EconomicDynamics Research Agenda

Volume 24, Issue 1 (April 2023)

Corina Boar and Virgilu Midrigan on “Market Power, Taxes and Inequality”

Corina Boar is an Assistant Professor in the Department of Economics at NYU and a Research Economist at the Federal Reserve Bank of Minneapolis. She is also a Faculty Research Fellow at the NBER and a Research Affiliate at the CEPR. Her research areas are Macroeconomics, Consumption, Inequality, Entrepreneurship. Boar’s profile.

Virgiliu Midrigan is the William R. Berkley Term Professor of Economics And Business in the Department of Economics at NYU. He is also a Research Associate at the NBER. His research areas are Macroeconomics, Monetary Economics, and International Finance. Midrigan’s IDEAS/RePEc profile.

1 Introduction

Our joint work seeks to understand the macroeconomic, distributional and welfare implications of various policies aimed at curbing inequality. In recent decades, the United States has experienced a sharp increase in income and wealth inequality, with the income share accruing to the richest 1% increasing from 10% in the 1980s to 20% today. Wealth inequality is even more pronounced: the wealthiest 1% in the United States hold more than 40% of all the wealth. There is a lively ongoing debate as to what may have caused these trends, but three explanations have emerged as particularly noteworthy. The first is that technological innovation and international trade have disproportionately impacted low-skilled workers; the second is the decline in top income tax rates; and the third is an increase in product market concentration and monopoly power. This increase in inequality has led to numerous policy proposals for redistribution by increasing marginal income taxes at the top, introducing a wealth tax and implementing product market policies aimed at curbing the increase in product market concentration and markups. The goal of our work is to understand the macroeconomic, distributional and welfare implications of these proposals so as to determine their effectiveness and help inform future policy decisions.

Markups and Inequality

Our paper on markups, Boar and Midrigan (2022b), is motivated by the growing concern that the increase in markups and product market concentration documented by Autor et al. (2020), De Loecker et al. (2020), Hall (2018) has led to a redistribution of income from workers towards firm owners. Since the ownership of firms, both public and private, is highly concentrated in the United States, these trends may have markedly increased inequality. This concern has led to numerous calls for competition policy to implicitly incorporate distributional concerns, not just concerns for maximizing production efficiency (Stiglitz2012Atkinson2015Baker and Salop2015Khan and Vaheesan2017).

Existing research in which markups emerge endogenously as a function of the competitive pressures a firm faces, such as Atkeson and Burstein (2008), ?Bilbiie et al. (2019) and Edmond et al. (2018), assumes a representative household that owns all firms; this research thereby abstracts from distributional considerations. In these settings, markups solely distort production choices. They do so via two channels. First, a high average level of markups is akin to a uniform tax that depresses production: if prices are on average too high relative to marginal cost, firms produce too little relative to what is socially optimal. Second, differences in markups across producers lead to a suboptimal allocation of factors of production across firms. High markup firms sell too little, and thus have a higher marginal product relative to lower-markup firms, an effect that reduces total factor productivity, as in the work of Hsieh and Klenow (2009) and Baqaee and Farhi (2018).

In an environment with perfect consumption sharing, these production inefficiencies can be remedied by introducing production subsidies that are proportional to each firm’s markup. Since firms that have a larger market share tend to have higher markups, in standard theories of oligopolistic or monopolistic competition and in the data, restoring production efficiency requires firm-specific subsidies that further increase the market share of large firms. These, in turn, increase their markups (as measured by the ratio of the after-subsidy price to marginal cost) and market concentration even further. Provided these subsidies can be financed with lump-sum transfers, they make the representative household, which owns all the firms, better off. Intuitively, the higher taxes are more than offset by the increase in the wage, capital and profit income. Since the latter is rebated back to the representative consumer who owns all firms, an increase in markups and product market concentration unambiguously benefits everyone.

Our work departs from this representative consumer setting. In the economy we study, firm ownership is highly concentrated, so an increase in markups and profits redistributes income from workers – via a reduction in real wages – to firm owners – via an increase in profits. Our analysis focuses solely on policies that change the firm size distribution and thus the amount of competition faced by individual firms, not policies that alter the overall level of production. As is well understood, the latter can be mimicked with labor and capital income taxes, which have been extensively studied in both public finance and macroeconomics, so we focus our analysis on the more novel considerations introduced by endogenously variable markups. We thus study the problem of a utilitarian regulator who can shape the degree of product market concentration, but is restricted to revenue-neutral interventions whereby subsidies that finance an increase in production in some firms must be financed by taxes on other firms, not other sources of household income.

One difficulty we have to confront is that in reality, product market interventions take many forms: for example, restrictions on market shares and prices or size-dependent production taxes. We thus opt to proceed in two steps. The first part of our paper studies a static economy in which we use a Mirrleesian mechanism design approach to characterize optimal product market interventions. The advantage of this approach is that we do not have to exogenously restrict the space of instruments the regulator can use. We then extend our analysis to a richer dynamic setting in which, motivated by the results of the static model, we consider size-dependent production subsidies and taxes that alter the firm size distribution.

In our static economy, we build on the approach of Baron and Myerson (1982), who study the problem of regulating a single monopolist. In contrast to their work, ours considers the problem of regulating all firms, taking into account how interventions shape the firm size distribution and equilibrium prices. As in the Mirrleesian literature, we assume that the regulator does not observe the ability of individual producers and thus faces incentive compatibility constraints. These constraints generate informational rents, which increase with the amount of output the regulator prescribes that an individual firm produces, as well as with the equilibrium wage. (In our static setting in which the number of producers is exogenously given, the regulator’s problem is trivial in the absence of information frictions: it levies a 100% profit tax on all firms and uses it to finance subsidies that restore production efficiency.)

We use optimal control techniques to characterize how the regulator’s prescribed quantity choices vary with firm productivity. Since we restrict attention to interventions in the product market, the regulator recognizes that it can increase the welfare of the workers only by increasing the equilibrium wage or, equivalently, by reducing firm prices. A robust result that emerges is that optimal regulation prescribes more product market concentration than observed in the data. Perhaps surprisingly, the more the regulator values the welfare of workers, the larger is the optimal degree of product market concentration. This is because product market interventions that encourage large firms to expand have two effects: they improve allocative efficiency by shifting inputs towards more productive firms, and they increase the labor share of output. Both of these effects increase the equilibrium wage. In fact, depending on the regulator’s weight on the welfare of the workers, it may choose to increase product market concentration by even more than required to fully restore production efficiency. In this case, the optimal intervention reduces aggregate productivity, but the resulting increase in the labor share more than compensates for the loss in efficiency and leads to an increase in the equilibrium wage.

We show that one can implement the optimal policy in the static setting with a size-dependent tax/subsidy on production. Though highly non-linear, the tax/subsidy schedule can be well-approximated with a simple three-parameter function similar to that used in the literature on optimal income taxation (Heathcote et al.2017), a result reminiscent of the findings of Heathcote and Tsujiyama (2019) in the context of labor income taxation. We find the simple function useful because each parameter (the lump-sum transfer, the average tax rate, the slope of the marginal tax schedule) is easily interpretable and allows us to build intuition for the nature of optimal product market interventions.

Motivated by these results, we extend our analysis to a dynamic setting in which privately held businesses compete alongside publicly traded firms, and households face uninsurable idiosyncratic risk and save in capital, equity and government bonds. A government provides redistribution via income taxes and transfers. This economy reproduces the degree of income and wealth inequality in the United States and the concentration of firm ownership, and it allows us to undertake a quantitative investigation of the effects of product market regulations. We restrict interventions to the three-parameter production subsidy class and calculate optimal policy, explicitly taking into account the long-lasting transition dynamics of the wealth distribution following policy interventions. Once again, we find that optimal policy greatly increases the market share of large firms, substantially reducing product market misallocation.

We thus conclude that product market concentration is not necessarily costly, even in an economy with highly concentrated firm ownership. What is costly are dispersion in the marginal product of capital and labor across producers and wedges that depress wages and interest rates. Our results thus caution against the widely-held view that reducing the market power of large firms unambiguously helps the poor. Though reducing concentration would indeed reduce monopoly power and markups in our model, the interventions required to do so have the unintended consequence of also reducing the labor share of income and aggregate productivity, and thus the equilibrium wage.

For reasons of tractability, we focus our analysis in this paper on a setting of monopolistic competition with a continuum of atomistic firms. The advantage of models of monopolistic competition is that they are tractable and can be used to study the dynamic effects of policy interventions. Unfortunately, such models do not allow one to study the impact of mergers among rivals that sell closely substitutable goods and evaluate anti-trust policies. We believe that a fruitful and exciting area of future research would be to explicitly introduce oligopolistic considerations as in Atkeson and Burstein (2008) and evaluate the implications of merger and antitrust policies, taking into account their distributional and efficiency implications. Additionally, in our analysis, we assume that firms are price-takers in the input market. A natural question that arises is what the effect of policies that change the degree of product market concentration is if larger firms also enjoy more monopsony power.

Efficient Redistribution

Concerns about increased inequality have led to numerous proposals aimed at curbing it and improving the welfare of the poor. Among these, proposals to introduce a wealth tax and increase marginal income taxes at the top have received particular attention in both academic and policy debates. One conclusion that permeates many quantitative studies of the pros and cons of such policies is that in an economy characterized by a large degree of wealth and income inequality, such as the United States, such policies unambiguously increase utilitarian welfare. Intuitively, a welfare objective that places equal weights on all households favors redistribution from wealthy households, whose marginal utility of consumption is low, to poor households, who value consumption a lot on the margin. Thus, despite the negative output consequences of such policy reforms, they increase utilitarian welfare.

Our starting point in our paper on this topic, Boar and Midrigan (2022a), is the observation that when policymakers have multiple instruments at their disposal, any way of achieving redistribution (e.g., increasing the level of marginal tax rates or the slope of the marginal tax schedule, or taxing wealth) increases the welfare of the poor, provided the revenue raised from tax policy reforms is used to finance lump-sum transfers that disproportionately benefit the poor. The question we therefore tackle is: What is the optimal combination of policy reforms that increases welfare?

Since we are wary about our results being sensitive to a particular welfare criterion, we consider various welfare objectives that place increasingly higher weight on the welfare of the poor. These include one that maximizes average consumption-equivalent welfare, a criterion that seeks to solely maximize productive and allocative efficiency, one that maximizes utilitarian welfare, and a Rawlsian objective. We study the optimal shape of non-linear income and wealth tax schedules in a setting with partially uninsurable idiosyncratic risks that reproduces the degree of wealth and income inequality in the United States, and takes into account the long-lived transition dynamics following changes in tax policy. The revenue raised with income and wealth taxes is used to finance lump-sum transfers to households.

Our main finding is that although introducing a wealth tax, increasing the level of marginal income taxes or making the marginal income tax schedule steeper can, in isolation, raise enough revenue to increase the welfare of the poor, the marginal gains from such policies are small relative to those obtained from a simple uniform flat tax on both capital and labor income. In our baseline calibration, which focuses on a utilitarian objective, the welfare gains from an optimally chosen flat and uniform tax are equivalent to a 7.4% permanent increase in consumption for all households. Allowing for upward-sloping marginal income and wealth tax schedules increases these gains to 8.5%, a relatively modest gain.

Interestingly, we also find that the households that benefit from a richer set of tax instruments are those in the middle of the distribution, not the poorer ones. The welfare of the latter actually falls when the tax system features non-linear income and wealth taxes. The intuition for this result is that a richer set of tax instruments allows the planner to reduce the marginal income taxes paid by households in the middle to lower end of the distribution at the expense of lowering lump-sum transfers. The latter must fall because of the larger output and therefore income losses stemming from distortionary taxes at the top. Since lump-sum transfers are more valuable than lower marginal income taxes for the households at the bottom of the distribution, their welfare falls at the expense of the welfare of those in the middle of the income distribution when the planner levies a wealth tax or taxes top incomes relatively more. This result stems from the fact that an optimally chosen flat income tax is very high, 56% in our baseline calibration, so further increasing income or wealth taxes is highly distortionary. Importantly, we find that the stronger the planner’s preference for redistribution, the smaller the marginal gains from deviating from uniform flat income taxation.

Should We Tax Capital Income or Wealth?

Our paper on whether to tax capital income or wealth, Boar and Midrigan (2022c), is motivated by the observation that in the US private businesses are an important driver of both real economic activity and inequality. For example, privately-held businesses collectively produce 40% of all output. Though owners of private businesses represent only 12% of households, according to the Survey of Consumer Finances, they earn one-third of all income and hold one-half of all wealth. A natural question that emerges is: How should the income of private business owners be taxed?

In considering this question, two opposing forces emerge. On one hand, the rigid ownership rules that private businesses face make them much more reliant on internal saving and collateralized borrowing, relative to publicly held firms, which can more easily issue equity (Dyrda and Pugsley2018). Thus, these firms are more likely to be financially constrained and face relatively high and dispersed marginal rates of return on saving, as pointed out by a large literature on entrepreneurship stimulated by Quadrini (2000) and Cagetti and De Nardi (2006). Intuitively, a constrained entrepreneur has a high return on acquiring an additional dollar, since that dollar can be used to finance more capital and labor and thus bring the firm closer to operating at its optimal scale. As Guvenen et al. (2023) showed in a recent, influential paper, rate of return differences among entrepreneurs generate an important distinction between capital income and wealth taxation. Taxing capital income, which includes the profits of private business owners, prevents productive entrepreneurs from accumulating internal equity, depressing production choices, capital accumulation and equilibrium wages in the aggregate. An alternative policy that taxes wealth would fall disproportionately on less productive agents and therefore increase production efficiency. A wealth tax that replaces a capital income tax is thus an implicit subsidy to productive entrepreneurs and may raise aggregate efficiency, a point echoed by the work of Itskhoki and Moll (2019), who study development policies. On the other hand, since private business owners are much wealthier and earn more income on average, subsidies on entrepreneurship would greatly exacerbate wealth and income inequality. Taxing capital income may thus achieve substantial redistribution, and may be preferred by a utilitarian welfare criterion, despite the resulting efficiency and wage declines.

Our paper quantifies the relative importance of these two forces using a model in which a fraction of households run private businesses, compete alongside publicly held corporate firms and face shocks to both labor market and entrepreneurial ability. Privately-held firms face a collateral constraint that limits their ability to expand production and generate heterogeneity in rates on return on saving. We calibrate the parameters of the model to reproduce the distribution of wealth and income in the data, for both workers and entrepreneurs, as well as the relative size of the private business sector. The tax reforms we consider are once-and-for-all unanticipated changes in the tax on labor income, capital income and wealth. The government uses the tax revenue to finance government spending and lump-sum transfers. We focus on a utilitarian social welfare function and flat taxes, but show that our results are robust to considering alternative preferences for redistribution and allowing for non-linear taxes.

We find that taxing capital income is preferable to taxing wealth if the planner is restricted to using only one of these two instruments. This result is a consequence of two features of our quantitative model. First, in the model, as in the data, the wealth share of private business owners is very high, so the redistributive motive dominates the efficiency motive. Second, in our economy, financial frictions generate relatively modest amounts of allocative inefficiency and productivity losses. As Hopenhayn (2014) pointed out, wedges in the firm’s optimality conditions for capital and labor can also generate large TFP losses if they generate rank reversals – the less productive firms use disproportionately more capital and labor relative to their more productive competitors. Financial frictions do not generate large rank reversals: though they preclude productive firms from growing, they do not generate a strong negative rank correlation between firm productivity and input choices in a setting in which productive entrepreneurs can self-finance and grow out of their borrowing constraints. For this reason, the efficiency gains from wealth taxation are swamped by the redistributional consequences. For example, if one were to replace the capital income tax with a wealth tax, thus implicitly subsidizing entrepreneurship, the wealth share of entrepreneurs would increase from 44% in the initial steady state to 75%. Though the losses from misallocation would indeed fall, since these are small to begin with (1.3% in the initial steady), the resulting halving of the productivity losses is dominated by the large increase in inequality.

In deriving our results, we keep the model purposefully simple to highlight the tradeoff between efficiency and redistribution induced by wealth and capital income taxes. In doing so, we abstract from a number of considerations, such as occupational choice, life-cycle dynamics, and inefficiencies due to markups. We believe that incorporating those dimensions into the analysis of tax policy is an important avenue for future work.

Why Are Returns to Private Business Wealth So Dispersed?

Our most recent paper starts from the observation that private businesses are characterized by an enormous amount of heterogeneity in rates of return on net worth (equity). For example, Fagereng et al. (2020) use Norwegian administrative data to document that the mean annual return on private business wealth is equal to 10%, with a standard deviation of 52%. These returns are much larger and much more dispersed than returns on financial wealth: in their sample period, the mean return on financial wealth is only 1%, with a standard deviation of 6%. The question we ask in Boar et al. (2023) is: What are the macro-economic and micro-economic consequences of the heterogeneity in returns to private business wealth?

In theory, accounting measures of return accrue to two factors. First, entrepreneurs may receive income owing to their human capital, entrepreneurial ability, or monopoly power their product may command. We think of this as a fixed factor and model it, following Lucas (1978), as arising from limited span of control. Second, private business owners may be financially constrained. Financial frictions may therefore drive a wedge between the marginal product of capital and labor and their respective prices and thus generate positive excess returns. We refer to the latter as marginal (or financial) returns, to distinguish them from average (or accounting) returns. Unlike the latter, which are typically observable, marginal returns to wealth are not readily available, since they answer a counterfactual question: How much would a firm’s income increase if it received an additional dollar of wealth?

The goal of our paper is to use micro data from Orbis on firm balance sheets and income statements, together with a model of firm dynamics under financial frictions, to understand the importance of financial frictions in generating dispersion in marginal returns and quantify their micro-economic and aggregate implications. We document a number of salient features of the data. First, in our sample, as in existing work, average returns to private business wealth are dispersed and persistent. Second, we show that firms in the data experience large and fat-tailed changes in output that are not fully accompanied by changes in their capital or wage bill and therefore generate large changes in the labor share, capital output ratio and firm profits. Since labor is the more intensively used factor of production (the labor share in value added exceeds 70% for firms in our sample), high-frequency fluctuations in a firm’s labor share account for the bulk of fluctuations in accounting profits.

We interpret this evidence using a model that follows Quadrini (2000), Cagetti and De Nardi (2006) and Buera et al. (2011) in assuming that each firm is owned by a single entrepreneur who can only partially insure against the business income risk by saving in a risk-free asset. Motivated by the high-frequency inflexibility of both capital and labor, we assume that firms choose capital and labor before observing their productivity in a given period. Despite the simplicity of this assumption, it allows us to match the high-frequency comovement of capital and labor with output very well. This time-to-build assumption generates a wedge between the marginal product of inputs and their price that reflects the risk premium stemming from the positive covariance between the entrepreneur’s productivity and its consumption. As the entrepreneur’s wealth grows, consumption becomes more and more insulated from the fortunes of the business, which allows the entrepreneur to take on more risk by expanding production. Risk therefore generates a positive marginal (financial) return on equity. In addition, collateral constraints prevent entrepreneurs from borrowing, so additional wealth relaxes this borrowing constraint, further increasing the marginal return on equity.

We focus our quantitative analysis on data from Spain, a country for which the Orbis dataset we use has particularly good coverage. All of the results we document, however, are robust across other countries. Matching the evidence requires that firms face large and fat-tailed shocks (both transitory and persistent) to their productivity. Such shocks lead to large changes in the firms’ profit share, consistent with the evidence, and imply an important role for risk, even though business owners have only a moderate degree of risk aversion. The model matches well the dispersion and persistence in average rates of return in the data, which range from 5% at the median to 35% at the 95th percentile.

We use the model to calculate the dispersion of marginal returns, to understand the sources of this dispersion, and to study the micro and macroeconomic implications of financial frictions. We find that expected marginal returns range from 2% at the 10th percentile to 17% at the 95th percentile and are three-fourths as dispersed as average returns. This dispersion in expected marginal returns is driven largely by risk, in contrast to models in which only capital is subject to time-to-build frictions. Intuitively, because the labor share is high, frictions that impede the adjustment of labor to productivity shocks have much large effects on profits and therefore the amount of risk faced by entrepreneurs.

We show that financial frictions have sizable micro economic consequences because they greatly depress firm production: in the absence of these frictions, the average business would be worth eight times more. In contrast, the macroeconomic consequences are more modest because of general equilibrium forces. Eliminating financial frictions altogether would increase aggregate productivity by only 6% and, assuming that labor is in fixed supply, aggregate output by 8%. These modest effects reflect that the losses from the misallocation of capital and labor in our economy are relatively low, even though the model reproduces the weak rank-rank correlation of 0.24 between wealth and productivity in the data. Our results therefore suggest that the macroeconomic gains from policies that increase the wealth share of productive entrepreneurs and thereby improve allocative efficiency are relatively low, consistent with Boar and Midrigan (2022a). Our results also suggest a need to further understand the effect of risk on firm behavior, which we view as a promising avenue for future research.


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