metadata: authors: 0: author: Sharma,Siddharth
count: World
docna: 0: docna: Financial development and innovation in
            small firms
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Social Policy,Legal Products,Real & Intellectual Property Law,Judicial System Reform,Industrial Economics,Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Common Property Resource Development,Legal Institutions of the Market Economy,Economic Growth,Legal Reform,Financial Economics,Legislation,Regulatory Regimes,Business Cycles and Stabilization Policies,Finance and Development,Intellectual Property Rights
teratopic: Finance and Financial Sector Development,Education
abstracts: cdata!: This paper uses firm level data from a
            cross-section of 57 countries to study how financial
            development affects innovation in small firms. The analysis
            finds that relative to large firms in the same industry,
            spending on research and development by small firms is more
            likely and sizable in countries at higher levels of
            financial development. The estimates imply that among firms
            doing research and development in a country like Romania,
            which is at the 20th percentile of financial development, a
            1 standard deviation decrease in firm size is associated
            with a decrease of 0.7 standard deviations in research and
            development spending. In contrast, this decrease is only 0.2
            standard deviations in a country like South Africa, which is
            at the 80th percentile of the distribution of financial
            development. Small firms also report producing more
            innovations per unit of research and development spending
            than large firms, and this gap is narrower in countries at
            higher levels of financial development. As a robustness
            check, the author shows that these patterns are stronger in
            industries inherently more reliant on external finance.
repnme: repnme: Financial development and innovation in
            small firms
display_title: Financial development and innovation
            in small firms
listing_relative_url: /research/2007/09/8621977/financial-development-innovation-small-firms
topicv3: Economic Growth m1326241 471,Manufacturing Sectors m1326521 1281,Patents m1326812 1041,Finance and Growth m1327404 1081,Financial Institutions m1505015 3797
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Finance and Financial Sector Development,Education
no_of_pages: 33
author_keys: 0: author_key: 717230
model_extractions: WPS4350 Policy ReseaRch WoRking PaPeR 4350 Financial Development and Innovation in Small Firms _Siddharth Sharma_ The World Bank Financial and Private Sector Vice Presidency Enterprise Analysis Unit September 2007
Policy ReseaRch WoRking PaPeR 4350

# **Abstract**

This paper uses firm level data from a cross-section of 57 countries to study how financial development affects innovation in small firms. The analysis finds that relative to large firms in the same industry, spending on research and development by small firms is more likely and sizable in countries at higher levels of financial development. The estimates imply that among firms doing research and development in a country like Romania, which is at the 20th percentile of financial development, a 1 standard deviation decrease in firm size is associated with a decrease of 0.7 standard deviations in research and development spending. In contrast, this decrease is only 0.2 standard deviations in a country like South Africa, which is at the 80th percentile of the distribution of financial development. Small firms also report producing more innovations per unit of research and development spending than large firms, and this gap is narrower in countries at higher levels of financial development. As a robustness check, the author shows that these patterns are stronger in industries inherently more reliant on external finance.

This paper—a product of theEnterprise Analysis Unit, Financial and Private Sector Vice Presidency—is part of a larger effort in the Bank to study the effects of financial development on firm performance. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at SSharma1@ifc.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Financial Development and Innovation in Small Firms

Siddharth Sharma<sup>∗†</sup> JEL Classification: G21; O16, O30

> ∗International Finance Corporation. E-mail: SSharma1@ifc.org. All views expressed are my own.

> †I am grateful to Mohammad Amin, Simeon Djankov, Ernesto Lopez-Cordova, Enrique Seira and participants at World Bank/IFC seminars for helpful suggestions.

1
# 1 Introduction

In their seminal work on finance and growth, Rajan and Zingales (1998) were able to show that industries more dependent on external finance grow faster in countries that are more developed financially. More recently, Guiso et al. (2004a) find that the smaller the firm, the stronger this association between financial development and growth. In another paper, using regional data from Italy, Guiso et al. (2004b) find that regional financial development is more beneficial to the growth of smaller firms. Levine et al. (2006) show that industries which for technological reasons have a larger share of small firms grow faster in economies with well-developed financial systems. Aghion et al. (2007) report that there is greater entry of small firms relative to large firms in countries at higher levels of financial development.

This suggests that financial development does not affect firms of different sizes equally, and that it matters more to the growth of small firms. However, our understanding of this differential effect is limited. Why are smaller firms more sensitive to financial development? It is possible that the informational asymmetries which cause financial market failures also cause these failures to hurt small firms more than large firms. Lenders might know less about smaller firms because they are more opaque, or because given the small loan size, it is not profitable to spend resources on acquiring information about small firms and monitoring small loans. Another explanation is that financial innovations reduce the need for collateral, affecting smaller firms disproportionately because they have fewer tangible assets to put up as collateral.

Among the activities of a firm, innovation is most susceptible to adverse selection and moral hazard. This is because the innovator is likely to have much better information about the chances of success than potential investors, and the latter are unlikely to have the knowledge necessary to effectively monitor the research project.<sup>1</sup> Another key feature of investment in innovation is that much of it goes into intangible assets, such as the specialized knowledge embodied in researchers.

A stylized fact in the literature on innovation by firms is that the smaller the firm, the less likely it is to engage in research and development, and that among firms engaged in R&D, the amount spent on innovative activities rises with firm size (Cohen and Klepper (1996)). Yet, studies which estimate the productivity of R&D indicate that innovations produced per dollar of R&D are higher in smaller firms.<sup>2</sup> Acs and Audretsch (1991a) report that small firms contribute more than twice as many innovations per employee than do large firms, while Plehn-Dujowich (2006) finds that on average, smaller firms obtain three times more patent citations per dollar of R&D. This association of firm size with rising investment and falling productivity in R&D suggests that there is underallocation of R&D investment to small In addition, Hall (2005) reports evidence for the presence of liquidity constraints in a number of studies of R&D investment by firms in various developed countries. Her survey of research on the venture capital industry indicates that the industry is concentrated precisely where innovative startups, which are mostly small firms, are most active, and that in spite of considerable entry into the industry, returns remain

> 1In a recent paper, Herrera and Minetti (2007) show that the length of a bank’s relationship with a firms is positively associated with more R&D by the firms. Interpreting the relationship length as a proxy for the bank’s information on the leads them to conclude that bank’s information matters to innovation.

> 2Cohen and Klepper (1996), Bound et al. (1984), Acs and Audretsch (1991b), Acs and Audretsch (1988).

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high. Hall’s conclusion is that “small and new innovative firms experience high costs of capital that are only partly mitigated by the presence of venture capital,” while “evidence for high costs of R&D capital for large firms is mixed”. In more recent work, Benfratello et al. (2006) use firm data from Italy to investigate the effect of regional banking development on innovative activities, and find evidence of a stronger positive for small Prior research thus suggests that financial development has a disproportionately positive affect on innovation by small firms. This innovation channel could be one reason behind the heterogenous impact of finance on firm growth. Moreover, the observed higher productivity and lower spending on innovation in small firms suggests that financial growth could lead to a more optimal interfirm allocation of spending on innovation. This hypothesis implies that as financial markets develop, there is relatively more R&D investment by smaller firms, and that relative R&D productivity in larger firms rises. In this paper, I use data on firms from 57 countries to see if this dual pattern shows up in cross-country data from developing economies.

I find that within industries, relative R&D spending in smaller firms is more likely and sizable in countries at higher levels of financial development. The estimates imply that among firms doing R&D in a country at the 20th percentile of financial development, a one standard deviation decrease in firm size is associated with a decrease of 0.7 standard deviation in R&D spending. In contrast, this decrease is only 0.2 if financial development is at the 80th percentile of its distribution across countries. My second finding also supports the hypothesis: small firms report producing more innovations per unit R&D than large firms, but this gap is narrower in countries at higher levels of financial development.

To verify further that the observed patterns relate to financing, I exploit the crossindustry dimension of my data, interacting financial development with a measure of an industry’s inherent reliance on external finance. I find that the association between financial development and innovation by small firms relative to large ones is stronger in industries more dependent on external finance. I also show that the patterns are robust to controlling for another factor that could have a heterogeneous effect on innovation, namely entry regulation.

Finally, I find that relative R&D by small firms is significantly associated with bank development but not with measures of stock market development. This is consistent with previous research on the source of financing of R&D projects. While banks are the main source of R&D financing in European countries, and a significant source in the U.S. (Herrera and Minetti (2007), Berger and Udell (1998)), the sources of funds vary with the size of the R&D project. Aghion et al. (2003) find that UK firms that report positive but low R&D use more debt finance than firms that report no R&D, but the use of debt finance falls with R&D intensity. They suggest that this is so because firms go first for debt as it involves giving up less control rights than new equity. But eventually, debt is harder because R&D involves intangible assets.

An ideal test of the hypothesis that financial development spurs innovation by small firms relative to large firms would involve comparing small and large firms across markets that randomly differ in the degree of financial development. Such exogenous variation is rarely possible in cross-country analysis, where it is likely that financial development is correlated with other determinants of innovative activities. For example, 3
countries with better financial institutions might also have better intellectual property rights. Since plausible correlates are too numerous to control for, any observed relationship between finance and innovation is open to alternative interpretations.

Subject to this caveat, the problem of correlated unobservable country level determinants is less of a concern in the present paper. The reason for this is that I focus on the differential effect of finance across firm size. Correlates of financial development which affect small and large firms to the same degree do not matter to the interpretation of my results. Moreover, such unobserved determinants of R&D activity are unlikely to cause both lower relative R&D spending and higher relative R&D productivity in small Another caveat that goes with this study is that the analysis essentially compares firm size and R&D activity across different industry-country cells. Unlike a panel study, it cannot distinguish between changes in the allocation of R&D to firms and in the composition of firms. The results are thus consistent with theories in which financial development affects the distribution of innovation across firms by either encouraging the entry of small innovative firms, or re-allocating finance from existing large firms to small The rest of the paper is organized as follows. Section 2 describes the data. Next, section 3 presents preliminary evidence to suggest that finance might matter to innovation by small firms. Section 4 spells out the estimated equations. I present the main probit and OLS estimation results in Section 5, robustness checks in Section 6, and then conclude in Section 7.

# 2 Data

## 2.1 Firm Data

I use firm level data from World Bank Enterprise Surveys<sup>3</sup> that were carried out between 2003 and 2006. Every survey consisted of a random sample of firms from one country, stratified by firm size and broad 2-digit industry. Enterprise Survey data from different countries are comparable because of similar sampling strategy and survey instruments. Since no country in my data set was surveyed twice during this period, I treat the data as a pooled cross-section of firms.<sup>4</sup> The focus being investment in R&D, firms from the service industry are excluded from the sample.<sup>5</sup> The full sample consists of nearly 21,000 manufacturing firms from 57 countries, of which 28 are in Eastern and Central Europe, 9 in Africa, 5 in Southeast Asia, and 15 in Latin America. Table 1 lists key summary statistics by country. While most are middle and low income countries, there are a few rich countries in the sample, notably South Korea, Portugal, Spain, Germany and Ireland. Thus, the data encompass a broad range of countries at different levels of development.

The sample size variation across countries is related to the variation in the total number of firms in these countries. All but the following four countries - Brazil, Mexico, Thailand and Egypt- contribute less than a thousand firms to the sample. In terms of

> 3See www.enterprisesurveys.org for detailed descriptions of the surveys.

> 4Note that the country-industry dummies in the estimations absorb all year dummies.

> 5This is not to say that such firms do not innovate. However, they are much less likely to take out patents, and so dropping them makes the data more comparable to those used in most other studies of innovation.

4
the number of surveyed firms, about 39% the sample is from Latin America, 27% from Europe, 18% from Southeast Asia, and 16% from Africa.

Following the convention in the literature, I measure firm size by the value of total annual sales (in million US dollars), and spending on innovation by annual expenditure on research and development (in ’000 US dollars).

The surveys categorize firms into two-digit (ISIC) industry groups; there are 16 such categories in the data. Since my main estimation exploits variation in the probability of engaging in R&D within country-industry cells, I do not use cells in which either all firms report strictly positive R&D expenditure, or no firm reports R&D. This amounts to dropping about 4% of the original sample. This leaves me with 654 country-industry cells, each containing about 30 firms on average. After dropping outliers in R&D spending and sales, the data set consists of 19845 firms.

Since not all innovative activity can be classified under an exclusive category, and since some R&D consists of fixed investment in equipment and facilities, it is likely that this current R&D spending is an understatement of a firm’s expenditure on innovative activities. It is also possible that different firms report different things under R&D spending. However, there is no reason to believe that this measurement error varies systematically across firm size and financial development.

The surveyed firms were asked if their own R&D resulted in a new product, a new process and a significant upgrading of the product. For every firm, I sum up these indicators to construct an index of innovative output that ranges in value from 0 to 3. This index differs from the most commonly used measure of innovative output, which is the number of patents taken out by a firm. Since not all innovative activity results in a new patent, the index is a more exhaustive and direct measure of innovation than patenting activity.<sup>6</sup> But it shares, with patents, the limitation of being a count measure instead of a direct estimate of the monetary value of the new products or processes. Furthermore, a “new product” introduced by a typical small firm in an industry is likely to have less monetary value than a new product introduced by large firms in the same industry. However, it is reasonable to assume that this interindustry reporting bias does not vary across countries.

Table 2 shows that about 26% of the sampled firms spent a positive amount on research and development. As reported in Table 1, there is considerable cross-country variation in this figure. Only 4% of the firms surveyed in Oman report having spent on R&D, while in South Africa this percentage is 52. National income figures in Table 1 also reveal that in general, more firms do R&D in larger economies.

Among firms that do spend on R&D, the average spending on R&D is 3% of total sales. Fewer than a tenth of these firms spend more than 10% of the value of their sales on R&D. The average value of the innovation index for firms engaged in R&D is 2; nearly a quarter of these firms have an innovation index of zero.

# 2.2 Measures of Financial Development

In keeping with common usage in the literature on finance and growth, my principal measure of a country’s financial development is the ratio of private credit to GDP,<sup>7</sup> where private credit is defined as the total credit from deposit-taking institutions to

> 6Although it misses the effect of R&D on technology adoption (Griffith et al. (2004)).

> 7See studies surveyed in Levine (2005).

5
the private sector. As shown in Table 1, there is considerable variation in private credit/GDP (the variable PvtCredit) across the countries in my sample; it ranges from a low of 0.04 in Kyrgyzstan to a high of 1.4 in Portugal, and the median country in the sample has a private credit/GDP value of 0.35. As alternatives to private credit/GDP, I use two other measures of a country’s financial development: deposit accounts (Deposit) and the interest rate spread (Spread ). The variable Deposit is the number of bank deposit accounts in a country. These include all checking, savings, and time deposit accounts for businesses, individuals, and others. This variable is taken from the World Development Indicators, where it has been compiled from surveys of banking and regulatory institutions by the World Bank. Spread is the difference between the interest rate charged by banks on loans to prime customers and that paid by banks on demand, time, or savings deposits. The source of the private credit and the interest rate data are the IMF International Financial Statistics.<sup>8</sup> Private Credit/GDP includes credit extended by all banks and non-bank financial institutions. The number of deposit accounts excludes financial intermediaries that do not take deposits, and so is more indicative of just banking sector coverage. The interest rate spread is a measure of the efficiency with which the banking sector intermediates funds; a narrow interest rate spread thus indicates a higher level of financial development. However, it is possible for the banking sector to have limited coverage and a low interest rate spread.<sup>9</sup> So, the three variables pick up closely related but not quite identical aspects of financial intermediation.<sup>10</sup> Table 3 shows that PvtCredit and Deposit are positively correlated, and as expected, Spread has a negative correlation with both variables. Since data on Deposit and Spread is missing for many countries in the sample, estimations using these measures are best viewed as robustness checks.<sup>11</sup> I use two alternative measures of a country’s stock market development, also derived from the World Development Indicators. The variable Stock is the total value of stocks traded in an economy, a measure of the size of stock markets. The second measure is the “turnover ratio” (TRatio), the ratio of stocks traded to stock market capitalization, and it measures stock market liquidity. TRatio ranges from a low of 0.3 to a high of 255 in the data. The two stock market measures are positively correlated with PvtCredit, but the correlation is less than 0.5.

# 2.3 Financial Dependence

I use the Rajan and Zingales (1998) measure of an industry’s dependence on external finance to see if the association between financial development and relative R&D by small firms is stronger in industries that use more external finance. Rajan and Zingales identified an industry’s need for external finance, defined as the difference between investments and cash generated from operations, from data on U.S. firms. Under the assumption that capital markets in the United States are relatively frictionless,

> 8The units of these country-level variables were chosen to make magnitudes comparable. For example, Deposit is measured in units of 10 millions, while PvtCredit is the ratio of private credit to GDP, both measured in the same unit. This makes the magnitude of coefficients comparable across alternative measures of financial development.

> 9Moreover, the interest rate spread measures efficiency under the assumption that interest rates are unregulated.

> 10Also note that being market equilibrium outcomes, they are imperfect measures of the “supply” side of finance.

> 11Results with respect to PvtCredit are not sensitive to limiting the sample to countries with full Deposit and Spread data.

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this method allowed them to identify an industry’s technological demand for external financing. Under the further assumption that such technological demand carries over to other countries, this measure gave them a ranking of industries by need for external finance that stayed constant across countries.

There are two limitations on the applicability of this industry level variable in the present study. First, the measure does not refer specifically to the financing of innovation. So, in ordering industries by this measure, I assume that firms in industries more reliant on external finance are also those with less internal funds for R&D. Second, since my data set consists of only sixteen two-digit industrial classes, I am unable to exploit the full extent of variation in the Rajan-Zingales measure.<sup>12</sup>

# 3 Preliminary Analysis

## 3.1 Comparing Firm Size Distribution Across Countries

The empirical analysis in this paper compares the association between innovation and firm size across different countries by regressing innovation on an interaction of firm size with financial development. Since firm size is measured in absolute terms and in the same unit across countries, the interpretation of the coefficient on the interaction term is less clear if size distribution varies significantly across countries. Figure 1 addresses this concern by comparing the size distribution of firms in the data across countries grouped by financial development. It depicts estimates of the size distribution in each of four randomly picked major industry groups for two sets of countries, those above and below the median value of PvtCredit.<sup>13</sup> It is apparent that in all four industries, there is no significant difference in the size distribution across the two sets of countries. The same is true of other industries, lending credence to the interpretation of the interaction term as a measure of the association between finance and relative innovation by small

## 3.2 Preliminary Evidence

In this section I present four patterns in the data which are suggestive of the hypothesis. First, firms doing R&D are more intensive users of bank finance. As mentioned in the introduction, prior evidence on the sources of funding for R&D is mixed. Banks are the main source of R&D financing in European countries, and a significant one in the United States. However, small innovative startups are also financed by the venture capital industry, particularly in the US (Hall (2005)). While I lack data on the source of funding for R&D, I can compare financing patterns in firms doing R&D to those not doing R&D. Table 4 looks at the percentage of new firm investment financed according to source. For each source, this percentage is regressed on R&D and country-industry dummies. The regressions show that compared to other firms, those that engage in R&D have significantly higher percentages of new investment financed by domestic banks, foreign banks and by government funds. They have a lower percentage financed

> 12For the most part, there was a one to one correspondence between Rajan and Zingales’s industry groups and my 2-digit ISIC categories. In those industries for which this was possible, a finer matching was achieved using my data on the firm’s product category.

> 13These are kernel density estimates of the logarithm of firm sales.

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by internal funds, while there is no statistically significant difference by R&D status in equity financing. I also find that these patterns hold equally for both small and large firms.<sup>14</sup> Thus, R&D activity certainly seems to be associated with bank funding, while the association with equity is unclear.

Second, there is evidence in the data that small firms report stronger financial obstacles than large firms. Surveyed firms were asked to rate finance as an obstacle to growth, and on average smaller firms’ ratings were higher. Being a subjective rating, this is open to the interpretation that small firms simply complain more. Nevertheless, unless this tendency to complain varies differentially by size across countries, it is interesting to note that the higher rating by small firms is less pronounced as we move to countries at higher levels of financial development. Table 5 regresses firm rating of financial obstacles on firm size interacted with private credit/GDP. Controlling for country-industry effects, the tendency of smaller firms to complain more about access to falls as PvtCredit rises.

Next, figures 2 and 3 give graphical previews of the main finding in this paper. Figure 2 plots R&D spending against firm size separately for countries above and below the median value of the private credit/GDP ratio.<sup>15</sup> A comparison of the two panels makes it evident that in my sample of 19,845 firms, the positive association between R&D spending and firm size is stronger in countries at lower levels of private credit.

Figure 3 graphs the innovation/R&D ratio against firm size for countries above and below the median value of the private credit/GDP ratio. It shows that while the innovation/R&D ratio falls with firm size in both set of countries, the decline is sharper in countries below the median value of private credit. Thus, consistent with an explanation based on financial inefficiency, patterns in R&D returns are the reverse of those seen in R&D spending, and there is greater dispersion in returns in low PvtCredit countries. The OLS and probit estimations reported in section 5 confirm these observations.

# 4 The Empirical Specification

## 4.1 Financial Development and The Probability of Spending on Innovation

Let rijc be a dummy variable that equals one if a risk-neutral firm i in industry j and country c engages in R&D. The probability that the firm does R&D can be modeled using a latent variable approach. The size of the R&D project is fixed. Suppose yijc is the firm’s expected profit from the project, defined as the discounted stream of revenue from the R&D output minus the discounted stream of cost of R&D inputs. If the firm needs external financing for R&D, then this cost includes the cost of external funds. Firm i does R&D if the expected profit is higher than a threshold y<sup>∗</sup> . In line with the observation in Hall (2005) that R&D spending by firms has the characteristics of fixed

> 14In regressions with R&D dummy interacted with firm size as an explanatory variable, the interaction term was insignificant.

> 15The lines, drawn for ease of illustration, are non-parametric locally weighted regression estimates. The graph is drawn for firms reporting non-zero R&D expenditure.

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investment, this threshold can be motivated as a fixed cost of investing in research and development.

The expected output of R&D depends on the size of the firm, since there may be economies of scale in R&D or complementarities with other inputs, and since the revenue from an innovation will depend on the total sales of a firm (Cohen et al. (1987)). Now, if financial development has a differential effect by firm size on the cost or availability of external funds for R&D, then yijc will depend on Sizeijc interacted with financial development. Thus, where γjc are country-industry dummies, FinDevc is a measure of the financial development of country c, and GDPc measures its income level. Financial development tends to be highly correlated with the total income level of an economy. It is possible that the size of the domestic market matters differentially to small and large firms. So in the above expression, as a control, I also allow national income to have a differential effect on R&D profits. Note also that the country-industry dummies absorb FinDevc and other country or industry level variables. Now, Assuming that ǫijc is normally distributed, the coefficients in the expression for yijc can be estimated by a probit model.<sup>16</sup> How does one interpret the coefficient α on the interaction of firm size with financial development? Owing to the non-linearity of the expression (equation 2) for the probability of doing R&D, the interaction coefficient cannot be interpreted the same way as in a linear probability model.<sup>17</sup> It is more straightforward to use equation 1 and interpret α and its estimated standard error in terms of the underlying linear model explaining the latent variable yijc − y<sup>∗</sup> , the expected profit (net of sunk costs) from entering into R&D. A negative α would indicate that financial development is associated with a higher net profit from R&D to small firms relative to large firms. Assuming that correlates of financial development do not have a differential effect by firm size on revenue from R&D, this would suggest that financial development lowers the cost of R&D financing to small firms relative to large firms.

To verify that the coefficient on the interaction of firm size with financial development does indeed reflect the financial channel, I test if the interaction effect is stronger in industries with a higher Rajan-Zingales measure of dependence on external finance (FinDep), estimating a Probit in which If the sign of the coefficient on the Sizeijc ∗ FinDevc term in equation 2 reflects the heterogenous effect of financial development, then I expect the coefficient on Sizeijc ∗

> 16Since the data consist of pooled country surveys, the estimation results in the paper report standard errors allowing for the clustering of errors by country.

> 17The parameter of interest, the cross derivative of P r(rijc = 1) w.r.t Size and F inDev, is not α but a more complicated expression involving all explanatory variables, μ, α and the normal density function. See Ai and Norton (2003) for a discussion on interaction terms in logit and probit models.

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FinDevc ∗FinDepj to be of the same sign; that is, I expect a stronger Sizeijc ∗FinDevc interaction effect in industries with higher FinDepj.<sup>18</sup>

# 4.2 Spending on Innovation

Let sijt be the amount spent on R&D (in the previous year) by a firm i, where rijc = 1. To examine how the intensity of innovation spending by small firms relative to large ones varies by financial development, I estimate the following equation by OLS: sijc = γjc<sup>s+ μsSizeijc+ αsSizeijc∗FinDevc+ βsSizeijc∗GDPc+ ǫs</sup> ijc (4) This equation is estimated for the set of firms that report non-zero R&D spending. Thus, it measures how relative spending on innovation varies among firms doing R&D. A negative α<sup>s</sup> indicates that in countries at higher levels of financial development, the intensity of R&D has a weaker association with firm size.

Note that if the coefficient α in equation 2 is negative, then relative to the set of large firms doing R&D, the set of small firms doing R&D is likely to be larger in more financially developed countries. It is possible that this higher (relative) incidence of innovation among smaller firms goes with lower (relative) average spending on innovation per firm. This is consistent with models in which the main impact of financial development is to enable more entry by small firms into R&D. On the other hand, it is also possible that financial development increases the relative availability of R&D funds to small firms to such an extent that even average R&D intensity among small firms rises. Hence, if the coefficient α in the probit equation is significantly different from zero, a positive α<sup>s</sup> does not contradict the hypothesis, although a negative α<sup>s</sup> does lend it further support.

# 4.3 The Productivity of Spending on Innovation

Several studies of R&D and patenting activity find that while small firms spend less on R&D, they take out more patents per dollar R&D (Cohen and Klepper (1996)). This indicates that the productivity of spending on innovation is higher in small firms. Assuming decreasing returns to R&D, it also suggests that with financial development, the reallocation of R&D from large to small firms would be accompanied by an increase in the productivity of R&D in large firms. In other words, it would lead to a more efficient allocation of investment in R&D. To test if there is evidence suggestive of this in cross-country data, I measure innovation produced per dollar R&D, pijt, by dividing firm i’s index of innovation by its R&D spending, and estimate the following equation: As suggested by prior patent based evidence, μ<sup>p</sup> should be negative: innovation produced per dollar R&D is lower for larger firms. More significantly, if this is caused by “over-investment” in innovation in larger firms, then α<sup>p</sup> should be positive: as financial markets develop, innovation produced per dollar R&D increases for large firms relative to small firms. Thus, I expect α<sup>p</sup> to have the opposite sign from the coefficient α<sup>s</sup> in equation 4.

> 18In equation 3, the lower order interaction terms FinDep and Findep*Findev are absorbed in the γjcs.

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5 Main Results

# 5.1 The Probability of Spending on Innovation: Probit Results

Table 6 presents the results from probit estimations of the probability of doing R&D on the full sample of 19845 firms. The main specification is the one spelled out in equation 2, and financial development is measured by private credit/GDP. The standard errors presented allow for clustering by country.

Columns (1) and (2) report results when the probit model includes only industry, and not country-industry dummies. In column (1), explanatory variables include firm size (measured by sales), private credit/GDP (PvtCredit) and size interacted with PvtCredit. The coefficient on firm size is positive and significant, indicating that within industries, larger firms are more likely to do R&D. The coefficient on PvtCredit is also positive and significant, indicating a higher incidence of R&D by firms in countries at higher levels of financial development. The concern with interpreting this correlation is that financial development is correlated with the overall level of development, and with other country characteristics that may be relevant to innovation. This problem becomes apparent in column (2), where I add gross national income (GNI) and its interaction with size as a control. The coefficient on PvtCredit falls and is no longer significant. The coefficient on the interaction of firm size with PvtCredit is negative, although not significant.<sup>19</sup> A comparison of the association between firm size and R&D across countries should also control for country-industry effects, since otherwise it might pick up cross-country differences in industry shares. Hence, my preferred specification is one that includes country-industry dummies γjc in the set of independent variables. The result from estimating this specification (equation 2) is shown in column (3). The coefficient on firm size is positive and significant, while that on the interaction of firm size with PvtCredit is negative and significant.<sup>20</sup> The negative sign implies that the positive association between size and profits from R&D is weaker in countries at higher levels of financial development. This suggests that in keeping with the hypothesis, financial development lowers the cost of R&D funds to a greater extent for smaller firms.

In order to get an idea of the magnitude of the Size*PvtCredit effect from its probit coefficient, one can use the estimates of μ and α from column (3) to measure how the underlying latent variable, the expected profit net of sunk costs of R&D, varies with firm size at different levels of PvtCredit. Consider a country at the 20th percentile of PvtCredit (0.08) in my sample of countries. The estimates imply that here, a one standard deviation (SD) decrease in firm size is associated with decrease of 0.17 units in expected R&D profits. In contrast, holding everything else constant, if PvtCredit is at the 80th percentile of its distribution (0.6), then this decrease is only 0.13 units. Assuming that all non-financial determinants of expected profits from R&D are uncorrelated with Size*PvtCredit, this implies that the increase in financing cost when firm size falls by 1 SD is 25% lower in the case of higher financial development.

> 19The coefficient that on the interaction of GNI with size is positive and significant. The latter stays positive and significant in nearly all the estimations, indicating that controlling for the differential effect of financial development, the positive association between firm size and the probability of doing R&D is stronger in economies with larger domestic markets.

> 20As mentioned in section 4.1, the interaction coefficient and its standard error can be interpreted in the standard way if one considers the underlying linear latent variable model instead of the predicted probability of R&D.

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In column (4) of Table 6, I show evidence to suggest that the interaction effect of firm size and PvtCredit is stronger in industries that are inherently more dependent on external finance. I do this by estimating, as expressed in equation 3, the coefficient on the interaction of Size*PvtCredit with FinDep, the Rajan-Zingales measure of industry reliance on external finance.<sup>21</sup> The coefficient on Size*PvtCredit* FinDep is negative, although the standard error puts the precision at 20% level of significance. Since FinDep is higher for industries more reliant on external finance, this indicates that the negative coefficient on Size*PvtCredit in column (3) was mainly driven by such industries.<sup>22</sup> This pattern, which I will show to be robust to using alternative measures of financial development, increases my confidence in my interpretation of the Size*PvtCredit coefficient in column (3).

Table 7 re-estimates equation 2 using two alternative measure of financial developmentthe number of bank deposits (Deposit) and the interest rate spread (Spread ).<sup>23</sup> To sum up, I find that the patterns seen in columns (3) and (4) of the previous table are verified by both alternative measures. In column (1), the coefficient on Size is positive while that on Size*Deposit is negative and significant. Thus, controlling for the size of the economy, an increase in the number of bank deposit accounts is disproportionately associated with R&D in smaller firms. Column (2) adds an interaction of FinDep with Size*Deposit to the specification; as with private credit/GDP, I find that the coefficient * * on Size Deposit FinDep is negative.

Columns(3) and (4) of Table 7 use the interest rate spread, a measure of the efficiency of the banking system. Note that unlike the previous measures, a higher Spread means lower efficiency in financial intermediation. Once again, the signs are consistent with * those for PvtCredit. The coefficient on the interaction term Size Spread is positive and significant, indicating that controlling for GNI, smaller firms are relatively more likely to do R&D in countries with lower interest rate spreads. Moreover, in column (4) we see that this differential effect of Spread is significantly stronger in industries that are inherently more dependent on financing: the coefficient on the interaction of Size*Spread with FinDep is positive and significant at 1% level.

# 5.2 Spending on Innovation: OLS Results

Table 8 presents OLS estimations of equation 4, examining the relationship between firm size, R&D expenditure and financial development in the subset of firms that do R&D. The results show two robust patterns: first, the relative intensity of R&D by small firms is higher in countries at higher levels of financial development; second, this association is significantly stronger in industries more reliant on external finance. This is evident in columns (1) and (2), which report estimations with PvtCredit as the measure of financial development. In column (1), the coefficient on firm size is positive and significant, while that on Size*PvtCredit is negative and significant.

What is the magnitude of the Size*PvtCredit effect on relative spending on R&D?

> 21Because matching was based on both industry code and product code, there are a few 2-digit industries within which FinDep varies. The estimation includes all lower order interaction terms, namely FinDep, Size*FinDep and Findep*Deposit (or Findep*Spread), as controls.

> 22As mentioned in section 2, because my data set consists of only sixteen two-digit industrial classes, I am unable to exploit the full extent of variation in this measure. This might explain the low precision of the estimate of the triple interaction.

> 23The estimation uses a subset of the full sample because these variables were not available for all countries.

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One can use the estimates of μ<sup>s</sup> and α<sup>s</sup> from column (1) to calculate the answer. Consider a country at the 20th percentile of PvtCredit (0.08). The estimates imply that here, among firms doing R&D, a 1 SD decrease in firm size is associated with a decrease of 0.7 SD in R&D spending. In contrast, holding everything else constant, if PvtCredit is at the 80th percentile of its distribution (0.6), then this decrease is only 0.2 SD. Thus, relative R&D spending in smaller firms shows substantial positive cross-country association with financial development.This result indicates that the disproportionate effect of financial development on innovative activities in small firms is stronger than that suggested by looking only at the number of firms that do R&D.

Moreover, in column (2) we see that the disproportionate impact on R&D spending is stronger in industries which we expect to be more affected by financial development: the coefficient on Size*PvtCredit*FinDep is negative and significant at 1% level.

Columns (3)-(6) confirm these findings using other measures of financial development. In column (3), the coefficient on Size*Deposit is negative and significant at 1% level, while in column (4), the triple interaction shows that this negative sign is stronger in industries with higher values of the Rajan-Zingales measure. Column (5) reports that the association between firm size and R&D spending falls in countries with lower interest rate spreads. Again, this is consistent with the patterns in the probability of engaging in R&D. In column (6), we see that the Size*Spread association is stronger in industries with higher FinDep.

# 5.3 The Productivity of Spending on Innovation: OLS Results

As discussed in section 4.3, the hypothesis implies that the association of financial development with relative R&D productivity in small firms is the reverse of that with relative R&D spending. In Table 9, I test for this by seeing how, among firms engaged in R&D, innovation produced per dollar R&D varies with firm size and financial development.

I measure innovation per dollar R&D by dividing the index of firm innovation by the amount spent of R&D. The count index of innovation has the limitation of being an imperfect and truncated measure of what I would ideally like to measure, which is the monetary value of the new products or processes that are developed by R&D. Since it has a maximum possible value of 3, the index is biased towards underreporting higher R&D returns. If a “new product” introduced by a small firm in an industry has less monetary value than that introduced by large firms in the same industry, a productivity measure based on this innovation index will be biased downwards for larger firms. However, it is reasonable to assume that this reporting bias does not vary systematically across countries. So, the coefficients on the interaction of size with country characteristics are still informative of the cross-country variation in the relative productivity of R&D by small firms.

Column (1) of Table 9 reports that the coefficient on Size is negative, while that * on Size PvtCredit is positive and significant. This says that in my sample of firms the gap between small and large firms in innovation per unit R&D is lower in countries with higher private credit/GDP. Thus, the patterns in R&D returns are the reverse of those seen in R&D spending. As columns (3) and (5) show, this correlation is robust to replacing PvtCredit with either bank deposit accounts or the interest rate spread.

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Taken together, the main findings are that as financial markets improve across countries, large firms do less R&D relative to small firms, but they produce more innovation per dollar R&D. This indicates that financial development lowers the gap in returns to R&D across small and large firms, and thereby increases the overall efficiency of R&D allocation across firms.

The reversal of the interaction sign when looking at R&D productivity also suggests that the sign of the coefficient on Size*PvtCredit in the previous R&D spending regressions could not have been driven by correlates of financial development that raise the relative returns to R&D in small firms. Had that been the case, the gap in R&D productivity would have widened with PvtCredit.

Unlike the previous correlations, the pattern between innovation per dollar R&D and Size*PvtCredit is not significantly stronger in industries with higher values of FinDep. This could be because of the small sample size and relatively small number of industry groups. It could also be the case that the innovation count is not comparable across industries, and in a way that varies across countries.

# 6 Robustness Checks

## 6.1 Stock Market Development

Table 10 presents probit estimates of the probability of R&D when interactions of stock market indicators with firm size are added to equations 2 and 3. The purpose is two-fold: firstly, equity and bank development tend to go together across countries, and since equity might be an important alternative source of R&D investment, it is useful to control for the differential effect of stock market development. Secondly, prior theoretical and empirical evidence on equity and R&D is mixed, and so the coefficient on the interaction of stock market indicators with firm size is interesting in itself.

The estimations use two alternative stock market indicators. Stock (columns (1)(2)), the total value of stocks traded in an economy, measures the size of stock markets. TRatio, or “turnover ratio” (columns (3)-(4)) is the ratio of stocks traded to market capitalization, and it measures stock market liquidity. Both measures give broadly similar results. Compared to the original estimate in column (3) of Table 6, both the point estimate and the precision of the coefficient on Size*PvtCredit is largely unchanged in Table 10. Similarly, there are no major changes in the coefficient on * * Size PvtCredit FinDep.

As for coefficients on the interaction of size with stock market indicators, Table 10 reports that they are negative but statistically insignificant for both measures. Moreover, there is no consistent pattern in the interaction of firm size with stock markets and FinDep. This indicates that there is no significant cross-country correlation between stock market development and R&D by small firms relative to large ones. This result is consistent with the low use of venture capital by small innovative firms in Europe (Herrera and Minetti (2007)) and even in the US (Berger and Udell (1998)).<sup>24</sup>

> 24It is also consistent with the observation in Hall (2005) that the returns to innovation by small farms are high even in sectors where venture capital is concentrated.

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# 6.2 Product Market Competition and Entry Regulation

It is possible that financial development is correlated with other country characteristics which affect innovation by firms. Potential candidates include the supply of scientists, the quality of intellectual property rights institutions, or the general contractual environment. However, unless the effect of such characteristics on innovation differs systematically by firm size, they should not matter to the interpretation of the coefficient on the interaction of firm size with financial development. The wages of scientists and engineers, for instance, vary across countries but are unlikely to vary across firms within the same country and industry.

There is, however, a concern that the interaction term picks up the effect of crosscountry variation in the product market competition faced by large firms. This concern arises because of two factors. One, standard IO theory predicts that since competition reduces the monopoly rents that reward successful innovators, innovation should decline with competition.<sup>25</sup> Two, the extent of competition might be related to entry regulation, which is negatively correlated with financial development. This is evident in Table 3, which shows that two cross-country measures of entry regulation, the Doing Business<sup>26</sup> estimates of the time to start a new business (StartTime) and the cost of procedures to start a new business (StartCost) are negatively correlated with PvtCredit. There is also evidence, shown in Table 11, to suggest that larger firms face more competition when entry barriers are lower.

The outcome variable in the regressions shown in Table 11 is a firm-reported measure of the number of its domestic product market competitors. In column (1), this measure of competition faced by a firm is regressed on StartTime. There is no significant correlation between the two, but in column (2), where the explanatory variables include Size and Size*StartTime, the coefficient on Size*StartTime is negative, indicating that larger firms face relatively less competitors as entry barriers rise. This correlation is robust to using StartCost to measure entry regulations. The coefficients are statistically insignificant, perhaps because the firm-reported measure of competition is available for only 15 countries. However, this negative correlation between entry regulation and competition faced by large firms relative to small firms suggests controlling for the differential effect of entry regulation on innovation.<sup>27</sup> Table 12 presents probit estimates of the probability of R&D when interactions of entry regulations (StartTime or StartCost) with firm size are added to equations 2 and 3 as controls. Irrespective of which procedural measure I interact with firm size, the coefficient on Size*PvtCredit in Table 12 is close to that in the preferred specification which was reported in column (3) of Table 6. Thus, the association between relative R&D by small firms and financial development is robust to controlling for entry barriers.

> 25However, empirical work such Geroski (1995) , Nickell (1996) and Griffith et al. (1999) has pointed to a positive correlation between product market competition and innovative output. Aghion et al. (2002) develop a model in which competition and innovation have a U-shaped relationship.

> 26See www.doingbusiness.org for details; these measures were first developed in Djankov et al. (2002).

> 27Note that since competition is endogenous to innovation, it should not be included as an explanatory variable in itself.

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7 Conclusion Innovation by firms is a important determinant of productivity and growth. There is evidence in theory that small firms find it relatively costly to finance innovation, and recent empirical work (Benfratello et al. (2006)) suggests that banking development encourages innovation by small firms. This channel could partly explain the growing cross-country evidence on the disproportionate association between financial development and growth in small firms. Looking at innovative activity by firms across 57 countries, I find that patterns in the data do fit this story.

Within industry, and relative to large firms, small firms are more likely to engage in R&D in countries at higher levels of financial development. Among firms engaged in R&D, a similar relationship holds for the amounts spent on R&D. These associations are robust to using different measures of banking development, and they are stronger in industries more reliant on external finance, indicating that they do indeed reflect the working of the financial channel. Moreover, in keeping with the hypothesis that financial underdevelopment leads to an underallocation of investment in small innovative firms, smaller firms report more innovation per unit R&D, and this gap is narrower in countries at higher levels of financial development.

These empirical findings suggest that by encouraging R&D in small firms that have high, untapped returns to innovative activities, the development of banks and other financial institutions can have positive growth and distributional consequences.

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