Piketty et al (2014) A Tale of Three Elasticities PDF

American Economic Journal: Economic Policy 2014, 6(1): 230–271 http://dx.doi.org/10.1257/pol.6.1.230 Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities† By Thomas Piketty, Emmanuel Saez, and Stefanie Stantcheva* This paper derives optimal top tax rate formulas in a model where top earners respond to taxes through three channels: labor supply, tax avoidance, and compensation bargaining. The optimal top tax rate increases when there are zero-sum compensation-bargaining effects. We present empirical evidence consistent with bargaining effects. Top tax rate cuts are associated with top one percent pretax income shares increases but not higher economic growth. US CEO “pay for luck” is quantitatively more prevalent when top tax rates are low. International CEO pay levels are negatively correlated with top tax rates, even controlling for firms’ characteristics and perfor- mance. (JEL D31, H21, H24, H26, M12) T he share of total pretax income accruing to upper income groups has increased sharply in the United States. The top percentile income share has more than dou- bled from less than 10 percent in the 1970s to over 20 percent in recent years (Piketty and Saez 2003). This trend toward income concentration has taken place in a number of other countries, especially English-speaking countries, but is much more modest in continental Europe or Japan (Atkinson, Piketty, and Saez 2011 and Alvaredo et al. 2011). At the same time, top tax rates on upper income earners have declined sharply in many OECD countries, again particularly in English-speaking countries. While there have been many discussions both in the academic literature and the public debate about the causes of the surge in top incomes, there is not a fully com- pelling explanation. Most explanations can be classified into market-driven changes versus institution-driven changes. The market-driven stories posit that technologi- cal progress and globalization have been skill-biased and have favored top earners relative to average earners (see, e.g., Gabaix and Landier 2008 for CEOs and Rosen 1981 for winner-take-all theories for superstars). Those pure market explanations cannot account for the fact that top income shares have only increased modestly in a number of advanced countries (including Japan, Germany, or France) which are also * Piketty: Paris School of Economics, 48 Boulevard Jourdan, 75014 Paris, France (e-mail: [email protected]); Saez: Department of Economics, University of California, Berkeley, 530 Evans Hall #3880, Berkeley, CA 94720 (e-mail: [email protected]); Stantcheva: Department of Economics, Massachusetts Institute of Technology, 50 Memorial Drive, Cambridge, MA 02142 (e-mail: [email protected]). We thank Marco Bassetto, Wojciech Kopczuk, Laszlo Sandor, Florian Scheuer, Joel Slemrod, two anonymous referees, and numerous seminar partici- pants for useful discussions and comments. Rolf Aaberge, Markus Jantti, Brian Nolan, Esben Schultz, and Floris Zoutman helped us gather international top marginal tax rate data. We are very thankful to Miguel Ferreira for shar- ing with us the international CEO data from Fernandes et al. (2013). We acknowledge financial support from the Center for Equitable Growth at UC Berkeley and the MacArthur foundation. † Go to http://dx.doi.org/10.1257/pol.6.1.230 to visit the article page for additional materials and author disclosure statement(s) or to comment in the online discussion forum. 230 Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 231 subject to the same technological forces. The institution-driven stories posit that changes in institutions, defined to include labor and financial market regulations, union policies, tax policy, and more broadly social norms regarding pay disparity, have played a key role in the evolution of inequality. The main difficulty is that “institutions” are multidimensional and it is difficult to estimate compellingly the contribution of each specific factor. Related, there is a wide empirical literature in public economics analyzing the effects of tax rates on pretax incomes (see Saez, Slemrod, and Giertz 2012 for a recent survey) that reaches two broad conclusions. First, there is compelling evidence that upper incomes respond to tax rates whenever the tax code offers opportunities for tax avoidance. Such responses can sometime be quite large, especially in the short run. Second however, when the tax base is broad and does not offer avoidance oppor- tunities, the estimated elasticities are never large at least in the short or medium run. To our knowledge, no study to date has been able to show convincing evidence in the short or medium run of large real economic activity responses of upper earners to tax rates. However, it is difficult to provide compelling estimates of long-run elasticities. As we shall see, international evidence shows a strong correlation between top tax rate cuts and increases in top income shares in OECD countries since 1960. There are three narratives of the link between top tax rates and upper incomes. First, after noting that top US incomes surged following the large top marginal tax rate cuts of the 1980s, Lindsey (1987) and Feldstein (1995) proposed a stan- dard supply-side story whereby lower tax rates stimulate economic activity among top income earners (work, entrepreneurship, savings, etc.). Second, it has been pointed out—originally by Slemrod (1996)—that many of those dramatic responses were actually primarily due to tax avoidance rather than real economic behavior. Although this argument started as a critique of the supply-side success story, it has more recently been used to deny that any real increase in income concentration actu- ally took place. Under this scenario, the real US top income shares were as high in the 1970s as they are today but a smaller fraction of top incomes was reported on tax returns in the 1970s than today. A third narrative contends that high top tax rates were part of the institutional set-up putting a brake on rent extraction among top earners. When top marginal tax rates are very high, the net reward to a highly paid executive for bargaining for more compensation is modest. When top tax rates fell, high earners started bargaining more aggressively to increase their compensation. The first goal of this paper is to present a very simple model of optimal top labor income taxation that can capture all three avenues of response, the standard supply-side response, the tax-avoidance response, and the compensation-bargain- ing response to assess how each narrative translates into tax policy implications. We therefore derive the optimal top tax rate formula as a function of the three elasticities corresponding to those three channels of responses. The first elastic- ity e1 (supply side) is the sole real factor limiting optimal top tax rates. A large tax-avoidance elasticity e2is a symptom of a poorly designed tax system. A very high top tax rate within such a system offering many tax-avoidance opportunities is counterproductive. Hence, the optimal tax system should be designed to minimize tax-avoidance o pportunities through a combination of tax enforcement, base broad- ening, and tax neutrality across income forms. In that case, the second elasticity 232 American Economic Journal: economic policy February 2014 (avoidance) becomes irrelevant. The optimal top tax rate increases with the third elasticity e 3 (bargaining) as bargaining efforts are wasteful and zero-sum in aggre- gate. If a substantial fraction of the behavioral response of top earners comes from bargaining effects and top earners are not paid less than their economic product, then the optimal top tax rate is much higher than the conventional formula and actu- ally goes to 100 percent if the real supply-side elasticity is very small.1 If bargaining effects are moderately large, the quasi-confiscatory top marginal tax rates—80 per- cent–90 percent or more—applied in the United States and the United Kingdom between the 1940s and the 1970s, might have been consistent with a sensibly speci- fied optimal tax model. The second goal of the paper is to provide empirical evidence on the decomposi- tion of the total behavioral response of top incomes to top tax rates into those three channels. We consider both macro-level cross-country/times series evidence and CEO pay micro-level evidence. The macro evidence uses time series on top income shares from the World Top Incomes Database, top income tax rates, and real GDP per capita data. We obtain three main results. First, we find a very clear correlation between the drop in top marginal tax rates and the surge in top income shares since 1960. This suggests that the long-run total elasticity of top incomes with respect to the net-of-tax rate is large, around 0.5. Second, examination of the US case suggests that the tax-avoidance response cannot account for a significant fraction of the long-run surge in top incomes because top income shares based on a broader definition of income (that includes realized capital gains and hence a significant part of avoidance channels) has increased virtually as much as top income shares based on a narrower definition of income subject to the progressive tax schedule. Third, we find no evidence of a correlation between growth in real GDP per capita and the drop in the top marginal tax rate in the period 1960 to the present. This evidence is consistent with the bargaining model whereby gains at the top come at the expense of lower income earners. This suggests that the first elasticity is modest in size and that the overall effect comes mostly from the third elasticity. The micro evidence uses data on CEO pay in the United States since 1970 and international CEO pay data for 2006. We obtain two main results. First, the US evidence shows that pay for firm’s performance outside of the control of the CEO (due to industry—wide performance as in Bertrand and Mullainathan 2001) is quan- titatively more important when top tax rates are low. This suggests that low top tax rates have induced CEOs to increase the component of their pay not directly related to their own performance. The main channel may have been the development of stock-options in the 1980s and 1990s which do not filter out performance unrelated to CEOs’ actions (Hall and Murphy 2003). Second, international CEO pay evidence for 2006 shows that CEO pay is strongly negatively correlated with top tax rates even controlling for firm’s characteristics and performance, and that this correlation is stronger in firms with poor governance. This suggests that the link between top tax rates and CEO pay does not run through firm performance but is likely due to 1 The optimal top tax rate is moderate if the supply elasticity is fairly large and top earners are underpaid relative to their product, a situation that is theoretically possible in our model and might exist in countries with very low income concentration. Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 233 bargaining effects as the bargaining position of the CEO is stronger when top rates are low and in firms with poorer governance. All those results suggests that bargaining effects play a role in the link between top incomes and top tax rates implying that optimal top tax rates could be higher than commonly assumed. Bringing together the model and the empirical evidence, in our preferred estimates, we find an overall elasticity e = 0.5, which can be decom- posed into e 1 = 0.2 (at most), e2 = 0 and e3 = 0.3 (at least). This corresponds to a socially optimal top tax rate τ ∗  = 83 percent—as compared to τ ∗  = 57 percent in the standard supply-side case with e = e1 = 0.5 and e 2 = e3 = 0. This illustrates the critical importance of this decomposition into three elasticities. Our paper is related to a large body of theoretical work in optimal income taxa- tion and empirical work on estimating behavioral responses to taxation. Previous work has focused mostly on the traditional supply-side channel and the tax-avoid- ance/evasion channels.2 There is much less work in optimal taxation using models where pay differs from marginal product. A few studies have analyzed optimal taxation in models with labor market imperfections such as search models, Union models, or efficiency wages models (Sørensen 1999 provides a survey). The main focus of those papers has been on efficiency issues rather than redistributive issues, with most of the focus on the employment versus unemployment margin. Fewer papers have addressed redistribu- tive optimal tax policy in models with imperfect labor markets.3 Motivated by recent events, a few papers have proposed models of optimal taxation with rent-seeking. Lockwood, Nathanson, and Weyl (2012) consider a model where each profession creates externalities that can only be targeted indirectly through a nonlinear income tax. If high-earning professions generate larger negative externalities, then progres- sive taxation is desirable on pure efficiency grounds (i.e., solely for correcting exter- nalities). Rothschild and Scheuer (2012) consider a model with a rent-seeking sector and a traditional sector and solve for the (sector blind) optimal nonlinear income tax. They obtain optimal tax formulas that include the standard Mirrleesian term as well as an additional externality correcting term. The externality correcting term is natu- rally positive but it can be smaller or larger than the pure Pigouvian correction term depending on whether the within-sector or the across-sector externality dominates. In our simpler model, the correcting term is always equal to the Pigouvian term. As we shall discuss, our optimal top rate formula also can be connected to their more general analysis. Finally, Besley and Ghatak (2013) show that the possibility of bailouts to financial intermediaries distorts the supply price of capital and creates an argument for taxing financial bonuses separately from other sources of income, in addition to the standard redistributive argument. Our theoretical value added is to bring together in a single framework the three channels of behavioral responses and show how optimal top tax rate formulas can be expressed in terms of the estimable elasticities corre- sponding to each response channel. Our empirical value added is to attempt to gauge 2 Piketty and Saez (2013) and Saez, Slemrod, and Giertz (2012) provide recent surveys of the optimal tax and empirical literatures. Slemrod and Yitzhaki (2002) review specifically the tax-avoidance/evasion literature. 3 Hungerbühler et al. (2006) analyze a search model with heterogeneous productivity, and Stantcheva (2011) considers optimal redistribution in a labor market screening setting where firms cannot observe perfectly the pro- ductivity of their employees. 234 American Economic Journal: economic policy February 2014 the importance of these three channels, most notably the rent-seeking channel, and to calibrate our theoretical formulas accordingly. The remainder of the paper is organized as follows. Section I presents our theo- retical model. Section II presents macro-level empirical results. Section III presents micro-level evidence using CEO pay. Section IV synthesizes the results, and pro- vides a brief conclusion. Extensions and data construction details are gathered in the online Appendix. All data are available online. I. Theoretical Model A. Standard Model: Supply-Side and Tax-Avoidance Responses In the paper, we denote by z taxable earnings and by T(z) the nonlinear tax sched- ule. We assume a constant marginal tax rate τ in the top bracket above a given income _ threshold z . We assume without loss of generality that the number of taxpayers in the top bracket has measure one at the optimum. We refer to this group as top bracket tax- _ payers. We focus on the determination of the optimal top tax rate τ, taking z  as given. The government maximizes a standard social welfare function of the form W = ∫    G(ui) dν(i), ∫    T(zi) dν(i) ≥ T0 , subject to where G(·) is increasing concave, u i is the utility of individual i, and dν(i) is the density mass of people of individuals of type i, and T0 ≥ 0 is an exogenous tax revenue requirement. Denoting by p the multiplier of the government budget constraint, we define the social marginal welfare weight on individual i as gi = G′(u i)uci/p. We assume that the average social marginal welfare weight among top bracket income earners is zero.4 In that case, the government sets τ to maximize tax revenue raised from top bracket taxpayers. Considering a zero marginal welfare weight allows us to obtain an upper bound on the optimal top tax rate.5 Supply-Side Responses.— We start with the standard model with only supply- side responses as in Saez (2001). See Piketty and Saez (2013) for a detailed presen- tation and survey of this classic case. We assume away income effects for simplicity and tractability, and consider utility functions of the form u i(c, z) = c − hi(z) where z is pretax earnings, c = z − T(z) is disposable income, and hi(z) denotes the labor supply cost of earning z which is increasing and convex in z. Optimal effort choice is given by the first-order condition h   ′i (z) = 1 − τ where τ is the marginal tax rate so that individual earnings zi(1 − τ) are solely a function of the net-of-tax rate 1 − τ. Aggregating over all top bracket taxpayers, we denote by z(1 − τ) the aver- age income reported by top bracket taxpayers, as a function of the net-of-tax rate. 4 If the social welfare function G(·) has curvature so that G′(u) → 0 when u → ∞, this will be the case when _ _ z  → ∞ and will hence approximately be true for large z . 5 As we shall discuss, formulas can be easily adapted if we instead put a positive social welfare weight g on the marginal consumption of top bracket earners (relative to average). Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 235 The aggregate elasticity of income in the top bracket with respect to the net-of-tax rate is therefore defined as 1−τ _ (1) e1 =  _ dz z    d(1 − τ) . This is the standard first elasticity that reflects real economic responses to the net-of-tax rate, which can be labeled as labor supply effects, broadly defined (more hours of work, more intense effort per hour worked, occupational choice, etc.) The optimal top tax rate maximizing tax revenue is given by (2) τ ∗ =  _  , 1 1 + a · e1 _ where a = z/(z − z ) > 1 is the Pareto parameter of the top tail of the distribution.6 The proof of formula (2) is straightforward and well known. The government _ chooses τ to maximize top bracket tax revenue T = τ [z(1 − τ) − z ]. The first-order _ condition is [z − z ] − τ [dz/d(1 − τ)] = 0, which can be immediately rearranged as (2) using the definition of e 1 from (1). Adding Tax-Avoidance Responses.— As shown by many empirical studies (see Saez, Slemrod, and Giertz 2012 for a recent survey), responses to tax rates can also take the form of tax avoidance. We can define tax avoidance as changes in reported income due to changes in the form of compensation but not in the total level of compensation. Tax-avoidance opportunities arise when taxpayers can shift part of their taxable income into another form or another time period that is treated more favorably from a tax perspective.7 The main distinction between real and tax-avoidance responses is that real responses reflect underlying, deep individual preferences for work and consump- tion while tax-avoidance responses depend critically on the design of the tax system and the avoidance opportunities it offers. While the government cannot drastically change underlying deep individual preferences and hence the size of the real elastic- ity, it can change the tax system to reduce avoidance opportunities. Naturally, this distinction is one of degree as some forms of tax avoidance cannot be easily elimi- nated due to technological constraints (see our discussion below) and, symmetri- cally, some real responses could be somewhat dampened by government policies. We can extend the standard model as follows to incorporate tax avoidance.8 Let us denote by y real income and by x sheltered income so that ordinary tax- able income is z = y − x. The latter is taxed at marginal tax rate τ in the top 6 If a positive social weight g > 0 is set on top earners’ marginal consumption, then the optimal top tax rate is τ = (1 − g)/(1 − g + ae1). 7 Examples of such avoidance/evasion are (i) reductions in current cash compensation for increased fringe benefits or deferred compensation such as stock-options or future pensions, (ii) increased consumption within the firm such as better offices, vacation disguised as business travel, private use of corporate jets, etc. (iii) changes in the form of business organization such as shifting profits from the individual income tax base to the corporate tax base, (iv) re-characterization of ordinary income into tax favored capital gains, (v) outright tax evasion such as using offshore accounts. 8 This follows and extends Saez (2004) and Saez, Slemrod, and Giertz (2012). A broad literature surveyed by Slemrod and Yitzhaki (2002) and Piketty and Saez (2013) has introduced tax avoidance in optimal tax models. 236 American Economic Journal: economic policy February 2014 bracket, while sheltered income x is taxed at a constant and uniform marginal tax rate t lower than τ.9 The utility function of individual i takes the form u i(c, y, x) = c − hi(y) − di(x), where c = y − τ z − tx + R = (1 − τ)y + (τ − t)x + R is _ _ disposable after tax income and R = τ z  − T(z ) denotes the virtual income coming out of the nonlinear tax schedule. hi( y) is the utility cost of earning real income y, and d i(x) is the cost of sheltering an amount of income x. There is a cost to shelter- ing, since sheltered income such as fringe benefits or deferred earnings are less valuable than cash income. We assume that both h i(·) and d i(·) are increasing and convex, and normalized so that h   i′ (0) = d  i′ (0) = 0. This model nests the standard model when the sheltering cost di(x) is infinitely large for any x > 0. Individual utility maximization implies that h  ′i (y) = 1 − τ and d  ′i (x) = τ − t, so that yiis an increasing function of 1 − τ and x iis an increasing function of the tax differential τ − t. Aggregating over all top bracket taxpayers, we have y = y(1 − τ) with real elasticity e1 = [(1 − τ)/y][dy/d(1 − τ)] > 0 as in (1) and x = x(τ − t) increasing in τ − t. Note that x(0) = 0 as there is sheltering only when τ > t. Hence z = z(1 − τ, t) = y(1 − τ) − x(τ − t) is increasing in 1 − τ and t. We denote by e = [(1 − τ)/z][dz/d(1 − τ)] > 0 the total elasticity of taxable income z with respect to 1 − τ when keeping t constant. We denote by s the fraction of the behavioral response of z to dτ due to tax avoidance, and by e 2 = s · e the tax-avoid- ance elasticity component __ dx/d(τ − t) dx/d(τ − t) (3)      =  _    s =          dy/d(1 − τ) + dx/d(τ − t) ∂z/∂(1 − τ) and _1−τ _ dx e2 = s · e =   z    d(τ − t)  . By construction, we have (1 − s)e = (y/z)e1, or equivalently e = (y/z)e1 + e2. If we start from a situation with no tax avoidance (y = z), then we simply have e = e1 + e2, i.e., the total elasticity is the sum of the standard labor supply elasticity and the tax-avoidance elasticity component. We can prove the following two results.10 Partial Optimum.—For a given t, the optimal top tax rate τ on taxable income is 1 + t · a · e2 (4) τ ∗ =  _        , 1+a·e where e = (y/z)e1+ e2is the elasticity of taxable income (keeping t constant), e 1 = [(1 − τ)/y][dy/d(1 − τ)] is the real labor supply elasticity, and e2 = [(1 − τ)/z][dx/d(τ − t)] is the tax-avoidance elasticity component. For example, in the case of nontaxable fringe benefits, t = 0. In the case of shifting ordinary income into tax 9 favored capital gains, we have t > 0 but with t significantly less than τ. 10 Our results easily extend to the more general case with utility c − di(x, y), which generates aggregate supply functions of the form z(τ, t), y(τ, t), x(τ, t). We used the separable case for simplicity of presentation. Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 237 Full Optimum.—If sheltering occurs only within top bracket earners and t can be changed at no cost to the government, the optimal global tax policy is to set t and τ equal to (5) t∗  = τ ∗  =  _  . 1 1 + a · e1 Proof: As there is a measure one of top bracket earners, the government chooses τ to _ maximize T = τ[z(1 − τ, t) − z ] + tx(τ − t). The first-order condition for τ is _ ∂z z ] − τ  _  + t  _  dx 0 = [z − ∂(1 − τ) d(τ − t) _ ∂z ∂z z ] − τ  _  + ts  _  , = [z − ∂(1 − τ) ∂(1 − τ) where the second expression is obtained using the definition of s from (3). The first two terms are the same as in the standard model. The third term captures the “fis- cal externality” as a fraction s of the behavioral response translates into sheltered income taxed at rate t. Using the definition of e = [(1 − τ)/z][dz/d(1 − τ)], we can _ rewrite the first-order condition as e(τ − ts)/(1 − τ) = (z − z )/z = 1/a, which can be rearranged into formula (4) using the fact that e2 = s · e from (3). The second part of the proof can be obtained by taking the first-order con- dition with respect to t. As z(1 − τ, t) = y(1 − τ) − x(τ − t), the first-order condition is d T/dt = x + [τ − t][dx/d(τ − t)] = 0.11 As x ≥ 0 and τ ≥ t and dx/d(τ − t) ≥ 0, this first-order condition can only hold for t = τ and x(τ − t = 0) = 0. Setting t = τ in equation (4), and noting that x = 0 implies that z = y and hence e − e2 = e1, we immediately obtain (5). Intuitively, as x is completely wasteful, it is optimal to deter x entirely by setting t = τ. Three comments are worth noting about these results. First, if t = 0 then τ = 1/(1 + a · e) as in the standard model. In the narrow framework where the tax system is taken as given (i.e., there is nothing the govern- ment can do about tax evasion and income shifting), and where sheltered income is totally untaxed, then whether e is due to real responses versus avoidance responses is irrelevant, a point made by Feldstein (1999). Second however, if t > 0, then sheltering creates a “fiscal externality,” as the shifted income is taxed at rate t and τ > 1/(1 + a · e). Third and most important, the government can improve effi- ciency and its ability to tax top incomes by closing tax-avoidance opportunities (setting t = τ in our model). Sheltering then becomes irrelevant and the real elas- ticity e 1is the only factor limiting taxes on upper incomes. Kopczuk (2005) shows that the Tax Reform Act of 1986 in the United States, which broadened the tax base and closed loopholes did reduce the elasticity of reported income with respect to the net-of-tax rate. Kleven and Schultz (2012) finds small yet very compellingly 11 Note that we have used the assumption stated in the proposition that sheltering happens only within top bracket taxpayers so that a change in t has no effect on individuals below the top bracket. 238 American Economic Journal: economic policy February 2014 identified elasticities for large top tax rate changes in Denmark, a very high tax country where tax-avoidance opportunities are indeed very limited. Actual tax-avoidance opportunities come in two varieties. Some are pure cre- ations of the tax system, such as exemption of fringe benefits or differential treat- ment of different income forms and hence could be eliminated by reforming the tax system. In that case, t is a free parameter that the government can change at no cost as in our model. Yet other tax-avoidance opportunities reflect real enforce- ment constraints that are costly—sometimes even impossible—for the government to eliminate.12 Slemrod and Kopczuk (2002) present a model with costs of enforce- ment. The government might also want to use differential taxes on different income sources for redistributive reasons or for efficiency reasons.13 Our simple model also ignores that there might be political hurdles to setting t = τ, for example if some types of tax sheltering are fiercely defended by special interests or lobbying groups. The important policy question is then what fraction of the tax-avoidance elasticity can be eliminated by tax redesign and tax enforcement. In a developing country with most economic activity taking place in small informal businesses, the tax-avoidance elasticity cannot be reduced to zero. But in a modern economy and with interna- tional cooperation, the tax-avoidance elasticity could likely be substantially reduced as most economic transactions, especially at the top end, are recorded and hence verifiable (Kleven, Kreiner, and Saez 2009). We come back to this issue below. B. Compensation-Bargaining Responses Motivation and Previous Work.— Pay may not equal marginal economic product for top income earners. In particular, executives can be overpaid if they are entrenched and use their power to influence compensation committees (Bebchuk and Fried 2006 survey the wide corporate finance literature on this issue). In principle, executives could also be underpaid relative to their marginal product if there are social norms against high compensation levels. In that case, a company might find it more profit- able to underpay its executives to buy peace with its other employees, customers, or the public in general.14 To the extent that top income earners generally have more opportunities to set their own pay than low and middle income earners, the first case seems more likely. But from a theoretical perspective both cases are interesting. More generally, pay can differ from marginal product in any model in which compensation is decided by on-the-job bargaining between an employer and an employee, as in the classic search model of Diamond-Mortensen-Pissarides. In that framework, there is a rent to be shared on the job because of frictions in the matching process and inability to commit to a wage before the match has occurred. Indeed, in such models, the wage rate is not pinned down and can be set to any value within 12 For example, it is very difficult for the government to tax profits from informal cash businesses. Fighting offshore tax evasion requires international cooperation. 13 The Ramsey model recommends to tax relatively less the most elastic goods. In the presence of income shift- ing, the gap between tax rates should be reduced (see our earlier working paper version). 14 Recent examples have arisen in the case of the 2008 and 2009 bailouts of financial firms in the United States—although the ultimate effects on executive compensation are unclear. Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 239 the outside options of the worker and his marginal product (Hall 2005).15 Typically, the wage is then determined by the relative bargaining powers of the employer and employee, for example through Nash bargaining with exogenous weights. In gen- eral, the wage rate is not efficient, unless the so-called Hosios condition is met.16 In more general models, given the substantial costs involved in replacing workers who quit in most modern work environments, especially for management positions where specific human capital is important, as well as imperfect information between firm and employee, it seems reasonable to think that there would be a band of possible compensation levels. In such a context, bargaining efforts on the job can conceiv- ably play a significant role in determining pay. Marginal tax rates affect the rewards to bargaining effort and can hence affect the level of such bargaining efforts.17 Yet another reason why pay may differ from marginal product is imperfect infor- mation. In the real world, it is often very difficult to estimate individual marginal products, especially for managers working in large corporations. For tasks that are performed similarly by many workers (e.g., one additional worker on a factory line), one can approximately compute the contribution to total output brought by an extra worker. But for tasks that are more or less unique, this is much more complex: one cannot run a company without a chief financial officer or a head of communication during a few years in order to see what the measurable impact on total output of the corporation is going to be. For such managerial tasks, it is very unlikely that market experimentation and competition can ever lead to full information about individual marginal products, especially in a rapidly changing corporate landscape. If marginal products are unknown, or are only known to belong to relatively large intervals, then institutions, market power, and beliefs systems can naturally play a major role for pay determination (see Rotemberg 2002). This is particularly relevant for the recent rise of top incomes. Using matched individual tax return data with occupa- tions and industries, Bakija, Cole, and Heim (2012) have recently shown that execu- tives, managers, supervisors, and financial professionals account for 70 percent of the increase in the share of national income going to the top 0.1 percent of the US income distribution between 1979 and 2005.18 15 In such simple models, pay is typically below marginal product if and only if the outside option of the employee is lower than his product on the job. In more complex settings, with the outside option and productivity on the job evolving over time, as well as switching costs for both employer and employee, pay can be also above marginal product. 16 Those standard search models stand in contrast to newer “directed search” models where the wage is negoti- ated ex ante and in which case efficiency is restored (see, e.g., Moen 1997). 17 To take an example familiar to most readers, academic faculty pay is often determined by outside options tak- ing the form of competitive offers from outside institutions. Because personal moving costs are difficult to observe by the upper administration of one’s home university, a formal competitive offer letter is often sufficient to trigger a pay increase in one’s current job. Obtaining an outside offer for the sole purposes of getting a pay raise is costly and time consuming (both for the academic and to potential recruiters). If the pay raise in the home institution does not trans- late into higher productivity, then this is a pure compensation-bargaining response. Obviously, lower tax rates make the pay raise more valuable and might encourage such type of behavior. If it can be raised by competitive outside offers, faculty pay will typically have to be below marginal product (for the home university). Faculty pay can also be above marginal product (if productivity declines) as pay is downward rigid and tenured faculty cannot be laid off. 18 Including about two thirds in the nonfinancial sector, and one third in the financial sector. In contrast, the combined share of the arts, sports and medias subsectors, usually used to illustrate winner-take-all theories, is only 3.1 percent of all top 0.1 percent taxpayers. See Bakija, Cole, and Heim (2012, table 1). 240 American Economic Journal: economic policy February 2014 Theoretical Model.— We consider the simplest model that can capture bargain- ing compensation effects. Individual i receives a fraction η of his/her real product y and can put productive effort both into increasing y and bargaining effort into increasing η. Both types of effort are costly and utility is given by ui(c, η, y) = c − hi(y) − ki(η), where c is disposable after-tax income, hi(y) is the cost of producing output y as in the standard model, and ki(η) is the cost of bargaining necessary in order to receive a share η of the product. Both h i and k i are increasing and convex.19 We again rule out income effects for simplicity.20 Let b = (η − 1)y be bargained earnings defined as the gap between received earnings ηy and actual product y. Note that the model allows both overpay (when η > 1 and hence b > 0) and underpay (when η < 1 and hence b < 0). Let us denote by E( b ) the average bargained earnings in the economy. In the aggregate, it must be the case that total product is equal to total compensation. Hence, if E(b) > 0, so that there is overpay on average, E( b ) must come at the expense of somebody. Symmetrically, if E( b ) < 0, then the average underpay −E( b ) must benefit some- body. For simplicity, we assume that any gain made through bargaining comes uni- formly at the expense of everybody else in the economy. Hence, individual incomes are all reduced by a uniform amount E( b )(or increased by a uniform amount −E(b) if E(b) < 0).21 In reality, bargaining pay likely comes at the expense of other employees or shareholders in the same company or sector. In online Appendix A.1, we discuss in detail how and in which class of models this uniformity assumption can be relaxed without affecting our results (we summarize those results below). Because the government uses a nonlinear income tax schedule, it can adjust the demogrant −T(0) to fully offset E( b ). Effectively, the government can always tax (or subsidize) E( b )at 100 percent before applying its nonlinear income tax. Hence, we can assume that the government absorbs one-for-one any change in E(b). Therefore, we can simply define earnings as z = ηy = y + b and assume that those earnings are taxed nonlinearly. This simplification is possible because of our key assumption that E( b ) affects all individuals uniformly (or, alternatively, in the class of models presented in online Appendix A.1). Individual i chooses y and η to maximize ui(c, η, y) = η · y − T(η · y) − hi(y) − ki(η), so that (1 − τ)η = h  ′i (y) and k  ′i (η), (1 − τ)y = 19 We could consider a general nonseparable cost of effort function hi(y, η) to allow for example for substitution between productive versus bargaining effort. The optimal tax formula would be identical, but the comparative stat- ics would be less transparent and would require additional assumptions. 20 This model nests the standard model if the cost function k is such that k( 1 ) = 0 and there is infinite disutility cost of pushing η above 1. 21 A simple but admittedly unrealistic scenario in which our uniformity assumption holds would be a situation where firms are owned equally in the population and bargaining for pay comes at the expense of profits. Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 241 where τ = T ′is the marginal tax rate. This naturally defines y iand η ias increasing functions of the net-of-tax rate 1 − τ. Hence zi = ηi · yiand bi = (1 − ηi) · yiare also functions of 1 − τ. Let us consider as in the previous section the optimal top tax rate τ for incomes _ above a threshold level z  and assume again that there is a measure one of taxpayers _ with incomes above z . Let us denote by z(1 − τ), y(1 − τ), and b(1 − τ) average reported income, productive earnings, and bargained earnings across all taxpayers in the top bracket. We can then define, as above, the real labor supply elasticity e1 and the total compensation elasticity e to be 1 − τ _ 1 − τ _ e1 =  _ e =  _ dy dz y    d(1 − τ)  ≥ 0 and z    d(1 − τ)  . We define s, the fraction of the marginal behavioral response due to bargaining and by e 3 = s · e the bargaining elasticity component _db/d(1 − τ) ___ db/d(1 − τ) (6) s =          =           dz/d(1 − τ) db/d(1 − τ) + dy/d(1 − τ) and _1 − τ _ db e3 = s · e =   z    d(1 − τ)  . This definition immediately implies that (y/z)e1 = (1 − s) · e. By construction, e = (y/z)e1 + e3. If we start from a situation where top taxpayers are paid their mar- ginal product (y = z), then we simply have e = e1 + e3. Importantly, s (and hence e 3) can be either positive or negative but it is always positive if individuals are over- paid (i.e., if η > 1). If individuals are underpaid (i.e., η < 1) then s (and hence e 3) can be negative. More precisely, we can easily prove e1 y · e1 s = 1 −  _     = 1 −  _ · e  ≤ 1 η( eη + e1  ) z with 1 − τ _ eη =  _ dη η    d(1 − τ)  = e − e1 ≥ 0. _ e1 s ≤ 0 if and only if η ≤     . If η > 1 then s > 0. e1 + eη We can now state our main proposition. Proposition 1: The optimal top tax rate is 1 + a · e3 a(y/z)e1 (7) τ ∗ =  _     = 1 −   _     , 1 + a · e 1 + a · e 242 American Economic Journal: economic policy February 2014 where e = (y/z)e1 + e3 is the elasticity of taxable income, e1 = [(1 − τ)/y][dy/d(1 − τ)] = z(1 − s)e/y the real labor supply elasticity, and e3 = s · e = [(1 − τ)/z][db/d(1 − τ)] the compensation-bargaining elasticity. ∗decreases with e (keeping e3 constant) and increases with e 3 (keeping e τ constant). τ∗decreases with the real elasticity e1 (keeping e and y/z constant) and increases with the level of overpayment η = z/y (keeping e 1 and e constant). If e1 = 0 then τ∗  = 1. If z ≥ y (top earners are overpaid) then e3 ≥ 0 and τ∗  ≥ 1/(1 + a · e1). Proof: The government aims to maximize taxes collected from taxpayers in the top _ bracket. Taxes collected from the latter are τ[z − z ] but the tax τ also impacts E( b ) and hence the government’s budget (as the government absorbs any change in E( b ) through the demogrant). Since the total size of the population is N, the government _ chooses τ to maximize T = τ[z(1 − τ) − z ] − N · E(b). If dτ triggers a change in b in the top bracket, that change is then reflected one-for-one in NE( b ). Hence we have NdE(b)/d(1 − τ) = db/d(1 − τ) and the first-order condition for τ is _ _   +  _  = 0, dz db z ] − τ  [z − d(1 − τ) d(1 − τ) _ _ τ − s z − ⇒ [τ − s]  _  = z − _   · e =  _ _ dz z  1 z , ⇒     =   a , d(1 − τ) 1 − τ z which leads to (7) using e3 = s · e. The rest of the proposition is straightforward. Proposition 1 shows that it is possible to obtain a simple optimal tax formula that nests the standard model in the case e 3 = 0 (no bargaining elasticity). Implementing the formula requires knowing the total elasticity e and the bargaining elasticity com- ponent e 3 (or equivalently the fraction s of the behavioral response at the margin due to bargaining effects). e 3can also be indirectly obtained by subtraction from e using the real labor supply elasticity e1and the ratio of product to pay y/z. Hence, imple- menting the formula requires knowledge of not only the compensation response (i.e., the taxable income elasticity e), but also of the real economic product responses to tax changes, which is considerably more difficult. Trickle-Up.— In the case where top earners are overpaid relative to their pro- ductivity (z > y), we have s > 0 and hence e3 > 0 and the optimal top tax rate is higher than in the standard model (i.e., τ∗  > 1/(1 + a · e)). This corresponds to a “trickle-up” situation where a tax cut on upper incomes shifts economic resources away from the bottom and toward the top. Those effects can be quantitatively large, as we will discuss in Section IV. Trickle-Down.— In the case where top earners are underpaid relative to their pro- ductivity (z < y) and it is possible that s < 0 and hence e 3 < 0, in which case the Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 243 optimal top tax rate is lower than in the standard model (i.e., τ < 1/(1 + a · e)). This corresponds to a “trickle-down” situation where a tax cut on upper incomes also shifts economic resources toward the bottom, as upper incomes work in part for the benefit of lower incomes. Pigouvian Interpretation.— Economically, the extra-term in formula (7) rela- tive to the standard formula τ = 1/(1 + a · e) can therefore be interpreted as the Pigouvian correction term for the rent-seeking externality. A $1 reduction in z due to a small increase in τ creates an $ s = e3/e positive externality. The optimal tax rate formula (7) takes the standard additive form of the conventional Mirrlees term plus the Pigouvian term.22 Regulation versus Taxation.— We have taken as given the bargaining opportuni- ties in the economy. Conceivably, the government can affect bargaining opportu- nities through regulations. A large literature in corporate finance analyzes whether regulations can impact executive compensation (see, e.g., Frydman and Jenter 2010 and Murphy 2012 for recent discussions). In a reduced form way, regulations would impact the cost of bargaining ki(η) but our analysis of the optimal tax would remain valid taking regulations are given. Ideally, as bargaining is a wasteful effort that shifts resources without any real productive effect, the government would want to com- pletely discourage it, so that pay would always be equal to real economic product. In that case, bargaining effects disappear and we naturally revert to the standard model. However, as long as some bargaining effects exist, our analysis remains relevant. Differentiated Taxation.— Some economic sectors or industries might be more prone to bargaining effects than others. For example, less competitive industries have higher rents and hence more scope for bargaining effects. In that case, differen- tiated tax rates across industries could be desirable. The same argument calls for dif- ferentiated tax rates in the standard model if some sectors have a higher labor supply elasticity. In practice, there are two important arguments against differentiated taxa- tion. First, it would be difficult to measure bargaining effects for each sector. This uncertainty might allow the better paid lobbyists to argue in favor of preferential tax rates for their industry. Second, differentiated tax rates create additional distortions if there are opportunities to shift income from one sector to another. Lockwood, Nathanson, and Weyl (2012) make this point and consider nonlinear income taxa- tion in a multi-sector model with different externalities across sectors. Nonuniform External Effects and Link with Rothschild and Scheuer (2012).— We have made the strong assumption that aggregate external effects E( b )are spread in a uniform and lumpsum fashion among all individuals, i.e., rent seekers reduce every- body else’s earnings uniformly. That simplifies the formula because the government 22 The additive form can be written as (τ − s)/(1 − τ) = 1/(a · e) where s is the externality and 1/(a · e) is the conventional Mirrlees term. This additive decomposition in optimal taxation with externalities is well-known since at least Sandmo (1975). Similarly, formula (4) in the case with tax avoidance in the sum of the conventional Mirrlees term and the corrective fiscal externality term t · e2/e so that (τ − te2/e)/(1 − τ) = 1/(a · e). 244 American Economic Journal: economic policy February 2014 can exactly undo the external effect by simply shifting the schedule and adjusting the demogrant. Realistically, the external effects will not be uniformly distributed. If the government can still adjust the nonlinear tax system to undo the external effect, then our formula carries over unchanged. We provide an example in online Appendix A.1 showing that this is possible in the case of the discrete version of the Mirrlees model (with a finite number of possible occupations) if we assume that bar- gaining takes place solely at the top and comes at the expense of lower occupations. This extension shows that our basic formula has wider applicability. However, if the government cannot undo the external effect, then formulas have to be modified. Rothschild and Scheuer (2012) consider such a model where external effects take place through sector level wages so that rent-seeking effects are propor- tional to earnings. They allow for both occupational choice across the productive and rent-seeking sectors and intensive responses within sector. They characterize the full optimal nonlinear in such a model (and not solely the optimal top tax rate as we do). Because the nonlinear tax system cannot undo external effects in their model, the for- mula they obtain is no longer the simple sum of the standard Mirrleesian term and the Pigouvian term. Instead, the externality correction term in their model can be either smaller or larger than the pure Pigouvian correction term depending on whether within- sector or across-sector externalities dominate. Rothschild and Scheuer (2012) also con- sider the optimal top tax rate and obtain a more general formula as the corrective term is not necessarily equal to the Pigouvian term but it is equal to our formula in the special case of their model where the corrective term equals to Pigouvian term.23 One case of interest is when rent-seekers gain solely at the expense of other top earners.24 In that case, bargaining effects are irrelevant in aggregate among top earn- ers and hence e = e1and the optimal tax formula boils down to the standard formula τ = 1/(1 + a · e1). Effectively, if top earners steal from top earners, decreasing the top tax rate stimulates stealing but this has no effect on the top income share as this is a wash across top earners. Hence, only e 1 matters. C. Putting the Three Elasticities Together We can put the three elasticities together in a single formula. If there are both avoidance effects and compensation-bargaining effects, then we can write the total elasticity of taxable income e as the sum of three terms: e = (y/z)e1 + e2 + e3. In case we start from a situation where there is no tax-avoidance activity and incomes are equal to marginal products, then y = z and we simply have: e = e1 + e2 + e3. For a given tax rate t on sheltered income, we have 1 + t · a · e2 + a · e3 (8) τ∗  =  __         . 1+a·e This happens when there is a single rent-seeking sector in their model (Section 3.5) or in the case where 23 within- and across-sector externalities just cancel out. 24 For example, an academic department with a fixed compensation budget in our previous illustration and assuming that all academics are top earners. Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 245 If the government can choose t to fully eliminate tax avoidance, we have τ∗ = t∗  = (1 + a · e3)/(1 + a · e). If government puts a social welfare weight 0 ≤ g < 1 on marginal consumption of top earners (relative to the average), then the optimal top rate formula (8) generalizes to τ∗  = (1 − g + t · a · e2 + a · e3)/(1 − g + a · e). II. Macro-Level Empirical Evidence In this section, we use our model to account for the evolution of top tax rates and top incomes in OECD countries. We first analyze US evidence and then turn to international evidence. A. US Evidence US evidence is depicted in graphical form in Figure 1 and key estimates are presented in Table 1. Panel A of Figure 1 depicts the top 1 percent income shares including realized capital gains (pictured with full diamonds) and excluding real- ized capital gains (the empty diamonds).25 Both top income share series display a U-shape over the century. Panel A also displays (on the right y-axis) the top mar- ginal tax rate for the federal individual income tax for ordinary income (dashed line) and for long-term realized capital gains (dotted line). Two lessons emerge. First, considering the top income share excluding realized capital gains, which corresponds roughly to income taxed according to the regular progressive schedule, there is a clear negative overall correlation between the top 1 percent income share and the top marginal tax rate: (i) the top 1 percent income share was high before the Great Depression when top tax rates were low (except for a short period from 1917 to 1922), (ii) the top 1 percent income share was consistently low between 1932 to 1980 when the top tax rate was uniformly high, (iii) the top 1 percent income share has increased significantly since 1980 after the top tax rate has been greatly lowered. If this correlation is due to a causal relationship from top tax rates to top income shares as in our theoretical model, the overall elasticity of reported incomes is high. For the recent period, the top 1 percent income share more than doubled from around 8 percent in 1960–1964 to around 18 percent in the last five years, while the net-of-tax (retention) rate increased from 15 percent (the top marginal tax rate was 85 percent on average in 1960–1964) to 65 percent (when the top tax rate is 35 percent). If we attribute the entire surge in the top income share to the decline in the top tax rate, this translates into an elasticity of top incomes with respect to the net-of-tax rate around 0.5, as shown in column 1, panel A of Table 1. Column 1 of panel B in Table 1 also shows a strong correlation between the net-of-tax rate and the top income share with a basic time series regression of the form log(Top 1 percent Income Share) = α + e · log(1 − Top MTR) + ε. 25 Those series are taken from Piketty and Saez (2003). They are based on the family unit (and not the individual adult). Income includes cash market income before individual taxes and credits, and excludes government transfers (such as Social Security benefits, unemployment insurance benefits, or means-tested transfers) as well as noncash benefits (such as employer or government provided health insurance). 246 American Economic Journal: economic policy February 2014 Panel A. Top 1 percent income shares and Top MTR 25 100 90 20 80 Top 1% income shares (%) Marginal tax rates (%) 70 15 60 50 10 40 30 5 20 Top 1 percent share Top MTR 10 Top 1 percent (excl. KG) MTR K gains 0 0 1913 1923 1933 1943 1953 1963 1973 1983 1993 2003 Year Panel B. Top 1 percent and bottom 99 percent income growth 100 500 90 Real Income per adult (1913 = 100) 80 400 Marginal tax rates (%) 70 60 300 50 40 200 30 100 20 Top 1 percent Top MTR 10 Bottom 99 percent 0 0 1913 1923 1933 1943 1953 1963 1973 1983 1993 2003 Year Figure 1. Top Marginal Tax Rates, Top Incomes Shares, and Income Growth: US Evidence Notes: Panel A depicts the top 1 percent income shares including realized capital gains in full diamonds and excluding realized capital gains in empty diamonds. Computations are based on family market cash income. Income excludes government transfers and is before individ- ual taxes (source is Piketty and Saez 2003, series updated to 2008). Panel A also depicts the top marginal tax rate on ordinary income and on realized long-term capital gains (source is Tax Policy Center). Panel B depicts real cash market income growth per adult of top 1 percent incomes and bottom 99 percent incomes (base 100 in 1913), assuming that individual adult top 1 percent and bottom 99 percent shares are the same as top 1 percent and bottom 99 per- cent family based shares. Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 247 Table 1—US Evidence on Top Income Elasticities Income Income including excluding capital gains capital (to control for gains tax avoidance) (1) (2) Panel A. 1975–1979 versus 2004–2008 Comparison Top marginal tax rate (MTR) 1960–4 85 percent 85 percent 2004–8 35 percent 35 percent Top 1 percent income share 1960–4 8.2 percent 10.2 percent 2004–8 17.7 percent 21.8 percent Elasticity estimate: Δ log (top 1 percent share)/Δ log (1 − Top MTR) 0.52 0.52 Panel B. Elasticity estimation (1913–2008): log(top 1 percent income share) = α + e × log(1 − Top MTR) + c × time + ε No time trend 0.25 0.26 (0.07) (0.06) Linear time trend 0.30 0.29 (0.06) (0.05) Number of observations 96 96 Panel C. Effect of top MTR on income growth (1913–2008): log(income) = α + β × log(1 − Top MTR) + c × time + ε Top 1 percent real income 0.265 0.261 (0.047) (0.041) Bottom 99 percent real income −0.080 −0.076 (0.040) (0.039) Average real income −0.027 −0.027 (0.018) (0.034) Number of observations 96 96 Notes: Estimates from panel A are obtained using series from Figure 1 (source is Piketty and Saez 2003 for top income shares and Tax Policy Center for top marginal tax rate). If the surge in top income shares since 1960 is explained solely by the reduction in the top marginal tax rate, then the elasticity is large, around 0.5. The elasticity is the same for income excluding capital gains and income including capital gains. As capital gains are treated more favorably and are the main channel of avoidance for top incomes, this implies that tax avoidance plays no role in the surge of top incomes in the long-run. Estimates from panels B and C are obtained by time-series regressions over the period 1913–2008 (96 observations) and using standard errors from Newey-West with 8 lags. Panel B shows significant elasticities of top 1 percent income shares with respect to the net-of-tax rate (using the top MTR). Elasticities are virtually the same when excluding or including capital gains and are robust to including a linear time trend in the regression. This shows that there is a strong link in the time-series between top income shares and top MTR as evidenced in Figure 1A. Panel C shows that real income growth of top 1 percent is strongly related to the net-of-tax rate (using the top MTR), confirming the results of panel B. Bottom 99 percent incomes are negatively related to the net-of-tax rate (using the top MTR) suggesting that top 1 percent income gains came at the expense of bottom 99 percent earners. Average incomes (including both the top 1 percent and bottom 99 percent) are not sig- nificantly related to the net-of-tax rate. Those results suggest that most of the elasticity of top incomes is due to bargaining effects and not real supply side effects. This link remains the same when including a linear time trend in the regression.26 The implied elasticity is around 0.25–0.30 and very significant. Importantly, as the average marginal tax rate faced by the top 1 percent was smaller than the statutory top 26 Naturally, the correlation disappears when additional polynomials in time are added as identification is based solely on time series variation. 248 American Economic Journal: economic policy February 2014 rate before the 1970s, our elasticity estimate is a lower bound. The solution would be to instead use the actual average marginal tax rate faced by the top 1 percent instru- mented with the top marginal tax rate (as in Saez 2004).27 Importantly, Piketty and Saez (2003) show that the surge in US top income shares since the 1970s is higher in the upper part of the top percentile (top 0.1 percent and especially top 0.01 percent). The marginal tax rate cuts are also much larger in the upper part of the top percentile so that the resulting elasticities are actually quite similar across sub-groups within the top 1 percent (Saez 2004, table 7). It is also conceivable that very high incomes have more opportunities to respond to tax rates through avoidance or bargaining effects. This could explain why estimated elasticities below the top 1 percent are much lower than in the top 1 percent (Saez 2004, table 7). Second, the correlation between the top shares and the top tax rate also holds for the series including capital gains. Realized capital gains have been traditionally tax favored (as illustrated by the gap between the top tax rate and the tax rate on realized capital gains in the figure) and have constituted the main channel for tax avoidance of upper incomes.28 Under the tax-avoidance scenario, taxable income subject to the progressive tax schedule should be much more elastic than a broader income defini- tion that also includes forms of income that are tax favored. Indeed, in the pure tax- avoidance scenario, total real income should be completely inelastic. However, both the graphical analysis of panel A and the estimates presented in Table 1, column 2 show that the link between the top tax rate is as strong for income including realized capital gains as it is for income excluding capital gains. The time series regressions also generate virtually identical estimates as the series excluding capital gains. This suggests that income shifting responses do not account for much of the long-term evolution in top income shares documented in Figure 1. In future work, it would be useful to sharpen this test by (i) subtracting deductions—such as charitable giving or interest paid on debt—from the narrow income definition to come closer to tax- able income, (ii) adding forms of income that are nontaxable—such as tax exempt interest, capital gains unrealized till death, or fringe benefits to further broaden the broader income definition. There is no easy route to do this as most of those items are not reported consistently and continuously in income tax statistics. In the short run, to be sure, there is strong evidence on panel A of large tax-avoidance responses in various tax reform episodes with clear differential responses for top incomes including versus excluding realized capital gains.29 But in the long run the income 27 Unfortunately, actual top 1 percent marginal tax rate series are not available before 1960 and would be very time consuming to construct. 28 When the individual top tax rate is high (relative to corporate and realized capital gains tax rates), it is advan- tageous for upper incomes to organize their business activity using the corporate form and retain profits in the cor- poration. Profits only show up on individual returns as realized capital gains when the corporate stock is eventually sold (see Gordon and Slemrod 2000 for an empirical analysis). 29 For example, in 1986, realized capital gains surged in anticipation of the increase in the capital gains tax rate from 20 to 28 percent (Auerbach 1988), creating a clear spike in the series including capital gains. From 1986 to 1988, income excluding realized capital gains surged as closely held businesses shifted from the corporate form to the individual form, and as many business owners paid themselves accumulated profits as wages and salaries (Slemrod 1996; Saez 2004). Such shifting increased reported ordinary income at the expense of realized capital gains, explaining why there is a big discontinuity in income excluding realized capital gains but not in income including realized capital gains. Finally, there is a clear surge in incomes in 1992 in anticipation of the increase in the top tax rate on ordinary income in 1993 due to re-timing in the exercise of stock-options for executives (Goolsbee 2000). See Saez, Slemrod, and Giertz (2012) for a much more detailed discussion. Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 249 shifting elasticity e 2 (as estimated along the ordinary income versus capital gains margin) appears to be small (say, e2 < 0.1). Clearly, capital gains are not the only channel through which tax avoidance can occur. Our estimates of e 2would be biased downward if those alternative tax-avoid- ance channels, such as offshore accounts or perquisites had sharply declined since the 1960s. However, if anything, it seems that those have increased at the same time as top rates have declined. For the former channel, Zucman (forthcoming) for example shows that a growing fraction of Swiss fiduciary deposits are recorded as belonging to tax havens since the 1970s. For the latter, it is notoriously hard to find historical data, as disclosure rules for perquisites have only recently been imposed30 but perquisites would have had to be huge pre-1970 to generate a high elasticity of avoidance through that channel.31 This analysis has been predicated on the assumption that the link between top tax rates and top income shares is causal. Reverse causality remains a possibility. For example, higher top income shares provide more political power to top earners to influence policy (via lobbying or campaign funding) and leads to lower top tax rates. This would lead to an upward bias in our elasticity estimates (but would not necessarily invalidate the tax-avoidance analysis just presented). We come back to this important issue when we consider international evidence. The even more difficult question to resolve is whether this large responsiveness of top incomes to tax rates is due to supply-side effects generating more economic activity as in the standard model or whether it is due to a zero-sum game transfer from the bottom 99 percent to the top 1 percent as in the bargaining model. This is critical in order to decompose the total elasticity e into its real (e1) and bargaining (e3) components. Panel B of Figure 1 tackles this issue by plotting the evolution of top 1 percent incomes and bottom 99 percent incomes adjusting for price inflation.32 The graph shows clearly that income growth for the bottom 99 percent was highest in the 1933 to 1973 period when top income tax rates were high and the growth of top 1 percent was modest. Conversely, the growth of bottom 99 percent incomes has slowed down since the 1970s when top tax rates came down and top 1 percent incomes grew very fast. Those findings can be captured by a basic regression analy- sis of the form log(Real Incomegt) = α + β · log(1 − Top TRt) + c · t + εt , where g indexes either the Bottom 99 percent or the top 1 percent or the overall average income and t denotes the year. We naturally control for time to capture 30 Regulation introduced in December 1978 required firms to disclose only the total amount of remuneration distributed in the form of securities or property, insurance benefits or reimbursement, and personal benefits. Only in 1993 were perquisites and other personal benefits (above a minimum threshold) separately reported. Even then, the data poses problems in terms of transparency and accuracy. 31 According to Yermack (2006); Grinstein, Weinbaum, and Yehuda (2008); and Frydman and Saks (2010), today’s perks are significantly larger than even the total taxable pay of top executives pre-1970s, casting doubt upon the idea that perks could have been even larger pre-1970. 32 To control for changes in the number of adults per family, we plot income per adult (aged 20 and over) assuming that the top 1 percent income share at the individual adult level is the same as at the family level. This assumption holds true in countries such as Canada where top income shares can be constructed both at the indi- vidual and family levels (Saez and Veall 2005). 250 American Economic Journal: economic policy February 2014 Table 2—International Evidence on Top Income Elasticities All 18 countries and fixed periods Bootstrapping period and country set 5th 95th 1960–2010 1960–1980 1981–2010 Median percentile percentile (1) (2) (3) (4) (5) (6) Panel A. Effect of the top marginal income tax rate on top 1 percent income share Regression: log(top 1 percent share) = α + e × log(1 − Top MTR) + ε No controls 0.324 0.163 0.803 0.364 0.128 0.821 (0.034) (0.039) (0.053) (0.043) (0.085) (0.032) Time trend control 0.375 0.182 0.656 0.425 0.191 0.761 (0.042) (0.030) (0.056) (0.045) (0.091) (0.032) Country fixed effects 0.314 0.007 0.626 0.267 0.008 0.595 (0.025) (0.039) (0.044) (0.035) (0.070) (0.026) Number of observations 774 292 482 286 132 516 Panel B. Effect of the top marginal income tax rate on real GDP per capita Regression: log(real GDP per capita) = α + β × log(1 − Top MTR) + c × time + ε No country fixed effects −0.064 −0.018 −0.097 0.002 −0.214 0.173 (0.033) (0.041) (0.043) (0.042) (0.080) (0.026) Country fixed effects −0.029 −0.082 0.037 −0.004 −0.087 0.071 (0.014) (0.016) (0.019) (0.016) (0.031) (0.011) Initial GDP per capita −0.095 −0.025 −0.023 −0.054 −0.149 0.022 (0.019) (0.016) (0.014) (0.017) (0.030) (0.011) Initial GDP per capita, time −0.088 0.004 −0.037 −0.060 −0.160 0.012 × intial GDP per capita (0.017) (0.011) (0.014) (0.016) (0.030) (0.011) Country fixed effects, time −0.018 0.000 0.008 −0.015 −0.069 0.040 × initial GDP per capita (0.011) (0.014) (0.017) (0.013) (0.031) (0.009) Number of observations 918 378 540 317 152 576 Notes: Panel A presents regression elasticity estimates to the top 1 percent income share with respect to the net-of- tax top rate. Those estimates are obtained by regressing log(top 1 percent income share) on the log(1-top MTR) where top MTR denotes the top marginal income tax rate (including both central and local income taxes). Columns 1–3 use the complete panel of top 1 percent income share series from the World Top Income Database for 18 OECD countries for three time periods: 1960 to 2010 in column 1, 1960 to 1980 in column 2, 1981 to 2010 in column 3. Estimates are not sensitive to the inclusion of a time trend or of country fixed effects. For the following 5 countries, the data start after 1960: Denmark (1980); Ireland (1975); Italy (1974); Portugal (1976); Spain (1981). For Switzerland, the data end in 1995 (they end in 2005 or after for all other countries). Panel B presents regressions of the log real GDP per capita (2010 PPP) on the log net-of-tax rate. All regressions include a time trend to account for growth. Regressions include the same 18 OECD countries as in panel A for three time periods: 1960 to 2010 in column 1, 1960 to 1980 in column 2, 1981 to 2010 in column 3. In contrast to panel A, the series are complete for all countries. The second regression include country fixed effects. The third regression includes initial GDP per capita. The fourth regression includes initial GDP per capita and the interaction of initial GDP per capita with a time trend (to capture catching up effects). The fifth regression includes country fixed effects and the interaction of initial GDP per capita with a time trend. Negative numbers imply that high top MTR lead to more growth (in contrast with the standard supply-side scenario). The effect of the top MTR on GDP per capita growth is small and insignificant when using the widest set of controls (last row). Columns 4 to 6 perform a robustness check by repeating the same regres- sion 500 times on 500 randomly selected samples. More precisely, we randomly select a time period (with a mini- mum of 17 years, i.e., 1/3 of our 51 year span) common to all countries, a subset of countries (between 6 and 18, i.e., at least 1/3 of our sample). We then compute the 500 coefficients and their standard deviations and report the median (column 4), fifth percentile (column 5), and 95th percentile (column 6). In panel A, all estimates are posi- tive (highly significant for the median and 95th percentile and mostly insignificant for the fifth percentile but still positive), implying that the correlation between top tax rates and top income shares is robust. In panel B, median estimates are either negative or insignificant. Fifth percentile estimates are always negative, while 95th percentile estimate are positive. Overall, there is no systematic evidence that GDP growth is related to top tax rates. overall exogenous growth independent of tax policy. The estimates for β, reported in Table 2, panel C, are positive and highly significant for the top 1 percent incomes, with a magnitude around 0.25 very similar to the time series elasticity estimation Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 251 of panel B. In contrast, the estimates for β are negative (and just significant at the 5 percent level with a t-statistics around 2) for the bottom 99 percent, and close to zero and insignificant for the overall average income. Again, the estimates are very similar for income excluding capital gains in column 1 and for income including capital gains in column 2. This evidence is consistent with the bargaining model where gains at the top have come at the expense of the bottom. In principle, the estimate β obtained for the overall average income can be used to compute e 1. I.e., if the model is well identi- fied we have: β = π · e1, where π is the initial income share of top marginal tax rate taxpayers. That is, if we take π = 10 percent,33 then a doubling of the net-of- top-marginal-tax-rate should lead to a β = 5 percent rise in the average real income of the economy if the real supply-side elasticity e 1were 0.5. Since we find that β is close to zero and insignificant for the overall average income, under our identifica- tion assumptions, e 1is also small and insignificant, and that the overall elasticity e comes mostly from bargaining effects through e3. This evidence can also be used to rule out the possibility of significant unrecorded tax-avoidance effects. That is, assume that in the 1950s–1970s top income earners were escaping high top rates via consumption within the firm or tax havens. Many of those tax-avoidance schemes are not recorded in GDP.34 If such tax avoidance had declined significantly in the recent period, then this should show up as extra eco- nomic growth. For example, in presence of such unrecorded tax-avoidance activi- ties, the estimate β should actually be equal to: β = π · (e1 + e2). This suggests that the overall elasticity e comes mostly from e 3 effects. However, this evidence relies on the strong OLS assumption that any deviation of growth from trend (captured by the error term εt) is uncorrelated with the top mar- ginal tax rate. It is conceivable that economic growth could have slowed down in the 1970s for reasons unrelated to the top tax rate decreases. This could have driven down the bottom 99 percent income growth as well. In that case, the cut in top tax rates could have increased top incomes growth as in the supply-side scenario without nega- tively impacting bottom 99 percent incomes. Indeed, growth slowed down in many OECD countries after the oil shocks of the 1970s. Therefore, this evidence based on a single country is at best suggestive. Hence, we next turn to international evidence. B. International Evidence Effects of Top Tax Rates on Top Income Shares.— To analyze international evidence, we use data on the income shares of the top 1 percent from 18 OECD countries, gathered in the World Top Incomes Database (Alvaredo et al. 2011) com- bined with top income tax rate data since 1960. We focus on the period since 1960 33 The exact fraction of taxpayers falling in the top marginal rate bracket varies over time. In recent decades, it is generally larger than the top 1 percent (it is often closer to the top 2 percent–3 percent), so π = 10 percent should be viewed as a lower bound (implying that the estimates for e1should be viewed as upper bounds). 34 For example, consumption within corporations such as fancy offices or restaurants, corporate jets, etc. are intermediate costs of production and hence unrecorded in GDP estimates. Incidentally, we know of no evidence showing that such intermediate consumption has declined since the 1960s (anecdotal evidence suggests that it might have risen, along with the rise of cash compensation). Importantly, other forms of tax avoidance, such as deferred compensation or legal income shifting toward fringe benefits, are recorded in GDP. 252 American Economic Journal: economic policy February 2014 because this allows us to include more countries (a number of countries in the top income database have data only for recent decades) and to be able to obtain top tax rate data for all countries. In addition, focus on the recent period is interesting because of the very divergent trends across countries in both top income shares and top tax rates.35 Top incomes are defined as cash market income excluding capital gains and subject to the regular income tax. Our top income tax rates series include both the central and local government top tax rates on ordinary income. We do not include payroll taxes as those taxes apply only to wage earnings which constitute only a fraction of top 1 percent incomes and are often capped. We do not include consumption taxes either. Details on the construction of top tax rates and other vari- ables, together with data sources, are in online Appendix A.2. We start in Figure 2 by showing the link across countries between the top tax rate and the top 1 percent income share for the periods 1960–1964 (panel A) and 2005–2009 (panel B). If the country does not have top income share data for those years, we select the first available five years after 1960 and the most recent five years.36 Panel A shows that there was a very wide dispersion in top tax rates across OECD countries in the early 1960s with rates as low as 45 percent for Spain and Switzerland and above 80 percent for the United Kingdom and the United States. The graph shows that there is virtually no correlation between top income shares and top tax rates in the early 1960s. The implied elasticity, obtained from a simple OLS regression of the log of the retention rate (one minus the top marginal tax rate) on the log of the top 1 percent share based on those 18 observations is very small (0.07) and insignificant. Panel B of Figure 2 shows a dramatic shift by 2005–2009. Top tax rates are much lower than they were in the 1960s with no country above 60 percent and a n umber of countries clustering around 40 percent including the United States and the United Kingdom. Those two countries have moved from being the highest top tax rate coun- tries in the 1960s to the lowest today. There is also much more heterogeneity in top income shares which vary from a low of 4 percent for Denmark to a high of almost 18 percent for the United States. Importantly, there is also a very strong negative cor- relation between top tax rates and top income shares in 2005–2009. As reported in the graph, the implied elasticity for 2005–2009 is extremely large at around 1.90 and highly significant. In order to extend the 1960s versus today comparison we did for the United States to our 18 OECD countries, Figure 3 plots the change in top income shares from 1960–1964 to 2005–2009 against the change in the top marginal tax rate for all the countries. The figure shows a very clear and strong correlation between the cut in top tax rates and the increase in the top 1 percent income share, with some interesting heterogeneity. Countries such as Germany, Spain, Denmark, or Switzerland which did not experience any significant top rate tax cut did not experience increases in 35 Roine, Vlachos, and Waldenström (2009) have used the database to explain the long-run determinants of inequality over the full century, including the top tax rate as an explanatory variable among many others. They pres- ent overall regressions without focusing specifically on the recent decades as we do here. 36 For the following five countries, the data start after 1960: Denmark (1980); Ireland (1975); Italy (1974); Portugal (1976); Spain (1981). For Switzerland, the data end in 1995 (they end in 2005 or after for all the other countries). Vol. 6 No. 1 Piketty et al.: Optimal Taxation of Top Labor Incomes 253 Panel A. Top 1 percent share and top marginal tax rate in 1960−1964 18 Top 1 percent income share (percent) 16 Elasticity = 0.07 (0.15) 14 12 Germany Switzerland Netherlands 10 Finland France Canada Japan UK 8 US Spain Australia NZ Sweden Italy Norway 6 Ireland Portugal 4 Denmark 40 50 60 70 80 90 Top marginal tax rate (percent) Panel B. Top 1 percent share and top marginal tax rate in 2005−2009 18 US Top 1 percent income share (percent) 16 Elasticity = 1.90 (0.43) UK 14 Canada 12 Ireland Norway Germany 10 PortugalItaly Spain Australia NZ France Japan 8 Switzerland Finland Netherlands Sweden 6 Denmark 4 40 50 60 70 80 90 Top marginal tax rate (percent) Figure 2. Top Income Shares and Top Marginal Tax Rates: International Evidence Notes: The figure depicts the top 1 percent income shares and top income tax rates (includ- ing both central and local government individual income taxes) across 18 OECD countries in 1960–1964 (panel A) and 2005–2009 (panel B). Source for top income shares is the World Top Incomes Database. Source for top income tax rates is OECD and country specific sources. If the country does not have top income share data for those years, we select the first five years after 1960 available and the most recent five years (full details in online Appendix A.2). For the following five countries, the data start after 1960: Denmark (1980); Ireland (1975); Italy (1974); Portugal (1976); Spain (1981). For Switzerland, the data end in 1995 (they end in

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