my model with perfect contract enforcement (φ = 1) andimperfect information (σ2

s , σ2e > 0) to moments from US data. I then study how weaker contract

enforcement and higher imperfect information impacts productivity and income per capita.

2.3.1 Calibration

The full set of parameters in this model are:γ, δ, α, θ, σ2

x, σ2e , µx, σ

2s , ρ, β, ψ

. I calibrate these pa-

rameters to match moments from US data, mostly following the approaches in Buera et al. [2011a]and Ranasinghe and Restuccia [2016]. I set the risk-aversion parameter γ = 1.5 and the depreciationrate δ = 0.06, which are standard values from the literature. I normalize the mean log-productivityby setting µx = −σ

2e

2 . Furthermore, the initial signal s is a modelling tool to encapsulate the perfectinformation economy. I therefore assume that the variance of the initial signal is equal to the varianceof the transitory shocks, which is what I propose determines the speed of learning (i.e. σ2

s = σ2e).

Although the remaining 6 parameters are calibrated jointly, for each parameter there is a momentthat is particularly informative. The fraction of income going to capital and labor α + θ is chosensuch that the fraction of the population that are entrepreneurs equals 7.5% (Cagetti and Nardi [2006]).Capital income share is then set to α

α+θ = 0.3. The discount rate β is set to target an equilibrium realinterest rate of r = 0.04. Dabla-Norris et al. [2015] report that the fraction of firms with access to creditis 95%, which disciplines the intermediation cost ψ.19 The variance of the productivity distribution (σ2

x)is disciplined by the fraction of income going to the top 5% of households.

A key feature of my model is that with perfect information and perfect contract enforcement, theexit rate of firms does not vary with firm age (proposition 15). However, with imperfect information,

18See Alfaro et al. [2016] for an example of how higher uncertainty and financial frictions interact.19I map this moment to the data as the fraction of firms who can, conditional on paying the intermediation cost, face

a non-zero credit limit (see proposition 11). Of course, this is different from the fraction of firms who choose to accessexternal credit.


the exit rate of young firms is higher than the exit rate of old firms. I therefore exploit the differencein the exit rate between young and old firms documented by Hsieh and Klenow [2014a] to disciplinethe amount of imperfect information. Old firms know their productivity and therefore exit only if theirproductivity changes and their new idea is not worth implementing. Therefore their exit rate of 6% isinformative of the persistence of the productivity process ρ. Firms younger than 5 years exit at a higherrate: From Hsieh and Klenow [2014a], I calculate that after 5 years, only 52% of the initial entrantsremain in operation. I use the higher exit rate for young firms to discipline the variance of the transitoryshocks, σ2

e . Figure 2.7 illustrates the argument.

Age

Ex

it r

ate

OldYoung

Perfect information

Figure 2.7: Disciplining Imperfect Information Parameters

Table 3.1 reports the values of the calibrated parameters.

Data Model Parameters Calibrated valueFraction entrepreneurs = 0.075 0.075 α+ θ 0.81Income share of top 5% = 0.3 0.3 σ2

x 0.31Fraction exiting within 5 years = 0.48 0.48 σ2

e 0.04Exit rate amongst old firms = 0.06 0.06 ρ 0.92

Real interest rate = 0.04 0.04 β 0.92Fraction with external finance = 0.95 0.95 ψ 0.16

Table 2.1: Calibrated Parameters

There are two additional moments of interest: the calibrated economy has a capital to output ratioof 3.1 which is similar to the US data. The external credit to GDP ratio is 1.88, which is less than the2.4 in the US (Beck et al. [2000]). However, this value is well within the range of estimates for developedcountries.20

20When calibrating, I found that matching the US external credit to GDP ratio requires changing the entrepreneurialshare of income (1−α−θ) and the variance of entrepreneurial productivity (σ2

x) in such a way that the fraction of households


Benchmark economy. I use the economy with perfect enforcement (φ = 1) and perfect information(σ2s = 0) as the benchmark and present results for all other economies relative to outcomes in this one.

This economy has the highest productivity and GDP per capita, and also corresponds to the benchmarkused in the literature. Table 2.2 compares the benchmark economy to the calibrated US economy.

Benchmark USTFP 100.0% 96.8%

GDP per capita 100.0% 96.7%capital-to-output 3.14 3.12

external credit to GDP 1.89 1.88

Table 2.2: Benchmark and Calibrated (US) Economies

Imperfect information lowers both productivity and GDP per capita by about 3%. This productivityloss is due mainly to firms choosing inputs under imperfect information about their productivity, andsecondly to misallocation of some households who should be entrepreneurs as workers.21

2.3.2 Weakening Contract Enforcement

I study what happens to productivity if contract enforcement is weakened, by reducing φ. In figure 2.8,I plot TFP and GDP per capita against relative external credit to GDP.22

Relative external credit to GDP

0.2 0.4 0.6 0.8 1

TF

P

(Perf

ect

info

rmati

on, perf

ect

enfo

rcem

ent

= 1

)

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

TFP

Imperfect information

Perfect information


0.2 0.4 0.6 0.8 1

GD

P p

er

capit

a

(Perf

ect

info

rmati

on, perf

ect

enfo

rcem

ent

= 1

)

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

GDP per capita


Perfect information

Figure 2.8: TFP and GDP per Capita for Different Levels of φ

In table 2.2, I reported that even with perfect contract enforcement, imperfect information lowers

that are entrepreneurs fall sharply. As the probability of having an idea worth implementing is a critical determinant ofthe incentive to experiment, I maintain the fraction of entrepreneurs as a target.

21See figure 2.9 for a decomposition of TFP losses due to various sources.22I report the results against relative external credit to GDP (i.e. relative to external credit to GDP in the benchmark

economy) because it is monotonically increasing with φ, and is actually an observable. For example, India has an externalcredit to GDP of about 0.3, which translates to 0.13 relative external credit to GDP in figure 2.8.


TFP by about 3%. This corresponds to the gap between the perfect and imperfect information plots inthe left panel, when relative external credit to GDP is 1.

Under both perfect and imperfect information, TFP falls monotonically as contract enforcement isweakened. Income per capita also falls monotonically, falling by about 30% in the worst-case economywith imperfect information. The drop is larger than the drop in productivity because incentives toaccumulate capital is also reduced and the capital to output ratio is lower than in the perfect-enforcementcase.

With imperfect information, TFP falls by 22.9% in the worst case scenario. With perfect information,TFP falls by 12.6% in the worst-case scenario. After accounting for the 3% TFP loss due to the directeffect of imperfect information, the steeper rate of TFP loss under imperfect information suggest thetwo frictions interact. I will explore this interaction below.

Remark on TFP loss under perfect information. The TFP loss from weakening contract en-forcement under perfect information is near the lower end of the range of estimates in the literature.The reason is that my persistence parameter ρ is higher than in comparable models. My persistence ishigher because while many papers target the average exit rate, I decompose the exit rate between thatof young and old entrepreneurs, and discipline the persistence by the exit rate of old firms, which islower than the average. With higher persistence and perfect information, highly productive firms havea stronger incentive and more time to overcome credit limits by saving (Moll [2014b]).

Decomposing the TFP losses. To understand how weak contract enforcement and imperfect infor-mation interact to reduce TFP, I decompose the total TFP loss into several components. For any givenvalue of φ, I start from the equilibrium and move toward the perfect information, perfect enforcementbenchmark economy by gradually undoing misallocation. I implement the following steps to both theimperfect and the perfect information economies.

i) Holding aggregate capital K, the number and distribution of entrepreneurs constant,

ia) under imperfect information, reallocate capital to equate expected marginal product of capital(reallocate capital)

ib) reveal quality (x) to entrepreneurs, then reallocate capital to equate expected marginal prod-uct of capital (reveal type, imperfect information economies only)23

ii) Holding aggregate capitalK and the number of entrepreneurs constant, choose the most productivehouseholds as entrepreneurs, and then under perfect information, reallocate capital to equateexpected marginal product of capital (reallocate talent)

iii) Allow capital and the number of entrepreneurs to adjust to benchmark economy levels (i.e. solveall problems and aggregate at benchmark economy prices)

In the first step, I reallocate inputs, taking aggregate resources and the productivity distribution ofoperating firms as given. This exercise is similar in spirit to Hsieh and Klenow [2007], who calculate forthe US, China and India the productivity gains from optimally reallocating factors while taking each

23I am equating expected MPK because, even with perfect information about x, entrepreneurs still choose inputs beforeobserving the transitory shock e.


country’s productivity distributions as given. However, because I have imperfect information, I equateexpected marginal product of capital rather than the realized marginal product of capital.

In step ii, I correct for distorted selection, by choosing the households with the most productiveideas into entrepreneurship. I should emphasize that I do this exercise while holding the underlyingdistribution of productivity from which entrepreneurs are selected to the calibrated US productivitydistribution.24

I report the results of this decomposition exercise in figure 2.9, with the results for economies withimperfect information in the left panel and those for the economies with perfect information in theright panel. The key insight is that weak contract enforcement distorts the selection of entrepreneursmuch more under imperfect information than under perfect information. In the imperfect informationcase, the loss due to distorted selection is the gap between the line labeled ‘reallocate talent’ and theline labeled ‘reveal type’. In the perfect information case, the loss due to distorted selection is the gapbetween ‘reallocate talent’ and ‘reallocate capital’.


0.2 0.4 0.6 0.8 1

TF

P

(perf

ect

info

rmati

on

, p

erf

ect

en

forc

em

en

t case

= 1

)

0.75

0.8

0.85

0.9

0.95

1


Total effect

Reallocate capital

Reveal type

Reallocate talent

Perfect info, enforcement


0.2 0.4 0.6 0.8 10.75

0.8

0.85

0.9

0.95

1

Perfect information

Total effect

Reallocate capital

Reallocate talent


Figure 2.9: Decomposing TFP Losses from Weaker Contract Enforcement

Table 2.3 summarizes the loss in the worst case:

Imperfect PerfectCapital misallocation (imperfect) 6.1% (6.1%)

Capital misallocation (perfect) 2.5% (8.6%) 7.8% (7.8%)Talent misallocation 11.6% (20.2%) 2.2% (10.0%)

Number of entrepreneurs 2.7% (22.9%) 2.4% (12.4%)Total loss 22.9% 12.4%

Table 2.3: Decomposing TFP Loss

24Maintaining the log-Normal assumption, productivity distributions in other countries can differ in the two momentsµx and σ2

x. Differences in µx can be normalized away. We have little evidence on how the second moment σ2x varies across

countries (Buera and Shin [2013]).


In each column, I report the loss due to each source of misallocation and the cumulative loss inbrackets. Standard capital misallocation is somewhat larger under imperfect information (8.6% vs 7.8%).However, the information regimes have starkly different losses from distorted selection (talent misallo-cation). With perfect information, distorted selection lowers TFP by 2.2% (17.5% of the total loss)whereas with imperfect information, distorted selection lowers TFP by 11.6% (50.6% of the total).

Under perfect information, there is very little TFP loss due to talent misallocation because highlyproductive households always enter. They then accumulate assets to relax credit limits.25 The largerTFP loss due to distorted selection is consistent with my hypothesis. Under imperfect information, manyhouseholds facing tight financing conditions forgo learning all together. Having foregone entrepreneur-ship, they have no incentive to accumulate assets to overcome credit credit constraints.

Other Effects of Weak Contract Enforcement

Access to credit with age. Chavis et al. [2011] document from the World Bank enterprise surveythat younger firms in developing countries have lower access to finance. They find that in developingcountries, the fraction of young firms (younger than 5 years) with access to credit is particularly low(∼ 35%) and rises with age. As discussed previously, imperfect information, by introducing uncertaintyabout output, tightens access to credit for poor young firms, and the impact is magnified as contractenforcement weakens.

Figure 2.10 reports the fraction of firms with access to credit in economies with different levels ofcontract enforcement under different information regimes, for ‘young’ (≤ 5 years) and ‘old’ (≥ 20 years)firms respectively.26 Access for young firms fall much more sharply under imperfect information thanunder perfect information. This is because under perfect information, although young firms are poorerthan old firms, they can use their high productivity to access credit. Under imperfect information, usingexpected output becomes harder for young firms.

Notice that there is not much difference across the two information regimes for old firms. This isbecause these firms are relatively wealthy and, in the case of imperfect information have observed manysignals so effectively know their idea’s quality.

The model overstates access to credit for young firms in the US (Robb and Robinson [2012]), becausewith a common intermediation cost, imperfect information alone is not able to generate a large gapin the access probability if lenders can seize all of young entrepreneurs’ output (perfect enforcement).However, as we see by comparing the left and the right panel, the imperfect information can help explainwhy young firms are particularly affected when contract enforcement is weak.27

Firm exit rate Hsieh and Klenow [2014a] document that firm exit rate profile with age is both lowerand flatter in India than in the US. Since I use the US exit rate profile to calibrate imperfect informationin my model, I ask what happens to the exit rate when I reduce contract enforcement to Indian levels.Figure 2.11 presents the exit rates in the model version of the two economies.

Consistent with Hsieh and Klenow [2014a], the exit rate profile is flatter in the economy with Indianlevel of financial development. This is because poor entrants enter only if their initial signal is very high

25The small loss due to selection under perfect information is similar to what Buera et al. [2011a] finds for the sectorwithout fixed costs (services) in their study.

26Ability to access credit depends on both expected productivity and assets here.27Matching the access rates in the US would require imposing a higher intermediation cost on young firms, which can be

justified by appealing to higher screening costs for these firms (Lerner [2009]). This would just amplify the productivitylosses presented here.



0.2 0.4 0.6 0.8 1

0.7

0.75

0.8

0.85

0.9

0.95

1Imperfect information

Young entrepreneurs

Old entrepreneurs


0.2 0.4 0.6 0.8 1

0.7

0.75

0.8

0.85

0.9

0.95

1Perfect information

Young entrepreneurs

Old entrepreneurs

Figure 2.10: Access to Credit by Age

Age (number of signals)

1 2 3 4 5 6 7 8 9 10

Exit

rat

e

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

US

India

Figure 2.11: Exit Rate with Age


(less experimentation) and therefore are less likely to drop out later. The outside option is also lower,so wealthy, low quality entrants are less likely to drop out.

These results go only part way to explaining the large differences in the exit rates between India andthe US. However, with perfect information the relative slopes of the exit rates would be counterfactual:the exit rate for the US would be flat, while India’s has a slight negative slope initially. Therefore, theexit rate profile in India would be steeper than the one in the US.

2.3.3 Increasing Imperfect Information

I found that the calibrated US economy has lower TFP than the benchmark economy due to the di-rect effects of imperfect information. Although we do not know how imperfect information about en-trepreneurial productivity and the speed of learning varies across countries, the literature finds thatother sources of uncertainty as well as the variance of transitory shocks are generally higher in develop-ing countries (e.g. Koren and Tenreyro [2007], David et al. [2016]). My model can capture all possiblelevels of imperfect information. Therefore I use it to investigate how increasing imperfect informationaffects TFP. I implement this experiment with perfect contract enforcement (φ = 1). I increase thevariance of the transitory shocks σ2

e , adjusting σ2s (σ2

s = σ2e) and µx (µx = −σ

2e

2 ) appropriately.

As the variance σ2e increases, the speed of learning falls and in the limit is zero. The intuition is that as

the variance increases, the households attribute much of the realized productivity z to transitory shocks,and therefore adjust beliefs slowly. In the limit as σ2

e → ∞, for any number of signals j, the momentsof the posterior distribution approaches the population mean and variance: (µj , σ

2j )→ (µx, σ

2x). Figure

2.12 presents the results.

Multiples of σ2

e,US

0 100 200 300 400 500

No

rmal

ized

TF

P

0.4

0.5

0.6

0.7

0.8

0.9

1

Vary σ2

e

No learning

Multiples of σ2

e,US

0 1 2 3 4 5

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Figure 2.12: TFP as Imperfect Information Increases

TFP declines monotonically with higher imperfect information and drops by 54% in the limitingeconomy with no learning.28

28As σ2e → ∞, all households behave as if they had the unconditional population productivity which is completely

persistent. Heterogeneity no longer plays a role and the economy collapses to a representative agent one.


Clearly, no country has a transitory shock distribution with variance 500× the US one. However,the experiment shows the maximum possible loss, and shows that the fall in TFP is steepest for smallmultiples of the US variance (right panel). What are plausible guesses for how much higher the variancemight be in developing countries? David et al. [2016] finds that the variance of the particular shocksthey study is up to 1.8 times higher in India relative to the US. A multiple of 2 in the right panelwould reduce TFP by an additional 3%. A multiple of 3 times would bring TFP down by 10% intotal, a magnitude that would compare to other direct explanations for TFP differences. Therefore,identifying cross-country differences in imperfect information might be a fruitful way to explain cross-country productivity differences.

2.3.4 Policy Intervention

In section 2.3.2, I quantified the impact of a novel channel through which weak contract enforcementimpacts TFP: I showed that weak contract enforcement substantially lowers TFP by discouraging exper-imentation by poor households. Countries with weak contract enforcement can increase productivity byreforming their legal institutions. By relaxing financing conditions for new entrepreneurs, more house-holds will experiment and more high productivity entrepreneurs will be discovered (Kerr and Nanda[2009]).

While many countries have made progress improving contract enforcement (e.g. Campello and Lar-rain [2015]), legal institutions are generally thought to be deeply dependent on history (e.g. Djankovet al. [2007]) and therefore difficult to change.

As an alternate tool, many governments run programs to support business development, targetingeither small or young businesses who they believe are credit constrained (Lerner [2009]).29I investigatewhether subsidy schemes targeted towards new entrepreneurs can support experimentation and thediscovery of new ideas.

Cost of experimentation. The cost of experimentation is static. It is the foregone wage W minusthe income from operating the firm. In particular, 30

C(a, µ, j) = max 0,W − π(a, µ, j) (2.27)

Subsidy program. The government gives a subsidy ξ to new entrepreneurs for the first four yearsof their time in operation, as in Arkolakis et al. [2014]. A new entrepreneur is defined as a householdthat has a new idea (j = 1) and was not an entrepreneur in the previous period. I assume that thegovernment knows that the household’s firm is new and is implementing a new idea. The governmentlearns this information because households have to register their business and describe what they intendto produce in order to get the subsidy.31 However, I assume the government does not screen based onassets or expected quality µ.

29Lerner [2009] also highlights the complicated incentive problems faced by the government when designing any businesssupport program and reviews the mixed results. To highlight the potential gains, I abstract from these issues in theseexperiments.

30I bound the cost at 0 because for entrepreneurs whose profit π(a, µ, j) > W , there is no cost of experimentation asthey would operate just to maximize income

31I assume the government can verify the idea is new to eliminate the incentive for households to switch into and out ofentrepreneurship to collect the subsidy.


The program is financed by a lump-sum tax T on all households, regardless of their occupation. Thegovernment balances its budget in each period. Therefore, if a fraction n of households are receiving thesubsidy, then the government’s budget constraint must satisfy:

ξn = T (2.28)

The subsidy benefits new entrepreneurs in several ways: first, the government pays the subsidyto the lender if the household defaults, and therefore it relaxes credit limits. Second, conditional onnot defaulting, the household keeps the subsidy and therefore is compensated for part of the cost ofexperimentation. Finally, the additional income due to the subsidy allows the household to save moreand relax credit constraints in the future.32 In general, the subsidy lowers the cost of experimentation.

C(a, µ, j; ξ) = max 0,W − π(a+ ξ, µ, j)− ξ

≤ max 0,W − π(a, µ, j)

= C(a, µ, j; 0)

Scope of program. In this investigation, I am mainly interested in exploring how a subsidy schemecan support the discovery of new ideas. I therefore limit the size of the subsidy schemes I consider tofocus on this channel. Financial frictions also introduce static misallocation, which other programs couldhelp correct (Buera et al. [2014]).

I explore the benefits of such a subsidy scheme using two experiments. In the first experiment, I takean economy with a level of financial development similar to the non-OECD average and evaluate theimpact of subsidizes of various sizes on TFP and income per capita. Notice that if all households couldearn at least the equilibrium wage as an entrepreneur, then the cost of experimentation would be zero.I consider subsidies that are various fractions of the pre-subsidy equilibrium wage. In particular,

ξ = ξW 0, ξ ∈ [0, 1] (2.29)

In the second exercise, I set the size to half of the pre-subsidy equilibrium wage in economies withvarying levels of financial development, and study the effect of this subsidy across different economies.In particular,

ξ(φ) =1

2W 0(φ) (2.30)

Exercise 1: Subsidizing new firms in a representative developing country. I choose theeconomy which, prior to the subsidy, has an external credit to GDP ratio of 0.3433 Figure 2.13 showsthe impact on TFP and income per capita as I vary the size of the subsidy.

In figure 2.13, at ξ = 0 there is no subsidy and the TFP and GDP per capita correspond to TFP andGDP per capita in figure 2.8 at a relative external credit to GDP of 0.16.34 Both TFP and GDP per

32By relaxing credit constraints in the future, it indirectly also increases the benefits of experimentation.33According to Beck et al. [2000], this is the average external credit to GDP amongst the non-OECD countries. It is

also close to the value for India.34Relative external credit to GDP of 0.16 corresponds to the non-OECD average divided by the benchmark economy’s

external credit to GDP of 1.89.


Subsidy ξ: fraction of W0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Nor

mal

ized

TF

P, G

DP

/cap

ita

0.74

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

TFP

GDP/capita

Figure 2.13: TFP and GDP per Capita with Subsidy Size

capita increases substantially as we increase the size of the subsidy, though the rate of increase declines.For example, TFP increases by 8% when the subsidy is at the largest value considered. The cost of thesubsidy program is increasing with the fraction ξ. The largest cost is about 1.82%. The reason why thisprogram can have a large impact is because once new entrepreneurs learn what their productivity is,they can optimally choose to save out of the collateral constraints.

I should note that this subsidy is correcting both capital misallocation by relaxing credit constraintsfor operating entrepreneurs and supporting experimentation. However, the above exercise suggests thatcorrecting the external margin can have a relatively large impact on productivity.

Exercise 2: Impact of subsidy in different economies. To investigate the impact of the subsidyacross economies, I set the level of the subsidy to half the pre-subsidy equilibrium wage and study theimpact on productivity. I decompose the TFP loss following the scheme outlined in section 2.3.2. Figure2.14 reports the results.

The left panel in figure 2.14 is the decomposition of TFP loss under imperfect information, withoutthe subsidy. In the right panel is the decomposition with the subsidy. In the economy with perfectenforcement, the subsidy lowers TFP a small amount by bringing in extra entrepreneurs but this iscanceled by the higher number of entrepreneurs. As I lower the level of contract enforcement, TFP fallsin both economies but by much less in the economy with the subsidy. The distortion to the selectionprocess is much smaller with the subsidy.

Discussion. I present this subsidy scheme to highlight that supporting the discovery of entrepreneurialtalent can have a large impact on productivity. In economies with weak contract enforcement, thisscheme can be very helpful because once the quality of the idea has been discovered, households cansave their way out of credit constraints. A subsidy scheme based on the firm’s age might also be harderfor entrepreneurs to game than a size-dependent subsidy. Furthermore, as the program does not targetparticular firms, it might not be subject to the capture as identified in Buera et al. [2012].



0.2 0.4 0.6 0.8 1

Nor

mal

ized

TF

P

0.75

0.8

0.85

0.9

0.95

1

Without subsidy

Total effect

Allocate capital

Reveal type

Reallocate talent



0.2 0.4 0.6 0.8 1

0.75

0.8

0.85

0.9

0.95

1

With subsidy (ξ = 0.5 × W0)

Total effect

Allocate capital

Reveal type

Reallocate talent


Figure 2.14: Decomposing TFP Gains from Subsidy

2.4 Conclusion

In this paper, I investigate the impact of financial frictions arising from weak contract enforcement onaggregate productivity. I highlight an important determinant of productivity, the discovery of productiveentrepreneurs, and show that weak contract enforcement distorts this discovery process. The impact offinancial frictions is significantly amplified, by up to 1.5 times.

I also find that imperfect information alone can account for potentially large TFP losses in developingcountries. Given the much larger estimates of other measures of uncertainty in developing countries, it isplausible that discovering entrepreneurial productivity takes longer in these countries as well. Disciplin-ing this hypothesis with data is a promising avenue for explaining cross-country productivity differences.


2.5 Appendix

Proof of proposition 9. I present the proof for an entrepreneur who has accessed external finance andthen defaulted (f = 1, d = 1). The proof for entrepreneurs who self-finance (f = 0) or access externalfinance but do not default (f = 1, d = 1) are similar.

The entrepreneur chooses the sequence ω(z)z∈R, the insurance payments for all realizations of thetotal productivity z. Because the insurer must break even in expectation, the sequence must satisfy:∫ ∞

−∞ω(z; k, l)F (dz|µ, j) = E

z[ω(k, l; z)|µ, j]

If the entrepreneur assigns y(z) to realization z, then their end of period resources will be:

y(z) = max 0, (1− φ)(ω(z)−Wl + (1− δ)k)

Let V E(y(z), a′, µ, j) be the post-production value function for an entrepreneur defined over theirend of period resources.

V E(y(z), a′, µ, j) = u(y(z)− a′) + β[ρV (a′, µ+1(z), j + 1) + (1− ρ)EV (a′, µ1, 1)]

It is obvious that the household will never choose y(z) ≤ a′ as that will give them zero consumption.Therefore y(z) > a′ ≥ 0. We can therefore restrict attention to allocations ω(z) that yield positive y(z).The household’s optimization problem is:

L = maxy(z)

∫z

V E(y(z), a′, µ, j)F (dz|µ, j) + λ

∫z

[E [ω(k, l; z)|µ, j]− y(z)] F (dz|µ, j)

Point-wise optimization gives:

y(z1) = y(z2), ∀z1, z2 ∈ R

So far, I have implicitly assumed that it is possible to satisfy y(z) > a′ for all z, which is equivalentto assuming:

(1− φ)[E[ω(k, l; z)|µ, j] + (1− δ)k −Wl] > a′

If the above assumption is not satisfied, the household has a non-zero probability of having zeroconsumption. Therefore, no matter the insurance allocation their expected payoff is equal to −∞. Thehousehold will never choose (a′, k, l, f, d) such that their expected payoff is −∞. Since the particularallocation in these off-equilibrium paths has no impact on the payoff (always −∞), WLOG I assumethey insure.

The only difference between the above case and the cases where the entrepreneur does not defaultor does not access finance is the components of their post-production wealth.

y(z) =

max 0, ω(z)−Wl + (1− δ)k + (1 + r)(a− k − ψ) if f = 1, d = 0

max 0, ω(z)−Wl + (1− δ)k + (1 + r)(a− k) if f = 0


Proof of proposition 10. Default is only a consideration if the lender has accessed external finance(f = 1). When deciding to default, the entrepreneur has also already chosen k, l, and a′. In proposition9, I showed that the entrepreneur will always insure themselves from the transitory shock, whether ornot they defaulted. We can then characterize the resources available to the entrepreneur based on theirdefault decision using equations (2.13) and (2.14).

yND(k; a, µ, j) = π(k;µ, j) + (1− δ)k + (1 + r)a− (1 + r)(k + ψ)

yD(k; a, µ, j) = (1− φ) [π(k;µ, j) + (1− δ)k]

Since a′ has already been chosen, by defaulting the entrepreneur can only affect his consumptionc = y − a′. The entrepreneur will therefore choose the option that gives them the highest payoff. Tomake this explicit,

i) If a′ ≤ minyND, yD

, V E(y, a′, µ, j) is increasing in y, and therefore is maximized by maximizing

income.

ii) If a′ ∈ [minyND, yD

,max

yND, yD

), then the entrepreneur should choose the option that

maximizes income (choosing the other option gives a payoff of −∞)

iii) If a′ ≥ maxyND, yD

, then either choice will give a payoff of −∞. WLOG, the household should

choose the one that gives higher income.

The above breakdown shows that no matter the choice of a′, the household’s default decision maxi-mizes expected income. Therefore the household cannot adjust a′ to reduce their incentive to default.

Proof of lemma 14. The results follow immediately from inspecting the incentive compatibility con-straint.

For the upper bound k(a, µ, j),

(1 + r)(a− ψ) = −φπ(k;µ, j) + (1 + r − φ(1− δ))k

Increasing either µ or a slackens the constraint, and k needs to increase for it to bind again.If the lower bound k(a, µ, j) = 0, then increasing assets or the expected quality µ has no effect. If

the lower bound k(a, µ, j) > 0, then increasing a or µ slackens the constraint which can be made to bindagain by lower k.

Proof of proposition 11. Lenders need to ensure that the IC constraint is satisfied:

LHS = (1 + r)(a− ψ) ≥ −φπ(k;µ, j) + (1 + r − φ(1− δ))k = RHS

If a ≥ ψ, then LHS ≥ 0, whereas the RHS = 0 at k = 0, for all values of µ. Therefore, whenentrepreneurs can afford to pay the access cost up front, the IC constraint is satisfied for at least smallloans and entrepreneurs can access credit.


If a < ψ, then the LHS < 0. The RHS has an unique minimum, therefore the IC constraint issatisfied for some values of k given µ if it is satisfied the minimum of the RHS. Define:

ˆπ (µ, j) = min −φπ (k;µ, j) + (1 + r − φ(1− δ)k)

The function ˆπ is strictly increasing in µ, and approaches −∞ (∞) as µ approaches −∞ (∞).Therefore, there exists some value of µ at which (1 + r)(a− ψ) = ˆπ (µ, j).

Proof of lemma 15. An entrepreneur with state variables (a, µ, j) has access to credit if there is someloan k for which the incentive-compatibility constraint is satisfied:

(1 + r)a ≥ −φ[π(k;µ, j)− 1 + r − φ(1− δ)

φk

]The left-hand side is non-negative because a ≥ 0. On the right-hand side, we can replace π(k;µ, j)

by equation (2.12), minimize with respect k to find that the right-hand side is always negative as longas exp

µ+

σ2j+σ2

e

2

> 0.

Proof of proposition 14. This proposition follows closely from proposition 11.

Proof of proposition 15. With perfect information, implementing the project has no affect on beliefs.Since occupational choice can be adjusted every period without cost, the optimal thing to do is to choosethe occupation that maximizes income. Therefore, the household chooses to be an entrepreneur (worker)if it yields the higher income.

Proof of proposition 16. The transitory shocks affect households in two ways: First, they affecthousehold’s beliefs about their productivity. Second, they determine total productivity z and thereforeoutput.

If σ2s = 0, then the initial signal perfectly reveals the idea’s quality x (i.e. µ1 = x and σ2

1 = 0).Future transitory shocks have no effects on beliefs. Since households always find it optimal to insuretheir output, and therefore transitory shocks have no effects.

E (exp z|x) = expx+

σ2e

2

Now consider two economies, same in every way except the variance of the transitory shocks and the

mean of idea’s quality. In one economy, these take the values(µ = − σ

2

2 , σ2)and in the other economy

these take the values(µ = − σ

2

2 , σ2). Consider entrepreneurs with idea quality ν standard deviations

away from the mean in the two economies. I show that their expected total productivity are the same.

E (exp z |x) = expµ+ νσx +

σ2

2

= exp νσx = exp

µ+ νσx +

σ2

2

= E (exp z |x)

It follows agents’ decisions and aggregates are exactly the same in both economies.


2.5.1 Modified Environment Where Wealth Smoothing is Optimal

I present an environment in which entrepreneurs will find it optimal to insure themselves against thetransitory shocks. In particular, I show that they will choose an insurance scheme that gives them thesame wealth for all realizations of z. This result is obtained because entrepreneurs create a plan for howto divide their expected wealth between consumption and savings for the next period prior to seeingtheir realized productivity z this period, and after observing z cannot profitably deviate from this plan.Therefore the decision to insure reduces to a decision regarding how to best allocate consumption todayacross possible states.

Remark. If agents were allowed to choose assets for the next period after observing z, then theywould choose to redistribute more than (less than) the expected value to low- (high-) realization states.The reason is that low realizations of z mean both less income today and less expected income in thefuture. Therefore, additional funds in these states are especially valuable. A separate issue is that thecontinuation value V is locally convex in assets at points where VW and V E intersect. The environmentpresented below overcomes these issues.

Figures 2.15 and 2.16 present the timelines for an entrepreneur and a worker, respectively. In thesefigures, the bold elements are decisions and events from the timeline presented in the main model, whilethe other elements are there to support the insurance mechanism.

1

2

3

4

5

6

7

8

9

10

11

choose deposits,

capital (k),access (f)

shopperbuys a’

fromretailerfor i(s)

choose insurance

plan

chooseoccupation

(W/E)

insurancepays out.labor paid

consume

choose l,choose

D/ND

producer sells a’

to retailerfor i(p)

z realized.production

plan(c, a’)

clearbalance

with retailer

shopper/producerseparate

shopper/producer

meet

Figure 2.15: Timeline for Entrepreneurs


1

2

3 5

6

7

8

9

10

11

shopperbuys a’

fromretailerfor i(s)

producer sells a’

to retailerfor i(p)

4

shopper/producer

meets

chooseoccupation

(W/E)

plan(c, a’)

choose deposits

paid wage

clearbalance

withretailer

consume

shopper/producerseparate

Figure 2.16: Timeline for Workers

Let me now discuss the new elements in the environment.

Shoppers and Producers. Each household is composed of two members: a shopper and a producer.The black elements are dealt with by the whole household, the blue are dealt with by producers only,and the red are dealt with by shoppers only. At the beginning of the period, the two members jointlychoose the occupation, plan how much to save and to consume, and then go to two separate islands.The producer takes all the assets with him, as his island contains all the financial institutions. The twomembers reunite at the end of the period right before consumption takes place.

Insurers. A competitive insurance market opens after producers have chosen inputs and whether todefault, but before the realization of total productivity z. The insurers are owned by households, haveno operating costs, and can observe the producers’ state variables related to beliefs about productivity(µ, j), the input choices (k, l), and the actual realization of z. They sell contracts that allow each pro-ducer to transfer wealth across states (realizations of z) as they wish, conditional on the insurer breakingeven.

Retailers. I assume that the consumption good produced by firms cannot be carried over as-is intothe next period without completely spoiling. However, a technology exists that can convert units ofthe consumption good into units of a one-period storeable good. The conversion rate is 1-to-1. This


technology is operated by a continuum of competitive firms, whom I call retailers, and they are ownedby the households. In particular, the conversion technology is:

ga(a) = a

Retailers have rational expectations about demand for storeable goods. They first go to the producers’island to buy the appropriate quantity of the consumption good, and transforms it into the one periodstorable good. Then, they go to the shoppers’ island and sell the storeable good to shoppers.

The retailers’ transactions with the shoppers and producers is based on short-term credit, as in eachtransaction there is one party that has nothing immediately at hand to give to the counterparty. Theretailer issues to a producer who sells a′ units of a the consumption good ip(a′) = a′ > 0 units of credits.The producers can use these credits to cover purchases of the storable good from the retailer, within theperiod. Since shoppers have no funds at hand, they purchase the saving good a′ on credit is(a′) = a′ < 0.When the two members of the household reunite, they clear their balance with the retailer by sendingthe IOU’s issued to the producer.

Issued credit expires at the beginning of the next period, and therefore excess amounts cannot beused for intertemporal saving. If the household cannot clear the balance by the end of the period, theretailers seize all their consumption.

Solution to the Worker’s Problem

Let me solve the worker’s problem first, since it is simpler and will help clarify the environment. Afterchoosing the occupation (working), the two members jointly plan for the period. As a worker household,their income ((1 + r)a+W ) is known, and they learn nothing new in this period. Since their income isfixed, there is no insurance problem to solve. However, they must still plan how much of the storablegood the shopper must acquire on her island and how much credit (ip) the producer must acquire onhis island, so that the balance clears at the end of the period. The optimal choice of a′ is given bymaximizing the worker’s problem (WP):

VW (a, µ, j) = maxc,a′

u(c) + β

[ρV (a′, µ, j) + (1− ρ) E

x,sV (a′, µ1(s), 1)

]s.t. c+ a′ ≤ (1 + r)a+W

Neither party has any incentive to deviate from this plan. If one party did deviate and as a resultthe household ended up with excess credit (is + ip > 0), then these would be useless and the householdwould be strictly worse off. On the other hand, if a deviation resulted in having not enough credit tocancel out the shopper’s obligations (ip + is < 0), then they would default on the retailer and lose allconsumption in the period and get V = −∞.

Solution to the Entrepreneur’s Problem

Relative to the timeline presented in the main model, the only new components are that the entrepreneurfinds it optimal to stick to a savings plan chosen prior to realizing z and that they choose to smoothwealth across states. I therefore focus on proving these two parts. I will begin by solving the insurance


problem. At the point where the producer must choose the insurance contract, she has already chosenthe asset for next period a′, financing and capital (f , k), labor (l), and whether to default (d). Take anyvalues for these choices.

Let’s define a couple of useful objects. First, to evaluate the value of wealth, let V (y, µ, j) be thevalue function defined over wealth y, right before consumption takes place. Let ω(z; k, l) = ezkαlθ bethe output generated by a firm with realized productivity z employing capital k and labor l. Finally, letFz(z|µ, j) be the prior distribution of z for an agent whose expected ability is µ and who has observedj signals.

The expected output of this agent is:

Eω(k, l, µ, j) = E (ω(z; k, l)|µ, j) =

∫ ∞−∞

ω(z; k, l)Fz(dz|µ, j)

Let ω(z; k, l)z∈R be an allocation of insurance payments across states.35 Then the break evencondition (BE) is:

Eω(k, l, µ, j) =

∫ ∞−∞

ω(z; k, l)F (dz|µ, j) (BE)

The components of the entrepreneur’s end of period wealth depends on whether they accessed externalfinancing (f ∈ 0, 1) and if they did access external finance, whether they defaulted (d ∈ 0, 1).I will only present in detail the derivation of the optimal insurance contract for the case where theentrepreneur has accessed external credit and then defaulted. The solution for the other two possiblecases are analogous.

Agent has defaulted. If the agent chooses insurance payment ω(z, ·) when total productivity isz, then the resulting wealth is:

y(z; k, l, a) = max 0, (1− φ) [ω(z, k, l) + (1− δ)k −Wl]

The minimum value is zero because entrepreneurs have limited liability. Agents will never want tohave zero consumption, and therefore any allocation of wealth across states must satisfy:

(1− φ) [ω(z, k, l) + (1− δ)k −Wl] > a′ ≥ 0

The agent’s problem then is to choose the optimal allocation of wealth y(z)z∈R across realizationsof z. This is:

maxy(z)z∈R

∫ ∞−∞

V (y(z), µ′(z), j + 1)F (dz|µ, j)

s.t. (BE) and

y(z) > a′ (non-zero consumption)

Ignoring the non-zero consumption constraint for now, the Lagrangian and the first order conditions35The no-insurance allocation sets ω(z; ·) = ω(z, ·) for all values of z ∈ R.


from point-wise optimization is:

L = maxy(z)z∈R,λ

∫ ∞−∞

V (y(z), µ′(z), j + 1)F (dz|µ, j)

+λ

[[Eω(k, l, µ, j) + (1− δ)k −Wl]−

∫ ∞−∞

y(z, k, l)F (dz|µ, j)]

dV

dy

Envelope=

1

(y(z)− a′)γ= λ, ∀z ∈ R

Equating first-order conditions across states, we find that the optimal wealth choice is the samefor every realization of z. The insurer’s break even condition implies that the expected wealth is thesolution.

yD(k, l;µ, j) = (1− φ) [Eω(k, l;µ, j) + (1− δ)k −Wl]

We can verify that the non-negative consumption constraint is satisfied as long as a′ < (1 −φ) [Eω(k, l;µ, j) + (1− δ)k −Wl]. This restriction is without loss of generality, as households will neverchoose a′ above their expected income. 36

No default. If the agent did not default and chose insurance scheme ω(z, ·)z∈R, then their realizedwealth is:

y(z; k, l, a) = max 0, ω(z, k, l)−Wl + (1− δ)k + (1 + r)a− (1 + r)(k + ψ)

The optimal insurance scheme assigns the expected wealth to each state.

yND(k, l, µ, j) = Eω(k, l;µ, j) + (1− δ)k + (1 + r)a−Wl − (1 + r)(k + ψ)

Default decision based on expected incomes. The entrepreneur optimally defaults if:

Ez

(V (yD(k, l;µ, j), µ, j)

)> E

z

(V (yND(k, l;µ, j), µ, j)

)After some expanding and rearranging terms, we can rewrite the problem as:

∫ ∞−∞

[V (yD(k, l;µ, j), µ′(z), j + 1)− V (yND(k, l, µ, j), µ′(z), j + 1)]F (dz|µ, j) > 0

For all values of µ′(z), the value function defined over wealth is strictly increasing in wealth. There-fore, the above holds true iff yD(k, l, µ, j) > yND(k, l, µ, j).

We can solve for the producer’s other decisions (f, k, l) exactly as in the main model. Although the

36Precisely, if they did choose such an a′ greater than their expected income, they will face a non-zero probability ofzero consumption


producer learns new information z which changes the value of carrying over assets to the next period, hehas no way to coordinate an adjustment to the plan with the shopper. Knowing that the shopper willstick to the plan, the producer knows that bringing back excess credit will be useless and bringing backless than the planned amount will lead to zero consumption. Therefore, they find it optimal to stick tothe plan.

The optimal choice of a′ is given by:

V E(a, µ, j) = maxc,a′

u(c) + β

(ρEz

(V (a′, µ′(z), j + 1)|µ, j) + (1− ρ) Ex,s

(V (a′, µ′1(s), 1))

)s.t. c+ a′ ≤ yE(a, µ, j)

This is exactly the same problem solved in the main model, under the assumption that agents insureagainst the transitory shock and assets are chosen prior to observing z.

Chapter 3

Contracting Frictions with Managers,Financial Frictions, and Misallocation

3.1 Introduction

Cross-country income differences are largely explained by differences in total factor productivity (TFP)[Caselli, 2005]. A recent literature argues that lower TFP in poor countries can be accounted for by severeresource misallocation, one potential cause being financial constraints on firms. A common feature ofthis literature is that financial frictions, often modelled as collateral constraints à la Buera et al. [2011b]and Moll [2014a], mainly constrain small firms, while large firms can self-finance to mitigate the effects.This is inconsistent with firm-level data from developing countries suggesting that large firms potentiallyface more severe distortions.1 In this paper, we propose that contracting frictions between firms andoutside managers cause significant misallocation by distorting the delegation decisions of large firms.We document evidence consistent with the idea that large firms are particularly distorted, and thatcontracting frictions with outside managers are particularly worse in developing countries. We thendevelop a model with both financial and managerial frictions, and quantitatively show how managerialfrictions are important for both generating large productivity losses and for matching the documentedrelationship between firm size and marginal productivity.

Hsieh and Olken [2014] documents that larger firms have higher marginal product of capital. In ourempirical work, we provide additional data to support this finding. We first decompose the dispersionof marginal product of capital (MPK) into the dispersion of the capital labor ratio and the dispersionof marginal product of labor (MPL). The dispersion in MPK indicates frictions in the capital market,while the dispersion in MPL indicates some other frictions as financial frictions do not distort the choiceof labor.

We propose that higher marginal product of labor of larger firms can be explained by contractingfrictions, which results wage premia for outside managers and reduced delegation. To support thisargument, we use household survey data from the Integrated Public Use Microdata Series (IPUMS) todocument two stylized facts: First, the fraction of the population working as managers increases withper capita GDP. Second, managers are paid a relatively higher wage premium (efficiency wage) in poor

1For example, Hsieh and Olken [2014] find that large firms have higher marginal products of capital and labor thansmall firms using micro data from India, Mexico, and Indonesia.

77

Chapter 3. Managerial Frictions, Financial Frictions and TFP 78

countries with weak contracting enforcement, after controlling for observed characteristics. These twostylized facts serve as evidence for our modelling of contracting frictions.

We build our model on Garicano and Rossi-Hansberg [2006], Grobovšek [2014] and Buera et al.[2011b]. In our framework, firms face endogenous collateral constraints as well as contracting frictionswith managers. Entrepreneurs can increase their span of control by adding managerial layers and fillingthem with outside managers. However, weak contract enforcement distorts these delegation decisions.In countries with weak contract enforcement, managers can steal a fraction of the firm’s output, and thefirm must ensure they do not do so by paying them extra wages. These wage premia are proportionalto the firm’s output, and therefore manifest as output wages. In addition to the wage premia, firmsalso respond by hiring fewer outside managers and scaling down their operations. Thus, our model isconsistent with our two stylized facts. Larger firms benefit more from outside managers than smallerfirms, which is why larger firms are more severely affected by the contracting friction. These larger firmsface higher output wedges which generates a positive relationship between marginal product and size,consistent with the data.

We calibrate our benchmark economy without financial frictions to U.S. data. Then we vary the levelof both frictions to study the impact on aggregate productivity. Productivity falls monotonically withboth frictions. Whereas financial frictions disproportionately affect smaller firms, managerial frictionsmainly affect large firms. TFP falls by 24% when managerial frictions completely shut down delegation.Contracting frictions have larger impacts on TFP than financial frictions because contracting frictionsdistort the larger firms who produce most of the output in the economy.

Our paper mainly contributes to the macro literature on the importance of firm management.2 Webuild on the framework of Grobovšek [2014], showing how managerial frictions can help account forobserved patterns of factor misallocation.

Our paper is also related to the recent macroeconomic literature on the firm size distribution andfirm dynamics, and their relationship to economic development.3 The closest related paper is Akcigitet al. [2017], who also argue that the lack of delegation explains why firms in poor countries have lowerproductivity and do not grow over their life cycles. Whereas their paper highlights the importance ofselection, we completely shut down this channel in our model. We instead emphasize that contractingfrictions with managers can reduce productivity by misallocating factors of production, something theyabstract from in their paper.

Our paper also contributes to the misallocation literature by building a framework to quantify theimportance of contracting frictions and lack of delegation.4 The contracting frictions with managersleads to endogenous output wedges that are positively correlated with firm productivity. Our workis also related to the literature studying the role of weak institutions as key obstacles of economicdevelopment. Weak contract enforcement is an often-cited result of weak institutions in poor countries.5

The paper proceeds as follows. Section 3.2 documents stylized facts both across firms in China andIndia and across countries. Section 3.3 describes our model. We quantify the impact of the two types offrictions in Section 3.4. Section 3.5 concludes the paper.

2See, for example, Garicano and Rossi-Hansberg [2006], Bloom and Reenen [2007], Bloom and Reenen [2010], andGrobovšek [2014], among others.

3See, for example, Haltiwanger et al. [2013b], Roys and Seshadri [2014], Hsieh and Klenow [2014b], and Akcigit et al.[2017], among others.

4For the misallocation literature, see, for example, Restuccia and Rogerson [2008], Hsieh and Klenow [2009], Bueraet al. [2011b], Moll [2014a], and Bento and Restuccia [2017], among others.

5For the literature on institutions and economic growth, see Alchian and Demsetz [1973] and Acemoglu et al. [2005]among others.


3.2 Evidence

In this section we document evidence on contracting frictions both across countries and across firms.

3.2.1 Firm-Level Evidence from China and India

A Simple Accounting Framework

We start by documenting firm-level evidence using data from the manufacturing sector of China andIndia. To guide our analysis, we consider a simple accounting framework. The profit maximizationproblem of firm i in industry j is given by

πij = τyijpiyij − τkijrkij − wlij .

πij denotes for the profit of this firm. yij , kij , and lij are the firm’s output, capital input, and labor input,respectively. pi is the price of output, which is constant for industry i. τyi,j and τ

kij are output and capital

wedges.6 We further assume that the production function is Cobb-Douglas: yij = z1−γij (kαij l

1−αij )γ . Then

the first order conditions are

αγτyijpiyijkij

= τkijr and (1− α)γτyijpiyijlij

= w. (3.1)

Define piyijkij

and piyijlij

as the revenue productivity of capital and labor (APKij and APLij). We canrewrite Equation 3.1 as

APKij ∝τkijτyij

and APLij ∝1

τyij. (3.2)

The capital-labor ratio (KOLij) of the firm can be written as

kijlij

=α

1− αw

τkijr∝ 1/τyij .

We can then show that APKij can be decomposed into APLij and the capital-labor ratio (KOLij):

APKij = APLij ·1

KOLij. (3.3)

Intuitively, equation (3.3) simply states that the average product of capital can be decomposed intotwo terms: the average product of labor which only depends on the output wedge but not the capitalwedge, and the capital-labor ratio which only depends on the capital wedge but not the output wedge.This decomposition helps us to identify the capital wedges relative to the output wedges in our firm leveldata.

Firm-Level Data from China and India

We now document stylized facts in the firm-level data of China and India, where the data cleaningprocess follows closely Hsieh and Klenow [2009]. The literature typically focuses on the differences inaverage product of capital (APK) across firms as evidence for capital misallocation. Figure 3.1 shows

6Note that it is equivalent to model the capital wedge and labor wedge without the output wedge, but we cannot haveall three wedges in this framework.


the APK across firms in the Indian data. We plot firms by their size (measured as the labor input) onthe horizontal axis and plot their APK on the vertical axis. In general, larger firms have higher APK,consistent with Hsieh and Olken [2014].

Figure 3.1: Average Product of Capital of Indian Firms

-1-.5

0.5

1Av

erag

e Pr

oduc

t of C

apita

l (Lo

g)

0 2 4 6 8Firm Size (Log Labor)

Note: The figure shows the average product of capital across firms of the Indian data in the year 1998. We control on thefirm’s age, ownership, location, and 2-digit industry and then use the residuals of APK to obtain the results in the figure.The data cleaning process is detailed in Appendix ??. The dashed lines show the 95 percent confidence interval.

In order to study why large firms have higher APK than small firms, we decompose the APK into theaverage product of labor (APL) and the capital-labor ratio (KOL) following equation (3.3). The resultsare in figure 3.2. The left panel of figure 3.2 shows the KOL across firms, where the dispersion arises fromthe capital wedges only. It is clear that there are severe capital misallocation across firms. Excludingthe very small firms, we find that larger firms have higher capital-labor ratio than smaller firms, whichis consistent with the story of collateral constraints. The right panel of figure 3.2 shows the APL acrossfirms, where the dispersion arises from the output wedges only. It is clear that larger firms have higherAPL, consistent with Hsieh and Olken [2014]. This indicates that larger firms face higher output wedgesthan smaller firms, and we need to find explanations other than financial frictions to explain why APLincreases with firm size. As we will show later, our model predicts that the contracting frictions betweenentrepreneurs and managers create output wedges that are increasing with firm size. Our model alsopredicts that APL should increases with firm size when the contract enforcement is weak, consistentwith these firm-level data.

Next, we turn to the Chinese firm-level data from 2004. The Chinese data is different from the Indiandata as the Chinese manufacturing survey only records firms whose gross output in the previous year isgreater than five million RMB (roughly 750,000 U.S. dollar in the year 2004). This criterion generatesselection effect that biases upward the estimated productivity of small firms: a small firm with only tenworkers has to be extremely productive to produce five million RMB and to be included in the survey,whereas a large firm with 100 workers can produce five million RMB and to be included in the surveyeven if it is not very productive. Therefore, we mainly discuss the pattern among large firms for theChina data.

Figure 3.3 shows the APK across firms in China. Larger firms have lower APK than smaller firms.Again this pattern depends on both capital wedges and output wedges, therefore we apply Equation(3.3) and decompose the pattern into KOL and APL across firms in Figure 3.4. If we focus only on


Figure 3.2: Decomposition of Wedges of Indian Firms-1

-.50

.51

Cap

ital-L

abor

Rat

io (L

og)


-1-.5

0.5

1Av

erag

e Pr

oduc

t of L

abor

(Log

)


Note: The left figure shows the capital-labor ratio across firms of the Indian data in the year 1998. The right figure showsthe average product of labor across firms. We control on the firm’s age, ownership, location, and 2-digit industry and thenuse the residuals to obtain the results in the figure. The data cleaning process is detailed in the appendix. The dashedlines show the 95 percent confidence interval.

Figure 3.3: Average Product of Capital of Chinese Firms

-.50

.5Av

erag

e Pr

oduc

t of C

apita

l (Lo

g)

2 4 6 8Firm Size (Log Labor)

Note: The figure shows the average product of capital across firms of the China data in the year 2004. We control on thefirm’s age, ownership (especially whether this firm is a state-owned enterprise), location, and 2-digit industry and then usethe residuals of APK to obtain the results in the figure. The data cleaning process is detailed in the appendix. The dashedlines show the 95 percent confidence interval.


large firms, we see that the KOL increases with firm size, consistent with the idea that smaller firmsface collateral constraints and have lower capital intensity. Therefore, there is also substantial capitalmisallocation in China, similar to what we find in the Indian data. The right panel of figure 3.4 showsthat the APL increases with firm size, in a pattern similar to the Indian data as well. Larger firms inChina also face higher output wedges that do not arise from capital frictions. This fact is also consistentwith our model that larger firms are constrained by an inability to delegate to outside managers andtherefore have higher output wedges.

Figure 3.4: Decomposition of Wedges of Chinese Firms

-.50

.5C

apita

l-Lab

or R

atio

(Log

)


-.50

.5Av

erag

e Pr

oduc

t of L

abor

(Log

)


Note: The left figure shows the capital-labor ratio across firms of the China data in the year 2004. The right figureshows the average product of labor across firms. We control on the firm’s age, ownership (especially whether this firm isa state-owned enterprise), location, and 2-digit industry and then use the residuals of APK to obtain the results in thefigure. The data cleaning process is detailed in the appendix. The dashed lines show the 95 percent confidence interval.

It is important to highlight the issue of selection in the China data. As is mentioned before, thecriterion for a firm to be in the survey is that its gross output of the previous year is greater than fivemillion RMB. One way to avoid the selection bias is to define firm size in gross output instead of labor.Figure 3.5 shows the same decomposition when firm size is measured by sales (which are closely relatedto gross output). We can see that both the capital-labor ratio and the labor productivity are (almost)monotonically increasing in firm size, confirming our findings in the Indian data that smaller firms facehigher capital wedges, while larger firms face higher output wedges. We further note that we do observelabor quality differences across firms: the data report the composition of workers with different educationlevels. The increasing pattern of APL is robust to controlling for these labor quality differences.

To conclude, firm-level data from both China and India suggest that large firms face substantiallyhigher output wedges, which do not arise from capital frictions. The increasing pattern of APL isconsistent with our conjecture that large firms are constrained by lack of delegation to outside managersdue to weak contract enforcement. The following section provides cross-country evidence to support ourmodelling choices regarding how lack of delegation is a problem for poor countries.

3.2.2 Cross-Country Differences in Contracting Frictions

We document two stylized facts on cross-country differences in contracting frictions. The first stylizedfact is that the fraction of individuals working as managers increases with a country’s GDP per capita.Figure 3.6 plots log GDP per capita (PPP adjusted) on the horizontal axis and the fraction of individuals


Figure 3.5: Decomposition of Wedges of Chinese Firms: Alternative Size Measure

-10

1C

apita

l-Lab

or R

atio

(Log

)

8 10 12 14Firm Size (Log Sales)

-10

1Av

erag

e Pr

oduc

t of L

abor

(Log

)

8 10 12 14Firm Size (Log Sales)

Note: The left figure shows the capital-labor ratio across firms of the China data in the year 2004. The right figureshows the average product of labor across firms. We control on the firm’s age, ownership (especially whether this firm isa state-owned enterprise), location, and 2-digit industry and then use the residuals of APK to obtain the results in thefigure. The data cleaning process is detailed in the appendix. The dashed lines show the 95 percent confidence interval.These two figures differ from Figure 3.4 since firm size is measured by sales instead of labor input.

working as managers on the vertical axis. The data is from the Integrated Public Use Microdata Series,International: Version 6.5 (IPUMS).7 Rich countries, such as the United States and Canada, havearound 10 percent of individuals working as managers. In contrast, in poor countries very few individualswork as managers. The slope is statistically significant at the one percent level. This stylized fact isconsistent with Akcigit et al. [2017], who also find that firms in poor countries tend to delegate lessfrequently and this lack of delegation explains why firms in poor countries grow slower over time [Hsiehand Klenow, 2014b].

The second stylized fact is that managers tend to earn higher income than individuals in other occu-pations, and the difference is larger in poor countries than in rich countries. In the IPUMS-Internationaldata, we observe individual’s income for only a few countries, but we do have information on individual’sconsumption, such as the number of rooms, for a large set of countries. We therefore use the number ofrooms of individuals as an approximation of income. Before we compare income among individuals ofdifferent occupations, we first run the standard Mincer regression to control for observed characteristics,such as education level, age, and gender. Given the fact that the number of rooms may be affected bythe number of people living in a same home, we further control for family size in the regression. We thenobtain the residuals from the regression and use them to calculate the income premium of managers,defined as the room number differences between managers and individuals of other occupations, for eachcountry. We then correlate this income premium of managers versus a country’s log GDP per capita.The results are shown in figure 3.7. Among the 45 countries for which we have data, poor countries ingeneral have larger manager income premia than rich countries. The slope is statistically significant atthe one percent level.

Note that we have controlled for observed heterogeneity among individuals in the Mincer regression,such as age, gender, and education, and only use the residuals to calculate this income premium ofmanagers. Therefore, higher managerial income premium in poor countries should not arise from theseobserved heterogeneity, such as education gaps between managers and individuals of other occupations.

7See section 3.6.1 in the appendix for details.


Figure 3.6: Fraction of Individuals Working as Managers

ARGARM

AUT

BLR

VEN

BRA

KHM

CAN

CHL

CUB

DOMECU

EGY

SLV

FJI

FRA

GHA

GRC

GINHTI

HUN

IND

ISRJAM

JOR

KGZ

MWIMLI

MEX

MNG

MARMOZ NGA

PAN

PER

PRT PRI

ROU

RWASEN

ESP

SDN

CHE

TZA TUR

USA

URY

VEN

ZMB

0.0

5.1

.15

Man

ager

s (P

erce

ntag

e)

7 8 9 10 11GDP per Capita, PPP (Log)

Note: The figure shows the correlation between the percentages of individuals working as managers and the country’sGDP per capita (PPP adjusted). There are 49 observations in the figure. Poor countries in general have lower portions ofindividuals working as managers. The regression coefficient is 0.026, significant at the one percent level, and R2 is 0.47.

Figure 3.7: Income Premium of Managers

ARG

ARMAUT

BLR

VEN

BRA

KHM

CHL

CUB

DOM

ECU

EGY

SLV

FJI

FRA

GHA

GRC

GIN

HTI

HUN

ISR

JAMJOR

KGZ

MWI

MLI

MEX

MNGMAR

MOZ

NGA

PAN

PER

PRTPRI

ROU

RWA

SEN ESPCHETUR USA

URY

VENZMB

-.20

.2.4

.6.8

Man

ager

Inco

me

Prem

ium

(Log

)

7 8 9 10 11GDP per Capita, PPP (Log)

Note: The figure shows the income differences between managers and individuals of other occupations versus the country’sGDP per capita (PPP adjusted). There are 45 observations in the figure. The income differences of managers are largerin poor countries. The regression coefficient is -0.078, significant at the one percent level, and R2 is 0.21.


Rather, it may reflect contracting frictions between entrepreneurs and managers, which result in efficiencywages paid to managers in poor countries. To further rule out the possibility that this income premiumis driven by the fact that human capital is scarce in poor countries, we also consider a placebo testthat calculates the income premium of doctors (physicians) across countries in the same way, sincethe occupation of doctors is human-capital intensive. The correlation coefficient between the incomepremium for doctors and a country’s GDP per capita is not statistically significant, suggesting that theincome premium for doctors is not significantly different between rich and poor countries.

To conclude, we find that poor countries have smaller portions of individuals working as managers, butthe income premium of managers are higher in poor countries than in rich countries. This is consistentwith our conjecture that weak contract enforcement in poor countries result in lacking delegation tooutside managers and higher compensation to managers (as efficiency wages). In the next section, weformally describe our model and show how our model with contracting frictions generates these twopatterns.

3.3 Model

This model builds on Grobovšek [2014] and Buera et al. [2011b]. As in Grobovšek [2014], entrepreneurscan increase their span of control by hiring outside managers, potentially employed in multiple layers. Ifcontract enforcement is not perfect, outside managers can get away with stealing a fraction of the outputthat passes through their hands, which reduces the gains from delegation. As in Buera et al. [2011b],financial frictions arise due to imperfect contract enforcement between entrepreneurs and lenders.

We make several assumptions which makes the integration of the two frameworks feasible, whilemaintaining the key features we wish to analyze. In our framework, both the distribution of wages andfirm life-cycle dynamics are endogenous, and would interact in non-trivial ways with endogenous entryinto entrepreneurship and with long-term contracting between managers and entrepreneurs. To avoidthese difficulties, we abstract from entry into entrepreneurship and restrict managers and entrepreneursto short-term contracts.

3.3.1 Households

The economy consists of two types of infinitely-lived households: worker households and entrepreneurialhouseholds.

Workers. There are a measure Nw of worker households. These households live hand-to-mouth anddo not save.8 Each of these households consist of a measure 1 of members. In each period, eachmember has one unit of time that they can supply to firms. Households pool their members’ incomesand allocate consumption across members to maximize the household’s utility. A worker household’sobjective function is:

maxct(h)h∈[0,1],t=1,...,∞

∞∑t=1

βt−1UH,t, where UH,t =

∫ 1

0

uH(ct(h))dh (3.4)

8This assumption is without loss of generality. This is an incomplete markets economy (no inter-temporal debt) wherethe equilibrium interest rate is less than 1

β− 1. Because these households face no income risk, they would choose to hold

no assets even if they could.


The households choose the sequence ct(h), which is household member h’s consumption in period t.Households face a distribution of wages with cdf Fw : R+ 7→ [0, 1], with associated pdf fw(w). Becausewe restrict our analysis to a stationary environment, the distribution Fw(w) does not change over time.

At the beginning of each period, each household sends its members to the labor market to findwork. Anticipating the labor market structure, each member draws a wage independently from the wagedistribution each period. After production takes place, the members return to their household with theirincome. The household then decides how to allocate consumption across members.

The law of large numbers tells us that the total income of the household is equal to the expected valueof wages multiplied by the number of members. The period budget constraint for a worker household is:

∫ 1

0

ct(h)dh ≤∫ 1

0

w(h)dh = Ew (3.5)

Entrepreneurs. There are a measure Ne of infinitely lived entrepreneurs. Each entrepreneur has aproduction technology that only they can operate. Entrepreneurs differ in their productivity z, whichhas a cumulative distribution Fz : R+ 7→ [0, 1] and associated pdf fz(z). An entrepreneur’s productivityhas some probability of changing each period: If in period t an entrepreneur has productivity z, then inperiod t+ 1 with probability ρ they keep the same productivity z and with probability 1− ρ they drawa new one z′ ∼ Fz.

An entrepreneur who begins the period with assets a and productivity z earns profit π(a, z) fromoperating his firm. We will describe shortly how profit π(a, z) is determined. Entrepreneurs maximizetheir expected lifetime utility subject to their period budget and borrowing constraints:

max

E∞∑t=1

βt−1 c1−γt

1− γ

subject to ct + at+1 ≤ (1 + r)at + π(at, zt)

at+1 ≥ 0, for t = 1, . . . ,∞ (3.6)

3.3.2 Production Technology

The production technology takes in labor and capital as variable inputs to produce output. There arethree distinct types of labor inputs: the entrepreneur’s, production workers’, and managerial workers’.The entrepreneur uses his one unit of time to supervise either production or managerial workers. Pro-duction workers and managerial workers need to be supervised. Managerial workers can supervise otherworkers.9

Two-layer firm. The simplest firm consists of an entrepreneur (in layer 2) supervising capital andproduction workers (in layer 1). The efficiency of the inputs in layer 1 depends on the amount of time theentrepreneur spends supervising them. If a firm employs k1 units of capital and m1 units of productionworkers, then the efficiency per unit of composite input is:

9Grobovšek [2014] considers a model with only workers, where managers use only their time to supervise. To keep thecapital-to-labor ratio across firms constant in our model with capital, we assume managers use their time and capital tosupervise the layer below them.


(1

kα1m1−α1

)θ, α, θ ∈ (0, 1) (3.7)

The parameter θ captures the idea that the entrepreneur’s marginal efficiency is decreasing in theamount of inputs he manages. The effective units of inputs are:

(1

kα1m1−α1

)θ×(kα1m

1−α1

)=(kα1m

1−α1

)1−θIf the entrepreneur has productivity z, then his total output is;

z(kα1m

1−α1

)1−θNotice that this is a standard decreasing returns to scale technology, with an entrepreneurial profit

share of θ.

Three-layer firm. The entrepreneur can increase the amount of supervision received by the produc-tion workers by adding a managerial layer and staffing it appropriately. Managerial inputs also needsupervision. Suppose the entrepreneur employs (k2,m2) units of capital and workers in the manageriallayer and (k1,m1) units of capital and labor in the production layer. The effective units of managerialinputs is:

(1

kα2m1−α2

)θ×(kα2m

1−α2

)=(kα2m

1−α2

)1−θThe effective units of managerial inputs are used to supervise the inputs in the production layer. The

effective units of production inputs is:

((kα2m

1−α2

)1−θkα1m

1−α1

)θ×(kα1m

1−α1

)=(kα2m

1−α2

)θ(1−θ) (kα1m

1−α1

)1−θThe output of this firm is:

z(kα2m

1−α2

)θ(1−θ) (kα1m

1−α1

)1−θThe entrepreneur may gain from adding the additional layer of managers because it increasing his

span of control by θ(1− θ).

L-layer firm. An entrepreneur may choose to add additional layers of managers to further increasehis span of control. Suppose a firm has L layers: the entrepreneur is at the top (Lth layer), managersare in layers 2 to L− 1, and production inputs are at the bottom layer (L = 1). This firm’s output is:

oL = z

L−1∏l=1

(kαl m

1−αl

)(1−θ)θl−1

(3.8)

3.3.3 Contracting Frictions

The economy is subject to two frictions, both arising from imperfect contract enforcement. First, man-agers can steal a fraction 1− λ of the output they manage. Second, entrepreneurs can default and run


away with a fraction 1 − φ of their operating income and depreciated capital. We describe each of ofthese frictions in detail when characterizing the firm’s problem.

3.3.4 Markets

Capital market. The capital market consists of competitive lenders who take in deposits from house-holds at the beginning of the period, promising an interest payment of r at the end of the period. Theythen loan the deposits out to entrepreneurs at the rental rate R. Because lenders earn zero profits,R = r + δ.

After production, lenders enforce the loan contracts with entrepreneurs, either collecting the specifiedpayment or recouping as much as possible if the entrepreneur defaults. At the end of the period, theypay back households their deposits with interest r. The interest rate r equates capital demand andsupply.

Labor market. The organization of the labor market follows Grobovšek [2014]. The economy poten-tially features a distribution of wages and positions, and therefore we need to consider how workers areassigned to each position. Since all workers are equally suitable for all positions, the various positionsare ordered by the wage they pay and filled sequentially.

3.3.5 Entrepreneur’s Problem and Characterization

Figure 3.8 shows the timeline of decisions and events entrepreneurs face. We will work backwardsthrough the timeline, starting from the default decision. To ease the presentation, We will characterizethe problem at each step.

Chooseconsumptionand saving

Choosenumber oflayers (L)

Production takesplace.

Workerspaid

Lenderenforcescontract

1 7

6

5

4

3

2 8

Managers decidewhether to

steal. Additionalcompensation (b)

paid

Hire workers and allocate

capitalfor layers

l = 1,...,L-1

Choosewhether

to default onlender (d)

Choosetotal

capital (k)

Figure 3.8: Entrepreneur’s Timeline


Entrepreneur’s Default Decision

Entrepreneurs can default on their lenders. A defaulting entrepreneur has full access to credit marketsin subsequent periods. Let πL(K; z) be the operating income of a firm with L-layers, K units of totalcapital, and productivity z. If an entrepreneur defaults, their lender can recoup a fraction φ of theoperating income and depreciated capital, and can seize all of the entrepreneur’s deposited assets.

Let yDL (K; a, z) and yNDL (K; a, z) be the entrepreneur’s total income if they default and do notdefault, respectively. These are:

yDL (K; a, z) =πL(z, k) + (1− δ)k − (1 + r)k + (1 + r)a

yNDL (K; a, z) =(1− φ) [πL(z, k) + (1− δ)k]

Lemma 16 states that an entrepreneur’s default decision reduces to a static income maximizationproblem.

Lemma 16 (Default decision ). An entrepreneur defaults if and only if their income from doing so isgreater than their income from not defaulting, i.e.

dL(K; a, z) =

1 if yDL (K; a, z) > yNDL (K; a, z)

0 if otherwise(3.9)

Hiring Workers and Managers

Managers can steal. After production takes place, the firm’s output moves up the layers to theentrepreneur. Each outside manager in the lth layer handles a fraction oL

mlof the total output. She can

steal a fraction 1− λ of this output. The total amount a manager at the lth layer can steal is:

(1− λ)

[oLml

]We assume that the relationships between the entrepreneur and all workers last one period, which

implies that the entrepreneur cannot use the threat of losing future employment to keep the managerfrom stealing. A manager in the lth layer receives the amount w + bl as compensation, where w is thewage paid to production workers and bl ≥ 0 captures efficiency wages. A stealing manager is detectedafter w is paid but before bl is paid. The entrepreneur imposes the maximum possible punishment onstealing managers, which is to not pay bl.

It is optimal for the manager to maximize his static income. Therefore, they will not steal if andonly if:

w + bl ≥w + (1− λ)

[oLml

]Lemma 17 characterizes the optimal excess compensation for managers in the lth layer.


Lemma 17. An entrepreneur operating a firm with L layers that produces output oL sets the excesscompensation for the outside manager in the lth layer to:

bl = (1− λ)

[oLml

]Where ml is the total number of managers employed at the lth layer.

We can now define the operating income of a firm with L layers, productivity z and rented capitalK.

Definition 7. The operating income (revenue minus labor compensation) for a firm with rented capitalK and productivity z is:

πL(K, z) = maxml,kl

z

L−1∏l=1

(kαl m

1−αl

)θl−1(1−θ) −L−1∑l=1

(w + bl)ml :

L−1∑l=1

kl ≤ K

Using the characterization of the excess compensation bl in lemma 17, we can re-write the operatingincome. Define Λ(L) ≡ 1− (1− λ) (L− 2). Then the operating income is:

πL(K, z) = maxml,kl

Λ(L)z

L−1∏l=1

(kαl m

1−αl

)θl−1(1−θ) −L−1∑l=1

wml :

L−1∑l=1

kl ≤ K

(3.10)

Optimal choices of kl and ml. Lemma 18 characterizes the optimal allocation of workers and capitalto layers as a function of total number of workers hired and capital rented.

Lemma 18 (Optimal allocation across layers.). The optimal allocation of capital and labor for a firmwith capital K and labor M solves the following output maximization problem:

yL(K,M, z) = maxkl,ml

z

L−1∏l=1

(kαl m

1−αl

)θl−1(1−θ):

L−1∑l=1

kl ≤ K,L−1∑l=1

mL ≤M

(3.11)

The optimal choices of capital and labor at each layer are:

kl = θl−1 1− θ1− θL−1

K (3.12)

ml = θl−1 1− θ1− θL−1

M (3.13)

Lemma 19 (Maximized output). The maximized output of a firm with capital K and labor M is:

yL(K,M, z) = zθ(L)(KαM1−α)ν(L) (3.14)


Where:

θ(L) ≡(

1− θ1− θL−1

)1−θL−1 (L−1∏l=1

θ(l−1)(1−θ)θl−1

)(3.15)

ν(L) ≡ 1− θL−1 (3.16)

The optimal choice of M is:

MdL(K, z) =

[zθ(L)Λ(L)Kαν(L)

((1− α)ν(L)

w

)] 11−ν(L)(1−α)

(3.17)

Lemma 20 (Operating income, redefined). The operating income of a firm with productivity z andemploying K units of capital is:

πL(z,K) = maxMΛ(L)yL(z,M,K)− wM

= maxM

Λ(L)zθ(L)

(KαM1−α)ν(L) − wM

Collateral Constraint and Borrowing Decision

Lenders anticipate the borrower’s subsequent decisions when deciding how much to lend, and ensuresthat the borrower does not default by imposing a collateral constraint. The collateral constraint isdefined in lemma 21.

Lemma 21 (Collateral constraint). The collateral constraint KL(a, z) for an entrepreneur with assetsa, productivity z and operating a firm with L-layer is the maximum amount they can borrow withoutdefaulting. It is the unique solution to the following equation.

(1 + r)a = −φπL(KL(a, z), z) +

((1 + r)− φ(1− δ)

φ

)KL(a, z) (3.18)

Lemma 22. The optimal capital choice (KdL(a, z)) for an L-layered firm solves:

πL(a, z) = maxK

πL(z,K)− (r + δ)K : subject to K ≤ KL(a, z)

(3.19)

Optimal Number of Layers

The fraction 1− Λ(L) = (1− λ)(L− 2) is the fraction of the output that the entrepreneur has to handover to managers as excess compensation. Define L(λ) as follows:

L(λ) = 2 +1

1− λ(3.20)


If a firm has more layers than L, then they will earn negative profits. Therefore, they will choosefewer layers than L(λ).

For example, if λ = 0 and managers can steal everything, then L = 3. If a firm hires up to threelayers, they will have to give all their output to their managers. Therefore, firms will choose to employtwo layers, i.e. operate without outside managers.

Lemma 23 defines the layer choice problem for a firm with assets a and productivity z.

Lemma 23 (Optimal layers and profit maximization). An entrepreneur with productivity z and assetsa chooses the number of layers to maximize profit:

π(a, z) = maxL<L(λ)

πL(a, z) (3.21)

Let L∗(a, z) be the solution to the above optimization problem.10 The associated capital and la-bor demand for this entrepreneur are Kd(a, z) = Kd

L∗(a,z)(a, z) and Md(a, z) = MdL∗(a,z)(a, z), where

KdL∗(a,z)(a, z) and Md

L∗(a,z)(a, z) are the optimal capital and labor choices as determined by lemmas 22and 20 respectively.

3.3.6 Recursive Formulation

We can now write the entrepreneur’s consumption-saving problem in recursive form:

V (a, z) = maxa′≥0

c1−γ

1− γ+ β

[ρV (a′, z) + (1− ρ)E

z′V (a′, z′)

]: c+ a′ ≤ (1 + r)a+ π(a, z)

(3.22)

On the right-hand side, the term V (a′, z) captures the value of having a′ assets when the entrepreneurkeeps their current productivity z. The term E

z′V (a′, z′) captures the expected value of having a′ assets

when the entrepreneur’s productivity changes.

3.3.7 Aggregation and Stationary Equilibrium

Let G(a, z) be the stationary distribution of entrepreneurial households over assets and productivity.Aggregate capital supply is the combined savings of the two types of households:

Ks = Ne

∫a,z

aG(da, dz) (3.23)

Aggregate capital demand, labor demand, and labor supply are:

Kd = Ne

∫a,z

Kd(a, z)G(da, dz) (3.24)

Md = Ne

∫a,z

Md(a, z)G(da, dz) (3.25)

Ms = Nw (3.26)

I now define the stationary equilibrium:10Note: I have not been able to show that there is an unique solution, though in practice there has always been an

unique solution. If there are multiple solutions, I take the smaller one.


Definition 8 (Stationary Equilibrium). A stationary equilibrium for this economy consists of prices r,w, and R, entrepreneurial household’s savings policy functions a′(a, z), optimal input and layer choicesKd(a, z), Md(a, z) and L∗(a, z), lender’s optimal collateral constraints KL(a, z), and a stationary dis-tribution G(a, z) over assets and productivity that satisfy the following conditions:

i) Given prices and collateral constraints, Kd(a, z), Md(a, z) and L∗(a, z) solves the firm’s problem.

ii) Given prices, a′(a, z) solves the entrepreneurial household’s saving-consumption problem.

iii) The interest rate r clears the capital market: Ks = Kd.

iv) The wage w clears the labor market: Ms =Md.

v) Lenders break even: R = r + δ

vi) The joint distribution of assets and productivity is stationary:

G(a, z) =ρ

∫(a,z)|z≤z,a′(a,z)≤a

G(da, dz)

+ (1− ρ)fz(z)

∫(a,z)|,a′(a,z)≤a

G(da, dz)

3.3.8 Model Properties

We now highlight some properties of the model relevant to our analysis.

Proposition 17. The optimal number of layers L∗(a, z) is increasing in entrepreneurial productivity(z) and assets (a).

The optimal number of layers is increasing in the firm’s productivity because firm productivity z

and effective units of inputs are complements. Therefore, a more productive firm gains more than a lessproductive firm from increasing the number of layers.

Lemma 24, which follows closely from proposition 17, shows that the support of the productivitydistribution can be partitioned into intervals within which all firms choose the same number of layers.

Lemma 24. There exists an increasing sequence of threshold productivities z(L) such that for z ∈[z(L), z(L+ 1)), the optimal number of layers L∗(z) is L.

Proposition 18. In the economy without financial frictions (φ = 1), capital and labor demand arestrictly increasing in the firm’s productivity z.

Lemma 25 (Constant MPK and MPL). In an economy without frictions (φ = λ = 1), the marginalproduct of capital and marginal product of labor are constant.

Economies with Contracting Frictions with Managers (λ < 1)

The contracting friction with outside managers disproportionately affects more productive firms. First,they are forced to reduce the number of layers in their organizational structure. Second, if they continueto hire outside managers, they must adjust their scale downward. Lemma 26 shows that this manifestsas a higher marginal product of capital.


Lemma 26. In an economy with λ ∈ (0, 1) where some firms still hire outside managers, the marginalproduct of capital is increasing in firm productivity z.

MPK(z) = αo(z)

k(z)= R

1

Λ(L∗(z))

Lemma 27 characterizes the wage premia earned by managers, as a function of the layer they areemployed in and their employer’s productivity z.

Lemma 27. The wage premium earned by an outside manager working at the lth layer at a firm withproductivity z is:

b(l, z) =1− λθl

[1

Λ(L∗(z))

(W

(1− θ)

)] 1ν(L∗(z))

The wage premium is increasing in the layer the manager works at (l) and the firm’s productivity z.

The wage premium is increasing with the manager’s layer not because higher-level managers are moreproductive, but because there are fewer of them. Since more output passes through each manager’s hands,they need to be compensated more to prevent stealing. The higher productivity of the firm increasesthe wage premium only if the firm employs more layers. Although a higher productivity also directlyincreases output, it also increases the number of managers at each level and these effects cancel out.

3.4 Preliminary Quantitative Analysis

We calibrate the stationary equilibrium of our model with perfect contract enforcement between en-trepreneurs and lenders (φ = 1) and imperfect contract enforcement between entrepreneurs and outsidemanagers (λ < 1) to moments from US data. We then study how worsening both types of contractenforcement affects aggregate productivity.

3.4.1 Calibration Strategy

We assume that entrepreneurial productivity z follows a log-Normal distribution with a mean of zero anda variance of σ2. The full set of parameters in our model is:

β, γ, δ, ρ, α, θ, λ, σ2, Ne, Nw

. In calibrating

these moments, we mostly follow the approaches of Grobovšek [2014] and Buera et al. [2011b].We set the risk-aversion parameter γ to 1.5 and the depreciation rate δ to 0.06. The persistence of

productivity ρ is set to 0.89, which is taken from Buera et al. [2011b].In our model, the division of aggregate income between entrepreneurial rent and factor payments

is endogenous. If a fraction ν goes to entrepreneurs, then a fraction 1 − ν goes to both factors. Thefraction of factor payments going to capital is determined by α, which we set to 1/3.

Cagetti and Nardi [2006] document that the fraction of entrepreneurs in the US equals 7.5%. Wematch this by setting Nw and Ne to 0.925 and 0.075 respectively.

We have four parameters left to calibrate, which we summarize in table 3.1. We discipline thevariance of the productivity distribution (σ2) by targeting the fraction of workers employed by firms inthe top 10% of the size distribution. Although the log-normal distribution typically cannot match theemployment shares in the tail of the size distribution, we are able to do better because these large firmsincrease their span of control by hiring outside managers.


The parameter θ affects the gains from delegation. We discipline this parameter by targeting thefraction of workers employed as outside managers. In our model, the only reason for wage premia arecontracting frictions, which are increasing in firm size. Therefore we discipline λ by targeting the firm-size wage elasticity in the US, as documented by Troske [1999]. Finally, the discount rate β is set tomatch an equilibrium real interest rate r of 0.04.

Target Parameter Calibrated valueTop 10-percentile employment share = 0.69 σ2 0.3

Fraction of workers who are managers = 0.35 θ 0.5Firm-size wage premium = 0.026 λ 0.97

Real interest rate = 0.04 β 0.92

Table 3.1: Calibrated Parameters

3.4.2 Contracting Frictions and Aggregate Productivity

In our first quantitative exercise, we investigate the effect of increasing the fraction that outside managerscan steal (i.e. reducing λ), while maintaining the assumption of no financial frictions (i.e. φ = 1). Figure3.9 presents the impact on aggregate productivity.

Fraction managers can steal (λ)0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

TF

P

0.75

0.8

0.85

0.9

0.95

1

Figure 3.9: TFP and Contracting Frictions with Managers

In figure 3.9, we normalize TFP by the level in the frictionless economy.11 Aggregate productivityfalls monotonically to 76% as the contracting friction with managers worsen. When the friction getssufficiently worse, entrepreneurs stop hiring outside managers.

11TFP equals 1 when λ = 1.


Figure 3.10 shows how the fraction of workers employed as outside managers changes as the con-tracting friction worsens. Entrepreneurs respond to the contracting frictions by hiring fewer outsidemanagers.

Contracting friction with outside manager (λ)0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Fra

ctio

n o

f w

ork

ers

em

plo

yed

as o

uts

ide

ma

na

ge

rs

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Figure 3.10: Fraction Employed as Outside Managers

We next study the impact of financial frictions (figure 3.11), by varying the fraction φ lenders canrecoup from defaulting entrepreneurs. We do this both for an economy without contracting frictionsbetween entrepreneurs and managers (blue line), and severe contracting frictions between entrepreneursand managers (red line). We again normalize productivity by that obtained in the frictionless economy.

Productivity falls monotonically as financial frictions worsen, but the total fall is about 5%. Theproductivity drop is at the low end of those reported in the literature because we have shut downoccupational choice. Distorted selection is often the main driver of productivity losses from financialfrictions (as in Buera et al. [2011b]).12

Figure 3.11 suggests that there is little interaction between the two frictions. It is interesting to notethat in the economy with severe managerial frictions, the impact of financial frictions is smaller. This isbecause managerial frictions, by effectively compressing the underlying distribution of firm productivity,reduce the scope for financial frictions to further lower aggregate productivity.

3.4.3 Cross-Sectional Properties

In figure 3.12, we present some preliminary analysis of how the managerial contracting friction affectsdelegation decisions and wedges. In figure 3.12, we plot the number of layers against firm productivity.Consistent with our analytical results, the number of layers is (weakly) increasing in firm productivity.

12We abstract from occupational choice both for technical reasons (see discussion in 3.3) and because our objective ismainly to asset factor misallocation across operating firms.


Financial friction (φ)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

TF

P

0.7

0.75

0.8

0.85

0.9

0.95

1

No managerial frictions (λ = 1)Managerial frictions

Figure 3.11: TFP and Financial Frictions

As we tighten contracting frictions, the number of managerial layers decline. As low-productivity firmsdo not employ outside managers in the absence of the friction, they are not affected at all as thefriction worsens. However, highly-productive firms do want to employ outside managers and thereforedisproportionately affected by worsening managerial frictions.

Next we illustrate how our model is able to generate larger distortions for larger firms. We considertwo economies: One economy has managerial frictions and the other does not.13. In the first economy,all firms equate marginal product of capital to the rental rate. In the economy with managerial frictions,large firm still find it optimal to hire outside managers. However, one way they reduce the incentive tosteal is by reducing their scale of operation which raises the marginal product of capital above the rentalrate.

3.5 Conclusion

In this paper, we propose that weak contract enforcement between firms and outside managers is animportant source of factor misallocation and productivity losses. We document that marginal productsof capital and labor are increasing in firm size and that managers in developing countries receive highercompensation. We develop a model where productive firms hire outside managers to increase theirspan of control. These firms respond to contracting frictions with managers by paying efficiency wages(which result in output wedges), and by reducing their scale of operation. Our preliminary quantitativeexercises show how this friction can lead to much larger productivity losses than financial frictions, andis consistent with the relationship between firm size and marginal products we document in the data.

13Both do not have financial frictions


Productivity (z)

Nu

mb

er

of

ma

na

ge

ria

l la

ye

rs

1

2

3

4

5

6

7

λ = 1λ = 0.9λ = 0.8

Figure 3.12: Number of Managerial Layers

Labor (vigintiles)0 2 4 6 8 10 12 14 16 18 20

MP

K -

R

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

No managerial frictions (λ = 1)Managerial frictions

Figure 3.13: Marginal Product of Capital and Firm Size


3.6 Appendix

3.6.1 Data

Firm-Level Data of India and China

The Indian data are from the Annual Survey of Industries, 2008-09. The raw data consist of roughly40,000 firms. We measure capital as the average of the fixed asset of the opening and closing balanceof the fiscal year. Labor is measured as the “full-time equivalent employment": firms report total laborhours, and we calculate the number of full-time equivalent workers by assuming that each worker worksfor 2,080 hours per year (40 hours per week times 52 weeks). Value added is calculated as the value ofgross output (sales) minus that of intermediate input plus other output or receipts.

The China data are from Annual Surveys of Industrial Production, 2004. The raw data consist ofmore than 200,000 firms in the year 2004. Capital is measured as net fixed asset. Labor is measured bythe number of employees. Value added is, however, a bit different. Usually we calculate value added asthe difference between gross output and intermediate input (production method). Alternatively, we canalso calculate it as the sum of total labor compensation, depreciation, profit, and tax (income method).Value added calculated by these two methods should be the same (accounting identity). In the Chinadata, however, they are not identical: the production method generates numbers of value added thatare around 30 percent higher than the income method. We therefore follow Brandt and Zhu [2010] anduse the income approach to calculate value added. We note that our results are similar if we use theproduction approach.

It is also important to characterize firms by ownership in China, as the state-owned enterprises(SOEs) behave differently from private firms. We define a firm as an SOE if the nation is the largestshare holder of this firm. We also define community-owned firms, private-owned firms, and foreign-owned firms accordingly. We explicitly control for the ownership in our analysis by regressing variablesof interest to dummies indicating ownership and obtaining residuals for further analysis.

Cross-Country Data

The cross-country data are from the Integrated Public Use Microdata Series, International: Version 6.5(IPUMS-International). The data include census on individual’s occupation as well as their age, gender,education, income, and some other characteristics over a large set of countries. I define an individual tobe a manager if her occupation falls into the category of managers. For example, for the United States,a person is considered as a manager if her occupation code falls in the range of 1 and 43 in the 2000 and2005 census. Then I obtain the results shown in Figure 3.6. GDP per capita is taken from the PennWorld Table (PWT) 8.0.

The information on individual’s labor income is only available for a few countries. Fortunately, wehave information on individual’s consumption, in particular the number of rooms, across a large set ofcountries. Therefore, we use the number of rooms to approximate individual’s income. Then we obtainthe results in Figure 3.7.


3.6.2 Model

Lemma 28. For any L ≥ 1, define:

rev(L; z) =

(zΛ(L)θ(L)ν(L)ν(L)

(αR

)ν(L)α(

1− αW

)ν(L)(1−α)) 1

1−ν(L)

(3.27)

There exists a threshold productivity level zR(L) such that if z ≥ zR(L) then rev(L+1; z) ≥ rev(L; z).If z ≤ zR(L), then rev(L+ 1; z) < rev(L; z). The threshold zR(L) is increasing in L (i.e. zR(L+ i) >

zR(L) for all i ≥ 1).

Lemma 29. If z ≤ zR(1), where zR(1) is as defined in 28, then the function rev(L; z) defined in equation3.27 is maximized when L = 1. If z ∈ [zR(L′), zR(L′ + 1)], then the function zR(L) is maximized whenL = L′. C

Proof of proposition 17. For a given z, I will provide a finite upper bound (call it L), below whichthe optimal number of layers must lie. In other words, I will show that πL(z)

πL+i(z)≥ 1, for all i ≥ 1. The

maximized profit for an L layered firm is equal to πL(z) = (1− ν(L))× rev(L; z). Then:

πL+i(z)

πL=

[(1− ν(L+ i))

(1− ν(L))

] [rev(L+ i; z)

rev(L; z)

]

The ratio 1−ν(L+i)1−ν(L) is always less than 1. Lemma 29 tells us how to find the number of layers that

maximizes rev(L; z), call that number of layers L. Lemma 29 also tells us that L is unique. For i ≥ 1, itfollows that rev(L+ i; z) < rev(L; z). Therefore, L is an upper bound on the profit maximizing numberof layers.

Proof of proposition 18. The optimal number of production workers for an L-layered firm with pro-ductivity z is:

m0(L, z) =

[zθ(L)

(αR

)α(γ(1− θ)W

)1−α] 1

αUC (L)

We wish to show that m0(z) = m0(L∗(z), z) > m0(L∗(z′), z′) = m0(z) for all z′ > z. Holding thenumber of layers constant, simple differentiation with respect to z shows that the number of productionworkers is increasing in z. Proposition 17 shows that the optimal number of layers is increasing in z.

Consider the productivity level z(L) define in lemma 24, which is indifferent between layers L andL+ 1 (i.e. πL+1(z(L)) = πL(z(L))). The ratio of optimal choice of production workers is:

m0(L+ 1; z)

m0(L; z)=

αUCLαUCL+1

> 1

Therefore, the number of production workers discretely jump at the thresholds z(L), and then increasemonotonically in the interval [z(L), z(L+ 1)).


Proof of lemma 26. A simple calculation leads to the result:

MPK(z) = αo(z)

k(z)

= α

[zθ(L∗(z))λ(L∗(z))α+γ(1−θL

∗(z))(αR

)α (γ(1−θ)W

)γ(1−θL∗(z))

] 1

αUC (L∗(z))

[zθ(L∗(z))λ(L∗(z))

(αR

)1−γ(1−θL∗(z))(γ(1−θ)W

)γ(1−θL∗(z))] 1

αUC (L∗(z))

=R

λ(L∗(z))

Since the optimal number of layers L∗(z) is weakly increasing in z, so is the marginal product ofcapital.

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