Corporate Tax Reform: Issues for Congress
Released: 2017-09-22T00:00:00

Summary:
Interest in corporate tax reform that lowers the rate and broadens the base has developed in the past several years. Some discussions by economists in opinion pieces have suggested there is an urgent need to lower the corporate tax rate, but not necessarily to broaden the tax base, an approach that presents some difficulties given current budget pressures. Others see the corporate tax as a potential source of revenue.
Arguments for lowering the corporate tax rate include the traditional concerns about economic distortions arising from the corporate tax and newer concerns arising from the increasingly global nature of the economy. Some claims have been made that lowering the corporate tax rate would raise revenue because of the behavioral responses, an effect that is linked to an open economy. Although the corporate tax has generally been viewed as contributing to a more progressive tax system because the burden falls on capital income and thus on higher-income individuals, claims have also been made that the burden falls not on owners of capital, but on labor income—an effect also linked to an open economy.
The analysis in this report suggests that many of the concerns expressed about the corporate tax are not supported by empirical evidence. Claims that behavioral responses could cause revenues to rise if rates were cut do not hold up on either a theoretical or an empirical basis. Studies that purport to show a revenue-maximizing corporate tax rate of 30% (a rate lower than the current statutory tax rate) contain econometric errors that lead to biased and inconsistent results; when those problems are corrected the results disappear. Cross-country studies to provide direct evidence showing that the burden of the corporate tax actually falls on labor yield unreasonable results and prove to suffer from econometric flaws that also lead to a disappearance of the results when corrected, in those cases where data were obtained and the results replicated. Many studies that have been cited are not relevant to the United States because they reflect wage bargaining approaches and unions have virtually disappeared from the private sector in the United States. Overall, the evidence suggests that the tax is largely borne by capital. Similarly, claims that high U.S. tax rates will create problems for the United States in a global economy suffer from a misrepresentation of the U.S. tax rate compared with other countries and are less important when capital is imperfectly mobile, as it appears to be.
Although these new arguments appear to rely on questionable methods, the traditional concerns about the corporate tax appear valid. While an argument may be made that the tax is still needed as a backstop to individual tax collections, it does result in some economic distortions. These economic distortions, however, have declined substantially over time as corporate rates and shares of output have fallen. Moreover, it is difficult to lower the corporate tax without creating a way of sheltering individual income given the low tax rates on dividends and capital gains.
A number of revenue-neutral changes are available that could reduce these distortions, allow for a lower corporate statutory tax rate, and lead to a more efficient corporate tax system. These changes include base broadening, reducing the benefits of debt finance through inflation indexing, taxing large pass-through firms as corporations, and reducing the tax at the firm level offset by an increase at the individual level. Nevertheless, the scope for reducing the tax rate in a revenue-neutral way may be limited.

subsections: section_title: Introduction
paragraphs: As Congress considers tax reform, an important and challenging component is the tax treatment of the corporation. Some proposals would cut the corporate rate by broadening the base, with an overall revenue-neutral treatment of the corporate sector, while others would propose raising or reducing revenues.
The traditional arguments surrounding the corporate tax, which largely focus on the distortions introduced by the tax, were a focus of a Treasury study issued in January 2017. This study also discussed choice of organizational form and international issues. The debate, however, has sometimes focused on arguments that cutting the corporate tax rate would stimulate economic growth, and even raise revenue, or on claims that the tax is a burden not on capital but on labor. Recently, Steven Mnuchin, Secretary of the Treasury, advanced the argument that the corporate tax is paid by workers, citing a recent study by Azémar and Hubbard as evidence. A recent news report indicated three additional articles referenced by the Treasury press office in support of the burden falling on wages (although the Treasury Office of Tax Analysis currently assigns most of the burden to capital income): studies by Randolph, Hassett and Mathur, and Lui and Altshuler.
Opinion pieces have referenced a variety of other studies that find large effects of corporate taxes on economic growth or that find the burden of the tax falls on wages, while others have expressed disagreement.
The current debate is similar to one that began over 10 years ago and might be viewed as the beginning of current proposals to cut the corporate rate and broaden the base. Before turning to the basic issues surrounding the corporate tax, it is useful to trace the discussion of issues and proposals for corporate reform.
In November 2005, President George W. Bush's Advisory Panel on Tax Reform reported on a variety of proposals for major reform of the tax system, including those for corporate and business income taxes. Hearings were held on these proposals in 2006, but no further action occurred. 
On July 16, 2007, The Wall Street Journal published an opinion article by Treasury Secretary Henry M. Paulson addressing concerns that the U.S. corporate tax rate is high relative to other countries and announcing a conference to be held July 26 that would examine the U.S. business tax system and its effects on the economy. The Treasury Department also released a background paper that addressed several issues associated with the corporate tax, and identified some base broadening provisions. An opinion piece by R. Glenn Hubbard, President Bush's first chairman of the Council of Economic Advisors, referred to the conference as well as to a study by Hassett and Mathur finding that the tax fell on labor and a study by Devereux considering the revenue-maximizing tax rate. Hubbard concluded by suggesting that cutting the corporate tax rate would reduce a tax that is largely, or even fully, borne by labor and that behavioral responses would offset much of the static revenue cost.
During the conference, discussions included whether business representatives would trade tax preferences for lower rates, whether reform should take the form of lower rates or write-offs of investments, and methods of avoiding the corporate tax by income shifting in a global economy. Some participants complained that the corporate tax is outdated, too complex, distorts decisions, and undermines the ability of firms to complete in a global economy. Echoing some issues raised in Hubbard's article, Kevin Hassett indicated that the corporate tax was not an effective way to raise revenues and suggested that lowering the rate would raise revenues.
At the time of the Treasury conference, Chairman Charles B. Rangel of the House Ways and Means Committee released a statement inviting the Bush Administration to discuss such issues as tax reform, especially the Alternative Minimum Tax (AMT), addressing tax havens, and increasing equity and fairness in the tax structure. Chairman Rangel introduced a bill, H.R. 3970 , on October 25, 2007, with a revenue-neutral subsection that included some of the base broadeners included in the 2007 Treasury study. The rate reduction, from 35% to 30.5%, was not as large as that discussed in the 2007 Treasury study, 27%. Base broadeners in H.R. 3970 were criticized by some business groups. 
The corporate tax debate and the issues of burden and effects on growth continued to be in the news. In May 2008, N. Gregory Mankiw published an article suggesting that most of the burden of the tax falls on labor, and citing research suggesting the corporate tax is borne by labor and that revenue losses may be fully or largely offset by behavioral responses. 
In the 111 th Congress, S. 3018 , introduced by Senators Ron Wyden and Judd Gregg, also provided for a lower corporate tax rate in exchange for a somewhat broader corporate tax base. A similar bill, S. 727 , was introduced by Senators Wyden and Coats in the 112 th Congress. The Fiscal Commission proposed a corporate reform similar to the Wyden-Gregg bill. In addition to the Wyden-Gregg and Wyden-Coats proposals and the Fiscal Commission proposals, there were general proposals by Republican leaders in the House (Majority Leader Eric Cantor, Ways and Means Chairman Dave Camp, and Budget Committee Chairman Paul Ryan) for corporate tax reform with rate reductions.
In 2014, Chairman Camp introduced H.R. 1 , a comprehensive proposal that reformed both individual and corporate income taxes and was revenue neutral during the 10-year budget horizon, as well as distributionally neutral. It cut the corporate tax rate to 25%. President Obama also supported revenue-neutral corporate tax reform, although some groups proposed raising additional revenue from corporations. During 2016, Senator Hatch, chairman of the Senate Finance Committee, indicated an interest in corporate tax integration (where only one level of tax would be imposed on corporate income). Most recently, Speaker Paul Ryan and Ways and Means Committee Chairman Kevin Brady proposed a major revision in the tax treatment of business income in their "Better Way" blueprint. It partially transformed the current income tax into, effectively, a domestic consumption tax. The border adjustments that make this proposal a domestic consumption tax appear no longer on the table and a new plan is being formulated in cooperation with the House, Senate, and Administration.
This report provides an overview of corporate tax issues and discusses potential reforms in the context of these issues, with particular attention to some of the research concerning large behavioral responses and their implications for revenue and distribution. The first section reviews the size and history of the corporate income tax, and discusses an important issue that has been given little attention by those who propose deep cuts in the corporate tax: its role in preventing the use of the corporate form as a tax shelter by wealthy business owners. This section also discusses the potential effect of behavioral responses on corporate tax revenues. The second section examines the role of the corporate tax in contributing to a progressive tax system and discusses claims that the burden falls on workers. The third section reviews arguments relating to efficiency and revenue yield, and traditional criticisms of the corporate tax as one that causes important behavioral distortions. One aspect of this discussion is the question of how the tax might be viewed differently in a more global economy. The final section examines options for reform.
section_title: The Corporate Tax as a Revenue Source
paragraphs: The corporate tax is the third-largest source of federal revenue, but its importance as a revenue source has diminished considerably over time.
subsections: section_title: Magnitude and Historical Pattern
paragraphs: Despite concerns expressed about the size of the corporate tax rate, current corporate taxes are extremely low by historical standards, whether measured as a share of output or based on the effective tax rate on income. In 1953, the corporate tax accounted for 5.6% of GDP and 30% of federal tax revenues. In recent years, the tax has fluctuated at around 2% of GDP and 10% of revenues, reaching a low of 1.2% of GDP in 2003, and standing at 2.7% in 2006 before falling as a share due to the recession and certain measures to stimulate the economy. The tax is projected to subsequently raise revenues of 1.6% to 1.7% of GPD for the years 2016 to 2027. Today, it is the third-largest federal revenue source, lagging behind the individual income tax, which is 8.4% of GDP in 2016, rising to 9.7% in FY2027, and the payroll tax, which was about 6% of GDP. It is much more significant, however, than excise taxes, which are slightly over 0.5%, and estate and gift taxes at less than 0.12%. In FY2017, the corporate tax is estimated at 9.4% of revenues, falling to 8.5% by FY2027.
Much of the historical decline arises from legislated reductions in the corporate effective tax rate on the return to new investment, which has fallen from 63% of corporate profits in 1953 to about 20% today. These changes include a reduction in the top statutory rate from 52% to 35%, more liberal depreciation rules, and the growth of tax favored intangibles investments. The total tax burden on corporate source income has declined even more due to lower rates on dividends and capital gains at the shareholder level and the increased fraction of stocks held in tax exempt form.
While a large fraction of the decline in corporate tax revenues is associated with these changes in rates and depreciation, other causes may be more liberal rules that allow firms to obtain benefits of corporate status (such as limited liability) while still being taxed as unincorporated businesses and tax evasion, particularly through international tax shelters. The 2007 Treasury study documented the significant rise in the share of total business net income received by unincorporated businesses from 1980 to 2004, from 21% of total net income to 50%. Whereas the share of proprietorships (which have no limited liability) has declined slightly, from 17% to 14%, the share of Subchapter S firms (firms that are incorporated but are allowed to elect taxation as an unincorporated business) rose from 1% to 15%. These changes followed a dramatic increase in the number of shareholders allowed for the election (the limit of 10 was raised to 35 in 1982, to 75 in 1996, and to 100 in 2004). Partnerships (including limited liability corporations and limited liability partnerships) increased from 3% to 21%, with most of the increase occurring after 1990. This growth reflects in part the growth of limited liability corporations established under state law (the first state adopted such a provision in 1982), which qualify as unincorporated business for corporate tax purposes. While Subchapter S firms are constrained by the shareholder limit, partnerships are not.
The latest data (for 2012) indicate that unincorporated businesses accounted for 59% of the total of flow through and corporate business net income, with S Corporations accounting for 16%, partnerships for 32%, and proprietorships for 11%. 
Although it has declined considerably in importance, the corporate tax remains a major source of federal revenue, and a significant change in individual income taxes would be required to offset a substantial reduction in corporate taxes in a revenue-neutral framework. For that reason, most proposals would trade off rate reductions, or possibly broad investment subsidies that reduce the effective burden on new investment, for base broadening, through reduction of corporate tax preferences.
section_title: The Role of the Corporate Tax in Backstopping the Individual Tax
paragraphs: Measuring corporate tax revenue falls short of describing the full role of the corporate tax in contributing to federal revenues because the corporate tax protects the collection of individual income taxes. As long as taxes on individual income are imposed, a significant corporate income tax is likely to be necessary to forestall the use of the corporation as a tax shelter. Without a corporate tax, high-income individuals could channel funds into corporations, and, with a large part of earnings retained, obtain lower tax rates than if they operated in partnership or proprietorship form or in a way that allowed them to be taxed as such. As suggested by the growth in unincorporated business forms above, wealthy business owners may be quick to take advantage of tax rate differentials, which currently tend to favor unincorporated businesses. In 1986, individual tax rates were lowered dramatically (the top rate fell from 70% to 28%, although it was eventually increased to 39.6%), but the combined corporate tax rate (on the firm and on distributions) has been high relative to the individual tax rate. The 2007 Treasury study indicated that 61% of the income of unincorporated businesses was associated with taxpayers in the top income tax bracket.
Although the top tax rate on corporations (35%) is close to the top individual rate (39.6%), the corporate tax is graduated. Consequently, for high-income taxpayers, there is an advantage to shifting part of one's income into a corporation because corporate tax rates are graduated (15% on the first $50,000 and 25% on the next $25,000) and are lower than the top marginal tax. This opportunity, however, is restricted by (1) limiting to one the number of corporations income can be shifted to; (2) the amount on which rates are graduated; and (3) disallowing graduated rates for personal service corporations. Out of 1.6 million corporations in 2013, there are 327,000 with tax of less than $6,000 due and 372,000 with tax of less than $10,000 due (tax on the first $50,000 is $7,500), suggesting some shifting occurs. In recognition of the potential use of the corporation as a shelter, tax law has in the past contained a tax on accumulated earnings. As long as dividends were taxed as ordinary income and the accumulated earnings tax was strict enough, it was difficult to use the corporate form to shelter a great deal of income.
This tax shelter constraint on lowering the corporate rate may be more binding today because of the lower rates on dividends enacted as part of the Administration's corporate relief package in 2003, although rates were increased in 2010 and 2013. Table 1 calculates the effective tax rate for operating through a corporation, versus an unincorporated business for two cases; one taxed at the top 39.6% rate and not subject to the additional 3.8% tax and one subject to the additional 3.8% tax with the total tax rate is 43.4%. If dividends are taxed at 23.8% and the corporate rate is lowered to 27% as suggested in the Treasury conference, the tax rate in the corporate form would be less than the tax rate on unincorporated businesses. In fact, with a 23.8% rate on dividends, corporations that distributed less than 94% of their income would present a tax shelter opportunity with a 27% tax rate for those unincorporated businesses subject to the additional 3.8% tax; it would represent a tax shelter if it distributed less than 73% of income for those whose Subchapter S business is predominantly capital income. This outcome would occur even without the benefit of graduated rates and could potentially benefit labor income as well as individual capital income. Moreover, although there are rules restricting accumulated earnings, it is common for corporations to reinvest a significant fraction of their earnings. This unlimited sheltering option would not exist as long as the corporate tax were as high as the individual tax, and its scope would be limited if dividends and capital gains were taxed at higher rates.
Some reforms might address these shelter issues directly, including raising tax rates on dividends and capital gains at the individual level while lowering the rate at the firm level, eliminating the graduated rate structure, and more formal methods of integrating the individual and corporate income taxes. 
Some tax reform proposals would not only lower individual rates but provide special lower rates for pass-through income from capital. For example, the "Better Way" tax plan proposes a rate of 20% for corporations, a top individual rate of 33% (with half of dividends and capital gains taxed), and a 25% rate for pass-through businesses, which could still make a corporation a better option with low distribution rates (of 37% or less). A special lower rate for pass-through business would also require pass-through firms to allocate income between labor and capital, an allocation not currently required for proprietorships and general partners.
section_title: Behavioral Responses and Revenue-Maximizing Tax Rate
paragraphs: Although it has long been recognized that there are behavioral responses to the corporate tax (even aside from the tax sheltering issues indicated above), and that these responses have important implications for the efficiency of the economy and the burden of the tax, the issue of a revenue-maximizing tax rate, popularly associated with the "Laffer" curve, has rarely entered into the discussion. A Laffer curve graphs revenue against the tax rate, and is based on the notion that revenue is zero at a zero tax rate and zero at a 100% tax rate (at least with respect to some taxes). In a Laffer curve, the revenue first rises with the tax rate and then falls, and at the point it reverses direction is the revenue-maximizing tax rate. 
The notion that a corporate tax cut could pay for itself continues to enter the debate in 2017, as it did more than 10 years ago during that corporate debate, where it was proposed or alluded to in several articles in the popular press during the debate. One is the article by Glenn Hubbard, cited above. In National Review , Kevin Hassett discusses the Laffer curve and presents a chart that he indicates is an illustration that appears to show a negative relationship between corporate revenues as a share of GDP and the tax rate. Only 13 countries are shown on this graph, however, and the negative relationship is clearly strongly affected by an outlier, Ireland, which is a well-known tax haven; most economists would not find this illustration persuasive proof. The Hubbard and Hassett articles do, however, cite some more sophisticated research. Hassett referred to a paper by Kimberly Clausing, and Hubbard referred to a paper by Michael Devereux. In addition, Alex Brill and Kevin Hassett also prepared a statistical analysis examining the change in the relationship over time. A cross-country study was also prepared by Mintz. Clausing, who is referred to in the Hassett article, is quoted as claiming that the United States is likely to the right of the revenue-maximizing point on the Laffer curve, but this statement, presumably from an earlier draft, is not found in her published article. That article finds a revenue-maximizing tax rate of 33%, in her simple specification, but as she added variables and accounted for other features the revenue-maximizing tax rate seemed to rise, as indicated in Table 2 . Large countries and countries that are less open, such as the United States, have a revenue-maximizing tax rate of 57%—much larger than the combined federal and state rate for U.S. firms of 39%.
Michael Devereux's paper indicates that, while he finds a revenue-maximizing rate of 33% under the same specification as Clausing, he finds only weak evidence of a relationship between tax rates and corporate tax revenues as a percentage of GDP. Many of his specifications do not yield statistically significant effects. Brill and Hassett find a rate of around 30%, which has been falling over time. Mintz finds a rate of 28%, but his data span only a few years (2001-2005).
The remainder of this section first discusses theoretical expectations of this relationship and then examines these empirical studies. Both the theoretical and empirical assessments suggest that the results of these analyses are questionable.
subsections: section_title: Theoretical Issues
paragraphs: The issue of a Laffer curve has not been a part of the historic debate on corporate taxes because the notion of a revenue-maximizing tax rate other than at very high tax rates is inconsistent with most of the models of the corporate tax. Traditionally, the main behavioral response associated with the corporate tax was the substitution of noncorporate capital for corporate capital within an economy where the amount of capital was fixed. Imposing a corporate tax (in excess of the noncorporate tax) caused capital to earn a lower return in the corporate sector and to flow out of that sector and into the noncorporate sector, thereby lowering the return in the noncorporate sector and raising the return, before taxes, in the corporate sector. The higher pretax return on capital also caused prices to go up in the corporate sector and fall in the noncorporate sector, causing a shift toward noncorporate sector total production. The corporate profits tax base, therefore, had two opposing forces: the amount of capital was falling but the profit rate was rising. The taxable base could, therefore, either increase as tax rates increased, or it could decrease. The direction depended on the substitutability of capital and labor in the corporate sector. The central tendency of most models (with unitary elasticities) suggested, however, that the tax base was relatively invariant to tax rates, and revenues would always rise with the tax rate. Consequently, under any reasonable set of assumptions there would either be no revenue-maximizing tax rate or an extremely high one.
If behavioral responses caused the total capital in the U.S. economy to contract, the outcome could be different. One such model, the open economy model, appears to be a motivation for the belief in a relatively low revenue-maximizing tax rate. Brill and Hassett discuss elasticity estimates of foreign capital flows to after tax returns in the range of 1.5 to 3 (they also cite a recent study with an elasticity of 3.3) in their paper that finds a revenue-maximizing tax rate of around 30%. They conclude that "[t]hese high elasticities are consistent with the view that reductions in corporate rates could lure a significant enough amount of economic activity to a locality to create a Laffer curve in the corporate tax space."
As shown in the Appendix A , however, this tax rate even with infinite elasticities cannot be achieved. In the most extreme case, where (1) the country is too small to affect worldwide prices and rates of return; (2) capital is perfectly mobile; and (3) products in international trade are perfectly substitutable, the revenue-maximizing tax rate would be the ratio of the labor share of income to the factor substitution elasticity. Assuming fairly common values for a model without depreciation of 75% for labor's share of income and a factor substitution elasticity of 1, the tax rate would be 75%—far above the rates of around 30% reported by Brill and Hassett. This rate could rise as these conditions are relaxed. If the United States is assumed to have 30% of world resources, the rate rises to 81%; if imperfect substitutability between investments across countries and between foreign and domestic products is allowed, it would rise further.
Although it is possible to have a revenue-maximizing tax rate that does not asymptotically approach 100%, it is probably not possible to find a rate that maximizes revenues as a percentage of GDP because GDP falls as well as tax revenues. In this case, the same circumstances apply as in the reallocation of capital in the closed economy: with unitary elasticities, the corporate share of income is constant relative to GDP, and with other elasticities, it can rise or fall.
A related circumstance where capital can contract would be in a model where savings responds so powerfully that the savings supply is infinitely elastic, that is, when a tax is imposed, the capital stock must contract so much, and the pretax rate of return rises so much that the after-tax return comes back to its original value. This extreme savings response model yields the same revenue-maximizing tax rate as the extreme open economy, 75%, and probably no revenue-maximizing tax rate for revenues as a percentage of GDP. Moreover, the slowness with which the capital stock adjusts (most models allow 150 years for full adjustments) means that the revenue would be affected by tax rates in the past.
The result of this discussion makes it clear that revenue-maximizing tax rates cannot arise from physical reallocations or contractions of capital. Nor are they likely to arise from a substitution between debt and equity, since the debt share has changed very little despite significant changes in the relative tax burden, and estimates of elasticities that do exist are small.
A remaining source of a different outcome is profit shifting. This effect could involve firms maintaining the same activity and shifting the form of operation to unincorporated businesses. Profit shifting could be a possibility (although the point of revenue maximization would be much too low because much of the tax has not disappeared, but rather has shifted). But, at least in the United States, this shift is probably less the result of high corporate tax rates and more the result of increasingly loose restrictions on operating with limited liability outside the corporate form, actions that have not been taken by other countries. The other profit shifting issue is the shifting of profits (rather than activity) to foreign countries. Such effects are possible, but it would seem unlikely that tax avoidance could be of this magnitude, given the amount of profits shifted and the behavioral response. Although a small low-income country, as is characteristic of most tax havens, might have little enough domestic capital that it could afford the loss from lowering the rate to attract more capital, such an outcome is much less likely for the United States. Recent estimates of elasticities also suggest that cutting the corporate tax rate would lower revenue much more than enough to offset with profits shifted back into the United States.
section_title: Revenue Feedback from a General Equilibrium Model to Illustrate Likelihood of a Laffer Curve Near Current Rates
paragraphs: A Laffer curve with a revenue-maximizing tax rate implies that there is a point where the tax base contracts so much that no revenue is gained from a tax increase, and, conversely that cutting tax rates could raise revenue. Revenue offsets that arise from behavioral responses are often referred to as a revenue feedback. For a tax cut, revenue feedback would be the revenue gain from an expanded base as a percentage of the original revenue loss (for a tax increase, it would be the loss from a contraction in the base as a percentage of the original gain). The revenue-maximizing tax rate is the point where induced changes in the tax rate provide 100% revenue feedback.
An approach that is empirically based but which is not the result of a direct estimate involves using a general equilibrium model, which is based on empirical estimates of underlying relationships (such as capital mobility). A recent CRS report used such a model and concluded that cutting the corporate tax from 35% to 25% in isolation would result in a revenue offset of 5% due to taxes on increased output in the United States. This effect was not due to the increase in corporate taxes on the additional output, which was negligible, but to an increase in both labor and capital income taxes on increased output. Thus the revenue-maximizing tax rate cannot be near the current 35% tax rate.
Some have argued that the revenue feedback for the corporate tax arises not from real changes in investment but from artificial profit shifting, where multinationals use a variety of techniques to declare income in low tax countries. Significant feedback effects from profit shifting were also estimated to be small. Even if all profit shifting ended, estimates suggest they were between 14% and 20% of corporate tax revenues and, thus, if they declined proportionally would add a feedback of no more than 20%. These are far from Laffer curve effects. Moreover, because the jurisdictions where profits are shifted have much lower (sometimes zero) tax rates, very little improvement in profit shifting might occur.
Finally, all of these feedback effects would be swamped for a stand-alone tax cut by the increase in the debt, which would crowd out capital and reduce output, leading to an additional loss of revenues of 23% by the 10 th year. This loss of revenues on reduced output is in addition to the direct effect on the budget deficit due to an increase in interest costs of 25% of the revenue loss over the first 10 years.
section_title: Reduced Form Empirical Analysis
paragraphs: As noted above, several recent studies have examined the relationship between corporate tax rates and corporate tax revenues as a percentage of GDP. The data used for two of these studies were obtained to replicate and extend the analyses. Both studies and the analysis estimate the effect of the top corporate tax rate (and its square) on corporate tax revenues as a percentage of GDP. Panel data for 29 OECD countries is used for the analysis.
section_title: Brill and Hassett Study
paragraphs: In their study, Brill and Hassett use panel data for the OECD countries from 1981 to 2003. They use regression analysis (OLS) to estimate the effects. Brill and Hassett find that the corporate tax rate has at first a positive effect on corporate tax revenues as a percentage of GDP and then a decreasing effect—the effect looks like an inverted U, the shape of the classic Laffer curve. All of their coefficient estimates are statistically significant. However, they do not account for problems often encountered with the use of panel data, and their coefficient estimates would appear to be biased and inconsistent.
The estimation results from the re-analysis of the Brill and Hassett study are reported in Table 3 . The regression includes a tax rate and a tax rate squared to allow for a curve. Panel A of the table displays the results for central government corporate tax data (in the case of the U.S., this is federal government tax data). The coefficient estimates for the full time period (1980 to 2003) and the four subperiods defined by Brill and Hassett are reported. In all cases, the coefficient estimates are fairly small and none are statistically significant at conventional confidence levels. Panel B of the table displays the results for total government (that is, governments at all levels) corporate tax data. Again, the coefficient estimates are fairly small and none are statistically significant. Once appropriate estimation methods are used to correct problems arising with panel data, there appears to be no statistically significant relation between corporate tax rates and corporate tax revenues as a percentage of GDP.
section_title: Clausing Study
paragraphs: Clausing uses panel data for the OECD countries from 1979 to 2002 to study the effect of corporate tax rates on corporate tax revenue as a percentage of GDP. She includes more explanatory variables than did Brill and Hassett, but her overall research findings and conclusions are essentially the same as theirs—there is a Laffer curve relationship between corporate tax rates and corporate tax revenue as a percentage of GDP. However, her estimation methods would lead to biased and inconsistent coefficient estimates.
The estimation results for five different specifications are reported in Table 4 . The five specifications differ by what explanatory variables are included in the analysis. In all five specifications, the coefficient estimates of the corporate tax rate (and its square) are smaller than those estimated by Clausing and have the opposite signs. Most of the coefficient estimates are not statistically significant at conventional confidence levels, but two are statistically significant at the 10% level only. (In these cases where the coefficients are significant on the tax squared term they still do not produce the Laffer curve shape but rather suggest rising revenue with a rising tax rate). Overall, these results suggest that the corporate tax rate has little effect on corporate tax revenues as a percentage of GDP. Consequently, there is little evidence to support the existence of a corporate tax Laffer curve.
Even if an empirical study found a statistically significant relationship that indicated a revenue-maximizing tax rate, such results could not be considered reliable if they do not control for base changes. If the rate is lowered but the base is broadened, the data could show rising tax revenues that would be due to the base changes. In a recent paper, Slemrod and Kawano provide estimates controlling for the direction of changes in the base (although not the magnitude, a much more daunting task) and find these controls raise the estimated revenue-maximizing tax rate. Thus, until studies can adequately control for the magnitude of changes in the base, they cannot be the basis for estimating a revenue-maximizing tax rate. 
section_title: Cross-Country Investment Estimates: The Djankov Study
paragraphs: Cross-country empirical studies, as noted above, have recently been employed to address the Laffer curve issue and, as will be discussed subsequently, the incidence of the corporate tax on wages. In addition to these direct estimates, there are numerous empirical studies that examine underlying relationships, such as the effect of the user cost of capital (which incorporates the tax rate along with other variables) on investment. Most of these studies have found modest effects on domestic investment and have employed times series estimates within the United States.
One recent study on investment, Djankov et al., is similar to the other studies in that it employs a cross-country data base and an independent variable reflecting the tax rate to directly estimate the effect of the corporate tax rate on investment, entrepreneurship and other variables. The study found no effect on investment for statutory tax rates, but very large effects for constructed first year and five year cash flow tax rates. This study, unlike the others discussed in this paper, is a single cross section, so there is no way to introduce fixed country effects.
subsections: section_title: Theoretical Issues
paragraphs: Several difficulties arise in the Djankov analysis. First, the cash flow tax rate variable they construct is a hypothetical one (for a hypothetical firm), which is not representative of the capital stock or the firm size in a country (or in all countries). The denominator is income measured before labor income taxes paid by the firm (such as social security taxes in the United States) and economic depreciation. The first is very problematic because the capital income tax rate increases as the labor income tax rate falls, which is a relationship that seems to have no obvious economic justification. It also measures taxes on a cash flow basis for the first year (or the first five years in an alternative scenario), rather than over the life of the investment.
An examination of scatter-plots of their data suggest that the results are highly affected by outliers, particularly Bolivia (which has a very high tax rate and a very low investment rate) and Mongolia, a low tax country where investment has been flowing in recently due to mining.
The tax rate for Bolivia is about twice the typical tax rate and is inconsistent with the corporate rate in Bolivia. According to the authors, the tax rate reflects an alternative transactions tax. However, a transactions tax is not a tax on corporate income but falls on all income in the economy. Assuming that about a quarter of income is capital incomes, the tax should be reduced by 75%.
As with the Laffer-curve estimates, the results of this study, at least for the United States, are not plausible. According to their estimates, a 10 percentage point drop in corporate tax increased investment by 2.2 percentage points. According to an open economy model developed by Gravelle and Smetters, however, U.S. capital would increase a maximum of 0.7 percentage points with the elimination of corporate tax; with more reasonable elasticities, it would increase by 0.3 percentage points. (This study was directed at the question of tax incidence and will be discussed in more detail in the section below which addresses distributional issues and the burden on labor). Moreover, these effects may understate the investment effects because they do not take into account debt. Thus, their results suggest an investment increase that is at least 11 times too large and that could be 25 or more times too large.
section_title: Empirical Analysis
paragraphs: Although the issue of fixed effects would cause this study to remain problematic in any case, this section explores the effects of the tax rate changes and of specifications that include multiple control variables.
The Djankov et al. sample consists of 2004 tax and economic data for 85 countries. They examine the effect of the corporate tax rate on (1) aggregate investment, (2) foreign direct investment, and (3) two measures of entrepreneurial activity. The main results of their study and the authors' reanalysis are reported in Table 5 . The first row of the table displays the coefficient estimate of the effective corporate tax rate variable taken from the Djankov et al. study. Their basic specification includes only the tax rate as an independent variable. The second row of the table reports the range of estimates when a single additional independent variable is added—the authors add 10 variables, one at a time. In all but one instance, the estimates are statistically significant at the 1% or 5% confidence level, and at the 10% level in the remaining case.
Their data was reanalyzed after correcting an error in their tax rate for Bolivia, and cumulatively adding selected independent variables that Djankov et al. included in their analysis; the new analysis also included a region-of-the-world variable for each country. The first row of the bottom panel in Table 5 presents the coefficient estimates for the basic model with only a single independent variable: the effective corporate tax rate. For each dependent variable, the coefficient estimate of the tax rate variable is smaller than Djankov et al.'s estimate, which illustrates the importance of Bolivia to their results. Furthermore, the estimated effect of the tax rate on aggregate investment is not statistically significant. The final row of Table 5 reports the coefficient estimate of the tax rate when the full set of independent variables is included in the analysis. The estimated effect of the tax rate on aggregate investment is much smaller than Djankov et al.'s estimate and not statistically significant. The estimated effect of the corporate tax rate on foreign direct investment and entrepreneurial activity is somewhat smaller than the effects estimated by Djankov et al., but the estimates are statistically significant.
a. Significant at 1% level. 
b. Significant at 5% level. 
c. Significant at 10% level. 
section_title: Distributional Effects
paragraphs: A second issue that was a focus of the Hubbard article was the distributional effects of the corporate income tax. This issue also has been recently referenced by Treasury Secretary Mnuchin, who cited a study by Azémar and Hubbard as evidence that most of the corporate tax is paid by workers. If the corporate tax falls on owners of the corporation, or on capital in general, it contributes to a progressive tax system, since higher income individuals have more income from capital than from labor. Based on tax data, for taxpayers with incomes up to $100,000, over 90% of income is labor income, whereas those with incomes over $1 million, less than a third is labor income. The traditional analysis of the corporate income tax indicates that the burden generally spread to all capital, but does not fall on labor income. Most government and private agencies that routinely do distributional analysis allocate the corporate tax largely to capital income.
Hubbard referred to three studies in his article: a working paper by economist Arnold Harberger, a working paper by William Randolph of the Congressional Budget Office, and a recent empirical cross-country study using data similar to the studies discussed above, by Hassett and Mathur. At about the same time or shortly thereafter three other empirical studies that use cross-country data were released in 2006-2008, by Felix, by Desai, Foley and Hines, and by Arulampalam, Devereux, and Maffini. Mankiw refers to the Randolph and Arulampalam, Devereux, and Maffini studies, although as will be shown subsequently the Arulampalam et al. study is examining an entirely different phenomenon which is unlikely to be very relevant to the United States corporate tax, as is the case with the Azémar and Hubbard article recently referred to by the Treasury Secretary. 
These studies reflect differing fundamental approaches to studying corporate tax incidence. One approach uses a general equilibrium model that estimates incidence based on empirical estimates of various behavioral responses and other aspects (such as size). The burden that falls on labor versus capital depends on international capital flows and how well they can be used in different countries (which in turn depend on the technology of production and the preferences of consumers). The second approach is to directly estimate wages as a function of tax rates and other variables from a set of data (this approach is called a reduced form estimate). These direct estimates, in turn, fall into two types: (1) some studies are considering the effects of international capital flows and (2) others are examining the share of the tax on excess profits (or rents) that is born by labor by reducing the share of rents that is captured by labor in wage bargaining. Of the studies mentioned in the previous paragraph, two (Harberger and Randolph) are of the general equilibrium type; three (Hassett and Mathur, Felix, and Desai, Foley, and Hines) are reduced form empirical estimates that reflect capital flows; and two (Arulampalam, Devereux, and Maffini and Azémar and Hubbard) are estimating rent sharing through wage bargaining. 
A recent news report indicated three articles referenced by the Treasury press office in support of the burden falling on wages (although the Treasury Office of Tax Analysis currently assigns most of the burden to capital income): two studies already mentioned, Randolph, and Hassett and Mathur, and a study by Lui and Altshuler. The last study does not clarify what behavioral response it is measuring, but because it is based on considering wage effects by industry it would be capturing wage bargaining effects.
subsections: section_title: The Harberger and Randolph Studies
paragraphs: The first two studies explicitly focus on the effects of an open economy. It is a standard finding that for a small open single-good economy with perfect capital mobility and perfect product substitution, the burden of any source based capital income tax falls on labor (whereas for residence based taxes, that is taxes that apply to domestic owners of capital regardless of where they are domiciled, the burden would fall on capital). The corporate tax has some aspects of a source based tax and some of a residence based tax.
Both the Harberger and the Randolph studies are based on this simple model of perfect substitution, altered to account for the United States as a large county (which lowers the elasticities) and to account for multiple sectors. Randolph's study does not so much predict the burden of the tax as explore incidence in certain types of models; he acknowledges that less capital mobility causes the burden to shift from labor to capital. Harberger's model has four sectors, corporate and noncorporate tradable sectors and corporate and noncorporate nontradable sectors. He assumes that the corporate tradable sector is more capital intensive than the average industry, which leads to a burden of greater than 100% of the tax falling on capital. Despite the vision of the manufacturing sector as highly capital intensive, it actually is not: housing services, which are 100% capital, account for over a third of the capital stock in the country, and many other industries, such as utilities and agriculture are also more capital intensive than manufacturing. Using the same assumptions about mobility, but with a less capital intensive manufacturing sector, Randolph finds 70% of the corporate tax burden falls on labor.
To permit other than perfect substitutability, a much more complex computable general equilibrium model would be required, which neither Harberger nor Randolph has provided. Such a model has been developed by Gravelle and Smetters who find, with reasonable elasticities, that capital still bears most of the burden, about 80%. A recent CBO working paper by Jennifer Gravelle provides an extensive review of the existing general equilibrium models and the factors that drive the results. She finds that five factors tend to move the burden toward falling on capital: a smaller willingness of consumers to substitute between foreign and domestic products, a higher substitutability of labor and capital in the production process, a smaller willingness of investors to substitute investments in different countries, a less capital intensive corporate tradable sector, and a larger country. Her review of the evidence on these factors suggests that, based on these models, the majority of the tax (about 60%) is born by capital, with results differing from the Gravelle and Smetters findings due to a lower substitution elasticity between capital and labor in production. She subsequently considers, however, other factors that could increase the burden on capital (and even benefit labor), including the use of debt (discussed below).
Although the general equilibrium models can be very complex, they still abstract from some important features of the corporate tax. There are several other factors that would further push the corporate tax burden toward capital. First, the current corporate tax has elements of a residence based tax, and the burden of a residence based tax falls on capital. Second, if some share of profits is rent, it would be expected to fall on capital in the United States, because only a small share of the private sector (less than 7%) is unionized. Finally, the current corporate tax actually subsidizes debt finance at the firm level, and if debt is much more substitutable than equity, total capital would be less likely to be exported: indeed, raising the corporate tax rate could cause capital to flow in. A study by Grubert and Mutti found that in a general equilibrium model that included debt, such a capital inflow occurred when capital income taxes were raised, an outcome that would lead to labor benefitting from the corporate tax.
Finally, note that as long as countries tend to choose tax rates similar to each other, which appears to be the case, the world becomes like the original closed economy, a model stressed by Harberger, with the burden falling on capital. According to the 2007 Treasury study, the U.S. combined state and federal corporate statutory rate was 39%, the G-7 average was 36%, and the OECD average was 31%. In 2013, the rates had declined slightly, with rates of 29% in the OECD and 30% for the largest 15 countries (both excluding the United States). Effective tax rates, which should govern the movement of capital, are even closer together, and in some cases are lower for the United States than for other countries. More recent updates of tax rates indicate that U.S. rates are similar to the rest of the world. Jennifer Gravelle uses OECD tax rates to estimate the share of the U.S. tax falling on labor using a global approach and finds that over 90% falls on capital. 
An argument is often made that the burden of any capital income tax tends to fall on labor because it reduces savings, an effect that would also occur in a closed economy. While one model predicts that the entire burden of a capital income tax eventually falls on labor, this model requires some extreme assumptions about human behavior such as perfect information, an infinite planning horizon, perfect liquidity, and asexual reproduction. Models allowing for finite lives (such as the life-cycle models) find results that vary, but if the revenue loss is made up by higher taxes on labor, there is little or no effect. Some economists believe that these models are inappropriate, as they assume too much information and skill on the part of individuals; they suggest that individuals use rules of thumb, such as fixed savings rates or targets, instead. These rules of thumb suggest that a cut in capital income taxes either has no effect on saving or reduces savings. These economists also point out that most empirical evidence does not point to an increase in savings; historically, savings rates do not appear to respond to reduced tax rates.
section_title: The Hassett and Mathur Study
paragraphs: While the general equilibrium models do not provide much support for the corporate tax burden falling on labor, Hubbard also referred to an empirical study by Hassett and Mathur that uses the corporate tax rate to explain differences in manufacturing wages. They find a statistically significant result that indicates a 1% increase in the corporate tax causes manufacturing wages to fall by 0.8% to 1%. These results are impossible, however, to reconcile with the magnitudes in the economy. Through competition, wage changes in manufacturing should be reflected in wages throughout the economy, implying that a 1% rise in corporate revenues would cause a 0.8% to 1% fall in wage income. However, corporate taxes are only about 2.5% of GDP at best, while labor income is about two thirds. These results imply that a dollar increase in the corporate tax would decrease wages by $22 to $26, an effect that no model could ever come close to predicting.
The lack of theoretical reasonableness of the results may be explained by statistical issues. The Hassett and Mathur study used data from 72 developed and developing countries for the 1981 to 2003 period. For their analysis, their dependent variable is the logarithm of the five-year average of the average manufacturing wage. They justify their use of the five-year average wage by (1) noting that due to capital adjustment costs, the economic effects of corporate tax rate changes show up over longer time periods, and (2) arguing that this may control for possible measurement error induced by the business cycle. The wage rates for all countries were converted to U.S. dollars using annual exchange rates. Hassett and Mathur include the price level of consumption as an explanatory variable to capture cost of living differences across countries. The main explanatory variable of interest is the logarithm of the top corporate tax rate. Hassett and Mathur also use the average effective and marginal effective corporate tax rates (in logarithms) as explanatory variables in some specifications.
The Hassett and Mathur basic estimation exercise was replicated: the results are reported in the first row of Table 6 . The coefficient estimate reported in the first column (-0.759) suggests that a 10% increase in the top corporate tax rate will lead to an 7.6% decrease in the average manufacturing wage rate. This estimate is statistically significant at the 5% level. The results are not as strong (the estimates are closer to zero) when using alternative measures of the corporate tax rate (see the next two columns of Table 6 ).
The exchange rate between two currencies reflects the relative supply and demand for those two currencies, and is affected by financial markets and government policies. Exchange rates may not be good indicators of the relative buying power of wage rates in two countries. Purchasing Power Parities (PPPs), however, are specifically designed to equalize the internal purchasing power of the currencies. Workers in Australia, for example, are concerned with what their wages will purchase in Australia, and not how many dollars their wages will buy. Using PPPs is a more appropriate way to convert national currencies to a common currency (U.S. dollars).
The second row of Table 6 reports the coefficient estimates when the wage rates are converted to U.S. dollars using the consumption PPPs. Consumption PPPs are more appropriate for converting wages than using general PPPs (over GDP) because they omit national expenditures for government and investment goods. Again, nominal wages are the dependent variable. The coefficient estimates are closer to zero than the estimates reported in the first row, but the coefficient estimate reported in the first column (-0.728) is statistically significant at the 5% level. The estimates for the alternative measures of the corporate tax rate are not statistically significant at the conventional confidence levels.
a. Significant at 5% level. 
b. Significant at 10% level. 
The most appropriate measure of wages is the inflation-adjusted consumption PPP-adjusted wage rate. Wages in each country were converted to U.S. dollars using the consumption PPP and then converted to constant (inflation-adjusted) dollars using the CPI-U before calculating the five-year average. The final row of Table 6 displays the coefficient estimates for the model using this measure as the dependent variable. The estimates are closer to zero than in the other two cases. The coefficient estimate in the first column (-0.488) is statistically significant at the 10% level but not at the 5% level. The other two estimates in columns two and three are not statistically significant at the conventional confidence levels. While there is still some evidence of corporate tax rates having a negative influence on wage rates in manufacturing, the effect is smaller and less robust than reported in the Hassett and Mathur study.
Hassett and Mathur averaged wages over five-year periods. They justify using five-year averages by arguing that it helps to control for possible measurement error induced by the business cycle. But, because of missing values in the wage data, 66 observations have the average wage based on less than five years of data (60 observations use only two consecutive years of data for the calculation of the average, which would likely not affect any measurement error). The bottom panel of Table 6 reports the estimation results when these 66 observations are excluded from the analysis (leaving 153 observations). In all cases, the coefficient estimates for all measures of the corporate tax rate are not statistically significant.
Averaging the wage data over five years and using the beginning of period value for the explanatory variables, however, eliminates much of the variation in wages and tax rates, thus throwing away much of the information needed to estimate the economic effects. The statistical analysis is repeated using annual data and including various lagged values of the corporate tax rate as explanatory variables. The results are reported in Table 7 . The first column of the table displays the coefficient estimates for the current value of the corporate tax rate (labeled t in the first column) and the values for the previous five years (t-1 to t-5), which allows for longer term effects of tax rates on wages. In each case, the coefficient estimates are negative but very close to zero; none are statistically significant at the conventional confidence levels. Furthermore, all the tax rate variables in column (1) are not jointly statistically significant. The next six columns report the results when the corporate tax rate values (current and lagged) are entered individually. In every case, the coefficient estimates are close to zero and are not statistically significant at conventional confidence levels. In using annual data, there is no evidence that changes in the top corporate tax rate affects wage rates in manufacturing.
Hassett and Mathur subsequently produced a revision of their initial paper. One of several generic problems with cross-country wage studies is that a proper specification should take into account not only the country tax rate but the rates of other countries. (Other generic problems include the direction of causation, for example, that countries with lower or slowly growing wages may choose to rely on corporate taxes as a revenue source, so that the wage changes may drive the corporate rate.) Hassett and Mathur address the first issue, in a limited fashion, by adding tax characteristics of neighboring or economically similar countries. This addition, in some cases, reduced the coefficient on taxes and made it statistically significant at a lower level. The study also included some local price indices, but this change did not fully address the issue of comparing wages using purchasing power and did not address other issues raised about the original Hassett and Mathur study. Their results continued to produce implausible estimates. In the case where average tax rates of countries with similar income levels was added, the percentage change in wages for a 1% change in corporate taxes is 0.5%. This level implies a decrease of $13 in wages for each dollar fall in corporate taxes.
section_title: Other Empirical Wage Studies
paragraphs: Several other studies have examined the incidence of the tax on labor income. They are discussed in three different categories: studies that rely on cross-country data as in the case of Hassett and Mathur, studies that rely on cross-state data, and studies that examine not the general incidence of the tax, but the share affecting wages through bargaining over excess profits. The Arulampalam, et al. study cited by Mankiw was the first of these latter types of studies.
subsections: section_title: Other Cross-Country Studies of General Burden
paragraphs: Three studies in addition to the Hassett and Mathur study have relied on cross-country data. Felix, in a study that controls for education, finds much smaller effects than Hassett and Mathur, but ones that are still too large to be predicted by a theoretical model (about $4 for each dollar of corporate tax revenue). This study has problems similar to those for Hassett and Mathur and, in addition, does not control for country fixed effects, therefore not controlling for unobserved country-specific factors. The sample is unusual as well, with 19 countries covered for varying years. Out of the total of 65 observations (countries and years), about a quarter of the sample is drawn from Italy and Mexico and seven of the 19 countries had only one or two years of data.
Another study, by Desai, Foley and Hines uses observations on foreign owned affiliates of U.S. firms across countries and in different time periods. This study uses data on multinational subsidiaries of U.S. firms to estimate the allocation of the tax burden between labor and capital using a seeming unrelated regression for capital income (which they measure by the interest rate) and labor income. In their model, labor and capital burdens are restricted to the total of taxes, and they impose a cross-equation restriction on the estimated burdens. They find the share of the burden on labor income to fall between about 45% and 75% of the total, a number that is not inconsistent with theoretical expectations.
This approach, however, has the fundamental theoretical problem that wages at an individual firm should not reflect tax burdens at an individual firm. In deriving a model that assumes it does, they assume that the price level of their goods is fixed and base their results only on their sample of firms (which is comprised solely of multinational corporate sector firms). This approach creates both econometric problems in their analysis and also means that their results cannot be construed as reflecting actual burdens in any of their economies, as discussed in more detail in Appendix C .
They also represented equity returns through the interest rate, under the assumptions that investors equate (net of risk) debt and equity returns. If these assets are generally substitutable, the increase in corporate tax should cause portfolios to shift toward debt and drive the interest rate up (while driving the equity return down). Moreover, the tax burdens on debt and equity differ at the individual level and those differences depend, among other things, on any special tax rates for dividends and capital gains, the deferral advantage of capital gains, and the inflation rate.
Aside from these theoretical problems, an important issue with their study is that it appears that their results are forced by the cross equation restriction. William Randolph, a discussant at a 2008 conference, found that if the restriction is eliminated there are no statistically significant results from their study. In an example he presented, the estimates of the wage effect was 48% of the burden, with a standard error of 18% in the original study; in a regression without the restriction the share was 19% with a standard error of 100%. Randolph considered a number of other specifications, including excluding the largest countries, but found no statistically significant results. He also suggested that only manufacturing subsidiaries be considered since other subsidiaries may be involved in tax sheltering operations. In the case where he considered only manufacturing subsidiaries, the sign reversed (indicating labor benefitted from the tax) but it was not statistically significant.
The most recent of the cross-country studies was undertaken by Clausing using a data set covering the OECD countries. Her study examined a number of different specifications, econometric approaches, and alternative data measurements. Two aspects that differed from the Hassett and Mathur study were comparing wages using purchasing power parity and excluding value-added variables, which Clausing suggests is capturing the effect of corporate taxes (whose burden on labor operates by reducing labor productivity). She expects this latter change would make results for the corporate tax variable larger. Overall, however, while trying many specifications and approaches, she characterizes the results as indicating no robust evidence that corporate tax burdens have large depressing effects of wages. She notes, however, that this outcome does not necessarily mean there is no incidence on labor, but that these effects cannot be detected with aggregate cross-country data, a point also made by Jennifer Gravelle in her review of empirical studies.
section_title: Cross-State Regressions
paragraphs: Three studies estimate tax incidence based on cross-state comparisons, as if each state were a separate country. Felix examines wages by residents of states depending, among other factors, on the state corporate tax rates. She finds a smaller effect than the Hassett and Mathur or her own cross-country study, although the results remain implausible, suggesting that a $1 dollar increase in taxes reduces wages by between $1.40 and $3.60. Other problems with her data set is that it is not a panel, so there is no individual specific control, and the data set also does not allow the identification of place of work, but rather place of residence.
Felix and Hines use a similar cross-state data set. Although the stated objective of this study is to examine rent sharing by considering union and non-union differentials, the paper also contains direct estimates of the effects on tax rates on wages. The relationships, however, are positive, not negative. Although the authors conclude that higher corporate tax rates reduce union wage differentials (a point associated with bargaining over surplus discussed in the next section), this differential arises in their empirical estimates because union wages rise less with corporate taxes than do nonunion wages. Thus these results directly contradict the results in the previous Felix study.
Carroll also examines individual workers across the states using a different data set. He estimates the effects of the statutory rate (combined federal and state) and also an average state tax rate. The first is only marginally statistically significant (and he does not highlight that result), but the second is highly significant. However, the average tax rate is measured not as taxes divided by profits but as taxes divided by personal income. Since personal income is strongly correlated with wages, this measure of tax would likely produce a powerful negative relationship without any direct relationship with taxes. As with other studies, the incidence estimated in this study is very large relative to the expected shares (he calculates $2.50 for every dollar of tax).
Another problem with cross-state studies is that states often allocate profits based on formulas and these formulas change the dynamics of capital flows. For example, if a firm's taxes are based on the share of sales, changing the location of production would not be relevant to the state tax burden. One recent study, by Serrato and Zidar, explicitly addressed the apportionment issue by controlling for the share of the tax that was based on a sales factor (other factors are capital and labor) and thus should not affect location. The study found 30% to 35% of the tax borne by labor. The study also used a spatial approach to address geographic location. A study by McKenzie and Ferede of the Canadian provinces did not control for the effect of formula apportionment (Canadian provincial taxes are levied 50% by sales and 50% by wages). The results of this study, were, however, implausible, finding a range of $0.96 to $1.59, depending on the province. 
One issue with cross-state studies is whether, even were there no concerns with particular studies, the results could provide guidance to the effects of the federal tax. Capital is likely significantly more mobile across states and products across states are probably closer substitutes, both factors that make the incidence more likely to fall on labor. Labor, however, is also mobile but its relative increase in mobility is probably less than that of capital. The states are also more like small economies on average. As in the case of cross-country studies, the tax rates of other states should be included in the regression. In addition, state corporate tax rates are much lower than the federal tax rate and it would be even more difficult to use this small explanatory variable to explain wages.
section_title: Rent Sharing Studies
paragraphs: Several studies have appeared recently that discuss the potential burden of the corporate tax on wages via an entirely different mechanism, which has been misinterpreted in some ways. As noted earlier, Greg Mankiw cited a study by Arulampalam, Devereux, and Maffini (hereinafter, ADM) finding a labor share of the corporate tax burden of 96% as evidence that the corporate tax fell largely on labor. (The most recent version of their study reports 49%). More recently, Treasury Secretary Steve Mnuchin cited a study of this type by Azémar and Hubbard (AH) as evidence that the burden falls largely on labor (they found 60%). ADM, AH and other studies of this nature do not estimate the general equilibrium effects of corporate taxes on economy wide wages but rather the share of the tax on excess profits that falls on workers due to bargaining and rent sharing, as do the other studies reviewed in this section. Because of the method of estimation, the Liu and Altshuler paper referenced by the Treasury Press Office would also be classed with rent-sharing studies. They have relatively little relevance to the general issue of the corporate income tax for the United States (in part, because the shares of workers who belong to unions that bargain on wages is so small). However, their results have been invoked as evidence on the general tax burden and these types of studies appear to be proliferating. The ADM study has apparently inspired several other studies of this nature, which are discussed here. These studies use individual firm or sector observations, which, as noted earlier, are not appropriate for the general incidence of the corporate tax, but are appropriate for the study of rent-sharing.
Before proceeding to examine both the ADM study and other studies specifically, it is important to make some general points about these types of studies as measures of the share of the corporate tax borne by labor. 
First, even if a reliable measure of labor's share could be found, the share cannot be interpreted as the share of total tax falling on wages because the analysis relates only to excess profits, which are in turn only a part, perhaps a small part, of total profits. The share of rents also suggests an upper boundary to the share of the tax which falls on labor that should be detected through these studies. A widely cited study by Gentry and Hubbard estimated that 60% of corporate profits represented earnings in excess of a risk-free return. Since some (perhaps most) of the excess return is a risk premiums and is part of the opportunity cost of capital (not excess profit), the excess profit share should be lower. Some evidence suggests that it is in the neighborhood of 10% to 20%. Every empirical study discussed in this section exceeds that level, with the smallest about 35% and the largest many multiples of 100%. Moreover, the burden relates only to those firms that both have some excess profits and engage in bargaining. While bargaining may be common in some European countries, in the United States, where unions would be expected to do the bargaining, less than 7% of private wage and salary workers are covered by unions. 
Second, there is an existing literature that has attempted to estimate the share of labor in excess profits (without focusing on tax issues). Most studies have found that, even in those circumstances where bargaining is to be expected, labor tends to capture a relatively small share, typically less than10% and rarely more than 20% or 30%. This small share suggests the amount of labor income due to rent sharing is small, and that is consistent with estimates that the union wage premium is about 15% (with a range of 0 to 30%). Thus the share of the total wage bill that reflects rents of union workers is 1% (the share of union workers, 7%, times the wage premium of 15%).
Thirdly, and perhaps the most important point to make, in the standard bargaining model (such as that employed by ADM), a corporate tax rate that applies to excess profits would not be expected to affect wages through the bargaining process. If taxes are treated in a standard way as a rate applied to a firm's revenue minus cost, the tax term does not appear (see Appendix D ). The workers and firm would split pretax profits, with each paying tax (corporate or individual) on their share. The economic intuition behind this is that while a higher tax rate reduces the surplus or size of the pie to be divided, it also makes the "price" of giving a dollar to labor lower because wages are deductible. Economists might think of these as offsetting income and substitution effects and in this model they offset exactly.
The only tax effect left is the one that arises (potentially) from the general equilibrium effects on the economy that occur due to the imposition of the tax on normal profits, an effect that applies to firms without excess profits and unions as well and could only be uncovered through some analysis appropriate to economy-wide effects. Under reasonable assumptions the proportional effect on rents is similar to the proportional effect of wages. Because the taxes on the excess profits themselves do not directly drive payments to labor, considering the possibility of rents simply means that an even smaller share of the total corporate tax burden falls on labor than suggested by the general equilibrium models. (For example, if the model estimates 20% of the burden will fall on labor and 25% of profits is excess, then only 75% times 20%, or 15%, of the burden falls on labor.) Given these theoretical insights, one might question why empirical studies of rent-sharing are being pursued at all as a question of tax incidence, and why such significant effects have been found. 
The ADM study used firm level data (for about 55,000 firms) from several European countries (primarily France, Italy, Spain and Germany) over a relatively short time frame of 1996-2003. It controlled for firm-specific effects. About a quarter of the observations are for only four years and about 45% only five years so that the panel, like that of Felix, shows changes over the short run. The same authors had an earlier version of their study with a smaller sample. Although the authors control for firm level fixed effects, they do not control for country-specific effects. The authors have subsequently revised their study reporting, for the preferred specification, that labor bears 64% of the tax in the short run and 49% in the long run. 
The ADM study properly derives a model where the tax on revenues minus wages disappears and claims not to consider the tax on normal profits. Instead the authors hypothesize an extra tax term that is not associated with profit that will affect wages directly. It is difficult to imagine exactly what type of tax provision would fall into this category. In any case, the share of the corporate tax arising from this type of provision seems likely to be vanishingly small. 
Whatever the authors theorize about, it is not what they include in their regression. The variable is total taxes paid per worker (although it is instrumented with tax rates and other variables). The study also excludes other important variables which cannot be observed such as the competitive wage (they use a minimum wage which is obviously far too low). The empirical implementation examines the change in wages as a function of the change in output and taxes (all taxes, not just lump sum taxes) which are closely linked as major elements of a contemporaneous identity and may explain their findings. Thus, it is possible that the statistically significant relationships obtained derive from some other linkage and do not represent a share of the tax burden. There are also some important reservations about the econometric methods. Panel data with short time periods (where persistence effects can be serious) and the need to control for firm specific effects face some significant econometric problems. The authors use a number of different specifications, with widely varying results, which suggest that the results are not robust. There are several other aspects of the econometrics that are not transparent.
Overall, it is not clear what relationship or phenomenon the study is measuring. Interest ideally is in how an exogenous tax change affects wages. Yet for some of the countries that constitute a large share of the data, there were no changes in tax rates. In others, tax rate changes were virtually all declines, with most of those declines occurring during the growth period of the late 1990s, when productivity and output was rising. It is possible that the results are capturing that phenomenon.
Another study using European data directed at capturing the bargaining share was recently released by aus dem Moore, Kasten, and Schmidt. This study compared the changes in wages of German manufacturing compared with French manufacturing, spanning a time when the German taxes were reformed (including rate cuts) and the French tax was not. This analysis finds a very large effect: an increase in German wages of 6.4% due to the rate cuts. This finding seems large. According to the reported means of the data, the ratio of wages to taxes is 11.9; that is wages are about 12 times the amount of taxes. If wages rose by 6.4%, that amount is 76% of the total corporate tax. It appears that the reduction in German taxes was around 20%, which implies, in dollar terms, that wages rose $4 for each dollar reduction in tax, when it should have been a share of only a small part of the tax. It seems likely that the empirical estimates are capturing some other type of influence, and the authors indicate their study is preliminary and uncertain. The authors never discuss the theoretical finding that this type of tax rate change is the kind of change that would not be expected to show up as a part of rent sharing.
Another study, by Dwenger, Rattenhuber, and Steiner, also uses firm data to examine the German tax cut. As with the aus dem Moore et al. study, they do not address theoretical concerns and simply assume that labor will bear some of the burden of the tax via bargaining. Their estimates of this initial wage effect indicate labor bears 156% of the tax. They also assume that the higher or lower wages will lead to employment shifts (so that when wages rise, employment falls and thus the wage bill does not fall as much), which results in a total wage bill effect of 47% of the tax. This line of reasoning regarding employment is also inconsistent with theory, as the wage does not change from the direct bargaining effect. Rather it arises from the increase in the cost of capital via increased taxes, which, while decreasing the demand for capital (assuming there is a non-taxed noncorporate or foreign sector), has effects on employment in the corporate sector that are uncertain. In a general equilibrium model, employment is assumed to be fixed in the economy. In any case, these general equilibrium effects cannot be uncovered with firm specific data within a country because the effect should not relate to the specific taxes of the firm. As with the aus dem Moore et al. study, it is not clear what the authors are measuring when they regress wage rates on tax rates, although it could reflect differential wage growth across industries. 
A study of subnational taxes in Germany by Bauer, Kasten, and Siemers found a significant effect of the corporate tax on wages. In some ways, this study was similar to the cross-state studies done in the United States in that the explanatory variable was the tax rate. But it also addressed rent sharing by examining the differences between low-skilled workers with less bargaining power. As is the case with some other studies, the results are implausible. They found that a 1% increase in tax rate decreased wages by between 0.28% and 0.46%. Although the incidence was not as large as the Hassett and Mathur results, using the same ratio of wages to taxes as the aus dem Moore, Kasten, and Schmidt study indicated a dollar of corporate tax reduced wages between $3.36 and $5.52 or by 336% to 550%.
Fuest, Peichl, and Sioegloch report an incidence of 47% in a wage bargaining model, using data from German municipalities and a series of tax changes in the local business tax. This 47% includes an externally estimated excess burden (efficiency cost); without it the incidence would be 36%. 
A study by aus dem Moore, comparing outcomes in France and the UK in a wage bargaining model follows the approach of ADM, and finds the share falling on wages 39% in France and 40% in the UK in the short run. In the long run, the results indicate a share of 66% in France and 73% in the UK. 
Azémar and Hubbard estimated the incidence in a wage bargaining model using data on 13 OECD countries. Using the values for 2004, their estimates indicate 60% of the burden falls on labor. Further estimates that include measures of union density indicate that this effect is highly driven by union density and would probably be negligible for the United States.
Two studies have been based on data in the United States. As noted earlier, Felix and Hines actually found wages to rise with increases in state tax rates, but the union differential fell. They indicate that their findings show that workers in a unionized firm bear 54% of the tax burden. Several important points should be understood about their analysis. First, as they make clear, they are not trying to estimate the effect of direct taxes on rents, as this effect disappears from their model. They are rather examining the indirect effect that would arise due to the increase in the cost of capital and the subsequent general equilibrium effects that would arise. Although they have correctly measured a statewide tax rate as their tax variable (rather than a firm specific rate), the model they use to drive their theoretical expectations has a mistake (as shown in Appendix D ) and the expectation from a properly derived model is likely a close to zero effect, and if not zero probably positive. Their estimate appears outside the range of reasonable theoretical prediction and probably in the wrong direction. In addition in calculating incidence they have applied the elasticity to the entire wage bill, not the share that is rent. If the rent share is about 15%, 8% of the tax, not 54%, falls on rents. As shown in the appendix, for a nationwide incidence taking into account union membership and theoretical expectations, the share of the tax that falls on rents is no more than 3% (keeping wages constant) and rents would more likely benefit. 
The most recent study of the United States is one by Liu and Altshuler. Their theoretical approach is difficult to interpret. As discussed in this review, there are general equilibrium effects that can shift the tax to wages, but within a closed economy with a fixed capital stock the central tendency is for the burden to be spread to all capital, but not to wages. Only in an open economy, where capital can flow across countries (and which would require country observations) could wage shares be estimated through this mechanism and the wage would be an economy-wide (country-wide) wage.
Generally, using a single country's data is aimed at measuring a burden that would fall on labor through the rent-sharing mechanism, except that the standard bargaining framework shows that while rents might be shared by labor, the tax on rents should not be. Liu and Altshuler never discuss a bargaining equilibrium and therefore never confront the offsetting price and income effects that tend to eliminate rent-sharing arising from taxes. In fact, at one point in their model, the wage rate becomes the numeraire (is fixed) that implies there are no industry wage differentials.
Their empirical approach is to examine how relative wage rates in each industry changed over time based on the mix of assets and the change in marginal tax rates over that period. They conclude that labor bears 60% to 80% of the tax. Why do they obtain such large effects, when theory says they should be zero or negligible? The most likely reason is because the marginal tax rate fell primarily for equipment, and those industries whose investments were more concentrated in equipment (manufacturing, transportation, construction, but especially manufacturing) probably saw slower wage growth over the period due to the decline in unions and international competition.
section_title: What Should Be Concluded About Incidence?
paragraphs: Although there has a resurgence of interest in direct empirical estimates of incidence, this review suggests that these reduced form empirical studies are seriously flawed, produce unreasonable estimates, are not robust (changes in specification change the results), or are inconsistent with theory, as is the case in the rent-sharing studies. Certainly, a serious problem with even the best of these studies is that the corporate tax tends to be dwarfed by the size of labor income so that it is difficult to detect this relationship or control for other factors that affect wages. The advantage of studying incidence through a general equilibrium model is that such a model can control for the factors affecting the incidence (including the limits to the effects), and, even though they are models, they are informed by empirical evidence.
Based on these models, it appears that most of the burden of the corporate tax falls on capital. The effect on capital flows without considering debt or rents suggest that labor bears 20% to 40% of the burden. If rents were 20% of total profits (and taxes) the labor share would fall to 16% to 32%. Consideration of debt could easily cause more that 100% of the burden to fall on capital. Thus the tax is a progressive one that falls on capital incomes and thus largely on higher incomes.
section_title: Economic Efficiency Issues
paragraphs: The traditional criticism of the corporate tax is that the tax causes distortions, and that these distortions are exacerbated by corporate tax preferences that prevent, for a given level of tax revenue, a lower tax rate. The issues discussed in this section include allocation of capital within the domestic economy, savings effects, and international capital flows.
subsections: section_title: Allocation of Capital Within the Domestic Economy
paragraphs: Traditionally, the efficiency concern about the corporate tax is related to the misallocation of resources between corporate and noncorporate production (including owner-occupied housing). Over time, efficiency issues have also encompassed differential taxation of the returns to assets of different physical types, and financial distortions, which affect the debt-equity ratio, payout choice, and decision to realize capital gains.
Some efficiency costs, including those that alter the mix of a firm's assets, arise not so much from the existence of a corporate tax but from its design. Table 8 captures the effects of the three most significant generally-available provisions that affect tax burdens on different assets: depreciation and capital cost recovery rules, the recently enacted production activities deduction, which in effect allows a lower tax rate on certain domestic activities that are deemed production (manufacturing, construction, etc.), and the credit for expenditures on research and development. The tax rates in this table account only for the corporate tax (that is, they do not include the benefits of deducting interest or the tax at the individual level on interest, dividends, and capital gains). They are also forward looking and marginal: they estimate the share of the return on a prospective investment that is paid in tax. If income were correctly measured and taxed that share would be the statutory rate; most assets face lower tax rates.
The variations within a column illustrate the distortions firms face in choosing the mix of capital within a firm. Overall the variations not only distort the mix of capital within a firm, but also the allocation of capital across different industries. Other things equal, firms eligible for the production activities deduction and firms that have a larger share of their capital stock in equipment or in research and development than average will be favored.
In the aggregate, the tax rate on equipment is estimated at about 24%, more than a full 10 percentage points below the statutory tax rate. The overall effective rate is 20%. 
The lowest rates are on intangible investments, such as research, advertising and investment in human capital. These costs are expensed (leading to a zero tax rate on those expenditures) and, in the case of research and development, eligible for a credit as well (leading to a negative rate). Spending on advertising is expensed and subject to a zero rate even though some advertising has future benefits.
 Table 9 reports the types of distortions that are an artifact of the corporate tax as a separate tax. These estimates, unlike those in Table 8 , take into account all levels of taxes. One of the complications of estimating these tax rates is whether the estimates should consider the significant (over 50%) fraction of individual passive income that is held in tax exempt form through pensions, IRAs, life insurance annuities and non-profits. In some ways, these sources can be viewed largely as not affecting marginal investment (for example, overall savings) because they are capped or not controlled directly by the investors and in other ways they affect choices (such as debt or equity of pension funds). Two sets of CRS estimates are provided which assume either tax exempt investment based on the distribution of shareholders or an alternative used by CBO which has a significantly smaller tax exempt share that reflects the marginal investments of U.S. citizens. These assumptions also differ in the share of borrowing and, to a small degree, in the individual tax rates on dividends, capital gains, and interest.
Within the corporate sector, in addition to asset differences, there is a larger differential with respect to debt versus equity finance. The aggregate tax burden on debt is negative, while equity is taxed at 22.4% or 26.5% depending on the estimate. Shareholder taxes do not add much to the burden, since the tax rate on equity accounting only for the firm level taxes is 19.7%. This small effect is due largely to the significant share of tax exempt investors, and, to a lesser extent, the lower tax rates applied to capital gains and dividends. If economic income were measured correctly, interest would be subject to the individual income tax rate, which is typically slightly above 20%. Debt is subsidized at the firm level, however, because nominal interest is deducted (including the inflation premium) while corporate profits before this deduction are effectively taxed at a rate below the statutory rate on real income. The result is that at the firm level debt is subsidized (a negative 53.5% tax rate). At the individual level, the tax on interest for taxable recipients is higher than the statutory rate because nominal interest is taxed, which pushes the overall tax rate toward a small but negative rate. The overall corporate tax rate at the firm level, which would be relevant to international allocation of capital is 5.7%.
Evidence on the size of this distortion is limited, but since there appears to be limited substitution between debt and equity, it is probably less than 5% of corporate tax revenue. Some simple measures, however, could significantly reduce this distortion (such as indexing interest payments for inflation). Lower corporate tax rates would also reduce this distortion.
The distortion that has probably received the most attention by those studying the corporate tax is the misallocation of capital between the corporate and noncorporate sectors. One source of the distortion arising from the corporate tax system was the taxation of corporate business plant and equipment at around 30%, while unincorporated business is taxed at only 20%. These estimates predate the inclusion of intangible assets that are uncommon in the noncorporate sector. They were also estimated at a time when a larger share of shareholders was taxable. The higher corporate tax also contributes to a larger wedge between corporate production and owner-occupied housing, which is generally taxed at a negligible rate. The magnitude of the estimated distortion produced by having a separate corporate tax varies depending on the model used and ranges from less than 10% of corporate tax revenue to about a third. Since the deadweight loss varies with the square of the tax rate, the recent decline in the differential due to lower tax rates on dividends and capital gains suggests the distortion relative to revenue would be smaller—probably no more than 4% to 7% of revenue, or perhaps even less taking into account intangibles and the increase in tax exempt shareholders.
A distortion not captured in Table 9 is the one that affects corporate payouts. Given that appreciation in stock values is not taxed until realized, there is a benefit to retaining earnings. There is a dispute about what determines payout ratios, and what the consequences of the tax are, but, in general, the welfare cost is small. There is also some distortion due to the lock-in effect for capital gains realizations.
Considering all of these distortions together, they are probably around 10% of corporate tax revenues, a magnitude that could be considered as a significant component of the burden of the tax. However, given the revenue needs of the government, there would also be distortions, perhaps smaller, associated with alternative taxes. Ways to reduce these distortions may, however, be worth considering.
section_title: Savings Effects
paragraphs: Much of the 2007 Treasury study's discussion emphasized effects on savings although this is not normally the focus of efficiency concerns about the corporate income tax. This distortion is not unique to corporate income taxes, but occurs with all capital income taxes. There are many difficulties with analyzing this issue. The first is that, as noted above in the discussion about the potential effect of savings on the wage rate, the economic distortion depends on the behavioral response of savings to tax changes, and what tax replaces them. Some economists have a strong view that taxes on the rate of return are always distorting, but these views are based on dynamic infinite-horizon models that may not be very realistic. With life-cycle models, the distortions depend on what revenue substitute is provided; substituting taxes on wages for taxes on capital, the most likely substitute in the U.S. tax system, could potentially increase distortions, depending on the responses in the models. In models of bounded rationality, where savings are based on rules of thumb such as fixed shares of income or fixed targets, there is no response, or only an income effect, which would not produce a distorting effect.
section_title: International Capital Flows
paragraphs: Tax rules can affect the efficiency of allocation of capital around the world, and, if the U.S. rate is different from other countries, it can cause misallocations of capital. According to a recent study, the U.S. corporate tax rate is 39% compared with an average of 30% for the largest 15 countries excluding the United States and an average of 28.4% for OECD countries excluding the United States (both weighted by output). For firms eligible for the U.S. production activities deductions, characteristic of most multinationals, the rate was 36.3%. The effective tax rate (taxes divided by profits) was about the same and the marginal effective tax rates much lower and about five percentage points higher than the OECD average.
These data do not indicate the United States is a notably high tax country with respect to investment. The main source of international distortion, therefore, is probably the increased investment that occurs in low-tax and tax-haven countries because the United States and other developed countries do not tax that income at all or tax it on a deferred basis. This inefficiency is not due to the corporate effective tax rate, but rather is due to the provision of a tax benefit for investment abroad.
Even when tax rates diverge, the efficiency costs appear to be relatively insignificant because the evidence suggests, as noted in previous sections, limited mobility of capital as a result of varying tax rates and natural constraints of the economy.
section_title: Potential Revisions in the Corporate Tax
paragraphs: A variety of potential revisions could be made to the corporate tax to permit lowering the rate. The revisions discussed here include (1) broadening the corporate tax base and using the revenues to reduce the rate or to provide investment incentives, (2) correcting interest deductions and income for inflation, and (3) increasing the individual level tax to permit a lower tax at the firm level or taxing large unincorporated firms as corporations. (To provide some reference, latest projections show corporate tax revenues at $300 billion in FY2016 and projected at $429 billion in FY2027. In 2007, prior to the recession they were $370 billion, but they were lower during and after the recession due to cyclical factors and legislative changes. )
The first part of this section summarizes the various base broadening tax reform proposals over the years, beginning in proposals advanced in the 2007 Treasury study and continuing through the latest budget proposal in 2016. The second part calculates how much the corporate rate could be reduced for corporate tax expenditures as well as other potential revisions. The remaining sections discuss two revenue estimates for two provisions that are not provided by other sources. 
subsections: section_title: Proposals for Eliminating Corporate Tax Preferences
paragraphs: One type of revision that would probably be supported by many economic analysts is to eliminate certain corporate preferences in exchange for a lower statutory corporate tax rate. The 2007 Treasury study estimated that eliminating corporate preferences would allow the tax rate to be lowered to 27%. Table 10 shows the preferences the Treasury study listed and the average FY2008-FY2017 revenue costs they reported at that time.
The largest preference in the list is expensing and accelerated depreciation ($41 billion) and the second largest is the production activities deduction ($21 billion); both provisions are captured in effective tax rates cited above. Other significant provisions (worth over $10 billion each in these years) include the exclusion of interest on state and local bonds, the research and experimentation tax credit, and the deferral of income from foreign sources, which is probably responsible for much of the international distortions.
Interestingly, their list did not include graduated rates for small corporations, which costs slightly more than $4 billion per year. Since owners of small corporations are typically as wealthy (or more wealthy) than owners of large ones, there appears to be little economic justification for not including these rates.
In addition, in 2007, H.R. 3970 (110 th Congress) was introduced by then-Chairman of the Ways and Means Committee Rangel. It was a more limited bill that would have lowered the tax rate to 30.5% (at a 10-year cost in FY2008-FY2017 of $363.8 billion), as well as allowing a permanent extension of provisions allowing expensing for small business (at a cost of $20.5 billion). As shown in Table 11 , this proposal did not alter depreciation, and eliminating the production activities deduction was the proposal's largest revenue raising provision. (Note that the revenue estimates were quite different, however.) It also included an alternative to eliminating the deferral of foreign source income that was somewhat more limited: disallowing expenses associated with foreign source income that is tax-deferred and allowing foreign tax credits only to the extent foreign income is currently subject to tax. The proposal also included two other international provisions, one eliminating a provision adopted in 2004 that included worldwide (rather than domestic) interest allocation rules for the foreign tax credit limit and one restricting the availability of lower withholding tax rates on income invested in the United States under treaty rules. However, a delay in the worldwide interest allocation has already been a revenue raiser for other legislation. Another major revenue raiser was a restriction in inventory accounting rules. The only depreciation base broadener in the proposal is one to extend the depreciation period for acquired intangibles. As is often the case in tax legislative proposals, revenue raisers are not always in the tax expenditure list.
Over several Congresses, Senator Wyden, along with cosponsors, has introduced a broad tax reform proposal. His proposal for the 111 th Congress, S. 3018 (cosponsored with Senator Gregg) was scored by the Joint Committee on Taxation. It would also eliminate a range of corporate tax preferences and lower the rate to 24%. This legislation would eliminate several of the provisions in Table 10 (accelerated depreciation, the production activities deduction, deferral, the inventory property sales source rule, and some smaller provisions), as well as index corporate debt for inflation (discussed below). This bill is able to achieve more rate reduction because it uses provisions outside the standard tax expenditures to raise revenue. As shown in Table 12 , a major revenue raiser in that study was a provision not in the tax expenditure list to provide a per country foreign tax credit limit (rather than an overall limit) for foreign source income and it was almost as large as accelerated depreciation. S. 3018 also raises significant revenue from disallowing interest deductions that reflect inflation (discussed below).
The Fiscal Commission proposed a measure very similar to the Wyden Gregg bill except that they did not include the deferral and per country foreign tax credit limit. Rather, they included a territorial tax that would raise somewhat less revenue than repealing deferral alone.
The Senate Finance Committee released discussion drafts on cost recovery and accounting in 2013 that relate to corporate taxation as well as a draft on international corporate tax issues. These proposals have not been scored. The cost recovery provisions would introduce a new depreciation system that would slow depreciation and approximate the present value of economic depreciation. Assets would be added to general pools rather than each vintage of investments being depreciated separately. Real property would be depreciated over 43 years. Research and development expenses would be deducted in equal increments over five years, as would half of advertising expenditures (the remainder would continue to be deducted when incurred). Oil extraction expenses would be recovered over five years and percentage depletion would be repealed. LIFO and lower of cost of market inventory would be repealed. In international tax rules all foreign source income would be subject to tax (equivalent to repealing deferral) but some income would be taxed at a lower rate than the statutory rate (i.e., a minimum tax would be imposed). 
President Obama's annual budgets have also included corporate tax reform provisions, concentrated in a few areas: international provisions, insurance provisions, inventory accounting, and fossil fuels. These provisions cover unincorporated businesses as well, but primarily affect corporations. The proposals changed in nature between the FY2015 and the FY2016 budget; the earlier set of changes is listed in Table 13 . The first two of the international provisions are the same allocation of deduction and foreign credit provisions contained in H.R. 3970 .
In the FY2016 budget, a new approach to international tax reform was taken, and the provisions for disallowing interest expense for unrepatriated income and foreign tax credit pooling were replaced by a minimum 19% tax on foreign source income. In the FY2017 budget it was projected to raise an average annual gain of $35 billion over FY2017-FY2026, with the remaining intangible provisions raising $0.3 billion. Most of the other proposals were the same. Overall the international proposals would raise an average of $48.4 billion over the period. (This number does not include a one-time 14% tax on existing unrepatriated income.) 
In 2014, revenue estimates were released for the Tax Reform Act of 2014 ( H.R. 1 ) introduced by Dave Camp, then chairman of the Ways and Means Committee. This proposal repealed or revised 115 corporate-related provisions including most corporate-related tax expenditures (which are discussed subsequently); estimates can be found in a Joint Committee on Taxation document. The most important tax expenditures in terms of revenue effect (annual averages over FY2014-FY23) were the slowing of accelerated depreciation ($27 billion), amortization of research and development ($19.3 billion), phase-out and repeal of the production activities deduction ($11.6 billion) and elimination of LIFO and lower of cost or market inventory accounting ($7.9 billion). Note that these provisions are scored under a phased in reduction of the corporate rate to 25% (as well as reduced individual rate). The plan also included some provisions not in the tax expenditure budget, such as the amortization of advertising ($16.9 billion) and allowing net operating losses to offset no more than 90% of income ($7.1 billion). For international tax treatment, the system moved to a territorial tax, but with stiffer anti-abuse rules, a system that lost revenue in the steady state. 
The CBO includes revenue raising corporate and business tax options in their budget options study, which are shown in Table 14 . Their options include a more limited proposal to restrict depreciation that raises less than half the revenue as replacing accelerated depreciation with the alternative depreciation system (which is the standard against which the tax expenditure is measured). The options also consider a different foreign tax return that would combine allocation of deductions rules with an exemption for active income, a territorial type of tax treatment.
How much could corporate tax rates be cut while maintaining revenue neutrality? Proposals discussed above have indicated rate reductions to 27% (Treasury 2007), to 24% ( S. 3018 , although there was a small corporate revenue loss), and to 25% for the Camp proposal.
Two important determinants of this potential rate reduction are whether to use revenues associated with unincorporated businesses which are included in these revenue raising options and how to treat provisions that arise largely from timing differences. Base broadeners that depend on timing such as accelerated depreciation would raise more revenue over the immediate budget horizon than they would over the steady state. The options listed in the tables above not only include unincorporated business provisions but also measure revenue gains in the first 10 years which can be almost twice as much as the steady state gain in the case of accelerated depreciation.
section_title: Rate Reductions Allowed by Tax Expenditures and Other Proposals
paragraphs: At one point, the Joint Committee on Taxation estimated that relying solely on elimination of corporate tax expenditures, the rate could be reduced to 28%, although this proposal did not include the repeal of deferral or other foreign provisions. However, since these revenues reflect the first 10 years, such a reform would lose revenue in the longer run. At the same time, the estimate could also be affected by changes in the baseline (such as making some provisions permanent, notably the R&D tax credit and deferral of tax on active financing income). Current estimates of the steady rate effects, as shown in Table 15 , where provisions are expressed in terms of their rate reduction capacity, indicate that eliminating all corporate tax expenditures other than deferral would achieve a revenue-neutral rate of 27% in the long run steady state. If deferral is included the rate could be imposed at 22%. 
In addition, as shown in the table, most traditional tax expenditures individually account for a very limited amount of rate reduction. Moreover, because each provision becomes less valuable the lower the rate, the tax reductions for a combination is slightly smaller than the sum of the individual points. By far, the most significant provision, in terms of revenue, is the deferral of tax on foreign source income. Of the remaining provisions, the most significant ones are accelerated depreciation and the production activities deduction.
A full discussion of the economic merits of these provisions is beyond the scope of this paper, but the standard tax expenditure items are discussed in the Senate Budget Committee Print, Tax Expenditure Compendium ; most would be regarded as provisions that lead to economic distortions. One possible exception is the Research and Experimentation (R&E) credit, because social returns to research and development appear higher than private returns, but many economists believe that the credit is probably poorly targeted and possibly abused. Arguments could also be made that the tax exempt bond benefit is shifted to state and local governments (which can charge lower interest rates) and that these assets and revenue loss would be shifted to individuals. Arguments could also be made that the benefits of the charitable contribution deduction and the low-income housing credit ultimately accrue to charities and lower-income tenants, at least in part. Many other provisions have some support, and may, therefore, be difficult to repeal.
Trading accelerated depreciation, the major revenue raiser from the tax expenditure provision, for a rate reduction would raise the cost of capital, because rate reductions provide windfalls for existing capital. How this effect is viewed depends on the objective of reform. If, for example, it reflects a concern about international capital flows, increasing the cost of capital is a concern. 
The 2007 Treasury study also discussed the possibility of using this base broadening to provide an investment incentive, such as a partial expensing. Currently full expensing has been discussed as part of the 2016 "Better Way" tax proposal in the House. Such a provision would lower the tax rate on new investment although the effect is limited because of the disallowance of interest deductions. It is difficult to design investment subsidies in a fashion that is both neutral across types of assets and generates an even revenue loss pattern over time. Historically, investment subsidies have been restricted to equipment. The provision used most frequently in the past is the investment tax credit which, if allowed at a flat rate, favors short-lived assets. Partial expensing is neutral across investments if allowed for all types but its revenue loss is very large in the short run. Accelerated depreciation can be designed to be neutral, but it also has an uneven revenue loss pattern and cannot be applied to non-depreciable assets, such as inventories. A benefit of lowering the statutory rate is that it reduces the incentive to shift profits abroad to tax havens, although that incentive would probably be considerably lessened in any case if deferral of taxation of foreign source income were ended, as proposed in S. 3018 .
Although there are large potential gains from taxing foreign source income, as in S. 3018 , and there are economic justifications for taxing foreign source income the same as domestic source income, and a lesser amount through ending deferral, international reforms are controversial. Indeed pressure has been exerted to move in the other direction, toward a territorial tax. Both the Chairman of the Ways and Means Committee in 2014 and the Fiscal Commission proposed a territorial tax. The "Better Way" proposal would also adopt a territorial tax. Depending on the design features, a territorial tax could raise revenue, lose revenue, or break even. The 2014 Ways and Means proposal would be revenue neutral in the budget horizon but lose revenue in the long run. There are, however, some more limited approaches. For example, the President's advisory panel proposed to exempt dividends of active businesses but disallow costs such as interest to the extent income is exempt. And, as proposed in H.R. 3970 and the President's proposals, one could also defer interest deductions associated with deferred income without making any other changes, or direct restrictive rules to tax havens.
section_title: Interest Deduction Inflation Correction
paragraphs: Based on the 2013 data, net interest paid, excluding finance and insurance, was $44 billion. Assuming half is due to inflation, multiplying by 35% and scaling up to reflect 2017 levels, the gains would be $8.3 billion, which would produce a 0.6 percentage point reduction in the rate. 
section_title: Reducing Tax at the Firm Level and Increasing Individual Level Taxes; Shifting Between Corporate and Individual Form
paragraphs: Given the value of lowering the corporate tax rate to reduce the shifting of income into tax havens and concerns over the U.S. position among other countries, one change that would allow this reduction is to raise the tax at the individual level and use the revenues to lower the corporate tax rate. Since individual taxes tend to be collected regardless of where income is earned, these taxes are neutral with respect to international allocation. This approach also allows more scope for lowering corporate tax rates without creating sheltering opportunities for high-income individuals. If the 2003 tax changes that lowered rates on dividends to 15% (eventually rising to 20% for very high income taxpayers in 2013) were rolled back, the federal corporate tax rate could be reduced to 32.9%. Additional revenue could be raised by taxing capital gains at higher rates, although, based on the JCT revenue estimating methodology the amount of additional revenue would be constrained by the behavioral effect on realizations. One could go even further, by taxing corporate capital gains on an accrual basis, which would yield dramatically more revenue. This type of change would also eliminate distortions arising from payout policies and realizations response. Even lower corporate rates could be achieved by taxing non-profits enough to offset their savings from the lower corporate rates—a change that would leave them unaffected, but would simply shift the source of tax collection. These latter proposals would arguably be broad enough to move much of the way toward an integration of the corporate and individual income taxes.
Another provision that might be used to raise revenues is to tax the increasing number of large pass-through as corporations. How much, if any, revenue that change would raise depends on any changes in taxation of dividends and capital gains and the individual and corporate income rates. The calculation in the table is based on measures that would restore the share of pass-through income to its old level (that is, moving it from 41% of business income to 79%). The calculation would depend on the rates of the individual and corporate taxes. The estimate assumes that the profits net of the corporate tax are taxed at an effective 15.7% rate that allows for a 20% rate and a share of capital gains not to be realized and that the current tax on pass-throughs is the same as the current corporate rate, 35%. Thus the tax imposed on the former pass-through businesses would be t + 0.157*(1-t), where t is the tax rate that equates new corporate tax revenues to the sum of the old corporate and pass-through revenues. 
section_title: Conclusion
paragraphs: Is there an urgent need to lower the corporate tax rate, as some recent discussions and analyses have suggested? On the whole, many of the new concerns expressed about the tax appear not to stand up under empirical examination. The claims that behavioral responses could cause revenues to rise if rates were cut do not hold up on both a theoretical basis and an empirical basis. Studies that purport to show a revenue-maximizing tax rate of 30% contain econometric errors that produce biased and inconsistent results; when those problems are corrected the results disappear. Cross-country studies to provide direct evidence showing that the burden of the corporate tax actually falls on labor in some cases yield unreasonable results and prove to suffer from econometric flaws that also lead to a disappearance of the results when corrected. Similarly, claims that high U.S. tax rates will create problems for the United States in a global economy suffer from a misrepresentation of the U.S. tax rate compared to other countries and are less important when capital is imperfectly mobile, as it appears to be.
Although these new arguments appear to rely on questionable data, the traditional concerns about the corporate tax appear valid. Although many economists believe that the tax is still needed as a backstop to individual tax collections, it does result in some economic distortions. These economic distortions, however, have declined substantially over time as corporate rates and shares of output have fallen. There are a number of revenue-neutral changes that could reduce these distortions, allow for a lower corporate statutory tax rate, and lead to a more efficient corporate tax system. At the same time, the amount of rate reduction that could be achieved with a long run, revenue-neutral corporate tax reform seems limited to a few percentage points.
Appendix A. Revenue-Maximizing Tax Rates in an Open Economy
For an exploration of corporate tax revenue, consider a very simplified example where there is a U.S. corporate sector and the rest of the world with no tax. The lowest revenue-maximizing rate would apply in a case where there is a small country which is a price-taker (that is, worldwide price and rate of return after tax are fixed because there is perfect capital mobility and perfect product substitutability). To determine the revenue-maximizing tax rate, begin with the equation for corporate tax revenues:
(A1)
where , the corporate capital stock, and , the after-tax rate of return, are potentially functions of the tax rate, . Revenue is maximized when the total differential of equation (A1) with respect to taxes is equal to zero, which is:
(A2)
Assuming the rest of the world can be treated as an aggregate and has a zero capital income tax rate, Gravelle and Smetters show that, in a case of a small country with perfect substitutability, does not change and
(A3)
where is the labor share of income and is the factor substitution elasticity.
Substituting equation (A3) into equation (A2) will obtain the revenue-maximizing rate of . To use some common values, if is 0.75 and is 1, the revenue-maximizing rate is 75%.
Since the United States is a large country, the rates would be even higher, because the tax can affect the world wide interest rate. The Gravelle and Smetters paper provide effects for and for a given country share, which can also be substituted into equation (A2). As a result, the revenue-maximizing tax rate is where is the output share. For example, if the United States has approximately 30% of the total output, the tax rate would be 81%. The rates would rise further if capital were not perfectly mobile or products not perfectly substitutable, since these factors would allow to fall further. At the extreme, it would return to a closed economy solution. Gravelle and Smetters present evidence to suggest that the outcome is more similar to a closed economy than a small open economy solution.
This same outcome, a 75% rate, would also apply for the most extreme case of growth models, the Ramsey model, where the supply of savings is perfectly elastic.
Note that in both of these extreme cases, the after tax return is fixed and the total burden falls on wage income, so that labor income would fall. One could also calculate a corporate tax rate than maximizes revenue while taking into account the effect on wages and keeping the wage rate constant. Again, relying on the model in Gravelle and Smetters and maximizing,
(A4)
Where is the tax rate wages, obtain a revenue-maximizing corporate tax rate of . With an approximate 20% tax rate on labor income, the revenue-maximizing corporate tax rate is 70%. Note however, that this is not the rate that would be found in the cross-section analysis.
Appendix B. Data and Estimation Methods
The data used in the Hassett and Mathur study and the Clausing study were obtained. The data used to replicate the Brill and Hassett study were obtained from the original sources cited in the study. The results reported for all studies were replicated.
The data are for several countries for a period of several years, and are known as panel data. The model of the relationship between the corporate tax rate (the independent variable) and the various dependent variables takes a linear form:
(B1)
where is the dependent variable, is the independent variable (the corporate tax rate in our case), and are the regression parameters to be estimated, and is a random error term. The subscripts, i and t , indicate that information for a particular observation comes from country i for year t (for example, information for Australia for 1992). The random error term, , is a random variable and captures omitted and unobservable factors or variables that affect the dependent variable. The error term will be discussed in further detail below.
If the following conditions are met:
the expected value (mean) of the random error term, , is zero; the variance of the random error term is constant for all observations; the random error term for one observation is uncorrelated with the error term for another observation; and the random error terms are uncorrelated with the explanatory variables...
then the ordinary least squares (OLS) estimators will yield the best linear unbiased estimators of the parameters ( and ). The parameter shows the true relationship between the dependent variable and the independent variable, and is the parameter of interest to us. Denote the estimate of as . Since is an estimate, it is a random variable drawn from a probability or sampling distribution with an expected value (mean) and variance. This estimator will have the following desirable properties:
unbiased: the expected value of is ; efficient: the variance of is smaller than the variance of all other unbiased estimators; and consistent: the probability distribution of collapses on as the number of observations gets arbitrarily large.
Estimation problems often arise with panel data because one or more of the conditions listed above are not met. The result is the OLS estimator will be biased and inconsistent. Problems arise with panel data, as is demonstrated when equation (B1) is rewritten as:
(B2)
The term is an effect (unobserved heterogeneity) specific to a particular country capturing differences among countries in (1) the measurement of economic data, (2) economic institutions, (3) laws and regulations applying to business, and (4) attitudes toward business, among other things. The term is a time specific effect capturing such things as the international business cycle. Since the corporate tax rate is a reflection of the attitudes toward business in a country, and will be correlated. Ignoring the country-specific unobserved heterogeneity means that the OLS estimate of is biased and inconsistent because the error term in equation (B1) is correlated with the explanatory variable—one of the conditions listed above is violated. Another problem often encountered with data that has a time dimension is the error terms are correlated from one year to the next year (called autocorrelation). Statistical tests indicate that these problems exist with the data obtained. Consequently, the parameters of the model are estimated using the fixed effect estimation procedure allowing for an AR(1) error structure.
Identification
Neither Brill and Hassett nor Clausing offer any justification in their studies for using OLS rather than the fixed effects method to estimate the parameters of their model. A well-known drawback of the fixed effects method is variables that vary across countries, but not across time within a country, cannot be included in the estimation (that is, the parameters associated with these variables are not identified). Devereux (2006) claims "changes in the statutory [corporate tax] rate within a country are comparatively rare. In practice, as found by Clausing (2006), there is not enough variation within country to identify an effect of the statutory rate, conditional on country fixed effects."
To check the correctness of this statement and the justification for using OLS, the variation of the corporate tax rate across countries and over time was directly examined. Table B -1 displays the results for the data from the three studies reanalyzed. The first row displays the relevant explanatory corporate tax rate variable used in the study. The second row reports of mean of the variable. The third row reports the standard deviation (a measure of variation of a variable) of the corporate tax rate variable. The last two rows decompose the standard deviation into the between country component and the within country component. If there is no variation in the variable over time within countries, then the within component of the standard deviation will be zero. Consequently, the effect of that variable on the dependent variable is not identified conditional on fixed effects (that is, it cannot be estimated using the fixed effects procedure). As can be seen from the table, there is almost as much variation within countries (the within component) as there is between countries (the between component).
In addition, all OECD countries changed their corporate tax rate at least once between 1979 and 2002. Four countries (Ireland, Norway, Spain, and Switzerland) changed their corporate tax rate only once during this period. In contrast, Luxembourg changed their corporate rate 12 times over this period. On average, OECD countries changed their corporate tax rates once every five years. Therefore, there is no evidence to support the argument that the effect of the corporate tax rate on corporate tax revenues is not identified conditional on fixed effects.
Appendix C. Modeling Problems of the Desai, Foley, and Hines Study
This appendix explains in further detail the modeling problems associated with the Desai, Foley, and Hines study (hereinafter, DFH), which include the failure to recognize price variability. This means that their cross-equation restriction is not justified (and that restriction is what gives rise to their results). The DFH study also fails to correctly interpret their results given that other sectors exist in the economy.
The DFH model effectively begins with an equation that forms a basic part of any general equilibrium model, namely that a percentage change in price is a weighted average of the percentage in costs for small changes. In the case of an imposition of a tax, that is:
(C1) 
where p is price, r is rate of return, w is the wage rate, is the tax rate and is the share of capital income. The hat notation refers to a percentage change except in the case of the tax variable, where the hat means the change in tax rate divided by one minus the tax rate. Beginning with a no tax world, that variable is simply . This relationship can be derived from a profit maximization problem. DFH derive such an equation to motivate their seemingly unrelated regression model. They then assume that p, the price of the good, does not change, which produces an equation of the form:
(C2) 
Since is an exogenous variable this equation indicates that the change in the tax would be shared by interest rates and wages, and this is the basis for the two seemingly unrelated regressions where the dependent variables are r and w, and the coefficients are constrained so that the burden will add up to one.
The argument for keeping the price fixed is that such a good would have its price fixed due to trade (e.g., all commodities have to sell at the same price). There are two difficulties with this assumption. First, if consumers in different countries have different preferences for goods based, in part, on country of origin (i.e., they do not consider French wine and German wine to be perfect substitutes) these prices will not be fixed. Indeed, this phenomenon is widely recognized, and the price responses are referred to as Armington elasticities—and they have been estimated empirically. Second, their observations are the weighted average of firms in each country but the firms themselves produce heterogeneous products, and all of these product prices cannot stay fixed because they have different capital intensities and because the products will vary from one country to another. Indeed, the trading of heterogeneous products means that fixed prices cannot be assumed because, in such a model, countries could not produce, consume and trade numerous products with differential taxation because such a world economy would be characterized by corner solutions (i.e., no internal equilibrium).
This problem means that there is another variable—price—that is affecting the results and presumably is correlated with the error term (that is, the price would tend to be higher when the tax rate is higher, making the regression suspect and that the coefficient restriction is not appropriate.
Even if these problems did not exist, there is an additional problem with the interpretation of their findings, namely that they did not adjust for other sectors in the economy, including non-traded sectors and sectors not subject to the corporate tax. Incidence results must be adjusted for the fact that the tax is only a partial one.
To illustrate in the simplest fashion, suppose the remaining sector of the economy is a non-corporate non-traded sector of the economy whose price is denoted by a capital P:
(C3) 
This commodity has no taxes and if the effects on r and w are estimated, those can be used to determine the change in P.
What ultimately to be determined is the fraction of the tax, rK c (where K c is the capital in the corporate traded sector) that falls on labor, that is what share of Ldw, where L is total labor in the economy, is of rK c .
To derive the real change in wages, the change in nominal wage is divided by the change in total price level in the economy, or, if the corporate sector is responsible for (1-) of output in the economy the percentage change in real wage (which is denoted with a capital W) can be expressed as follows:
(C4) 
If s is the share of the burden falling on labor income, from equation (1), and .
And, by substitution of these values into (3) and in turn into (4), and allowing the initial price level to be normalized at 1, obtain the equation for incidence in the economy, noting that equals rK c /wL c :
(C5) 
The first term, total labor divided by labor in the tax sector reflects the increased burden from the spread of the nominal fall in wages to the other sector, while the negative terms inside the next parenthesis reflects the rise in real wages due to the fall in the price of the untaxed sector. Whether the burden rises or falls depends on a variety of factors. As the capital intensity of the untaxed sector rises the burden falls; at the extreme when becomes 1, the first term collapses to 1 and the second term is less than s, so the total burden on labor is less in the economy than it is in the estimation. This possibility is more important than it might initially appear, because one of the most important uses of capital not subject to the corporate income tax is in housing in the United States.
Appendix D. Bargaining Models and Rent-Sharing of Corporate Taxes
With a number of studies appealing to a bargaining model and rent sharing, it is important to understand the theory implied. 
Bargaining models start from a standard Nash equilibrium which maximizes the product of the welfare of the two recipients. Using the ADM notation:
(D1) B = {[u(w)-u(w*)] N} (1- µ) {Π-Π*} µ 
where w is the wage earned, u(w) is the utility of the wage earned, w* is the competitive wage, u(w*) is the utility of the competitive wage, N is the number of employees, Π is the profit in the current undertaking and Π* is the alternative profit that could be earned in the competitive industry. The exponents (1- µ) and µ reflect the bargaining strength of the parties. The first term in curly brackets is the value of an excess wage to the workers, while the second is the value of excess profits to the owners.
Begin with a no tax world. To maximize B differentiate with respect to the wage (which appears in the value of excess profits because they are reduced by wN), the number of employees and the capital stock (which is embedded in profits). The result is a bargaining solution of the form:
(D2) wN= w*N+[(1- µ)/µ] (Π-Π*)
This solution is derived in ADM although they express all of their variables in per worker terms. 
Assuming away intermediate goods and other costs (which will make no difference) Π can be defined as PQ-wL (where P is price and Q is quantity). Π* can be defined as rK where r is the return required to attract capital and the amount earned in the competitive sector. 
(D3) wN= w*N + [(1- µ)/µ] (PQ-wN-rK)
This form of the bargaining formula is used by ADM because they are estimating wages.
It is more instructive in understanding the model, however, to examine not the wage but the excess wage. With some manipulation, and now dividing the variables by N to get per capita amounts (with lower cases indicating per capita), obtain
(D4) w-w* = (1- µ) (Pq-w*-rk)
The last term on the right hand side is excess profit (revenue minus the competitive wage minus the competitive return. The left hand side is the wage in excess of the competitive wage. The workers share is (1- µ) and it is an estimate of this coefficient that the empirical rent sharing literature is intended to identify.
Suppose now this bargaining model is being estimated assuming a tax of τ. Now profit, (Π-Π*) is now equal to (PQ – wN)(1- τ) –rK. The first order conditions for wages and labor now contain a tax term to reflect the fact that wages are deductible from the tax. Therefore equation D2 now becomes:
(D5) wN= w*N+[(1- µ)/µ] [(Π-Π*)/(1- τ)]
Since the tax term is in the denominator, it suggests that the wage would go up through this effect, which basically indicates that adding to wages saves taxes, and hence the price of paying the surplus in wages is smaller. 
At the same time the excess profit is reduced because taxes are applied to revenues, with wages, but not capital deducted, making the profit term (PQ-wN)(1- τ) –rK.
When this term is substituted to provide a version of (4) the tax term in the numerator cancels with the tax term in the denominator with the only effect of taxes on rK.
(D6) w-w* = (1- µ) (Pq-w*-rk/(1- τ))
A term similar to this one is contained in the Felix and Hines study. 
The important point that comes from this last equation is that in discussing rent-sharing the burden of the tax that falls directly on excess profits is not considered because that tax effect disappears from the formula. Although the pie is smaller by τ(Pq-w), the price of the wage share is also lower so the owners bear the entire direct burden of the tax on the firm's excess profits. The only way that taxes enter is to increase the normal cost of capital.
ADM ignore this term in their model because this term and its effects on wages are part of the indirect burden (which would be determined by general equilibrium economy-wide results). That is, they are interested in the direct effect of taxes outside the general equilibrium effects. They posit a term (which is neither observable nor clearly defined) which is not related to profit, of the form;
(D7) w-w* = (1- µ) (Pq-w*-ϕ/(1- τ) - rk/(1- τ))
where ϕ represents a tax payment that is not part of profits or of the cost of capital. It is not clear what qualifies as part of ϕ or how important it is. Most of the examples they mention such as deductions for interest and contributions to pension funds seem to qualify as either part of deductible costs of funds or wage compensation. And when actually estimating the relationship in D(7) they have no way to measure this value so the regression they run is actually roughly on total taxes per worker (conceptually τ(VA –w) + ϕ) where VA is value added. The tax term is estimated using instrumental variables such as tax rates since w is a left hand side variable and VA. Because of this issue, it is difficult to interpret the importance of their result even if they are capturing a rent-sharing effect rather than some other relationship. 
Felix and Hines are estimating the union wage premium, and their version of (D6) is not per worker and the premium is divided by the non-union (competitive) wage. To use their notation, they use L to denote labor. The left hand side variable is the total excess labor return, (w-w*)L which is equal to R. Also they denote the competitive wage as w. They also use α as the bargaining share. 
(D8) R = α (Q-wL-rK/(1- τ))
One peculiar point, to return to, is that they do not have a product price P. 
They then divide the equation by wL to obtain a ratio:
(D8) R/(wL)= α (Q/wL-1-rK/(wL(1- τ)))
They want to deal with the effect of tax rates on the demand for capital and labor and obtain an expression for (D8). They also use an optimization model for the firm's factory choices to simplify the expression and this term contains both w and the tax rate.
The Felix Hines derivation is in error because they have omitted the product price; as quantity changes so do prices. The proper form of (D8) is:
(D9) R/(wL)= α (PQ/wL-1-rK/(wL(1- τ)))
First, to maximize profit:
(D10) Profit = PQ-wL –rK = P(Q(K,L)Q(K,L) –wL –rK/(1- τ).
Q is a function of K and L and P is a function of Q which is in turn a function of K and L. Q in turn is a Cobb Douglas function:
(D11) Q = aK γ L (1-γ)
The two first order conditions for K and L are:
(D12) P(1-1/e)γQ/K = r/(1- τ)
(D13) P(1-1/e)(1-γ)Q/L = w
where e is the absolute value of the elasticity of demand.
One can see from equation (D13) that PQ/wL = (e/(1-e))(1/(1- γ)) and that the last term by dividing D12 by D13 is γ/(1- γ). Combining all of the terms together:
(D14) R/(wL) = α [{1/(e-1)}{1/(1-γ)}]
What equation (D14) indicates is that there is no effect of the tax or any other factor price on the wage premium. It is also quite sensible. If e is infinite which would be the case with a competitive price taking firm, the premium is zero; as e falls toward one with a less elastic demand (although one that is of necessity greater than 1) the premium becomes larger. In any case, for a Cobb Douglas function there is no reason to estimate a wage premium as a function of tax rates.
It also means that rent per employee would fall proportionally with wages.
Without presenting the complicated mathematics, the ratio will rise with higher taxes with a factor substitution elasticity of less than one and decline with a factor substitution elasticity higher than one. In the latter case the effect of the tax on rents via general equilibrium effects is ambiguous. That is (D14) becomes:
(D14) R/(wL) = α [{1/(e-1)}{1+ (b/(1-b) s (r/(w(1- τ ))(1-s) }]
where s is the factor substitution elasticity. It is easier to see what happens if expressed as an elasticity:
(D15) d(R/wl)/(R/wL) = (1-s) γ(dr/r –dw/w+d τ /(1- τ))
The last set of terms is expected to be positive, and measures how much the ratio of returns to wages changes. Calculations indicate this is a small semi-elasticity (assuming an overall federal and state tax rate of 30%). If the entire burden is borne by capital the semi-elasticity, as s ranges from 0.5 to 1.5 is 0.09 to -0.09, (as compared with the elasticity of 0.36 found in the study). If the burden were borne entirely by wages, the elasticity would range from 0.21 to -0.21. These calculations assume that γ is 0.25 in the sector under consideration and in the economy as a whole, and the corporate capital stock is half of the total capital stock. If the incidence falls on returns, Kdr = -rK 1 dt/(1- τ)) where K is the total capital stock and K 1 is the corporate. If the incidence falls on wages, Ldw = -rK 1 dt/(1- τ)). Since evidence suggests that, if the factor substitution elasticity is not one, it is probably below 1, the expectation is that ratio of rents to wages 
It is difficult to interpret these results without knowing the effect on wages which, in their estimates was actually positive (although not always statistically significant). However, their interpretation that 54% of the tax falls on rents is not consistent because they are calculating a reduction in the entire corporate wage bill, not the small portion that is the rent. Assume, for example, that the wage does not change and take their 0.36 semi-elasticity. Their formula indicates that dR/R = -.36d τ. To translate that into incidence on rents, multiply 0.36 times the ratio of rents to corporate tax collects. Rents are the rent premium (15%) times the union share (7%) times the wage share (about 70%), which is 0.7% of output. Corporate taxes are around 2% of output, so the ratio is .0.37. Thus, at their elasticity the share would 13%. If the highest elasticity assuming the tax is borne by capital is used the share is about 3% and if the highest amount assuming the tax is fully borne by capital is used, the share is about 5%.