metadata: authors: 0: author: Bachas,Pierre Jean
1: author: Fattal Jaef,Roberto N.
2: author: Jensen,Anders
count: World
docna: 0: docna: Size-dependent tax enforcement and
            compliance : global evidence and aggregate implications
docty: Policy Research Working Paper
subtopic: Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics,Public Sector Development,Tax Law,Law and Development,Tax Administration,Economic Adjustment and Lending,Macroeconomics and Economic Growth,Macro-Fiscal Policy,Taxation & Subsidies,Labor Markets,Common Carriers Industry,Pulp & Paper Industry,Business Cycles and Stabilization Policies,Food & Beverage Industry,Industry,Textiles, Apparel & Leather Industry,Construction Industry,General Manufacturing,Plastics & Rubber Industry,Private Sector Development,Business in Development
teratopic: Law and Development,Industry,Social Protections and Labor,Macroeconomics and Economic Growth,Private Sector Development,Public Sector Development
abstracts: cdata!: This paper studies the prevalence and
            consequences of size-dependent tax enforcement and
            compliance. The identification strategy uses the ranking of
            industries' average firm size in the United States as
            an instrument for the size ranking of the same industries in
            developing countries. Data on 125,000 firms in 140 countries
            show that tax enforcement and compliance increase with size.
            Size-dependence is more prevalent in low-income countries,
            and concentrated at the top of the size distribution. When
            quantified in a general equilibrium model, removing size
            dependent enforcement leads to gains in Total Factor
            Productivity of up to 0.8 percent.
repnme: repnme: Size-dependent tax enforcement and
            compliance : global evidence and aggregate implications
display_title: Size-dependent tax enforcement and
            compliance : global evidence and aggregate implications
listing_relative_url: /research/2018/03/29711220/size-dependent-tax-enforcement-compliance-global-evidence-aggregate-implications
topicv3: Business Entry and Startup and One Stop
            Shops m1326294 1278,Manufacturing Sectors m1326521 1281,Tax and Revenue Policy and Administration
            m1327008 720,Taxation m1327615 1121,Labor Demand m1583073 4422
publishtoextweb_dt: 2018-03-12T00:00:00Z
historic_topic: Law and Development,Industry,Social Protections and Labor,Macroeconomics and Economic Growth,Private Sector Development,Public Sector Development
no_of_pages: 66
author_keys: 0: author_key: 1245385
1: author_key: 1253388
2: author_key: 1008515
model_extractions: 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 size-dependent tax enforcement and compliance. The identification strategy uses the ranking of industries’ average firm size in the United States as an instrument for the size ranking of the same industries in developing countries. Data on 125,000 firms in 140 countries show that tax enforcement and compliance increase with size. Size-dependence is more prevalent in low-income countries, and concentrated at the top of the size distribution. When quantified in a general equilibrium model, removing size dependent enforcement leads to gains in Total Factor Productivity of up to 0.8 percent.

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<sup>_∗_</sup>

**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, anders_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, Munir 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 the most are smaller and the least are dependence: productive firms productive firms larger than the output-maximizing allocation. This property of misallocation can emerge through government policies that target firm size; for example size-dependent labor regulations, 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 employees, 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 impacts firms‘ effective tax rates. Second, many firms report facing large costs of dealing with the tax administration (World Bank 2017).<sup>1</sup> Third, reliance on size-dependent policies 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 enforcement units for large taxpayers. While large taxpayer units hint at stringent enforcement at the top of the firm-size distribution, countries have also adopted enforcement policies targeted at small and medium firms.<sup>2</sup> Therefore how tax inspection and compliance 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 compliance<sup>3</sup> 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 technological 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 optimal 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.<sup>4</sup> 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

> 1The World Bank 2017 Doing Business publication reports that " _on average taxpayers spend 25 hours complying with the requirements of an auditor, and go through several rounds of interactions during 10.6 weeks."_ 2Many countries implemented small and medium taxpayer offices alongside the large taxpayer office, which tailored audit algorithms to the evasion risks specific to smaller firms.

> 3The 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 compliance. Instead we only require that the answers accurately represent the industry’s average compliance.

> 4This 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.

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a WBES country from the size ranking in the US of the same ISIC3 industries.<sup>5</sup> The first stage relation, that is the conditional expectation of a WBES country’s industry 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 distribution has the same power to predict industry size ranking in Ethiopia, Indonesia or Brazil.<sup>6</sup> 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 under 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 following 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,<sup>7</sup> 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.<sup>8</sup> 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.<sup>9</sup> Finally we support the exclusion restriction by showing that the predicted WBES size-ranking is

> 5Since 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.

> 6This supports the following type of statement: “If the average car manufacturer requires more workers than the average retail firm in the US, then this ranking of industries by size also holds in Ethiopia, Indonesia, and Brazil.”

> 7We 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. 8The selection of firms with five or more employees also matches the sampling strategy of the WBES. 9We 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 sizerank 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 “Manufacture 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 inspection and compliance suggests that size-based tax inspection may explain part of the compliance 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 reliance on with decreasing size-dependent policies development 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 in4
centives to invest in innovation.<sup>10</sup> Our strategy to calibrate a productivity-dependent enforcement profile in the model is consistent with the identification strategy in the empirical 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’ implication 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 productivity of the firms. We then evaluate the TFP gains from reversing the size-dependence in taxation. Our baseline exercise the of at the level corre- fixes probability compliance 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.

> 10By 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 accumulation that may indeed constitute path-breaking innovations but could also refer to adoption of frontier technologies or implementation of better management practices.

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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 underlying policies generating the misallocation that magnifies the TFP losses associated with it. The pervasiveness of misallocation motivated the emergence of a number of studies 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 policy, 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 information (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 entire 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 inspection 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 average 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.<sup>11</sup> The random stratified sampling is done at the industrylevel, corresponding to the 2-digit ISIC level, and over-samples from large firms to capture 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 impact 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,<sup>12</sup> 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.<sup>13</sup> 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 We construct extensive and intensive margin measures of tax inspection within an

> 11Sometimes supplemented with the list of firms registered with the chamber of commerce. 12Sectors follow version 3.1 of the ISIC international industry classification.

> 13In 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].

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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 that the answer to the own assuming corresponds firm’s 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).<sup>14</sup> 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 represented and a median at 52. The average industry surveys 10 firms. Table 1 displays the

> 14We collected the statutory sales and corporate tax rates in the relevant year of the WBES country-year cell using the KPMG worldwide tax summaries.

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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 available for earlier surveys.<sup>15</sup> 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:

> 15The question on formal tax compliance was dropped from the harmonized survey after 2007. In surveys 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.

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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 consider 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 instrument for the average size of firms in the same industry in lower-income countries. The first stage is estimated with the following regression: Where Rank size _ict_ is the average firm-size rank of ISIC3 industry _i_ , in country _c_ , at time _t_ , and Rank size _i_ , _US_ ,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.<sup>16</sup> The slope-coefficient _α_ 1 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-

> 16This 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.

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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.<sup>17</sup> Second, the rank-rank specification appears more able to untangle technological size-differences from non-technological differences. Nondrivers such as technological 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 example, 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

> 17This 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 orthogonal 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 (Blumenthal 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.<sup>18</sup> Finally, in section 4.3 we show that for the richest countries in the WBES (countries with per capita GDP above $21,000)<sup>19</sup> the estimated coefficients of size on tax inspection is zero. This evidence supports the first stage identifying 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 for the exclusion restriction holds as as only indirectly (e.g. by proxying capital) long 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

> 18Amadeus data are collected from annual financial statements filed with the business registry and audited annual reports presented to shareholders. These firms are subject to a broader and deeper set of reporting requirements and hence in this sample tax inspection is unlikely to be driven by crude size-proxies.

> 19The $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 controlling 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: Where Tax outcome _ict_ 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 size _i_ , _US_ ,01 is the size-ranking of industry _i_ in the US, and _γct_ are country-year fixed effects. The coefficient _δ_ 1 identifies the reducedform size gradient.

The IV specification is: Where Rank size _ict_ of industry _i_ in country _c_ at time _t_ is instrumented with Rank size _i_ , _US_ ,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_ containing 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 outcome _ict_ = _β_ 0 + _β_ 1 _·_ Rank size _ict_ + (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 outcome _ict_ = _β_ 0 + _β_ 1 _·_ Rank size _ict_ + (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).<sup>20</sup> In the panel model, we add fixed-effects at the 3-digit ISIC level to the two previous models. Identification 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 outcome _ict_ = _β_ 0 + _β_ 1 _·_ Rank size _ict_ + (ISIC2) _ict ×_ (Year) _t ×_ (Country) _c_ + ISIC3 _i_ + _εict_ We report the coefficients _β_ 1 of size on tax outcomes from all three sets of specifications

> 20Note that in the panel regressions we do not use the instrumental variable strategy.

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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 _β_ 1 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. Figure 4 plots for each of the six largest countries in our sample,<sup>21</sup> 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 associated 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 gradients 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

> 21Bangladesh, Brazil, China, India, Indonesia and Mexico.

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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 specifications 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, repeats 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 the extent to which the size determines gauge gradient endogenously we the OLS to the IV columns 1 firm-size, compare coefficient (respectively, comparing 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, _NUS_ , 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 _N_<sup>�</sup> _US_ 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 compare 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 distribution. 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.<sup>22</sup> Figure 6 shows the reduced form and IV coefficients for the likelihood of tax inspection at each income level.<sup>23</sup> The magnitude of the tax inspection size-gradient is decreasing over levels of development, both in the reduced form and IV specifications.<sup>24</sup> While we cannot reject that lower-middle, middle and higher-middle income groups have different sizegradients,<sup>25</sup> 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.

> 22The 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.

> 23The first stage coefficients are constant across income levels and the 1st stage F-statistic is well above 10 at each income level.

> 24The 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.

> 25These levels of development include the countries often studied in the misallocation literature such as China, India and Mexico.

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# **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.<sup>26</sup> 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.

> 26The first stage is constant across development-levels for each census wave (Figures A1 & A2).

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# **Is worker-size proxying for capital intensity?**

A potential limitation to our identification strategy is that firm size, as measured by number 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.<sup>27</sup>

# **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.<sup>28</sup> The coefficients on tax compliance and informal payments have opposite signs, which suggests substitution between formal and informal taxation. Full substitution could mitigate 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-

> 27As 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.

> 28The negative slope shows that informal payments are regressive across firms. This finding complements Olken and Singhal [2011], who find that informal tax payments are regressive across households.

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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).<sup>29</sup> 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 sizedistribution 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

> 29We 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.

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affect aggregate productivity: resource misallocation among incumbents, entry and exit of firms, and incentives to invest in innovation.<sup>30</sup> The former connects our policy counterfactuals to the traditional literature on idiosyncratic distortions and resource misallocation (Hsieh and Klenow 2009, Restuccia and Rogerson 2008). Entry and exit, and endogenous firm growth represent potential propagating channels for which size-dependent enforcement affects the and hence should be taken into account for the macroeconomy quantification of its aggregate effects.

# **5.1 Technologies**

There is a competitive representative producer of a final good that is produced combining a continuum of differentiated varieties of intermediate inputs into a CES production function with elasticity _ρ_ where _q_ ( _ω_ ) is the quantity demanded of variety _ω_ , and _M_ ( _ω_ ) denotes the mass of producers of variety _ω_ . Profit maximization under perfect competition yields the familiar demand functions 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 Producers of intermediate varieties, in turn, operate under monopolistic competition

> 30By 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.

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and produce their variety according to the following technology: <u>1</u> The idiosyncratic productivity, denoted with ( _e_<sup>_ω_</sup> ) _ρ−_ 1 , evolves endogenously as a result of the firms’ investments in innovation subject to risky outcomes. More concretely, productivity follows a binomial process in which technology experiences upward or downward jumps of exogenously determined size ∆, according to a probability _q_ ( _ω_ ) which is under control of the in innovation.<sup>31</sup> consider a firm through expenses Formally, firm with current productivity _e_<sup>_ω_</sup> . In the next period, productivity transitions to In order to achieve a probability of upgrading equal to _q_ ( _ω_ ) , the firms must incur in a labor-denominated cost given by 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 _<u>τ</u>_<sup>_~~π~~_</sup> and a sales tax _<u>τ</u>_<sup>_~~s~~_</sup> . The key property of taxation systems in

> 31The 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.

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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 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 following<sup>32</sup> where we are _τ_<sup>_π_</sup> _ω_ and _τ_<sup>_s_</sup> _ω_ as the “effective” tax rates confronted the defining ( ) ( ) by firms which we formally define as follows 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

> 32Strictly speaking, there is a difference between the expected profits in 10 and the one in 11, which is equal to _ε_ ( _ω_ ) _<u>τ</u>_<sup>_~~π~~_</sup> _<u>τ</u>_<sup>_~~s~~_</sup> (1 _− ε_ ( _ω_ )). This difference, however, is quantitatively negligible.

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offer a calibration of such profile of idiosyncratic taxes based on our estimate of sizedependent tax compliance.

# **5.2 Static and Dynamic Choices**

We can now turn to describing the firms’ optimal decisions regarding labor demand, investments in innovation, entry, and exit. Firms choose the labor demand and the price for their varieties solving the following static profit maximization problem subject to the demand function for varieties given in 8 and subject to the production technology defined in 9. Solving it gives The expression shows that only the sales tax carry a distortionary effect on labor demand, which is independent from corporate profit taxation. Thus, size-dependent enforcement will have a detrimental effect on aggregate productivity through the misallocation 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 _e_<sup>_ω_</sup> where _π_<sup>_v_</sup> ( _ω_ ) = [1 _− τ_<sup>_s_</sup> ( _ω_ )] _p_<sup>_∗_</sup> ( _ω_ ) _y_<sup>_∗_</sup> ( _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 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 the of and exit. The latter follows in from the describing process entry part exogenous probability _δ_ which affects all firms uniformly,<sup>33</sup> 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 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-

> 33This exit 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.

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suming positive entry in equilibrium, the following free-entry condition must hold: where notice that, as is standard in the literature, we are assuming a one-period lag between 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 ∑<sup>_∞_</sup> _t_ =0<sup>_βt_[</sup><sup>_log_(</sup><sup>_Ct_)], where</sup> _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: where _Qt_ denotes inter-temporal prices, _M_ 0 is the initial endowment of wealth (claims to the profits and losses from the initial distribution of firms), and _Tt_ represents the lumpsum 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 wasteful consumption of goods from the government. Lastly, notice that the inter-temporal accumulation of wealth pins down the economy’s interest rate, given by _Rt_ =<sup>_<u>Q</u>_</sup> _Q_<sup>_<u>t</u>_</sup><sup><u>+</u></sup> _t_<sup><u>1</u>.</sup>

# **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: 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 productivity 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 downward to have less than or to _ω_ . There is also an of new productivity equal inflow 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_ ( _<u>ω</u>_ + ∆)] _Mt_ ( _<u>ω</u>_ + ∆).

A _stationary competitive equilibrium_ in this economy is given by: 1) consumption decisions 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_<sup>_d_</sup> ( _ω_ )� ; 4) a stationary distribution of firms _M_ ( _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 _<u>τ</u>_<sup>_~~π~~_</sup> and _<u>τ</u>_<sup>_~~s~~_</sup> , 8) a distribution of productivity at entry Γ( _ω_ ), and 9) an initial wealth of the household _M_ 0 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: 29
_C_ = _Y_ where _Lp_ , _t_ , _Lfc_ , _t_ , and _Lfp_ , _t_ are the aggregate demands for labor in production, labor in innovation, and fixed costs of operation; defined by:

#

A well known property of CES production functions is that aggregate output inherits the functional form from individual technologies, with the aggregate _TFP_ given by a geometric weighted average of individual productivity. In the context of the current model economy with distortions, we can write aggregate output as follows: where _M_<sup>�</sup> ( _ω_ ) is the probability distribution function associated with the distribution of _M_<sup>�</sup> _ω M_ <u>(</u> _ω_ <u>)</u> the mass of firms, ( ) = <u>�</u> _dM_ ( _ω_ )<sup>.</sup> Equation 15 reveals the channels through which size-dependent tax enforcement manifests in aggregate productivity. For a given number of firms and a given distribution of _M_<sup>�</sup> _ω_ firms across productivity levels ( ), size dependent taxes reduce aggregate productivity 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 technological upgrading. In this case, both the profit and the sales tax contribute to shaping the in innovation taxation affects _TFP_ response expenses. Lastly, size-dependent through _M_ . entry and exit, which manifest in the total number of varieties in the economy,

# **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 distribution 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 taxation. Our baseline exercise consists of the TFP accru- dependent computing gains<sup>34</sup> 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.

> 34Notice 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 _TFP_ .

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# **6.1 Calibration of Parameter Values**

Table 5 reproduces our calibration values for parameters that remain fixed across all experiments, 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 employment accounted for by the top 10% of firms in the U.S. manufacturing sector in 2007, and the ratio of of 21-25 relative to of 1 in the same employment firms aged firms age 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 distribution 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 distribution 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 to back-out a between the of tax en- equilibrium, gradient probability 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 distribution 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 masks non-linearities average size-gradient 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 regressions, we compute the probability of enforcement at a given decile of the size-distribution where _decile_ 1 is the smallest decile. This representation maps directly into the interpretation 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 distribution 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 sizein our Notice that in the where we gradient preferred specification). rightmost figure, 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 of The as stages development. income-specific gradients, well as the income-specific statutory corporate and sales tax rates that we feed into our 4. model are presented in table

# **6.3 Results**

Our baseline exercise for the quantification of the gains from reversing size-dependent taxation consists of the of taxation at a common value across fixing probability firms, while keeping the tax rates constant at their statutory levels. Since taxation is disruptive 34
in our model, even absent size-dependence,<sup>35</sup> 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 _TFP_ , 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

> 35An 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.

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about differences in the size distribution and the of across coun- life-cycle growth firms 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 compliance. 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 properties of these adjustments in the model are consistent with the data.

The increasing nature of the probability of tax enforcement is the key for understanding the decline in entry and the rise in average firm size that takes place when the sizedependence is reversed. To see this, consider first the allocation under size-dependent taxation assuming that innovation decisions do not change. Given the pattern of lifecycle 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 entrants 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 future 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 average 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 innovation 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 results. At first sight, keeping in mind the magnitude of the productivity gaps across countries, 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 policies 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 studies the and of tax enforcement paper prevalence consequences size-dependent and compliance in 140 countries. The identification strategy uses the relative ranking of industries’ in the US as an instrument for the relative of average industry-size ranking 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 concentrated 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 equilibrium 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 substitute 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 (Boning et al. 2018).

we that tax arise as an Finally, recognize size-dependent inspection may endogenously optimal policy under information and resource constraints (Kleven et al. 2016, Bigio and Zilberman 2011). Therefore while we quantify the TFP distortions generated by sizedependence, we do not measure the revenue gains from this policy, and do not make a normative statement. However, we hope that our description and quantification of distortions induced by size-dependence helps in understanding tax policy in low fiscal capacity countries, where both positive and normative issues remain active areas of research.

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