WPS8363 Policy Research Working Paper 8363 Size-Dependent Tax Enforcement and Compliance Global Evidence and Aggregate Implications Pierre Bachas Roberto N. Fattal Jaef Anders Jensen Development Research Group Macroeconomics and Growth Team March 2018 Policy Research Working Paper 8363 Abstract This paper studies the prevalence and consequences of and compliance increase with size. Size-dependence is more size-dependent tax enforcement and compliance. The iden- prevalent in low-income countries, and concentrated at the tification strategy uses the ranking of industries’ average firm top of the size distribution. When quantified in a general size in the United States as an instrument for the size rank- equilibrium model, removing size dependent enforcement ing of the same industries in developing countries. Data on leads to gains in Total Factor Productivity of up to 0.8 percent. 125,000 firms in 140 countries show that tax enforcement This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at pbachas@worldbank.org and rfattaljaef@worldbank.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 Size-Dependent Tax Enforcement and Compliance: Global Evidence and Aggregate Implications Pierre Bachas, Roberto N. Fattal Jaef, and Anders Jensen∗ JEL codes: H25, H26, O23, O43, D61 ∗ Pierre Bachas: World Bank Research, pbachas@worldbank.org - Roberto Fattal Jaef: World Bank Research, rfattaljaef@worldbank.org - Anders Jensen: Harvard Kennedy School and NBER, an- ders_jensen@hks.harvard.edu We are grateful to Alan Auerbach, Tim Besley, Michael Best, Natalie Cox, Tom Cunningham, Simon Galle, Roger Gordon, Michael Keen, Henrik Kleven, Camille Landais, Florian Misch, Ted Miguel, Torsten Persson, Andres Rodriguez-Clare, Emmanuel Saez, Johannes Spinnewijn, Mu- nir Squires, Owen Zidar and seminar participants at the LSE, the 69th IIPF Congress and the 2014 ZEW Public Finance conference for valuable comments. Bachas gratefully acknowledges financial support from the Center for Equitable Growth and the Julis-Rabinowitz Center for Public Policy and Finance. Jensen gratefully acknowledges financial support from the Peter G. Foundation Grant No.16017 and the ESRC. 1 Introduction An influential literature explains cross-country differences in income and productivity through the misallocation of resources across firms (Restuccia and Rogerson 2008, Hsieh and Klenow 2009). One salient property of measured misallocation is its productivity dependence: the most productive firms are smaller and the least productive firms are larger than the output-maximizing allocation. This property of misallocation can emerge through government policies that target firm size; for example size-dependent labor reg- ulations, tax rates or accounting requirements can discourage firm growth and impact the firm size distribution (Gollin 1995, Guner et al. 2008, Bento and Restuccia 2017). In this paper, we perform a quantitative evaluation of a specific feature of taxation which exerts a heterogeneous distortionary effect: size-dependent tax enforcement and compliance. We document the pervasiveness of this phenomenon around the world and provide estimates of the size-gradients across development levels and across the firm size distribution. We then characterize the implications of these size gradients for Total Factor Productivity in the context of a general equilibrium model of firm heterogeneity. Exploiting arguably exogenous variation in an industry’s optimal labor scale, we find a robust positive slope of industry average firm-size, as measured by the number of em- ployees, on tax inspection probability and compliance. This slope captures the average effect and masks non-linearities: inspection and compliance increase at the top of the size distribution and appear similarly lax among small and medium industries. Moreover, the magnitude of the gradient increases with development, from zero for rich countries to its highest value in the poorest economies. When feeding our estimated size-gradients into a general equilibrium model of firm dynamics, we find improvements in TFP of up to 0.8% when removing the size dependence component of taxation. These gains accrue both from the reversal of the misallocation as well as the subsequent increase in the firms’ expenses on innovation and growth. Tax enforcement is relevant for the study of policy-driven distortions for at least three 1 reasons. First, enforcement reduces the scope for tax evasion and therefore directly im- pacts firms‘ effective tax rates. Second, many firms report facing large costs of dealing with the tax administration (World Bank 2017).1 Third, reliance on size-dependent poli- cies for tax enforcement has increased over time, as international institutions encouraged tax administrations to segment taxpayers (Kanbur and Keen 2014). To illustrate this trend, Figure 1 shows that over the past 20 years, more than 70 countries adopted special en- forcement units for large taxpayers. While large taxpayer units hint at stringent enforce- ment at the top of the firm-size distribution, countries have also adopted enforcement policies targeted at small and medium firms.2 Therefore how tax inspection and compli- ance vary with firm size and in countries around the world, is an empirical question. The empirical analysis uses the comprehensive World Bank Enterprise Surveys (WBES), which contain firm-level data on self-reported tax inspection and tax compliance3 for a sample of 125,000 firms in 140 countries. Identification is based on the idea that firm size is partially determined by technological factors (Lucas 1969; Kremer 1993). These tech- nological factors pin down firms’ optimal scale of operation (Bain 1954, Burnside 1996, Kumar et al. 1999, Basu and Fernald 2016). If firms in an industry share a common opti- mal scale across countries, then the relative ranking of two industries’ scale in a plausibly undistorted market such as the US can serve as an instrument for the relative ranking of the same two industries’ optimal scale in a developing country’s distorted market.4 We measure scale as the number of employees and take the average at three digit ISIC sectors. Identification relies on predicting the size ranking of industries at the 3-digit ISIC level in 1 The World Bank 2017 Doing Business publication reports that "on average taxpayers spend 25 hours com- plying with the requirements of an auditor, and go through several rounds of interactions during 10.6 weeks." 2 Many countries implemented small and medium taxpayer offices alongside the large taxpayer office, which tailored audit algorithms to the evasion risks specific to smaller firms. 3 The question on tax compliance is asked at the industry level. Since all our specifications are at the industry-country level, we do not require that the reported answers represent the firm’s own tax compli- ance. Instead we only require that the answers accurately represent the industry’s average compliance. 4 This idea follows Rajan and Zingales 1998, who studied if industries reliant on external finance grew faster in countries with more developed financial institutions. They instrument an industry’s reliance on external finance with the external finance usage of the same sector in the US. 2 a WBES country from the size ranking in the US of the same ISIC3 industries.5 The first stage relation, that is the conditional expectation of a WBES country’s indus- try size rank across ranks of US industry size, is positive and linear. When repeated across subsamples of countries at different income levels, the slope remains constant: the US dis- tribution has the same power to predict industry size ranking in Ethiopia, Indonesia or Brazil.6 This suggests that the identification strategy captures technological differences in labor demand, which vary across industries but not across countries. The US Census industry size distribution is a valid source of exogenous variation un- der the assumption that US firms determine their size orthogonally to tax enforcement. This assumption might be reasonable in the US, where the Internal Revenue Service has access to comprehensive sources of third-party information and might not need to rely on imprecise size-proxies for tax enforcement. In contrast, tax authorities in developing countries with low fiscal capacity may be constrained to use size-proxies. We take the fol- lowing steps to alleviate concerns with the identifying assumption. First, the estimates are robust when using the industry ranking based on European firms from Amadeus data,7 instead of the US Census. These firms are subject to comprehensive financial reporting, and hence size-proxies might no longer be determinants of tax inspection. Second, since it has been documented that tax evasion is important among the self-employed in the U.S. (Blumenthal et al. 2001), we only consider firms with more than five employees in the US Census.8 Third, for the few countries in the WBES with similar GDP as the US and thus similar tax enforcement capacity, we find no size gradient in tax inspection.9 Finally we support the exclusion restriction by showing that the predicted WBES size-ranking is 5 Since our identification relies on industry comparisons of firm size, we do not use the within-industry size variation. In effect, this reduces our sample to 12,152 ISIC3-country-year observations. 6 This supports the following type of statement: “If the average car manufacturer requires more work- ers than the average retail firm in the US, then this ranking of industries by size also holds in Ethiopia, Indonesia, and Brazil.” 7 We use Amadeus data for German and British firms. Germany data derive from financial statements filed with the business registry. British data come from audited annual reports presented to shareholders. 8 The selection of firms with five or more employees also matches the sampling strategy of the WBES. 9 We cannot test this directly on the US since it does not have a World Bank Enterprise Survey. 3 not just proxying for competing channels that might drive tax inspection policies, namely capital intensity and reliance on external finance (Gordon and Li 2009). The IV estimated size-gradients imply that a 10 percentile increase in the WBES size- rank increases a firm’s probability of tax inspection by 2.3% (a 3.8% increase relative to a mean of 61%) and its tax compliance rate by 2.2% (a 2.7% increase relative to a mean of 81%). We estimate two main control models which allow non-parametrically for the tax inspection function to vary over firm characteristics or over two digit ISIC industries in every country-year. The latter specification exploits size variation between narrow ISIC3 industries such as “Manufacture of rubber products” (category 251) compared to “Man- ufacture of plastics products” (category 252), within the ISIC2 category 25. In addition, we find comparable coefficients in panel models which exploit within a country variation in the ranking of 3-digit ISIC industry over time. The size gradients mask non-linearities over the size distribution. Inspection and compliance appear concentrated among large firms, but no different for small and medium firms. The symmetry of results on inspec- tion and compliance suggests that size-based tax inspection may explain part of the com- pliance behavior. Finally, we study heterogeneity across countries’ income levels: the size-gradient appears to fall with development and the size-gradient for countries with similar income level as the United States is zero and statistically different from that of low-income countries. A decreasing reliance on size-dependent policies with develop- ment is consistent with evidence showing that countries with weak fiscal capacity rely on production-inefficient tax instruments (Best et al. 2015, Bachas and Soto 2016). In order to quantitatively evaluate the macroeconomic implications of the estimated size-gradients, we appeal to a standard general equilibrium model of firm dynamics. Our closest reference in the literature is a closed economy version of Atkeson and Burstein [2010]. It features three channels through which size dependent effective taxation can affect TFP: resource misallocation among incumbents, entry and exit of firms, and in- 4 centives to invest in innovation.10 Our strategy to calibrate a productivity-dependent enforcement profile in the model is consistent with the identification strategy in the em- pirical analysis. Taking the estimates for the average size-gradient from the IV regressions for each income group, we use the firm size distribution in the US, and the models’ im- plication that size maps one to one with productivity in the undistorted equilibrium, to back-out a gradient between the probability of tax enforcement and the underlying pro- ductivity of the firms. We then evaluate the TFP gains from reversing the size-dependence in taxation. Our baseline exercise fixes the probability of compliance at the level corre- sponding to the median size and applies it to all firms in the economy while keeping the statutory revenue and profit tax rates unchanged. As an alternative, we consider a case where, in addition to fixing the probability of taxation across firms, we readjust the tax rates so as to preserve the overall share of tax revenue to GDP, and the share of profit-tax in total revenue. Our baseline counterfactual yields a TFP gain of 0.8% for the least developed group of countries, where the size-gradient is the highest, and is neutral for the richest group, where the compliance profile is flat. At the micro-level, the model yields predictions that are consistent with the evidence on cross-country differences in the average size and life-cycle growth of firms (Bento and Restuccia 2017, Hsieh and Klenow 2014). Average firm size increases by up to 30%, and the aggregate innovation intensity in the economy expands by more than 10% . The magnitude of the aggregate gains are weakened in the counterfactual with constant tax collection, reaching 0.3% for the lowest income group. The reason for the decline is that revenue and profit tax rates are increased in order to raise tax revenue to maintain its share in GDP. Since profit taxes discourage entry and innovation, even in the absence of size-dependence, the magnitude of the TFP gain is mitigated. 10 By investment in innovation we do not constraint to thinking just about R&D that leads to frontier changing innovations or new patents, but rather we think of a broader concept of intangible capital accu- mulation that may indeed constitute path-breaking innovations but could also refer to adoption of frontier technologies or implementation of better management practices. 5 Quantitatively, we find lower distortions than those generated by financial frictions but comparable in size to those found when evaluating labor market policies. In the context of the latter, for instance, Hopenhayn and Rogerson [1993] find TFP losses of 1 to 2% from taxes to firing and hiring workers. Gourio and Roys [2014] and Garicano et al. [2016] find almost zero gains from reversing a legislation that reduces the taxation of labor for small firms. Financial frictions are the most costly distortion, with potential gains from improving credit markets ranging from 5 to 40% depending on the margins of adjustment allowed for in the models (Midrigan and Xu 2014, Buera et al. 2011, Moll 2014). 1.1 Related Literature Our paper participates to two distinct literatures. First, an influential literature analyzes cross-country income differences through the misallocation of factor inputs across firms and sectors. Since the seminal work of Hsieh and Klenow [2009] and Bartelsman et al. [2013], many studies applied the same methodologies to characterize the full extent of misallocation around the world. Furthermore, Restuccia and Rogerson [2008] and Guner et al. [2008] helped gain awareness of the importance of the size-dependent component of the idiosyncratic distortions, showing that this is an important feature of the under- lying policies generating the misallocation that magnifies the TFP losses associated with it. The pervasiveness of misallocation motivated the emergence of a number of stud- ies investigating the allocative properties of specific policies or distortions. Among the most notable ones in this group are Hopenhayn and Rogerson [1993], Gourio and Roys [2014], and Garicano et al. [2016], evaluating policies related to labor-market regulation, and Buera et al. [2011], Midrigan and Xu [2014] and Moll [2014] focusing on credit market distortions. Our work contributes to the misallocation literature from the same angle as the latter set of studies. We provide identified estimates of a particular distortionary pol- icy, size-dependence in tax enforcement and compliance, and quantify the implications of 6 this policy for aggregate TFP and firm behavior. Second, our exercise is related to the literature on tax enforcement and third-party in- formation (Kopczuk and Slemrod 2006, Gordon and Li 2009, de Paula and Scheinkman 2010, Pomeranz 2015, Naritomi 2016). Almunia and Lopez-Rodriguez [2017] show that Spanish firm bunch at the size-threshold of the large taxpayer unit, while Zareh and Peichl [2016] find that Armenian firms bunch at the full account reporting threshold. Our results provide empirical support to theories where firm size is correlated with tax compliance (Kleven et al. 2016, Bigio and Zilberman 2011). In Kleven et al. [2016], tax avoidance strategies such as double book-keeping and collusion with employees to hide operations are impossible to sustain for large firms, since a single whistle blower can reveal the en- tire operation. Therefore, large firms disclose third-party information and comply with their tax obligations. In this model the government enforcement strategy is fixed, and increased tax compliance with development is driven by firms’ size growth. However, our results are also consistent with models where increased tax inspection with size is an optimal government policy, given fiscal capacity constraints (Bigio and Zilberman 2011, Ito and Sallee 2016). The paper is structured as follows. Section 2 discusses the data. Section 3 presents the identification strategy and empirical specifications. Section 4 shows the empirical results and their robustness. Section 5 presents the general equilibrium model, which is calibrated in Section 6 to quantify distortions from size-dependent tax enforcement. Section 7 concludes. 2 Data To provide global evidence on the relation between industry average firm size, tax inspec- tion and tax compliance, we use the comprehensive firm-level data from the World Bank Enterprise Surveys (WBES). The surveys cover 125,000 firms in 140 countries between 7 2003 and 2015. A subset of countries have multiple surveys over time, with an aver- age of 1.9 surveys per country. The World Bank outsources data collection to third-party agencies in order to remove the official affiliation of the surveyors and not contaminate responses. The survey agencies draw upon the list of registered establishments provided by the national statistics office.11 The random stratified sampling is done at the industry- level, corresponding to the 2-digit ISIC level, and over-samples from large firms to cap- ture a large share of economic activity. Given the industry stratification, over-sampling of large firms does not impact the relative size of ISIC-2 industries. However it could im- pact the relative size of ISIC3 industries, which we use in some specifications, and where we have to assume that within ISIC3, firm sizes follow similar distribution shapes such that over-sampling at the top does not impact relative rankings. Firms with fewer than five employees, government-owned establishments and co-operatives are dropped from the sampling frame. The surveyors contact firms from this stratified-random sample and conduct the surveys with the person who most often deals with banks or government agencies. We measure size as the average of the log of number of employees per firm in a three digit ISIC sector,12 excluding part-time and temporary workers. We calculate size for all ISIC3-country-year cells in the WBES. The size distribution in the US is drawn from the 2002 Census of Employment and Wages. To be consistent with sampling in the WBES, we exclude firms with five employees or less from the Census.13 One caveat to is that we solely use industry level variation in average firm size. In the data, the intraclass correlation between log employee size and industries is 15%, and hence a large share of firm size variation arises within industries. We construct extensive and intensive margin measures of tax inspection within an 11 Sometimes supplemented with the list of firms registered with the chamber of commerce. 12 Sectors follow version 3.1 of the ISIC international industry classification. 13 In robustness tests we use an alternative size measure which places additional weight on the firms which have a higher proportion of the total sectoral employment as suggested by Davis and Henrekson [1999] and Kumar et al. [1999]. 8 ISIC3-country-year cell as, respectively, the share of firms which report an inspection by tax officials in the past 12 months, and the number of inspections over that period. To study tax compliance, we use the answer to the question: “Recognizing the difficulties many enterprises face in fully complying with taxes and regulations, what percentage of sales would you estimate the typical establishment in your area of activity reports for tax purposes?”. Full compliance is defined as the share of firms that report all of their sales. The reference to a “typical establishment in your area of activity” is meant to encourage firms to truthfully report – either a reference group’s behavior or the firm’s own behavior. While we cannot infer whose behavior the firm is precisely referring to, we only require that the firm’s reported compliance rate corresponds to its own ISIC 3 industry, a plausible assumption, and weaker than assuming that the answer corresponds to the firm’s own compliance rate. We also construct the effective tax rate, defined as the product of the compliance rate and the statutory tax rate, where the tax rate is the sum of the corporate income tax rate and the general sales tax rate (or VAT).14 In robustness tests we use informal payments, defined with the question: “It is said that establishments like this one are sometimes required to make gifts or informal payments to public officials to “get things done” with regard to customs, taxes, licenses, regulations. On average, what percent of total annual sales do establishments like this one pay in informal payments or gifts to public officials for this purpose?”. This question provides a direct measure of the informal tax rate, since the informal payments are expressed as a percentage of sales. Since we study outcomes at the industry level, we report summary statistics at the country-year-industry level, where the industry corresponds to the 3-digit ISIC. The 272 country-year surveys cover 140 countries, with on average 50 ISIC3 industries repre- sented and a median at 52. The average industry surveys 10 firms. Table 1 displays the 14 We collected the statutory sales and corporate tax rates in the relevant year of the WBES country-year cell using the KPMG worldwide tax summaries. 9 number of observations, mean, standard deviation, and quartiles for each of the variables described above. The average number of tax inspections is just under 2 and 62% of firms receive at least one tax inspection visit in the year. The average compliance rate with taxes is 81%, and 57% of firms report full compliance. The average informal payment corresponds to 1.6% of firms’ sales and 26% of firms make such informal payments. Since the survey over-samples from larger firms it is not surprising to see that 22% of firms are exporters. Since the sampling frame is defined at the two digit ISIC level, manufacturing firms, which occupy a disproportionate share of the ISIC 2 categories, represent 58% of the sample of 3-digit industries. Finally, the average ISIC3 industry has 69 workers in the WBES, while the average industry has 53 workers in the 2001 US Census. Two points worth highlighting concern sample size and survey weights. First, while the core tax inspection variable is always available, data on tax compliance are only avail- able for earlier surveys.15 Second, when possible we apply survey weights. However weights are missing from some early surveys. The core tax inspection results are drawn from the sample with survey weights, but to preserve sample size, we report results on tax compliance without dropping observations with missing weights. We show in the appendix that results remain unchanged in the smaller sample with full survey weights. 3 Identification and Econometric Specifications 3.1 Identification and First-Stage Our objective is to estimate how firm size impacts tax inspection: Tax inspectionict = α + β · Sizeict + γct + εict (1) 15 The question on formal tax compliance was dropped from the harmonized survey after 2007. In sur- veys after 2007 administered in Angola, Botswana, Congo (Dem. Rep), Ethiopia, Iraq, Mali and Rwanda, we extracted the tax compliance question from the non-harmonized raw data. 10 The OLS regression of firm size on tax inspection is likely to suffer from reverse causality and omitted variable bias. In particular, firms might reduce their size to prevent facing more stringent tax inspection. To address this issue we turn to an instrumental variable strategy. A valid instrument predicts firm size and only impacts tax inspection through its effect on firm size. A vast literature finds that industries vary in their optimal scales and that there exists a structural technological demand for labor at the industry level. Our identification strategy follows the intuition of Rajan and Zingales [1998]: if we con- sider the US as an undistorted market, then US firms achieve their optimal unconstrained size, which depends on the structural scale parameter of their industry and idiosyncratic shocks. This suggests using the average size of firms in industries in the US as an instru- ment for the average size of firms in the same industry in lower-income countries. The first stage is estimated with the following regression: Rank sizeict = α0 + α1 · Rank sizei,U S 01 + γct + εict (2) Where Rank sizeict is the average firm-size rank of ISIC3 industry i, in country c, at time t, and Rank sizei,U S ,01 is the rank by firm-size, of industry i, in the US census in 2001. γct are country-year fixed effects. The US industry ranking is drawn relative to the set of industries present in a given country-year, and we weight the regression results by the number of observations in a given ISIC3-country-year cell.16 The slope-coefficient α1 measures the increase in the size-ranking of an industry in its country, when moving along the ranking of industry size in the US. Table A1 shows that the results are robust to using average number of workers per industry rather than industry ranking based on number of workers. We implement the first stage with a rank-rank specification for two reasons. First, by using an industry‘s ranking in terms of average workers, the coefficient β only depends on the joint distribution of average size in the WBES country and aver- 16 This allows for ISIC3-country-year cells measured with greater precision to carry more weight in the estimates. Omitting weights does not change qualitatively the results, which remain significant. 11 age size in the US. Unlike the log-log specification, it does not depend on the marginal distributions of WBES and US industry-size. In other words, in a rank-rank specification β is not impacted by the ratio of US to WBES industry-size variances. The rank-rank specification is thus more stable across subsamples of different development levels with widely varying WBES size-variances.17 Second, the rank-rank specification appears more able to untangle technological size-differences from non-technological differences. Non- technological drivers such as availability of labor-saving instruments, labor regulations, and legal quality may differ substantially across countries and impact relative firm size, thus a wedge between WBES level-differences in size and US level-differences in size. Such non-technological drivers of size will not impact β so long as they do not overturn the ranking of industries in WBES relative to the US. Figure 2 displays non-parametrically the first stage relation between industries’ size ranks in the WBES countries and the US Census. ISIC3 industries are ranked relative to other industries in the same country-year survey. The WBES and US Census ranks are then grouped into 50 equal sized (two percentile) bins. Figure 2 plots the mean WBES size rank percentile within each 50-quantile US size rank percentile and the best-fit line. We find a steep positive slope and a linear relation between industries’ size-ranks in the US Census and their size-ranks in WBES countries. In Figure 3 we show that the rank-rank coefficients are constant by countries’ income levels: the US industry-size distribution has the same power to predict average firm size over the full size-distribution, in for exam- ple, Ethiopia, Indonesia and Mexico. In robustness analysis in Section 4.4, we show that predictive power does not hinge on using the 2001 Census, and remains almost identical when using either an earlier wave of the Census (1991) or a later wave (2015). Finally, the first stage remains strong and positive when we restrict our analysis to the manufacturing sector, a common restriction for studies using cross-industry variation. The WBES country size-ranking predicted from the US ranking of industries is an 17 This is also the main reason why a rank-rank specification is chosen over the log-log specification in recent studies of income mobility (Chetty et al. 2014). 12 exogenous source of size-variation under the assumption that the size of US firms is or- thogonal to tax enforcement. Arguably, for large firms the IRS bases its decision directly on third-party reports and risk scores from economic activity and not indirectly based on size. In countries with high fiscal capacity, it is well-documented that non-compliance is concentrated among the self-employed and family firms with few employees (Blumen- thal et al. 2001, Kleven et al. 2011). To alleviate concerns, we remove all firms with fewer than 5 employees in the US Census, which also matches the WBES sampling design. In Section 4.4, we show that the results hold when constructing the exogenous size-ranking with British and German firms in the Amadeus dataset, which are subject to stringent information reporting requirements.18 Finally, in section 4.3 we show that for the richest countries in the WBES (countries with per capita GDP above $21,000)19 the estimated co- efficients of size on tax inspection is zero. This evidence supports the first stage identify- ing assumption that in high fiscal capacity countries, firm size is not driven by size-based inspection. The IV strategy provides a causal estimate of the size-gradient under the first stage validity, discussed above, and the exclusion restriction. The exclusion restriction assumes that the US size-ranking of WBES industries only impacts tax inspection in the WBES country through the WBES size-ranking. If tax inspection depends on employee-size only indirectly (e.g. by proxying for capital) the exclusion restriction holds as long as technological demand for labor does not impact capital other than through labor input. However, this assumption fails if the first-stage coefficient does not capture technological differences in employee-size, but is instead an imperfect proxy for capital input demand. To try to address this issue we construct two measures of demand for capital input in the US industry distribution: the demand for external reliance (Rajan and Zingales 1998) and 18 Amadeus data are collected from annual financial statements filed with the business registry and au- dited annual reports presented to shareholders. These firms are subject to a broader and deeper set of re- porting requirements and hence in this sample tax inspection is unlikely to be driven by crude size-proxies. 19 The $21,000 cutoff was chosen to correspond to the 90th percentile of income in the WBES such that these countries are comparable to the US in terms of fiscal capacity. 13 the capital to labor ratio (Gordon and Li 2009). We show in Section 4.4 that when control- ling for capital intensity, the coefficient on size remains unchanged, while the coefficient on capital intensity is insignificant. This suggests that technological demand for labor does not impact tax inspection indirectly through its interaction with capital. 3.2 Empirical Specifications The reduced-form size gradient is estimated by directly regressing the WBES industries’ tax outcomes on the US industries size rank: Tax outcomeict = δ0 + δ1 · Rank sizei,U S ,01 + γct + εict (3) Where Tax outcomeict is a tax outcome of industry i in country j at time t (e.g. likelihood of tax inspection over the past 12 months), Rank sizei,U S ,01 is the size-ranking of industry i in the US, and γct are country-year fixed effects. The coefficient δ1 identifies the reduced- form size gradient. The IV specification is: Tax outcomeict = β0 + β1 · Rank sizeict + γct + εict (4) Where Rank sizeict of industry i in country c at time t is instrumented with Rank sizei,U S ,01 of industry i in the US. In practice, we estimate three different empirical models. The first model adds a set of controls to the above equations. It allows for tax outcomes to differ non-parametrically and interactively in every country and year across a set of industry characteristics. We code all industries as belonging to above or below their country-year median age, share of exporters and share of foreign firms. We then create the matrix (Characteristics)ict con- taining the full set of interactions across characteristics. The model allows for all factors 14 to impact tax outcomes in an interactive way, resulting in 1,937 fixed effects: Tax outcomeict = β0 + β1 · Rank sizeict + (Characteristics)ict × (Year)t × (Country)i + εict (5) The second model allows for the tax outcome to differ in every country, year and ISIC2 industry. This implies that variation relies on size differences of 3-digit ISIC industries within a 2-digit ISIC industry. For example, within ISIC category 25 "Manufacture of rubber and plastics products" it exploits variation in firm size between "Manufacture of rubber products" (Category 251) and "Manufacture of plastics products" (Category 252). This model estimates 6,130 fixed effects: Tax outcomeict = β0 + β1 · Rank sizeict + (ISIC2)ict × (Year)t × (Country)c + εict (6) Note that in practice, some ISIC2 sectors define the ISIC3 sectors, which leads to a drop in sample size. Further, the drop in size is larger for less developed countries where a smaller degree of specialization implies that some ISIC3 sectors are not represented for a given ISIC2. For transparency, we present results from each model side by side. The third specification exploits the panel structure of the data, which is available for a subset of countries (the average number of surveys per country is 1.9).20 In the panel model, we add fixed-effects at the 3-digit ISIC level to the two previous models. Identifi- cation comes from variation in industries’ relative size ranks within a country and across time. For example the panel model mirroring equation 6 is defined as: Tax outcomeict = β0 + β1 · Rank sizeict + (ISIC2)ict × (Year)t × (Country)c + ISIC3i + εict (7) We report the coefficients β1 of size on tax outcomes from all three sets of specifications 20 Note that in the panel regressions we do not use the instrumental variable strategy. 15 for tax inspection and informal payments. Since the question on tax compliance was discontinued after 2007, we have very few repeated country surveys. Therefore we only report the coefficients β1 of size on tax compliance for the first two models. 4 Results 4.1 Reduced Form and IV Estimates of Size Gradients Tax Inspection In this section we implement the econometric specification described in section 3.2. Fig- ure 4 plots for each of the six largest countries in our sample,21 an industry’s size ranking on its average probability of tax inspection. Each dot represents an ISIC 3 industry and the size of the dot is proportional to its share of total employment within the country (based on the WBES). We plot the linear fit of size rank on tax inspection which slopes up in all six countries. We also note that on average industries with higher total employment have larger average firm sizes, however there is significant variation and some industries with a high share of total employment rank in the bottom half of average firm size. Table 2 reports the size gradient in tax enforcement along the extensive margin (any tax inspection over the past 12 months, Panel A) and the intensive margin (number of tax inspections over the past 12 months, Panel B). Panel A shows that industry-size is associ- ated with a higher likelihood of tax inspection. Columns 3 and 4 show that the reduced form coefficients are significant in both types of (cross-sectional) fixed effect models. In columns 5 and 6, we estimate the corresponding IV-coefficients for each model. The first stage coefficients are strong (F-statistic of 260 and 105, respectively), and the size gradi- ents are precisely estimated. The coefficient from our preferred specification in column 5 implies that a 10 percentile increase in exogenous WBES size-rank is associated with a 2.3 21 Bangladesh, Brazil, China, India, Indonesia and Mexico. 16 percentage point increase in the likelihood of tax inspection, a 3.8% increase relative to a mean tax inspection probability of 61.9%. Columns 7 and 8 exploit the panel dimension of the data, for the subset of WBES countries with multiple surveys. In these specifica- tions the size gradients are estimated from changes in inspection from a switch in the relative ranking of ISIC3 industries across time. The coefficients in the panel regression are positive and significant and of similar magnitude as the IV estimates. Panel B, re- peats the above regressions using as an outcome the number of tax inspections in the past 12 months. The coefficients remain significant and positive across specifications. The IV coefficient in column 5 suggests that a 10 percentile points increase in exogenous WBES size-rank is associated with a 0.14 increase in the number of tax inspections, relative to a mean of 1.98 inspections. The panel coefficients (columns 7-8) are very similar to the IV estimates. To gauge the extent to which the size gradient endogenously determines firm-size, we compare the OLS to the IV coefficient (respectively, comparing columns 1 and 5, and columns 2 and 6). The IV coefficient is larger in three out of four specifications, suggesting that firms might reduce their size to avoid increased tax inspection. Tax Compliance We now study the size gradient in tax compliance, which could, in part, be explained by increasing tax inspection with size. While the identification strategy is the same as above, the question on tax compliance only appears in the first waves of the WBES (2003 to 2007), which implies a smaller sample size and insufficient repeated country surveys to run panel regressions. Table 3 shows the size gradient on the extensive and intensive margins of tax compliance, where the extensive margin is the probability of full compliance (Panel A), and the intensive margin is the share of sales reported for tax purpose (Panel B). The IV coefficient in column 5 points to sizable effects of firm size on tax compliance: a 10 percentile increase in the WBES size-rank is associated with a 5.2 percentage point increase in the likelihood of full compliance, a 10.6% increase relative to a mean of 61.8% 17 and a 2.2 percentage point increase in the share of sales reported for tax purpose (relative to a mean of 80.9%). The wedge between the OLS and the IV coefficients suggests that firms depress their reported size in order to reduce tax compliance. 4.2 Non-linearities of Tax Inspection and Compliance with Size In Section 4.1 we show that tax inspection and tax compliance increase with industry size. Here we study whether this relation is linear or concentrated among specific segments of the size distribution. We present non-parametrically the reduced form relation between tax outcomes and the industry size ranking in the US. We first residualize the industry size-ranking in the US Census, NU S , with respect to controls and country and year fixed effects as in equation 5. Similarly, we residualize the tax outcome of interest (e.g. tax inspection likelihood) with respect to the controls and fixed effects. We then split the residualized industry size-ranking NU S into the size deciles, and normalize to zero the median industry’s size. Figure 5 shows for each decile of industry size how tax inspection and compliance com- pare to the level of the 5th decile. Panel A shows that tax inspection is concentrated at the top of the industry size distribution and is flat in the bottom and middle of the distribu- tion. Industries at the top of the size distribution appear 3% more likely to be inspected compared to the median industry. Panel B shows that the tax compliance rate mirrors inspection: an industry at the top of the size distribution reports 2% more sales compared to an industry in the middle. The mirroring pattern of tax inspection and tax compliance suggests that tax compliance is partly driven by size-dependent tax inspection. 4.3 Heterogeneity across Development Levels Reliance on size-dependent policies for tax enforcement could originate in state capacity: at lower levels of development the tax authority is constrained by a lack of information 18 on firms and has to resort to imperfect proxies such as size-dependent polices (Best et al. 2015, Bachas and Soto 2016). As a country’s fiscal capacity grows (Kleven et al. 2016, Jensen 2016), the tax authority’s reliance on size-dependent policies can be weakened. We therefore hypothesize that the size gradient in tax inspection decreases with a country’s income level. To test this hypothesis, we estimate the tax inspection size gradient across subsamples of countries at five different levels of development.22 Figure 6 shows the reduced form and IV coefficients for the likelihood of tax inspection at each income level.23 The magnitude of the tax inspection size-gradient is decreasing over levels of development, both in the reduced form and IV specifications.24 While we cannot reject that lower-middle, middle and higher-middle income groups have different size- gradients,25 we can reject that their size-gradient is equal to that of high-income countries. In high-income countries both the reduced form and IV coefficients are centered at zero. The absence of size-dependent policies at high income levels is consistent with the theory that countries with strong fiscal capacity decrease their reliance on production-inefficient tax instruments. It also provides some support to the identifying assumption that tax inspection is orthogonal to size in a high tax capacity environment. 22 The groups correspond to the World Bank income classification, except for the top income group (above USD 21,000) which corresponds to the 90th percentile of income in the WBES and was chosen such that countries are comparable to the US in terms of fiscal capacity. 23 The first stage coefficients are constant across income levels and the 1st stage F-statistic is well above 10 at each income level. 24 The coefficients for the lowest income countries (GDP per capita below $1,100) are the largest but are only significantly different from zero at the 10% level. There are two explanations for this. First, this group contains fewer country-year observations than lower-middle, middle and higher-middle income groups. Second we weight ISIC-3 industries by their number of observations. Surveys in the poorest countries tend to be smaller in terms of number of firms and have fewer ISIC-3 industries represented. 25 These levels of development include the countries often studied in the misallocation literature such as China, India and Mexico. 19 4.4 Robustness Using different instruments The core results use the industry-size rank in the 2001 US Census. This section shows that results are robust to the choice of the exogenous size-distribution used as an instrument. Table A1 presents the first stage and IV coefficients on tax inspection, for six different definitions of the instrumental variable. Columns 1-3 report results using each of the last three waves of the US firm Census (1991, 2001, 2015). We obtain the same ranking of WBES size and similar IV coefficients.26 Since the validity of the instrument rests on the assumption that the firm-size distribution in the US is undistorted by tax enforcement, using size rankings from other high fiscal capacity OECD countries should yield similar results. We test this by constructing the IV with British and German firms in the Amadeus database. In Great Britain the data are derived from audited annual reports presented to shareholders. In Germany, the data come from annual financial statements filed with the business registry. While these firms represent a selected sample compared to the US Census, they are subject to stringent reporting requirements and hence it is less likely that size proxies are used by tax authorities. Column 4 in Table A1 shows that the Amadeus size-ranking predicts a similar first-stage, and a large and significant IV coefficient. Restricting the sample to manufacturing To exclude the possibility that results are driven by a small set of peculiar ISIC3 industries, we limit the sample to manufacturing, which is over-sampled in the WBES (60% of WBES firms) and where most industries are well represented across countries. Table A2 shows the reduced form and IV results on the intensive and extensive margins of tax inspection. The 1st stage coefficient is the same as the coefficient in the full sample. The reduced form and IV coefficients are larger than in the full sample. 26 The first stage is constant across development-levels for each census wave (Figures A1 & A2). 20 Is worker-size proxying for capital intensity? A potential limitation to our identification strategy is that firm size, as measured by num- ber of workers, could proxy for capital intensity. If this was the case, we are not capturing the direct impact of industry-size but rather the impact of more capital on tax inspection. To mitigate this concern, we construct an industry capital intensity ranking, using (1) the measure of reliance on external funds as in Rajan and Zingales [1998] and (2) the capital to labor ratio as in Gordon and Li [2009]. We then regress jointly industry-size ranking and capital ranking measures on tax inspection (Table A3). The inclusion of controls for capital intensity does not impact the results, and the coefficients on capital rankings are very small in magnitude and insignificant.27 Substitution between formal and informal taxes along the size distribution Table A4 shows the size gradient on the likelihood of making an informal payment (Panel A) and the intensive margin as informal tax payments as a share of sales (Panel B). We find no effect on the extensive margin but do find an effect on the intensive margin. The IV coefficient in column (5) suggests that a 10 percentile increase in exogenous WBES size-rank is associated with a 0.11 percentage point decrease in the informal tax rate, a 7% increase relative to a base of 1.58% in sales for informal payments.28 The coefficients on tax compliance and informal payments have opposite signs, which suggests substitution between formal and informal taxation. Full substitution could mit- igate the importance of size-dependent tax enforcement. To test for substitution, we need both the informal and formal effective tax rates. Since firms report informal payments as a share of sales, we already have the effective informal tax rate. we construct the ef- 27 As an additional robustness test, we find that in the reduced form the US-size ranking is associated with outcomes which are predicted by theory to vary with labor demand (Lucas 1969; Kremer 1993): we find an increase in sales growth, labor cost per permanent employee, perceived constraints due to labor regulation, likelihood of having quality certification and likelihood of being part of a larger firm. 28 The negative slope shows that informal payments are regressive across firms. This finding comple- ments Olken and Singhal [2011], who find that informal tax payments are regressive across households. 21 fective formal tax rate as the product of an industry’s compliance rate with its country’s statutory tax rate (defined as the sum of the corporate and sales tax rates).29 Figure A4 plots the residualized formal and informal effective tax rates, for each vingtile of the firm size distribution. While the informal tax rate rises (falls) over the portions of the size- distribution where the formal tax rate falls (rises), Panel A shows that the effective formal tax payments are much larger than informal payments. As a result, substitution between formal and informal taxes only explains a small share of the size-gradient. Size gradient interaction with statutory tax rates When the statutory tax rate is high, firms have incentives to evade more taxes. For the tax authority this implies that the returns to size dependent taxation are larger, and hence the gradient in tax inspection steeper. To test this hypothesis we regress tax outcomes on the interaction between rank-size and a high tax dummy variable. The high tax dummy equals one if a country’s statutory tax rates is above the sample’s median and we define the statutory tax rate as the sum of the corporate and sales tax rates. Table A5 shows that the interaction term between the industry’s size rank and the high tax dummy is positive for tax inspection and compliance. This suggests that in countries with high tax rates the tax inspection and compliance gradients are steeper. 5 Aggregate Implications of Size-Dependent Enforcement This section proposes a model of firm dynamics to evaluate the aggregate implications of size-dependent tax enforcement and compliance. Our closest reference in the literature is a closed economy version the model in Atkeson and Burstein [2010]. It features three channels through which size dependent effective corporate profit and revenue taxes can 29 We recognize that this methodology faces several issues. (1) Statutory tax rates could depend on firm size. (2) We assume that the tax compliance question applies to the sales and corporate income tax, while the question does not refer to a specific tax. (3) The tax base could vary across taxes. 22 affect aggregate productivity: resource misallocation among incumbents, entry and exit of firms, and incentives to invest in innovation.30 The former connects our policy counter- factuals to the traditional literature on idiosyncratic distortions and resource misalloca- tion (Hsieh and Klenow 2009, Restuccia and Rogerson 2008). Entry and exit, and endoge- nous firm growth represent potential propagating channels for which size-dependent enforcement affects the macroeconomy and hence should be taken into account for the quantification of its aggregate effects. 5.1 Technologies There is a competitive representative producer of a final good that is produced combin- ing a continuum of differentiated varieties of intermediate inputs into a CES production function with elasticity ρ ρ ρ −1 ρ−1 Y = q (ω ) ρ dM (ω ) where q (ω ) is the quantity demanded of variety ω , and M (ω ) denotes the mass of pro- ducers of variety ω . Profit maximization under perfect competition yields the familiar demand functions −ρ d p (ω ) qk (ω , λ) = Y (8) P where P is the price index for the final good, and p (ω ) is the price of the variety. The price index for the final good is defined by 1 1−ρ 1−ρ P = p (ω ) dM (ω ) Producers of intermediate varieties, in turn, operate under monopolistic competition 30 By investment in innovation we are not constraining the analysis to thinking just about R&D that leads to frontier changing innovations or new patents, but rather we think of a broader concept of intangible capital accumulation that may indeed constitute path-breaking innovations but could also refer to adoption of frontier technologies or implementation of better management practices. 23 and produce their variety according to the following technology: 1 y (ω ) = (eω ) ρ−1 l (ω ) (9) 1 The idiosyncratic productivity, denoted with (eω ) ρ−1 , evolves endogenously as a re- sult of the firms’ investments in innovation subject to risky outcomes. More concretely, productivity follows a binomial process in which technology experiences upward or down- ward jumps of exogenously determined size ∆, according to a probability q (ω ) which is under control of the firm through expenses in innovation.31 Formally, consider a firm with current productivity eω . In the next period, productivity transitions to   eω + ∆   with probability q (ω ) eω =  eω − ∆   with probability 1 − q (ω ) In order to achieve a probability of upgrading equal to q (ω ) , the firms must incur in a labor-denominated cost given by χt (q , ω ) = eω × µ eφq (ω ) − 1 Notice that the innovation cost is scaled by the current productivity of the firm. This is an important assumption that allows the model to be consistent with innovation patterns of large firms in the U.S. (Gibralt’s Law) , which is our target economy for the calibration of parameters that are kept constant across economies. Size-Dependent Taxation The operations of intermediate good producers are affected by a corporate profit tax τ π and a sales tax τ s . The key property of taxation systems in 31 The appeal of this shock process, as opposed to any other mean reverting one, is that it constitutes a discrete approximation to a geometric brownian motion, a process under which the properties of the equilibrium size distribution of firms can be characterized in closed form (Luttmer 2007) and hence from which the calibration of parameters can be easily mapped into moments of the size distribution in the data. 24 developing countries, that we incorporate in the model, is that each producer confronts an idiosyncratic probability of being inspected by the tax authorities and being enforced to comply with the payment of the taxes. This probability is positively related with the size of the firm. We defer for later the discussion of the exact parameterization of the implementation of the size dependent inspection probability, for now lets denote such probability with ε (ω ). The expected profits of an intermediate good producer, then, are given by e ε (ω ) (1 − τ π ) [(1 − τ s ) p (ω ) y (ω ) − wl (ω )] π (ω ) = (10) + [1 − ε (ω )] [p (ω ) y (ω ) − wl (ω )] − wχt (q , ω ) The first term represents the after-tax stream of profits in the event of enforcement, while the second terms are the profits in the event of no compliance. Notice that, when enforced, profits are taxed gross of innovation expenses. Working out the algebra it follows that a more convenient presentation of the expected profits is the following32 π (ω ) = [1 − τ π (ω )] {[1 − τ s (ω )] p (ω ) y (ω ) − wl (ω )} − wχt (q , ω ) (11) where we are defining τ π (ω ) and τ s (ω ) as the “effective” tax rates confronted by the firms which we formally define as follows τ π (ω ) = ε (ω ) τ π τ s (ω ) = ε (ω ) τ s Notice, then, that we have recast the firms’ problem into the standard representation in the misallocation literature where firm face idiosyncratic taxes. Our contribution is to 32 Strictly speaking, there is a difference between the expected profits in 10 and the one in 11, which is equal to ε (ω ) τ π τ s (1 − ε (ω )). This difference, however, is quantitatively negligible. 25 offer a calibration of such profile of idiosyncratic taxes based on our estimate of size- dependent tax compliance. 5.2 Static and Dynamic Choices We can now turn to describing the firms’ optimal decisions regarding labor demand, in- vestments in innovation, entry, and exit. Firms choose the labor demand and the price for their varieties solving the following static profit maximization problem maxl(ω ),p(ω ) {[1 − τ π (ω )] {[1 − τ s (ω )] p (ω ) y (ω ) − wl (ω )} − wχt (q , ω )} subject to the demand function for varieties given in 8 and subject to the production tech- nology defined in 9. Solving it gives ρ ρ−1 Yt ω s ρ l (ω ) = ρ e [1 − τ (ω )] ρ wt The expression shows that only the sales tax carry a distortionary effect on labor de- mand, which is independent from corporate profit taxation. Thus, size-dependent en- forcement will have a detrimental effect on aggregate productivity through the misallo- cation of labor, only to the extent determined by the interaction of the size gradient in tax inspection efforts and the sales tax rate. Corporate taxation, on the other hand, does have a distortionary effect on the dynamic decisions of the firms. To see this, consider the value of an operating firm with current productivity eω   [1 − τ π (ω )] π v (ω ) − weω ×µ eφq (ω ) − 1 − wfc +     v o (ω ) = maxq (ω )  β (1 − δ ) q (ω ) v (ω + ∆) + β (1 − δ ) [1 − q (ω )] v (ω − ∆)    where π v (ω ) = [1 − τ s (ω )] p∗ (ω ) y ∗ (ω ) denotes the indirect variable profit function that 26 embodies the optimal choices of labor and prices described above, and where wfc is the labor-denominated fixed costs of production, which is a driving force of the exit decisions of firms. Taking first order conditions with respect to innovation choices we get wµφeφq (ω ) = β (1 − δ ) [v (ω + ∆) − v (ω − ∆)] The expression shows that corporate taxation affects innovation through its impact on the rate of return to firm growth, which is embodied in the value-differential that firms enjoy in the event of a technological upgrade. To the extent that corporate taxation is increasing in idiosyncratic productivity, the differential gain in valuation that an innovation would allow for is reduced by the profile of corporate taxation, so we should expect to see less innovation, and hence a lower aggregate productivity, through this channel. Having characterized the decisions of an operating establishment, we turn now to describing the process of entry and exit. The latter follows in part from the exogenous probability δ which affects all firms uniformly,33 but also reacts to the firms’ endogenous decisions about the profitability of continuing in operation. Let ι (ω ) = 1 if the firm stays in operation, and equal to zero otherwise, then v (ω ) = maxι(ω ) [v o (ω ) , 0] which is the standard definition of the value of a firm as the maximum between staying in operation and the exit value of zero. In terms of entry, we assume that there is an infinite pool of potential entrants that must incur a labor-denominated sunk cost of entry equal to fe , in order to get a random realization of its initial idiosyncratic productivity from a known distribution Γ (ω ). As- 33 Thisexit shock helps rationalize the model with empirical exit by large firms, which the model cannot account for endogenously. Thus, it will be calibrated by the exit rate of large firms in the US economy. 27 suming positive entry in equilibrium, the following free-entry condition must hold: wfe = β (1 − δ ) v (ω ) dΓ (ω ) where notice that, as is standard in the literature, we are assuming a one-period lag be- tween the payment of the entry cost and the realization of the productivity draw. 5.3 Household’s Problem There is a representative household with preferences of the form ∑∞ t t=0 β [log (Ct )], where Ct is the single final good produced in the economy. Lifetime utility maximization is done subject to a standard inter-temporal budget constraint of the form: Σ∞ t=0 Qt [Ct − Wt L − Tt ] ≤ M0 where Qt denotes inter-temporal prices, M0 is the initial endowment of wealth (claims to the profits and losses from the initial distribution of firms), and Tt represents the lump- sum tax/transfer that balances the deficit or surplus from the collection of idiosyncratic taxes and subsidies. Note that by rebating revenue back to (or taking it away from) the household, we are ensuring that all the aggregate implications of misallocation frictions manifest solely through their effect on aggregate productivity, rather than from waste- ful consumption of goods from the government. Lastly, notice that the inter-temporal Qt + 1 accumulation of wealth pins down the economy’s interest rate, given by Rt = Qt . 5.4 Definition of Equilibrium The remaining step in the characterization of the equilibrium is to aggregate the outcomes of the firm up to the level of the macroeconomy. Key for the aggregation is the distribution of firms across firm-wide productivity, which we denote with Mt (ω ). This distribution 28 evolves according to the following law of motion: Mt+1 (ω ) = (1 − δ )q (ω − ∆) Mt (ω − ∆) (12) + (1 − δ ) [1 − q (ω + ∆)] Mt (ω + ∆) + (1 − δ ) Me,t Γ (ω ) The expression establishes that a fraction (1 − δ ) q (ω − ∆) of firms with productivity less than or equal to (ω − ∆) survives the exogenous exit shock and transitions to a produc- tivity level that is less than or equal to ω . A fraction (1 − δ ) (1 − q (ω + ∆)) of the mass of firms with productivity between ω and (ω + ∆) survives the exit shock and jumps down- ward to have productivity less than or equal to ω . There is also an inflow of new firms into this group which is given by the mass of entrants, (1 − δ ) Me,t Γ (ω ) . Endogenous exit will be driven by the mass of firms that transition downwards from the productivity cutoff, (1 − δ ) [1 − q (ω + ∆)] Mt (ω + ∆). A stationary competitive equilibrium in this economy is given by: 1) consumption deci- sions from the household C 2) sequences of prices, labor demands,innovation decisions, value functions, and exit decisions for the producers of varieties, {p(ω ), l (ω ) , q (ω ) , v (ω ), ι (ω )}; 3) a sequence of final good quantities and demand functions for intermediate variety Y , y d (ω ) ; 4) a stationary distribution of firmsM (ω ) and its law of motion (equation 12), 5) a measure of entrants Me 6) a vector of prices and transfers {w, R, P , Q, T } ; 7) a profile of size-dependent inspection probabilities ε (ω ) and the profit and sales tax rates τ π and τ s , 8) a distribution of productivity at entry Γ(ω ), and 9) an initial wealth of the household M0 such that: a) given 6, 4, and 9, 1 solves household’s optimization problem, b) given 6, 3 and 8, 2 solves the incumbents’ dynamic optimization problem, c) given p (ω ), 3 solves the final good sector’s profit maximization problem, d) Me is such that the free entry condition is satisfied in every period, and e) markets clear in every period: L = Lp + LI + Lf c + fe Me 29 C=Y where Lp,t , Lf c,t , and Lf p,t are the aggregate demands for labor in production, labor in innovation, and fixed costs of operation; defined by: ρ−1 Y ρ Lp = eω [1 − τ s (ω )] dM (ω ) (13) ρ wρ Lf c = fc dM (ω ) LI = eω × µ eφq (ω ) − 1 dM (ω ) Definition of GDP and TFP A well known property of CES production functions is that aggregate output inherits the functional form from individual technologies, with the aggregate T F P given by a geo- metric weighted average of individual productivity. In the context of the current model economy with distortions, we can write aggregate output as follows: Y = ALp (14) ρ (1 − τ s (ω ))ρ−1 dM ρ−1 1 eω (ω ) A = M θ −1 θ (15) eω (1 − τ s (ω )) dM (ω ) where M (ω ) is the probability distribution function associated with the distribution of M (ω ) the mass of firms, M (ω ) = dM (ω ) . Equation 15 reveals the channels through which size-dependent tax enforcement man- ifests in aggregate productivity. For a given number of firms and a given distribution of firms across productivity levels M (ω ), size dependent taxes reduce aggregate productiv- ity by inefficiently allocating labor across production units. As mentioned earlier, only the sales tax exerts a distortion on allocative efficiency, with no effect stemming from profit taxation. The aggregate effects are also shaped by the response in innovation decisions 30 of firms, which reduce aggregate productivity by discouraging investments in technolog- ical upgrading. In this case, both the profit and the sales tax contribute to shaping the response in innovation expenses. Lastly, size-dependent taxation affects T F P through entry and exit, which manifest in the total number of varieties in the economy, M . 6 Quantitative Analysis We turn now to quantifying the macroeconomic implications, and the contributions of the micro-channels underlying it, of our estimates of size-dependent tax compliance. We calibrate parameters of the shock process, fixed costs, entry costs, innovation costs, and the distribution of productivity at entry to replicate properties of the firm size distri- bution and the life-cycle of firms in the US. Then, we implement a strategy to map our estimates of the size-gradient to turn it into a productivity-dependent profile of profit and sales taxes. We consider two counterfactuals for the evaluation of the gains from reversing size dependent taxation. Our baseline exercise consists of computing the TFP gains34 accru- ing from fixing the probability of compliance of all firms at the level corresponding to the median decile in the size distribution, while keeping statutory tax rates unchanged. Since this policy does not ensure that aggregate tax collection is unchanged, we balance the government’s budget through lump sum transfers to or from the household. As a complementary exercise, we consider a case where in addition to flattening the profile of enforcement, we adjust tax rates so as to keep the share of tax collection in GDP and the relative contribution of profit taxation constant at their levels prior to the reform. We provide more details about the construction of the counterfactuals below. 34 Notice that the undistorted version of our model, which is the basis for the calibration, is one in which the equilibrium is Pareto Optimal. This means that any form of taxation will be detrimental to welfare and, hence, we could interpret our aggregate results as proxies for the welfare losses from size dependent taxation. Since we are abstracting from other distortions that this pattern of taxation could be helping minimize, we prefer to refrain from making inferences about welfare and characterize our results solely in terms of the implications for T F P . 31 6.1 Calibration of Parameter Values Table 5 reproduces our calibration values for parameters that remain fixed across all ex- periments, which are determined in order to match properties of the firm size distribution and the life-cycle of firms in the U.S. manufacturing sector. Specifically, the parameters in the innovation cost function, µ and φ, are calibrated to jointly match the share of employ- ment accounted for by the top 10% of firms in the U.S. manufacturing sector in 2007, and the ratio of employment of firms aged 21-25 relative to firms of age 1 in the same year. The exogenous component of the exit rate of firms in the model, given by δ , is set so as to replicate the exit rate of large firms in the U.S. manufacturing sector, which is equal to 2.5%. The variance of the shock process, in turn, which is given by ∆, is chosen so as to match the standard deviation of employment growth rates in the cross section of U.S. firms, as reported by Atkeson and Burstein [2010]. Lastly, we are assuming a Pareto dis- tribution of entrants’ productivity, the tail parameter of which we discipline by requiring that the models’ relative size of the average entrant to the average incumbent equals 20%, which is the value observed in the U.S. in 2007. 6.2 Calibration of the Enforcement Size-Gradient The identification strategy in the empirical analysis adopts the U.S. industry-size distribu- tion as an instrument for exogenously assessing the size variation of tax enforcement in all countries in the sample. We follow a strategy for calibrating the productivity-dependent size enforcement in the model that is consistent with this empirical strategy. Taking the estimates for the average size-gradient from the IV regressions, we use the U.S. firm size distribution, and the model’s implication that size maps one to one with productivity in the undistorted equilibrium, to back-out a gradient between the probability of tax en- forcement and the underlying productivity of the firms. There is, however, a remaining difference between the identification strategy in the 32 empirical analysis and the calibration of the model. This difference lies in that, while the identification of the average size-gradients stems from the rank of industries across the industry-level size distribution, these size-gradients are then fed into the firm size distri- bution in the model. The implicit assumption which rationalizes this choice is that the industry-level gradient of taxation applies also across firms of different sizes within each industry. Based on theory, we cannot unambiguously conclude whether this assumption magnifies the quantitative results we find below or weakens them. A supporting piece of evidence in favor of the latter is that the average size-gradient masks non-linearities across the industry size distribution (Section 4.2). In particular, larger industries carry a disproportionate burden of taxation than smaller industries. Given the higher variance in the within industry firm-size distribution, this non-linearity in taxation would translate in higher average gradients if these were estimated at the firm level. However, we cannot exclude the possibility that there is less variation in tax-enforcement within industries, and that most distortions occur at the industry level, in which case the macroeconomic effects would be weaker. To formalize the parameterization of the size-dependent enforcement profile in the model, we proceed as follows. First, we identify 10 deciles of the size distribution in the undistorted economy. Then, using a given estimate of the gradient from the IV rank regres- sions, we compute the probability of enforcement at a given decile of the size-distribution q (decilei>1 ) = q (decile1 ) + gradient ∗ decilei>1 where decile1 is the smallest decile. This representation maps directly into the interpreta- tion of the IV coefficients in tables 2 and 3. For instance, taking the average gradient of 0.234 from column 5 of table 2 implies that going from a given decile of the size distribu- tion to the next one increases the probability of inspection by 2.3%. As mentioned above, deciles in the space of employment map directly into the space of physical productivity in the case of the undistorted economy, so the equation above also 33 provides us with a probability of inspection at ten points of the productivity distribution. We generate probabilities of tax inspection for the entire spectrum of productivity levels taking a linear interpolation for the points in between the deciles. As an example, consider figure 7 which illustrates the enforcement probability and the effective tax profiles under the assumption of a probability of inspection at the lowest decile of 40%, a tax rate of 30%, and a size gradient of 0.234 (Equal to the average size- gradient in our preferred specification). Notice that in the rightmost figure, where we measure the effective sales tax rate on the vertical axis, we get two different slopes. That is in reflection of the skewness of the firm size distribution in the US, whereby the top 10% largest firms account for the bulk of employment. So, the firms at the top decile are much larger than in the bottom 9 deciles. When we take the linear interpolation, the first 9 interpolation nodes are close to each other, whereas the node corresponding to the 10th decile is much further apart. Even though, in the space of probability-rank, each rank is equidistant from each other, that is not true in the space of the sizes associated with each rank, thus the flatter portion of the tax profile when going from the 9th to the 10th decile. In the quantitative exploration that follows, we split countries into 5 income groups, from poorest to richest, and use the income-specific estimates of enforcement gradients to evaluate the macro and micro implications of a hypothetical reform that eliminates all taxes for countries at various stages of development. The income-specific gradients, as well as the income-specific statutory corporate and sales tax rates that we feed into our model are presented in table 4. 6.3 Results Our baseline exercise for the quantification of the gains from reversing size-dependent taxation consists of fixing the probability of taxation at a common value across firms, while keeping the tax rates constant at their statutory levels. Since taxation is disruptive 34 in our model, even absent size-dependence,35 the level at which we fix the probability of compliance matters for the aggregate implications. Thus, as our benchmark, we adopt the case where the size-dependent profile of probability of compliance rotates at the level corresponding to the median of the size distribution, and becomes flat across all firms. We also conduct a complementary exercise in which we adjust the statutory rates of revenue and profit taxation to ensure that the aggregate collection of tax revenue as a share of GDP, and the breakdown between revenue and profit collection, remain the same as in the allocation with size-dependent taxation. Notice that in this case the level at which we fix the probability of compliance does not matter, given that the tax rates will ultimately be adjusted to achieve a common target. We report in figure 8 the counter-factual gains in T F P , as well as the underlying changes in the average firm size, the rate of aggregate expenditure on innovation, and the number of entering firms. All variables are measured as ratios between their values in the counterfactual and the initial allocation. Income groups are ordered from poor to rich on the horizontal axis. Consider first the results from the benchmark counterfactual, labeled "Median Prob. of Enforcement" in figure 8. The top-left panel shows that size-dependent tax compliance is preventing the least developed countries from appropriating a 0.8% gain in TFP relative to a regime that taxes all firms with the median probability. Underlying these productivity gains are an increase in average firm size of more than 30%, an increase of up to 10% in aggregate innovation intensity, and a 25% potential drop in the number of entrants. The aggregate and firm-level response featured by development group 5 is virtually none. This is clearly due to the fact that the size gradient in tax compliance was almost equal to zero among these countries. The firm-level responses behind our aggregate results are consistent with stylized facts 35 An established property of our underlying model is that while a common revenue tax rate across all firms is neutral for TFP, a common profit tax rate is not. Profit taxes reduce TFP through lower entry and reduced innovation. 35 about differences in the size distribution and the life-cycle growth of firms across coun- tries. For instance, Bento and Restuccia [2017] document the strong positive relationship between average firm size and economic development. Our results suggest that part of these differences can be attributed to cross-country differences in size-dependent tax com- pliance. Furthermore, the decline in innovation intensity in the model, which translates into slower growth of firms over the life cycle, is consistent with the evidence presented in Hsieh and Olken [2014], which establishes the flatter path of firm growth in India and Mexico relative to the U.S. Since the aggregate effects in our counterfactuals are tightly linked to the firm-level adjustments in the economy, it is reassuring to find that the prop- erties of these adjustments in the model are consistent with the data. The increasing nature of the probability of tax enforcement is the key for understand- ing the decline in entry and the rise in average firm size that takes place when the size- dependence is reversed. To see this, consider first the allocation under size-dependent taxation assuming that innovation decisions do not change. Given the pattern of life- cycle growth endowed to the firms through the calibration of the shock process, a profile of taxation probabilities that is more binding as firms get large is more detrimental to the average incumbents than it is to to the average entrant. The reason for this is that en- trants benefit from the lack of taxation when young and suffer the higher taxation when old. With a positive interest rate, however, this higher probability of taxation in the fu- ture is discounted at the equilibrium interest rate ex-ante, which reduces the detrimental effect of taxation on the entrant’s expected profitability. However, from the point of view of the cross section of firms, such weakening of effect does not happen. Thus, the average profits of incumbents fall relative to entrants, requiring an increase in entry to restore the equilibrium. The endogenous response in innovation provides another channel through which av- erage firm size falls, and justifies the decline in innovation intensities illustrated in the bottom-left plot. In this case, the outcome is more intuitive: firms anticipate a higher 36 effective tax rate if they become more productive, thus respond by cutting down on inno- vation expenditure. We turn now to discussing the counterfactual in which we adjust tax rates at the same time we remove size-dependence in compliance. We find that the gains from this exercise (illustrated in figure8 under the label "Fixed Tax Revenue") are weakened relative to the baseline, reaching a maximum of 0.3%. The mechanisms at work are the same, as reflected by the identical qualitative response of the economy. However, the increase in average profit tax rates that is required to attain the targeted revenue mitigates the efficiency gains from reversing the size-dependent component of taxation. The baseline counterfactual delivered shares of revenue to GDP that fell short of what was being collected by the government under size-dependent taxation. Except for the highest income group, for which the size gradient was almost zero and hence there is no difference between the initial allocation and the counterfactual, the share of tax revenue to GDP was 80% of the share under size-dependence. In order to attain the exact same share, without appealing only to revenue taxes (which are neutral to TFP) we had to increase the profit tax rate, which, as mentioned earlier, hinders TFP by holding down the rise in innovation intensity (bottom left panel) and strengthening the decline in entry (bottom right panel). We close the numerical analysis with a discussion of the quantitive relevance of our re- sults. At first sight, keeping in mind the magnitude of the productivity gaps across coun- tries, our findings do not seem to be first order in the quest to catch up with the rest of the world. Even if we benchmark our gains relative to the productivity improvements that arise from removing all forms of idiosyncratic distortions, which average at about 60%, the magnitude of the gains in our exercise are still small. However, when benchmarking against other studies that have carefully evaluated a single policy, our results start to fall in the ballpark of the literature. Evaluations of size dependent labor market regulations, such as Gourio and Roys [2014] and Garicano et al. [2016] find gains that are even lower than ours, in the order of 0.03%. Also in the context of labor regulation, but considering a 37 potentially more damaging policy, such as taxes to hire and fire workers, Hopenhayn and Rogerson [1993] find TFP gains of up to 2% from removing plausibly calibrated values of these taxes. The highest gains are obtained in the financial frictions literature, where TFP rises between 7% and 40% when improving access to credit, depending on the features of the model (Buera et al. 2011, Moll 2014, Midrigan and Xu 2014). We interpret these findings as suggesting that observed misallocation is the outcome of a collection of poli- cies that combine mild distortions with more damaging ones, and that size-dependent tax enforcement and compliance appears to be part of the former group. 7 Conclusion This paper studies the prevalence and consequences of size-dependent tax enforcement and compliance in 140 countries. The identification strategy uses the relative ranking of industries’ average industry-size in the US as an instrument for the relative ranking of the same industries’ size in developing countries. We find a positive size gradient in tax inspection and tax compliance. This result is robust across specifications with flexible controls, variation in size within narrowly defined industries and variation in industries’ size over time within a country. Moreover, we find that size-based enforcement is concen- trated at the top of the industry size distribution and prevalent in lower-income countries, while it does not appear to be used in rich countries. When quantified in an general equi- librium model of firm dynamics, size-dependence in tax enforcement generates a drop in TFP of up to 0.8% in lowest-income countries, which is driven by a decline in average firm size and a reduction in innovation intensity. There are several limitations to our study. First, given that the WBES sample only covers registered firms, it is unclear to what extent our estimates of size-dependent tax policy would generalize to non-registered firms. The second limitation is that we proxy for tax enforcement using only in-person physical inspections by tax inspectors. Tax authorities 38 have other tools at their disposal to collect information and enforce taxes, including third party data-sources which allow tax inspectors to flag irregular reporting behavior and deter evasion through letters and on-line communication with taxpayers. These indirect means of enforcement are more prevalent in rich countries and it is possible that they sub- stitute for physical audits, however recent research shows that even in the US, in-person visits by tax inspectors remain prevalent and have positive impacts on compliance (Bon- ing et al. 2018). Finally, we recognize that size-dependent tax inspection may arise endogenously as an optimal policy under information and resource constraints (Kleven et al. 2016, Bigio and Zilberman 2011). Therefore while we quantify the TFP distortions generated by size- dependence, we do not measure the revenue gains from this policy, and do not make a normative statement. 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Pomeranz, Dina, “No Taxation without Information: Deterrence and Self-Enforcement in 41 the Value Added Tax,” American Economic Review, 2015, (8), 2539–2569. Rajan, Raghuram G and Luigi Zingales, “American Economic Association,” The Ameri- can Economic Review, 1998, 88 (3), 559–586. Restuccia, Diego and Richard Rogerson, “Policy distortions and aggregate productivity with heterogeneous establishments,” Review of Economic Dynamics, 2008, 11 (4), 707–720. World Bank, “Doing Business 2017: Equal Opportunity for All.,” Washington, DC: World Bank. DOI: 10.1596/978-1-4648-0948-4. License: Creative Commons Attribution CC BY 3.0 IGO, 2017. Zareh, Asatryan and Andreas Peichl, “Responses of Firms to Tax, Administrative and Accounting Rules: Evidence from Armenia,” 2016. 42 F IGURE 1: N UMBER OF C OUNTRIES WITH A L ARGE TAXPAYER U NIT O VER T IME 100 Countries with a Large Taxpayer Unit 80 60 40 20 0 1960 1970 1980 1990 2000 2010 Year Source: Data collected by the authors. All 113 countries, with more than one million inhabitants. In the past twenty years more than a 100 countries adopted a Large Taxpayer Unit (LTU). This development is part of an increased trend of taxpayer segmentation, recommended by international institutions. F IGURE 2: US I NDUSTRY S IZE ON WBES I NDUSTRY S IZE [F IRST S TAGE ] 40 35 Mean WBES Size Rank 20 25 15 30 Rank−Rank Slope=.439 (.008) 10 0 10 20 30 40 50 US Census Size Rank Source: US Census 2001 and World Bank Enterprise Surveys 2003-2015. Figure 2 presents non-parametric binned scatterplot of the relationship between WBES countries and US firm size ranks, as discussed in Section 3.1. WBES size rank is the rank of an ISIC3 by number of permanent employees per firm in the WBES country-year. US Census size rank is the ISIC3 rank of number of employ- ees per firm in 2001, excluding firms with less than 5 employees. In each country-year, ISIC3 industries are ranked relative to other industries in the same country-year survey. The WBES and US Census ranks are then grouped into 50 equal sized (two percentile) bins. 43 F IGURE 3: I NDUSTRY S IZE IN THE US ON I NDUSTRY S IZE IN THE WBES BY I NCOME L EVEL Low income countries Lower−middle income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.471 Rank−Rank Slope=.479 (.040) (.017) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 US Census Size Rank US Census Size Rank Upper−middle income countries High−income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.424 Rank−Rank Slope=.411 (.013) (.014) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 US Census Size Rank US Census Size Rank Source: US Census 2001 and World Bank Enterprise Surveys 2003-2015. Figure 3 presents non-parametric binned scatterplot of the relationship between WBES countries and US firm size ranks, in the four per capita income groups based on the World Bank income classification. These results are discussed in Section 3.1 The cut-off per-capita income values are: 1100 for low income countries; between 1100 and 3900 for lower-middle income countries; between 3900 and 12730 for upper-middle in- come countries; above 12730 for high income countries. WBES size rank is the ISIC3 rank of number of permanent employees per firm in the WBES country-year. US Census size rank is the ISIC3 rank of number of employees per establishment in 2001, where we exclude establishments with less than 5 employees. In each country-year, ISIC3 industries are ranked relative to other industries in the same country-year sur- vey. Within each per capita income group, the WBES and US Census ranks are then grouped into 25 equal sized bins. For each per capita income group, this graph plots the mean WBES size rank percentile within each 25-quantile US size rank percentile, together with a best-fit line. The rank-rank slope coefficient and standard error are estimated in each per capita income group. 44 F IGURE 4: I NDUSTRY S IZE AND TAX I NSPECTION IN M AJOR C OUNTRIES Bangladesh Brazil China 100 100 100 80 80 80 Likelihood of tax inspection Likelihood of tax inspection Likelihood of tax inspection 60 60 60 40 40 40 20 20 20 0 0 0 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 Size Rank Size Rank Size Rank India Indonesia Mexico 100 100 100 80 80 80 Likelihood of tax inspection Likelihood of tax inspection Likelihood of tax inspection 60 60 60 40 40 40 20 20 20 0 0 0 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 Size Rank Size Rank Size Rank ISIC3 Industry Average Linear fit Source: World Bank Enterprise Surveys 2003-2015. Figure 4 plots each ISIC 3 industry by its firm size rank on the probability of tax inspection in the six most populous countries, as discussed in Section 4.1. When multiple surveys exist for a country we use the latest survey. The size of the dots is the share of total employment (in our sample) within the country. Therefore dot size are not comparable across countries but only show relative size of industries within a country. The red line plots the linear fit of size rank on tax inspection. 45 F IGURE 5: N ON -L INEAR I MPACT OF F IRM S IZE ON TAX I NSPECTION & C OMPLIANCE ( A ) PANEL A: TAX I NSPECTION Probability of tax inspection, relative to median industry size] −1 −.5 0 .5 1 1.5 2 2.5 3 3.5 1 2 3 4 5 6 7 8 9 10 Deciles of industry average size ( B ) PANEL B: TAX C OMPLIANCE Probability of tax inspection, relative to median industry size] −.5 0 .5 1 1.5 2 2.5 3 1 2 3 4 5 6 7 8 9 10 Deciles of industry average size Source: US Census 2001 and World Bank Enterprise Surveys 2003-2015. Figure 5 shows for each decile of industry-size the likelihood of tax inspection and tax compliance com- pared to the median industry-size, as discussed in section 4.2. To construct these figures, we first residualize the tax outcomes and industry-size variables with respect to the country-year-control interactive fixed ef- fects. We then group the residualized industry-size into deciles and plot the average of the residualized tax outcome within each bin. We winsorize at the 5% level within industry size-deciles. The specification cor- responds to the regressions in Column 3 of Table 2 (Panel A) and Column 3 of Table 3 (Panel B) respectively, and use the same sample restrictions and variable definitions. 46 F IGURE 6: S IZE G RADIENTS BY I NCOME L EVELS .04 Size−Gradient in Tax Enforcement .03 .02 .01 0 [540,1100] (1100,3900] (3900,12730] (12730,21000] (21000,47100] Income Group (GDP per capita in PPP) Reduced form 5pct signif Reduced form 5pct non−signif IV 5pct signif IV 5pct non−signif Source: US Census 2001 and World Bank Enterprise Surveys 2003-2015. Figure 6 show the reduced form (diamonds) and IV coefficients (triangles), replicating the regressions in Columns 3 and 5 of Table 2 for each development level, as discussed in Section 4.3. The groups correspond to the World Bank income classification, except for the top income group (above USD 21,000) which corre- sponds to the 90th percentile of income in the WBES and was chosen such that countries are comparable to the US in terms of economic development. F IGURE 7: TAX P ROFILES Probability of Inspection vs Decile Effective Tax vs Log Empl 0.24 0.60 0.22 0.55 0.20 effective tax proba[, 1] 0.50 0.18 0.45 0.16 0.40 0.14 2 4 6 8 10 0 10 20 30 decile log Empl The left panel of Figure 7 shows the enforcement probability against deciles of the employment size dis- tribution, as discussed in Section 6.2. It assumes an average size-gradient of 0.023, and a probability of inspection at the lowest decile of 40%. The right panel shows the corresponding effective sales tax rates, assuming a statutory sales tax rate of 30% 47 F IGURE 8: A GGREGATE AND M ICRO I MPLICATIONS OF S IZE -D EPENDENT I NSPEC - TION TFP Av.Firm Size 1.010 1.5 1.008 Median Prob. of Enforcement 1.4 Fixed Tax Revenue 1.006 1.3 1.004 1.2 1.002 1.1 1.000 1.0 1 2 3 4 5 1 2 3 4 5 Development Group (1 = poorest) Development Group (1 = poorest) Average Innovation Intensity Entry of Firms 1.15 1.00 0.95 1.10 0.90 0.85 1.05 0.80 1.00 0.75 1 2 3 4 5 1 2 3 4 5 Development Group (1 = poorest) Development Group (1 = poorest) Figure 8 shows results from baseline counter-factual that equalizes probability of compliance at the level of the median-size firm, keeping fixed the revenue and profit tax rates; and the counterfactual that also adjusts tax rates to achieve the same share of tax revenue to GDP, and the same share of profit revenue over total revenue, as in the initial allocations. The former is labeled "Median Prob. of Enforcement", while the latter is labeled "Fixed Tax Revenue". All variables are illustrated as ratios between their values in the counterfactual and their values in the equilibrium with size-dependent taxation. Income groups in the horizontal axes are ranked from low to high. 48 TABLE 1: S UMMARY S TATISTICS (1) (2) (3) (4) (5) (6) Variable N Mean s.d. p25 p50 p75 Panel A: Industry Level Outcomes (ISIC3) Any Tax Inspection [0,100%] 12,152 61.88 35.65 37.50 66.67 100 Number of Tax Inspections 12,152 1.98 2.13 0.67 1.48 2.72 Full Compliance [0,100%] 3,343 57 38.1 25 60 100 Compliance Rate 3,343 80.93 23.6 70 89.6 100 Any Informal Payments [0,100%] 10,013 26.00 36.41 0 0 50 Informal Payments, Share of Sales 10,013 1.58 4.22 0 0 1.50 Formal Tax Payments, Share of Sales 3,048 33.28 11.9 25.8 35 42 Formal and Informal Tax Payments, Share of Sales 2,864 34.97 12.04 27.63 36 42.46 Panel B: Inudustry Level Covariates (ISIC3) Age 12,152 18.64 13.16 10.75 15.57 22.67 Share of Establishment Owned by Foreign Companies 12,149 0.137 0.266 0 0 0.15 Share of Annual Sales Destined for Direct Export 12,093 0.228 0.326 0 0 0.36 Manufacturing Sector {0,1} 12,152 0.58 0.49 0 1 1 Statutory Corporate Tax Rate + Sales Tax Rate 11,524 0.39 0.09 0.35 0.40 0.45 GDP Per Capita, Constant USD 2011 12,117 10,673 8,554 3,736 8,837 16,459 Panel C: Industry Size Characteristics (ISIC3) WBES Size 12,146 69.42 289.5 12.94 24.66 52.84 US Census 1991 Size 11,330 48.2 39.09 27.33 38.28 66.18 US Census 2001 Size 11,962 52.95 43.73 28.20 40.48 67.95 US Census 2015 Size 11,958 51.65 40.89 27.79 37.40 62.47 EU Amadeus 2007 Size 12,032 393.7 891.7 116.76 184.05 346.84 WBES RKZ-Weighted Size 12,146 262.3 840.3 21.06 67.40 200.57 US Census 2001 RKZ-Weighted Size 12,001 302.2 306.60 125.58 218.41 384.67 Source: World Bank Enterprise Surveys 2003-2015. Table 1 displays the summary statistics at the industry-country-year level, as described in section 2. In- dustries are defined at the 3-digit ISIC level, using the UN classification version 3.1. Column 1 reports the number of industry level observations, column 2 the mean, column 3 the standard deviation and columns 4-6 the quartiles (25% percentile, median and 75% percentile). All statistics are reported for the full sample which includes some observations for which a sampling weights are missing. 49 TABLE 2: I MPACT OF F IRM S IZE ON TAX I NSPECTION OLS Reduced Form IV Panel: OLS (1) (2) (3) (4) (5) (6) (7) (8) Panel A Outcome: Tax Inspection {0,1} Industry Size Rank (World Bank) 0.197 0.232 0.234 0.189 0.303 0.276 (0.054) (0.043) (0.055) (0.109) (0.065) (0.067) Industry Size Rank (US Census) 0.073 0.050 (0.017) (0.030) FE country year controls     FE country year ISIC2     FE ISIC3   F-Stat 259.68 105.49 R-squared 0.650 0.772 0.641 0.766 0.650 0.772 0.890 0.906 Panel B Outcome: # of Tax Inspections Industry Size Rank (World Bank) 0.0112 0.0161 0.0142 0.0181 0.0170 0.0155 (0.0030) (0.0025) (0.0034) (0.0056) (0.0046) (0.0038) Industry Size Rank (US Census) 0.0045 0.0048 (0.0010) (0.0017) (0.017) (0.030) FE country year controls     FE country year ISIC2     FE ISIC3   F-stat 259.68 105.49 R-squared 0.600 0.734 0.591 0.725 0.599 0.734 0.886 0.896 Observations 9,772 7,864 9,772 7,864 9,772 7,864 5,048 4,176 Number of clusters 131 131 131 131 131 131 75 77 Source: US Census 2001 and World Bank Enterprise Surveys 2003-2015. Robust standard errors in parentheses, clustered at the country level. Table 2 shows the coefficients of regressions of industry firm-size ranking on tax inspection, discussed in section 4.1. Panel A measures tax inspection as a dummy which takes the value one if the firm was vis- ited during the year. Panel B measures tax inspection as the number of times the firm was visited by tax inspectors. Odd number columns include interactive fixed effects between country, year and 3 dummies indicating whether the ISIC3 industry was above median in the country-year distributions of age, export- share, and foreign-industry share. Even number columns include interactive fixed effects between country, year and 2-digit ISIC codes. In this case, size-rank coefficients are estimated using variation between 3-digit ISIC codes, controlling non-parametrically for country-year-2digit ISIC effects. For a given specification, the sample size in the even columns is smaller than in the odd columns. This is because the ISIC2 interac- tive fixed effect specification drops all cells where there does not exist more than one ISIC3-country-year observation within a ISIC2-country-year observation. The sample drop occurs in industries that are less specialized, which are more prevalent in less developed countries. In columns (5) & (6), we instrument for the World Bank size rank using the US Census size-rank. The F-statistic comes from the first stage rank- rank regression of World Bank size rank on US Census size rank. In columns (7) & (8), we add ISIC 3-digit fixed effects, so that the size-rank coefficients are estimated using variation within ISIC3 over time in its country-year industry rank. The ISIC3 fixed effect models result in a drop in sample size because the ISIC3 panel structure does not exist for some of the early WBES country surveys. 50 TABLE 3: I MPACT OF F IRM S IZE ON TAX C OMPLIANCE OLS Reduced Form IV (1) (2) (3) (4) (5) (6) Panel A Outcome: Full Tax Compliance {0,1} Industry Size Rank (World Bank) 0.244 0.256 0.519 0.401 (0.045) (0.072) (0.138) (0.169) Industry Size Rank (US Census) 0.175 0.132 (0.045) (0.062) FE country year controls    FE country year ISIC2    F-stat 35.12 38.80 R-squared 0.626 0.736 0.624 0.733 0.617 0.735 Panel B Outcome: % Sales Reported Industry Size Rank (World Bank) 0.152 0.150 0.221 0.183 (0.034) (0.047) (0.088) (0.114) Industry Size Rank (US Census) 0.075 0.060 (0.035) (0.041) FE country year controls    FE country year ISIC2    F-stat 35.12 38.80 R-squared 0.719 0.795 0.715 0.793 0.718 0.795 Observations 3,187 2,348 3,187 2,348 3,187 2,348 Number of clusters 83 83 83 83 83 83 Source: 2001 US Census and World Bank Enterprise Surveys 2003-2007. Robust standard errors in parentheses, clustered at the country level. Table 3 shows the coefficients of regressions of industry firm-size ranking on tax compliance, discussed in section 4.1. Tax compliance is measured as the response to the survey question: "Recognizing the difficulties many enterprises face in fully complying with taxes and regulations, what percentage of sales would you estimate the typical establishment in your area of activity reports for tax purposes?". Panel A defines full tax compliance as a dummy equal to one if a firm reports reporting 100% of its sales for tax purposes. Panel B uses the percentage of sales reported for tax purpose. Odd number columns include interactive fixed effects between country, year and 3 dummies indicating whether the ISIC3 industry was above median in the country-year distributions of age, export-share, and foreign-industry share. Even number columns include interactive fixed effects between country, year and 2-digit ISIC codes. In this case, size-rank coefficients are estimated using variation between 3-digit ISIC codes, controlling non-parametrically for country-year- 2digit ISIC effects. For a given specification, the sample size in the even columns is smaller than in the odd columns. This is because the ISIC2 interactive fixed effect specification drops all cells where there does not exist more than one ISIC3-country-year observation within a ISIC2-country-year observation. The sample drop occurs in industries that are less specialized, which are more prevalent in less developed countries. In columns (5) & (6), we instrument for the World Bank size rank using the US Census size-rank. The F- statistic comes from the first stage rank-rank regression of World Bank size rank on US Census size rank.The tax compliance question was only administered in the earlier waves of the WBES surveys which were not structured as panels. Hence, we cannot estimate panel models for the tax compliance outcomes. 51 TABLE 4: G RADIENTS AND TAX R ATES BY I NCOME G ROUP Income Level Gradient Sales Tax Corporate Tax 1 (poorest) 3.98% 9.06% 25.66% 2 2.44% 12.94% 21.35% 3 3.27% 11.98% 19.47% 4 2.04% 16.14% 18.6% 5 0 16.13 23.59 Note: Estimates of gradients by income group are drawn from Figure 7, panel A. Statutory tax rates are averages among countries in each income group TABLE 5: PARAMETER VALUES AND C ALIBRATION TARGETS Parameter Value Target ρ 3 Hsieh and Klenow (2009), Broda and Weinstein (2006) 1 β 1.05 Interest Rate of 5% δ 0.025 Employment-Based Exit Rate of Large Firms of 2.5% ∆ 0.25 Std Dev. Employment Growth rate φ 15 Top 10% Employment Share µ 0.00041 Employment Age 21-25 relative to Age 1 G(ω ) P areto,η = 4.46 Empl. Ratio Entrants to Incumbents fc fe 0.1 Exit Rate of 5% Note: The top 10% employment share, the average employment ratio between 21-25 and 1 year old firms, and the average employment ratio between entrants and incumbents were computed from Business Dy- namics Statistics database for the year 2007. Numbers are for the manufacturing sector. Standard deviation of employment growth rates for large firms are reported in Atkeson and Burstein (2010). 52 A Appendix Figures & Tables (Not for Publication) F IGURE A1: I NDUSTRY S IZE IN US C ENSUS 91 ON I NDUSTRY S IZE IN WBES BY I N - COME Low−income countries Lower−middle income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.438 Rank−Rank Slope=.485 (.041) (.017) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 US 1991 Census Size Rank US 1991 Census Size Rank Upper−middle income countries High−income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.416 Rank−Rank Slope=.406 (.013) (.014) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 US 1991 Census Size Rank US 1991 Census Size Rank Source: 1991 US Census and World Bank Enterprise Surveys 2003-2015. Figure A1 presents non-parametric binned scatterplot of the relationship between WBES countries’ and US’ 1991 percentile firm size ranks in the four per capita income groups based on the World Bank classification. The USD cut-off values used for the classification are: 1100 for low income countries; between 1100 and 3900 for lower-middle income countries; between 3900 and 12730 for upper-middle income countries; above 12730 for high income countries. This figure is based on the full WBES sample and the US Census 1991. WBES size rank is the ISIC3 rank of number of permanent employees per firm in the WBES country-year. US Census size rank is the ISIC3 rank of number of employees per establishment in 199, where we exclude establishments with less than 5 employees. Within each per capita income group, the WBES and US Census ranks are then grouped into 25 equal sized bins. For each per capita income group, this graph plots the mean WBES size rank percentile within each 25-quantile US size rank percentile, together with a best-fit line. The rank-rank slope coefficient and standard error are estimated in each per capita income group using the underlying ISIC3-year-country data. 53 F IGURE A2: I NDUSTRY S IZE IN US C ENSUS 15 ON I NDUSTRY S IZE IN WBES BY I N - COME Low income countries Lower−middle income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.411 Rank−Rank Slope=.451 (.046) (.018) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 US 2015 Census Size Rank US 2015 Census Size Rank Upper−middle income countries High income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.399 Rank−Rank Slope=.402 (.014) (.016) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 US 2015 Census Size Rank US 2015 Census Size Rank Source: 2015 US Census and World Bank Enterprise Surveys 2003-2015. Figure A2 presents non-parametric binned scatterplot of the relationship between WBES countries’ and US 2015 percentile firm size ranks in the four per capita income groups based on the World Bank classification. The USD cut-off values used for the classification are: 1100 for low income countries; between 1100 and 3900 for lower-middle income countries; between 3900 and 12730 for upper-middle income countries; above 12730 for high income countries. This figure is based on the full WBES sample and the US Census 2015. WBES size rank is the ISIC3 rank of number of permanent employees per firm in the WBES country-year. US Census size rank is the ISIC3 rank of number of employees per establishment in 2015, where we exclude establishments with less than 5 employees. Within each per capita income group, the WBES and US Census ranks are then grouped into 25 equal sized bins. For each per capita income group, this graph plots the mean WBES size rank percentile within each 25-quantile US size rank percentile, together with a best-fit line. The rank-rank slope coefficient and standard error are estimated in each per capita income group using the underlying ISIC3-year-country data 54 F IGURE A3: I NDUSTRY S IZE IN EU A MADEUS 07 ON I NDUSTRY S IZE IN WBES BY I NCOME Low income countries Lower−middle income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.403 Rank−Rank Slope=.372 (.041) (.017) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 EU Amadeus Size Rank EU Amadeus Size Rank Higher−middle income countries High−income countries 20 20 Mean WBES Size Rank Mean WBES Size Rank 15 15 10 10 Rank−Rank Slope=.306 Rank−Rank Slope=.269 (.014) (.015) 5 5 0 5 10 15 20 25 0 5 10 15 20 25 EU Amadeus Size Rank EU Amadeus Size Rank Source: 2007 EU Amadeus and World Bank Enterprise Surveys 2003-2015. Figure A3 presents non-parametric binned scatterplot of the relationship between WBES countries’ and EU’ percentile firm size ranks in the four per capita income groups based on the World Bank classification. The USD cut-off values used for the classification are: 1100 for low income countries; between 1100 and 3900 for lower-middle income countries; between 3900 and 12730 for upper-middle income countries; above 12730 for high income countries. This figure is based on the full WBES sample and the EU Amadeus sample of UK and German firms in 2007. WBES size rank is the ISIC3 rank of number of permanent employees per firm in the WBES country-year. EU Amadeus Census size rank is the ISIC3 rank of number of employees per establishment in 2007 in Germany and UK. Within each per capita income group, the WBES and EU Amadeus ranks are then grouped into 25 equal sized bins. For each per capita income group, this graph plots the mean WBES size rank percentile within each 25-quantile EU Amadeus size rank percentile, to- gether with a best-fit line. The rank-rank slope coefficient and standard error are estimated in each per capita income group using the underlying ISIC3-year-country data. 55 F IGURE A4: N ON -L INEAR I MPACT OF F IRM S IZE ON F ORMAL & I NFORMAL TAX R ATES ( A ) PANEL A 2 Residualized coefficent [percentage points] −.5 0 .5 1 1.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Vingtiles of residualized firm size Formal effective tax rate Informal effective tax rate ( B ) PANEL B: AS P ERCENTAGE OF M EAN OF O UTCOMES .1 Residualized coefficient [% of mean] 0 −.1 −.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Vingtiles of residualized firm size Formal effective tax rate Informal effective tax rate Source: US Census 2001 and World Bank Enterprise Surveys 2003-2015. Figure A4 shows binned scatter plots of the effective formal and informal tax rates on firm size, discussed in section ??. These plots correspond to the regressions in Column 3 of Table 3 Panel B and Table 4 Panel A respectively, and use the same sample restrictions and variable definitions. To construct these panels, we first residualize the y-axis and x-axis variables with respect to the country-year-control interactive fixed effects (defined in Section X equation Y). We then group the residualized firm-size into twenty equal-sized bins (vingtiles) and plot the median of the y-variable residual within each bin. The median is chosen to reduce the impact of residual outliers. 56 TABLE A1: F IRST-S TAGE AND IV FOR D IFFERENT I NSTRUMENTAL VARIABLES Panel A: First Stage Industry Size Rank (WBES) (1) (2) (3) (4) (5) (6) Industry Size Rank (US Census 01) 0.308 (0.019) Industry Size Rank (US Census 91) 0.337 (0.022) Industry Size Rank (US Census 15) 0.253 (0.020) Industry Size Rank (EU Amadeus 07) 0.101 (0.017) Industry Size Rank (KRZ weighting) 0.082 (0.031) Industry Size Mean (US Census 01) 0.342 (0.048) R-squared 0.552 0.562 0.524 0.501 0.624 0.140 Panel B: IV Results Tax Inspection {0,1} (1) (2) (3) (4) (5) (6) Industry Size Rank (WBES) 0.242 (0.053) Industry Size Rank (WBES) 0.188 (0.048) Industry Size Rank (WBES) 0.167 (0.050) Industry Size Rank (WBES) 0.765 (0.217) Industry Size Rank (WBES) 0.492 (0.152) Industry Size Mean (WBES) 0.091 (0.020) 1st stage rank-rank based on sample USCen01 USCen91 USCen15 EUAma07 USCen01RKZ USCen01 1st stage F-statistic 276.83 227.40 159.62 35.52 6.94 50.87 R-squared 0.662 0.662 0.659 0.584 0.628 0.554 FE country year controls       Observations 11,675 11,671 11,031 11,743 11,710 11,675 Number of clusters 140 140 140 140 140 140 Sources: World Bank Enterprise Surveys 2003-2015 and US firm census 2001. Robust standard errors in parentheses, clustered at the country level. Table A1 shows first stage regressions and IV regressions on tax inspections across different samples of first stage industry firm-size. All regressions include interactive fixed effects between country, year and 3 dummies indicating whether the ISIC3 industry was above median in the country-year distributions of age, export-share, and foreign-industry share. In Panel A row 1-3, US industry size is constructed using the 2001, 1991, and 2015 US Census of firm employment. In Panel A row 4, the industry size is constructed using the Amadeus sample in the UK and Germany between 1998 and 2007. In Panel A row 5, the industry average firm-size is constructed using the Kumar et al. [1999] ’employee-weighted’ methodology (KRZ). This methodology effectively places more weight on firms that concentrate large shares of total employment when calculating the industry-wide average firm size. In Panel A row 6, the industry size mean (as opposed to rank) in the US Census 2001 is used as the regressor. In Panel A Cols.1-4, the outcome variable is the WBES size rank as defined in the main tables. In Panel A Column 5, the outcome variable is the average firm size in all WBES countries calculated using the employee-weighted KRZ methodology. In Panel A Column 6, the outcome variable is the industry mean firm size (as opposed to rank). In Panel B, the outcome variable is a dummy taking a value of one if the firm has had any tax inspections over the past year: please see Table 1 for more details. In Panel B, Columns 1-5, the WBES industry size rank is instrumented for using a size rank constructed from different samples, respectively: US Census 2001, US Census 1991, US Census 2015, EU Amadeus, US Census 2001 RKZ reweigthed. In Panel B Column 6, the WBES industry size mean is instrumented for using the US Census 2001 industry size mean. 57 TABLE A2: I MPACT OF F IRM S IZE ON TAX I NSPECTION , R ESTRICTED TO M ANUFAC - TURING Outcome: Industry Size Rank (WBES) Tax Inspection {0,1} # Inspections (1) (2) (3) (4) (5) 1st Stage Red. Form IV Red. Form IV Industry Size Rank (US Census) 0.310 0.135 0.009 (0.029) (0.034) (0.002) Industry Size Rank (WBES) 0.434 0.0289 (0.089) (0.005) 1st stage F-statistic 114.36 114.36 FE country year controls      R-squared 0.667 0.685 0.688 0.614 0.617 Observations 6,726 6,726 6,726 6,726 6,726 Number of clusters 138 138 138 138 138 Sources: World Bank Enterprise Surveys 2003-2015 and US firm Census 2001. Robust standard errors in parentheses, clustered at the country level. Table A2 shows the coefficients of regressions of industry firm-size ranking on various outcomes, limiting the sample to manufacturing industries. All regressions include interactive fixed effects between country, year and 3 dummies indicating whether the ISIC3 industry was above median in the country-year dis- tributions of age, export-share, and foreign-industry share. Manufacturing is defined as the set of ISIC2 industries which lie between code-number 15 and 37, using the ISIC Classification version 3.1. Size rank is constructed similarly to the main tables: please see Table 1 for further details. In Column 1, the out- come is WBES industry size rank. In Columns 2-3, the outcome variable is constructed similarly to Table 1. In Columns 4-5, the outcome variable is constructed similarly to Table 2. In Columns 3 and 5, the WBES industry size rank is instrumented for using the US industry size rank. 58 TABLE A3: TAX INSPECTION ON F IRM S IZE AND C APITAL N EEDS Outcome: Tax Inspection {0,1} # Inspections (1) (2) (3) (4) Industry Size Rank (US Census) 0.063 0.090 0.003 0.006 (0.020) (0.032) (0.001) (0.002) Industry External Reliance Rank (US Compustat) -0.001 -0.001 (0.023) (0.001) Industry Capital-Labor Ratio Rank (US Compustat) -0.001 0.002 (0.027) (0.002) FE countryyearcontrols     R-squared 0.580 0.624 0.534 0.562 Observations 9,715 5,320 9,715 5,320 Number of clusters 131 106 131 106 Sources: World Bank Enterprise Surveys 2003-2015 and US firm census 2001. Robust standard errors in parentheses, clustered at the country level. Table A3 shows the coefficients of regressions of industry size ranking and industry capital ranking on various outcomes. All regressions include interactive fixed effects between country, year and three dum- mies indicating whether the ISIC3 industry was above median in the country-year distributions of age, export-share, and foreign-industry share. Columns 1 and 3 include the industry external reliance rank as an additional explanatory variable. External reliance is defined as the share of capital expenditure not fi- nanced by cash flow of operations. This measure can directly be constructed for a subsample of firms in WBES. In the US, we rely on Compustat firm-level data between 1997 and 2007. We follow the methodol- ogy of Rajan and Zingales [1998] to construct the ISIC3 measure of external reliance. Having constructed the external reliance at the firm level in both the US and WBES, we construct ISIC3-country-year rankings similar to the industry employee-size rankings. Columns 2 and 4 include the industry capital-labor ratio rank as an additional explanatory variable. The capital-labor ratio is defined as the ratio of assets to number of permanent employees. This measure can be constructed for a subsample of firms in WBES. In the US, we rely on Compustat firm-level data between 1997 and 2007. The drop in sample size in columns 2 and 4 is due to the missing observations on assets for firms in the WBES surveys. 59 TABLE A4: I MPACT OF F IRM S IZE ON I NFORMAL TAX PAYMENTS OLS Reduced Form IV Panel: OLS (1) (2) (3) (4) (5) (6) (7) (8) Panel A Outcome: Any Informal Payment? {0,1} Industry Size Rank (World Bank) 0.011 -0.024 -0.048 -0.019 -0.041 -0.046 (0.015) (0.017) (0.032) (0.073) (0.041) (0.058) Industry Size Rank (US Census) -0.015 -0.008 (0.010) (0.017) FE country year controls     FE country year ISIC2     FE ISIC3   F-stat 184.39 116.58 R-squared 0.745 0.825 0.745 0.825 0.744 0.896 0.912 0.924 Panel B Outcome: % Sales Paid Informally Industry Size Rank (World Bank) -0.0036 -0.0072 -0.0114 -0.0135 -0.0198 -0.0221 (0.0024) (0.0025) (0.0047) (0.0089) (0.0059) (0.0075) Industry Size Rank (US Census) -0.0036 -0.0036 (0.0015) (0.0024) FE country year controls     FE country year ISIC2     FE ISIC3   F-stat 184.39 116.58 R-squared 0.466 0.604 0.466 0.604 0.464 0.604 0.778 0.777 Observations 9,538 7,261 9,538 7,261 9,538 7,261 4,381 3,390 Number of clusters 137 137 137 137 137 137 74 78 Source: US Census 2001 and World Bank Enterprise Surveys 2003-2015. Robust standard errors in parentheses, clustered at the country level. Table A4 shows the coefficients of regressions of industry firm-size ranking on informal tax payments, dis- cussed in section ??. Informal tax payments are measured as the answer to the question: "We’ve heard that establishments are sometimes required to make gifts or informal payments to public officials to ‘get things done’ with regards to customs, taxes, licenses, regulations, services,etc. On average, what percent of total annual sales do establishments like this one pay in informal payments or gifts to public officials for tihs purpose?". Panel A defines informal tax payment as a dummy equal to one if a firm reports paying any strictly positive amount of informal payments. Panel B uses the percentage of sales paid in informal payments. World Bank size rank is the ISIC 3-digit ranking of number of permanent employees per firm in the WBES country-year. US Census size rank is the ISIC 3-digit rank of number of employees per establish- ment in 2001, where we exclude establishments with less than 5 employees. Odd number columns include interactive fixed effects between country, year and three dummies indicating whether the ISIC3 industry was above median in the country-year distributions of age, export-share, and foreign-industry share. Even number columns include interactive fixed effects between country, year and 2-digit ISIC codes. For a given specification, the sample size in the even columns is smaller than in the odd columns. This is because the ISIC2 interactive fixed effect specification drops all cells where there does not exist more than one ISIC3- country-year observation within a ISIC2-country-year observation. The sample drop occurs in industries that are less specialized, which are more prevalent in less developed countries. In columns (5) & (6), we instrument for the World Bank size rank using the US Census size-rank. The F-statistic comes from the first stage rank-rank regression of World Bank size rank on US Census size rank. In columns (7) & (8), we add ISIC 3-digit fixed effects, so that the size-rank coefficients are estimated using variation within ISIC3 over time in its country-year industry rank. The ISIC3 fixed effect models result in a drop in sample size because some countries do not have repeated surveys. 60 TABLE A5: S IZE - GRADIENTS INTERACTION WITH STATUTORY TAX RATES (1) (2) (3) (4) Outcome: Tax Inspection {0,1} # Inspections Tax Compliance Informal Tax Industry Size Rank (US Census) 0.041 0.003 -0.003 -0.003 (0.024) (0.002) (0.053) (0.002) Industry Size Rank1(High Tax Rate) 0.061 0.003 0.129 -0.002 (0.030) (0.002) (0.062) (0.003) FE countryyearcontrols     F-test joint significance [Rank + Rank1(High Rate)] 32.66 57.08 4.43 14.93 P-value 0.0000 0.0000 0.0373 0.0002 R-squared 0.649 0.579 0.712 0.468 Observations 11,103 11,103 2,920 9,033 Number of clusters 127 127 125 74 Sources: World Bank Enterprise Surveys 2003-2015 and US firm Census 2001. Table A5 shows the coefficients of regressions of industry firm-size ranking, and its interaction with statu- tory tax rate, on tax inspection, formal compliance, and informal tax payments. US Census size rank is the ISIC 3-digit rank of number of employees per establishment in 2001, where we exclude establishments with less than 5 employees. All regressions include interactive fixed effects between country, year and 3 dummies indicating whether the ISIC3 industry was above median in the country-year distributions of age, export-share, and foreign-industry share. In addition, all regressions include an interaction between the Census size rank and a country-year varying dummy which takes a value of 1 if the WBES country-year statutory rate was above the median in the WBES sample distribution. The statutory rate is constructed as the sum of the corporate tax rate and the indirect tax rate. The F-test value and p-value report the results from an F-test on the joint significance of the industry size rank coefficient and the interaction coefficient between size rank and the high tax rate dummy. 61 TABLE A6: C ORRELATION OF SIZE WITH PERFORMANCE (1) (2) (3) (4) (5) (6) (7) Outcome: Log Sales Cost per Employee Labor regulations Intl. Certificate Part of Larger Firm Formal Training Finance Constraints Industry Size Rank (US Census) 0.011 0.011 0.002 0.003 0.001 0.001 -0.001 (0.001) (0.002) (0.000) (0.000) (0.000) (0.000) (0.000) FE countryyearcontrols        R-squared 0.892 0.896 0.516 0.456 0.580 0.624 0.213 Observations 9,415 9,175 8,160 9,544 9,553 9,691 9,705 Number of clusters 131 130 129 131 131 130 131 Sources: World Bank Enterprise Surveys 2003-2015 and US firm census 2001. Robust standard errors in parentheses, clustered at the country-year level. p<0.01, p<0.05, p<0.1 Table A6 shows the coefficients of regressions of industry size ranking on various outcomes. All regressions include interactive fixed effects between country, year and 3 dummies indicating whether the ISIC3 indus- try was above median in the country-year distributions of age, export-share, and foreign-industry share. Industry size rank is constructed similarly to the main tables: please see Table 1 for further details. In Col- umn 1, the outcome is the natural logarithm of annual firm sales. In Column 2, the outcome is the ratio of annual full-time permanent employee labor costs to the total number of full-time permanent employees. In Column 3, the outcome variable is the response to the answer "are labor regulations no/minor/major/very severe obstacle to the current operations of this establishment?" (higher value meaning more of an obsta- cle). In Column 4, the outcome variable is a dummy taking value one if the establishment reports having an internationally-recognized quality certification. In Column 5, the outcome variable is a dummy taking value one if the establishment is part of a larger firm. In Column 6, the outcome variable is a dummy taking value one if the establishment reports having formal training courses for its permanent employ- ees. In Column 7, the outcome variable is the response to the answer "is access to finance (availability and cost) no/minor/major/very severe obstacle to the current operations of this establishment?" (higher value meaning more of an obstacle). 62 TABLE A7: I MPACT OF F IRM S IZE ON F ORMAL AND T OTAL E FFECTIVE TAX R ATES OLS Reduced Form IV (1) (2) (3) (4) (5) (6) Panel A Outcome: Formal Effective Tax Rate = Tax Rate Share of Sales Reported Industry Size Rank (World Bank) 0.065 0.069 0.112 0.100 (0.015) (0.019) (0.035) (0.045) Industry Size Rank (US Census) 0.038 0.034 (0.015) (0.017) FE country year controls    FE country year ISIC2    F-Stat 33.99 38.73 R-squared 0.719 0.795 0.715 0.793 0.718 0.795 Observations 2,920 2,149 2,920 2,149 2,920 2,149 Number of clusters 74 74 74 74 74 74 Panel B Outcome: Total Effective Tax Rate = Sum of Formal and Informal Industry Size Rank (World Bank) 0.064 0.069 0.033 0.024 (0.023) (0.022) (0.059) (0.075) Industry Size Rank (US Census) 0.011 0.008 (0.021) (0.026) FE countryyearcontrols    FE countryyearISIC2    F-stat 33.38 38.73 R-squared 0.753 0.811 0.750 0.809 0.752 0.810 Observations 2,731 1,970 2,731 1,970 2,731 1,970 Number of clusters 74 74 74 74 74 74 Source: 2001 US Census and World Bank Enterprise Surveys 2003-2007 and tax rates collected by the au- thors based on the KPMG’s corporate and indirect tax rates tables. Robust standard errors in parentheses, clustered at the country level. Table A7 shows the coefficients of regressions of industry firm-size ranking on the formal effective tax rate (Panel A) and the total effective tax rate (Panel B), discussed in Section ??. In Panel A, the effective formal tax rate is calculated as the product of the (firm-specific) share of sales reported for tax purpose (outcome in Table 3) and the (country-yea specific) sum of the indirect and corporate tax rates. In Panel B, the total ef- fective tax rate is calculated, at the firm level, as the sum of formal tax payments and informal tax payments (outcome in Table A4) as a share of a firms’ sales. Odd number columns include interactive fixed effects between country, year and 3 dummies indicating whether the ISIC3 industry was above median in the country-year distributions of age, export-share, and foreign-industry share. Even number columns include interactive fixed effects between country, year and 2-digit ISIC codes. In this case, size-rank coefficients are estimated using variation between 3-digit ISIC codes, controlling non-parametrically for country-year- 2digit ISIC effects. For a given specification, the sample size in the even columns is smaller than in the odd columns. This is because the ISIC2 fixed effect specification drops all cells where there does not exist more than one ISIC3-country-year observation within a ISIC2-country-year observation. In columns (5) & (6), we instrument for the World Bank size rank using the US Census size-rank. The F-statistic comes from the first stage rank-rank regression of World Bank size rank on US Census size rank. The question on formal tax payments was only administered in the earlier waves of the WBES surveys which were not structured as panels. Hence, we can not estimate panel models for the formal and total effective tax rate. 63