Financial Constraints, Innovation Quality, and Growth ∗

Yu Cao†

December 2019

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Abstract

This paper investigates the role of nancial constraints in shaping innovation quality

and rm-growth dynamics through heterogeneous innovation. I build a unique data-set

combining patent activities with the operating data of private Chinese manufacturing

rms and show a strong negative relationship between the severity of nancial con-

straints and a) rm growth, b) innovation intensity, and c) innovation quality. Based

on these empirical regularities, I build a tractable endogenous growth model in which a

multi-product rm invests in heterogeneous innovation in the face of imperfect nancial

markets. Tighter nancial constraints cause rms to undertake more low-quality inno-

vation, which yields temporary payos but no longer-term productivity improvements.

This lowers rm and aggregate growth rates. The quantitative model suggests nancial

frictions reduce rm R&D investment by 50.7 percent on average and slows aggregate

annual productivity growth by 17.5 percent.

∗I am grateful to my advisor Caroline Betts for her guidance and support. For helpful comments, Ithank Dirk Czarnitzki (discussant), Joel David, Robert Dekle, Miroslav Gabrovski, Pablo Kurlat, Shawn Ni,Vincenzo Quadrini, Romain Ranciere, Gilles Saint-Paul, and seminar and conference audiences at USC, theCES NA Annual Conference in Lawrence, and the WEAI Annual Conference in San Francisco. All errorsare mine.†University of Southern California. Email: cyu812@usc.edu

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1 Introduction

A large body of work argues that nancial market development plays an important role in

driving economic growth (see Kerr and Nanda (2015) for a recent review). In this paper,

I explore empirically and theoretically one potential important source of this relationship:

Investment in R&D has limited collateral value, in contrast to investment in physical capital.

Less developed nancial markets can therefore hinder a rm's innovation activities, and po-

tentially limit both rm and aggregate growth rats. In addition, not all types of innovation

are created equal. For example, I nd that more than 40 percent of patent applications

among Chinese manufacturing rms are classied as industrial design patents, which are

believed to bear limited value. (I describe in detail the interpretation of patent classications

in section 2). In contrast, in the United States industrial designs account for only 6 percent

of patent applications. In addition, there is substantial disparity in rm-level innovation cat-

egory and quality, yet little is known about the relationship between innovation composition

and nancial market development. Do rms facing more severe nancial constraints that

limit innovation activities conduct relatively more low-quality innovation, such as indus-

trial design, reducing their growth potential, and if so what is the mechanism by which

this occurs?

I build a unique dataset of innovation quality for a large sample of privately-owned Chi-

nese manufacturing rms. I match each patent application by a rm in my sample, recorded

by the State Intellectual Property Oce of China (SIPO), to patent citation data in Google

Patent. I exploit the forward citation data to construct a measurement of innovation qual-

ity. Utilizing information on a patent's backward citations and technology eld, I classify

a rm's innovation into three types: industrial design, internal innovation, and external

innovation. A rm conducts industrial design to boost its current prots temporarily by at-

tracting more customers. A rm undertakes internal innovation to improve the productivity

of its current product lines permanently while it undertakes external innovation to improve

the productivity of a second rm's product lines and capture markets from it. Both internal

and external innovations are productivity-enhancing innovations and take time to complete.

To my knowledge, this is the rst paper to construct such a quality and category index for

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Chinese patents.

I then link the patent data to annual operating data from the Chinese Annual Survey of

Manufacturing (ASM). Using this merged dataset, I connect measures of rm-level patent

activity to nancial conditions. I also compute a set of measurements of a rm's nancial

constraints, as well as rm size and growth. I measure a rm's nancial condition following

Hovakimian and Titman (2006) and Almeida and Campello (2007), as the investment to

cash ow sensitivity. I measure a rm's innovation intensity for each type of innovation as

the ratio of the number of citation/quality-adjusted patents to deated rm sales revenue.

These measurements enable me to establish a set of new empirical facts for Chinese private

manufacturing rms.

My key empirical ndings are: 1) Internal and external patent intensity decreases with a

rm's nancial constraint. On average, industrial design intensity increases by 1.54 percent,

internal innovation intensity decreases by 1.11 percent, and external innovation intensity

decreases by 1.73 percent with a 1 percent increase in a rm's probability of being nancially

constrained. 2) The innovation composition of rms that are subject to tighter nancial

constraints is more concentrated in industrial design and lower quality patents. 3) A rm's

one-year sales growth rate drops by 0.85 percentage points with a 1 percent increase in a

rm's probability of being nancially constrained, even after controlling for rm size and

rm age.

Next, I build an endogenous growth model that incorporates 1) dierent forms of inno-

vation, one of which industrial design has only immediate prot and cash ow benets

for a rm, and 2) nancial constraints into a rm's choices, which provides an important

channel linking nance and endogenous growth through innovation. The model is tractable

and yields a clear prediction for innovation composition across nancially constrained rms.

Once subject to nancial constraints, a rm's available cash ow restricts its R&D invest-

ment expenditure on innovation. As patenting in industrial design immediately boosts a

rm's current prot and cash ow, a nancially constrained rm undertakes more indus-

trial design patenting to relax its current nancial constraint. Compared with nancially

unconstrained rms, nancially constrained rms then conduct less productivity-enhancing

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innovation, as their total investment expenditure is restricted. A tighter nancial constraint

forces a rm to substitute into industrial design patenting and out of productivity-enhancing

innovation, which hinders its future growth. The existence of nancial constraints changes

rms' innovation composition as well as its potential growth. Such changes vary across rm

size.

In the model, a small rm's R&D investment is nancially constrained. Thus, small

rms undertake more industrial design and less productivity-enhancing innovation than is

optimal, and this results in a lower growth rate. Once a rm grows large enough, its R&D

investment is no longer nancially constrained. Financial market frictions have a smaller

impact on a large rm's innovation composition and growth.

I then calibrate the model to match the empirical facts I have identied for Chinese

manufacturing rms relating to rm dynamics, innovation intensity, and nancial conditions.

The calibrated model can replicate the observed rm size distribution in the Chinese data,

as well as the relationships between nancial constraints, innovation intensity, quality, and

rm growth. The model implies that, even conditioning on rm size, on average, nancial

constraints play a quantitatively important role in shaping a rm's innovation intensity. A 10

percent decrease in a rm's nancial constraint would, on average, result in a 0.7 percentage

points increase in the share of external innovation and a 1.1 percentage point decrease in

industrial design patenting share. This shift from industrial design patenting to external

innovation raises a rm's growth rate by 3.1 percent. In addition, while industrial design

relaxes a rm's nancial constraint temporarily, it reduces a small rm's prot and sales

through increased competition. Thus, sub-optimally high industrial design patenting in the

presence of nancial constraints could be detrimental to aggregate growth. I nd that, rst, if

all nancial constraints were removed, the aggregate growth rate would rise by 21.3 percent,

with much of this increase being attributable to higher internal and external innovation and

lower industrial design. Second, shutting down patenting on industrial design would increase

the aggregate growth rate by 11.8 percent, and encourage slightly higher entry rates by new

rms by 0.03 percent. Finally, I show that type-dependent R&D tax incentives, under which

only R&D expenses on internal and external innovation are entitled to a super deduction in

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computing corporate income tax base, would generate higher aggregate growth and a larger

welfare gain than currently implemented uniform R&D tax incentives.

This paper relates to several branches of literature. First, I build closely on the seminal

work of Klette and Kortum (2004), Lentz and Mortensen (2016), and Akcigit and Kerr (2018).

These frameworks allow rms to own multiple product lines through external innovation.

Akcigit and Kerr (2018) and Garcia-Macia, Hsieh, and Klenow (2019) also introduce internal

innovation and let rms innovate over their existing product lines. Internal innovation is

found to be a quantitatively important channel in promoting aggregate productivity growth.

I extend these frameworks in three main ways. First, I introduce patenting in industrial

design. Second, I introduce nancial constraints. I show the existence of nancial constraints

can help explain the relatively low level of R&D intensity and a higher level of industrial

design observed for Chinese manufacturing rms.

This paper also relates to the literature on nance and R&D investment, nancial con-

straints and productivity growth. A well-functioning nancial market is believed to play an

important role in spurring economic growth. A large body of work investigates how nancial

development would potentially aect R&D nancing and innovation. Brown, Fazzari, and

Petersen (2009), Hall and Lerner (2010), Brown, Martinsson, and Petersen (2013), and Hsu,

Tian, and Xu (2014) are examples. Their empirical studies show that small rms face a

high cost of R&D capital, and their R&D investments are more sensitive to cash ow than

large rms. Thus, rms in countries with less developed nancial markets would be more

likely to underinvest in innovation. Aghion, Angeletos, Banerjee, and Manova (2010) build

a model in which credit constraints change a rm's investment composition. In particular,

with imperfect nancial markets, investment shifts from long-run to short-run. I build on

this literature by developing a model in which rms can use industrial design as a device

to boost their current prots. Thus, nancial constraints not only aect the quantity of

R&D investment, but also its composition. Once a rm's R&D investment is restricted by

nancial constraints, it concentrates more on industrial design, which does not contribute to

a rm's future growth. The model then explores this new channel through which nancial

constraints aect a rm's growth. With this element, the model can t the empirical regu-

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larities observed in the data. My results, both analytically and quantitatively, highlight the

importance of nancial constraints in shaping the relationship between innovation, rm size

and growth.

The rest of the paper is organized as follows. Section 2 documents my data set construc-

tion and empirical analysis for the private, innovative rms in Chinese manufacturing from

2002 to 2013. Section 3 layout the theoretical model and its analytical implications. Sec-

tion 4 and 5 conducts a quantitative analysis of the model and derives policy implications.

Section 6 concludes.

2 Data and Empirical Analysis

In this section, I document empirical relationships between nancial constraints, innovation,

and rm size and growth for a large sample of Chinese Manufacturing rms. I rst doc-

ument data sources and my construction of the sample. I then describe my measurement

of patent type, patent quality, and nancial constraints. Finally, I examine econometrically

how nancial constraints alter a rm's innovation intensity and quality. These empirical

regularities motivate the specication of my theoretical model, and I use them to discipline

the quantitative analysis of the model.

2.1 Data Source

To assess the empirical relationship between nancial constraints, innovation, and rm

growth, I construct a panel data sample for Chinese private manufacturing rms from 2002

to 2013. I draw the data from three large panel data sets.

The rst is the patent data from China's State Intellectual Property Oce (SIPO). It

contains basic "front page" data for patents issued from 1985 to 2016. The variables I use

are a patent's number, application and granting dates, technology domain, and description,

and the assignee's name and location. The second is the relatively well-studied rm-level

operation data from the Chinese Annual Survey of Manufacturing (ASM), which includes

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industrial rms with annual sales greater than 5 million RMB (approximately $800,000) from

1998 to 2013 1. I clean the dataset and construct a panel following the method outlined in

Brandt, Van Biesebroeck, and Zhang (2014). I use rms' balance-sheet information from

ASM to construct a set of measurements on rms' nancial constraints, rm size, and rm

growth. These two data sources are collected by dierent agencies and do not share the same

identication number for each rm. They do, however, provide rms' names and locations.

My linking of the two datasets follows the methodology proposed in He, Tong, Zhang and

He (2016).

I supplement the patent data with information on patent citations from Google patents.

Previous studies of innovation activities among Chinese rms focus only on innovation fre-

quencies measured by simple patent counts, making it dicult to gauge patent quality and

value. Patent value varies across technology elds, and dierent patents have diverse im-

pacts on a rm's size and productivity growth. One major innovation could generate more

future prot and productivity growth than several minor innovations. I, therefore, construct

a panel of patent citations for each granted patent in SIPO using Google Patent. Google

patent documents the date and technology domain of a patent when cited. This enables me

to adjust each SIPO patent's citations based on the time window in which they occur, and

the patent's technology eld. After these adjustments, I can compare patents over time and

technology domains.

As state-owned rms and foreign-owned rms might have dierent patenting incentives

than privately-owned rms, I only use private, non-foreign owned, innovative rms in my

sample. I dene innovative rms as rms that patent at least once in the period 2002-

2013. I dene private, non-foreign owned rms as rms that not registered as state-owned or

foreign-owned, or have controlling shareholders that are non-state and non-foreign entities.

To remove the impact of outliers, I trim the nal sample at the 1 percent tails of rms'

sales revenue. The nal merged sample contains 119,026 observations with 14,826 unique

private rms. Firms in my sample applied for 392,765 patents between year 2002 to year

2013, comprising 126,959 "invention patents", 135,005 "utility model" patents and 130,801

1After 2010, the ASM only contains rms with annual sales greater than 20 million RMB (approximately$3,200,000)

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"industrial design" patents. I describe the properties of each type of patent in detail below.

Appendix A.1 discusses in detail those datasets and the method I used to merge them.

2.2 Measuring Patent type, quality and nancial constraints

Next, I briey introduce the main variables I use in my empirical studies. Appendix A.1

provides detailed information on measurements of each variable, and Table A4 in appendix

A.4.1 lists summary statistics for key variables.

Patent Type. Under SIPO classication of patents, 1) invention patents are patents that

make "signicant progress" relative to previous technology, 2) utility models are patents

that represent a minor improvement of current products and are insucient to be granted

as invention patents, and 3) industrial design are patents of ornamental or aesthetic design

of physical or digital goods with a practical purpose. In my sample, around 70 percent of

industrial design patents are packaging, or design of clothing, jewelry or furniture, which

do not contribute to the improvement of a rm's production process. Invention and utility

models, however, contribute to a rm's production process and, thus its productivity. I

regroup and reclassify invention and utility models into two categories: 1) Internal innova-

tion, and 2) external innovation. Internal innovation patents are "exploitation" innovations,

which aim to improve a rm's existing production method or process. One can view these

innovations as renements and extensions of current technology. External innovation patents

are "exploration" innovations, which aim to increase the number of a rm's product lines by

introducing new products or an entirely new production technology. As internal innovation

relies more on the rm's previous technology, a rm's external innovation patent cites less

its own, previous patents but cites more patents owned by other rms than does an internal

innovation patent 2.

I classify internal innovation patents in two steps. First, for patents with backward

citations, I classify a patent as internal innovation if more than 50 percent of backward cita-

2Galasso and Simcoe (2011) and Akcigit and Kerr (2018)). Levinthal and March (1993) and March (1991)provide detailed distinguish on exploration and exploitation innovations

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tions are self-citations. Second, for patents without backward citations 3, I classify a patent

as internal innovation if a) its technology domains belong to the rm's previous patent's

technology domains, and b) there is a statement similar to "improving current production

process" in the patent description, or if the rm reports "no new product is produced" in

the year of the patent's application 4. Using this method for distinguishing internal from

external patents, there are 129,479 internal patents and 132,485 external patents in the sam-

ple period. My method is slightly dierent from the method proposed by Akcigit and Kerr

(2018). I compare these two methods in detail in Appendix A.1. In general, my method

yields a more restrictive denition of external, exploratory innovation.

Patent Quality. Follows the literature 5, I measure patent quality by the number of

forward citations a given patent received in a time window of ve years from its publication

date 6. I use a ve-year window to account for truncation issues in the citation data;

namely, more recently published patents have less time to accumulate citations. Next, I

account for the fact that patent citations vary a lot across technology elds. To make patent

quality comparable over dierent technology domains, I compute a patent's relative quality

by dividing its citation count by the average citation count for a patent within a three-digit

IPC eld. Then, I dene the relative quality of patent j applied for by rm f at time t, and

rm f 's total quality-adjusted patent application at time t, as:

qfjt =

∑t+5τ=t citationsfjτ

1Nt

∑Ntf=1

∑t+5τ=t citationsjτ

, Patft =

Npt∑j=1

qfjt

3In the merged sample, around 42 percent of invention patents lack backward citation data and all utilitypatents do not have backward citation.

4In ASM, rms were asked to provide information on whether their current products are produced usingnew technology or new production process.

5See Hall, Jae and Trajtenberg (2001), Jae and Trajtenberg (2001), Aghion (2017)6For utility and industrial design patents, grant date is publish date. For invention patents, publish

date is earlier than grant date. In China, invention patents can be available to the public (i.e. published)after preliminary examination by patent examiner. Then it should undergo "substantive examination". Apublished patent can be rejected by examiners if it is found to be neither innovative enough nor conictswith patent law. As patent become available to the public after its publishing date, it starts accumulatingcitations. I use a ve-year window for two reasons. First available data restrict the window; the merged rmsample ends in 2013, and the citation data ends in 2018, so patent granted or published in the last year ofmy merged rm sample period have only ve years to accumulate citations. Second, it is the most relevant,citation-active window; on average, a patent in SIPO receives more than 87 percent of its ten-year-forwardcitations within ve years of its publication date.

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Here, citationfjτ denotes the number of citations of rm f 's patent j in year τ ≥ t, t ≥ t

is the patent's publishing year recorded by Google patents, Nt denotes the total number of

patents applied by Chinese rms in the SIPO oce at time t which are granted or published

later during sample period, and Npt is the total number of patent applications led by rm

f in year t that are granted later during the sample period. Patappft is my measure of

the innovation rate of rm f at date t. I can compute this only for internal and external

innovation, as citation dates are only observable for internal patents and external patents.

Thus, I am forced to use simple patent count data instead of citation/quality-adjusted patent

data to measure the rate of industrial design innovation for rm f at year t.

Financial Constraint. A rm becomes nancially constrained when external nancing

through either debt or equity is not available. R&D investment by nancially constrained

rms then heavily depends on its internal cash ow. R&D investment cash-ow sensitivity

can then be used to approximate the degree of nancial constraint faced by a rm 7. I measure

investment cash-ow sensitivity, following Hovakimian and Titman (2006) and Almeida and

Campello (2007), by using an endogenous switching regression. There are two advantages

under their methodology: 1) The estimation does not rely on an a priori assignment of

rms into constrained and unconstrained categories; 2) investment-cash-ow sensitivity, as

well as the probability of being nancially constrained, can be jointly estimated through an

investment equation and an endogenous selection equation. Thus, following their framework,

I approximate a rm's nancial constraint in two steps.

First, I jointly estimate following investment (equation 1) and selection (equation 2)

equations. Second, I compute the probability of being nancially constrained using the

estimated selection equation. I then use this probability to approximate a rm's nancial

constraints. The regression equations are,

RDInvj,iht =α1jRDInvj,iht−1 + α2jGrowOppj,iht−1 + α3jCashj,iht−1 + µht + εj,iht, j = 1, 2

(1)

7See Hall and Lerner (2010), Brown, Fazzari and Petersen (2009) and Brown, Martinsson and Petersen(2013) on Compustat rms; Poncet, Steingress and Vandenbussche (2010), Guariglia, Liu and Song (2011)and Howell (2016) for Chinese Manufacturing rms.

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y∗it =β0 + Z ′it−1β + uit (2)

In (1), rms are indexed by i, h indexes a rm's industry, t indexes time, µht measures

industrial-year xed eects. j indicates regime 1 and regime 2. A rm makes a constrained

investment under regime 1, or an unconstrained investment under regime 2. In addition.

GrowOppit is an investment opportunity for rm i, which is approximated by the ratio of

the rm's change in turnover to real capital. Cashj,iht−1 is dened as real net income plus

real current depreciation, divided by the rm's real capital stock at the beginning of current

period. The dependent variable, RDInvj,iht is the real R&D investment of rm i normalized

by the rm's real capital stock at the beginning of period t. A one year lagged value of

the dependent variable is included to allow for the correlation between previous and current

R&D investment decisions.

In (2), y∗ is a latent variable that establishes a rm's probability of being in the con-

strained regime (regime 1) and unconstrained regime (regime 2). The vector Zit−1 is a set

of selection variables that determine a rm's propensity of being in either regime. Following

Almeida and Campello (2007) and Hovakimian and Titman (2006), Z contains 1) the log of

total assets, 2) log age of rm, 3) the rm's ratio of short-term debt to total assets, 4) the

rm's ratio of long-term debt to total asset, 5) nancial slackness measured as a rm's cash

and marketable securities to total assets, and 6) Tangibility, which is used to approximate

the expected liquidation value of a rm's operating assets. Following Berger, Ofek, and Swary

(1996) and Almeida and Campello (2007), I compute Tangibilit as Tangibility = 0.715 ×

Receivablesit + 0.547× Inventoryit + 0.535×FixedAssetit +Cash+MarketableSecurities,

scaled by total assets, whereReceivablesit are account receivables. Cash and marketable

securities are computed as liquid assets minus account receivables. These variables all enter

in lagged form in the selection equation.

The parameters set α in equation (1) and β in equation (2), are then estimated jointly

using the Expectation Maximization algorithm (see Appendix A.1.2 for details). Ideally,

for nancially constrained rms, we would expect α3 > 0, that is a rm's R&D investment

would increase with its cash ow. Table A3 and A2 show the estimation results. Cash ow

sensitivity is statistically signicant under the constrained regime, and larger than cash ow

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sensitivity under the unconstrained regime. I then dene a rm's nancial constraint score,

FC, as its probability of being nancially constrained. The probability can be recovered

through a Probit regression: FCit ≡ probit = Φ(β0 + Z ′it−1β) where Φ is the cumulative

normal distribution. A rm with a higher likelihood of being constrained has a higher

nancial constraint score FC.

The average probability of being nancially constrained for rms in my sample is 0.532.

2.3 Empirical Results

I now present the key empirical results on the link between nancial constraints, innovation

quality, and rm growth 8. To do so, I rst estimate a simple linear regressions of the

following form:

yijt = β0 + β1 log(Salesijt) + β2Ageijt + β3FCijt + µjt + εijt

where yijt are rm i (in industry j), year t dependent variables - such as: rm sales growth,

industrial design intensity, internal innovation intensity, external innovation intensity, in-

dustrial design patent share, and external and internal innovation share. A rm's annual

sales growth is dened as ∆saleit+1

saleit. I set this growth rate to −1 if a rm exits the market.

Innovation intensity is dened as PatitSaleit

. Recall that patent applications are all granted or

published in the sample period and citation adjusted for internal and external innovations.

A rm's patent share in industrial design is the number of industrial design patents applied

at time t over all patents the rm applied for in the same period. Firm size is measured by

the log of a rm's real sales Saleijt. FCijt measures a rm's nancial constraint, measured

in the previous section, as the likelihood that a rm faces friction in the access to the credit

market. µjt controls for industry-year xed eects, removing any unobservable year and

industry-specic demand shifters. The regression results are recorded in Table 1.

8My empirical studies on innovative private rms in Chinese manufacturing also provide some otherinteresting patterns on rm size and innovation, rm size and nancial constraints. Appendix A.4 documentthese additional empirical results.

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Fact 1. Financial constraints increase a rm's investment in industrial design and lower

a rm's investment in internal and external innovation.

Table 1: Firm Size, Growth and Innovation Intensity

Growth Patent Intensity Patent Share(1) (2) (3) (4) (5) (6) (7)

∆Saleit+1

Saleit

PatditSaleit

PatIitSaleit

PatXitSaleit

PatditPatTit

PatIitPatTit

PatXitPatTit

log(Sale)it −0.091∗∗∗ −0.103∗∗∗ −0.112∗∗∗ −0.066∗∗∗ −0.004 −0.023∗∗∗ 0.009∗∗∗

(0.007) (0.018) (0.005) (0.004) (0.003) (0.002) (0.002)FCit −0.853∗∗∗ 0.328∗ −0.308∗∗∗ −0.390∗∗∗ 0.211∗∗∗ 0.108∗∗∗ −0.276∗∗∗

(0.075) (0.175) (0.060) (0.083) (0.032) (0.030) (0.028)FE Yes Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes YesN. Obs 93, 879 75, 073 77, 929 74, 214 26, 577 29, 433 25, 718

R-squared 0.084 0.013 0.031 0.010 0.197 0.169 0.222

Note: Firm size is measured by real sales, log(sale). Patit is (citation-weighted) patent applicationsfor industrial design (denoted as d in the superscript), long-run internal (I) and long-run external

(x) innovation. PatTit is a rm's total patent applications at time t. FCit measures a rm's nancial

condition dened as probability of being constrained, which is calculated via endogenous switching

regression in section 2.3. Industry-year xed eects and rm age are included as controls, but I do

not report in regression. Robust standard errors clustered at rm level are in parentheses. ∗ ∗ ∗, ∗∗and ∗ indicate signicant at levels 1%, 5% and 10%, respectively.

Columns (2) to (4) show that if a rm's nancial constraints tighten, it reduces patenting

in internal and external innovation, and increases patenting in industrial design, which is

non-productivity enhancing. The coecient estimate β3 indicates that with a 1 percent in-

crease in its probability of being nancially constrained, a rm would increase its patenting

in industrial design by 0.33 per unit of real sales, whereas it would reduce its patenting in

internal and external innovation by 0.31 and 0.39 per real sales unit respectively. The reduc-

tion in external innovation intensity is higher. This results in a drop in external innovation

share, and an increase in both internal innovation and industrial design share. Columns

(5) to (7) document that a one unit change in rm's FC score is associated with 21 per-

cent increase in industrial design share of innovation, an 11 percent increase in its internal

innovation share, and a 28 percent reduction in its external innovation share.

Financial constraints not only aect a rm's choice of innovation type, but also its choice

of innovation quality. To estimate this, I rst construct a patent quality distribution, based

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on each patent's external citations within 5 years of its publication date. For each year, I

calculate the percentage of internal and external patent applications in each quality quartile,

to construct a variable named patent share. Then, I estimate the regression of the form:

PatQualShareq,ijt = β0 + β1Xijt + µjt + εijt

Where PatQualShareq,ijt is patent share in each quartile q. with [0, 25) denoting the lowest-

quality quartile and [75, 100] denoting the highest-quality quartile. Xijt are independent

variables: A rm's size and its nancial constraints measure. Again, industry and year xed

eects are controlled. Table 2 records the results. The coecients in each row naturally sum

to zero.

Table 2: Firm size, Financial Constraint and Patent Quality Distribution

Panel A: Share of Firm's Internal Patents in Quality Distribution[0, 25) [25, 50) [50, 75) [75, 100] [0, 25) [25, 50) [50, 75) [75, 100]

log(Saleit) −0.013∗∗∗ −0.004∗∗ 0.005∗∗∗ 0.012∗∗∗

(0.002) (0.002) (0.002) (0.002)FCit 0.202∗∗∗ 0.009 −0.120∗∗∗ −0.091∗∗∗

(0.033) (0.027) (0.026) (0.024)Panel B: Share of Firm's External Patents in Quality Distribution

[0, 25) [25, 50) [50, 75) [75, 100] [0, 25) [25, 50) [50, 75) [75, 100]log(Saleit) −0.005∗ −0.004∗ 0.005∗∗ 0.004

(0.003) (0.002) (0.002) (0.003)FCit 0.128∗∗∗ 0.003 −0.031 −0.100∗∗∗

(0.039) (0.031) (0.032) (0.035)

Note: The dependent variable is the share of a rm's patents in each quartile of the patent quality

distribution. The quality distribution is calculated using external citations. Each cell from column

(1) to (4) reports the estimated OLS coecients on rms size, measured as log of real sales rev-

enue. Each cell from column (5) to (8) reports the estimated OLS coecients on rms's nancial

constraints. Year and industry xed eects are included in the regression, but I do not report the

result. Panel A reports the regression coecients for internal patents, and Panel B reports the

coecients for external patents. Robust standard errors clustered at rm level are in parentheses.

∗ ∗ ∗, ∗∗ and ∗ indicate signicant at levels 1%, 5% and 10%, respectively.

Fact 2. Innovation quality increases with rm size, and decreases with nancial constraints.

The tightening of nancial constraints is associated with a shift in rms' patent appli-

cations from the top quality quartile into the bottom quality quartile for both internal and

14

external patents. Coecients on row FCit imply that a 10 percent increase in a rm's prob-

ability of being nancially constrained is associated with 2 percent increase in the fraction

of a rm's internal patents in the bottom quartile of the patent quality distribution. A 10

percent increase in FC is associated with 0.9 percent decrease in the fraction of a rm's

internal patents in the top quartile of the patent quality distribution. As large rms are

less likely to be nancially constrained 9, they have a comparative advantage in achieving

high-quality innovations. A 10 percent increase in rm size is associated with 0.13 per-

cent reduction in the fraction of rm's internal patent among the bottom quartile of the

patent quality distribution, and a 0.12 percent increase in the fraction of rm's internal

patent among the top quartile of the patent distribution. Similar patterns can be found in

a rm's external innovation. Large and nancially unconstrained rms concentrate more on

high-quality patents.

Fact 3. Tighter nancial constraints are associated with a lower rm growth rate.

Column (1) in Table 1 documents a strong negative relationship between nancial con-

straints and a rm's size growth. A 10 percent increase in a rm's likelihood of being

nancially constrained is associated with an 8.53 percent decrease in a rm's sales growth

rate. Facts 1 and 2 show that tightened nancial constraints are associated with lower quan-

tity and quality of a rm's internal and external innovation. To further gauge potential

sources of the negative relationship between nancial constraints and rm growth, I assess

the relationship between the innovation activity of the rm and its future growth. I estimate

the following specication:

logSalesijt+k − logSalesijt = β0 + β1 log(Patgranthit + 1) + β2Xijt + µjt + εijt

Here, logSalesijt+k − logSalesijt is a rm's sales growth in k = 1, 2, 3 years' ahead of time

t. Patgranthit is a rm's time t granted patents in category h - industrial design, internal

and external. Xijt are other rm-level controls as rm size and age. The industry-year xed

eect is included to account for unobservable factors at the industry and year level. Table 3

9Table A2 in Appendix A.1.2 document the estimation result of selection equation 2. Firms with largesize (measured with total assets) have lower probability switching into constrained region.

15

reports the results.

Table 3: Firm Growth and Innovation

One Period Ahead Two Period Ahead Three Period Ahead(1) (2) (3) (4) (5) (6) (7) (8) (9)

log(D + 1) 0.032∗∗∗ 0.026 0.031(0.007) (0.018) (0.023)

log(LTE + 1) 0.076∗∗∗ 0.088∗∗∗ 0.178∗∗∗

(0.016) (0.023) (0.057)log(LTI + 1) 0.050∗∗∗ 0.072∗∗∗ 0.104∗∗∗

(0.009) (0.017) (0.025)FE Yes Yes Yes Yes Yes Yes Yes Yes Yes

Controls Yes Yes Yes Yes Yes Yes Yes Yes YesN. Obs 77, 564 66, 134 66, 134 41, 161 78, 353 51, 109 51, 109 41, 161 41, 161

R-squared 0.072 0.128 0.128 0.104 0.098 0.098 0.101 0.101 0.101

Dependent variables are rm's growth rate in real sales. Dit is the log of number of industrial design

patenting application at time t, LTit is the number of productivity-enhancing patents: invention

and utility models. Current, one period and two period are dependent variable measures rm's real

sales growth in one, two and three years, respectively. Past real sales, rm age and Industry-year

xed eects are included as controls, but I do not report in regression. Robust standard errors

clustered at rm level are in parentheses. ∗ ∗ ∗, ∗∗ and ∗ indicate signicant at levels 1%, 5% and

10%, respectively.

The rm's current growth in one year is strongly positively associated with all three

types of innovation. However, the relationship between future growth (i.e. sales growth in

two and three years) and industrial design innovation activity is statistically insignicant and

economically small. Similar qualitative results can also be found if the dependent variable

is replaced with TFP growth. Table A9 in Appendix A shows the result. Both internal and

external innovation exert a strong positive impact on a rm's future growth, and this impact

increases with the time horizon. For example, a 10 percent increase in granted external

innovation would raise a rm's current sales growth by 0.76 percent and future growth by

0.88 percent in two years and 1.78 percent in three years. Internal innovation contributes

less to a rm's future growth than external innovation at all horizons. It is also notable that

the average number of external forward citations is 1.45 per patent for internal innovation,

and 1.89 for external innovation, suggesting that the social value of internal innovation is

also smaller than that of external innovation.

Facts 1 and 2 imply that tighter nancial constraints shift a rm's innovation composition

16

towards industrial design and low-quality innovations. Fact 3 suggests that such changes

in innovation composition lower a rm's growth rate. Thus, rm choices over innovation

quality and type provides a channel through which nancial constraints could lower rm and

aggregate growth.

3 Theoretical Model

I now build an endogenous growth model to investigate a rm's innovation choice, condi-

tioning on the severity of its nancial constraint. The basic structure of the model is similar

to that of Akcigit and Kerr (2018), with three key dierences: 1) I introduce patenting in

industrial design as a demand shifter; 2) I include rm nancial constraints; and 3) I use a

more general specication of decreasing returns to scale in innovation technologies.

3.1 Preferences, Technology and Market Structure

Household. I assume a representative household with family size L = Lf + L. L is the

number of workers employed in the intermediate goods sector and Lf is the number of

workers employed in the nal goods sector. Labor is supplied in-elastically; hence, L equals

aggregate employment and the aggregate labor endowment. Let w be the equilibrium wage

at time t. The household maximize the lifetime utility function:

U =

∫ ∞0

e−ρt logC(t)dt

where C(t) is the instantaneous consumption rate of a single nal good with output Y (t),

which is produced competitively by a representative nal goods producer. This maximization

is subject to the budget constraint:

S(t) + C(t) ≤ r(t)S(t) + w(t)L

Here S(t) =∫Vk(t)dk is the total asset held by the representative household. And Vk(t) is

rm value of each intermediate producer k and nal goods producer. r(t) is the equilibrium

17

interest rate on assets.

Final Goods. Output of the nal good, Y (t), is produced using labor input Lf and a

continuum of intermediate goods j ∈ [0, 1] on a unit circle. The production technology is:

Y (t) =Lfσ(t)

1− σ

∫ 1

0

Aσj (t)q1−σj (t)dj

where qj(t) is the quantity of intermediate good j, Aj(t) is the quality of intermediate goods

j in nal goods production, and σ ∈ (0, 1) measures return to scale and is the inverse

of the substitution elasticity between intermediate goods. Industrial design patenting -

R&D activity that aims to increase the quality of an intermediate good - Aj(t) can be

expressed as Aj(t) = A0(1 +φ(hdj(t))), where A0 is a rm's quality at instant t ex industrial

design innovation, and φ(hdj(t)) is the return function of industrial design innovation hdj(t).

Hence, φ(hdj(t)) is an instantaneous demand shifter, as seen in the advertising literature

(for example, Cavenaile and Roldan-Blanco (2019)). Based on the empirical results in Table

3, I assume that industrial design innovation hdj has only an instantaneous impact on the

quality of good j Aj(t). That is, good j's quality is reset to A0 before any industrial design

patenting takes place in the instant t + ∆t. I normalize the price of the nal good Y to be

one in each period.

Intermediate Goods Producer. There is a set of rms with measure M that produce

intermediate goods under monopolistic competition. Each intermediate goods j is exclusively

owned and produced by rm f with technology:

qj(t) = Zzσ

1−σj lj

where Z =∫ 1

0zjdj is the average productivity in t prior to any innovation. The production

function is linear in aggregate productivity Z and labor input l; but exhibits curvature over

current own productivity zj. This production function features a positive spillover eect

from productivity-enhancing innovation; rm j's innovation in t can increase both future

aggregate Z, and any rm's future total productivity Zzσ

1−σj . I explain this in detail below.

18

Each rm f can produce several dierent intermediate goods, j. Let nf be the total

number of product lines owned by rm f at any instant t. Let zf = zj : j ∈ nf be the

productivity portfolio in rm f . Each intermediate goods producer can be characterized by

the state vector: (nf , zf ).

3.2 Innovation and Financial Constraint

As I show below, the prot earned by a monopoly producer f of good j increases with current

productivity zjj∈nf as well as the number of product lines it owns. For each product line

rm f produces, it earns monopoly rents until it is being replaced by another incumbent

or new entrant. Thus, both an incumbent and new entrants have incentives to improve

their current technology and add new product lines. Before any production takes place, an

intermediate goods producer can conduct three types of innovation.

Industrial Design. Incumbent rms can patent in industrial design to temporarily im-

prove the quality instantaneously of any of its existing product lines. Specically, the current

quality will instantaneously increase from A0 to A0(1 + φ(hdj)) for sure with an expenditure

of Rdj unit of nal goods. Rdj is dened, for a rm with number of product lines n,

Rdj = xdhψddj n

αdZ

where xd > 0 is a scalar to facilitate calibration, hdj is the number of industrial design

patents for each product line j. ψd > 1 is the cost elasticity of R&D input and the term nαd

with αd > 0 governs decreasing return to scale in rm size. The cost of industrial design is

also linear in aggregate productivity Z, implying that when aggregate productivity is high,

patenting in industrial design becomes harder. This reects the fact, that I record in Table

1, that industrial design patenting intensity, hdj, decreases with rm size. As a rm grows

larger, a quality improvement of a current product line is more costly, for example because

of higher managerial or coordination costs.

The return function for rm f 's patenting in industrial design, φ(hdj), is given as: φ(hdj) =

19

hdjZ

zj, which is linear in aggregate productivity Z and decrease in own productivity zj. The

linear eects of aggregate productivity on the cost and on the return of industrial design

R&D cancel, leaving the quality improvement hdj depending solely on the number of a rm's

product lines. The assumption that this improvement is only instantaneous captures the

empirical evidence I have presented that current industrial design has no signicant positive

impact on a rm's future sales growth.

Internal Innovation An incumbent undertakes internal innovation to improve the future

productivity of its current product lines. An expenditure RIj unit of nal goods by a rm

with n product lines generates hIj units of internal patents in each product line j. The return

on internal innovation is realized with Poisson ow hIj. The expenditure RIj is dened as

RIj = xIhψIIj n

αI Z

where xI > 0 is a scalar to facilitate calibration, ψI > 1 is the cost elasticity of internal R&D

input, and αI measures the degree of decreasing return in rm size. This is used to capture

the fact recorded in Table 1 that internal innovation intensity decreases with rm size, even

controlling for nancial constraints.

Successful internal innovation increases the quality of product line j to zj(t+ ∆t) = zj(t) + λZ.

In contrast to Aghion, Harris, Howitt, and Vickers (2001) and Akcigit and Kerr (2008), for

example, the increase in future productivity accomplished through internal innovation is in-

dependent of a rm's own current productivity in the product line, zj, rather than an increase

that is proportional to that current productivity. A similar specication is used by Akcigit

(2009). This simplies the model, and yields a clear prediction on nancial constraints'

impact on optimal R&D investment.

External Innovation External innovation is conducted by both incumbents and potential

new entrants, to obtain product lines they do not currently own. I discuss the case of new

entrants below. An incumbent with n > 0 product lines, produces nhx external patents by

spending nRx units of nal goods. It can then take over the previous producer's product

20

line with a Poisson ow rate of nhx. Rx is dened as:

Rx = xxhψxx n

αxZ

where xx > 0 is a scalar to facilitate calibration, and ψx > 1 is the cost elasticity of external

R&D input. Like internal innovation, external innovation is linear in aggregate productivity,

Z, indicating that when aggregate productivity is higher, replacing another rm's product

line becomes harder. In addition, αx governs the degree of return to scale. If αx = 0, we

have the Klette and Kortum (2004) model, where external innovation perfectly scales up

with rm size. αx > 0 we have the case studied by Akcigit and Kerr (2018), where a rm's

external innovation intensity decreases sharply with its size. This latter case is consistent

with the empirical ndings in Table 1.

As external R&D eorts are undirected, innovation can be realized for any product line

j in rm s with equal probability. Let product line j's productivity be zj when owned by

rm s. Upon a successful external innovation and taken over by the rm s, the line is taken

over by rm s, and the productivity of that line is increased to zj + νZ. Successful external

innovation extends a rm's current product lines into nf (t + ∆t) = nf (t) + 1 and the he

productivity portfolio into zf (t+ ∆t) = zf (t) ∪ zj + νZ.

Financial Constraint. Total R&D expenditure for an incumbent intermediate goods pro-

ducer with product line nf is Rnf =∑nf

j=1Rdj +∑nf

j=1 RIj + nfRx units of nal goods. I

discuss the case of new entrants below. As rms undertake R&D before production occurs,

each monopoly producer has to collateral its current product lines to generate cash ow. I

assume the collateral constraint is static, and the value of rm's collateral has two compo-

nents: 1) The value of rm's one-period cash ow without patenting κnZ 10 and 2) the value

of industrial design patenting∑nf

j=1 H(hdj), where H(hdj) increases with hdj and is deter-

mined in equilibrium. The collateral value of industrial design comes from the assumption

10Assume there is an information asymmetry between the monopoly producer and the lender. The lendercannot verify and observe rm's average productivity, zf . Hence, it evaluate rm's one-period cash owbased on average productivity Z. Once a rm is default on paying back the borrowing, the lender has tooccur a recovery cost to take all of the rm's collateral. κ is the lender's evaluation of rm's product linesafter considering this recovery cost. See Appendix A.2 for details.

21

that its outcome is certain. Through a limited enforcement argument 11, a rm's total R&D

expenditure Rnf is limited by a multiplier, µ, times its collateral value:

Rnf (t) ≤ µ

[nf∑j=1

H(hIj) + κnZ

](3)

In (3), µ measures the degree of credit market imperfection: µ = ∞ implies a perfect

credit market and µ = 1 implies that all R&D expenditure needs to be self-nanced by

each intermediate goods producer. H(hdj) increases with hdj. Patenting in industrial design

not only increases a rm's instantaneous prot, but also relaxes its nancial constraints by

raising its collateral value.

3.3 Entry, Exit and Resource Constraint

New entrants can invest in external R&D to become monopoly intermediate producers upon

successful innovation. Let the Poisson arrival rate of a successful innovation be he and the

corresponding R&D cost be Re = xeheZ. xe measures the entry cost. A new entrant's

optimization problem is:

rV0 − V0 = maxhe

he[EjV (zj + νZ)− V0

]−Re

where V0 is a new entrant's the expected value of successful innovation and V (zj + νZ) is

the value of a rm of one product line with productivity of zj + νZ. Notice that entrants

do not face nancial constraints when enter the market. As my analysis only focuses on the

relationship between nancial constraints and innovation composition among incumbents.

Analyzing nancial constraints' impact on entry is not a major focus of this paper.

Through external innovation, incumbents and potential new entrants expand into new

product lines, and some incumbents lose current product lines. Let τ be the aggregate

creative destruction rate faced by each product line. It is endogenously determined through

incumbents and new entrant's R&D decision on external innovation. A rm is assumed to

11see Banerjee and Newman (2003), Buera and Shin (2009) and Moll (2014) for similar motivation

22

exit the market if it loses all of its product lines.

The economy is closed by assuming that labor market clears and resource constraint

holds. Labor market clearing implies:

L = Lf (t) +

∫ 1

0

ljdj

where Lf (t) is labor employed in the nal goods sector and lj is labor demand by the producer

of intermediate goods j. The resource constraint at time t is

Y (t) = C(t) +∞∑n=1

MηnRnf (t) +Re(t)

Here, M is the total measure of rms, and ηn is the proportion of rms with n product lines.

The rm size distribution parameter ηn and M are endogenously determined. Rnf (t) is the

total R&D expenditure of an intermediate goods producer f with n > 0 product lines. Re

is the total R&D expenditure by new entrants.

3.4 Equilibrium and Balanced Growth Path

In this section, I characterize agents' optimization problems and corresponding policy func-

tions. Then I solve for the model's balanced growth path, on which the aggregate variables

Y , w, Z, C, Rf and Re grow at the constant rate g.

Household The optimization problem of a representative household yields the Euler Equa-

tion: CC

= r− ρ. On a balanced growth path where consumption grows at a constant rate g,

asset returns are endogenously determined as g = r − ρ.

Producers The nal goods producer's optimization problem generates a demand function

for labor: w = σ1−σL

f,σ−1∫ 1

0Aσj q

1−σj dj; , and an inverse demand function for each variety j

as: qdj = p− 1σ

j LfAj. The marginal cost for each intermediate goods producer j is w

Zzσ

1−σj

.

Intermediate goods producers compete in a monopolistic market. Given the inverse de-

23

mand function for intermediate good j, the prot maximization problem of each monopolist

gives the optimal quantity and price for that intermediate good j:

p∗j =w

(1− σ)Zzσ

1−σj

, q∗j =

w

(1− σ)Zzσ

1−σj

− 1σ

LfAj (4)

Each intermediate goods producer charges the monopolistic price p∗j which is a constant

markup 11−σ over its marginal prot. In addition, note that q∗j is linear in the demand shifter

parameter Aj = A0(1 + φ(hdj)), while p∗j decreases in the rm's productivity zj as well as

aggregate productivity Z. Internal and external innovation increase the optimal quantity

produced of product line j, q∗j by decreasing its optimal price p∗j . Industrial design has a

direct impact on the optimal quantity q∗j through the demand shifter Aj.

Equilibrium wages and output Equation (4) together with the nal good producer's

optimal labor demand pin down the equilibrium wage rate in the economy.

w = σσ(1− σ)1−2σA[1 + Φ]σZ (5)

where A = Aσ0 and Φ =∑∞

n=1Mηnnhdn is aggregate patenting in industrial design, and hdn

is the total number of industrial design patents in a rm with n > 0 product lines. Notably,

Φ is constant on a balanced growth path (I show this below). Higher aggregate industrial

design increases the equilibrium wage through an increase in the nal good producer's output

and labor demand. From equation (4), the increase in the equilibrium wage raises the price

if each intermediate good and reduces the optimal quantity q∗j .

Imposing the labor market clearing condition, L(t) = Lf (t) +∫ 1

0ljdj labor demand and

output for the nal goods are:

Y =σσ(1− σ)1−2σ

(1− σ)2 + σALZ [1 + Φ]σ , L =

σ

(1− σ)2 + σL (6)

24

Producer's Prot Given equilibrium wages and labor demand, intermediate good pro-

ducer f 's prot is

πf =

nf∑j=1

σpjqj = π(1 + Φ)σ−1

nf∑j=1

(zj + hdjZ)

where π = σσ+1(1−σ)2−2σ

(1−σ)2+σAL is a scalar and independent of state variables z, nf and Z. Firm

f sales are salef =πfσ. Both sales revenue and prot are decreasing in aggregate industrial

design, Φ, and increasing in rm f 's own productivity and in its industrial design patenting

hdj. As σ < 1 the term (1 + Φ)σ−1 captures a negative spillover eect from other rms '

industrial design patenting activities. As a result, rms have an incentive to patent in

industrial design to avoid losing market share.

Prot, πf , is linear in hdj. π(1+Φ)σ−1∑nf

j=1 Z can thus be viewed as the marginal benet

of patenting one additional unit of industrial design. The collateral value of industrial design

for rm f in equation (3) is equal to H(hdj) = π(1 + Φ)σ−1∑nf

j=1 hdjZ. The value of the

rm's industrial design patenting decreases with aggregate industrial design activity, Φ, as

higher Φ reduces rms' prot by raising equilibrium wages, and lowering demand from the

nal good producer. Given the collateral value of industrial design, the Appendix A.2.2

shows that the collateral value of a rm's product lines equals a multiplier times a rm's

per-period prots without innovation. That is: κ = 1−Φ2π(1 + Φ)σ−1.

Value Function and R&D choices Research input is determined by an intermediate

good producers optimization of its discounted future value. Let V (z, n) be rm's value with

n product lines and productivity portfolio z. Given the equilibrium value of τ ∗, r∗ and g∗, a

25

rm chooses optimal R&D eort hdj, hIjj∈nf and hx to maximize the value,

r∗V (z, n)− V (z, n) = maxhdj ,hIjj∈nf ,hx

n∑j=1

[π(1 + Φ)σ−1(zj + hdjZ)− xdhψddj n

αdZ]

+n∑j=1

[hIj[V (z \ zj ∪ (zj + λZ), n)− V (z, n)

]− xIhψIIj n

αI Z]

+ nhx[EiV (z ∪ (zi + νZ), n+ 1)− V (z, n)

]− xxhψxx nαx+1Z

+n∑j=1

τ [V (z \ zj, n− 1)− V (z, n)]

s.t. xxhψxx n

αx+1Z +n∑j=1

[xdh

ψddj n

αdZ + xIhψIIj n

αI Z]≤ µ

[n∑j=1

hdjπ(1 + Φ)σ−1Z + κnZ

](7)

Here, r∗ is the equilibrium interest rate. Intermediate goods producers use the same discount

rate ρ as the household. In addition, τ ∗ is the equilibrium creative destruction rate, with

ow τ ∗, the rm loses one of its product lines. The second term on the LHS implies changes

in a rm's value due to changes in aggregate conditions. The rst line on the RHS is the

instantaneous prot conditional on current patenting in industrial design. The second line is

the change in rm value after internal innovation, net of internal R&D cost. The third line

is the change in the rm's value after adding a new product line through external innovation

net of the corresponding R&D cost. The last line shows the change in rm value after losing

one of its product lines. Let the policy function of each innovation be h∗dj, h∗Ij and h∗x.

Below, I show that those policy - patenting - functions are independent of the rm's current

productivity portfolio z, but depends on the number of rm's product lines n. By this

construction, the equilibrium aggregate industrial design Φ =∑∞

n=1Mηnnhdn is constant on

a balanced growth path.

The R&D choice from new entrants can be determined through the free entry condition.

Normalize the value of the outside option as V0 = 0. Given positive entry, both the free

entry and the optimization condition for a new entrant imply:

EjV (zj + sZ) = xeZ (8)

26

Firm Size Distribution On a balanced growth path, the rm size distribution should be

stationary. The equilibrium invariant distribution can be written (see Appendix A.2.1 for

derivation):

ηn =he

M∗τ ∗

n−1∏i=1

(h∗x(i)

τ ∗

)1

n(9)

where ηn ∈ [0, 1]. ηn denotes the percentage of rms that own n > 0 product lines. As h∗x(i)

is independent of the productivity portfolio z, the rm size distribution is independent of

the productivity distribution. M∗ is the equilibrium mass of rms, it is solved through the

equation:∑∞

n=1 ηn = 1. τ ∗, the equilibrium creative destruction rate, is the sum of optimal

external innovation hx and the realized entry rate he: τ∗ =

∑∞n=1 M

∗η∗nnh∗x(n) + h∗e

The growth rate of aggregate productivity is determined by internal innovation eort as

well as the aggregate creative destruction rate τ . Proposition I describes it.

Proposition I: Aggregate Growth Rate Let the rm size distribution be η∗n and the

equilibrium measure of rms beM∗. Then the balanced growth rate of aggregate productivity

is

g∗ = h∗eν +∞∑n=1

M∗η∗nnh∗x(n)ν +

∞∑n=1

M∗η∗nnh∗I(n)λ (10)

On a balanced growth path, the aggregate variable Y ∗, w∗, C∗, and total R&D expenditure

R also grow at the aggregate growth rate g∗.

Proof. See appendix.

In (10), h∗x(n) and h∗I(n) are the optimal choice of external and internal innovation for

rms with n > 0 product lines. ν is the step size, i.e. productivity improvement per

unit of innovation for external innovation, and λ is the step size for internal innovation.

The aggregate growth rate depends on rm size distributions, as both h∗x(n) and h∗I(n)

depend on rm size. The aggregate growth rate can be decomposed into three parts: The

contribution from new entrants, the contribution from incumbents' internal innovation and

the contribution from incumbents' external innovation. If total innovation eort - nh∗x and

nh∗I - increases with rm size, large rms contribute more to this aggregate growth rate.

27

Given the aggregate growth rate g∗, I normalize (de-trend) a rm's value V and produc-

tivity as V = VZand z = zj

Z: j ∈ n. The value function in equation (7) can then be

rewritten in terms of the new state variable z and V (z, n) = −gV (z, n) + g∑n

j=1∂V (z,n)∂z

zj.

The following assumptions guarantee the existence of the value function and the rm's value

satisfying the transversality condition: limt→∞

[e−

∫ t0 rsdsV (z, n)

]= 0

Assumption I Parameter values satisfy ψd − 1 ≥ αd ≥ 0, ψI − 1 ≥ αI ≥ 0 and ψx − 1 ≥

αx ≥ 0.

Under assumption I, the following proposition holds; the value function can be expressed

in a tractable form, and is bounded above, and well behaved.

Proposition II Let assumption 1 hold, and let the entry rate be positive, he > 0. Then

i) an intermediate producer's value function can be written as:

V (z, n) = Bn∑i=1

zi +Bn

where B = πρ+τ+g

(1 + Φ)σ−1 and Bn is a function of n, and the solution to the problem

ρBn = maxhd,hI ,hx

nπ(1 + Φ)σ−1hd + nBλhI + nhx[B(1 + ν) +Bn+1 −Bn]− xdhψdd n

αd+1

− xIhψII nαI+1 − xxhψxx nαx+1 + nτ(Bn−1 −Bn)

s.t. xdh

ψdd n

αd+1 + xIhψII n

αI+1 + xxhψxx n

αx+1 ≤ µnπ(1 + Φ)σ−1hd + µnκ

ii) Bn is an increasing function of n and bounded above.

iii) Bn+1 −Bn decreases in n.

Proof. See Appendix

B is the average de-trended value of product line j. It is the discounted sum of future

prots from the line, in the absence of innovation. B decreases with aggregate patenting

in industrial design (Φ). The higher the elasticity of substitution between dierentiated

28

intermediate goods (σ), the more negative the impact from other rms' industrial design

patents on a rm's current prot. Recall that a rm's collateral value in equation (3)

depends on the prot margin generated by industrial design as well as per-period prot ow

π(1 + Φ)σ−1. Thus, a higher Φ not only negatively aect a rm's instantaneous prot πf ,

but also tightens its nancial constraints by lowering the collateral value of its product lines.

Bn denotes a rm's value in conducting innovation activities. The above proposition states

that there's a decreasing returns to scale in a rm's value function. The marginal benet of

expanding product lines in large rms is smaller than that in small rms.

Let ϕn ≥ 0 be the Lagrange multiplier on nancial constraint for a rm with n product

lines. The optimal R&D intensity for each product line can be expressed as

h∗d =

(π(1 + Φ)σ−1

xdψd

1 + µϕn1 + ϕn

) 1ψd−1

nαd

h∗I =

(λB

xIψI

1

1 + ϕn

) 1ψI−1

nαI

h∗x =

(B(1 + ν) +Bn+1 −Bn

xxψx

1

1 + ϕn

) 1ψx−1

nαx

(11)

where αd = − αdψd−1

< 0, αI = − αIψI−1

< 0 and αx = − αxψx−1

< 0. The multiplier ϕn is then

dened through the nancial constraint,

µκ+ µπ(1 + Φ)σ−1h∗d = xdh∗ψdd nαd + xIh

∗ψII nαI + xxh

∗ψxx nαx (12)

A rm that faces a more severe nancial constraint has a higher value of ϕn. I therefore

use ϕn to measure rm-specic nancial friction. For unconstrained rms, ϕn = 0. The

optimal R&D choices all decrease in n. The return to scale parameters αd, αI and αx plays

a crucial role at shaping the negative relationship between rm size and R&D intensities.

Now consider the case where the αs are all equal to zero. Then ϕn is independent of n.

Given the value of µ, either all rms are nancially constrained or all rms are nancially

unconstrained. The model is then equivalent to that studied by Klette and Kortum (2004),

where Bn = Bn for B > 0. That is, the benet of acquiring one additional product line is

constant across rm size. Thus, h∗d, h∗I and h

∗n are constant across rms. R&D expenditure

29

on all types of innovation perfectly scale with rm size.

Given the optimal R&D choices, it is easy to verify that the aggregate R&D expenditure

R ≡∑∞

n=1 M∗η∗nR

∗n +Re is linear in aggregate productivity, Z. Equations (5) and (6) show

that the equilibrium wage and aggregate output are linear in Z. Thus, from the resource

constraint, consumption C is also linear in Z. The aggregate variables Y , C, w and R all

therefore grow at the same rate as Z: g∗ = CC

= YY

=˙RR

= ww

=˙ZZ, where, g∗ is dened

in proposition I. Aggregate h∗d, h∗I and h∗n, on the other hand, are constant on a balanced

growth path. Hence, Φ =∑∞

n=1 M∗η∗nnhd(n) is also constant on a balanced growth path.

Another requirement for a balanced growth path equilibrium is positive entry. That is

the entry cost xe < B + B1. This condition implies that the cost of entry should less than

the gain from acquiring the rst product line. As the model does not have an analytical

solution for B1, I ex-post check the condition xe < B + B1 in my computational analysis. I

now dene a balanced growth path equilibrium.

Denition 1 (Balanced Growth Path Equilibrium) A Balanced Growth Equilibrium

Path is

p∗j(t), q∗j (t), l∗j (t), h∗dj(t), h∗Ij(t), h∗x(t), h∗e(t), Lf∗(t), Y ∗(t), C∗(t), w∗(t),Φ∗(t), r∗, g∗, η∗n,M∗

such that: 1) Given the wage, Y ∗(t) and L∗(t) solve the nal goods producer's problem and

Y ∗(t) and L∗(t) satisfy equation (6); 2) l∗j (t), q∗j (t) and p∗j(t) solve the intermediate goods

producer's problem and q∗j (t) and p∗j(t) satisfy equation (4); 3) optimal R&D intensities

h∗dj, h∗Ij and h∗x in equation (11) solves the value function in equation (7); 4) h∗e satises

the free entry condition of equation (8); 5) the invariant distribution of rm size and the

equilibrium mass of rms satisfy equation (9); 6) the balanced growth rate satises (10); 7)

the equilibrium interest rate satises: g∗ = r∗ − ρ; 8) the aggregate industrial design, Φ,

satises Φ =∑∞

n=1 M∗η∗nnhd(n); 9) the equilibrium wage w∗ in equation (5) clears the labor

market; and 10) resource constraint holds.

30

3.5 Analytical Results

The following propositions lay out the main analytical results and show that the model

is qualitatively consistent with the facts that I document in Section 2: 1) Firms shift from

productivity-enhancing to industrial design when nancial constraints tighten; 2) small rms

are more likely to be nancially constrained, and 3) nancial constraints lowers a rm's

growth rate.

Proposition III (Firm Size and Financial Frictions) Large rms face a lower rm-

specic nancial friction ϕn. That is, ϕn decreases with rm size n.

Proof. Take derivatives with respect to n on each side of a rm's nancial constraint (12)

and rearranging:

dϕndn

=1

n

αIR∗I(1 + ϕn) + αxR

∗x(1 + ϕn) + αdψdR

∗d

1+ϕn1+µϕn

[(µ− 1

ψd) + µϕn(1− 1

ψd)]

R∗IψIψI−1

+R∗xψxψx−1

+(

µ−1(1+µϕn)

)2

R∗dψdψd−1

< 0

The numerator is negative as µ ≥ 1 > 1ψd

and αd < 0, αI < 0 and αx < 0.

As ϕn decreases with n and is bounded below by 0, large rms are more likely to be

nancially unconstrained. The decreasing return to scale parameters αd, αI and αx are

important in shaping the relationship between ϕn and n. If R&D cost scales perfectly with

rm size (i.e. in the case of αd = αI = αx = 0), ϕn is independent of n. If one of these αs is

greater than zero, total R&D intensity decreases with rm size. Thus, a rm with relatively

larger size undertakes less investment per product line, relies less on external nance, and is

less likely to be nancially constrained.

Proposition IV (Financial constraint and innovation intensity) Let h∗d, h∗I and h

∗x

be a rm's optimal innovation intensities. For nancially constrained rms: 1) An increase

in credit market imperfectness, a reduction in µ, reduces productivity-enhancing innovation;

2) if the elasticity of ϕn satisesdϕndµ

µϕn< − µ

µ−1(1 +ϕn), a reduction in µ increases industrial

design patenting. Otherwise, innovation intensity in all categories increases with µ.

31

Proof. Once rm is nancially constrained (ϕn > 0), ϕn is determined through a rm's

collateral constraint. Take derivatives with respect to µ on each side of the equation (12)

and rearrange it:

dϕndµ

= (1 + ϕn)−κ− ψdR∗d

1+ϕn1+µϕn

− ψdψd−1

R∗dµ−1

1+µϕn1

1+µϕn

R∗IψIψI−1

+R∗xψxψx−1

+(

µ−1(1+µϕn)

)2

R∗dψdψd−1

< 0

The left hand side of this expression is negative if µ ≥ 1. A higher µ implies lower nancial

constraint. Hence, as ϕn decreases with µ, ϕn is positively related to the degree of a rm's

nancial constraint. Then, for each innovation intensity measure,

dh∗xdµ

=− h∗x1

1 + ϕn

1

1− ψxdϕndµ

> 0

dh∗Idµ

=− h∗I1

1 + ϕn

1

1− ψIdϕndµ

> 0

dh∗ddµ

=h∗d1

1 + µϕn

1

ψd − 1

[µ− 1

1 + ϕn

dϕndµ

+ ϕn

]< 0 if

dϕndµ

µ

ϕn< − µ

µ− 1(1 + ϕn)

This proposition shows that productivity-enhancing innovation intensity is negatively

related to the degree of a rm's nancial constraint. A higher credit market constraint (a

lower µ) increases a rm's marginal cost of innovating. Thus, it reduces rm's incentive to

conduct both internal and external innovation. However, it is ambiguous how µ aects a

rm's industrial design patenting. First, for the self-nanced rm (µ = 1), industrial design

is independent of credit market imperfection. When µ is close to 1,dh∗ddµ≈ ϕn

1+µϕn

h∗dψd−1

> 0.

Thus, relaxing a nancial constraint from µ = 1 would increase patenting in industrial

design. Second, in the case of µ > 1, whether hd increases or decreases with µ depends on

the elasticity of ϕn with respect to µ. A reduction in µ increases a rm's marginal cost as

well as the marginal benet of patenting industrial designs. When ϕn is more elastic, a unit

decrease in µ would cause more than a unit change in ϕn. Thus, a rm has an incentive

to undertake industrial design. In appendix A.2.4 I show that a sucient condition for

dϕndµ

µϕn

< − µµ−1

(1 + ϕn) under a quadratic cost function (i.e. ψd = ψI = ψx = 2) is that

ϕn ≤ 12µ−1µ. As shown in proposition III, ϕn decreases with n. Thus, a relatively large

32

constrained rm reduce patenting in industrial design by more when its nancial constraint

is relaxed. However, for small constrained rms with high value of ϕn, industrial patenting

increase with µ.

This result also implies that changes in µ shift a rm's innovation composition. If the

elasticity of ϕn is large enough, a reduction in µ forces a rm to shift from productivity-

enhancing innovation into industrial design patenting. To see this, consider the case where all

R&D cost functions are quadratic in innovation intensity (i.e. ψd = ψI = ψx = 2). Then the

industrial-design/internal innovation ratio and industrial-design/external innovation ratio

are:h∗dh∗I∝ 1 + µϕn and

h∗dh∗x∝ 1 + µϕn. If dϕn

dµµϕn

< −1, both ratios decrease with µ. The

following corollary summarize this result.

Corollary I (Financial constraint and innovation composition) If ψd = ψI = ψx

and if the elasticity of ϕn satises:dϕndµ

µϕn< −1, a rm shift out of its productivity-enhancing

innovation into industrial design patenting if its nancial constraint tightens.

Notice that as µµ−1

(1 + ϕn) > 1, oncedh∗ddµ

< 0 is satised, it must be true thath∗dh∗I

andh∗dh∗x

decrease with µ. Under quadratic innovation costs, dϕndµ

µϕn

< − µµ−1

(1 + ϕn) is not necessary

to guarantee such shift in innovation composition. Even if all types of innovation intensity

decrease with a reduction in µ, innovation composition can shift in favor of industrial design

as long as the decrease in industrial design is less than the decrease in internal and external

innovation. In Appendix A.2.4, I show that one sucient condition for dϕndµ

µϕn< −1 is ϕn ≤ 1.

As ϕn decreases with n, constrained rms with relatively large size would be most likely to

meet this condition. Thus, constrained large rms would shift their productivity-enhancing

innovation into industrial design if their nancial constraints tighten.

The rm's growth rate depends on its productivity-enhancing innovations. If a rm shifts

its innovation composition in favor of industrial design when its nancial constraint tightens,

its growth rate will decline. Let zf =∑nf

j=1 zj be the total productivity of a rm with nf

product lines, the following proposition states the relationship between nancial constraints

and the rm productivity growth rate, gf =zfzf.

33

Proposition V Financial constraints lowers rm's productivity growth rate, gf , and mit-

igates the negative relationship between rm size and rm growth.

Proof. Given a rm's optimal R&D decision, its productivity g rate can be written as:

gf =zfzf

= lim∆→0

zf (t+ ∆t)− zfzf

=1

zf[λh∗I + (1 + ν)h∗x]

where zf =zfnf

is the average productivity of rm f . And we have:

dgfdµ

=− 1

zf

[h∗x

1

1− ψx+ h∗I

1

1− ψI

]1

1 + ϕn

dϕndµ

> 0

dgfdnf

=1

zf

[λh∗I

αInf

+ (1 + ν)h∗xαxnf

]− 1

zf

dϕndnf

1

1 + ϕn

[λh∗IψI − 1

+(1 + ν)h∗xψx − 1

]

The rst term on the right hand side ofdgfdnf

is negative due to the decreasing returns to

scale in internal and external innovation. It governs the relationship between rm size and

rm growth when a rm is nancially unconstrained. The last term on the right hand side

ofdgfdnf

is positive, since −dϕndn

> 0. Thus, the existence of nancial constraints mitigates an

otherwise negative relationship between rm size and rm growth.

This proposition implies that nancial constraints lower a rm's growth rate through a

reduction in investment in internal and external innovation. It also implies that when rms

are all nancially constrained, a large rm might not necessarily have lower growth rate even

though productivity-enhancing innovation intensity decrease with rm size. If ϕn is elastic

enough, the cost of internal and external innovation would drop rapidly as rms grows larger.

Thus, large rms invest more in productivity-enhancing innovation to increase their growth

rate. The term dϕndnf

11+ϕn

captures the eect of cost reduction. If λ and ν is large enough,

even though internal and external intensity decreases with rm size, a positive relationship

between rm size and rm growth can still hold. This is captured by the termλh∗IψI−1

+ (1+ν)h∗xψx−1

.

As λh∗IαInf

+ (1 + ν)h∗xαxnf

captures the eect from decreasing returns to scale, if it oset the

eect of cost reduction, a rm's growth rate is then independent of rm size. This result

is also found by Klette and Kortum (2004) and consistent with Gibrat's law. If the eect

from decreasing returns to scale outweighs the eect of cost reduction, a rm's growth rate

34

is negatively related to its rm size. However, if the eect from cost reduction outweighs the

eect from decreasing return to scale, large rms could grow faster than small rms.

4 Quantative Analysis

In this section, I calibrate the model using the data discussed in section 2. Specically, I rst

solve the model on a balanced growth path using the uniformization method described in

Acemoglu and Akcigit (2010) 12. Then I match empirical moments and regression coecients

with model-implied moments and regression slopes from the simulating the solved model.

4.1 Calibration Strategy

The model has 17 parameters to be identied: L, A, ρ, σ, ψd, ψI , ψx, µ, xd, xI , xx, xe, αd, αI , αx, λ, ν.

Some of them are calibrated externally to match aggregate moments in the data or from the

extant literature. The remaining are calibrated by targeting relevant moments for rms in

the sample.

4.1.1 Externally Calibrated Parameters

The parameter ρ is the discount rate. I set ρ equals 0.04 to match the annual discount factor

of 0.96 in China. The parameter σ measures the quality share in nal goods production.

The theoretical model implies that σ can be expressed as σ =πfsalef

. I set σ = 0.144

to match the average prot to sales ratio in all private rms in the sample of section 2.

The parameters ψd, ψI and ψx measure the curvature of industrial design, internal, external

innovation respectively. I take these values from Akcigit and Kerr (2018), setting them equal

to ψd = ψI = ψx = 2. This implies that the elasticity of patenting with respect to R&D

expenditure is around 0.5, which is supported by many empirical papers (Blundell, Grith,

and Windmeijer (2002) and Acemoglu, Akcigit, Alp, Bloom and Kerr (2019) for examples). L

is normalized to 2. Using my theoretical results, the median sales for intermediate producer

12see Appendix A.3 for detail

35

without patenting in industrial design is σσ+1(1−σ)2−2σ

(1−σ)2+σAL, , which is linear in A. Thus, I

choose the level A = 3.421 to roughly match with the median of real sales for rms without

industrial design patenting the sample.

4.1.2 Indirect Inference

The remaining 10 parameters Θ = µ, xd, xI , xx, xe, αd, αI , αx, λ, ν are calibrated via in-

direct inference approach. Θ is estimated by minimizing the following value using several

model-implied moments from simulation, and data-generated moments:

Θ = argminΘ

10∑k=1

‖model(Θ)k − datak‖12‖model(Θ)k‖+ 1

2‖datak‖

With a guess of Θ, the model is solved using uniformization method (see Appendix A.3 for

the solution algorithm). The value of moment k ∈ 1, · · · , 10 is computed by simulating

the model. datak is the corresponding moment k from data. Θ is estimated by minimizing

the above criteria. The model is simulated using 8, 192 rms and discretizes time to T = 150

periods with time interval ∆t = 0.02. Since the model does not have a closed-form solution, I

cannot express model-simulated moments in analytical form. Below I provide some intuition

for my choice of moments.

Entry cost Consider the case where innovation intensity is independent of rm size. From

equation (9), it is easy to verify that ∂hx∂τ

< 0, and ∂he∂τ

> 0. As the creative destruction rate

decreases with entry cost xe, the entry rate he also decreases with the entry cost. Higher

entry rate implies a lower entry cost. The entry rate can then be used to identify entry

cost. Entry rate he = 0.076 is computed following Song and Hsieh (2015), dened as "the

number of new private rms created in a year relative to the number of all private rms in

that year". The implied entry cost is then xe = 5.542 in the sample.

Return to scale Consider the case without nancial constraints, where ϕn = 0. From

the rm's optimal choice (11), the return to scale parameters αd, αI and αx, govern the

36

Table 4: Parameters

Parameter Description Value Identication/SourcePanel A: External Calibrated

ρ discount Rate 0.04 annual discount factorσ substitution elasticity 0.144 prot to sales ratioA aggregate demand shifter 3.421 median of rm sales: 4.643L total labor supply 2ψd curvature of industrial design 2 quadratic cost functionψl curvature of internal innovation 2 Akcigit and Kerr (2018)ψx curvature of external innovation 2 Akcigit and Kerr (2018)

Panel B: Indirect Inferencexd scale of industrial design 1.256

R&D Intensity andPatent Shares

xI scale of internal innovation 0.148xx scale of external innovation 4.294xe entry cost 5.542 entry rateαd return to scale in industrial design 0.379

intensity-sizeregression coe.

αI return to scale in internal innovation 0.508αx return to scale in external innovation 0.358λ productivity multiplier of internal innovation 0.084

citation ratio andgrowth rateν productivity multiplier of external innovation 0.109

µ credit market imperfectness 1.256 growth-size regression

relationship between optimal R&D intensity and rm size. A higher value of an α generates

a more negative relationship between optimal R&D intensity and rm size. If αd = αI =

αx = 0, innovation intensity h∗d, h∗I and h

∗x are independent of rm size. Hence, the αs can be

identied by matching the intensity-size regression coecients using date generated from the

simulated model to the same intensity-regression coecient using empirical date in section

2. The value of the regression coecients can be found in Table A6 in the Appendix.

My estimation on αs nds decreasing returns to scale in all types of innovations. Speci-

cally, αd = 0.311, αI = 0.246 and αx = 0.323. Firm size has the greatest negative impact on

internal innovation and the least negative impact on industrial design. Internal innovation

drops most rapidly when a rm grows larger, making external innovation share increases.

This is opposite to the ndings of Akcigit and Kerr (2018) and others; there, process inno-

vation is tightly linked to rm size (Cohen and Klepper (1996)).

37

Productivity multiplier Equation (10) shows that, given optimal R&D investment, the

equilibrium growth rate g∗ increases with the productivity multipliers, λ and ν. If higher

citations imply a larger productivity improvement, the citation ratio of internal versus ex-

ternal patents in the data can be used to discipline the relationship between the parameters

λ and ν. Thus, I calibrate the relative value λνusing the average internal versus external

citation ratio in my data. During the sample period, I nd λν

= 0.765 for all private rms.

The theoretical result implies that g∗ = τ ∗ν + Γλ, where Γ =∑∞

n=1M∗ηnnhI(n) is the

aggregate internal innovation. Thus, given the citation ratio, λν

= 0.765, the absolute value

of λ and ν can identied by matching the model implied aggregate growth rate g∗ to the

average annual growth rate in the data sample. On a balanced growth path, the equilibrium

growth rate g∗ equals the growth rate of aggregate total factor productivity. To measure this,

I rst compute each rm's total factor productivity, and following David and Venkateswaran

(2019) to remove the impact of labor distorion issues in the Chinese manufacturing data.

I them compute annual aggregate TFP growth following Foster, Haltiwanger, and Krizan

(2001)'s aggregation method 13. Lastly, I compute the equilibrium aggregate growth rate

g∗ as the geometric mean of annual aggregate TFP productivity growth during the sample

years. The computed aggregate growth rate for all private innovative rms is 4.5 percent.

This is slightly higher than Zhu (2012)'s computation of 3.7 percent for non-state rms, as

I include only innovative rms (those that patent at least once) in the sample.

Scale of innovation The scale parameters, xd, xI and xx govern the share of industrial

design, internal and external innovation as well as R&D intensity. From a rm's nancial

constraint (12) and optimal R&D choice (11), an increase in xd would lower a rm's invest-

ment share in industrial design, regardless of whether a rm is constrained or not. Similarly,

13As the model does not have capital accumulation, in order to remove the eect from capital deepeningon the output growth rate (Chang, Chen, Waggoner and Zha (2016) nd that capital deepening contributes73.9% growth in GDP per capita in China from 1998 to 2011), I use TFP instead of labor productivity toestimate productivity growth during the sample period. Productivity is calculated as ln(zit) = vait − αkitwith α = 0.62. va is the log of real value added and k is the log of real capital stock after removing all year andindustry xed eect. I The aggregate TFP ln(Z) is then computed as value-added weighted sum of individual

productivities: ln(Zt) =∑

i θQit ln(zit). Then the growth rate of aggregate productivity is adjusted for rm's

entry and exit: ∆ln(Zt) =∑

i∈survivor

[θQit ln(zit)− θQit−1ln(zit−1)

]+∑

e∈entrant θQet

[ln(zet)− ln(Zt−1)

]−∑

e∈exit θQxt−1

[ln(zet−1)− ln(Zt−1)

]where θQit is the share of real value added in gross value added.

38

an increase in xI (or xx) lowers the internal innovation share (or external share) in total

innovation. Thus, I use industrial design and internal innovation shares, and measured R&D

intensities to x the scale of each type of R&D expenditure. The average R&D intensity in

my sample is 2.9% for all innovative private rms. The industrial design and internal inno-

vation share are 33.3 percent and 33 percent for all innovative private rms. The estimated

scale parameters are then: xd = 1.088, xI = 0.137 and xx = 3.935.

Financial constraints For nancially constrained rms, µ aects the available cash ow

for a rm to invest. A higher µ indicates less nancial friction (lower ϕn) and encourages

investment in internal and external innovation. Hence, µ alters the relationship between rm

growth and rm size as discussed in Proposition V. A higher nancial friction mitigates the

negative relationship between rm growth and rm size. Thus the coecient on rm size from

the growth-size regression is highly sensitive in µ. µ can hen be identied by matching the

growth-size regression coecient using date generated from the simulated model to the same

growth-size coecient using empirical date in section 2. The value of the empirical regression

coecient can be found in Table A6 in the Appendix. The estimated µ is µ = 1.256.

4.2 Result

Table 4 lists a full set of calibrated parameter values. Table 5 shows the value of simulated

moments, compared to the values generated in the data. Overall, the model closely matches

the targeted moments except for the R&D intensity and entry rates. The R&D to sales

ratio is higher in the model than in the data. As R&D expenditure is available only in the

year 2005 to 2007 and the year 2010, the average R&D to sales ratio in the sample might

underestimate a rm's true R&D intensity. The entry rate is also slightly higher in the model

than in the data. The ASM data only contains medium to large scale rms, so the estimated

entry rate only reects a rm entered as a medium to large scale and neglects small entrants.

The estimated entry rate in the sample can therefore be lower than the true entry rate.

The model also produces a similar rm size distribution (measured using real sales) as

the empirical one. Figure 3 compares the two distributions. The left panel is the estimated

39

Table 5: Moments

Moments Data ModelR&D intensity 2.9% 7.4%Share of internal patents 0.330 0.312Share of industrial design patents 0.333 0.308Average growth rate 4.5% 4.5%Entry rate 0.076 0.120Internal to external citation ratio 0.765 0.765industrial design patent intensity vs. size -0.110 -0.111Internal patent intensity vs. size -0.112 -0.112External patent intensity vs. size -0.061 -0.062Sales growth vs. size -0.083 -0.088

rm size distribution simulated from model and the right panel is the actual rm's size

distribution measured in real sales (millions of RMB) in the sample (from 2002 to 2013).

Firm size is heavily right-skewed. The simulated distribution is slightly more widely spread

than the empirical distribution. The lower left panel of gure 3 shows that rm value Bn

increases with the number of product lines a rm owns, but at a decreasing rate. Bn also

reects a rm's value in conducting innovation. This result therefore implies that the gain of

innovation becomes smaller as a rm grows larger. ϕn decreases with the number of product

lines. Consistent with proposition III, small rms faces more severe nancial constraints. In

more simulated model ϕn becomes zero once a rm owns more than 12 product lines. This

is the model-implied threshold for a rm being nancially unconstrained. Once a rm is

nancially constrained, the share of patenting in industrial design decreases with rm size.

As stated in section 3, nancially constrained rms rely on patenting in industrial design to

generate instantaneous prot and relax their nancial constraints. Thus, the more severe

nancial constraint a rm faces, the more patenting in industrial design it will conduct. As

seen above, the return of investment in industrial design suers less from decreasing return to

scale (αd is smaller than αx and αI), so the share of patenting in industrial design increases

with rm size once rm become nancially unconstrained. In my simulation, only 0.012

percent of rms own more than 12 product lines. That is, most of the rms in the simulated

sample are nancially constrained. Hence, the negative relationship between rm size and

the share of industrial design dominates.

40

Figure 1: Firm Size Distribution and Firm Value

0.1

.2.3

Fra

ction

0 2 4 6 8 10Firm Size Distribution (in 10 Million real RMB)

2 4 6 8 10 12 14

Number of Product Lines

3

4

5

6

7

8

9

10

11

12

13

0

0.2

0.4

0.6

0.8

1

1.2

1.4

2 4 6 8 10 12 14

Number of Product Lines

0.25

0.3

0.35

0.4

Note: Upper left panel is the estimated rm size distribution from the model the upper right panel is theactual rm size distribution in my data. The lower left panel is the relationship between rm size, rm valueand rm-level nancial distortion ϕn from simulated model and the lower right panel is the relationshipbetween rm size and patent share in industrial design from simulated model

41

Growth Rate Decomposition I use the estimated parameters to decompose the aggre-

gate growth rate into three parts: 1) growth from new entrants, 2) growth from incumbents'

internal innovation and 3) growth from incumbents' external innovation. Column (2) in

Table 6 presents the result. In the calibrated model, the aggregate growth rate is 4.5 percent

annually. Of this, 47.6 percent derives from external innovation conducted by the incum-

bents, 38.9 percent derives from internal innovation conducted by the incumbents, and the

remaining 13.4 percent is contributed by new entrants. The productivity multiplier of in-

ternal innovation is smaller than external innovation. The estimated productivity multiplier

for internal innovation is λ = 0.095; whereas estimated productivity multiplier for external

innovation is ν = 0.125. Thus, on average, external patents have about 31.5 percent higher

impact for productivity than internal innovation. This is consistent with the nding in Table

3 that internal innovation empirically contributes less to rms' growth than external innova-

tion. However, the estimation of cost scalar parameters xs shows the R&D cost parameter

for external innovation is about 28.6 times larger than for internal innovation. Conduct-

ing internal innovation costs much less than external innovation. Thus, the contribution to

aggregate growth rate from internal innovation is mainly through the extensive margin.

Furthermore, Column (2) of Panel C in Table 6 shows that among incumbent rms,

on average, share of internal patent application is about 2.2 percent higher than share of

external patent application. As the cost of external innovation is higher for new entrant than

for incumbents, the entry rate in the economy is low. New entrants conduct less external

innovations and contribute less to the aggregate growth rate than incumbents. Column (2)

of Panel C in Table 6 documents that most of the creative destruction rate comes from

incumbent external innovation rather than new entrants' external innovation.

5 Counterfactual Analysis

In this section, I rst quantify the implications of nancial constraints and industrial design

patent on rm R&D choices and the aggregate growth rate. To do so, I perform two coun-

terfactual analyses: 1) I consider the impact of alternative values of credit market friction

42

Table 6: Growth and R&D Decomposition (Changes in Financial Constraints)

Self-Financed Baseline Increase 10% Increase 50% Unconstrained(µ = 1) (µ = 1.26) (µ = 1.38) (µ = 1.88) (µ→∞)(1) (2) (3) (4) (5)Panel A: Growth Decomposition

Aggregate Growth Rate 0.0420 0.0447 0.0461 0.0506 0.0542from incu. Ext. innov. 45.6% 48.4% 49.7% 49.8% 50.3%from incu. Int. innov. 37.4% 39.9% 42.6% 42.5% 44.5%from new entrant 17.0% 13.4% 11.9% 7.8% 5.2%

Panel B: Firm Distribution DecompositionThreshold n 24 12 10 5 0Creative destruction rate 0.241 0.250 0.254 0.266 0.275from incumbent 72.8% 78.0% 80.3% 86.5% 90.7%from new entrant 27.2% 22.0% 19.7% 13.5% 9.3%Firm Measure M 0.510 0.458 0.433 0.369 0.343Entry Rate 0.128 0.120 0.116 0.098 0.075

Panel C: R&D intensity and Innovation DecompositionR&D intensity 0.058 0.075 0.082 0.108 0.113ave. industrial design% 34.9% 33.6% 32.5% 28.2% 24.1%ave. internal% 33.6% 34.3% 35.0% 37.9% 40.7%ave. external% 31.4% 32.1% 32.5% 33.9% 35.2%

µ; 2) I compute the eects of banning industrial design patenting. Table 6 documents the

results. Second, I evaluate the R&D tax-incentive policy currently implemented in China.

5.1 The role of nancial constraint

An increase in the credit market friction tightens a rm's nancial constraint and it patent

more in industrial design. Panel C of Table 6 documents the quantitative changes. A 10

percent increase in µ (decrease in credit market friction) results in a 1.1 percent decrease in

the share of patent application in industrial design. If the nancial constraint is removed

(µ → ∞), on average, a rm's patent applications in industrial design fall by 28.3 percent.

At the same time, patent applications in both internal and external innovation increase

with µ. Column (3) in Table 6 shows that a 10 percent increase in µ would result in a 2.7

percent increase in the aggregate growth rate and most of this increase is contributed by

incumbents' internal innovation. Column (4) in Table 6 shows that the aggregate growth rate

would increase by 21.3 percent if all rms were nancially unconstrained. Again, internal

43

innovation contributes most of the increase in aggregate growth rate, because of the higher

cost of external innovation. My empirical analysis in section 2 shows that internal patents

have less external citation than external patents; and each internal innovation contribute

less to rm's growth rate than external innovation. Likewise, in the model, the contribution

to aggregate productivity growth from internal innovation is mostly at an extensive margin.

Given the number of product lines, an increase in µ reduces a rm's specic nancial

friction ϕn (see Proposition III and Figure 2 for illustration). The rst row of Panel B in Table

6 documents the threshold number of product lines, n, at which rms become nancially

unconstrained in the model. A 50 percent increase in µ reduce this threshold from 12 into

5, and 17.6 percent of rms become nancially unconstrained. In the case, when µ is set

to be 1, this threshold is n = 23. All rms in this economy are nancially constrained. An

increase in µ encourages a rm's R&D investment in productivity-enhancing innovation and

discourages its R&D investment in industrial design. As external innovation is more costly

than internal innovation, once a rm's nancial constraint is relaxed, it would undertake

more internal innovations than external innovations. The last two rows of Panel C in Table

6 document these changes.

Figure 2: Firm Size Distribution and the Value of ϕn

1 2 3 4 5 6 7 8 9 10 11 12

Number of Product Lines

0

0.1

0.2

0.3

0.4

0.5

0.6

Fra

ctio

n

= 1

=1.26

=1.88

=

1 2 3 4 5 6 7 8 9 10 11 12

Number of Product Lines

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

= 1

=1.26

=1.88

=

Note: Left panel is estimated distribution of product lines from model under dierent µ. The right panel isestimated rm-level nancial distortion ϕn under dierent µ.

Though a larger µ encourages more R&D investment among incumbents, it discourages

innovation and entry among new potential entrants. With the decrease in credit market

44

distortion, the entry rate drops and new entrants contribute less to the aggregate growth

rate. As a result, fewer rms exist in the economy and most of creative destruction rate

comes from incumbent rm's external innovations. In the case in which even incumbents

are not subject to nancial constraints, the contribution to growth from new entrant drops

from 13.4 percent in the baseline case to 5.2 percent. It is then the incumbents conduct the

most creative destruction activities.

Figure 2 also shows that the rm size distribution becomes less right-skewed once nancial

constraint is relaxed. With nancial constraints, around 48.7 percent of rms have only one

product line. The number drops to 27.2 percent if the nancial constraint is removed. In

the case without nancial constraint, rm size distribution is more spread.

To sum up, an improvement in credit market perfection would encourage more productivity-

enhancing R&D expenditure among incumbents, reduce entry, and raise the a higher aggre-

gate growth rate.

5.2 The role of industrial design patenting

Patenting in industrial design increases nal output and consumption through changes in

products qualities. However it decreases prot and sales among intermediate goods producers

by raising competition and the equilibrium wage (recall section 3.4 for this theoretical anal-

ysis). Higher aggregate patenting in industrial design Φ, results in a lower optimal quantity

of intermediate goods as well as lower intermediate producers' prot. This tightens a rm's

nancial constraint by reducing the collateral value of its product lines. Though patenting in

industrial design increase an individual rm's current prot instantaneously, this rm-level

positive eect is less than the aggregate negative eect attributable to increasing competition

and reducing prot.

To mitigate this negative aggregate eect of industrial design, I introduce an investment

tax td on industrial design patents. Table 7 records the numerical results. A rm's optimal

45

industrial design intensity reects the tax, becoming:

h∗d =

(π(1 + Φ)σ−1

xdψd

1 + µϕn(1 + ϕn)(1 + td)

) 1ψd−1

nαd

In Appendix A.2.5, I show that dϕndtd

< 0 anddh∗ddtd

< 0. That is, a higher investment tax td

lower a rms's nancial constraint, by discouraging investment in industrial design. As the

relative cost of internal and external innovation decreases, rms conduct more productivity-

enhancing innovations (see Appendix A.2.5 for the proof ofdh∗Idtd

> 0 and dh∗xdtd

> 0). The

aggregate growth rate increases by only 0.02 percent-point when the tax rate is 0.1 and it

increases by 0.08 percent-point when the tax rate is raised to 0.5. The small improvement

in aggregate growth rate implies that imposing an investment tax on industrial design is

quantitatively ineective.

Table 7: Growth and R&D Decomposition (tax on industrial design)

cost-reduced Baseline tax rate 25% tax rate 50% remove design(td = −0.1) (td = 0) (td = 0.25) (td = 0.5) (xd →∞)

(1) (2) (3) (4) (5)Panel A: Growth Decomposition

Aggregate Growth Rate 0.0442 0.0447 0.0456 0.0462 0.0500from incu. Ext. innov. 47.6% 47.6% 47.6% 47.5% 47.1%from incu. Int. innov. 38.7% 38.9% 39.3% 39.6% 41.2%from new entrant 13.6% 13.4% 13.1% 12.9% 11.6%

Panel B: Firm Distribution DecompositionThreshold n 12 11 11 10 8Creative destruction rate 0.248 0.250 0.253 0.256 0.269from incumbent 77.7% 78.0% 78.4% 78.7% 80.2%from new entrant 22.3% 22.0% 21.6% 21.3% 19.8%Firm Measure M 0.460 0.458 0.453 0.449 0.431Entry Rate 0.120 0.120 0.121 0.121 0.124

Panel C: R&D intensity and Innovation DecompositionR&D intensity 0.075 0.075 0.075 0.075 0.077ave. industrial design% 36.0% 33.6% 28.7% 25.0% 0.0%ave. internal% 32.9% 34.3% 37.0% 39.1% 53.3%ave. external% 31.0% 32.1% 34.3% 35.9% 46.7%

Consider an extreme case, where patenting in industrial design is not allowed. Column (5)

in Table 7 documents these model-implied changes. Shutting down patenting in industrial

design would increase each intermediate producer's prot, and relax its nancial constraints.

46

The aggregate growth rate would increase by 11.8 percent, which is 0.53 percentage-points

higher than the baseline growth rate. Most of this increase comes from incumbents' internal

innovation. By contrast to removing nancial constraints, banning industrial design patent-

ing encourages R&D investment among potential entrants. Entry rate slightly increases,

whereas the growth contribution from the new entrants decreases. Recall that rms' prot

ow decreases with aggregate patenting in industrial design. Shutting down industrial de-

sign would increase rm's per period prot as well as relax its nancial constraints. Thus,

investment in productivity-enhancing innovation increases. This push up the creative de-

struction rate and the aggregate growth rate. This is similar to ndings in the advertising and

growth literature in which advertising is modeled as demand shifter. For instance, Cavenaile

and Roldan-Blancoz (2019) nd that shutting down the advertising sector would increase a

rm's R&D expenditure as well as the aggregate growth rate. Firms do not face nancial

constraints in their paper, thus, the estimated increase in aggregate growth rate is higher

than the estimated value in this paper. Specically, in this paper, patenting in industrial

design does not only have a negative aggregate spillover eect. It also has a positive eect as

it can increase a rm's liquidity and relax its nancial constraints. Thus, removing industrial

design patenting might have a negative eect that partially cancels the positive eect from

increasing an intermediate good producer's prot and total R&D expenditure. Thus, the

increase in the growth rate after shutting down industrial design is lower in the case with

nancial constraints, comparing to the case without nancial constraints.

To sum up, the aggregate growth rate increase due to more entrants, higher creative

destruction conducted by incumbent, the improvement over existing product lines, and less

industrial design patenting, when industrial design is prohibited.

5.3 Welfare Analysis

Following Acemoglu, Akcigit, Alp, Bloom, and Kerr (2018), I conduct welfare analysis by

comparing the consumption-equivalent changes, ξ, along the balanced growth path for two

47

economies: One with nancial constraint, s1, and one without nancial constraint s2.

U(ξc10(s1), g1(s1)) = U(c2

0(s2), g2(s2))

Here, c10 and g1 are initial consumption and the aggregate growth rate of the economy with

nancial constraints and c20 and g2 are those for the economy without nancial constraints.

ξ can then be viewed as the fraction of initial consumption in economy s1 (with nancial

constraint) that will ensure the same discounted lifetime utility as s2 (without nancial

constraint). The discounted utility under log preferences can be written as:

U0(c0, g) =

∫ ∞0

exp(−ρt) logCtdt =1

ρ

[log c0 +

g

ρ

]

The required welfare compensation ξ − 1 is

ξ − 1 = exp

log c20 − log c1

0︸ ︷︷ ︸changes in consumption

+g2

ρ− g1

ρ︸ ︷︷ ︸changes in growth

− 1

The consumption-equivalent changes can be decomposed into two parts: 1) Changes in the

(initial) consumption level, and 2) changes in the aggregate growth rate. In addition to

comparing economies with and without nancial constraint, I also compare economies with

and without industrial design, and the economy, removing both nancial constraints and

patenting in industrial design. Table 8 lists the results.

Table 8: Welfare Decomposition

welfare gain changes in consumption changes in growth rate(ξ − 1) (∆ logC) (∆g

ρ)

Remove Financial Constraint 0.257 -0.008 0.237Remove Industrial Design 0.113 -0.026 0.133Remove Both 0.339 -0.030 0.322

The welfare gain after removing nancial constraints is 0.257, with a small negative

change in consumption and a higher, positive changes in the aggregate growth rate. Once

48

rms are nancially unconstrained, rms have less incentive to patent in industrial design.

Thus, the aggregate demand shifter Φ decreases, lowering the aggregate nal goods output

as well as consumptions. As the decrease in consumption is lower than the gain in aggregate

growth rate, the overall eect gives rise to a welfare gain after removing nancial constraints.

Similarly, the increase in the growth rate is higher than the decrease in consumption level

after removing industrial design. Shutting down patenting in industrial design then results

in a welfare gain. The welfare gain is even higher if both nancial constraints and industrial

design patenting are removed.

5.4 Policy Implication: Type-dependent tax Incentive

In this section, I evaluate China's current volume-based R&D tax incentive policy in the

model of this paper. Starting in 2003, eligible R&D expenses can be deducted at a 150

percent rate when calculating a rm's corporate income tax base. In 2018, this deduction rate

was increased to 175 percent, and some qualied rms can receive a 200 percent deduction

rate 14. The purpose of this tax incentive policy is to stimulate more innovation and higher

rm growth. However, it does not distinguish R&D expenditure by patent category. R&D

expenses for industrial design receive the same deduction as R&D expenses for internal and

external innovations. This tax incentive policy encourages not only productivity-enhancing

innovation, but also patenting in industrial design. One potential problem for this tax

incentive policy is that nancially constrained rm might conduct more industrial design

patents, which can be detrimental to rms and the aggregate growth rate. The following

proposition explains the mechanism. Let s be the rate of super-deduction and tax be the

14Data is from State Taxation Administration

49

corporate income tax rate, and the optimal R&D investment can be written as:

h∗d =

((1− tax)π(1 + Φ)σ−1

xdψd

1 + µϕn(1 + ϕn)(1− s× tax)

) 1ψd−1

nαd

h∗I =

(λB

xIψI

1

(1 + ϕn)(1− s× tax)

) 1ψI−1

nαI

h∗x =

(B(1 + ν) +Bn+1 −Bn

xxψx

1

(1 + ϕn)(1− s× tax)

) 1ψx−1

nαx

(13)

Proposition VI Under a uniform tax incentive, 1) innovation intensities h∗d, h∗I and h∗x

increase with the deduction rate, s; 2) with a quadratic cost function, a higher deduction

rate s encourages rms to concentrate innovation in industrial design:

dh∗dds

> 0dh∗Ids

> 0dh∗xds

> 0

dh∗dh∗I

ds> 0

dh∗dh∗x

ds> 0

Proof. see Appendix.

In the appendix A.2.6, I show that dϕnds

> 0. A higher deduction decreases a rm's

marginal cost in conducting innovation and increase innovation intensity. However, it won't

relax a rm's nancial constraint. Thus, the rm becomes more likely to be nancially

constrained with an increment in the deduction rate s. This increases the marginal benet of

relaxing nancial constraints via patenting more industrial design. Hence, a rm's innovation

choice shifts from productivity-enhancing innovation into industrial design. Given calibrated

parameters, ψd = ψI = ψx = 2,h∗dh∗I∝ 1 + ϕnµ and

h∗dh∗x∝ 1 + ϕnµ, these two ratios increase

with s as dϕnds

> 0. The over-investment in industrial design is detrimental to a rm's and

aggregate growth rate.

I propose a type-dependent tax incentive policies, such that only R&D expenses on

internal and external innovation are entitled to a super deduction. The following proposition

shows that under a type-dependent tax incentive policy, R&D investment shifts towards

productivity-enhancing innovation.

50

Proposition VII Under a type-dependent tax incentive policy, such that only R&D ex-

penses on internal and external innovation are entitled to deduction rate s, a higher deduction

rate s shifts R&D investment towards productivity-enhancing innovation.

dh∗dh∗I

ds< 0

dh∗dh∗x

ds< 0

Proof. see Appendix.

Similar to the uniform tax incentive policy, ϕn increases with the deduction rate s. An

increase in s reduce the eective marginal cost of internal and external innovation, and thus

increases corresponding innovation intensities. Patenting in industrial design also increases,

as a larger s raises the marginal benet of relaxing a rm's nancial constraints by increasing

current prot. However, industrial design patenting does not receive the super deduction

when computing the tax base. The relative cost of conducting industrial design patents thus

increases. An increase in s stimulate internal and external innovation more than industrial

design patents.

Under this type-dependent tax incentive policy, the aggregate growth rate would be

higher than under a uniform tax incentive policy. To quantify the impact of this tax incentive

policy on the aggregate growth rate, I use the calibrated parameters 15 in Table 4 to conduct

three counterfactuals: 1) No deduction, 2) higher deduction rate and 3) type-dependent tax

incentive policy. Table 9 compares the aggregate growth rate and welfare gain under those

counterfactuals.

Column (2) in Table 9 is the baseline case, that is the currently implemented tax incentive

policy where all types of R&D investment receive a super deductible rate of 1.5. Column

(1) is the counterfactual that no R&D investments receive a super-deduction. The currently

implemented tax incentive policy increases the annual aggregate growth rate by 5.7 per-

cent, which is 0.24 percentage points. Most of this increase is contributed by new entrants.

Columns (2) and (4) compare the result under uniform tax incentives, and type-dependent

15My baseline parameters in previous session is calibrated under a modied model with a corporate incometax rate equals to 0.25 and a deduction rate of 1.5. So the impact from tax rate and tax deductions are notreected in my calibrated parameters.

51

Table 9: Growth Decomposition and Welfare Gain Under Two Policy Regimes

No Incentive Uniform Type-dependenttax = 0.25 s = 1 s = 1.5 s = 2 s = 1.5 s = 2

(1) (2) Baseline (3) (4) (5)Aggregate Growth Rate 0.0423 0.0447 0.0466 0.0461 0.0514from incu. Ext. innov. 50.3% 47.6% 42.8% 47.8% 44.1%from incu. Int. innov. 41.2% 38.9% 36.1% 39.6% 38.0%from new entrant 8.6% 13.4% 21.1% 12.6% 17.9%R&D Intensity 0.076 0.075 0.072 0.075 0.074Share of Industrial Design 26.4% 30.8% 36.6% 26.4% 26.0%Welfare gain 0.026 0.042 0.061 0.169

tax incentives, when the deduction rate is 150 percent, and Columns (3) and (5) compare

these two policies when the deduction rate is raised to 200 percent. Comparing to the case

without super deductibles, The aggregate growth rate increase by 5.7 percent (10.2 percent

under 200 percent deduction) under uniform tax incentives and increase by 9.0 percent (21.5

percent under 200 percent deduction) under type-dependent tax incentives when the deduc-

tion rate is 150 percent (or 200 percent). The share of patenting in industrial design drops

under a type-dependent tax incentive policy due to a relative increase in its R&D cost. The

reduction is larger with a higher deduction rate. However, under a uniform tax incentive

policy, the share of industrial design in total innovation rises. This increase is greater with

higher deduction rate. Thus, type-dependent tax incentive generate more aggregate growth

than uniform tax incentive. The dierence between these two policies is larger when the de-

duction rate is higher. The welfare gain is also higher under a type-dependent tax incentive

policy.

To sum up, a type-dependent tax incentive policy would generate a higher aggregate

growth and welfare by shifting rms' patenting towards productivity-enhancing innovations.

6 Conclusion

In this paper, I build a model of endogenous growth through choices over innovation quality

when rms confront nancial constraints. I have shown both theoretically and empirically

52

that nancial constraints alter a rm's R&D composition. When nancial constraints restrict

a rm's total R&D investment, the rm substitutes for productivity-enhancing innovation

activity with industrial design. Such changes in innovation composition lower the aggregate

growth rate. When I prohibit rms from patenting in industrial design in the model, the

aggregate growth rate increases by 11.8 percent. I nd that imposing taxes on industrial

design patenting is ineective, in that consequent increases in the aggregate growth rate are

negligible. Moreover, developing nancial markets is more eective for promoting growth

and raising welfare than imposing taxes on, or prohibiting, industrial design. I also show

that a type-dependent R&D tax incentive, under which only R&D expenses on internal

and external innovation are entitled to a super deduction when computing a corporation's

income tax base, would generate higher aggregate growth and a larger welfare gain than

currently implemented uniform R&D tax incentives. A potential extension is to consider

size-dependent R&D tax incentives, in which small rms receive a larger super deduction

than large rms. This would relax small rms' nancial constraints and generate a higher

aggregate growth rate.

In the model, I use reduced-form nancial constraints, derived from a limited enforcement

problem, to study the impact of nancial constraints on rms' innovation strategies. One

natural extension is to introduce nance intermediaries, and derive an explicit microfoun-

dation for a rm's intermediated borrowing problem. In addition, equity nancing is not

allowed in the model. An empirical study by Brown, Fazzari, and Peterson (2009) shows that

better access to equity nance can substantially increase rms' R&D investment. Thus, al-

lowing rms choosing from equity and debt nancing for innovation activity is potentially an

important extension of the model. Furthermore, new entrants in my model do not face nan-

cial constraints when entering the market; my analysis focuses on the relationship between

nancial constraints and innovation composition among incumbents. Imposing nancial con-

straints on entrants' innovation choices is a third potential extension. Finally, in the model,

I assume the innovation decision on industrial design is static. Industrial design aects cur-

rent demand, but has no long-run eects for consumer demand. I could allow the impact

of industrial design to accumulate over time, contributing to a rm's brand equity. In such

a setting, investing in industrial design relaxes a rm's current and future borrowing con-

53

straints which might aect a rm's current and future investment in productivity-enhancing

innovations. Beyond the scope of the current paper, I leave this avenues for future research.

54

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60

A Appendix

A.1 Data Construction

A.1.1 Patent Types

Patents are classied into three categories under SIPO: 1) invention patents, those that make

"signicant progress" relative to previous technology; 2) utility models, those that represent

a minor improvement of current products and are insucient to be granted as invention

patents; and 3) industrial design, those of ornamental or aesthetic design of physical or

digital goods with a practical purpose. Invention patents are intensively examined by patent

ocers, and usually taken two to ve years to be granted. The protection period for invention

patents is up to twenty years, or based on a rm's own termination choice prior to the twenty

year limit. The protection period for utility models and industrial designs are up to ten years,

or based on a rm's own termination choice within those ten years. Hence, invention patents

are usually harder to obtain.

I reclassify patents into three alternative categories: 1) industrial design patenting; 2)

long-run internal innovation, and 3) long-run external innovation. Industrial design patents

are patents that do not contribute to a rm's long-run productivity growth, and have short

application and protection periods. Firm engaged in industrial design patenting to increase

its instantaneous prot only. It do not contain any social values nor have any positive

spillover eect over either rm's or aggregate productivity growth 16 . Long-run internal

innovation patents represent innovations aiming to improve a rm's existing production

method or process, and thus its long-run productivity. Long-run external innovation patents

represent innovations aiming to increase the number of rm's product lines by introducing

new products or an entirely new production technology. Internal innovations are "exploita-

tion" innovations and it can be viewed as renements and extension of current technology

(March (1991), Gatignon, Tushman, Smith and Anderson (2002)). Thus, a rm's internal

16In my sample, around 70% of industrial designing are packaging, designing of clothing, jewelry andfurniture, which do not contribute to the improvement of rm's production process. But those patents mayshift customers' preference instantaneously.

61

Table A1: Summary Statistics of Patent Category and Average Citation

Design Internal Innovation External InnovationTotal Total Mean Std Dev. Total Mean Std Dev.

Patent Application 130,801 129,479 132,485Backward Citation 18,513 0.143 0.755 306,191 2.311 2.749

self cited 11,468 0.086 0.467 29,725 0.224 0.505Forward Citation 212,726 1.643 2.895 283,804 2.142 3.656

external 187,803 1.450 2.730 251,106 1.895 3.445

patent would cite its previous patents more than other rm's patents. External innovation,

on the other hand, are "exploration" innovations. A rm conduct external innovation to

explore new technology that it does not currently owned. Thus, a rm's external innovation

cite less its previous patents but more on patents owned by other rms. As rm might open

a new technology eld through external innovation, external patents usually receives more

citations from subsequent patents applied by other rms (Galasso and Simcoe (2011) and

Akcigit and Kerr (2018)). Levinthal and March (1993) and March (1991) provide detailed

distinguish on exploration and exploitation innovations.

Patent value, both social and private value, are positively related to its forward citations,

which is measured as the number of subsequent patents that cite the specic patent a rm

les (Trajtenberg (1990) and Hall, Adam and Trajtenberg (2001)). Patent without any

forward citations might bear limited social values. Hence, as industrial design patents does

not have any forward citations, it does not have any spillover eect on economy's aggregate

productivity. The remaining patents, utility and invention patents, classify as productivity-

enhancing patents. In the nal patent sample, there are 130,801 industrial design application

during the sample period (see Table A1).

Next, I classify productivity-enhancing patents into internal and external innovation.

My classication of internal and external patents follows the method proposed by Akcigit

and Kerr (2018), with some modications. Based on USPTO patents applied by US census

rms, Akcigit and Kerr classify patents as internal innovation if more than 50 percent of

backward citations, which is measured as the number of previous patents a patent cite in its

application document, are self-citations. However, in SIPO patent data, around 30 percent of

62

patents do not have any backward citations, making it dicult to use their method to classify

patents as internal innovation. To overcome this, I utilize information on a rm's patent

description, technology domain and product information 17. I classify internal innovation in

two steps. First, those patents with backward citations, I classify as internal innovation if

more than 50 percent of backward citations are self-citations. Second, for patents without

backward citation, I classify a patent as internal innovation if a) its technology domains

belongs to the rm's previous patent's technology domains, and b) there is a statement

similar to "improving current production process" in the patent description, or if the rm

reports "no new product is produced" in the year of the patent's application. Using this

modied classication method, I have 129,479 internal patents and 132,485 external patents

in the sample period. Using Akcigit and Kerr (2018)'s classication, there would be 35,702

internal patents in 226,262 external patents in my data. My method yields a more restrictive

denition for external, exploratory innovation.

Figure 3 shows the citation distribution of internal and external patents for my sample

of Chinese rms based on the patent classications suggested by Akcigit and Kerr (2018)

with the citation distribution based on my modied method. Ideally, internal patents are

"exploitation" patents and external patents are "exploration" patents, and the latter have

a deeper inuence on technology evolution. Hence, internal patents should receive fewer

external (non-self) citations than external patents. Applying Akcigit and Kerr (2018)'s

method to China's patent data, yields a very similar distribution for internal and external

patents. The average number of external citations for each internal patent is 1.89 and

it is 1.91 for external patents. However, my modied method yields a somewhat larger

distinction between external citations for the two patent types; the average external citation

for each internal patent is 1.45 and for external patents is 1.90. Table A1 lists the summary

statistics. In addition, external innovations, on average, have way less self citation than

internal innovations.

17In ASM, rms are asked to provide information on whether their current products are produced usingnew technology or new production process.

63

Figure 3: External Citation Distribution by External and Internal Patent

0 2 4 6 8 10 12 14

Number of External Citations Received

0.2

0.4

0.6

0.8

1

Cu

mu

lati

ve

Dis

trib

uti

on

of

Pat

ents

Following Akcigit and Kerr (2018)

Internal

External

0 2 4 6 8 10 12 14

Number of External Citations Received

0.2

0.4

0.6

0.8

1

Cum

ula

tive D

istr

ibution o

f P

ate

nts

Adjusted by Tech Field

Internal

External

Note: Left panel is based on patent classications suggested by Akcigit and Kerr (2018). Patent dened asinternal if more than 50% of backward citations are self-cited. Right panel is based on my modied method.

A.1.2 Measuring Financial Constriant

Following Almeida and Campello (2007), the investment equation under constrained and

unconstrained regimes can be written as

I1it =Xitα1 + u1it

I2it =Xitα2 + u2it

y∗it =β0 + Zitβ + vit

where I1it and I2it are R&D investment under regime 1 and regime 2. Xit are a vector of

exogenous variable that governs rm's investment decision: 1) one period lagged R&D in-

vestment, 2) growth opportunities, which is measured as turnover over real capital; 3) real

cash ow divided by rm's real capital stock at the beginning of current period. y∗it is unob-

served determinants of rm's nancial conditions. If y∗it < 0 rm is nancially constrained

and Iit = I1it. If y∗it > 0, rm is nancially unconstrained and Iit = I2it. Thus Zit deter-

mine the probability that whether rm would be nancially constrained or not. Following

Almeida and Campello (2007) and Hovakimian and Titman (2006), Zit contains 1) log of

64

total asset, 2) log age, 3) the ratio of short term debt to total asset, 4) the ratio of long

term debt to total asset, 5) nancial slackness measured as cash and marketable securities

to total asset, and 6)Tangibilityit, which is used to approximate the expected liquidation

value of rm's operating assets. Following Berger, Ofek and Swary (1996) and Almeida and

Campello (2007), I compute Tangibilit as Tangibilityit = 0.715 × Receivablesit + 0.547 ×

Inventoryit + 0.535× FixedAssetit + Cash + MarketableSecurities, scaled by total asset.

Where Receviables are account receivables. Cash and marketable securities are computed

as liquid asset minus account receivables. This variables are all entered in lagged form in the

selection equation. Following Hovakimian and Titman (2006), the model can be estimated

using Expectation-Maximization Algorithm.

lnL =n∑i=1

ln

1

σ1

φ(u2i

σ

)[1− Φ

(−Zitβ − ρ2

u2iσ√

1− ρ22

)]+

1

σ1

φ(u1i

σ

)Φ

(−Zitβ − ρ2

u1iσ√

1− ρ21

)

where ρj =σjvσjσv

. And the covariant matrix is dened as: Ω =

σ11 σ12 σ1v

σ21 σ22 σ2v

σv1 σv2 σvv

with

σ1v 6= 0, σ2v 6= 0 and normalize σvv = 1.

The parameter sets αs and βs are estimated in following steps. 1) Guess an initial sep-

aration of the sample between two regimes. I use tangibility to compute the initial guess.

Firms with tangibility less than sample average is classied as nancially constrained and

Firms with tangibility more than sample average is classied as nancially unconstrained.

2) Estimate the initial value of α and β after the initial guess, by using the above likelihood

function. 3) Use the estimated α and β to calculate the probabilities that observation i

belongs to each group. 4) Plug these probabilities into the above log likelihood function,

and then maximized again. The maximization of the above log likelihood function will give

new estimates of α and β. 5) Keep doing step 3) and 4) until α and β converged. Table A2

and Column (1) and (2) in Table A3 lists the estimation results. As R&D investment relies

heavily on rm's internal cash ow if it is nancially constrained, one should expect the coef-

cient on CashF low to be statistically signicant positive under constrained regime (regime

65

1). For a robust check, I also run the regression suggested by Almeida and Campello (2007)

using physical investment and include tangibility and its interactive term with cash ow. The

interactive term of Cashflow and Tangibility captures the idea that tangibility increase the

collateral value that can be captured by lenders if rm default. Higher tangibility mitigates

the wedge between internal and external nance and thus increase rm's investment cash

ow sensitivity. For nancially constrained rms, one should expect the coecient before

the interactive term becomes positive. Column (3) and (4) in Table A3 documents the result.

Table A2: Endogenous Selection Regression

Coecient Standard Deviationlog(TotalAsset)it−1 −0.0684∗∗∗ (0.0014)log(Age)it−1 0.1611∗∗∗ (0.0022)(ShortTermDebtTotalAsset

)it−1

0.4110∗∗∗ (0.0074)(LongTermDebtTotalAsset

)it−1

0.6708∗∗∗ (0.0156)

FinancialSlackit−1 −0.5065∗∗∗ (0.0171)Tangibilityit−1 −0.4046∗∗∗ (0.0261)Constant 0.4872∗∗∗ (0.0221)N. Obs 19,940R-squared 0.6010

Note: log(TotalAsset)it−1 is measured as log of total asset.(ShortTermDebtTotalAsset

)it−1

and(LongTermDebtTotalAsset

)it−1

is short term debt and long-term debt over total asset.FinancialSlackit−1

is the ratio of cash and marketable securities to total assets. Tangibilityit−1 is measured fol-

lowing Almeida and Campello (2007) and Berger, Ofek and Swary (1996). Tangibility =0.715 × Receivables + 0.547 × Inventory + 0.535 × FixedAsset + Cash + MarketableSecuritiesscaled by total asset. Robust standard errors clustered at rm level are reported in parentheses.

∗ ∗ ∗, ∗∗ and ∗ indicate signicant level at 1%, 5% and 10%, respectively.

66

Table A3: Endogenous Switching Regression

R&D Investment Regression Physical Investment RegressionConstrained Unconstrained Constrained Unconstrained

(1) (2) (3) (4)Investmentit−1 0.6999∗∗∗ 0.0591 0.0007 0.0001

(0.1890) (0.0491) (0.0008) (0.0001)GrowthOppit−1 0.0046 0.0019 0.0063 −0.0021

(0.0050) (0.0015) (0.0099) (0.0104)CashF lowit−1 0.1146∗∗ 0.0273 0.6610∗∗∗ 0.9011

(0.0462) (0.0204) (0.1374) (1.2196)Tangibilityit−1 1.0102 1.8933

(0.6869) (2.0722)CashF lowit−1 × Tangibilityit−1 0.0460 −0.9023

(0.3235) (1.7803)Industry Fix Yes Yes Yes YesYear Fix Yes Yes Yes YesN. Obs 18, 816 16, 474 64, 545 46, 474R-Squared 0.2177 0.0769 0.0096 0.0185

Note: GrowthOpportunity is measured as total output growth at 3-digit industry level. Cash is

measured as cash ow over total asset. Cash ow is dened as net income plus current deprecia-

tion. Tangibility is measured following Almeida and Campello (2007) and Berger, Ofek and Swary

(1996). Tangibility = 0.715 × Receivables + 0.547 × Inventory + 0.535 × FixedAsset + Cash +MarketableSecurities scaled by total asset. Robust standard errors clustered at rm level are

reported in parentheses. ∗ ∗ ∗, ∗∗ and ∗ indicate signicant level at 1%, 5% and 10%, respectively.

67

A.2 Proofs and Additional Theoretical Result

A.2.1 Firm Size Distribution

Following Akcigit and Kerr (2018), I write out following ow equations for the fraction of

rms with n product lines. In a steady-state equilibrium, the innovation size distribution

should be stable. Thus, under each size level n, one should expect that the inow of product

lines (second column) should equal outow of the product lines (third column):

State Inow Outow

n = 0 Mη1τ = he

n = 1 Mη22τ + he = Mη1(hx(n) + τ)

n ≥ 2 Mηn+1(n+ 1)τ +Mηn−1(n− 1)hx(n) = Mηn(nhx(n) + nτ)

where ηn is the fraction of rms with n product lines. M is the total measure of rms.

Combining the above ow equations yield a relationship between ηn and ηn−1:

ηn = ηn−1n− 1

n

hx(n)

τ

Then ηn can be written as:

ηn =heMτ

n−1∏i=1

(hx(i)

τ

)1

n

A.2.2 Financial Constraints

The total R&D expenditure for an intermediate goods producer with nf product lines is

Rf units of nal goods. R&D is taken before production, each monopoly producer has to

collateral its ex post prot to generate cash to fund its R&D investment. At equilibrium,

for a rm with nf product lines and hdj industrial design patents, its ex post prot is∑nfj=1 π(1 + Φ)σ−1zj +

∑nfj=1 π(1 + Φ)σ−1hdjZ. The rst term is the prot ow without any

innovation and the second term is the additional prot margin generated by patenting in

industrial design. Now, suppose there are information asymmetries between lenders and

borrowers. That is lenders cannot observe rms' productivity level. It then evaluate the

68

prot ow at the average productivity Z. Following a limited enforcement argument, suppose

a rm can steal 1µ(with µ ≥ 1) amount of its borrowing. As a punishment it would lose

all of its collateral value, but receive a verication cost paid by the lender. It's nancial

constraints can then be written as:

Rnf (t) ≤ µ

[nf∑j=1

π(1 + Φ)σ−1hdjZ + nf π(1 + Φ)σ−1Z − cnf π(1 + Φ)σ−1Z

]

The last term cnf π(1 + Φ)σ−1Z is the verication cost paid by the lender to the borrower in

order to take all of the borrower's collateral. Lender set c so that the aggregate borrowing do

not exceed the aggregate collateral. Let c = 1+Φ2, The nancial constraints can be rewritten

as:

Rnf (t) ≤ µ

[nf∑j=1

π(1 + Φ)σ−1hdjZ + nfκZ

]

Here, κ = 1−Φ2π(1 + Φ)σ−1.

A.2.3 Proof of Proposition I

By rm's optimal R&D investment (11), long-run optimal innovation intensity h∗x and

hI only depends on number of product line n only. Hence, the aggregate innovation only

depends on the distribution of product lines, independent of any quality distribution. The

aggregate quality Z changes after an instant ∆t is:

Z(t+ ∆t)− Z = Z

[∆tτν + ∆t

∞∑n=1

M∗ηnnh∗I(n)λZ

]

where µn is percentage of rms with product line n andM is the total measure of rms. The

creative destruction rate is endogenously determined and equals total number of product

lines that be replaced:

τ ∗ = h∗e +∞∑n=1

M∗ηnnh∗x(n)

69

The aggregate growth rate then can be written as:

g =˙Z(t)

Z(t)= lim

∆t→0

Z(t+ ∆t)− Z(t)

Z(t)∆t= h∗eν +

∞∑n=1

M∗ηnnh∗x(n)ν +

∞∑n=1

M∗ηnnh∗I(n)λ

A.2.4 Proof of Proposition II

Step I: Detrending Normalize rm's value V and quality with V = VZand z = zj

Z: j ∈

n, the value function can be rewritten in new state variable z and V (z, n) = −gV (z, n) +

g∑n

j=1∂V (z,n)∂z

zj. Rewrite the value function (7) as:

(r − g)V (z, n) + g

n∑i=1

∂V (z, n)

∂zjzj = max

hdj ,hIjj∈nf ,hx

n∑j=1

[π(1 + Φ)σ−1(zj + hdj)− xdhψddj n

αd]

+n∑j=1

[hIj

[V (z \ zj ∪ (zj + λ), n)− V (z, n)

]− xIhψIIj n

αI]

+ nhx

[EiV (z ∪ (zi + ν), n+ 1)− V (z, n)

]− xxhψxx nαx+1

+n∑j=1

τ[V (z \ zj, n− 1)− V (z, n)

]

s.t.n∑j=1

[xdh

ψddj n

αd + xIhψIIj n

αI]

+ xxhψxx n

αx ≤ µ

[n∑j=1

hdjπ(1 + Φ)σ−1 + κn

]

Step II: Value Function Guess the value function of the form V (z, n) = B∑n

i=1 zi+Bn.

Substitute the conjecture into the above value function and equating the terms with zi and

constant, one can get the following:

(r − g + g + τ)Bn∑i=1

zi = π(1 + Φ)σ−1

n∑i=1

zi

and

(r − g)Bn = maxhdj ,hIjj∈nf ,hx

n∑j=1

[π(1 + Φ)σ−1hdj − xdhψddj n

αd]

+n∑j=1

[hIjλB − xIhψIIj n

αI]

+ nhx[Ei(B(1 + ν) +Bn+1 −Bn)

]− xxhψxx nαx+1 +

n∑j=1

τ [Bn−1 −Bn]

70

Combining the equilibrium condition that g = r − ρ, then B can be solved as:

B =π(1 + Φ)σ−1

ρ+ g + τ

Take the rst order conditions,:

h∗dj =

(π(1 + Φ)σ−1

xdψd

1 + µϕn1 + ϕn

) 1ψd−1

nαd ∀j

h∗Ij =

(λB

xIψI

1

1 + ϕn

) 1ψI−1

nαI ∀j

h∗x =

(B(1 + ν) +Bn+1 −Bn

xxψx

1

1 + ϕn

) 1ψx−1

nαx

where αd = − αdψd−1

< 0, αI = − αIψI−1

< 0 and αx = − αxψx−1

< 0. As hdj are hIj are independent

of individual relative quality zj, it can be written as: h∗dj = h∗d∀j and h∗Ij = h∗I∀j. The ϕn

then dened through the nancial constraint:

µκ+ µπ(1 + Φ)σ−1h∗d = xdh∗ψdd nαd + xIh

∗ψII nαI + xxh

∗ψxx nαx

Plug in the optimal solution into Bn and the budget constraints, Bn and ϕn can be solved

as:

µκ =−[µ−

(1 + µϕn1 + ϕn

)1

ψd

]π(1 + Φ)σ−1

(1 + µϕn1 + ϕn

π(1 + Φ)σ−1

xdψd

) 1ψd−1

nαd + xI

(1

1 + ϕn

λB

ψIxI

) ψIψI−1

+ xx

(1

1 + ϕn

B(1 + ν) +Bn+1 −Bn

ψxxx

) ψxψx−1

nαx

ρBn =n

[1−

(1 + µϕn1 + ϕn

)1

ψd

]π(1 + Φ)σ−1

(1 + µϕn1 + ϕn

π

xdψd

) 1ψd−1

nαd

+ n

[1−

(1

1 + ϕn

)1

ψI

]λB

(1

1 + ϕn

λB

xIψI

) 1ψI−1

nαI

+ n

[1−

(1

1 + ϕn

)1

ψx

] (B(1 + ν) +Bn+1 −Bn

)( 1

1 + ϕn

B(1 + ν) +Bn+1 −Bn

xxψx

) 1ψx−1

nαx

+ nτ(Bn−1 −Bn)

If the solution of ϕn < 0, set ϕn = 0 and rm is nancially unconstrained.

71

Step III: Lemma I Bn is bounded above.

Proof. As Bn|ϕn>0 < Bn|ϕn=0, Let's consider the case where ϕn = 0. Consider per-period

return:

Π(hd, hI , hx, n) = nπ(1+Φ)σ−1hd+nhIλB+nhxB(1+ν)−xdhψdd nαd+1−xIhψII n

αI+1−xxhψxx nαx+1

Then, B(n) ≤ Π(hd,hI ,hx,n)ρ

. Dene [hd, hI , hx] ≡ arg maxhd,hI ,hx Π(hd, hI , hx, n). They are

determined through rst order condition: xdψdhψd−1d nαd = π(1 + Φ)σ−1, xIψIh

ψI−1I nαI = λB

and xxψxhψx−1x = nB(1 + ν). The max exists as ψd > 1, ψI > 1 and ψx > 1. It must

be true that Π(hd, hI , hx, n) ≤ Π(hd, hI , hx, n). Dene n ≡ arg maxn Π(hd, hI , hx, n). As

minαd, αI , αx > 0, the existence of n is ensured by the strict convexity. Then, it must be

true that:

Π(hd, hI , hx, n) ≤ Π(hd, hI , hx, n)

Hence:

Bn|ϕn>0 < Bn|ϕn=0 ≤ Bmaxn ≡ Π(hd, hI , hx, n)

ρ

Notice that: ρBn can also be written as: ρBn = ρBn − τn(Bn − Bn−1). Dene ∆n+1 =

Bn+1 −Bn, then:

ρBn

n= ρ

Bn

n+ τ∆n

where:

ρBn

n= π(1 + Φ)σ−1hdn + hI,nB(1 + ν) + hx,nB(1 + ν)− xdhψddnn

αd − xIhψII,nnαI + hx,n∆n+1

is rm's value without considering creative destruction. By the similar argument, we must

also have:

Bn|ϕn>0 < Bn|ϕn=0 ≤ Bmaxn ≡ Π(hd, hI , hx, n)

ρ

That is Bn is also bounded above.

72

Step IV: Lemma II

Bnn

∞n=1

is a decreasing sequence.

Proof. Let B∗(n) be the optimal value in which innovation intensity at its optimal value:

hd = h∗d,n, hI = h∗I,n, hx = h∗x,n. Then:

ρB∗nn

= π(1 + Φ)σ−1h∗d,n + h∗I,nλB + h∗x,nB(1 + ν)− xdh∗ψdd,n nαd − xIh∗ψII,n n

αI − xxh∗ψxx,n nαx + h∗x,n∆n+1

. Then it must be true that (as h∗I,n+1, h∗x,n+1 and hd,n+1 is not optimal policy under n):

ρBn

n≥ π(1+Φ)σ−1h∗d,n+1+h∗I,n+1λB+h∗x,n+1B(1+ν)−xdh∗ψdd,n+1n

αd−xIh∗ψII,n+1nαI−xxh∗ψxx,n+1n

αx+h∗x,n+1∆nt+1

Then

ρBn+1

n+ 1− ρBn

n≤ g(n, n+ 1) + h∗I,n+1[∆n+2 −∆n+1]

where

g(n, n+1) = xdh∗ψdd,n+1 [nαd − (n+ 1)αd ]+xIh

∗ψII,n+1 [nαI − (n+ 1)αI ]+xxh

∗ψxx,n+1 [nαx − (n+ 1)αx ] < 0

Suppose ∃N such that BNN≤ BN+1

N+1. As g(N,N + 1) < 0. It then must be true that:

h∗x,N+1[∆N+2 −∆N+1] ≥ ρ

[BN+1

N + 1− BN

N

]− g(N,N + 1) > 0

That is: ∆N+2 > ∆N+1. To sum up, given BNN≤ BN+1

N+1, it must be true that ∆N+2 > ∆N+1.

That is if

Bnn

∞n=1

is nondecreasing sequence, we can nd n > N such that ∆n+1 > ∆n

always hold. This contradict with Lemma I that Bn is bounded from above. Hence, it must

be true that

Bnn

∞n=1

is an decreasing sequence.

Step V: Lemma III If

Bnn

∞n=1

is a decreasing sequence, and if ∃N such that ∆N+1 >

∆N , then: 1) 2BN > N(∆N+1 + ∆N) and BN+1

N+1− 2BN

N+ BN−1

N−1> 0; and 2) ∆N+1 > ∆N and

2BN > N(∆N+1 + ∆N), where ∆N = BN − BN−1

73

Proof. As

Bnn

∞n=1

is a decreasing sequence, and by the denition of Bn, it must be true

that:

ρBn

n+ τ∆n > ρ

Bn+1

n+ 1+ τ∆n+1

rearrange it:

ρ

[Bn

n− Bn+1

n+ 1

]> τ [∆n+1 −∆n]

If ∆N+1 > ∆N , by the above inequality, BNN> BN+1

N+1. Hence:

BN

N− BN+1

N + 1=BN(N + 1)−BN+1N

N(N + 1)=BN −N∆N+1

N(N + 1)> 0

Thus, BN > N∆N+1 > N∆N . That is: 2BN > N(∆N+1 + ∆N)

BN+1

N + 1− 2

BN

N+BN−1

N − 1=NBN+1 − (N + 1)BN

(N + 1)N+NBN−1 − (N − 1)BN

(N − 1)N

=N∆N+1 −BN

(N + 1)N− N∆N −BN

(N − 1)N

=[N2(∆N+1 −∆N) + 2BN −N(∆N+1 + ∆N)]

(N + 1)(N − 1)N> 0

The last line hold as 2BN > N(∆N+1 + ∆N)

For statement 2), in order to prove ∆N+1 > ∆N , it is equivalent to prove that ρBN+1 +

τ(N + 1)∆N+1 − ρBN − τN∆N > ρBN + τN∆N − ρBN−1 − τ(N − 1)∆N−1. Rearrange it,

we need to prove:

ρ[∆N+1 −∆N ] + τ(∆N+1 −∆N−1)τN [∆N+1 + ∆N−1 − 2∆N ] > 0

Case 1): if ∆N−1 ≥ ∆N , the above inequality hold for sure under ∆N+1 > ∆N . Case 2): if

∆N−1 < ∆N , prove by contradiction. Suppose ∆N+1 < ∆N , then by the above inequality,

we must have: ∆N+1 + ∆N−1− 2∆N < 0. This implies: BNN− BN−1

N−1> BN

N− BN+1

N+1. Rearrange

it, we have: BN+1

N+1− 2BN

N+ BN−1

N−1< 0. Contradict with statement 1). Hence, we must have:

74

∆N+1 > ∆N if ∆N+1 > ∆N . With the same argument:

BN

N− BN+1

N + 1=BN(N + 1)− BN+1N

N(N + 1)=BN −N∆N+1

N(N + 1)> 0

Thus, BN > N∆N+1 > N∆N and 2BN > N(∆N + ∆N+1).

Step VI: Lemma IV Bn+1 −Bn decreases with n.

Proof. Prove by contradiction. Assume ∃N such that ∆N+1 > ∆N , as:

ρBN+1

N + 1− ρBN

N≤ g(N,N + 1) + h∗x,N+1[∆N+2 −∆N+1]

ρBN

N− ρ BN−1

N − 1≥ −g(N,N − 1) + h∗x,N−1[∆N+1 −∆N ]

Then:

ρ

[BN+1

N + 1− 2

BN

N+BN−1

N − 1

]≤ g(N,N+1)+g(N,N−1)+h∗x,N+1[∆N+2−∆N+1]−h∗x,N [∆N+1−∆N ]

where g(N,N + 1) + g(N,N − 1) < 0. As ∆N+1 > ∆N , then

ρ

[BN+1

N + 1− 2

BN

N+BN−1

N − 1

]< h∗x,N+1[∆N+2 −∆N+1]

Re-write the LHS:

ρ

[BN+1

N + 1− 2

BN

N+BN−1

N − 1

]=ρ

[NBN+1 − (N + 1)BN

(N + 1)N+NBN−1 − (N − 1)BN

(N − 1)N

]

=ρ

[N∆N+1 − BN

(N + 1)N− N∆N − BN

(N − 1)N

]=

ρ

(N + 1)(N − 1)N

[N2(∆N+1 − ∆N) + 2BN −N(∆N+1 + ∆N)

]> 0

75

The last line hold under Lemma III statement 2). Thus, we have:

ρ

[BN+1

N + 1− 2

BN

N+BN−1

N − 1

]> 0

As the LHS>0, it must be true that ∆N+2 −∆N+1 > 0. To sum up, given ∆N+1 > ∆N andBnn

∞n=1

is a decreasing sequence, we must have ∆N+2 > ∆N+1. Hence, we can nd n > N

such that ∆n+1 > ∆n always hold. This contradict with Lemma I that Bn is bounded from

above. Hence, we cannot nd N with ∆N > ∆N−1. Thus, ∆n decreases with n. That is

Bn −Bn−1 decreases in n.

A.2.5 Omitted Proofs of Proposition IV

Taking derivatives with respect to µ on rm's nancial constraint (12):

dR∗ddµ

+dR∗Idµ

+dR∗xdµ

κ+ π(1 + Φ)σ−1h∗d + µπ(1 + Φ)σ−1dh∗d

dµ

By equation (11):

dh∗ddµ

=h∗d

ψd − 1

1

1 + µϕn

(µ− 1

1 + ϕn

dϕndµ

+ ϕn

)dR∗ddµ

=ψdxdhψd−1d nαd

dh∗ddµ

=ψd

ψd − 1R∗d

1

1 + µϕn

(µ− 1

1 + ϕn

dϕndµ

+ ϕn

)dh∗Idµ

=− hI1− ψI

1

1 + ϕn

dϕndµ

,dR∗Idµ

= − ψI1− ψI

R∗I1 + ϕn

dϕndµ

dh∗xdµ

=− hx1− ψx

1

1 + ϕn

dϕndµ

,dR∗xdµ

= − ψx1− ψx

R∗x1 + ϕn

dϕndµ

using the fact that:

π(1 + Φ)σ−1h∗d = ψdxd1 + ϕn

1 + µϕn

(π(1 + Φ)σ−1

ψdxd

1 + µϕn1 + ϕn

) ψdψd−1

nαd = ψdR∗d

1 + ϕn1 + µϕn

76

Combine the above derivatives and rearrange it:

dϕndµ

= (1 + ϕn)−κ− ψdR∗d

1+ϕn1+µϕn

− ψdψd−1

R∗dµ−1

1+µϕn1

1+µϕn

R∗IψIψI−1

+R∗xψxψx−1

+(

µ−1(1+µϕn)

)2

R∗dψdψd−1

< 0

Consider the case where ψI = ψx = ψd = 2, the above derivatives can be simplied to:

dϕndµ

= (1 + ϕn)−1

2κ−R∗d

1+ϕn1+µϕn

−R∗dµ−1

1+µϕn1

1+µϕn

R∗I +R∗x +(

µ−1(1+µϕn)

)2

R∗d

If constrained:

R∗I +R∗x =µπ(1 + Φ)σ−1h∗d + µκ−R∗d

=

(µψd

1 + ϕn1 + µϕn

− 1

)R∗d + µκ

=R∗d2µ− 1 + µϕn

1 + µϕn+ µκ (withψd = 2)

Thus: dϕndµ

µϕn< −1 implies

1− ϕn1 + ϕn

(R∗I +R∗x) +

(2

(µ− 1)µ

(1 + µϕn)2+ 1

)R∗d > 0

The above equation is hold when ϕn ≤ 1. Similarly, dϕndµ

µ−11+ϕn

< −ϕn implies

(µ− 1

µ− 2ϕn

)(R∗I +R∗x) +

(µ− 1

µ+ 2

(µ− 1

1 + µϕn

)2

(1− ϕ)n

)Rd > 0

The above equation is hold when ϕn ≤ 12µ−1µ< 1

2.

A.2.6 Omitted proof in section 5.2

With investment tax td on industrial design, the cost parameter xd changes to xd(1 + td) and

the optimal quantity of h∗d becomes:

h∗d =

(π(1 + Φ)σ−1

xdψd

1 + µϕn1 + ϕn

1

1 + td

) 1ψd−1

nα

77

Taking derivatives with respect to µ on rm's nancial constraint (12) and rearrange it:

dϕndtd

= −(1 + ϕn)R∗d

ψdψd−1

µ−11+µϕn

R∗dψdψd−1

(µ−1

1+µϕn

)2

(1 + td) +R∗IψIψI−1

+R∗xψxψx−1

< 0

With µ > 1, dϕndtd

< 0. Hence, if rm is not self-nanced (i.e. µ > 1), taxing on industrial

design patents decrease rm-specic nancial friction ϕn. And:

dh∗ddtd

=hd

ψd − 1

[µ− 1

1 + ϕn

1

1 + µϕn

dµndtd− 1

1 + td

]< 0

dh∗Idtd

=− h∗IψI − 1

dϕndtd

1

1 + ϕn> 0

dh∗xdtd

=− h∗xψx − 1

dϕndtd

1

1 + ϕn> 0

Hence, by taxing on industrial design patents, R&D investment is shifted to productivity-

enhancing innovation. The higher the tax rate, the larger decrease in industrial design

patenting and more increase in internal and external innovation.

A.2.7 Proof on Proposition VI

Under uniform tax incentive, where all types of innovation receive super-deductable when

calculating rms' tax bases, the nancial constraint becomes:

(1− s× tax)(Rd +RI +Rx) ≤ µπ(1 + Φ)σ−1(1− tax)hd + µκ

where s < 1tax

. Taking derivatives w.r.p.t s on above nancial constraint and rearrange it:

dϕnds

=

R∗IψI−1

+ R∗xψx−1

+R∗dψd−1

− µ(1+ϕn)1+ϕnµ

R∗d

R∗dψdψd−1

(µ−1

1+µϕn

)2

+R∗IψIψI−1

+R∗xψxψx−1

tax(1 + ϕn)

1− s× tax

Under quadratic cost function ψd = ψI = ψx = 2, the nancial constraints implies:

R∗I +R∗x +R∗d = 2µ(1 + ϕn)

1 + µϕnR∗d +

µκ

1− s× tax

78

Hence, the numerator of dϕnds

becomes: R∗I +R∗x +R∗d−µ(1+ϕn)1+µϕn

R∗d = µ(1+ϕn)1+µϕn

R∗d + µκ1−s×tax > 0.

Thus, dϕnds

> 0. An increase in deduction rate s tightens rm's nancial constraints. And:

dh∗dds

=h∗d

ψd − 1

[µ− 1

1 + ϕn

1

1 + µϕn

dϕnds

+tax

1− s× tax

]dh∗Ids

=h∗I

ψI − 1

[−dϕnds

1

1 + ϕn+

tax

1− s× tax

]dh∗xds

=h∗x

ψx − 1

[−dϕnds

1

1 + ϕn+

tax

1− s× tax

]dh∗dds

> 0 as µ > 1 and dϕnds

> 0. For dh∗xds

> 0 anddh∗Ids

> 0, need:

dϕnds

<tax

1− s× tax(1 + ϕn)

Under quadratic cost functions, this requires:

R∗I +R∗x +R∗d −µ(1+ϕn)1+µϕn

R∗d

2R∗d

(µ−1

1+µϕn

)2

+ 2R∗I + 2R∗x

< 1

⇒ R∗I +R∗x +R∗d −µ(1 + ϕn)

1 + µϕnR∗d < 2R∗d

(µ− 1

1 + µϕn

)2

+ 2R∗I + 2R∗x

⇒

[1− µ(1 + ϕn)

1 + µϕn− 2

(µ− 1

1 + µϕn

)2]R∗d < R∗I +R∗x

⇒ −

[µ− 1

1 + µϕn+ 2

(µ− 1

1 + µϕn

)2]R∗d < R∗I +R∗x

With µ ≥ 1, the above inequality is hold for sure with positive R&D investment. Hence,

dh∗xds

> 0 anddh∗Ids

> 0. Under uniform tax incentive, higher deduction rate s increases

rm's investment in all types of innovation. However, the increase in internal and external

innovation is less than the increase in industrial design. This increases the share of industrial

design.

dh∗dh∗I

ds∝ d1 + µϕn

ds∝ µ

dϕnds

> 0

dh∗dh∗x

ds∝ d1 + µϕn

ds∝ µ

dϕnds

> 0

79

A.2.8 Proof on Proposition VII

Under type-dependent tax incentive, where only internal and external innovation can receive

super-deduction when calculating tax bases, the nancial constraint becomes:

(1− tax)Rd + (1− s× tax)(RI +Rx) ≤ µπ(1 + Φ)σ−1(1− tax)hd + µκ

where s < 1tax

. Taking derivatives w.r.p.t s on above nancial constraint and rearrange it:

dϕnds

=

R∗IψI−1

+ R∗xψx−1

1−tax1−s×taxR

∗d

ψdψd−1

(µ−1

1+µϕn

)2

+R∗IψIψI−1

+R∗xψxψx−1

tax(1 + ϕn)

1− s× tax> 0

Hence:dh∗dds

=h∗d

ψd − 1

µ− 1

1 + ϕn

1

1 + µϕn

dϕnds

> 0

dh∗Ids

=h∗I

ψI − 1

[−dϕnds

1

1 + ϕn+

tax

1− s× tax

]> 0

dh∗xds

=h∗x

ψx − 1

[−dϕnds

1

1 + ϕn+

tax

1− s× tax

]> 0

The last two inequality hold under quadratic cost function. To see this, for dϕnds

< tax1−s×tax(1+

ϕn) need:R∗I +R∗x

1−tax1−s×tax2R∗d

(µ−1

1+µϕn

)2

+ 2R∗I + 2R∗x

< 1

⇒ 21− tax

1− s× taxR∗d

(µ− 1

1 + µϕn

)2

+R∗I +R∗x > 0

The last line holds for sure. The derivatives of industrial-design-internal ratio w.r.p.t s is

then:dh∗dh∗I

ds∝d(1 + µϕn)1−s×tax

1−tax

ds∝ µ

1− s× tax1− tax

dµnds− (1 + µϕn)

tax

1− s× taxThe ratio is less than 0 if

dµnds

<1 + µϕn

µ

tax

1− s× tax

80

Under quadratic cost function, this requires:

R∗I +R∗x < 21− tax

1− s× taxR∗d

(µ− 1)2

(1 + µϕn)(1 + ϕn)µ+ (2R∗I + 2R∗x)

1 + µϕnµ(1 + ϕn)

⇒21− tax

1− s× taxR∗d

(µ− 1)2

(1 + µϕn)(1 + ϕn)µ+ (R∗I +R∗x)

2− µ+ µϕnµ(1 + ϕn)

> 0

The last line holds under our calibration with µ = 1.29 < 2. Hence,dh∗dh∗I

ds< 0 and with the

similar steps, one can prove thatdh∗dh∗xds

< 0. Hence, under type-dependent tax incentive, with

an increase in deduction rate s, share of internal and external innovation increases.

A.2.9 Additional Theoretical Result

My theoretical framework also generates a negative relationship between innovation intensity

and rm size. Such negative relationship stems from decreasing return to scale in external

innovation. The following proposition shows that the existence of nancial constraints, mit-

igates the negative relationship between internal and external innovation intensity, whereas

it strengthen the negative relationship between industrial design.

Proposition VIII (Firm Size and R&D intensity) 1) Firm size is negatively related

to R&D intensity. 2) As larger rms are less likely to be constrained: i.e. dϕndn

< 0, rm size

might not have a strong negative relationship with internal and external innovation intensity,

but have more stronger negative relationship with R&D intensity in industrial design. That

is:dh∗ddn|ϕn>0 <

dhddn|ϕn=0 < 0,

dh∗Idn|ϕn>0 >

dhIdn|ϕn=0,

dh∗xdn|ϕn>0 >

dhxdn|ϕn=0

Proof. From rm's optimal R&D decision (11):

dh∗ddn|ϕn>0 =h∗d

1

ψd − 1

µ− 1

(1 + µϕn)(1 + ϕn)

dϕndn

+ h∗dαdn< δ∗

αdn

=dhddn|ϕn=0

dh∗Idn|ϕn>0 =− h∗I

1

ψI − 1

1

1 + ϕn

dϕndn

+ h∗IαIn> h∗I

αIn

=dhIdn|ϕn=0

dh∗xdn|ϕn>0 =− h∗x

1

ψx − 1

1

1 + ϕn

dϕndn

+ h∗xαxn> h∗I

αxn

=dhxdn|ϕn=0

81

For nancially constrained rm, ϕn decreases as rm grows larger. Thus, the marginal ef-

fective cost of productivity-enhancing innovation drops. This increases rm's incentive to do

both internal and external innovation. The term−h∗I 1ψI−1

11+ϕn

dϕndn

> 0 and−h∗x 1ψx−1

11+ϕn

dϕndn

>

0 measure the decreases in a rm's marginal cost due to reducing its nancial friction ϕn

when it grows larger. This reduction in marginal cost alleviate decreasing return to scale

in internal and external innovation. Hence, for nancially constrained rm, both internal

and external innovation become less sensitive to rm size, comparing with nancially uncon-

strained rm. If −h∗I 1ψI−1

11+ϕn

dϕndn

> 0 or −h∗x 1ψx−1

11+ϕn

dϕndn

> 0 is large enough. It is possible

that internal or external intensity increases with rm size under nancial constraint. Sim-

ilarly, the marginal benet of patenting in industrial design decreases with rm size, as

larger rm benets less in relaxing its nancial constraints. Large rms has less incentive

in patenting industrial design. This is captured by the term h∗d1

ψd−1µ−1

(1+µϕn)(1+ϕn)dϕndn

< 0.

Hence, for nancially constrained rms, return on patenting in industrial design exhibits

more decreasing return to scale, comparing with nancially unconstrained rms.

A.3 Computational Algorithm

Following Acemoglu and Akcigit (2010), the optimization problem can be transferred into a

discrete time control problem through uniformization. Rewrite the optimization problem as:

(ρ+ nτ + nhx)Bn = maxhd,hI ,hx

nπ(1 + Φ)σ−1hd + nhIλB + nhxB(1 + ν)− xdhψdd n

αd+1 − xIhψII nαI+1

− xxhψxx nαx+1 + nhxBn+1 + nτBn−1

s.t. xdh

ψdd n

αd + xIhψII n

αI + xxhψxx n

αx ≤ µκ+ µπ(1 + Φ)σ−1hd

Redene

Π(hd, hI , hx, n) =nπ(1 + Φ)σ−1hd + nhIλB + nhxB(1 + ν)− xdhψdd nαd+1 − xIhψII nαI+1 − xxhψxx nαx+1

ρ+ nτ + nhx

82

where n is the state variable. Dene two transit probability: pn,n+1 as transfer from state n

to state n+ 1 and pn,n−1 as transfer from n to n− 1:

pn,n+1 =nhx

nτ + nhx, pn,n−1 =

nτ

nτ + nhx

dene a discount factor:

β =nτ + nhx

ρ+ nτ + nhx

The problem can be re-written as:

Bn = maxhd,hI ,hx

Π(hd, hI , hx, n) + ρEBn′

s.t. xdh

ψdd n

αd + xIhψII n

αI + xxhψxx n

αx ≤ µκ+ µπ(1 + Φ)σ−1hd

Bn is well dened and bounded above (see the proof of proposition II). Then Bn can be

solved through value function iteration. The equilibrium is solved through following steps:

1. Guess aggregate patenting in industrial design Φ.

2. Guess growth rate g and creative destruction rate τ .

(a) solve value function Bn using uniformization method.

(b) solve the policy function hd, hI and hx for each product lines in each rm as a

function of (g, τ,Φ).

3. Solve the equilibrium stationary distributionM , ηn and implied τ . Verify the free-entry

condition (8). Loop until τ converged and free-entry condition (8) hold.

4. Verify the growth rate g∗ in (10). Loop until g converged.

5. Verify the aggregate Φ through Φ =∑∞

n=1 ηnMnhd(n). Loop until g converged.

83

A.4 Additional Empirical and Result

A.4.1 Summary Statistics

Table A4: Summary Statistics

Domestic Private Firms Unconstrained Firms Constrained FirmsMean St.Dev Mean St.Dev Mean St.Dev

log(sale) 1.656 1.322 2.043 1.381 1.365 1.261SaleGrowth 0.211 1.803 0.255 2.063 0.174 1.682TFP 0.15 0.875 0.26 0.872 0.101 0.89LP 0.071 0.844 0.271 0.845 -0.055 0.849RDIntensity 0.009 0.038 0.012 0.043 0.007 0.031Cash 0.113 0.176 0.124 0.174 0.103 0.186Tangibility 0.567 0.22 0.595 0.228 0.552 0.217FC 0.532 0.114 0.434 0.079 0.624 0.093LongrunInnov 3.962 33.249 5.711 47.094 3.087 30.779TotalPat 2.382 17.806 3.139 27.337 1.984 13.995IndDesIntensity 0.213 3.047 0.16 2.78 0.268 3.801InternalIntensity 0.277 1.682 0.284 1.778 0.273 1.709ExternalIntensity 0.225 1.955 0.257 2.463 0.219 1.907IndDesShare 0.229 0.38 0.204 0.36 0.252 0.396ExternalShare 0.353 0.375 0.369 0.37 0.342 0.377N.Obs 118,548 32,267 33,751

Note: log(sale) is measured as real total sale. SaleGrowth is annual growth rate in real total

sales. TFP is total factor productivity, calculated following David and Venkateswaran (2019). LPis labor productivity, calculated as real value added over employment after removing industrial

and year eect. R&D intensity is dened as R&D over sales. Cash is measured as cash ow over

total asset. Cash ow is dened as net income plus current depreciation. Tangibilityit−1 is mea-

sured following Almeida and Campello (2007) and Berger, Ofek and Swary (1996). Tangibility =0.715 × Receivables + 0.547 × Inventory + 0.535 × FixedAsset + Cash + MarketableSecuritiesscaled by total asset. FCit measure rm's nancial condition dened as probability of being con-

strained, which is calculated via endogenous switching regression in section 2.3. LongrunInnov is

the citation-weighted average application in long-run innovation. TotalPat is total patent applica-tion without citation adjustment. industrial design, Internal and External intensity is dened as

number of patent application in industrial design, internal and external over sales (per ten million

RMB). industrial design patent share is the percentage of industrial design patenting in total patent

application. External innovation share is the percentage of external patenting in total patent ap-

plication. Firms with estimated likelihood of being nancial constrained in the bottom tertile is

classied as unconstrained rms and in the upper tertile is classied as constrained rms.

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A.4.2 Financial constraint and rm-size-innovation-intensity relationship

Table A5: Firm Size, Growth and Innovation Intensity (Prob of Constrained)

Growth Patent Intensity Patent Share(1) (2) (3) (4) (5) (6)

∆Saleit+1

Saleit

PatappditSaleit

PatappIitSaleit

PatappXitSaleit

PatappditPatappTit

PatappXitPatappTit

log(Sale)it −0.108∗∗∗ −0.105∗∗∗ −0.110∗∗∗ −0.073∗∗∗ −0.005 0.011∗∗∗

(0.010) (0.027) (0.006) (0.008) (0.003) (0.003)Ageit 0.001 −0.003∗∗∗ −0.002∗∗∗ −0.001∗∗ −0.002∗∗∗ 0.001∗∗∗

(0.001) (0.001) (0.000) (0.000) (0.000) (0.000)FCit −1.186∗∗∗ 0.431 −0.294∗∗∗ −0.464∗∗∗ 0.213∗∗∗ −0.274∗∗∗

(0.122) (0.357) (0.094) (0.116) (0.045) (0.039)log(Sale)× ProbIndit 0.050∗∗∗ −0.022 −0.002 0.007 −0.001 0.001

(0.009) (0.025) (0.007) (0.009) (0.004) (0.003)Industry Fix Yes Yes Yes Yes Yes Yes

Year Fix Yes Yes Yes Yes Yes YesN 61, 209 49, 144 50, 995 48, 584 17, 146 16, 586

R-squared 0.076 0.015 0.029 0.008 0.204 0.212

Note: log(sale) is measured in real total sales. Patappit is the citation-weighted patent application

in industrial design (denoted as d in superscript), long-run internal (I), external (x). PatappTitis rm's total patent application at time t. FCit measure rm's nancial condition dened as

probability of being constrained, which is calculated via endogenous switching regression in section

2.3. ProbIndit is an index which equals 1 if rm is nancially constrained (i.e. probability of being

constrained greater than 0.5). Industry-year xed eect is controlled but not reported. Robust

standard errors clustered at rm level are reported in parentheses. ∗∗∗, ∗∗ and ∗ indicate signicantlevel at 1%, 5% and 10%, respectively.

Table A6: Firm Size, Growth and Innovation Intensity

Growth Patent Intensity Patent Share(1) (2) (3) (4) (5) (6)

∆Saleit+1

Saleit

PatappditSaleit

PatappIitSaleit

PatappXitSaleit

PatappditPatappTit

PatappXitPatappTit

log(Sale)it −0.083∗∗∗ −0.110∗∗∗ −0.112∗∗∗ −0.061∗∗∗ −0.011∗∗∗ 0.014∗∗∗

(0.006) (0.015) (0.004) (0.004) (0.003) (0.002)Industry Fix Yes Yes Yes Yes Yes Yes

Year Fix Yes Yes Yes Yes Yes YesN. Obs 110, 329 85, 760 89, 120 84, 727 30, 229 29, 196

R-squared 0.063 0.013 0.030 0.009 0.199 0.208

Note: Industry-year xed eects are included as controls, but I do not report in regression. Robust

standard errors clustered at rm level are in parentheses. ∗∗∗, ∗∗ and ∗ indicate signicant at levels1%, 5% and 10%, respectively.

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Table A7: Firm Size, Growth and Innovation Intensity (Cash ow Sensitivity)

Growth Patent Intensity Patent Share(1) (2) (3) (4) (5) (6)

∆Saleit+1

Saleit

PatappditSaleit

PatappIitSaleit

PatappXitSaleit

PatappditPatappTit

PatappXitPatappTit

log(Sale)it −0.091∗∗∗ −0.113∗∗∗ −0.111∗∗∗ −0.063∗∗∗ −0.006∗∗ 0.014∗∗∗

(0.006) (0.019) (0.005) (0.004) (0.003) (0.002)Ageit −0.002∗∗∗ −0.002∗∗∗ −0.004∗∗∗ −0.002∗∗∗ −0.001∗∗∗ 0.000

(0.000) (0.001) (0.000) (0.000) (0.000) (0.000)Cash 0.083∗∗∗ −0.004 0.016∗∗∗ 0.015∗∗∗ −0.010∗∗∗ 0.004∗

(0.007) (0.008) (0.004) (0.005) (0.003) (0.002)Industry Fix Y es Y es Y es Y es Y es Y es

Year Fix Y es Y es Y es Y es Y es Y esN 88, 843 70, 288 73, 026 69, 476 25, 297 24, 485

R-squared 0.098 0.014 0.031 0.009 0.194 0.206

Note: log(sale) is measured in real total sales. Patappit is the citation-weighted patent application

in industrial design (denoted as d in superscript), long-run internal (I), external (x). PatappTit isrm's total patent application at time t. Cash is measured as cash ow over total asset. Cash ow

is dened as net income plus current depreciation. Tangibilityit−1 is measured following Almeida

and Campello (2007) and Berger, Ofek and Swary (1996). Industry-year xed eect is controlled

but not reported. Robust standard errors clustered at rm level are reported in parentheses. ∗ ∗ ∗,∗∗ and ∗ indicate signicant level at 1%, 5% and 10%, respectively.

Table A8: Firm Size, Growth and Innovation Intensity

Growth Patent Intensity Patent Share(1) (2) (3) (4) (5) (6)

∆Saleit+1

Saleit

PatappditSaleit

PatappIitSaleit

PatappXitSaleit

PatappditPatappTit

PatappXitPatappLit

unconstrained −0.113∗∗∗ −0.092∗∗∗ −0.113∗∗∗ −0.074∗∗∗ −0.001 0.014∗∗∗

(0.011) (0.029) (0.008) (0.009) (0.004) (0.003)constrained −0.041∗∗∗ −0.147∗∗∗ −0.107∗∗∗ −0.062∗∗∗ −0.011∗∗ 0.013∗∗∗

(0.011) (0.035) (0.007) (0.006) (0.005) (0.004)

Note: Each cell reports the estimated OLS coecients on rms size, measured as log of real sales

revenue. Firm age, FC score, and year and industry xed eects are included in the regression, but

I do not report the result. Row 1 reports the regression coecient on rm size for constrained rms,

and row 2 reports the coecient for unconstrained rms. Robust standard errors clustered at rm

level are in parentheses. ∗ ∗ ∗, ∗∗ and ∗ indicate signicant at levels 1%, 5% and 10%, respectively.

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Table A9: Firm Growth and Innovation

One Period Ahead Two Period Ahead Three Period Ahead(1) (2) (3) (4) (5) (6) (7) (8) (9)

log(D + 1) 0.013∗ 0.004 0.002(0.007) (0.012) (0.013)

log(LTE + 1) 0.024 ∗ ∗∗ 0.024 ∗ ∗ 0.050 ∗ ∗∗(0.006) (0.010) (0.018)

log(LTI + 1) 0.012 ∗ ∗ 0.019 ∗ ∗ 0.027 ∗ ∗∗(0.005) (0.008) (0.009)

FE Yes Yes Yes Yes Yes Yes Yes Yes YesControls Yes Yes Yes Yes Yes Yes Yes Yes YesN. Obs 77, 564 66, 134 66, 134 41, 161 78, 353 51, 109 51, 109 41, 161 41, 161

R-squared 0.072 0.128 0.128 0.104 0.098 0.098 0.101 0.101 0.101

Dependent variables are rm's growth rate in real sales. Dit is the log of number of industrial design

patenting application at time t, LTit is the number of productivity-enhancing patents: invention

and utility models. Current, one period and two period are dependent variable measures rm's real

sales growth in one, two and three years, respectively. Past real sales, rm age and Industry-year

xed eects are included as controls, but I do not report in regression. Robust standard errors

clustered at rm level are in parentheses. ∗ ∗ ∗, ∗∗ and ∗ indicate signicant at levels 1%, 5% and

10%, respectively.

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