metadata: authors: 0: author: Zaourak,Gabriel Roberto
count: United States
docna: 0: docna: Lobbying for capital tax benefits and
            misallocation of resources during a credit crunch
docty: Policy Research Working Paper
subtopic: Taxation & Subsidies,Macro-Fiscal Policy,Public Finance Decentralization and
            Poverty Reduction,Public Sector Economics,Economic Adjustment and Lending,International Trade and Trade Rules,Renewable Energy,Rural and Renewable Energy,Textiles, Apparel & Leather Industry,Common Carriers Industry,Plastics & Rubber Industry,General Manufacturing,Business Cycles and Stabilization Policies,Construction Industry,Food & Beverage Industry,Pulp & Paper Industry
teratopic: Industry,Rural Development,International Economics and Trade,Energy,Macroeconomics and Economic Growth,Public Sector Development
abstracts: cdata!: Corporations often have strong
            incentives to exert influence on the tax code and obtain
            additional tax benefits through lobbying. For the U.S.
            financial crisis of 2007-09, this paper shows that lobbying
            activity intensified, driven by large firms in sectors that
            depend more on external finance. Using a heterogeneous agent
            model with financial frictions and endogenous lobbying, the
            paper studies the aggregate consequences of this rise in
            lobbying activity. When calibrated to U.S. micro data, the
            model generates an increase in lobbying that matches the
            magnitude and the cross-sector and within-sector variation
            observed in the data. The analysis finds that lobbying for
            capital tax benefits, together with financial frictions,
            accounts for 80 percent of the decline in output and almost
            all the drop in total factor productivity observed during
            the crisis for the non-financial corporate sector. Relative
            to an economy without lobbying, this mechanism increases the
            dispersion in the marginal product of capital and amplifies
            the credit shock, leading to a one-third larger decline in
            output. The paper also studies the long run effects of
            lobbying. Restricting lobbying implies welfare gains of 0.3
            percent after considering the transitional dynamics to the
            new steady state.
geo_reg_key: 119228,517191
repnme: repnme: Lobbying for capital tax benefits and
            misallocation of resources during a credit crunch
display_title: Lobbying for capital tax benefits
            and misallocation of resources during a credit crunch
listing_relative_url: /research/2018/04/29772972/lobbying-capital-tax-benefits-misallocation-resources-during-credit-crunch
topicv3: Renewable Energy m1326170 525,Tax Law m1326225 1893,Manufacturing Sectors m1326521 1281,Trade m1326924 698,Taxation m1327615 1121
publishtoextweb_dt: 2018-04-02T00:00:00Z
historic_topic: Industry,Rural Development,International Economics and Trade,Energy,Macroeconomics and Economic Growth,Public Sector Development
no_of_pages: 62
author_keys: 0: author_key: 1594959
model_extractions: WPS8394 Policy Research Working Paper 8394 Lobbying for Capital Tax Benefits and Misallocation of Resources during a Credit Crunch _Gabriel Zaourak_ Macroeconomics, Trade and Investment Global Practice April 2018
Policy Research Working Paper 8394

# **Abstract**

Corporations often have strong incentives to exert influence on the tax code and obtain additional tax benefits through lobbying. For the U.S. financial crisis of 2007–09, this paper shows that lobbying activity intensified, driven by large firms in sectors that depend more on external finance. Using a heterogeneous agent model with financial frictions and endogenous lobbying, the paper studies the aggregate consequences of this rise in lobbying activity. When calibrated to U.S. micro data, the model generates an increase in lobbying that matches the magnitude and the cross-sector and within-sector variation observed in the data. The analysis finds that lobbying for capital tax benefits, together with financial frictions, accounts for 80 percent of the decline in output and almost all the drop in total factor productivity observed during the crisis for the non-financial corporate sector. Relative to an economy without lobbying, this mechanism increases the dispersion in the marginal product of capital and amplifies the credit shock, leading to a one-third larger decline in output. The paper also studies the long run effects of lobbying. Restricting lobbying implies welfare gains of 0.3 percent after considering the transitional dynamics to the new steady state.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. 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 author may be contacted at gzaourak@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
# Lobbying for Capital Tax Benets and Misallocation of Resources during a Credit Crunch<sup>_∗_</sup>

Gabriel Zaourak<sup>_†_</sup> World Bank Please, click here for the latestversion

## JEL Classication: E44, E62; L25, O16.

Keywords: Financial Frictions, Misallocation, Lobbying, Credit Crunch.

> _∗_ Gabriel Zaourak is a Young Professional at the Macroeconomics, Trade and Investment Global Practice at the World Bank. I am extremely grateful to Francisco Buera, Ariel Burstein and Lee Ohanian for their comments and guidance. I am thankful to Andrew Atkeson, Devin Bunten, Sam Choi, Pablo Fajgelbaum, Roger Farmer, Fernando Giuliano, Federico Grinberg, Andreas Gulyas, Gary Hansen, Ioannis Kospentaris, Dennis Kuo, Musa Orak, and Liyan Shi for insightful discussions, and participants at the Macro Proseminar and Macro student seminar at UCLA. Last, I want to thank the Center for Responsive Politics (CRP) for providing the lobbying data. The views expressed herein are only my own and should not be attributed to the World Bank, its executive directors, or the countries they represent.

> _†_ Email: gzaourak@worldbank.org
# 1 Introduction

Understanding the factors that contribute to large declines in total factor productivity (TFP) during nancial crises is key for designing policies that lead to robust recoveries. A growing consensus among economists views resource allocation among rms as an important driver of TFP over time (Obereld (2013) and Gopinath et al. (2015)). During periods of nancial distress, nancial frictions can prevent productive rms from operating at the optimal scale leading to misallocation and lower TFP (Khan and Thomas (2013)). In this paper, I show that nancial frictions aect lobbying decisions that aim to extract tax benets, and that this channel is relevant to explaining the changes in TFP observed during nancial crises. I focus on tax benets associated to capital, since those are the most important ones in the tax code.<sup>1</sup> I make three contributions. First, I document the increase in lobbying activity intended to aect the tax code that occurred during the U.S. nancial crisis in 2007-2009.<sup>2</sup> Second, I contribute to the literature that studies the eects of nancial frictions on resource allocation and productivity uctuations over business cycles by quantifying a new channel lobbying that interacts with nancial frictions and changes the eects of that source of misallocation. Third, I conduct counterfactual experiments to study the long run implications of lobbying and scal reforms.

The main nding of the paper is that lobbying for capital tax benets amplies the misallocation that arises due to nancial frictions during a credit crunch. The interaction between lobbying and nancial frictions generates two opposing eects, one that increases misallocation and one that alleviates the distortions. In the calibrated economy, the rst eect dominates. Compared to an economy without lobbying, I nd that the lobbying economy amplies the distortions arising from nancial frictions, leading to a one-third larger decline in output.

Using data from Compustat that I match with rm-level lobbying expenditures from the Center for Responsive Politics (CRP), I document three novel facts on lobbying during a nancial crisis. First, aggregate lobbying expenditure increased during the crisis. Between 2007 and 2009, the deviation from a linear trend in aggregate lobbying expenditure increased by 15 percentage points. This captures changes in both the extensive (number of rms) and intensive (average expenditure) margins. Second, sectors that depend more on external nance (Rajan and Zingales (1998)), and therefore are more likely to be aected by the shock, drove the increase in lobbying activity. I show that the share of these sectors in total lobbying expenditure increased from 53% in 2007 to 63% by 2010. Third, I use a triple dierence approach that exploits variations in time (before and

> 1The U.S. government provides dierent types of tax breaks to corporations allowing them to reduce their tax burden. The literature has found that the tax code can be inuenced through lobbying. Since lobbying entails substantial xed costs, then large and capital intensive rms can target those benets to themselves. Special tax provisions for individual rms have been documented by Siegfried (1974), Barlett and Steele (1988) and McIntyre and Nguyen (2004). See Richter et al. (2009) and Arayavenchkit et al. (2014) for a discussion of dierent tax benets associated with capital and the endogeneity of the tax code.

> 2Throughout, I will refer to lobbying to aect the tax code and lobbying for capital tax benets simply as lobbying. In the lobbying data there are 77 issues that rms can choose to lobby for. The one that rms use to try to inuence the tax code is Taxation. This is the most important issue in terms of expenditure, and it is the one used in the empirical analysis.

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after the shock), rm size (small and large), and external nancial dependence (low and high) to show that large rms increased lobbying expenditure relative to small rms, and that this dierence is disproportionately larger in sectors that rely more on external nance. In addition, small rms reduced lobbying, and this reduction was larger in sectors that depend more on external nance. This nding suggests that the crisis aected the incentives of small rms and large rms dierently, negatively aecting smaller rms, and favoring larger rms. Since rms in sectors that rely more on external nance are empirically more capital intensive, this has implications for the allocation of the tax benets associated with capital.

Motivated by this evidenceand the corresponding increase in resources devoted to the corporate sector by the U.S. government during the crisisI ask whether lobbying reinforces or alleviates the misallocation created by nancial frictions when the economy suers a credit crunch.<sup>3</sup> To address this question, I introduce lobbying into a standard general equilibrium model in which nancial shocks aect the allocation of capital among producers. Lobbying varies across rms according to their nancial position and their productivity. Because the credit shock aects the ow of funds among rms, it also has an eect on the decision to lobby. I use the model to quantify the contribution of the lobbying channel to the behavior of TFP and the macroeconomy after a nancial disruption.<sup>4</sup> The main analysis focuses on the model's ability to match the data on TFP and output for the non-nancial corporate sector. I feed a credit shock into the model to produce the observed decline in the ratio of external nance to capital for the non-nancial corporate sector between the end of 2007 and 2010. The calibrated model captures 80% of the decline in output and almost all of the decline in TFP observed in the data by the end of 2009. The model also captures the change in aggregate lobbying expenditure observed during the crisis both at the intensive and extensive margins, and partially captures the increase in the participation of the sectors that rely more on external nance in total lobbying expenditure. Regarding within sectors variation, the model delivers similar patterns as in the econometric framework.

The model I use for the analysis is a continuous time version of the two-sector economy in Buera et al. (2011). I augment this framework by introducing a government that grants tax benets associated to capital that can be partly inuenced by endogenous lobbying.<sup>5</sup> Agents are heterogeneous with respect to their productivity and wealth. Productivity is subject to idiosyncratic stochastic shocks, while wealth is determined by saving decisions. Producers face a collateral constraint on the amount of capital they can rent, preventing them from borrowing more than a fraction of their

> 3Here I list some important examples regarding the increase in resources to corporations. Bill H.R. 6049 approved by the House includes extensions of several temporary tax benets (commonly referred as extenders) as well as new tax cuts to corporations. The renewable energy tax incentives in this bill cost a total of $17 billion and the largest is the 3-year extension of the section 45 tax credit for the production of energy from renewable resources. As another example, bill H.R. 4853 extended many of the provisions to corporations that are known as Bush tax cuts, and created new ones. For more examples, see the Tax Relief Act of 2008, among others.

> 4The adjustments of the economy to nancial shocks have been studied by Khan and Thomas (2013), Buera et al. (2015), and Shourideh and Zetlin Jones (2016), among others.

> 5Consider the solar energy-specic tax break, the fossil and renewable energy tax break or the research and experimentation tax break. All of these benets are associated with capital, and as a result are exploited by capital intensive rms.

3
wealth. Production in each sector is subject to decreasing returns to scale and a per-period sectorspecic xed cost, which generates the dierences in nancing needs across sectors to map the model and the data. A nancial crisis in this framework is modeled as an exogenous, unforeseen tightening of the collateral constraint that slowly reverts over time.

Firms choose lobbying subject to variable and a xed cost that is calibrated to match the fact that only a fraction of rms engage in lobbying. The tax benet schedule per unit of capital consists of two components. The rst component is exogenous and common to all rms, while the second is endogenous and increasing in lobbying eort. This implies that the tax benets that rms receive are heterogeneous and depend on two factors: (i) rms that use more capital receive more tax benets; (ii) conditional on capital, rms that pay the xed cost receive tax benets according to their lobbying eort. An implication of the tax benet schedule is that lobbying aects the unconstrained optimal size of rms by changing the choice of capital. Since lobbying generates additional tax benets per unit of capital, then unconstrained lobbying rms have incentives to increase the demand for this factor. As a result, there is a complementarity between lobbying and capital that increases the optimal rm size.

The tightening of the collateral constraint increases misallocation and unambiguously lowers TFP. Firms with low net worth and positive productivity shocks become constrained and have to downsize, reducing the demand for capital. In general equilibrium, the interest rate falls, and unproductive rms with high net worth expand. Capital reallocates from productive and constrained rms to unproductive and unconstrained rms.

The interaction between lobbying and nancial frictions during a crisis introduces two opposing eects. On one hand, lobbying increases the misallocation of capital and lowers TFP. Since lobbying and capital are complementary, the increase in capital by unconstrained rms is accompanied by an increase in lobbying that reinforces the incentive to use more capital, amplifying the misallocation. On the other hand, there is a positive eect of lobbying: it provides additional cash ows that can be used to increase savings for rms that are nancially constrained and choose to lobby. By being able to lobby, these rms can alleviate part of the misallocation caused by the nancial shock by saving part of those resources to overcome the nancing constraint.

In order to understand which of these forces dominates, I study the eect of the increase in distortions coming only from nancial frictions. To that end, I analyze the response of a re-calibrated economy without lobbying when it is exposed to the same credit shock.<sup>6</sup> This exercise shows that lobbying amplies the distortions arising from nancial frictions, leading to one-third larger decline in output. Comparing impulse responses across models, the dispersion of the marginal product of capitala measure of misallocation increases to 12.6% with lobbying and to 10% without lobbying, all relative to the initial steady state. In addition, the quantitative results show that most of the increase in misallocation as a result of lobbying comes from adjustments at the intensive margin.

The model is also useful for understanding the long run implications of policies that change the

> 6The credit shock is re-calibrated in this model in order to match the observed decline in the ratio of external nance to capital for the non-nancial corporate sector.

4
structure of the economy. In the rst experiment, I study the eects of banning lobbying. Since the tax benet acts as a subsidy on capital and lobbying changes how much these rms can claim, eliminating this component reduces the incentives to save. Compared to the pre-crisis economy, the new steady state output and capital decrease 1.2% and 4%, and TFP increases by 0.8%.<sup>7</sup> What are the welfare implications of this policy? Restricting lobbying implies welfare gains of 0.3% after accounting for the full transition between steady states. Finally, I also consider the implications of a scal reform. The experiment implies a removal of all capital tax breaks while at the same time keeping the revenue neutral by reducing the corporate tax rate.

The rest of the paper is structured as follows. Section (2) discusses the related literature. Section (3) presents the empirical evidence on corporate lobbying for taxation during U.S. the great recession. Section (4) lays out the model with nancial frictions on the producer side and endogenous lobbying to obtain capital tax breaks. Section (5) presents the calibration strategy, both for the steady state and for the shock. Section (6) has three parts. First, I study the main quantitative exercises. Then I test the ability of the model to generate the empirical facts shown in section (3). Lastly, I discuss the long run implications of lobbying and some policy reforms, with special attention to the eects on TFP and on welfare. Section (7) concludes with some nal remarks and policy implications.

# 2 Literature Review

This paper ts into a large body of papers that studies the role of nancial market imperfections explaining business cycle uctuations, following Bernanke and Gertler (1989), Kiyotaki et al. (1997), Jermann and Quadrini (2012) and Brunnermeier and Sannikov (2014). I share with papers like Khan and Thomas (2013), Buera et al. (2015) and Shourideh and Zetlin Jones (2016) the focus on the eects of nancial frictions on the allocation of capital at the rm level, especially during a credit crunch. I dierentiate my paper by introducing a rm level endogenous mechanism (lobbying) that interacts with the nancial frictions, especially during a nancial crisis. In addition, the model generates new testable implications at the rm level during those episodes, which closely match the patterns seen in the data.

The paper is also related to the important literature that stresses the role of misallocation of resources. Restuccia and Rogerson (2008) and Hsieh and Klenow (2009) focused on abstract distortions that aect the allocation of capital and labor across rms to explain the variability in the returns to those factors across countries. They show that the dispersion of marginal products caused by those micro-level distortions are the main drivers of the cross-country dierences in TFP observed between the U.S. and developing countries. A derived implication of these studies is that an increase in a factor's return could be the result of increasing levels of distortions that aect the ecient allocation of resources, which negatively aect TFP. Continuing this line of research, a growing and active literature started to use quantitative general equilibrium models to quantify the

> 7The capital stock includes the capital used for production plus the xed costs in this economy.

5
amount of misallocation particular frictions can produce and their eects on long run output.<sup>8</sup> As in Obereld (2013) and Sandleris and Wright (2014), this paper focuses on the dynamics of misallocation over time. Following an approach similar to Hsieh and Klenow (2009), they show that the misallocation of resources across rms accounts for a large portion of TFP losses during a nancial crisis. Kehrig (2015) documents that the dispersion in revenue productivity in U.S. manufacturing increases during recessions, and especially during the last nancial crisis.<sup>9</sup> I relate to this line of research by studying two mechanisms contributing to the increase in the dispersion of the marginal product of capital and revenue productivity: nancial frictions and lobbying for capital tax breaks.

A closely related paper is Arayavenchkit et al. (2014). They show that lobbying for capital tax benets is another mechanism that generates dispersion in the allocation of capital using a partial equilibrium model with complete markets. This paper integrates nancial market imperfections with lobbying in order to understand whether lobbying amplies or mitigates the misallocation coming from the credit market imperfection, both in the long-run and during a credit crunch.

The paper is also related to the empirical literature that looks at the cross-section implications of lobbying. This paper conrms most of the cross-section facts and extends our understanding by providing new evidence on lobbying for taxation along the business cycle.<sup>10</sup> Finally, the paper relates to the theoretical literature on rent-seeking. My contribution is twofold. First, I provide a quantitative model of one type of rent-seeking stressed in that literature (Murphy et al. (1993)), and I evaluate the long run implications. Second, after calibrating the model I quantify the welfare cost of this rent-seeking activity. To my knowledge, this is the rst attempt.

# 3 Empirical Motivation

This section provides evidence on rm level lobbying activity for taxation issues during a nancial crisis. I document four related facts based on the case event provided by the U.S. credit crunch in 2007-2009. In addition to contributing to the understanding of political participation during credit crunches, these facts also provide a guidance to construct the model in section (4).

First, during the crisis, lobbying activity increased substantially along both intensive and extensive margins. Second, eective tax rates (ETR) for both lobbying and non-lobbying rms declined signicantly. Consistent with the fact that lobbying rms have lower ETR, the decline after the crisis was more drastic for lobbying rms. Third, the increase in lobbying activity for taxation was driven mostly by industries that depend more heavily on external nance (Rajan and Zingales, 1998).<sup>11</sup> In

> 8Hopenhayn and Rogerson (1993) study the eects on misallocation of having ring costs. Peters (2012) studies the implications of variable markups for misallocation and for rm level innovation. An important amount of attention has been devoted to nancial frictions, which aect the allocation of capital. Prominent examples are Jeong and Townsend (2007), Amaral and Quintin (2010), Buera et al. (2011), Midrigan and Xu (2014) and Moll (2014).

> 9Complementary to this nding, Chen and Song (2013) nd that the dispersion in the marginal product of capital for Compustat rms is also countercyclical. Since revenue productivity is a weighted average of the marginal product of capital and the marginal product of labor, these ndings are mutually consistent.

> 10See Richter et al. (2009), Kerr et al. (2014), Igan et al. (2011), Arayavenchkit et al. (2014), and references therein.

> 11According to these authors, these sectors are larger in scale and more capital intensive. As discussed in the

6
particular, I show that these industries account for more than 50% of total lobbying expenditure, and that this participation increases during the credit crunch. Finally, I provide evidence of heterogeneity in lobbying behavior within sectors of external nance as large rms increased their lobbying expenditure relative to small rms during the crisis. Furthermore, this relative dierence was once again stronger in sectors that depend more on external nance. In fact, small rms in externally nanced sectors reduce their lobbying expenditure for taxation issues which is consistent with the idea that small rms should be more aected with the credit shock.

# 3.1 Data and Summary Statistics

In order to follow rms over time for the empirical part of the paper, I name-match lobbying expenditure data with rm level characteristics. In this section, I describe the main features of each dataset and the matching procedure.

Firm level lobbying data is based on more that 1,100,000 lobbying reports that became available under the lobbying Disclosure Act of 1995.<sup>12</sup> This act, together with the Honest Leadership and Open Government Act (2007) established a set of provisions to be followed by anyone lobbying the federal government at congress.<sup>13</sup> Firms, organizations, or individuals that want to lobby have to le a semi-annual report to the Secretary of the Senate's Oce of Public records (SOPR) including the following information: (i) the name of the client, address and general business description; (ii) the total amount of income or expenditure in the lobbying activity, depending whether it is an inhouse or an external lobbyist; (iii) all of the general issues for which they are lobbying. Firms that are trying to inuence the government to modify the tax code and obtain tax benets targeted to themselves have to declare that they are doing lobbying for taxation, allowing me to focus only on those rms.<sup>14</sup> Finally, since any non-prot organization, individual, or rm can engage in lobbying activity, I clean the original dataset to keep only those observations that correspond to rms. To do this, I scrape the data with text-parsing methods to look for keywords that allow me to eliminate entries that do not correspond to rms. After that, I manually check the remaining observations to eliminate non-prots or individuals.<sup>15</sup> The nal dataset contains information from 2000 to 2014.

introduction, a rm's capital level is important because most of the tax benets granted by the government are tied to capital.

> 12The information is provided by the Center of Responsive Politics (CRP), which collected the data from the Senate Oce of Public Records. Data is available upon request at www.opensecrets.org/lobby/.

> 13A lobbyist is any individual who is employed or under a contract to lobby on behalf of a client. An In-House Lobbyist is an employee hired by an organization to lobby for them. An External Lobbyist is typically an organization or person that works under a contract for the lobbying organization. Organizations could be one of 3 types: non-prot associations, rms, or groups of individuals.

> The Lobbying Disclosure Act denes "lobbying activity" as lobbying contacts and eorts in support of such contacts, including preparation and planning activities, research and other background work that is intended, at the time it is performed, for use in contacts, and coordination with the lobbying activities of others.

> 14There are 77 issues such as trade, taxes, agriculture, etc. A list of all the issues can be found here: https://www.opensecrets.org/lobby/alphalist_issue.php. In online appendix C I include an example of a form led by a lobbying rm.

> 15See the online data appendix for a description of the procedure, including the keywords used to eliminate observations.

7
However, for most of the analysis I restrict my attention to the period 2004-2014.

Financial data by parent rm is primarily taken from Compustat North America. This dataset contains information on publicly traded companies in the United States, including sales, employment, industry classication, assets, and useful information to compute eective tax rates, which I describe below. The balance sheet presentation in Compustat is consolidated at the parent level. This is a problem, because a single organization could have more than one entry. To deal with this issue, I aggregate the information at the ultimate owner level using parent-subsidiary identiers from the NBER patent data project to assign each entry from Compustat to one unique parent. In addition, I also use the dataset ORBIS compiled by the by Bureau van Dijk Electronic Publishing (BvD) to check Parent-subsidiary relationships. After obtaining these relationships, I name-match the lobbying data with Compustat using open rene, which provides a reconciliation service that uses a probabilistic matching algorithm to pair entries between the two datasets.<sup>16</sup> Data on external nancial dependence of 63 2-digit SIC sectors is computed with data from Compustat. To construct this measure (proposed by Rajan and Zingales (1998)), I follow the methodology described in Cetorelli and Strahan (2006). External nancial dependence is dened as the fraction of capital expenditure that is not nanced with internal cash ows from operations . A positive value implies that a rm must use external sources of funds to nance investment, while a negative value indicates that rms have enough cash ows to fund investments. Appendix C.4 contains the method used to construct the index and the measure of external nancial dependence for each sector.

According to Rajan and Zingales (1998), the external nance measure varies across industries due to technological factors aecting initial project scale, gestation period, the cash harvest period, and the requirement for continuing investment. Consequently, these technological factors determine the demand for external nancing and as a result, industries like metal mining or oil and gas extraction heavily dependent on external annce should be more aected by a credit shock than industries like leather. For the remainder of the paper, I exclude the nancial sector and the agricultural sector.

Later in the paper, I will classify rms into two broad sectors: those producing in sectors that rely more on external nance and those producing in sectors that depend less on external nance. The former includes all the 2-digits SIC sectors with a measure of external nancing need below 0. The rest of the sectors will be categorized as sectors that rely more on external nance.

Lastly, to compute eective tax rates I also use data from Compustat. To compute this measure, I use the denition provided by Gupta and Newberry (1997) and used in Richter et al. (2009) and Arayavenchkit et al. (2014). The eective tax rate for each rm is computed as The numerator is a measure of how much a rm paid in taxes, while the denominator computes the taxable income coming from balance sheet data. In general, the eective tax rate will be below 16 Open rene is available at www.openrene.org. See online appendix C.2 for additional details of the procedure.

8
the statutory corporate tax rate of 35 % .<sup>17</sup> In the next section, I discuss this feature in detail.

# 3.1.1 Cross-Section Facts and Summary Statistics

In this subsection I briey describe the data and I provide some summary statistics. The raw data after matching Compustat and the CRP data for corporations gives a total number of 46,831 rmyear observations. Between 2004 and 2014, 1,544 rms lobbied for some of the 77 issues in at least one year. From those observations, there are 567 rms that lobbied for taxation issues at least one time between 2007 and 2014. The low participation of public rms in lobbying activity has been previously documented by Richter et al. (2009) and others. For this sample, the average fraction of lobbying rms is 8.9 % . As shown in table (1) lobbying for taxation is the most important issue in terms of expenditure between 2004-2014. In fact, it is the top lobbying issue in each individual year of this sample. This ranking by issues is consistent with evidence provided by Kerr et al. (2014) and Arayavenchkit et al. (2014) for dierent periods of time, which shows that taxation is the most relevant issue for lobbying.

Table (2) shows summary statistics for rms lobbying for taxation issues in at least one year in the sample and for rms that did not lobby for taxation issues at all. The table also displays the well documented feature that lobbying rms are larger than non-lobbying rms. For example, the data shows that sales are almost 6 times larger for lobbying rms. This is also true for capital (12 times), assets (1.8 times) and employment (7 times). Another fact consistent with previous work is that lobbying expenditures are relatively small. For the sample, the average lobbying expenditure in the sample is close to $0.27 million with a standard deviation of 0.7 million. Considering that the returns for lobbying are thought to be quite large, the fact that lobbying rms are so few and that they spend so little money remains a puzzle for political scientists.

Table (2) also shows one of the key ndings in this literature: lobbying rms pay lower eective tax rates. The tax code in the U.S. allows corporations to claim tax benets, reducing their tax burden. According to the Government Accountability Oce (GAO), in 2011 a third of the corporate tax revenue was lost in tax benets rebated to corporations. In fact, special tax provisions for individual rms have been documented by Siegfried (1974), Barlett and Steele (1988) and McIntyre and Nguyen (2004). Consistent with this anecdotal evidence, Richter et al. (2009) and Arayavenchkit et al. (2014) have shown that rms that lobby for taxation issues pay lower eective taxes as a result of tax benets targeted to them. The mechanisms through which rms obtain favorable tax benets are the existence of narrow research and development credits, tax depreciation schedules tailored to specic types of capital and thorough numerous industry-specic tax breaks related to capital.<sup>18</sup> Based on this discussion, I compute the eective tax rates for lobbying and non-lobbying rms for the sample. The average eective tax rate for lobbying rms is 18.8 % , while the average eective

> 17Appendix C contains information related to the computation of this variable and details about other measures from compustat.

> 18The fairness and implications of a system that grants tax benets to corporations is a theme of continuous debate in the media and the political arena. See for example CNN Tax breaks. The concern for the existence of lobbying corporations has also been remarked by the president of the United States in the State of the Union speech in 2011.

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tax rate for non-lobbying rms is equal to 21.4 % _._

# 3.2 Evolution of Lobbying Expenditure and Tax Rates

Now I turn my attention to aggregate patterns in the data for lobbying for taxation, focusing on the 2007-2009 credit crunch. I document that during the last U.S. credit crunch there was an unusual increase in lobbying activity for taxation, which holds at both extensive and intensive margins.<sup>19</sup> Figure (1) shows the evolution of aggregate lobbying expenditure for taxation between 2001 and 2014 as percentage deviation from linear trend.<sup>20</sup> By 2009 lobbying expenditure deviates 15% from trend suggesting an exacerbation of rent-seeking activity during this time. As mentioned before, this rise is due to the increase in the number of lobbying rms and the increase in the average expenditure that each rm is doing for that purpose. Between 2004 and 2007, on average 7.1 % of rms in Compustat lobby for taxation, while for the period 2008-2011 the average fraction of rms was 10.35 % , indicating an increase in lobbying activity on the extensive margin. The intensive margin follows a similar pattern. For the period 2004-2007, the average lobbying expenditure was $0.26 million, but for the period 2008-2011 it increased to $0.31 million. If we look at deviations from trend, we see a similar pattern. Figure (2) displays the evolution of the intensity of lobbying relative to the linear trend, and as expected there is an important increase in the values observed during the period of the study. This data raises a natural question: why do we observe such an increase in lobbying activity to inuence the tax code?

One possible reason could come from the increase in rents that corporations can extract. Evidence provided by the Government Accountability Oce (GAO,2013) shows that between 2007 and 2010 the amount of tax benets that the government granted to corporations increased from 0.6 % of the GDP to 1.2 % . Even though we cannot argue that the government increased those resources due to the corporate pressure, we can certainly think that the allocation of some of those funds among rms was inuenced by corporate lobbying.

If lobbying aects the tax code and benets certain rms and sectors, we should observe that lobbying rms reduce their eective tax rate as a result of the increase in lobbying activity during the crisis. In order to show this feature in the data, I compute the average eective tax rate for lobbying and non-lobbying rms in my sample. The results between 2007 and 2014 are displayed in Figure (3). The gure shows that both groups of rms saw declines in tax rates. However, those that engaged in lobbying obtained a bigger decline, consistent with the increase in lobbying activity.

To test whether the tax rates of lobbying and non-lobbying rms diverged during the crisis, I run the projection of rm level eective tax rates on time dummies _βt_ , the interaction of those dummies with an indicator for lobbying for rm _i_ in period _t_ , and industry xed eects _inds_ ,

> 19Unless otherwise noted, I will refer to lobbying for taxation as simply lobbying.

> 20Lobbying variables are deated by the CPI with 2007 as base year. I use a linear trend since there is not enough data available to apply a Hodrick-Prescott lter. In the Online Appendix 4.1, I provide a similar gure with a quadratic detrending.

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The coecient for the interaction term of this regression with the condence bands are plotted in gure (4). The gure shows the evolution of the dierence between the eective tax rate for non-lobbying rms and lobbying rms. As with gure (3), we see that there is an increase in the dierence between the tax rate paid by lobbying rms and the non-lobbying rms during the crisis. This indicates that, in a statistical sense, lobbying rms had a decline in eective tax rates relative to non-lobbying rms.

# 3.3 Sectoral variation

In this section, I provide evidence that the increase in lobbying activity was mostly driven by a particular group of rms. In principal, it is not clear which type of rms should increase their lobbying activity during nancial crises. Previous work by Rajan and Zingales (1998) has shown that there are sectors that are more sensitive to variations in the supply of credit due to the reliance on external nance. It is natural to think that these sectors (and rms) would be more aected during a credit crunch and therefore would try to disproportionately inuence the government to obtain tax benets. To study this hypothesis I look at the lobbying expenditure of all rms in sectors that depend more on external nance as a share of total lobbying expenditure, focusing on taxation. I nd that those rms tend to lobby more, both in the cross section and over time. Additionally, these rms increased their lobbying activity the most during the recent crisis. Figure (5) illustrates these two facts. The participation in total lobbying expenditure for taxation of the industries that rely more on external nance went from 53 % at the bottom of 2007 to 63% at the peak of the time period, and coinciding with the crisis. Consistent with the fact that lobbying reduces the tax obligation, gure (6) shows the eective tax rates as a function of the Rajan and Zingales measure of nancial dependence. The gure reveals that sectors that are more capital intensive and exert more lobbying tend to have a lower tax rate.

The evidence provided in these graphs, in principle, supports the original hypothesis: sectors and rms that are in more trouble tend to lobby more the government to try to obtain preferential tax treatment. However, it is not clear ex ante whether large or small rms were responsible for the increase in lobbying during the crisis. On one hand, small rms are more likely to be aected by monetary or nancial shocks, especially in those sectors that depend more on external nance.<sup>21</sup> Following this argument, we should observe that these rms increased lobbying activity. On the other hand, large rms may have the necessary political connections or resources to spare during a crisis (Faccio (2006) and Faccio et al. (2006)). In the next section, I study this issue more closely.

> 21Gertler and Gilchrist (1994) nd that the growth in sales, inventories, and bank debt of small manufacturing rms are more aected by monetary shocks. Sharpe (1994) found that small rms have a disproportional response, relative to large rms, to nancial shocks. Using CPS data Duygan-Bump et al. (2015) nd that the 2007-2009 credit shock increased the probability of going to the unemployment pool for workers in small rms in sectors that depend more on external nance.

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# 3.4 Within Sector Variation

In the previous section, I established that the increase in lobbying activity observed during the 2007-2009 nancial crisis was driven by rms in sectors that depend more on external nance. These sectors are therefore more likely to obtain tax benets targeted to them.

In order to understand which rms are behind the increase in lobbying activity, I use a triple dierence approach to show the dierential eect of the credit shock across sectors with dierent degrees of external dependence, accounting for dierences in size. The econometric specication is the following: where _lobbysit_ is the log of lobbying for taxation of a rm _i_ in sector _s_ at period _t_ (lobbying intensity).

The variable denoted by _ωst_ is a set of industry-state xed eects that controls for industry-state time invariant observable and unobservable factors aecting the lobbying decision of rms. On the other hand, _Xsit_ is a vector of rm level characteristics measured in _t −_ 1 . This vector includes assets, sales, and capital.

In the proposed regression, the three key variables are _Tt, SMEt−_ 1 and _Fdepsi_ . Following the recommendation of the Trade Commission, I assign the label _SME_ to those rms with fewer than 500 employees. According to this denition, I construct the dummy variable _SMEit−_ 1 that takes a value of 1 if the rm in the previous period was considered a small-medium rm. This variable captures the fact that lobbying intensity is dierent in the cross section depending on size. The variable _Tt_ is an indicator that takes a value of 1 in the years 2008-2010 and 0 between 2005-2007. This allows me to focus on a 3 year window around the crisis. Finally, _Fdepsi_ is an indicator variable that takes a value of 1 for rms in sectors that depend more on external nance and 0 otherwise. This variable allows me to account for the dierences in lobbying observed across sectors based on nancial needs.

To study the eect of the nancial crisis on the incentives of corporations to lobby , I also include all the interaction terms between the main three variables. The coecient _δ_ 6 captures the eect of the crisis on lobbying for small rms relative to large rms in industries with low external nancial dependence (this is the dierence-in-dierence coecient). On the other hand, the coecient _δ_ 7 measures how much small rms relative to large rms are aected in sectors that depend more on external nance on top of the eect found in sectors with low external nancial dependence. This estimate uses variations in three margins: time (before and after the crisis), rm size (small vs large), and external nancial dependence (low and high).

I estimate equation (1) using an ordinary least squares regression on a balanced panel of 3,402 parent companies and 20,412 rm-year observations. To evaluate the signicance of the coecient, 12
I cluster the standard errors by state and industry to allow for correlations among rms in the same industry and state. The results of the estimation of equation (1) are displayed in table (3). To simplify the exposition, I show the results based on size and nancial dependence along the columns. An important rst observation is that large rms in both sectors increased lobbying activity during the crisis, and large rms in sectors with high external dependence had a higher increase. In addition, small rms in industries with high external dependence reduce the amount of lobbying relative to pre-crisis. It follows that the dierence between large and small rms in both sectors increased with the crisis, indicating that the observed rise in aggregate lobbying is driven by large rms.<sup>22</sup> The second observation to notice is that this increase in lobbying intensity by large rms relative to small rms is larger in sectors with high external dependence. This is shown in the second row. Finally, the third row of the table is the triple dierence ( _DDD_ ) estimate, or simply _δ_ 7 . This estimate indicates that the relative eect of the crisis for large and small rms on lobbying in the second sector (high dependence) is 0.18 percentage points bigger than in the rst sector (low dependence). In other words, large rms relative to small rms increased an additional 0.18 % over the relative increase of large and small in the rst sector.

Similar results are obtained by looking at the probability of starting to lobby during the crisis rather than the intensity. For this specication, I replace _lobbysit_ by and indicator function that takes value of 1 if the rms _i_ in sector _s_ at period _t_ is lobbying and 0 otherwise. The results of this regression are displayed in table (4). The results are similar in sign to the ones obtained in table (3).

All of these results are consistent with the idea that large unconstrained rms are wealthier and have more resources to spare during the crisis in order to extract more rent. On the other hand, small rms, especially those in sectors more aected by the shock, have more trouble operating during these episodes and have to reduce their expenditure on lobbying.

The results presented in this section provide a set of useful guidelines for a model that attempts to explain the eect of lobbying on the economy. First, given the fact that only a small fraction of rms are doing lobbying, I propose a model with endogenous lobbying decision subject to a xed cost required to inuence the government. In this way, since lobbying entails xed costs, larger and wealthier rms will be the ones engaging in this activity. Second, given that I observe that sectors that depend more on external nance tend to lobby more, I will have an economy with two sectors that will have dierences in their scale of production to capture the dierences in nancing needs. Third, given that I observe a dierent response to the crisis based on size and the sector of operation of each rm, I will allow for rm level heterogeneity in terms of productivity and wealth, that together with decreasing returns to scale generate the dierent impulse responses of lobbying. Finally, and related to the previous point, I will introduce nancial frictions in the form of a collateral constraint. This assumption will allow me to hit the economy with a credit supply shock that will

> 22The negative value is due to the dummy _SME_ being an indicator for small and medium rms. A negative value means that small rms are reducing the intensity of lobbying relative to large rms, so large rms are doing relatively more.

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have dierent eects on rms of dierent sizes and producing in dierent sectors.

# 4 The Model

In this section, I present a model in which the misallocation of capital arises endogenously due to the existence of nancial market imperfections and lobbying for capital tax benets. The aim of the model is to measure to what extent the proposed mechanisms explain the dynamics of total factor productivity and output, as well as understand the implications for economic recovery during a credit crunch. To this end, I propose a variant of the standard span of control framework of establishment size as in Lucas (1978) extended to allow for nancial frictions following Kiyotaki and Moore (1997), Albuquerque and Hopenhayn (2004) and Buera et al. (2011). I depart from those papers in the following way: (i) there is a government that collects taxes and grants capital tax benets to rms, (ii) rms can choose to lobby the government to receive preferential treatment and obtain more tax benets that reduce the tax burden, and (iii) because lobbying is costly, rms have to decide whether to pay a xed cost to engage in lobbying activity or just receive the common component of the tax benet. In order to capture the observed dierences in external nancial dependence across sectors, I introduce sector specic xed costs as in Buera et al. (2011).

## 4.1 Environment

Time is continuous. There are two intermediate goods, which are the only factors of production required to produce a single nal good.

The economy is populated by a unit mass of innitely-lived households/agents that have a homogeneous endowment of time to be used either as a worker or in running a rm. I assume that a xed measure _q_ of the population has the ability to produce in sector 1 (type 1 agent), and a fraction 1 _− q_ has the ability to produce in sector 2 (type 2 agent).<sup>23</sup> Individual preferences are described by the following expected utility from consumption of the nal good _Cst_ where _ρ ∈_ [0 _,_ 1] is the impatience rate and _s ∈{_ 1 _,_ 2 _}_ denotes the type of agent. The instantaneous utility function _u_ ( _Cst_ ) is isoelastic with the inverse elasticity of intertemporal substitution equal to _θ_ Agents of type _s ∈{_ 1 _,_ 2 _}_ are heterogeneous with respect to their productivity to produce _zst_ , and

> 23This is an extreme version of Buera et al. (2011). In their paper, agents have a pair of productivities that come from independent draws from the same distribution. Each productivity is used to produce in one sector. Given those draws, they select into one of those sectors based on which productivity generates higher income. To simplify my quantitative part, I assume only one productivity and I separate agents on types.

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with respect to their nancial wealth _ast_ . The evolution of the ability is determined stochastically. When born, each agent receives an ability coming from an invariant distribution _Gs_ ( _z_ ) ,which evolves based on a continuous time analog of a markov process where _Wst_ is a wiener process, _μ_ ( _zst_ ) and _σ_ ( _zst_ ) are the drift and diusion of the process respectively. Given an initial level of wealth when born, the evolution of this variable is determined in general equilibrium as an outcome of savings decisions. In this economy, savings take the form of risk-free claims on physical capital. As discussed below, savings will serve two purposes: as self-insurance against idiosyncratic shocks, and as a collateral to nance working capital requirements. As in Aiyagari (1994), agents also face a borrowing constraint, which implies that _ast ≥_ 0 at each point in time.

At the beginning of the period, an agent of type _s_ chooses his occupation based on his productivity _zst_ and his wealth _ast_ . They can work for a competitive market wage _wt_ or they can operate the technology in sector _s_ for a prot _V_<sup> ̃</sup> _s_<sup>_p_.Tooperateinsector</sup><sup>_s_,agentshavetopayaxedcost</sup><sup>_f_</sup> _s_<sup>in</sup> units of capital every period. This xed cost is specic to each sector, and I assume that _f_ 1 _< f_ 2 . This assumption is motivated by the fact that capital intensity is higher in sector 2, and it helps to map the theory with the data in terms of nancial dependence. After paying the xed cost, the technology available in sector _s_ is given by a decreasing return to scale technology in labor and capital, adjusted by productivity or ability _zst_ ,<sup>24</sup> The production of the nal good used for consumption, investment and lobbying is generated by a set of competitive rms that use the two intermediate inputs denoted by _y_ 1 _t_ and _y_ 2 _t_ . These two inputs are combined using a constant returns to scale technology, where _γ ∈_ (0 _,_ 1) and _ε ∈_ [0 _, ∞_ ) . All producers in this sector are homogeneous with respect to productivity, and they are not subject to nancial constraints. The problem of these rms can be reduced to the following relationship coming from the rst order condition:

> 24This assumption implies that there is an optimal size for rms, and it is a way of introducing a meaningful rm size distribution. Alternatively, one could choose to work with monopolistic competition and constant returns to scale.

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Finally, there is free entry in the sector, and therefore zero prots. If this is the case, From now on, we assume that the nal good is the numeraire of the economy.

The economy features two mechanisms aecting the intermediate producers that distort the economy in steady state, and especially during a credit crunch. The rst one is related to nancial frictions, which restrict how much capital an agent running a rm can borrow. The second one is the existence of capital tax benets and the possibility to lobby the government to obtain preferential tax treatment. I describe them separately. After that, I describe the problems and constraints involved in the economy in detail.

# Financial Markets

In this economy, productive capital is the only asset. There is a perfectly competitive nancial intermediary that receives deposits and rents capital to rms. The return on the deposits is given by the interest rate _rt_ . The zero prot condition of the nancial intermediary implies that the rental rate is equal to the user cost of capital: that is _Rt_ =<sup>_<u>r</u>_</sup> 1<sup>_<u>t</u>_</sup> _−_<sup><u>+</u></sup> _τ_<sup>_<u>δ</u>_where</sup><sup>_δ_isthedepreciationrateofthe</sup> economy and _τ_ is the tax rate that the government charges on operating income.<sup>25</sup> Capital rented _kst_ has to be returned at the end of the period, and due to the existence of limited commitment, the amount of capital that the rm can rent is partly determined by wealth. This assumption implies that agents running the rm are subject to a collateral constraint of the form _kst ≤ λtast_ , where _λt ≥_ 1 summarizes the credit constraints in the economy.<sup>26</sup> A low value for _λt_ is associated with low access to credit. In particular, in the case where _λt_ = 1 rms have to self-nance all their capital rental and therefore there is a strong incentive to save in order to allow production. On the other extreme, when _λt →∞_ there are perfect capital markets. In this case, saving decisions are independent of production decisions and the only motive for saving in this economy is consumption smoothing.

# Lobbying For Capital Tax Benets

The second source of distortion comes from the existence of capital tax benets that can be inuenced through lobbying. As a result, corporate lobbying distorts the allocation of this input relative to an

> 25The structure of the rental market is standard in the nancial friction literature. See Buera and Shin (2011), Blaum (2013), Midrigan and Xu (2014) and Moll (2014) among others. Moll (2014) shows that this representation is equivalent to having a rm owning capital in a model with nancial frictions and no government. The Online Appendix D.3 shows that this equivalence continues to hold when the government collects taxes and grants capital tax benets. The proper rental rate emerges from this problem.

> 26A way to rationalize the constraint is the following: rms have access to a competitive nancial intermediary who receives deposits and rents capital to rms. In this economy, lending directly to rms is not possible. After the production process, the rm could default on its loan with probabily _λ_ <u>1</u><sup>,andiftheydothat,theykeeptheremaining</sup> undepreciated capital stock. On the other hand, the nancial intermediary can seize the nancial assets of the rm (the deposits), without any other cost imposed to the defaulter. This simple model implies that the rm can only borrow at most _λast_ .

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economy where the government does not oer these type of tax benets.

After selling in the market, rms have to pay a tax rate _τ_ on operating income. However, the government grants tax benets associated with capital that allow rms to reduce their tax burden. Before production, operating rms in each sector can decide to engage in lobbying activity by paying an upfront cost in units of capital _fl_ . As discussed by Kerr et al. (2014), this cost could include the initial cost of searching for and hiring the right lobbyist, educating these new hires about the details of the rm's interest, or nding out which legislature should be targeted.<sup>27</sup> Paying the upfront cost _fl_ gives rms the ability to inuence the government through costly lobbying in order to get tax benets tailored to them. The cost of lobbying represents all the variable costs that rms have to pay in order to contact legislators at congress, and it is assumed to be given by where _est_ is the lobbying eort of an agent of type _s_ in period _t_ , and _h >_ 0 . As in Arayavenchkit et al. (2014), tax benets are composed of two parts: 1) A part that is standard and applies to all rms, even those that did not pay the xed cost _fl_ ; 2) A second part that is inuenced by lobbying eort _est_ , which is only available to rms that are paying _fl_ .<sup>28</sup> Furthermore, given that most of the tax benets that the government grants are associated with capital, the tax benet schedule depends positively on the capital used by the rm. Taken together, the tax benets are given by The term (1 _− τ_ ) _kstφ_ captures the returns that all rms are getting without any expenditure on lobbying.<sup>29</sup> However, if they do decide to hire a lobbyist, rms obtain preferential treatment that is increasing in the lobbying eort _est_ . The amount of benets per unit of lobbying depends on two parameters: the parameter _ν ∈_ (0 _,_ 1) , which is the elasticity that maps lobbying eort into changes in the tax benets (and therefore the eective tax rate); and the parameter _μ_ , which is a scale parameter.

In order to be consistent with the fact that the eective tax rates are bounded from below , the amount that rms can claim as tax benets on capital is at most a fraction of the tax obligation with the government. Therefore, rms incorporate the following constraint when taking production

> 27From a modeling point of view, the xed cost _fl_ is introduced to capture the empirical fact that only a fraction of public rms are engaging in lobbying for taxation issues as we saw in section 3. Bombardini (2008) also used xed costs to rationalize this fact in the context of international trade.

> 28Compared to that paper, I use a modied version of the tax benet schedule. In their paper, they do not have this xed cost and the government selects who is receiving the tax benets based on the amount of lobbying expenditure. As a result, there is a cuto lobbying eort such that if you cannot reach that level you will not spend resources in equilibrium. In addition, they provide a partial equilibrium analysis without nancial frictions and with dierences in the timing of decisions.

> 29 We can think of _φ_ as tax advantages that were introduced when the statutory tax on rms was set. The scaling by 1 _− τ_ allows me to keep tractability when solving the problem of a lobbying rm.

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and lobbying decisions: where _π_ ̃ _st_ is the operating income to be dened below and is a positive scale parameter.

# 4.2 Intermediate Firm

Now that we are familiar with the distortions aecting the operation of intermediate rms, we focus on their optimization problem. The timing of events is as follows: 1) conditional on running a rm in sector _s_ , the agent has to decide whether or not to lobby the government by paying the xed cost _fl_ ; 2) the rental market opens, production is decided and lobbying takes place for those that paid the xed cost. In equilibrium, and given the xed cost of lobbying _fl_ , there is selection into lobbying activity depending on the ow of income generated in that activity. Next, I formulate and solve the problem of an intermediate rm for each case.

## Lobbying Firm

Suppose the agent of type _s_ has decided to produce in sector _s_ . Given his productivity and wealth, ( _zst, ast_ ) _,_ the prot when a rm is engaging in lobbying activity is a slight modication of the standard problem of an rm facing nancial frictions. First, dene pretax income by _π_ ̃ _st_ , _η_ where _yst_ = _zst_ � _kst_<sup>_αl_</sup> _st_<sup>1</sup><sup>_−α_</sup> � . After producing and selling the output, rms have to pay a statutory tax ̄ _τ_ . However, this tax burden is reduced by the capital tax benet _τ_ ( _kst, φ, est_ ) that depends on the lobbying eort _est_ . As described at the beginning of this section, the amount of capital tax benets that a rm can claim is subject to the inequality (9). Putting everything together, the problem to solve is the following Here, Ω _t_ is the set of aggregate variables that the rm takes as given when making decisions, and _π_<sup>_lob_</sup> ( _ast, zst,_ Ω _t_ ) is the prot obtained after lobbying.

## Non-Lobbying Firm

Suppose the agent of type _s_ has decided to produce in sector _s_ . Given his productivity and wealth, ( _zst, ast_ ) _,_ the prot when the rm is not participating in lobbying activity is almost identical to the previous one. However, because rms are not spending resources on lobbying activity, the reduction 18
in the tax burden is given by _τ_ ̄( _kst, φ,_ 0) = (1 _− τ_ ) _kstφ_ . Considering this result, the problem for a non-lobbying rm is where _π_<sup>_nlob_</sup> ( _ast, zst,_ Ω _t_ ) is what the agent can obtain if he is not doing lobbying.

# Discussion: Interaction Financial Frictions, Capital Tax Benets and Lobbying

The existence of nancial frictions, capital tax benets and lobbying have implications for the allocation of capital in the economy (misallocation). Additionally these factors have the potential to alter occupation choices, introducing a second channel of distortion. Below, I discuss each margin.

In order to understand the key mechanisms that produce misallocation of capital, it is useful to resort to the rst order condition.<sup>30</sup> Letting _δ_<sup>_∗_</sup> be the lagrange multiplier on the collateral constraint we have, Following Hsieh and Klenow (2009), there is capital misallocation when the marginal product of capital ( _MPK_ ) is not equal to the rental cost cost capital _Rt._ In the right hand side of (11) we have the three mechanisms at play: the nancial frictions (in red), the existence of capital tax benets (in blue) and lobbying for those benets (in green). I rst describe the eects having only nancial frictions, and then I add each mechanism individually to reach all the elements of the right hand side of equation (11).

Only Financial Frictions In an economy where there are no tax benets and rms cannot lobby the government, the rst order condition for capital is given by, As is well known, the existence of nancial frictions distorts the allocation of capital across rms. The key insight from the misallocation literature is that higher dispersion in the marginal product of capital indicates higher degree of misallocation of that factor. In other words, a reallocation of capital from unproductive and wealthy rms towards productive and constrained rms would allow a higher level of output, keeping the level of aggregate capital constant. The distortion in

> 30The complete set of rst order conditions and derivations can be found in Online Appendix D. Here, for simplicity, I assume that the collateral constraint on the tax benets that rms u can claim is not binding. For the calibrated version of the model, this constraint is not relevant for most of the rms.

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the allocation of capital can be inferred from the presence of the lagrange multiplier _δst_<sup>_∗_inequation</sup> (12). For a given level of productivity, a rm that is nancially constrained has a strictly positive multiplier _δst_<sup>_∗_.Thismeansthatthe</sup><sup>_MPK_ishigherrelativetoarmwiththesameproductivity</sup> that has enough wealth to operate at the optimal scale of production. As a result, constrained rms have a lower level of capital, labor, production and prots other things equal. A reallocation of capital from rms with low _MPK_ to rms with high _MPK_ would be benecial for the economy. Financial Frictions and Capital Tax Benets Now, as a second step, suppose the economy has tax benets but it does not allow for lobbying. The rst order condition in this modied version would be The introduction of tax benets adds an extra term that aects the MPK. The capital tax benets change the optimal scale of production because now there is an additional source of revenue coming from the tax rebate. Figure (7) illustrates this point. A rm that is not nancially constrained chooses capital to maximize operating income, which is equivalent to maximizing prots in the absence of tax benets. The optimal value before tax benets is given by _k_ 1 _._ However, the introduction of tax benets implies that rms will not maximize operating income _π_ ̃ _s,_ and instead will be maximizing considering that they have to pay taxes and receive tax benets that depend on capital. In gure (7), that corresponds to _k_ 2 .

With nancial frictions, the tax benet has a dierent impact for rms that are close to the constraint. For those rms that are nancially constrained absent the tax benet, the nancial situation is worsened because they require much more capital in order to produce at the new optimal scale. There is a second group of rms that absent the tax benet would not be nancially constrained. However, once we introduce this tax advantage they become constrained, worsening the misallocation of capital. Finally, there is a group of rms that are wealthy enough so that this mechanism causes an increase in their size, leading to a higher level of capital and lower MPK. Combining the three eects, the introduction of capital tax benets increases the dispersion of the MPK and therefore the allocation of resources in this economy is worse than in the rst case.

A nal comment is worth mentioning. In the case of a tightening of the collateral constraint (the nancial crisis), the common component will not play a role since it aects all rms symmetrically and does not vary with the crisis. Therefore, it will not have an eect on the allocation of resources.

Full Model Finally, we include lobbying as the the last mechanism in the model. By introducing lobbying we generate another source of variability in the marginal product of capital, and therefore it is an amplier of the eects described before. Financially unconstrained rms can now invest resources to obtain additional tax benets, reducing the marginal product of capital even further. Financially constrained rms would also like to expand, making the nancial friction more severe. Finally, those rms that without lobbying were producing at the optimal scale, could now become nancially constrained due to fact that with lobbying there is a new optimal level of production. Notice that lobbying will play a role during the nancial crisis. Because lobbying varies across 20
individual rms and reacts to changes in the environment, it will have an eect on the allocation of capital during a credit crunch. I will discuss the implications of lobbying during a nancial crisis in section (6).

The second channel through which the economy can be aected is selection, i.e the decision to run a rm. At the beginning of the period each agent of type _s_ has to decide an occupation based on the maximum earning available at that time, given his productivity and his wealth. In other words, his decision is based on _max wt, V_<sup> ̃</sup> _s_<sup>_p_(</sup><sup>_a_</sup> _st_<sup>_, z_</sup> _st_<sup>_,_Ω</sup> _t_<sup>)</sup> where _wt_ is the market wage and _V_<sup> ̃</sup> _s_<sup>_p_(</sup><sup>_a_</sup> _st_<sup>_, z_</sup> _st_<sup>_,_Ω</sup> _t_<sup>)</sup> � � is the prot obtained by running a rm after the lobbying decision, In an economy without nancial frictions, tax benets, and lobbying, the decision to run a rm only depends on the productivity _zst._ Those agents that generate prots above the market wage choose to run a rm, the rest sort into the labor market. With nancial frictions, wealth is also a determinant of the decision to run a rm. Productive but poor agents end up working for a wage instead of running a rm, until they overcome the nancial constraint through savings. On the other hand, unproductive but wealthy entrepreneurs remain in business. The incorporation of tax benets and lobbying introduce new margins that distort the decision to run a rm. Wealthy but unproductive rms now have another source of revenue coming from the tax benet and the possibility of lobbying. This feature could make some rms stay in business for a longer period of time. On the other hand, without tax benets the unique source of cash ow for nancially constrained rms is production. The introduction of tax benets increases the current period prot, generating more resources that could be used for saving. With these additional funds, agents could overcome their nancing constraint through self-nancing much faster and therefore they could operate at the optimal scale.

Overall, the aggregate eect of having nancial frictions and capital tax benets that can be inuenced through lobbying is not unambiguously determined. In order to understand the aggregate implications of these mechanisms, a quantitative assessment is necessary.

# 4.3 The Problem of the Agent and Aggregation

Given nancial wealth _ast_ , productivity _zst_ and state variables Ω _t_ , the agent of type _s_ maximizes expected utility by choosing consumption, nancial wealth, his occupation, amount of lobbying, and production input choices (conditional on running a rm) subject to a sequence of budget constraints and nancial constraints. The budget constraint for period _t_ is given by where Ω _t_ is the vector of the aggregate states of the economy, _rt_ is the return on wealth and _Tt_ is a lump sum transfer from the government. Here, the max operator is reecting the fact that the 21
agent is choosing his occupation by comparing the earnings from each activity.<sup>31</sup> Given preferences and budget constraints, the stochastic optimal control problem of the agent that can operate in sector _s_ is given by The value function of the optimal control problem satises the Hamilton-Jacobi-Bellman (HJB), which can be used to characterize the solution of the agent's problem where _μ_ ( _zst_ ) and _σ_<sup>2</sup> ( _zst_ ) are the drift and difussion process of _zst_ , and where _Mst_ ( _ast, zst, t_ ) is the optimal saving rule in period _t_ , The HJB equation is a second order dierential equation. The value function _Vs_ depends on _t_ due to the fact that prices may be changing along the transition path.

For the quantitative part, I will assume that _log zst_ follows a mean reverting diusion process given by where as before _Wst_ is a Brownian Motion. In this particular process, the parameter _ψ_ measures the speed of reversion and _log z_ ̄ is the long run mean. One particular property of the process is the

> 31In order to do this computation, agents need to know the aggregate state of the economy. In particular, they need to know prices, and how the dierent choices that they are making will aect earnings. In a more complicated model with uncertainty about those variables, the agent would be choosing based on expectations about potential earnings.

22
fact that the autocorrelation is given by That is, the autocorrelation depends on _ψ_ and the time interval. In addition, this process features a long run stationary distribution with mean _log z_ ̄ and variance 2<sup>_<u>σ</u>_</sup> _ψ_<sup>2.Bothpropertieswillbeuseful</sup> for the calibration of the model in section (5).<sup>32</sup> In this economy, the aggregate state of the economy is represented by the joint distributions of productivities and wealth _Gs_ ( _a, z, t_ ) for each type of agent _s._ The evolution of the distribution of type _s_ agents over time is given by the the Kolgomorov forward (or Fokker-Planck) equation where I am omitting the sub-indexes on the state variables to save notation. Here, I denote _gs_ ( _a, z, t_ ) the density of the distribution _Gs_ ( _a, z, t_ ) .

For future reference, I denote _gs_<sup>_∗_(</sup><sup>_a, z, t_)tothedensityscaledbythefractionofagentsoftype</sup><sup>_s._</sup> That is, _g_ 1<sup>_∗_(</sup><sup>_a, z, t_) =</sup><sup>_qg_1(</sup><sup>_a, z, t_)and</sup><sup>_g_</sup> 2<sup>_∗_(</sup><sup>_a, z, t_) = (1</sup><sup>_−q_)</sup><sup>_g_2(</sup><sup>_a, z, t_)</sup><sup>_._</sup>

# 4.4 Government

The government in this model is passive and the amount of tax benets granted to corporations is such that the budget is balanced in steady state The left hand side is the total revenue from the government, which for simplicity is only composed by taxes on operating income _ROIt_ . Those sources of funds need to be equal to the \ tax benets granted to rms and the lump sum transfer to consumers _Tt_ . Taxes on operating income are dened as where _oc_ 1 _t_ = _{_ 1 _}_ and _oc_ 2 _t_ = _{_ 2 _}_ denotes an agent operating a rm in sector 1 and sector 2 respectively.<sup>33</sup> Out of steady state, transfers _Tt_ adjust every period in order to keep the budget balanced.

> 32See Dixit and Pindyck (1994) and Stokey (2008) for details about these two properties of the process.

> 33To be more specic, _ocst_ = _{s}_ is an indicator function that takes the value of 1 if agent of type _s_ is operating a rm and a value of 0 if it is a worker, for any period of time _t._

23
# 4.5 Equilibrium

In this section, I describe the equilibrium conditions for this economy. Most of the features are standard denitions with the exception of the lobbying expenditure and the government budget constraint that considers tax benets. For simplicity, I avoid explicitly denoting the dependence of all variables with respect to _ast_ and _zst_ .

Given an initial joint distribution of wealth and entrepreneurial ability _Gs_ ( _z, a,_ 0) , and a marginal stationary distribution _Gs_ ( _z_ ) , a recursive stationary equilibrium in this economy consists of: 1) policy functions for consumption, asset accumulation and occupational choices for each type of agent _s_ , _{Cst, Mst, ocst}_<sup>_∞_</sup> _t_ =0<sup>;2);protsforlobbyingandnon-lobbyingrmsineachsector</sup><sup>_s_</sup> � _πst_<sup>_lob, π_</sup> _st_<sup>_nlob_</sup> � _∞t_ =0 and a sequence of demand functions for each intermediate; 3) a sequence of prices for the intermediate goods _{p_ 1 _, p_ 2 _}_<sup>_∞_</sup> _t_ =0<sup>;4)labordemands,capitaldemand,lobbyingparticipationandlobbying</sup> spending in each sector _s_ , _{lst, kst, lobst,est}_<sup>_∞_</sup> _t_ =0<sup>;5)asequenceofwages,interestrates,aggregate</sup> prices, gross interest rates, nancial state and transfers _{wt, rt, Pt, Rt, λt, Tt}_<sup>_∞_</sup> _t_ =0<sup>;6)asequenceof</sup> distributions _{Gs_ ( _z, a, t_ ) _}_<sup>_∞_</sup> _t_ =0<sup>foreachtypeofagents</sup><sup>_s_andthecorrespondingprobabilitydensity</sup> functions _gs_ ( _z, a, t_ ) , such that

1. Given _{p_ 1 _, p_ 2 _}_<sup>_∞_</sup> _t_ =0<sup>and</sup><sup>_{wt, rt, Pt, Rtλt}∞_</sup> _t_ =0<sup>,</sup><sup>_{lst, kst, lobst,est}∞_</sup> _t_ =0<sup>solves the problem of interme-</sup> diate rms, and � _πst_<sup>_lob, π_</sup> _st_<sup>_nlob_</sup> � _∞t_ =0<sup>aregeneratedineachsector</sup><sup>_s,_</sup>

2. Given � _πst_<sup>_lob, π_</sup> _st_<sup>_nlob_</sup> � and _{wt, rt, Pt, Rt, λt, Tt}_<sup>_∞_</sup> _t_ =0<sup>,</sup><sup>_{Cst, Mst, ocst}∞_</sup> _t_ =0<sup>solves the problem of each</sup> agent 3. Labor market, capital market, and intermediates market clear 4. The evolution of the density function _gs_ ( _a, z, t_ ) over time is given by the the following Kolgomorov forward equation: 24
which in steady state implies 5. The government satises the scal budget.

where _g_ 1<sup>_∗_(</sup><sup>_a, z, t_) =</sup><sup>_qg_1(</sup><sup>_a, z, t_)and</sup><sup>_g_</sup> 2<sup>_∗_(</sup><sup>_a, z, t_) = (1</sup><sup>_−q_)</sup><sup>_g_2(</sup><sup>_a, z, t_)</sup><sup>_._</sup>

# 5 Calibration

All parameters are calibrated to the U.S. economy prior to the great recession using an annual frequency. For the sake of clarity in the explanation, I will classify the parameters into four groups: 1) _{ρ, θ, δ, }_ are the standard parameters; 2) _{η, α, f_ 2 _, γ, ε, ψ, σ}_ are technological parameters ; 3) _{h, φ, ν, μ, fl}_ are parameters related to the lobbying activity and tax benets; 4) _{λt, τ, ⊖}_ are the institutional parameters for the U.S. economy.

The strategy used to calibrate the parameters in steady state has 3 parts. First, I estimate the elasticity of substitution _ε_ based on aggregate data using a reduced form equation coming from the model. Second, given the number of parameters to calibrate and the computational burden of this process, I set some of them according to existing microeconomic and macroeconomic evidence. Finally, given that the mapping between the model and the targeted data moments is multidimensional, I do a joint calibration of the remaining parameters. In subsection (5.1) I explain the numerical procedure to calibrate the model. Subsection (5.2) discusses the targeted moments and the relevance of each parameter to aect each moment. Subsection (5.3) evaluates the performance of the model to match moments of the data that are not targeted during the calibration. The last part of this section is devoted to the calibration of the credit shock that is used in the quantitative results.

## 5.1 Procedure for Calibration

For those parameters that are not taken from the literature or estimated using a reduced form equation, I implement a Simulated Method of Moments (SMM). Suppose we have a vector _A_<sup>_d_</sup> of 1 _×n_ moments from the data that corresponds to moments from the steady state distribution coming from the model.<sup>34</sup> Given a vector Θ of parameters to estimate, the model produces a vector of _n_ corresponding moments _A_<sup>_m_</sup> (Θ) . The SMM estimator Θ<sup>ˆ</sup> minimizes the weighted square sum of the distances between the model simulated moment and the corresponding counterpart in the data.

> 34In particular, these _n_ moments include the market clearing conditions and budget constraint from the model.

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Explicitly, it solves where _Wd_ is a weighting matrix, which may be a function of the data. For now, the weighting matrix is going to be the identity matrix. As a result, the estimates are consistent, but not ecient.<sup>35</sup> The implementation of the estimation is as follows: for a given vector of parameters Θ , I simulate the model and as a rst step to nd the vector Θ<sup>ˆ</sup> that minimizes the objective function I use an annealing algorithm. This is a global optimization routine that jumps randomly around the parameter space while at the same time decreasing the frequency of landing in non-optimal ares in each iteration. After reaching a certain number of iterations where the objective function seems to be reaching a global maximum, I use a local search method to obtain the calibrated parameters.<sup>36</sup> In the next subsection, I describe the selected moments and the data used for the calibration.

# 5.2 Estimation and Moments

First, I explain the methodology and results to estimate the elasticity of substitution of the intermediate inputs _ε_ and then describe a set of relevant moments chosen to calibrate the remaining parameters. Even though all parameters aect the value of all moments, I also discuss the eects of each parameter on each moment individually.

## 5.2.1 Estimation of the Elasticity of Substitution between Intermediates

To calibrate the elasticity of substitution _ε_ between the two sectors, I follow a similar approach to Acemoglu and Guerrieri (2008). Using equation (6) and taking logs we obtain an equation that allows for estimation I exploit time variation in relative value added at current prices for the low and high nancially dependent sector, and variations in the ratio of real value added<sup>_<u>y</u>_</sup> _y_<sup><u>1</u></sup> 2<sup>_<u>t</u>_</sup> _t_<sup>toestimatetheelasticityof</sup> substitution between intermediates _ε_ .

The data used to estimate equation (19) comes from EUKLEMS. I use data for the U.S. from 1970 to 2005. First, I separate the 2-digit SIC industries provided in EUKLEMS in low and high external dependence following the measure of Rajan and Zingales (1998) for manufacturing and services, excluding the nancial sector. To construct sectoral value added at constant prices, I divide each industry current price value added by the corresponding price deator and I sum across sectors to construct the low and high nancially dependent sectors.<sup>37</sup> Using those two inputs, I

> 35If the model is overidentied, the weighting of each moment is extremely relevant as in the standard GMM. In particular, we need to put more weight on better identied moments. This would be implemented by using the inverse of the variance-covariate matrix of the data moments.

> 36To be more specic, I use the matlab function fminsearch that comes with the optimization toolbox.

> 37Refer to the Online Appendix C for all the steps in the procedure.

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estimate _ε_ using OLS with robust standard errors. The resulting value for _ε_ is 0.67, which is in line with the estimates of Acemoglu and Guerrieri (2008) for a similar group of industries.<sup>38</sup> Table (5) presents the results.

# 5.2.2 Moment Selection and Calibration

Standard Parameters The impatience rate _ρ_ is calibrated to match the real interest rate for the period 2004-2007. Given an annual nominal interest rate for the period of 5 % and a core annual ination of 3%, I target a real interest rate _r_ of 2 % . This implies a calibrated impatience rate of 0.05. The depreciation rate _δ_ is taken to imply an average investment to capital ratio of approximately 6 % _,_ which corresponds to the average value for the private capital stock in the U.S. xed asset tables, after considering growth. Finally, I use a constant relative risk aversion coecient _σ_ equal to 1.5, which is in the range of values used in quantitative studies with heterogeneous agents. The values of these parameters can be found in table 6.

Technological Parameters Given _ε,_ we have 6 remaining technological parameters to calibrate: _{η, α, f_ 2 _, γ, ψ, σ}_ . Based on empirical evidence on estimates of the degree of returns to scale at the rm level, I set _η_ = 0 _._ 78 , in line with Thomas (2002), Pavcnik (2002) and Restuccia and Rogerson (2008).<sup>39</sup> As usual, _α_ controls the share of payments to capital observed in the data, which is equal to 0.3. However, due to the presence of xed cost and nancial frictions, that share of payments will no longer be equal to _α_ .<sup>40</sup> In particular, the aggregate capital income share could be lower than the value of _α._ To capture the sector specic xed costs I match the relative capital intensity between the low and high nancially dependent sectors. If there were no xed costs, the capital intensities would be equalized across sectors since the nancial frictions and lobbying xed cost aect both sectors in the same way. Given a xed value for _f_ 1 and using the fact that _f_ 1 _< f_ 2 , an increase in _f_ 2 implies that the sector 2 is more capital intensive, that is, ( _k_ 2 + _f_ 2) _/l_ 2 _>_ ( _k_ 1 + _f_ 1) _/l_ 1 .<sup>41</sup> In this economy, the production of the intermediate sectors _y_ 1 and _y_ 2 are the only contributors to value added since the nal producer only "bundles" those goods. In addition, they do not require any other intermediate good to produce. This implies that _pjyj_ can be interpreted as value added in sector _j._ Following this logic, we can think of 1 _− γ_ driving the share of the externally dependent sector in _GDP_ . Using the same data and the same classication for sectors used to estimate the elasticity of substitution of intermediates _ε_ , on average during the period 1970 to 2005 the share in

> 38 They estimate _ε_ using data from NIPA for 22 industries classied with NAICS. Then, they separate those industries by capital intensity and they run the same regression.

> 39Values for this parameter used in the literature range from 0.7 to 0.9. See references in Restuccia and Rogerson (2008) and in Atkeson and Kehoe (2005).

> 40Even with no nancial frictions this statement would be true due to the presence of rents to entrepreneurship. However, if we assume as in Gollin (2002) that those rents are split evenly between workers and capitalists, we return to a world with capital share of 1 _/_ 3 .

> 41See Blaum (2013) for a discussion of partial versus general equilibrium identication of xed costs in these types of models.

27
_GDP_ of the high externally dependent sector is 70.4 % . I use this moment to calibrate _γ_ .

Finally, we have two parameters related to the stochastic process of productivity: _{ψ, σ}_ . The parameter _ψ_ measures the persistence of the process and therefore it has a direct impact on the wealth share of the top 10 % of households. I target the 2007 wealth share, which was equal to 73 _._ 1% .<sup>42</sup> In the case of _σ_ , it is calibrated to match the fraction of labor employed by the top 10 % of establishments, which is equal to 63 % according to the U.S. Census in 2012. The calibrated technological parameters can be found in table (7).

Lobbying and Tax Benet Parameters To calibrate _{h, φ, ν, μ, fl}_ , I resort to the microdata on lobbying and eective tax rates analyzed in section (3).

Although lobbying is in principle available to all rms, based on the micro data, there is a striking dierence between public and private rms: most of the lobbying rms are public rms. In fact, as a share of private rms, lobbying rms are negligible in number. For this reason, I assume that there is a fraction _m ∈_ [0 _,_ 1] of all rms in the model that map to the "private" rms in the data. The dierence between _m_ and all the rms in the model is going to be dened as "public rms". These rms will be used as a reference sample to match the moments related to lobbying activity.<sup>43</sup> To choose _m,_ I compute the domestic (U.S.) gross value of production by public rms in Compustat and I compare this aggregate of public rm output against the value of production of the non-nancial corporate sector from the BEA. Using those numbers, I nd that 57 % of the production in the non-nancial corporate sector is carried out by public rms for the pre-crisis period. In other words, 43% of the production of the non-nancial corporate sector is due to private rms. Given that private rms usually have low level of employment and that in the model small rms do not choose to lobby, the set _m_ of rms is going to be composed of the smallest non-lobbying rms that accumulate 43 % of the production in the model.<sup>44</sup> The xed cost of lobbying _fl_ has a rst order eect on the share of lobbying rms in the economy. By increasing this parameter, the number of rms that can aord this costly activity is reduced. Given that in Compustat the number of lobbying rms for taxation issues is 7 _._ 1% on average between 2004 and 2007, I calibrate _fl_ to obtain that fraction over the sub-sample of public rms from the model. The scale parameter _h_ controls how lobbying eort translates into lobbying expenditure. For this reason, I choose to match the average lobbying expenditure to sales from the microdata, which is equal to 0.08 % .

The common component associated to the tax benet _φ_ is targeted to match the average eective tax rate of non-lobbying rms in Compustat, which is equal to 21.4 % . The parameter _ν_ controls

> 42This moment is taken from Wol (2012). Using data from the Survey of Consumer Finance (SCF) he computed wealth distributions for a series of periods of time. For an intuition of the relationship between wealth concentration and persistence of the process refer to Moll (2014). To calibrate these parameters, I exploit the fact that the autocorrelation of the process depends on _ψ_ and that given _ψ,_ the stationary variance is given by 2<sup>_<u>σ</u>_</sup> _ψ_<sup>2.</sup>

> 43We can think of _m_ as the fraction of potential agents that could start a private rm. In general, these agents will not have the connections or the information necessary to lobby at congress, at least for the short run.

> 44For a discussion of the main rm level characteristics of private rms versus public rms in the U.S. see Davis et al. (2007) and Asker et al. (2011).

28
the tax benets that lobbying rms are obtaining from the government. Consequently, I target the eective tax rate of public lobbying rms, which in the data is equal to 18.8 % . Finally, the parameter _μ_ is the scale parameter of the tax benet policy, which controls the amount of resources the government is losing due to tax benets tied to capital. Based on statistics from the IRS, 33% of all the corporate tax revenue is lost in tax benets. I calibrate _μ_ such that in the pre-crisis steady state that relationship holds. The values used for these parameters can be found in table (8).

Institutional Parameters There are 3 parameters to calibrate. I set the tax rate for rms to be equal to 35% in the benchmark economy. The parameter _⊖_ determines the fraction of the rm level tax collection from the government that a rm can claim on tax benets. In the benchmark calibration I set this to 1 . The parameter that measures the degree of credit depth of the economy, _λt_ , governs the aggregate ratio of external nance to capital. To measure this statistic in the data, I take the ratio of the stock of credit market liabilities to non-nancial assets of the non-nancial corporate sector. The numerator corresponds to credit market liabilities of the non-nancial corporate sector, line 5 from table _D._ 3 from the ow of funds coming from the Federal Reserve.<sup>45</sup> The stock of non-nancial assets is constructed using the net stock of xed assets for the corporate non-nancial sector from the U.S. Bureau of Economic Analysis (BEA). I adjust the value to level it to 2007 using current values. To calibrate _λ_ in steady state (pre-crisis), I target a ratio of external nance to non-nancial assets of 0.65, which is the value at the peak of the pre-crisis period in 2007. The values of these parameters and moments can be found in table (9).

To sum up, there are 11 parameters that are jointly calibrated, given that _ρ_ is solved in general equilibrium for a given value of _ε_ :<sup>46</sup> Despite solving a rather complicated multidimensional mapping, the model targets all moments quite closely. The only two moments that the model nds diculty to match are the eective tax rate paid by lobbying rms, which is lower than the same moment in the data, and the right tail of the distribution of wealth that I am targeting with _σ._

# 5.3 Model Testing

We have seen that the model hits the proposed targets quite closely after the calibration. Here, I evaluate the performance of the model using additional moments that were not targeted during the calibration. Table (10) shows some selected moments. Overall, the model behaves extremely well in matching the targeted moments and the non-targeted moments. For example, the model

> 45Line 5 is the total credit market liabilities of the non-nancial corporate business (series LA144104005.Q). It includes the stock of bank loans, and the stock of commercial papers, municipal securities and corporate bonds of the corporate sector.

> 46As a reminder, this parameter has been estimated using a reduced form equation coming from the rst order conditions of the model.

29
does a particularly good job in matching eective tax rates across sectors and in accounting for the dispersion in capital and marginal product of capital for public rms. In summary, I consider the results coming from this table as a success of the calibration strategy. Next, I discuss the calibration of the shock.

# 5.4 Credit Crunch Shock

## Evidence

Between the second quarter of 2008 and the second quarter of 2010, small business loans made by commercial banks declined by over $40 billion (Duygan-Bump et al. (2015)). While this could be a result of a change in the demand for credit, evidence provided by Ivashina and Scharfstein (2010) suggests that there was a change in the supply of credit. Using data on syndicated new loans they nd strong evidence of a reduction in lending around the 2007-2009 recession.<sup>47</sup> Between 2007 and 2008 they found that loans targeted for investment in equipment and machinery fell 48 % _._ Another piece of evidence can be found in the responses to the Federal Reserve's Senior Loan Ocer Survey on Bank Lending Practices. The surveyed banks indicated that they signicantly increased the requirements to approve new commercial or industrial loans to rms around that period of time. More convincing evidence of an exogenous shock to the supply of credit is provided by Almeida et al. (2009), Duchin et al (2010) and Huang and Stephens (2011). Based on the evidence, I take a stand on the nature of the shock and model it as a credit supply shock that will aect the collateral constraint in the model.

## Calibration

In order to replicate the dynamics of the credit conditions of the economy, I hit the model with an aggregate nancial shock modeled as an unexpected decrease in the collateral constraint parameter _λ._ After the initial shock, the future path of _λt_ is perfectly known by all agents. This experiment is similar to the credit crunch in Khan and Thomas (2013), Buera et al. (2015) and Shourideh and Zetlin Jones (2016).

The calibrated shock reduces the value of _λ_ upon impact and the eect of this shock decays over time until the economy returns to the pre-crisis level (under perfect foresight). The initial shock implies a reduction of almost 20 % to the value of the parameter _λ,_ which is consistent with the actual decline in the ratio of external nance to capital observed in the data between the end of 2007 and the rst quarter of 2010.<sup>48</sup> Figure (8) depicts the evolution of the credit conditions in the model and in the data. The left panel shows the ratio of external nance to capital stock using the denitions described in subsection (5.1). For the model, I compute percentage deviations from steady state values. For the data, I show the dierence with respect to the value in the fourth quarter of 2007 of the percentage deviation from HP-lter trend (in Q4-2007, the ratio was 4.8 % above the HP trend).

> 47This market is the main vehicle through which banks lend to large corporations.

> 48The values for the collateral constraint are, _{_ 4 _._ 21 _,_ 2 _._ 95 _,_ 2 _._ 21 _,_ 2 _._ 71 _,_ 3 _._ 8 _}_ . After that, _λt_ = _λt−_ 1 + 0 _._ 2 ( _λt−_ 1 _− λ∗_ ) where _λ_<sup>_∗_</sup> is the steady state value, which is equal to 4.21 in _t_ = 0 . The rst period of the transition is 2007.

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In comparison with the data, the model reproduces the qualitative path of the the external nance ratio quite well. Between 2008 and 2009, the model captures almost all the decline in the ratio of external nance to capital that is observed in the data, and therefore the calibration of the credit shock appears to be successful. However, the model goes back to the steady state much faster than in the data. The implied series of _λt_ used in the quantitative part is shown in the right panel of Figure (8).

# 6 Quantitative results

This section provides the main results of the paper. First, I discuss some of the main features of the model economy in steady state. After that, in section (6.2) I discuss the main ndings of the paper in three parts. In the rst, I ask whether the model can account for the decline in TFP and the evolution of other aggregates relevant to the dynamics of the economy in the aftermath of the nancial crisis. In the second part I study whether an economy with lobbying for capital tax benets amplies or mitigates the eects of the credit crunch. Lastly, I compare the micro implications for lobbying coming from the model and those found in section (3). I use this comparison as a test of the model. Section (6.3) evaluates the long run implications of lobbying for capital tax benets, proposes some policy counterfactual and evaluates the implications of those policies in terms of welfare.

## 6.1 Benchmark Economy Steady State

Although the results presented in this subsection are not novel, I describe the main features from the benchmark stationary equilibrium for completeness. Two of the most important outputs of the stationary equilibrium of the benchmark economy are the stationary distribution for productivity and the wealth distribution. In particular, the model features a log-normal stationary distribution for productivity where an important proportion of the population have low levels of productivity (left panel in gure (9)). On the other hand, the distribution of wealth is also highly skewed, a result that is common in models with incomplete markets and with nancial frictions, and that is derived from the optimal saving decisions of agents. One important consequence of this distribution of assets, is the fact that the model features agents that are nancially constrained when operating the production technology. In order to produce, agents need to rent capital and to do so, they have to collateralize their wealth. Given that the distribution is skewed to the left and that there are decreasing returns to scale in production, an important fraction of the economy is operating at sub-optimal levels. As a result, total factor productivity, output and capital stock will be lower relative to an economy with no nancial frictions (see Greenwood and Jovanovic (1990), Jeong and Townsend (2007), Buera et al. (2011) and Moll (2014) among others).

Figure (10) shows the policy functions for saving for three types of agents in sector _s_ . A feature of models with nancial frictions is that the pattern of savings dier across agents. An economy without nancial frictions generates saving decisions that are decreasing in wealth for all levels of 31
productivity. However, when nancial frictions are introduced, a non-linearity in the saving function arises. Highly productive agents (green dashed line) cannot operate the technology when poor and have to select into the labor market. After saving some funds, they are able to run a rm but under nancing constraints. For this reason,they will start saving even more as they increase the scale of production, generating the increasing part of the saving policy function. At some level of wealth, agents running a rm reach their optimal level of production and the return to an extra unit of saving is equal to the prevailing interest rate in the market. After that point, consumption is more important than saving and the policy function starts decreasing. Notice that the non-linearity does not emerge for low productivity agents. Independently of the level of wealth, these agents are not productive enough to run a rm that generates prots higher than the current market wage.

# 6.2 Dynamics

In this section I examine the response of the model economy to an aggregate nancial shock modeled as a tightening of the credit conditions in the economy. The evolution of the credit conditions are determined by the path of _λ_ , which I have calibrated in (5.4). After the initial shock, credit conditions in the economy recover slowly to the steady state value. In subsection (6.2.1) I study the behavior of the model in comparison with the data for the full model. Section (6.2.2) evaluates the role of lobbying to explain the dynamics of TFP and output for the non-nancial corporate sector. In particular, I show that lobbying amplies the aggregate eects generated due to the nancial frictions when facing a nancial shock. Finally, in subsection (6.2.3) I test whether the calibrated model can generate the patterns described in (3).

## 6.2.1 Benchmark Economy

Figure (11) displays the evolution of aggregate output, measured productivity (TFP), investment rate and lobbying expenditure for the data and the simulated economy. The data for output and TFP have been detrended using a Hodrick-Prescott lter with a quarterly frequency. For lobbying expenditure, the data has been detrended using a linear trend. In the case of output, TFP and lobbying expenditure, the impulse responses from the model are deviations from steady state. For the data, the gure shows dierences with respect to the value of each series in the fourth quarter of 2007. In the case of the investment rate, the gure shows dierences with respect to the steady state for the model, and the dierence with respect to the fourth quarter of 2007 for the U.S. data.<sup>49</sup> The blue line in each panel represents the full model with nancial frictions, tax benets, and lobbying. The model generates GDP dynamics close to the one observed in the data, explaining most of the decline in output. The credit crunch in the model generates a reduction in output of almost 80 % of the decline observed in the data between 2007 and 2009. By the end of 2009, the model predicts a fall of 5.9 % of GDP relative to the steady state. For the same period of time the data showed a decline of 7.5 % .

> 49Appendix C.7 explains in detail the data used for the construction of each variable.

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A second observation is that the model is able to generate TFP dynamics matching the data: a large fall at the beginning, followed by a slower but steady recovery. The TFP in 2009 was 4.2 % below the level of the fourth quarter of 2007, and the model generates a decline of 4.4 % . However, relative to the data, the model seems to converge to the steady state more quickly.

The reduction in output comes from two forces: the aforementioned decline in the aggregate productivity of the economy, and a small decrease in the stock of capital. The downward movement in TFP is the result of a sudden increase in the misallocation of resources in the economy, which is reected in the increase in the dispersion of the marginal product of capital across rms in the right panel of gure (12).<sup>50</sup> With the credit shock, the fraction of rms that are nancially constrained rises, inducing a reduction in the demand for capital and labor. The fall in the demand for these factors of production translates into a decrease in the interest rate (gure (12)) and the wage of the economy. In response to this general equilibrium eect, large unconstrained rms expand and choose to produce at the new optimal scale, particularly the "public" rms in the model. By demanding more capital, large rms reduce their marginal product of that input, while those that have to downsize will increase their misallocation due to worsening credit conditions. Combining these eects, the disperison in the marginal product of capital increases.

For investment, the model generates a decline of almost 6 % at its lowest point. This prediction is slightly counterfactual, since the the decline in the data is close to 5% . To understand the U- shape pattern of investment, it is useful to look at the evolution of the interest rate in the economy at gure (12). With the credit crunch, the return on asset accumulation for the agents decreases, inducing a reduction in the supply of capital and a decrease in the investment rate of the economy that bottoms out in 2010. When the credit conditions start to go back to normal levels around 2010, the incentive to accumulate assets reappears and the investment rate turns around to return to steady state values. Overall, the model seems to be capturing extremely well the behavior of this agreggate, as well as TFP and output.

What is the role of the capital tax benet and lobbying in this adjustment? The fact that we have capital tax benets and a lobbying decision makes the reallocation of capital even stronger. In section (6.2.2) I show quantitatively that the dispersion in the marginal product of capital, hence the misallocation, is larger in a model with lobbying. Here, I discuss the implications of the credit crunch on aggregate lobbying, which is driven by the public rms in the model. This dynamic is inuenced by three forces. Firms that were lobbying the government prior to the shock and that are still nancially unconstrained increase lobbying expenditure due to the drop in the interest rate. Notice that these rms are public rms. Since lobbying and capital are complementary for unconstrained rms, the increase in the capital stock for these rms induces an increase in lobbying that generates

> 50The increase in dispersion in the model is consistent with evidence provided by Bloom et. al (2009) and Chen and Song (2013). The rst one shows that various measures of rm level dispersion increase during the last crisis. Chen and Song (2013) show that the dispersion in the marginal product of capital went up during the last U.S. recession using data from Compustat. Using plant level data, Kehrig (2015) nds that the dispersion in revenue productivity (TFPR) is greater in recessions. Given that TFPR is a weighted average of the marginal product of capital and marginal product of labor, this is also consistent with an increase in MPK.

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a second round eect on their demand for capital. We can see this from the rst order conditions for capital and lobbying for rms that are not nancially constrained, From equation (20) it is easy to see that when the interest rate drops, unconstrained rms increase capital. The second round eect is through equation (21). Since tax beneftis are tied to capital, when capital increases rms try to increase lobbying expenditure in order to extract more tax benets.

On the other hand, there is an increase in the fraction of rms that are lobbying the government as it becomes more protable to pay the xed cost and start lobbying as a result of the decline in factor prices. Lastly, the credit shock has a negative eect on rms that were engaging in lobbying activity but are now nancially constrained. For these rms, the crisis induces a reduction in lobbying expenditure. This eect can also be seen from equation (21). For a constrained rms capital is determined by the collateral constraint. Since there is a decline in the amount a rm can rent during the crisis, the capital stock declines together with the lobbying eort. However, as we can see in gure (11), this reduction is not suciently strong to force an aggregate drop. Since lobbying rms in the model are the largest rms that are on average nancially unconstrained, it is natural that the total eect during the crisis is a rise in aggregate lobbying. Overall, the model predicts an increase in lobbying expenditure that is close to the one observed in the micro-data: by 2010, the model accounts for 75 % of the increase in lobbying expenditure.

An implication coming from this adjustment in aggregate lobbying is that the dispersion in lobbying expenditure increases during a nancial crisis. Do we observe that in the data? The answer for this lies in gure (13). As expected, the data conrms that during the crisis there was an increase in the dispersion of lobbying expenditure for taxation issues. Also, notice that when the economy starts recovering around 2009 the dispersion almost reaches its maximum and starts declining. This pattern is also observed in the model.

Before studying the role of lobbying in the adjustment of the economy, it is worth mentioning some evidence related to the mechanism described in the previous paragraphs. We have discussed that the largest rms are on average public and nancially unconstrained rms. We have also mentioned that these are the rms that are driving the increase in lobbying as a result of the increase in production. If this is true, we should observe in the data that public rms expand during the credit crunch. Evidence provided by Shourideh and Zetlin Jones (2016) goes in this direction. Consistent with this mechanism, they show that the production of public rms increased during the last nancial crisis.

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# 6.2.2 Lobbying for Capital Tax Benets and Misallocation

To evaluate the role of lobbying for capital tax benets for the dynamics of the economy, I simulate a credit crunch of a similar magnitude to the benchmark economy but abstract from the possibility of lobbying. In order to do this counterfactual, I set the lobbying xed cost _fl →∞_ and re-calibrate the model to compute the counterfactual steady state and the corresponding transition after the credit crunch. The results of this experiment for GDP are displayed in the left panel of gure (14) under the label No Lobbying (green dotted line). The model without the lobbying mechanism predicts a milder recession in comparison to the benchmark economy. Relative to each particular steady state, the model without lobbying generates a decline of GDP by the end of 2009 of 4.5% versus a reduction in the full model of 5.9 % . This result indicates that lobbying for capital tax benets amplies the aggregate eect of the credit crunch by 1.4% of GDP, or that almost 24 % of the reduction of the GDP by 2009 can be attributed to the lobbying mechanism.

The dierences between the two dynamics for GDP can be mainly attributed to the aggregate productivity of the economy. The right panel of gure (14) contrasts the evolution of the benchmark economy with the one coming from the model without lobbying. The latter has a decline at the trough of the recession of 2.65 % relative to the steady state, while the benchmark model suered a reduction of 4 _._ 4% _._ This means that 1.77 % of the decline in TFP would be associated with the amplication eect of lobbying.

In order to understand the forces driving the dierences across these two models, it is useful to look at the reallocation of capital that results from the credit crunch in both models. As seen in gure (15), the dierence in the dispersion in the marginal product of capital generates much of this dierence. The green dotted line in the gure is the counterfactual dynamics of the model in the absence of lobbying for capital tax benets. We see that the dispersion increases in both models, but the reallocation of capital triggered by the credit crunch is larger when we allow rms to lobby for capital tax benets. With the reduction in the interest rate, unconstrained rms that were doing lobbying prior to the credit shock now increase their demand for capital. Because lobbying is an increasing function of the amount of capital and rms can extract more rents according to lobbying, the marginal product of capital of these rms goes down even further and capital expands even more (see equation (11)). On the other hand, in a model with lobbying, constrained rms are facing tighter nancial conditions after the shock: in an economy with perfect capital markets, they would like to expand relatively more in a model with lobbying than in a model without lobbying. Finally, there is an extensive margin of lobbying. The reduction in the interest rate makes lobbying protable for some rms, generating an additional source of variation of the marginal product of capital given that these rms now expand relatively more than in a model without lobbying for capital tax benets. The model predicts that the fraction of public rms doing lobbying increases to 9.7 % by 2009, consistent with the surge in lobbying activity at the extensive margin documented in section (3.1). Combining these eects, the disperison in the marginal product of capital increases relatively more with lobbying.

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In order to decompose the eects of the extensive margin and the intensive margin of lobbying, I propose another counterfactual. Because the credit shock induces an increase in lobbying at the intensive margin as a result of the decline in the interest rate and the subsequent increase in the demand for capital, to study the contribution of this change in lobbying intensity on misallocation I propose a counterfactual where I keep the level of lobbying constant at the initial steady state values. In other words, I allow rms to lobby for capital tax benets, but I prevent them from reacting to the new environment by changing the level of lobbying. What the model captures with this exercise is the increase in misallocation that results only from the increase in the fraction of lobbying rms. As we can see in gure (14), the eects are almost identical to the case where we do not have lobbying. Even though the fraction of lobbying rms increases and the dispersion of the marginal product of capital increases as a result of more rms doing lobbying, the eects on TFP and output are negligible. This result suggests that almost all the increase in misallocation from the model with lobbying is generated by the intensive margin.

# 6.2.3 Testing Implications for Lobbying and Tax Rates

We have discussed the ability of the model to reproduce some of the most salient features of the U.S. credit crisis of 2007-2009, including the aggregate lobbying behavior in the economy. Here, I assess the performance of the calibrated model to match the empirical patterns documented in section (3).

# Changes of Eective Tax Rates

Using data from Compustat, Section (3) established that after the nancial crisis the eective tax rates paid by lobbying and non-lobbying rms declined sharply. In addition, consistent with the observed increase in lobbying activity for taxation, the decline is more drastic for lobbying rms.

Figure (16) compares the data and the model. For the model, I compute the eective tax rates for lobbying and non-lobbying public rms and I compute the cumulative change with respect to the value in 2007 for each case.<sup>51</sup> The data shows dierences with respect to the tax rate in 2007.

In the case of the eective tax rate of lobbying rms, the left panel of gure (16) shows that the model ts the general pattern of the average tax rate for lobbying rms after the credit shock. In particular, it captures 53 % of the decline in the eective tax rate by 2009. With the credit shock, lobbying rms start increasing their lobbying activity and as a result the amount of tax benets they are obtaining is bigger. In addition, the amount of capital these rms are using is also higher, which also reduces the eective tax rate. As a result, the tax rates for those rms start declining until 2009. After bottoming in that year, the model converges to the steady state faster than in the data. This is explained partly because the interest rate returns to the steady state level after that period, inducing a reduction of the capital demand for public rms and in lobbying eort. Following that retraction in capital and lobbying, the amount of tax benets goes down.

> 51In order to map the model to the data, I use the procedure described in section 5 to assign rms to the private and public groups.

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For the eective tax rate of non-lobbying rms, the general picture applies. The model captures the evolution of the average tax rate for that group pretty well until 2009. Similarly to lobbying rms, public non-lobbying rms on average expand. Because these rms are richer than private rms, typically they are not nancially constrained and they react to the decline of prices with an expansion of production. Consequently, the demand for capital after the credit crunch increases and the amount of tax benets claimed accompanies the pattern of capital until 2009. After that, it returns back to steady state while the data keeps falling for one additional period of time. At that point, we see that the tax rate of non-lobbying rms turns around and starts returning to the pre-crisis value. Overall, the model performs surprisingly well in accounting for the decline in tax rates for lobbying and non-lobbying rms.

# Increase of the share of Lobbying Expenditure of Sector 2

Using data on lobbying for taxation issues, section (3) established that sectors that rely more on external nance increased their participation in total lobbying expenditure during the last nancial crisis.

In the model, the presence of the xed cost _f_ 2 _> f_ 1 aecting the collateral constraint makes sector 2 more dependent on external funds and more capital intensive. We have seen in table (10) that the model over predicts the share of lobbying expenditure in that sector (65 % in steady state versus 53 % in the data). Here, I evaluate the performance of the model over time after the crisis. Figure (17) displays the dierence with respect to the steady state for the model, and the dierence from 2007 for the U.S. data. As in the data, the model generates an increase in the participation of the sector that depends more on external nance (sector 2) after the credit shock. In addition, the model also picks the same year in comparison with the data. However, it cannot capture the magnitude of the change: for the data, by 2010 the share of lobbying expenditure for taxation issues increases by 9 _._ 1% , while the model increases by 2.3 % _._ In other words, the model accounts for almost 25 % of the change in the share of lobbying expenditure incurred by those sectors that rely more on external nance. Finally, note that the model is successful in capturing the inverted U-shaped pattern of the data. However, and once again, it seems to be returning to the levels of the pre-crisis period in a shorter period of time.

# Size-Dependent responses

In section (3.4) I showed that the response of rms with dierent sizes depends on external nancial dependence (EFD). In particular, large rms in both sectors as well as small rms in sectors less dependent on external nance increase their lobbying expenditure relative to the pre-crisis period. Only small rms in sectors that rely more heavily on external nance exhibit a reduction in lobbying activity. In addition, sectors that depend more on external nance have larger dierences in the change to lobbying expenditure due to the crisis. Next, I test the ability of the model to deliver those results based on a simulated model-based regression.

37
To consider the rm-level implications of the model for lobbying after a credit crunch, I simulate a sample of 500,000 rms from the model and follow them for four periods after the shock, keeping track of the size in terms of employment. In section (3.4) I use the small-medium rm (SME) label for a rm with fewer than 500 employees following the classication used by the Trade Commission. The data from the Business Dynamics Statistics (BDS) for 2007 shows that the employment share of rms with fewer than 500 employees was equal to 50.4 % _,_ which is almost equal to the median of employment. In order to map my model to the size variable I look for the employment size such that below that level the employment share is equal to 50.4 % . Then, I classify those rms below that level as SME and those above that as a large rms. As before, sector one in the model is represents sectors that rely less on external nance and sector two represents the remaining.

Table (11) reports the results of running the regression on equation (1) using the simulated data and it reproduces the same results from section (3.4). To run this regression, I control for the same variables as in the empirical regression (capital, asets and sales). The table decomposes the results into two groups, low external dependence and high external dependence sectors. The model delivers almost all the signs of the regression, but misses the change in lobbying expenditure for small-medium rms in the sectors that relies less on external nance. While the data delivers a positive correlation, the model displays a negative one. Nevertheless, that coecient is not statistically signicant in the data. The model captures the sign of the changes for lobbying expenditure before and after the crisis for 3 groups: large rms in sectors that depend less on external nance; small-medium rms in sectors that rely more on external nance; and large rms in sectors that rely more on external nance. The model-based regression nds that the change in lobbying expenditure for small-medium rms in the sectors that rely less on external nance should be negative. In the data, the coecient was found to be negative. However, given that the coecient is not statistically signicant and close to zero, the negative coecient coming from the model it is certainly possible.

In the model, a reduction in input prices implies an increase in capital demand and lobbying activity for unconstrained public rms in both sectors. This mechanism drives the signs in the model based regression for the change in the intensity of lobbying in column (4) for rms in the low external dependence sector and in the high external dependence sector. On the other hand, with the credit crunch some public rms become nancially constrained in the model and therefore the amount of capital used is lower than before. According to the model, the lobbying expenditure of those rms is also smaller and this eect drives the signs in columns (3) for both groups of rms.

To summarize, the evidence provided in this section shows that the modeling strategy is successful in capturing the micro level implications of lobbying during a nancial crisis. In addition, it reinforces the validity of the calibration strategy. Together, these two features imply that the model could be used to study policy relevant questions with the certainty that the model represents closely the most salient features of this activity.

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# 6.3 Normative analysis: Long-Run Counterfactuals

In the previous sections I discussed the implication of lobbying at the business cycle frequency for output, TFP and micro-level implications. However, the model is also useful to answer questions related to the long run behavior of the economy. To that end, I propose several exercises that are relevant for policy and normative analysis.

## 6.3.1 Role of Misallocation in the Long-Run

In this experiment I try to assess the impact of lobbying on total factor productivity in the long run. Since lobbying acts as a subsidy on capital, eliminating this distortion has an impact on capital accumulation. Considering that rms can no longer get access to the preferential tax treatment that made them larger, there will be a reduction in the demand of capital. As a result, the capital stock in the economy would go down. To counterbalance this aggregate eect, and in the spirit of Restuccia and Rogerson (2008), I adjust the corporate tax rate _τ_ so that the capital stock in the new steady state is the same as the initial value. In this sense, I am focusing on the TFP eects associated with the elimination of lobbying through reallocation of capital and selection. Operationally, I take the xed cost of lobbying ( _fl_ ) to innity so that no rm can do lobbying in the new steady state and at the same time I reduce the corporate tax rate.

Column 2 in Table (12) shows selected statistics such as aggregate output, capital, consumption, wage and total factor productivity (TFP) for this experiment relative to the benchmark economy when both are in steady state. We can see that output and TFP increase by 0.7 % and 0.9 % respectively without lobbying. As discussed in section (4.2), lobbying increases the dispersion of the marginal product of capital relative to an economy without lobbying. Then, banning this activity implies gains in eciency on the production side. An important point to stress is that the gains are larger in the second sector, which is the one where lobbying is more intensive. Because of this dierential intensity of lobbying, the dispersion in the marginal product of capital is larger in that sector. Finally, notice that the combination of these policies increases the number of rms in the economy. Although wages are going up and therefore labor is more expensive, the reduction in the tax rate that the government is proposing makes running a rm more protable for a group of agents.

## 6.3.2 Institutional Reform: Banning Lobbying

In the previous exercise I discussed the eects of banning lobbying while at the same time reducing the corporate tax rate in order to keep the level of capital constant. In this counterfactual I propose to analyze the full eect of banning lobbying without adjusting the corporate tax rate.

The results for the rst experiment in the new steady state are shown in column 2. Relative to the benchmark steady state we observe that output decreases 1.2 % , capital used for production is 4 % lower, TFP has an increase of 0.8 % , and consumption goes up almost 1% .

39
The outcomes from this experiment follow from dierences at both the intensive and the extensive margins of production. At the intensive margin, incumbent rms are negatively aected due to the elimination of the lobbying activity that was used in the benchmark equilibrium by constrained and unconstrained rms. As I previously discussed, the capital stock in this economy declines due to the lower incentive to accumulate assets in order to exploit the tax benet schedule. The reduction in capital accumulation comes from three forces. Because lobbying generates an increase in the optimal size of rms, without this force rms reduce capital demand and therefore there has to be a downward adjustment in savings for these rms. Second, with lobbying, some rms accumulate wealth with the expectation that at some point they will be able to lobby. Abstracting from this activity removes this force and therefore there is a reduction in savings. Third, lobbying allows some nancially constrained rms to increase saving in order to overcome nancing constraints. Absent lobbying, those rms reduce their saving decisions and reduce capital accumulation.

In section (4.2) I discussed the implications of the tax benet schedule on misallocation and selection. Without lobbying, we see that TFP in the economy goes up, indicating some misallocation as a negative consequence of lobbying. This is reected in the decrease in the marginal product of capital in the counterfactual scenario.

At the extensive margin, there is a small increase in the number of rms in the economy, explained by the decline in wages and interest rate resulting from the reduction in inputs. However, this increase in new producers is counterbalanced with a decline of the average size of rms (measured using labor or capital, since both are complements) and in the capital to labor ratio of the economy as a whole and in both sectors.

Finally, lobbying seems to be welfare improving as suggested by the decrease in total consumption when we move from the benchmark economy to an economy without lobbying. Lobbying increases factor demands, drives up wages and prots that more than compensate the increase in savings. However, we need to be careful about this last statement, which only considers consumption levels between steady states. In order to consider the implications for welfare, we should also take into consideration the transition from one steady state to the other. I consider this in section (6.3.4).

# 6.3.3 Fiscal Reform: No Heterogeneity in Eective Tax Rates

The evidence shows that eective tax rates that public rms pay are lower than the 35 % that the law establishes. In addition, there is a lot of heterogeneity even within this set of wealthy and large producers. Since the government is losing a considerable amount of resources to this group of rms that could be used for health, social security or foster small business growth, lobbying policy is an issue of constant debate in the media and the policy arena.<sup>52</sup> Other arguments point to the `unfairness' of lower tax rates for big corporations and the distortions that tax breaks generate to the economy.

In order to contribute to this debate, the second experiment proposes to take out all the sources of

> 52See the report by the Goverment Accountability Oce (GAO 2013) or McIntyre et al. (2011) as examples in this debate.

40
variation in the eective tax rate while at the same time keeping the government's revenue constant. The economy starts in steady state, and the government decides to restrict lobbying ( _fl →∞_ ) and abolish the existence of common components of capital tax benets. Because this implies that rms now face a higher eective tax rate, the government lowers the corporate tax rate in order to keep the revenue constant taking in consideration the revenues generated during the transition to the new steady state. Technically, the government keeps the revenue constant in present value terms.

This experiment measures the aggregate eects of equalizing the eective tax rate for all rms. In other words, if all rms face the legal corporate tax rate, what would be the macroeconomic consequences. According to the quantitative results, the corporate tax rate necessary to satisfy the same present value of revenue is equal to 31%. Column 3 of table (12) presents the results for this experiment. This counterfactual implies a reduction in long run output of 2 _._ 5% , an increase of 1.1 % in TFP, and an increase in consumption of 1.3 % . We see that misallocation is reduced due to the decrease in the dispersion of marginal product of capital, which is reected in the increase in TFP. As discussed in (4.2), the introduction of the tax benet schedule increases the dispersion of the marginal product of capital relative to an economy with nancial frictions. Then, by making all rms pay the same eective tax rate we are abstracting from that source of variation and increasing eciency in production.

Regarding capital, we see that in this economy it declines 9.4 % for the same reason studied before: without any tax rebate associated to capital the optimal size of all rms shrink. With a lower optimal size, the demand for capital of rms will be lower in the aggregate, the incentives to save will be smaller, and the capital stock of the economy contracts.

Dierent from the previous case, we observe that consumption in this economy rises 1 _._ 3% as a result of the decline in savings. Because the optimal size of rms is smaller, it is not necessary to keep the levels of assets as in the benchmark economy.

# 6.3.4 Welfare

In this subsection, I turn my attention to the computation of welfare. First, I analyze the welfare implications for banning lobbying. Then, I compute the welfare implications for the scal reform.

For the case where we ban lobbying, we have seen that consumption in the new steady state declines. From there, we would be tempted to infer that welfare in this economy would be lower. However, in order to compute welfare, the correct comparison should consider the full transition path between steady states since that implies a sequence of consumption that are not incorporated when looking at steady states.

Denote the aggregate welfare in the benchmark stationary equilibrium by _W∞_<sup>_full_.Thisvalueis</sup> computed by integrating the individual value functions with respect to the invariant distribution of wealth and ability, accounting for each type of agent: 41
where _vs_<sup>_full_</sup> ( _a, z_ ) for _s ∈{_ 1 _,_ 2 _}_ is the individual value function in steady state of the benchmark model of agent of type _s_ , and _gs_<sup>_full_</sup> _∞_<sup>(</sup><sup>_a, z_)for</sup><sup>_s∈{_1</sup><sup>_,_2</sup><sup>_}_isthejointprobabilitydistributionfunction</sup> for agents of type _s_ in the stationary equilibrium of the benchmark model.

To compute the welfare change Θ from eliminating lobbying, I construct the permanent consumption compensation necessary to make an individual indierent between the benchmark stationary equilibrium and an economy with no lobbying but with nancial frictions and capital tax benets, accounting for the transition. This expression is given by where _WTr_<sup>_nlob_</sup> is the lifetime welfare of transitioning from the benchmark economy to an economy that forbids lobbying. This welfare value is given by where _vs_ ( _a, z_ ) for _s ∈{_ 1 _,_ 2 _}_ is the value function that takes into account the transition from the benchmark stationary equilibrium to the new stationary equilibrium. In other words, _vs_ ( _a, z_ ) is the instant value after the change in policy.

The quantitative results show that there is welfare gain of 0.3 % while banning lobbying, or a welfare cost of 0.3% of keeping it. By comparing steady states, we obtain that welfare decreases by 0.9%. The inclusion of the transition implies an osetting eect over the welfare calculation derived from comparing steady states.

In the case of the scal reform, if one looks at the steady state we observe that consumption increases. Then, welfare goes in the same direction as the transition and the scal reform generates a welfare gain of 1.1%.

# 7 Conclusions

In this paper, I document the increase in lobbying activity to aect the tax code that took place during the 2007-2009 U.S. nancial crisis. Based on Compustat data matched with lobbying expenditure at the rm level, I show that this increase in rent-seeking behavior was driven by large rms in sectors that rely more on external sources of funds to nance capital expenditure. Based on this evidence, and given the creation and extension of tax provisions during that time, I study whether lobbying amplies the misallocation created by the nancial frictions when the economy suers a credit crunch.

To address this question, I use a model with nancial frictions in the form of collateral constraint and a government that grants tax benets associated to capital and can be inuenced through costly lobbying pressure. In this economy, all rms can claim tax benets that are tied to capital. However, rms that decide to lobby can also modify the tax code to obtain preferential tax treatment on top 42
of a common component. In order to lobby, rms have to pay a xed cost, and as a result there is selection into lobbying activity where only a small fraction of rms engage in this activity.

The presence of lobbying in an environment with nancial frictions simultaneously generates positive and negative eects on misallocation. Consequently, the eects are not unambiguously determined and depend on which force dominates. To study the aggregate eects of the credit shock, I calibrate the model using micro-data on lobbying expenditure and eective tax rates that corporations paid before the crisis, and I calibrate the credit shock to replicate the observed decline in the ratio of external nance to capital for the non-nancial corporate sector.

One of the main ndings of the paper is that lobbying increases the misallocation of resources that arises with nancial frictions when the economy receives a nancial shock. The presented model accounts for 80% of the decline in output and almost all the decline in TFP observed in the data by the end of 2009. Compared to an economy without lobbying, I nd that the lobbying economy amplies the distortions produced by nancial frictions, leading to a one-third larger decline in output. The model is also able to capture the increase in lobbying activity observed in the data, as well as the impulse responses of rms according to size and industry nancial dependence.

A derived implications is that, not only it is important to have policy tools during these events, but it is even more important how the policy is designed in order to be eective. As we have seen, the government provides tax advantages, but most of those resources are assigned to unproductive and wealthy rms, enhancing the misallocation of resources. In this environment, and given the same scal cost, policies that subsidize credit to those rms in distress are more eective to foster the recovery.

Finally, the paper also discussed long run implications of lobbying and policy reforms, focusing on output and TFP. Banning lobbying implies that in the long run output is lower due to a decline in capital accumulation, and TFP increases as a result of lower misallocation of capital. From a welfare perspective, this institutional change implies a gain of 0.3%. In terms of policy, an elimination of all capital tax breaks while keeping the revenue neutral through reductions in the corporate tax rate have similar results in terms of signs, but the magnitudes are magnied. In this case, welfare increases by 1.1%.

One limitation of the analysis is the fact that rms can only adjust the production margin with the nancial shock, which is a direct result of the perfect competition framework. However, the empirical evidence suggests that market power is a relevant feature in modern economies and therefore rms can also adjust prices during a downturn. The interaction between nancial conditions and market power has been studied by Giuliano and Zaourak (2015) and by Gilchrist et al. (2015). The incorporation of market power in this framework is left for future research.

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