Informality and International Business Cycles ∗

Carlos A. Yepez†

May 30, 2019

Abstract

We examine the role of informal production in the international trans-mission of shocks. Our novel contribution is to show that informal produc-tion has an important impact on the observed cyclical properties of con-sumption, employment, and trade, which is effected through expenditureswitching and labor re-allocation in response to productivity shocks. Assuch, the presence of an informal sector helps rationalize distinct empiri-cal regularities that differentiate emerging from advanced economies. Ourquantitative results highlight key structural aspects of the informal sectorthat are informative for the conduct of stabilization and labor market policyin emerging economies. The model is quantitatively assessed for the case ofMexico vis-a-vis the U.S.

Keywords: International Finance, Business Cycles, Open Economy, Informality,Emerging Market Economies.

JEL codes: E21, E24, E32, F40, F41, F44, J21, O11

∗The author thanks anonymous referees for detailed and constructive comments, as well as seminar par-

ticipants at the World Congress of the International Economics Association (IEA), the Asian Meeting of the

Econometrics Society (AMES), the annual conference of the Canadian Economics Association (CEA), and the

International Symposium in Computational Economics and Finance (ISCEF) for helpful discussions, comments,

and suggestions. Financial support from UM/SSHRC Explore Grant Project #49673 is gratefully acknowledged.†Department of Economics. University of Manitoba. 501 Fletcher Argue Bldg., Winnipeg, MB. R3T 5V5.

E-mail: carlos.yepez@umanitoba.ca

1 Introduction

The informal economy is a widespread phenomenon in most low- and middle-income countries. The informal economy is defined as “unreported income from theproduction of legal goods and services, either from monetary or barter transactions;hence all economic activities that would generally be taxable were reported to thetax authorities” (Schneider and Enste, 2000). The informal sector is characterizedby economic activity with low levels of productivity, low barriers to entry, whichis largely not-taxed and unregulated (e.g., street vendors, roadside market stalls,and other unregulated forms self-employment). In contrast, firms in the formalsector are more productive, have specific demands for the skills of their workers,are regulated, and pay taxes.

Informality is particularly problematic in low- and middle-income economiesthat usually grapple with large informal sectors. Over the last 30 years, a sizablenumber of rapidly growing middle-income economies, henceforth Emerging Mar-ket Economies (EMEs), have become significant contributors to global trade andfinancial markets. EMEs greater dependence on trade and financial integrationhas increased these economies exposure to international macroeconomic risk asfrequently observed by the large swings in capital flows.

In this study, we conjecture that EMEs have an unobserved margin for thediversification of risk, namely informal production. Our aim is to explore theimplications of informality from an open economy perspective. From a domesticperspective, there is evidence that informality works as an insurance mechanismagainst idiosyncrastic labor risk. For instance, Fernandez and Meza (2015) useself-employment as a proxy for informality and find evidence of counter-cyclicalinformal employment in Mexico. Puzzlingly, when measuring risk using an interna-tional lens, we find evidence of a lower scope for insurance against macroeconomicrisk in EMEs. This observation has been documented in Bai and Zhang (2012),who report that financial liberalization during the 80s is associated with an ac-tual decrease (rather than increase) of risk sharing in EMEs; and Yepez (2017)who provides novel evidence that EMEs exhibit a significantly lower degree ofinternational risk sharing compared to advanced economies.

We develop a model that extends the informal production mechanism of Restrepo-Echavarria (2014) to a two-country framework where one country is an emergingeconomy and the other an advanced one. In each country there are two goods,formal (tradable) and informal (non-tradable). Both goods are traded in the do-mestic market, but informal goods are imperfectly measured. Further, we assumethat hiring and firing costs are more prevalent in formal labor markets, whereaswe view informal labor markets as more flexible and with low barriers to entry(Zenou, 2008; Albretch et. al, 2009; Satchi and Temple, 2009).

On the empirical side, we provide new evidence that tradable prices are the

1

main source of bilateral real exchange rate fluctuations between Mexico and theU.S., a result that is in line with the findings of Engel (1999) for the case ofadvanced economies. We interpret our evidence to be consistent with our treatmentof informal goods as non-tradable goods, and as such have a negligible impact oninternational prices.

On the theory side, we show that informal sector production has an importanteffect on quantities and a minor one on prices. This result helps us rationalizethe observed excess volatility of macroeconomic variables, the perceived lack ofinternational risk sharing, and the weak international synchronization of businesscycles observed in EMEs. Notably, our theoretical analysis suggests that actualrisk sharing in EMEs may not be as bad as it seems. That is, the perceived lack ofconsumption risk may well be a bi-product of the inherent measurement problemassociated with accounting for the informal market in the reported governmentstatistics. More importantly, our findings ring a cautionary note for the conductof stabilization and labor market policy in EMEs. When informality matters foraggregate fluctuations, policy-making informed by data that is likely to be plaguedwith measurement error is ultimately due to miss its objective.

The model works as follows. In response to a positive domestic shock to formalsector production there is a large increase in investment spending that is financedby borrowing from abroad creating a trade deficit. Consequently, labor re-allocatesfrom the informal sector to the more productive formal sector raising consumptionand income, which amplifies the expansion. On the other hand, when an expan-sion occurs abroad, the exchange rate appreciates turning domestic formal goodsrelatively more expensive; households then substitute formal goods consumptionfor cheaper informal goods at the expense of lowering formal production, but witha modest impact on measured output. Overall, the model implies that householdshave a margin to self-insure against risk via expenditure switching and labor re-allocation between sectors. Due to the fact that this behavior goes unobservedin measured statistics, the latter tend to over-state the severity of macroeconomicrisk implied by the data.

Related Literature

This study is related to four separate strands of the literature. First, is the bur-geoning body of theoretical literature that examines the role of the informal econ-omy. In particular, our research relates to the literature where the informal sec-tor operates due to the tension between tax-compliance and tax-evasion (Rauch1991, Amaral and Quintin 2006, de Paula and Sheinkman 2011, Prado 2011, LealOrdonez 2014, Orsi et al. 2014, Restrepo-Echavarria 2014). One general findingof this literature is that the size of the informal sector is positively associatedwith higher taxation and lower monitoring (punishments). This study also relates

2

to the literature that examines the effects of shocks and/or labor regulations onformal and informal labor markets ( Conesa et al. 2002, Zenou 2008, Albretchet. al 2009, Satchi and Temple 2009, Fernandez and Meza 2015, Meghir et al.2015, Hovarth 2018). This literature points to sizable labor market re-allocationin response to shocks and regulation. There is also the literature that examinesthe role of optimal government policy in the presence of an informal sector (Kore-shkova 2006, Arouba 2010). This literature finds that there is a positive relationbetween inflation and the size of the informal economy. Similarly, another litera-ture considers the implications of informality on the relationship between inflationand output (Castillo and Montoro 2012, Ait Lahcen 2018) Overall, this latter lit-erature suggests that inflation affects the composition of the labor force betweenformal and informal jobs which in turn has important implications for the shapeof the Phillips curve. Importantly, the aforementioned literature emphasizes thestudy of informality from a domestic perspective. Our contribution to this liter-ature is to examine the role of informality from an international perspective thatincorporates international trade and financial linkages into the analysis.

Second, our study is related to the international economy literature that studiesthe determinants of exchange rate movements (Engel 1993, Engel 1999, Burnsteinet al. 2006, Corsetti et al. 2012, Burnstein and Gopinath 2014). This literature islargely empirical and suggests a robust finding that tradable goods prices drive realexchange rate movements. Our study adds to this literature by providing furtherevidence of the predominance of tradable prices on real exchange rate changes forthe case of EMEs.

Third, this study adds to the literature that investigates the effects of interna-tional financial markets on the sharing of risk across countries (Backus and Smith,1993; Benigno and Thoenissen, 2008; Corsetti et al., 2008; Bai and Zhang, 2012;Corsetti et al. 2012; Yepez 2017). This literature generally assumes incompletefinancial markets, and examines the impact of the trade elasticity and the per-sistence of shocks on risk sharing. We extend this literature showing that a newmechanism, namely informal production, matters for international risk sharingeven when financial markets are complete.

Last, and more generally, our study is related to the home production literature(Benhabib et al. 1991; Canova and Ubide 1998; Karabarbounis, 2014; Chen et al.2018). In this literature, home production is a non-traded non-market good andtherefore unregulated. The crucial distinction of our study with this literature isthat our object of inquiry, informal production, is a non-tradable market good,and as such relevant for government policy.

This paper is organized as follows. Section 2 provides evidence on determinantsof real exchange rate fluctuations for the case of Mexico. Section 3 presents thetheoretical model. Section 4 presents the model calibration, examines the trans-

3

mission mechanisms, and discusses the quantitative implications of the model.Section 5 concludes.

2 Evidence on exchange rate determinants: The case of Mex-

ico

The documented evidence that movements of exchange rates are not in the direc-tion required to enhance risk sharing (Backus and Smith, 1993; Corsetti et al.,2008; Corsetti et al. 2012; Yepez 2017) begs the question about what determinesreal exchange rate movements? Engel (1999) examines this question by decom-posing the CPI-based real exchange rate (RER) across a sample of high-incomecountries into two parts: Movements in the relative price of tradable goods, andmovements in the price of non-tradable relative to tradable goods. He finds thatmovements in the relative price of tradable goods explain most of the variability inmovements of overal RERs. In this study, we provide a basic empirical assessmentof the validity of Engel (1999) finding for the case of the bilateral RER between USand Mexico, where we consider the latter country as a representative EME. To thisend, we measure the overall RER based on nominal exchange rates and CPI pricelevel data from both countries, and also construct a measure of the tradable RERusing nominal exchange rates and PPI price level data for manufactured goodsfrom both countries.1

40%

30%

20%

10%

0%

-10%

-20%

cpi-based rer (hp filtered) ppi-based rer (hp filtered)

Figure 1. Overall (CPI-based) RER vs tradable (PPI-based) RER

1See online appendix for description of data sources and statistics.

4

(1987 - 2012, HP-filtered, quarterly)

Figure 1 shows that both the overall (CPI-based) RER and the tradable (PPI-based RER) track each other closely. Similarly, Table 1 lists, for these two countriesduring the period 1987-2012 (depending on data availability), the relative standarddeviations and correlations of monthly and quarterly price data. The centralpattern that emerges is that the tradable RER between US and Mexico has roughlythe same magnitude of fluctuations as the corresponding overall RER, and thatthe correlation between the two series is close to 0.9. Importantly, our evidencefor the case of Mexico vis-a-vis US is consistent with Engel (1999) and impliesthat movements in the relative price of non-tradable to tradable goods is not animportant source of variation in RERs for the case of Mexico as a representativeEME.2

Relative to Overall CPI-based RER Stdev CorrelManufacturing PPI Annual difference 92.0% 78.0%

(monthly frequency)

Manufacturing PPI Annual difference 94.3% 85.1%

(quarterly frequency) HP-filtered 94.9% 86.1%

Table 1. Relation between bilateral US-Mexico tradable RER and OverallCPI-based RER (1987 (or higher)-2012)

Note: Monthly nominal exchange rate, CPI and PPI (1994-2011); quarterly nominal exchangerate, CPI and PPI (1987-2012).

3 Model

The model is an open economy extension of the informality model of Restrepo-Echavarria (2014). There are two countries, one is an advanced economy (AE)and the other is an emerging market economy (EME). In addition, there are twomarket sectors in the economy, namely formal and informal. Furthermore, formalgoods are tradable whereas informal goods are non-tradable. Importantly, themodel incorporates empirically-relevant heterogeneity between the two countries.Namely, compared to the AE, the EME: i) has a larger informal sector; ii) issubject to an international productivity spillover originating in the AE; and iii) ismore open to trade. Lastly, consistent with the small open economy assumptionfor the EME, there is no cross-country correlation of innovations.

2In a companion paper, Yepez (2018) examines the external validity of the relative importanceof tradable prices in real exchange rate movements. Using a representative sample of EMEs, theauthor provides further evidence for the predominance of tradable price changes in real exchangerate fluctuations of EMEs.

5

The representative household chooses whether to work in the formal sector andpay income taxes or work in the informal sector and evade taxes, but in the lattercase there is positive probability to be audited in which case there is a punishmentfor tax evasion. The government collects tax revenues from the formal sector anduses some of these resources to monitor and audit informal activity.3

Production in each country takes place in two sectors, formal (F) and informal(N). The labor market in the N-sector is fully flexible while employment in the F-sector is subject to hiring frictions. Finally, we assume that international financialmarkets are complete over the history of events st = (st, ..., s0), in order to analyzeand isolate the role of the informal sector on equilibrium outcomes.

Households

Each household in country i = EME,AE chooses sequences of formal and infor-mal consumption, and formal and informal work, and a complete set of securitiesto maximize the conditional expectation of the discounted present value of lifetimeutility:

maxCFi,t,CNi,t,NF

i,t,NMi,t ,Bi(st+1|st)∞

t=0

∞∑t=r

∑st|sr

βtπ(st|sr) 1

1− σU(C(st|sr)i,t, Li,t(s

t|sr))1−σ

subject to:Pi,tC

Fi,t + PN

i,tCNi,t +

∑Q(st+1|st)Bi(st+1|st) =

(1− τ)[Wi,tN

Fi,t + ptφP

Ni,ty

Ni,t

]+ (1− pt)PNi,tyNi,t +Bi(st|st−1) + Ti,t (1)

where π(st|sr) denotes the conditional probability, and (1) is the household’sbudget constraint that relates consumption of formal and informal goods plus netasset holdings with after-tax formal sector income, net informal sector income, andgovernment transfers.

Aggregate consumption is given by a basket of formal and informal goods

Ci,t ≡[(1− ahi)

1

εhi (CFi,t)εhi−1

εhi + a1

εhi

hi (CNi,t)εhi−1

εhi

] εhi

εhi−1

(2)

3To our knowledge, the model developed here is the first to introduce informal production intothe international business cycle model (IRBC) of Backus, Kehoe and Kydland (1994). Karabar-bounis (2014) follows a similar approach by introducing home production into the standard IRBCmodel. Most importantly, in this work informal production is different from home productionin that the former refers to a marketable activity. As such, informality is a relevant economicactivity for the conduct of government policy while home production is not. In both modelshowever, re-allocation between sectors affects aggregate variables.

6

whereCNi,t = (1− ptφτ)yNi,t (3)

In (2), εhi > 0 is the elasticity of substitution between F and N goods, and ahi > 0is the share of formal sector goods in consumption.

In (3), in country i′s consumption of the informal sector good (CNi,t) is deter-

mined by the share of informal production (yNi,t) that that effectively evades taxcompliance where τ is the income tax rate, pt is the probability for the informalfirm to be caught, and φ denotes a government penalty.

Household preferences between aggregate consumption and labor, are given by:

U(Ci,t, Li,t) = C1−aLi,t LaLi,t

where 1 > aL > 0 is the consumer’s preference weight on leisure. Last, the timeendowment is divided in 1 = NF

i,t +NFi,t + Li,t.

Formal Production

A representative wholesale goods firm produces intermediate inputs that are pack-aged and sold in competitive markets by a representative retail goods firm.

Wholesale Goods Firm

In the formal sector F , each wholesale goods firm in country i = AE,EMEmaximizes profits in a competitive market:

maxKF

i,t,NFi,tPii,tYii,t − ri,tKF

i,t −Wi,tNFi,t −

κ

2H2i,tPi,t

where Pii,t is the price of formal output, Wi,t is the nominal wage rate, H2i,t rep-

resents a quadratic net hiring cost of formal employment, and ri,t is the nominalrental rate of capital, and Pi,t is the price level.

Intermediate goods production is given by:

Yii,t = zFi,t(KFi,t)

αF (NFi,t)

1−αF (4)

Formal productivity zFi,t follows:

log zFi,t = ρFi log zFi,t−1 + ρFji log zFj,t−1 + εFi,t (5)

with s = F,N, j = AE,EME, i 6= j, |ρsi | < 1, |ρFji| < 1 is the F-sectorinternational spillover, and εFi,t ∼ i.i.d.(0, ω2

i,s).

7

Formal employment adjustment is costly due to hiring frictions, Hi,t is nethiring in F sector and κ is a hiring cost weight. The evolution of formal employmentfollows:

NFi,t = (1− θ)NF

i,t−1 +Hi,t (6)

Retail Goods Firm

Final goods producers in country i package intermediate domestic and foreigngoods using technology:

Yi,t =

[(aci)

1

εciCεci−1

εci

ii,t + (1− aci)1

εciCεci−1

εci

ji,t

] εci

εci−1

(7)

the retail good is sold at the corresponding price:

Pi,t =[aciP

(1−εci)ii,t + (1− aci)P (1−εci)

ji,t

] 1

1−εci

where εci > 0 is the trade elasticity of substitution, and aci >12

is the openness(home bias) parameter.

Informal Production

Sector N firms in country i produce informal goods in a competitive market using:

yNi,t = zNi,t(KNi,t)

αN (NNi,t)

1−αN (8)

where informal productivity zNi,t follows:

log zNi,t = ρNi log zNi,t−1 + ρFNi log zFj,t + εNi,t (9)

with s = F,N, j = AE,EME, i 6= j, |ρsi | < 1, |ρFNi | < 1 is a productivityspillover from F-sector to N-sector, and εNi,t ∼ i.i.d.(0, ω2

i,s).

Government

Government revenues are funded from taxes to formal firms and a small fraction ofaudited informal firms. Informal production is imperfectly observed so the fractionof informal firms that comply with taxes is a function of the probability that thegovernment catches a non-compliant firm:

Gi,t = τWi,tNFi,t + τpi,tφP

Ni,ty

Ni,t. (10)

8

As in Restrepo-Echavarria (2014), the probability of catching an informal firmis an increasing function of government revenues and the size of the informal sector:

pi,t = Gi,t(yNi,t)

γ, γ > 0. (11)

Tax revenues from formal production are directly rebated to consumers (Ti,t),but revenue from auditing informal firms is only used to monitor the informalsector and as such is ’wasteful’ government spending.

Competitive Equilibrium

Given prices, households and firms in each country i = AE,EME solve their op-timal allocation problems subject to the state vector st−1 = KF

i,t−1, KNi,t−1; Λi,t−1,

the technology matrix Λi,t = ΩΛi,t−1 + εt, with Ω a matrix of spillovers andΛi = [zFi,t, z

Ni,t]; and all markets clear.

Market clearing

In equilibrium, goods and factor markets clear.

• Goods markets clearing:

Yii,t = Cii,t + Cji,t,

Yi,t = Ii,t + CFi,t

• Factor markets clearing:

Ki,t = KFi,t +KN

i,t,

Ni,t = NFi,t +NN

i,t .

with j = AE,EME, Li,t is leisure in country i, and i 6= j.

Finally, capital accumulation in country i is given by:

Ki,t = Ii,t + (1− δ)Ki,t−1

9

4 Results

First, we calibrate the model for the case of Mexico vis-a-vis U.S. as representativeEME and AE, respectively. The moments are calculated using quarterly dataduring the period 1985Q1-2005Q4 from OECD national accounts data and IMFinternational financial statistics. Second, we examine the transmission mechanismsthrough impulse response analysis. Last, we discuss the quantitative implicationsof the calibrated model.

4.1 Calibration

We begin our calibration by drawing on a widely used set of open economy param-eters from Backus, Kehoe and Kydland (1994), henceforth BKK 1994, where theU.S. is a representative AE. In addition, due to the lack of cross-country estimateson sectoral productivity, we draw on the open economy calibrated parameters andestimates for the home production sector in the U.S. from Karabarbounis (2014),henceforth K 2014. Due to the lack of country-specific estimates of sectoral produc-tivity, we opt to preserve the ratio of sectoral persistence and sectoral volatility ofmarket and non-market production estimated by K 2014 for both countries. How-ever, we re-calibrate the productivity processes and domestic consumption shareparameters to match long-run statistics in the data. Namely, our target momentsare the country-specific volatility and auto-correlation of output, as well as theempirical import ratios.

Preferences and Technology

Risk aversion σ 2.00

Capital share (Formal) αF 0.36

Capital share (Informal) αN 0.08

Elasticity of substitution:

- Home and Foreign goods εc 1.50

- Formal and informal goods (AE) εhd 3.93

- Formal and informal goods (EME)* εhe 6.00

Consumption share of:

- Formal goods (AE)* ahd 0.39

- Formal goods (EME)* ahe 0.35

- Domestic goods (AE)* acd 0.94

- Domestic goods (EME)* ace 0.87

Depreciation rate δ 0.02

Discount factor β 0.99

Table 2A. Structural parameters.

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Source: BKK 1994, K 2014, *simulated.

Sectoral productivity shocks

Persistence (AE, F-sector)* ρFzd 0.570

Persistence (AE, N-sector)* ρNzd 0.500

Standard deviation (AE, F-sector)* σFzd 1.000

Standard deviation (AE, N-sector)* σNzd 1.613

Persistence (EME, F-sector)* ρFze 0.280

Persistence (EME, N-sector)* ρNze 0.246

Standard deviation (EME, F-sector)* σFze 1.700

Standard deviation (EME, N-sector)* σNze 2.742

International productivity spillover (1-way) ρzFi ,zFj 0.088

Cross-correlation sectoral innovations corr(ηF , ηN) 0.661

Table 2B. Productivity processes (benchmark specification, quarterly).

Source: BKK 1994, K 2014 *simulated.

The benchmark model calibration is summarized in Table 2. As describednext, we fix some parameters to standard values used in the literature, and thencalibrate the other parameters to match steady state ratios in the data. PanelA presents the preference and technology parameters. Following BKK 1994 therisk aversion parameter is set at σ = 2, the capital share of income in the formalsector at αF = 0.36, the elasticity of substitution between domestic and foreigngoods at εc = 1.5, the quarterly depreciation rate at δ = 2.5%, and the subjectivediscount factor at β = 0.99. Informal production tends to be more labor intensive,accordingly we set the capital share of income in the informal sector to the homeproduction estimate of K 2014 at αN = 0.08. To our knowledge, there are no cross-country estimates of the elasticity of substitution between formal and informalgoods, therefore we use the analogue between market and home goods to proxyfor this parameter. Specifically, for the U.S. we employ the estimate of K 2014 witha value of εhd = 3.93. For the case of Mexico, Cardoso-Lecourtois (2002) estimatesa higher elasticity between market to home goods than in the U.S., therefore we setthis parameter at εhe = 6.00 in Mexico, which lies between the home productionelasticity used by Chen et al. (2018) at 4, and the informality analogue used byFernandez and Meza (2015) at 8. Next, Hicks (2015) estimates expenditure shareswith potential for non-market substitution at about ten percentage points larger inMexico than in the U.S. We therefore calibrate the consumption shares of formalgoods in Mexico and the U.S. at ahd = 0.35 and ahe = 0.39, implying informal-to-formal consumption shares of 35% and 25% respectively. Last, we calibratethe consumption shares of domestic goods of Mexico at ace = 0.87 and the U.S.

11

at acd = 0.94 to match the empirical import ratios at 16% and 2% respectively,which implies that Mexico is more open to trade than the U.S.

Panel B presents the cross-sectoral productivity parameters. Consistent withthe small open economy assumption for the EME, we assume that the cross-country correlation of innovations between U.S. and Mexico is zero. Relatedly, weallow for a one-way spillover effect originating in the AE and set it to ρzFi ,zFj =0.088, in the spirit of BKK 1994. At the sectoral level, we allow for a cross-correlation of innovations between formal-and-informal sectors and set it to 0.66,which is the market-to-home cross-correlation analogue estimated by K 2014. Fi-nally, to calibrate the sectoral persistence and volatility parameters we first fixthe formal-to-informal productivity ratios to their market-to-home productivity

analogues estimated by K 2014. Specifically, we fix the relative ratios at ρFzρNz

= 0.9

and σFzσNz

= 1.6, and then set the persistence and volatility parameters to match theauto-correlation and volatility of output in each country, respectively. Our cali-brated parameters suggest higher persistence of shocks in the AE but with lowervolatility than in the EME.

4.2 Transmission Mechanisms

We now use the calibrated model to analyze the channels through which productiv-ity shocks in the formal sector are transmitted into the economy. We first considera positive productivity shock originating in the foreign (AE) country (Figure 2).Second, we examine the impact of a domestic productivity shock (Figure 3).

Figures 2 and 3 summarize the impulse responses of key (EME) macroeco-nomic variables to shocks. The variables include formal output (y EME), in-vestment (invt EME), informal consumption (c-n EME), formal consumption (c-fEME), the trade balance ratio (tby EME), informal employment (n-n EME), for-mal employment (n-f EME), and the real exchange rate (rer) defined as the relativeprice of foreign goods in terms of domestic goods.

12

10 20 30 40−0.2

−0.1

0

0.1

0.2y EME

10 20 30 40−0.2

−0.1

0

0.1

0.2invt EME

10 20 30 400

1

2

3y AE

10 20 30 40−0.05

0

0.05

0.1

0.15c_n EME

10 20 30 40−0.2

−0.15

−0.1

−0.05

0c_f EME

10 20 30 40−0.05

0

0.05

0.1

0.15tby EME

10 20 30 400

0.01

0.02

0.03

0.04n_n EME

10 20 30 40−0.03

−0.02

−0.01

0

0.01n_f EME

10 20 30 40−0.4

−0.3

−0.2

−0.1

0rer

Figure 2. Impulse responses (EME) to a foreign productivity shock

Figure 2 shows the responses to a one standard deviation foreign productivity shockthat raises formal output (y AE) by 2 percentage points on impact. As the pricelevel in the AE falls, it causes an appreciation of real exchange rate. As a resultthe trade balance in the EME improves, but households switch expenditures fromthe relatively expensive formal consumption into cheaper informal consumption.Labor re-allocates from the formal into the informal sector as the former sectorexperiences lower domestic demand. In turn, lower formal labor and higher relativeprices of formal goods lowers investment spending on impact, along with formaloutput. The negative effect on investment is short-lived as firms acquire morecapital over the next few periods to satisfy excess demand leading to a short-livedrebound in formal output. On balance, the persistence of negative wealth effectdue to sectoral re-allocation and the real appreciation dominates the transitorypositive foreign demand effect on formal production as shown in the transitionalpath of consumption, employment and output to the steady state.

Figure 3 presents the responses to a one standard deviation positive productiv-ity shock in the domestic formal economy. Formal output increases by 3 percentagepoints on impact and the price level falls causing a real depreciation. As formalsector firms ramp up production, investment spending raises by about 3 percentagepoints on impact, which is financed by borrowing from abroad as reflected by thetemporary trade deficit. At the same time, because of the productivity spillover toinformal production, lower prices of informal goods boost informal consumption

13

on impact. This effect does not last however, since formal goods are relativelycheaper for a longer period of time, and hence households substitute from infor-mal to formal consumption over time. On balance, the higher productivity of theformal sector drives the sectoral re-allocation from informal to formal employment,while the persistent depreciation ensures that expenditure switching from infor-mal to formal goods consumption persists over the medium- to long-run duringthe transitional path to the steady state.4

10 20 30 400

1

2

3

4y EME

10 20 30 40−2

0

2

4invt EME

10 20 30 40−0.4

−0.2

0

0.2

0.4y AE

10 20 30 40−0.2

−0.1

0

0.1

0.2c_n EME

10 20 30 400

0.1

0.2

0.3

0.4c_f EME

10 20 30 40−0.2

−0.1

0

0.1

0.2tby EME

10 20 30 40−0.2

−0.15

−0.1

−0.05

0n_n EME

10 20 30 400

0.1

0.2

0.3

0.4n_f EME

10 20 30 400

0.1

0.2

0.3

0.4rer

Figure 3. Impulse responses (EME) to a domestic productivity shock in theformal sector

4.3 Quantitative Analysis

We now proceed to examine the quantitative fit of the model vis-a-vis the data.For our analysis, we perform a moment matching exercise with emphasis on: i)within-country moments of employment, income, consumption, and investment;and ii) international co-movements (Table 5).5

4In the model even a relatively small response of employment and consumption can be eco-nomically important. This is because low-income countries tend to have large populations whereinformality is a predominant feature of the economy.

5The data period is 1985:Q1-2005:Q4, the data is HP-detrended at quarterly frequency witha smoothing parameter of 1, 600.

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Within-country co-movementsModel specification Data ASYM BM1 BM2 BM3 BM4ρ(NF

MEX , YMEX) 0.45 0.89 0.85 0.87 0.78 0.85ρ(NF

US, YUS) 0.63 0.85 0.86 0.86 0.86 0.87ρ(NN

MEX , YMEX)∗ -0.47 -0.48 -0.06 -0.11 -0.10 -0.47ρ(YMEX , Y−1MEX) 0.27 0.65 0.26 0.28 0.29 0.26ρ(YUS, Y−1US) 0.53 0.53 0.52 0.52 0.52 0.49

Notes: ASYM(Het. spill.), BM1(Het. Prod, IR),BM2(Het. N-sector),

BM3(εh < εf ),BM4(F-to-N spill.), * from Fernandez and Meza (2015).

Table 3. Within-country co-movements

Tables 3 and 4 summarize the data and simulated moments for five model specifi-cations, which we use to examine key elements of country-specific heterogeneity be-tween the AE and the EME. Namely, 1) ASYM in which the productivity processesare calibrated (symmetrically) to match output volatility and auto-correlation forthe case of U.S. Here, since the foreign country is assumed to be a small open econ-omy, we set the cross-correlation of innovations at zero and allow only for a 1-wayspillover effect from home to foreign. 2) In the BM1 model we re-calibrate theproductivity processes of the foreign country to match Mexico’s output volatilityand cross-correlation in the data; in addition we calibrate the shares of domesticconsumption (i.e., home bias) of each country to match the empirical import ratiosof U.S. and Mexico. 3) Specification BM2 examines the impact of increasing thesize of the informal sector in the EME. 4) BM3 allows for a higher elasticity ofsubstitution between formal and informal goods in Mexico. Finally, 5)BM4 shutsdown the cross-sectoral correlations of innovations in both countries and insteadimposes a cross-sectoral spillover effect calibrated to match the counter-cyclicalityof informal employment for the case of Mexico.

Table 3 examines co-movements of formal and informal labor with GDP. Thedata indicates that i) formal labor is more pro-cyclical in the U.S. than in Mexicoconsistent with the empirical regularity documented by Li (2011) for the case ofadvanced and emerging economies respectively; and ii) informal labor is counter-cyclical in Mexico as documented by Fernandez and Meza (2015). In terms ofthe first observation, only specifications BM3 and BM4 are consistent with it.On the other hand, specification ASYM has a close match with the counter-cyclicality of informal employment. From the other specifications, only BM4 hasa perfect fit but in this latter case is an artifact of our calibration strategy. Itis notable however, that the BM4 model does match the relative ranking of thepro-cyclicality of formal employment between the EME and the AE.

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Within-country standard deviationsModel specification Data ASYM BM1 BM2 BM3 BM4σCMEX

/σYMEX1.45 0.63 0.59 0.73 0.90 0.95

σCUS/σYUS 0.94 0.53 0.47 0.48 0.48 0.71σNF

MEX/σYMEX

0.48 0.15 0.12 0.14 0.16 0.19

σNFUS/σYUS 0.59 0.13 0.13 0.13 0.13 0.15

σIMEX/σYMEX

3.68 1.01 1.35 1.42 1.47 1.18σIUS/σYUS 2.80 1.19 1.13 1.12 1.12 1.00

Notes: ASYM(Het. spill.), BM1(Het. Prod, IR),BM2(Het. N-sector),

BM3(εh < εf ),BM4(F-to-N spill.)

Table 4. Relative standard deviations.

Table 4 presents the volatility of consumption, formal labor, and investment rel-ative to GDP volatility. In this case our data is consistent with the empiricalobservation documented by Aguiar and Gopinath (2007) that consumption andinvestment are more volatile than income in EMEs than in AEs. In addition,the relative volatility of formal employment is slightly higher in the U.S. than inMexico. All model specifications are consistent with a higher relative volatility ofconsumption in the EME, however the last three specifications imply a larger ratiobetween the EME and the AE, more in line with the data. In terms of relativeinvestment volatility, specifications BM1-BM4 are consistent with the relativeranking of this moment between EMEs and AEs, with BM3 implying the largestratio between the EME and AE similar to the data. Finally, only the BM1 spec-ifications implies a smaller relative volatility of formal employment in the EMEas in the data; nevertheless the differences for this particular moment tend to besmall for the other specifications.6

Open economy momentsModel specification Data ASYM BM1 BM2 BM3 BM4

ρ(RERMEX ,CMEX

CUS) -0.60 0.35 0.02 0.00 -0.04 -0.05

ρ(YMEX , YUS) 0.11 0.05 0.05 0.05 0.05 0.03ρ(CMEX , CUS) -0.07 -0.05 -0.01 -0.02 -0.01 -0.02ρ(IMEX , IUS) -0.02 -0.07 -0.16 -0.13 -0.12 -0.12

ρ(TBYMEX , YMEX) -0.50 -0.62 -0.80 -0.81 -0.81 -0.84ρ(TBYUS, YUS) -0.59 -0.66 -0.51 -0.50 -0.50 -0.49

Notes: ASYM(Het. spill.), BM1(Het. Prod, IR),BM2(Het. N-sector),

BM3(εh < εf ),BM4(F-to-N spill.)

Table 5. International co-movements

6We attribute the discrepancies vis-a-vis the relative volatility of formal employment to thenon-separability of preferences, as it places certain constraints on the relative responses of con-sumption and leisure (see Jaimovich and Rebelo (2009)).

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Last, Table 5 examines the model implications on international co-movements.First, the data shows a severe international risk sharing condition or Backus-Smith anomaly; that is, a strongly negative correlation between the real exchangerate and relative consumption as documented by Yepez (2017). Similarly, interna-tional output, consumption, and investment correlations are small, and negativein the case of the latter two moments; showing the lack of synchronization of busi-ness cycles between EMEs and AEs. Second, the trade balance ratio is stronglycounter-cyclical in both countries, but slightly more so in U.S. Nonetheless, allspecifications are consistent with the observed lack of business cycle synchroniza-tion in terms of international correlations of output, consumption and investment.More importantly however, models BM1-BM4 incorporate explicit heterogeneityin the EME and imply a very low scope for risk sharing. Further, only the lattertwo models BM3 and BM4 imply a negative Backus-Smith statistic as in thedata. Last, models BM1-BM4 suggest a more counter-cyclical trade balance inMexico, which is counter-factual given our data, but is more generally in line withthe empirical observation of Aguiar and Gopinath (2007) for EMEs.7

Overall, our quantitative exercise highlights two key aspects of heterogene-ity between EMEs and AEs. The first deals with plain heterogeneity betweenproductivity processes and degree of openness in both types of countries (BM1),which is a necessary condition to account for the observed lack of international risksharing and a strongly counter-cyclical trade balance in the EME. Notably, thesecond aspect relates to the relative importance of the informal sector. We findthat a larger informal sector in BM2 further reduces risk sharing while it accentu-ates the counter-cyclicality of informal employment in response to shocks. Next,higher substitutability between formal and informal goods (BM3) further low-ers risk sharing, increases the distance in terms of relative consumption volatilitybetween EMEs and AEs, and suggests a relatively less pro-cyclical formal em-ployment in the EME than in the AE in line with the data. Finally, we examinethe implications of an alternative cross-sectoral spillover effect in BM4 and findthat it marginally improves the fit with observed labor mobility patterns, relativevolatilies, and risk sharing. In sum, our theoretical results indicate that informalityplays an important role in the international transmission of shocks.

5 Conclusions

A prominent feature in the economic makeup of low- and middle-income countriesis the prevalence of large informal markets. Due to its very nature, informalactivity is plagued by measurement issues. As such, this important structural

7Aguiar and Gopinath (2007) document evidence of more counter-cyclical trade balance ratiosin EMEs than in AEs.

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feature in lower income countries is usually overlooked. Worryingly, economic andpolicy analyses in these countries may be based on potentially biased data, thusjeopardizing the achievement of any given policy objective. Although a burgeoningliterature examines the role of the informal sector in developing economies, thisliterature does so from a domestic perspective, overlooking important interactionswith global markets. In this study we bridge this gap by examining the implicationsof informal production in an international context.

Empirically, we show that tradable goods prices are the main determinants ofbilateral real exchange rate fluctuations between Mexico and the U.S. We interpretthe evidence as supportive of our view that informality is largely a non-tradableactivity. We then proceed to examine informal production using an open economyframework. Our theoretical analysis suggests that the informal sector in EMEsworks as a insurance mechanism against both domestic and foreign shocks, andas such plays a non-trivial role at the aggregate level. This mechanism operatesvia expenditure and labor re-allocation between formal and informal sectors inresponse to shocks, which has important implications for aggregate consumption,employment and output.

Our results suggest that the pseudo-empirical verdict that informality doesnot matter for the international transmission of shocks is misleading. In fact, wefind that informal production is a crucial aspect to help rationalize the observedlow degree of consumption risk sharing in EMEs. Importantly, the formal marketbias of national accounts in EMEs represents a warning for the conduct of bothstabilization and labor market policy that disregards important linkages with theinformal market.

Our result that informality is not as bad as it seems should be taken withcaution however. Our analysis abstracts from crucial aspects of firm and workerheterogeneity, which are fundamental aspects to consider when analyzing the in-equality and aggregate welfare consequences of informality 8 Another caveat of ourparsimonious approach is to ignore other structural elements of the economy. Forinstance, lower-income economies tend to have less developed financial markets,while others may differ regarding the extent of their trade barriers. Further, ouranalysis also abstracts from the impact of price rigidity and thus monetary policy.Thus, a fruitful avenue for future research would be to apply our framework tostudy the impact of real and nominal frictions along with the corresponding policyanalysis.

8Ulyssea (2018) provides a recent examination of worker and firm heterogeneity for the caseof Brazil.

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