Saez et al (2012) The Elasticity of Taxable Income PDF

Journal of Economic Literature 2012, 50:1, 3–50 http://dx/doi=10.1257/jel.50.1.3 The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review Emmanuel Saez, J...

Journal http://dx/doi=10.1257/jel.50.1.3 The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review Emmanuel Saez, Joel This paper critically surveys of taxable income with respect provide a theoretical framework be used as a sufficient statistic other parameters should be estimated Second, we discuss conceptually of the elasticity of taxable tax rate increase in the United critical discussion of selected in light of the theoretical and avenues for future research. 1. Introduction T he notion of a behavioral elasticity pies a critical place in the ysis of taxation. Graduate textbooks teach that the two central aspects of the public sector, optimal progressivity of the tax-and- transfer system, as well as the optimal size of the public sector, depend (inversely) on the compensated elasticity of labor supply with * Saez: University of California, Slemrod: University of Michigan and NBER. Giertz: University of Nebraska. We thank Sören Chetty, Henrik Kleven, Wojciech Kopczuk, Jonathan Shaw, Caroline Weber, David Weiner, Roger Gor- don, and two anonymous referees for helpful comments and discussions, and Jonathan Adams for invaluable research assistance. NSF Grant SES-0134946 is gratefully acknowledged. 01_Saez.indd 3 4 Journal of for married women the responsiveness of labor force participation appears to be sig- nificant. Overall, though, the compensated elasticity of labor appears to be fairly small. In models with only a labor–leisure choice, this implies that the efficiency cost per dollar raised of taxing labor income—to redistrib- ute revenue to others or to provide public goods—is bound to be low, as well. Although evidence of a substantial com- pensated labor supply elasticity has been hard to find, evidence that taxpayers respond to tax system changes more generally has decidedly not been hard to find. For exam- ple, the timing of capital gains realizations appears to react strongly to changes in capi- tal gains tax rates, as evidenced by the surge in capital gains realizations in 1986, after the United States announced increased tax rates on realizations beginning in 1987 (Auerbach 1988). Dropping the top individual tax rate to below the corporate tax rate in the same act led to a significant shift in business activ- ity toward pass-through entities, which are not subject to the corporate tax (Auerbach and Slemrod 1997). Addressing these other margins of behav- ioral response is crucial because, under some assumptions, all responses to taxation are symptomatic of deadweight loss. Taxes trig- ger a host of behavioral responses intended to minimize the burden on the individual. In the absence of externalities or other market failure, and putting aside income effects, all such responses are sources of inefficiency, whether they take the form of reduced labor supply, increased charitable contributions or mortgage interest payments, increased expenditures for tax professionals, or a dif- ferent form of business organization, and thus they add to the burden of taxes from society’s perspective. Because in principle the elasticity of taxable income (which we abbreviate from now on using the stan- dard acronym ETI) can capture all of these responses, it holds the promise of more 01_Saez.indd 4 Saez, Slemrod, a narrow base and many deductions and avoidance opportunities is likely to generate high elasticities and hence large efficiency costs. In that context, broadening the tax base and eliminating avoidance opportuni- ties such as to reduce the elasticity is likely to be more efficient and more equitable than altering tax rates within the old system. The remainder of the paper is organized as follows. Section 2 presents the theoretical framework underlying the taxable income elasticity concept. Section 3 presents the key identification issues that arise in the empiri- cal estimation of the taxable income elastic- ity, using as an illustration the taxable income response to the 1993 top tax rate increase in the United States. Section 4 reviews the results of some selected empirical studies in light of our discussion of the conceptual and empirical issues. Section 5 concludes and discusses the most promising avenues for future research. Appendices present a sum- mary of the key U.S. legislated tax changes that have been studied in the U.S. literature and a brief description of existing U.S. tax return data. 2. Conceptual Framework 2.1 Basic Model In the standard labor supply model, indi- viduals maximize a utility function u(c, l) where c is disposable income, equal to con- sumption in a one-period model, and l is labor supply measured by hours of work. Earnings are given by w · l, where w is the exogenous wage rate. The (linearized) bud- get constraint is c = w · l · (1 − τ) + E, where τ is the marginal tax rate and E is vir- tual income. The taxable income elasticity literature generalizes this model by noting that hours of work are only one component of the behavioral response to income taxation. Individuals can respond to taxation through 01_Saez.indd 5 6 Journal only on the net-of-tax rate.3 In the absence of compelling evidence about significant income effects in the case of overall reported income, it seems reasonable to consider the case with no income effects, which simpli- fies considerably the presentation of effi- ciency effects. It might seem unintuitive to assume away the effect of changes in exog- enous income on (reported taxable) income. However, in the reported income context, E is defined exclusively as virtual income cre- ated by the tax/transfer budget constraint and hence is not part of taxable income z. Another difference is that the labor compo- nent of z is labor income (w · l) rather than labor hours (l); this difference requires us to address the incidence of tax rate changes (i.e., their effect on w), which we do briefly in section 2.2.5. The ETI literature has attempted to esti- mate the elasticity of reported incomes with respect to the net-of-tax rate, defined as (1) 1 −  e =  _ τ ·  _ z ∂ (1 − τ) the percent change in reported income when the net-of-tax rate increases by 1 per- cent. With no income effects, this elasticity is equal to both the compensated and uncom- pensated elasticity. Importantly, and as rec- ognized in the labor supply literature, the elasticity for a given individual may not be constant and depends on the tax system. As a result, an elasticity estimated around the cur- rent tax system may not apply to a hypotheti- cal large tax change. As shown in Feldstein 3There is no consensus in the about the size of income effects, ing small income effects, but with finding large income effects (see Blundell and MaCurdy 1999 for a survey). There is much on the magnitude of income effects literature. Gruber and Saez (2002) estimate both income and substitution effects in the case and find small and insignificant income effects. 01_Saez.indd 6 Saez, when the top bracket rate is τ. We denote by zm(1 − τ) the average income reported by those N top taxpayers, as a function of the net-of-tax rate. The aggregate elasticity of tax- able income in the top bracket with respect to the net-of-tax rate is therefore defined as e = [(1 − τ)/zm] · aggregate elasticity is equal to the average of the individual elasticities weighted vidual income, so that individuals contribute to the aggregate elasticity in proportion their incomes.6 Suppose that the government increases the top tax rate τ by a small amount d τ (with no change in the tax schedule for _ incomes below z ). This small two effects on tax revenue. First, there is a “mechanical” increase in tax revenue due to the fact that taxpayers face a higher tax rate _ on their incomes above z . The total mechani- cal effect is _ (2) dM ≡ N · (zm This mechanical effect is the projected increase in tax revenue, absent any behav- ioral response. Second, the increase in the tax rate triggers a behavioral response that reduces the aver- age reported income of top N taxpayers by d zm  = −e · zm reported income of dzm changes by τ d zm. Hence, the m 6 Formally, z = [z1 e = [(1 − τ)/z ] · [∂ z m m = (1 − τ) · [∂ z1 /∂ = [e1· z1+.. where eiis the elasticity of individual i. 7 The change d τ could induce N taxpayers to leave (or join if d τ As long as behavioral responses take intensive margin, each individual to d τ so that the total revenue second order (d N · d τ) derivation. 01_Saez.indd 7 8 Journal thicker the tail of the distribution, the larger _ is zm relative to z , and hence the smaller is a. Using the definition of a, we can rewrite the effect of the small reform on tax revenue dR simply as: (5) dR = dM · 1 −  _ [ τ 1−τ Formula (5) shows that the fraction of tax revenue lost through behavioral responses— the second term in the square bracket expression—is a simple function increas- ing in the tax rate τ, the elasticity e, and the Pareto parameter a. This expression is of pri- mary importance to the welfare analysis of taxation because τ · e · a/(1 − τ) is exactly equal to the marginal deadweight burden created by the increase in the tax rate, under the assumptions we have made and that we discuss below. This can be seen as follows: Because of the envelope theorem, the behav- ioral response to a small tax change dτ cre- ates no additional welfare loss and thus the utility loss (measured in dollar terms) cre- ated by the tax increase is exactly equal to the mechanical effect dM.10 However, tax reve- nue collected is only dR = dM + dB < dM because dB < 0. Thus −dB represents the extra amount lost in utility over and above the tax revenue collected dR. From (5) and because dR = dM + dB, the marginal excess burden per dollar of extra taxes collected is defined as (6) − dB/dR =  __ e·a·τ . 1−τ−e·a·τ In other words, for each extra dollar of taxes raised, the government imposes an extra 10 Formally, V(1 − τ, E) = z that d V = uc · (−zdτ fore, the (money-metric) marginal is indeed equal to the mechanical by individual. 01_Saez.indd 8 Saez, Slemrod, elasticity estimate of e = 0.25 (correspond- ing, as we discuss later, to the mid-range of the estimates from the literature), the frac- tion of tax revenue lost through behavioral responses (−dB/dM), should the top tax rate be slightly increased, would be 27.7 percent, slightly above a quarter of the mechanical (i.e., ignoring behavioral responses) pro- jected increase in tax revenue. In terms of marginal excess burden, increasing tax rev- enue by dR = $1 causes a utility loss (equal to the MECF) of 1/(1 − 0.277) = $1.38 for taxpayers, and hence a marginal excess bur- den of −dB/dR = $0.38, or 38 percent of the extra $1 tax collected. Following the supply-side debates of the early 1980s, much attention has been focused on the revenue-maximizing tax rate. The revenue-maximizing tax rate τ* is such that the bracketed expression in equation (5) is exactly zero when τ = τ*. Rearranging this equation, we obtain the following simple for- mula for the revenue-maximizing tax rate τ* for the top bracket: τ* =  _ 1 (7)  . 1 + a·e A top tax rate above τ* is inefficient because decreasing the tax rate would both increase the utility of the affected taxpayers with _ income above z and increase government revenue, which could in principle be used to benefit other taxpayers.13 The optimal income taxation literature following Mirrlees (1971) shows that formula (7) is the opti- mal top tax rate if the social marginal util- ity of consumption decreases to zero when income is large (see Saez 2001). At the tax rate τ*, the marginal excess b urden 13 Formally, this a second-best come as there is a feasible government duce a Pareto improvement, ignoring the utility of some individuals enters ity functions of others. 01_Saez.indd 9 10 Journal of Economic In the basic model we have considered, the ETI e is a sufficient statistic to estimate the efficiency costs of taxation as it is not neces- sary to estimate the structural parameters of the underlying individual preferences. Such sufficient statistics for welfare and normative analysis have been used in various contexts in the field of public economics in recent years (see Chetty 2009c for a recent survey). However, it is important to understand the limitations of this approach and the strong assumptions required to apply it, as we show in the next subsections. 2.2 Fiscal Externalities and Income The analysis has assumed so far that the reduction in reported incomes due to a tax rate increase has no other effect on tax rev- enue. This is a reasonable assumption if the reduction in incomes is due to reduced labor supply (and hence an increase in untaxed leisure time), or due to a shift from taxable cash compensation toward untaxed fringe benefits or perquisites (more gener- ous health insurance, better offices, com- pany cars, etc.) or tax evasion. However, in many instances the reduction in reported incomes is due in part to a shift away from taxable individual income toward other forms of taxable income such as corporate income, or deferred compensation that will be taxable to the individual at a (see Slemrod 1998). For example, Slemrod (1996) and Gordon and Slemrod (2000) argue that part of the surge in top incomes after the Tax Reform Act of 1986 in the United States, which reduced indi- vidual income tax rates relative to corporate tax rates (see appendix A), was due of taxable income from the corporate sector toward the individual sector. For a tax change in a given base z, we define a fiscal externality as a change in the present value of tax revenue that occurs in any tax base z′ other than z due to the behav- ioral response of private agents to the tax 01_Saez.indd 10 Saez, Slemrod, The same envelope theorem logic applies for welfare analysis: the income that is shifted to another tax base at the margin does not generate any direct change in welfare because the taxpayer is indifferent between reporting marginal income in the individual income tax base versus the alternative tax base. Therefore, as above, −dB represents the marginal deadweight burden of the indi- vidual income tax, and the marginal excess burden expressed in terms of extra taxes col- lected can be written as dB  =  __ (10) −  _     . dR 1 − τ − e The revenue-maximizing tax rate (7) becomes: 1 + s·t·a·e τ  *s  =  __ (11) 1+ a·e If we assume again that a = 1.5, e = 0.25, τ = 0.425, but that half (s = 0.5) of marginal income disappearing from the individual base is taxed on average at t = 0.3,15 the fraction of revenue lost due to behavioral responses drops from 27.7 percent to 17.9 percent, and the marginal excess burden (expressed as a percentage of extra taxes raised) decreases from 38 percent to 22 percent. The revenue- maximizing tax rate increases from 72.7 per- cent to 76.8 percent. This simple theoretical analysis shows therefore that, in addition to estimating the elasticity e, it is critical to analyze the source or destination of changes in reported individual incomes is another tax base, either a concurrent one or in another time period. Thus two additional param- eters, in addition to the taxable income elas- ticity e, are crucial in the estimation of the tax revenue effects and marginal deadweight 15 We show below that s = 0.5 and numbers to capture the shift from taxable income following the Tax Reform Act of 1986. 01_Saez.indd 11 12 Journal individual level may choose to incorporate where they would be subjected to the cor- porate income tax instead.17 In that case, the standard taxable income elasticity be large and the individual income tax rev- enue consequences significant. However, corporate income tax revenue will increase and partially offset the loss in revenue on the individual side. It is possible to provide a micro-founded model capturing those effects.18 If businesses face heterogeneous costs of switching organizational form (rep- resenting both transaction costs and nontax considerations) and the aggregate shifting response to tax rate changes is smooth, then marginal welfare analysis would still be appli- cable. As a result, formula (9) is a sufficient statistic to derive the welfare costs of taxation in that case.19 Estimating s and t empirically would require knowing the imputed corpo- rate profits of individual shareholders. This issue was quite significant for analy- ses of the Tax Reform Act of 1986 because of the sharp decline (and change in sign!) in the difference between the top personal and cor- porate tax rates, which created an incentive to shift business income from the corpora- tion tax base to pass-through entities such as partnerships or Subchapter S corporations, so that the business income shows up in the individual income tax base (see appendix A for a description of the 1986 tax reform). This phenomenon was indeed widespread immediately after the Tax Reform Act of 1986 (documented by Slemrod 1996, Robert 17 Again, to the extent that dividends are taxed, shareholders would not vidual income tax. 18 Alvaredo and Saez (2009) develop such a model in the case of the Spanish wealth tax, closely held companies is excluded individuals who own at least 15 percent are substantially involved in management. 19 It is a reduced-form formula rules about business organization the behavioral elasticity. 01_Saez.indd 12 Saez, Slemrod, differ.22 The ETI literature has focused on a simpler framework (usually) with no income effects and within which intertem- poral issues cannot be modeled adequately. This is an important issue to keep in mind when evaluating existing empirical studies of the ETI; future research should develop an intertemporal framework to account for expected future tax rate changes, so as to distinguish responses to temporarily high, or low, tax rates. Such a dynamic framework has been developed for specific components of taxable income such as realized capital gains (Burman and Randolph 1994) and charitable contributions (Bakija and Heim 2008). If current income tax rates increase, but long-term future expected income tax rates do not, individuals might decide to defer some of their incomes, for example, in the form of future pension payments23 (deferred compensation) or future realized capital gains.24 In that case, a current tax increase might have a positive fiscal externality in future years; such a fiscal externality affects the welfare cost of taxation as we described above. A similar issue applies whenever a change in tax rates affects business invest- ment decisions undertaken by individuals. If, for example, a lower tax rate proprietors or principals in pass-through entities to expand investment, the short-term effect on taxable income may be n egative, reflecting the deductible net expenses in the early years of an investment project. 22 In the labor supply literature, rary wage rate changes are captured ity, which is higher than the compensated respect to permanent changes. 23 In the United States, individual tively set aside a fraction of their plans (traditional IRAs and 401(k)s) vide increased retirement contributions current compensation. In both cases, butions are taxed as income when the 24 For example, companies, on holders, may decide to reduce current and retain earnings that generate taxed later when the stock is sold. 01_Saez.indd 13 14 Journal medium-term (up to five year) responses, and is not able to convincingly identify very long-term responses. The issue of long-term responses is par- ticularly important in the case of capital income, as capital income is the consequence of past savings and investment decisions. For example, a higher top income tax rate might discourage wealth accumulation or contribute to the dissipation of existing for- tunes faster. Conversely, reductions in this rate might trigger an increase in the growth rate of capital income for high-income indi- viduals. The new long-term wealth distribu- tion equilibrium might not be reached for decades or even generations, which makes it particularly difficult to estimate. Estimating the effects on capital accumulation would require developing a dynamic model of tax responses, which has not yet been developed in the context of the ETI literature. This would be a promising way to connect the ETI literature to the macroeconomic litera- ture on savings behavior. 2.2.4 Tax Evasion Suppose that a tax increase leads to a higher level of tax evasion.25 In that case, there might be increases in taxes collected on evading taxpayers following audits. This increased audit-generated tax revenue is another form of a positive fiscal externality. In practice, most empirical studies are car- ried out using tax return data before audits take place, and therefore do not fully capture the revenue consequences. Chetty (2009b) makes this point formally and shows that, under risk neutrality assumptions, at the margin the tax revenue lost due to tax evasion is exactly recouped (in tion) by increased tax revenue collected at audit. As a result, in that case the elasticity that matters for deadweight burden is not 25 Whether in theory one would not clear. See Yitzhaki (1974). 01_Saez.indd 14 Saez, Slemrod, a progressive income tax), then those inci- dence effects will have fiscal consequences. However, because those incidence effects are transfers, in principle the government can readjust tax rates on each factor to undo those incidence effects at no fiscal cost. Therefore, in a standard competitive model, incidence effects do not matter for the effi- ciency analysis or for optimal tax design.27 2.3 Classical Externalities There are situations where individual responses to taxation may involve clas- sical externalities. Two often mentioned cases are charitable giving and mortgage interest payments for residential housing, which in the United States and some other countries may be deductible from taxable income, a tax treatment which is often jus- tified on the grounds of classical exter- nalities. Contributions to charitable causes create positive externalities if contributions increase the utility of the beneficiaries of the nonprofit organizations. To the extent that mortgage interest deductions increase home ownership, they can arguably create posi- tive externalities in neighborhoods. In both cases, however, there are reasons to be skep- tical of the externality argument in practice. Using U.S. and French tax reforms, Fack and Landais (2010) show that the response of charitable deductions to tax rates is concen- trated primarily along the avoidance margin (rather than the real contribution margin).28 Glaeser and Shapiro (2003) examine the U.S. mortgage interest deduction and conclude that it subsidizes housing ownership along the intensive margin (size of the home) but 27 Indeed, Diamond and Mirrlees optimal tax formulas are the same prices of factors (with no incidence with variable prices (with incidence effects). 28 There is a large earlier literature cant responses of charitable giving income tax rates. See, for example, Auten, Sieg, and Clotfelter (2002). 01_Saez.indd 15 16 Journal applicable to welfare analysis. As discussed above, we are skeptical that itemized deduc- tions in the U.S. tax code necessarily produce strong positive externalities. Therefore, we will ignore this possibility and treat itemized deduction responses to tax rates as efficiency costs in the following sections. Classical externalities might also arise in agency models where executives set their own pay by expending efforts to influence the board of directors.30 It is conceivable that such pay-setting efforts depend on the level of the top income tax rate and would increase following a top tax rate cut. In such a case, top executives’ compensation increases come at the expense of share- holders’ returns, which produces a nega- tive externality.31 Such an externality would reduce the efficiency costs of taxation (as in that case correcting the externality dictates a positive tax). 2.4 Changes in the Tax Base Definition and Tax Erosion As pointed out by Slemrod (1995) and Slemrod and Kopczuk (2002), how broadly the tax base is defined affects the taxable income elasticity. In their model, the more tax deductions that are allowed, the higher will be the taxable income elasticity. This implies that the taxable income elasticity depends not only on individual p references (as we posited in our basic model in section 2.1), but also on the tax structure. Therefore, 30 Under perfect information and tives would not be able to set their from their marginal product. In reality, uct of top executives cannot be perfectly creates scope for influencing pay, in Bebchuk and Fried (2004). 31 Such externalities would fit oped by Chetty (2009b). Following and Saez (2010), such agency models ity only if the pay contract is not cient, e.g., it is set by executives the board without taking into account small shareholders outside the board. 01_Saez.indd 16 Saez, Slemrod, start from a comprehensive tax base where z is taxed at rate τ, so that c = (1 − τ) · z + E (E denotes a lump-sum transfer). In that case, sheltering income is costly no tax benefit; individuals choose the welfare analysis proceeds as in section 3.1 where the relevant elasticity ticity of total income z with respect Now recognize that the tax base by excluding y from taxation. In that case, c = (1 − τ) · w + y + E = (1 − τ) · z + τ · y + E. Therefore, individuals will find it profitable to shelter their income up to the point where τ · uc indirect utility v(c′, w) = maxy y, y) and the analysis of section 3.1 applies using the elasticity of taxable income w with respect to 1 − τ. Because w = z − y and sheltered income y responds (positively) to the tax rate τ, the elasticity of w is larger than the elasticity of z and hence the deadweight burden of taxation per dollar raised with the narrower base. Intuitively, giving preferential treatment to y induces to waste resources to shelter income y, which is pure deadweight burden. As a result, start- ing from the eroded tax base and introduc- ing a small tax dt > 0 on y actually reduces the deadweight burden from taxation, show- ing that the eroded tax base is a suboptimal policy choice.34 Therefore, comprehensive tax bases with low elasticities are preferable to narrow bases with large elasticities. Of course this conclusion abstracts from possible legitimate reasons for narrowing the tax base, such as administrative simplicity (as in the Slemrod and Kopczuk 2002),35 redistributive 34 This can be proved easily in no income effects where u(c, z, y) 35 In many practical cases, however, comprehensive tax base (such as a administratively simpler than a complex income tax with many exemptions and a narrower base. 01_Saez.indd 17 18 Journal exact realization of potential income revisit these assumptions below. Even within the context of this simple model, an OLS regression of log  log (1 − τit) would e in the presence of a graduated income tax schedule because τit is positively correlated with potential log-income log z because the marginal tax rate may increase with realized income z. Therefore, it is nec- essary to find instruments correlated but uncorrelated with potential log-income, log z  0it,  to taxable income elasticity literature has used changes in the tax rate structure created by tax reforms to obtain such instruments. Intuitively, in order to isolate the effects of the net-of-tax rate, one would want to com- pare observed reported incomes after the tax rate change to the incomes that would have been reported had the tax change not taken place. Obviously, the latter are not observed and must be estimated. We describe in this section the methods that have been pro- posed to estimate e and to address this iden- tification issue. 3.2 Simple before and after Reform Comparison One simple approach uses reported incomes before a tax reform as a proxy for reported incomes after the reform (had the reform not taken place). This simple differ- ence estimation method amounts to com- paring reported incomes before and after the reform and attributing the change in reported incomes to the changes in tax rates. 39 This issue arises in any context price of the studied behavior depends income tax rate, such as charitable such as this, though, a powerful instrument tax rate that would apply in the event a “first-dollar” marginal tax ior is taxable income, this instrument generally zero for everyone. 01_Saez.indd 18 Saez, Slemrod, 3.3 Share Analysis When the group affected by the tax reform is relatively small, one can simply normalize incomes of the group affected by a tax change by the average income in the population to control for macroeconomic growth. Indeed, recently the most dramatic changes in U.S. marginal federal income tax rates have taken place at the top percentile of the income distribution. Therefore, and following Feenberg and Poterba (1993) and Slemrod (1996), a natural measure of the evolution of top incomes relative to the aver- age is the change in the share of total income reported by the top percentile.40 Panel A of Economic Literature 2012, 50:1, 3–50 Slemrod, and Seth H. Giertz* the large and growing literature estimating the elasticity to marginal tax rates using tax return data. First, we showing under what assumptions this elasticity can for efficiency and optimal tax analysis. We discuss what when the elasticity is not a sufficient statistic. the key issues that arise in the empirical estimation income using the example of the 1993 top individual income States to illustrate those issues. Third, we provide a empirical analyses of the elasticity of taxable income empirical framework we laid out. Finally, we discuss ( JEL H24, H31, J22) respect to the marginal tax rate. Indeed, until recently, the labor supply elasticity was the occu- economic anal- closest thing that public finance economics had to a central parameter. In a static model where people value only two commodities— leisure and a composite consumption good— the real wage in terms of the consumption good is the only relative price at issue. This real wage is equal to the amount of goods that can be consumed per hour of leisure foregone (or, equivalently, per hour of labor Berkeley, and NBER. supplied). At the margin, substitution possi- bilities, and therefore the excess burden of Blomquist, Raj Håkan Selin, taxation, can be captured by a compensated labor supply elasticity. With some notable exceptions, the profes- and Caroline Weber Financial support from sion has settled on a value for this elasticity close to zero for prime-age males, although 3 2/27/12 3:49 PM Economic Literature, Vol. L (March 2012) accurately summarizing the marginal effi- ciency cost of taxation than a narrower mea- sure of taxpayer response such as the labor supply elasticity, and therefore is a worthy topic of investigation. Although the literature reviewed in this article addresses the behavioral response to individual income taxation, many of the issues apply to any tax base. Certainly the idea that, under some assumptions, all responses are symptoms of inefficiency applies gener- ally. For example, consider a state imposing a cigarette excise tax. Under some assump- tions, the central empirical parameter is the elasticity of the cigarette tax base, which includes not only the response of smoking to tax rate changes but also the impact on the tax base of smuggling and tax-free Internet purchases. The new focus (on the ETI) raises the possibility that the efficiency cost of taxa- tion is significantly higher than is implied if labor supply is the sole, or principal, mar- gin of behavioral response. Indeed, some of the first empirical estimates of the elas- ticity of taxable income implied very sizable responses and therefore a very high marginal efficiency cost of funds. However, the subse- quent literature found substantially smaller elasticities, and raised questions about both our ability to identify this key parameter and about the claim that it alone is a sufficient statistic for welfare analysis of the tax sys- tem. Whether the taxable income elasticity is an accurate indicator of the revenue leak- age due to behavioral response, the ultimate indicator of efficiency cost, depends on the situation. First, if revenue leakage in cur- rent year tax revenue is substantially offset by revenue gain in other years or in other tax bases, it is misleading. Second, if some of the response involves changes in activities with externalities, such as charitable giving behav- ior, then the elasticity is not a sufficient sta- tistic for welfare analysis. Third, the elasticity depends on the tax system. A tax system with 2/27/12 3:49 PM and Giertz: The Elasticity of Taxable Income 5 other margins such as intensity of work, career choices, form and timing of com- pensation, tax avoidance, or tax evasion. As a result, an individual’s wage rate w might depend on effort and respond to tax rates, and reported taxable income might differ from w · l as individuals split their gross earnings between taxable cash compensation and nontaxable compensation such as fringe benefits, or even fail to report their full tax- able income because of tax evasion. As shown by Feldstein (1999), a simple way to model all those behavioral responses is to posit that utility depends positively on disposable income (equal to consump- tion) c and negatively on reported income z (because activities that generate income are costly, for example because they may require foregoing leisure). Hence, individuals choose (c, z) to maximize a utility function u(c, z) subject to a budget constraint of the form c = (1 − τ) · z + E. Such maximization generates an individual “reported income” supply function z(1 − τ, E) where z depends on the net-of-marginal-tax rate 1 − τ and virtual income E generated by the tax/trans- fer system.1 Each individual has a particular reported income supply function reflecting his/her skills, taste for labor, opportunities for avoidance, and so on.2 In most of what follows, we assume away income effects so that the income func- tion z does not depend on E and depends 1 This reported income supply function remains valid in the case of nonlinear tax schedules as c = (1 − τ)z + E is the linearized budget constraint at the utility-maximizing point, just as in the basic labor supply model. 2 We could have posited a more general model in which c = y − τ z + E, where y is real income and z is reported income that may differ from real income because of, for example, tax evasion and avoidance. Utility would be u(c, y, y − z) which is increasing in c, decreasing in y (earnings effort), and decreasing in y − z (costs of avoid- ing or evading taxes). Such a utility function would still generate a reported income supply function of the form z(1 − τ, E) and our analysis would go through. We come back to such a more general model in section 2.4. 2/27/12 3:49 PM of Economic Literature, Vol. L (March 2012) (1999), this elasticity captures not only the hours of work response, but also all other behavioral responses to marginal tax rates. Furthermore, it depends on features of the tax system, such as the availability of deduc- tions, and other avoidance opportunities—a very important point for the interpretation of empirical results, as we discuss below. Therefore, the elasticity is not a structural parameter depending solely on individual preferences. As we discuss later, a number of empiri- cal studies have found that the behavioral response to changes in marginal tax rates is concentrated in the top of the income distribution, with less evidence of any response for the middle and upper-middle income class (see sections 3 and 4 below).4 Moreover, in the United States, because of graduated rates as well as exemptions and low-income tax credits, individual income tax liabilities are very skewed: the top quintile (top percentile) tax filers remitted 86.3 per- ∂ z   , cent (39.1 percent) of all individual income taxes in 2006 (Congressional Budget Office 2009). Therefore, it is useful to focus on the analysis of the effects of changing the mar- ginal tax rate on the upper end of the income distribution. Let us therefore assume that incomes in the top bracket, above a given _ reported income threshold z , face a constant marginal tax rate τ. 5 As in the conceptual framework just described, we assume that individual incomes reported in the top bracket depend on the net-of-tax rate 1 − τ. Let us assume that there _ are N individuals in the top bracket (above z ) 4 The behavioral response at the low end of the income labor supply literature distribution is for the most part out of the scope of the pres- with many studies obtain- ent paper. The large literature on responses to welfare and several important studies income transfer programs targeted toward low incomes has, however, displayed evidence of significant labor supply less empirical evidence responses (see, e.g., Meyer and Rosenbaum 2001). in the reported income 5 For example, in the case of tax year 2008 federal income _ tax law in the United States, taxable incomes above of reported incomes, z  = $357,700 are taxed at the top marginal tax rate of τ = 0.35. 2/27/12 3:49 PM Slemrod, and Giertz: The Elasticity of Taxable Income 7 revenue due to the behavioral response is equal to (3) dB ≡ −N · e · zm  ·  _τ  . d τ < 0. 1−τ Summing the mechanical and the behavioral [∂ zm /∂ (1 − τ)]. This effect, we obtain the total change in tax rev- enue due to the tax change: by indi- (4) dR = dM + dB to _   − z) = N · (zm [ ] · 1 − e ·  _ zm τ · d τ. _   ·  _ z   − z 1 − τ m tax reform has _ Let us denote by a the ratio z m/(zm   − z). Note that in general a ≥ 1, and that a = 1 when a single flat tax rate applies to all incomes, as in this case the top bracket starts _ at zero (z  = 0). If the top tail of the distribu- tion is Pareto distributed,8 then the parame- _ − z) · d τ > 0. ter a does not vary with z and is exactly equal to the Pareto parameter. As the tails of actual income distributions are very well approxi- mated by Pareto distributions, within a given year, the coefficient a is extremely stable in _ the United States for z above $300,000 and equals approximately 1.5 in recent years.9 The parameter a measures the thinness of · dτ/(1 − τ).7 A change in the top tail of the income distribution: the tax revenue aggregate change in tax 8 A Pareto distribution has a density function of the form f (z) = C/z1+α, where C and α are constant parameters. The parameter α is called the Pareto parameter. _ In that +.. + zN]/N and hence case, zm = ∫     z  · f_(z)· dz/∫_z ∞ _z∞     f (z) · dz = z  · α/(α − 1) /(z   − z) = α. m /∂ (1 − τ)] and hence z m 9 Saez (2001) provides such an empirical analysis for (1 − τ) +.. + ∂ zN/∂ (1 − τ)]/[N · zm ] + eN · zN ]/[z1+.. + zN ], 1992 and 1993 reported wage incomes using U.S. tax return data. Piketty _ and Saez (2003) provide estimates of thresholds z and average incomes z m corresponding to a small fraction d N of the various fractiles within the top decile of the U.S. income < 0) the top bracket. distribution from 1913 to 2008, allowing a straightforward place only along the estimation of the parameter a for any year and income response is proportional threshold. As U.S. income concentration has increased in effect of such responses is recent decades, the Pareto parameter a has correspond- and hence can be ignored in our ingly fallen from about 2 in the 1970s to about 1.5 in most recent years. 2/27/12 3:49 PM of Economic Literature, Vol. L (March 2012) cost equal to −dB/dR > 0 on taxpayers. We can also define the “marginal efficiency cost of funds’’ (MECF) as 1 − dB/dR = (1 − τ)/(1 − τ − e · a ·τ). These formu- las are valid for any tax rate τ and income distribution as long as income effects are · e · a. ] assumed away, even if individuals have het- erogeneous utility functions and behavioral elasticities.11 The parameters τ and a are relatively straightforward to measure, so that the elasticity parameter e is the central parameter necessary to calculate formulas (5) and (6). Marginal deadweight burden or marginal efficiency cost of funds mea- sure solely efficiency costs and abstract from distributional considerations. The optimal income tax progressivity literature precisely brings together the efficiency formulas derived here with welfare weights captur- ing distributional concerns. Therefore, the behavioral response elasticity is also a key parameter for characterizing optimal pro- gressivity (Saez 2001). To illustrate these formulas, consider the following example using U.S. data. In recent years, for the top 1 percent income cut-off (corresponding approximately to the top 35 percent federal income tax bracket in that year), Piketty and Saez (2003) estimate that a = 1.5. When combining the maximum federal and average state income, Medicare, and typical sales tax rates in the United States, the top marginal tax rate for ordinary income is 42.5 percent as of 2009.12 For an 11 In contrast, the Harberger triangle (Harberger 1964) approximations are valid only for small tax rates. This expression also abstracts from any marginal compli- ance costs caused by raising rates, and from any marginal administrative costs unless dR is interpreted as revenue net of administrative costs. See Slemrod and Yitzhaki (2002). 12 A top federal tax rate of 35 percent, combined with an average top state income tax rate of 5.9 percent, the Medicare 2.9 percent payroll tax, and an average sales tax max u(z(1 − τ) + E, z) so rate of 2.3 percent generate a total top marginal tax rate of _ + dE) = −uc · (z − z ) d τ. There- 42.5 percent, when considering that state income taxes are utility cost of the reform deductible when calculating federal income taxes and the tax increase, individual employer’s share of the Medicare tax is deductible for both state and federal income tax calculations. 2/27/12 3:49 PM and Giertz: The Elasticity of Taxable Income 9 becomes infinite as raising more tax rev- enue becomes impossible. Using our pre- vious example with e = 0.25 and a = 1.5, the revenue-maximizing tax rate τ* would be 72.7 percent, much higher than the cur- rent U.S. top tax rate of 42.5 percent when combining all taxes. Keeping state income and sales taxes, and Medicare taxes con- stant, this would correspond to a top federal individual income tax rate of 68.4 percent, very substantially higher than the current 35 percent but lower than the top federal income tax rate prior to 1982. Note that when the tax system has a single _ tax rate (i.e., when z  = 0), the tax-revenue- maximizing rate becomes the well-known expression τ* = 1/(1 + e). As a ≥ 1, the revenue-maximizing flat rate is always larger than the revenue-maximizing rate applied to high incomes only. This is because increasing just the top tax rate collects extra taxes only on the portion of incomes above the bracket _ threshold z , but produces a behavioral response for high-income taxpayers as large as an identical across-the-board increase in marginal tax rates. Giertz (2009) applies the formulas pre- sented in this section to tax return data from published Statistics of Income tables produced by the Internal Revenue Service (IRS) to analyze the impact of the potential expiration of the Bush administration tax cuts in 2011. Giertz shows that exactly where the ETI falls within the range found in the empirical literature has significant effects on the efficiency and revenue implications for tax policy. For example, Giertz reports that for ETIs of 0.2, 0.5, and 1.0, behav- ioral responses would respectively erase 12, 31, and 62 percent of the mechanical rev- enue gain. When offsets to payroll and state income taxes are taken into account, these Pareto-inefficient out- numbers increase by 28 percent. Likewise, policy that can pro- estimates for the marginal cost of public the possibility that negatively in the util- funds and the revenue-maximizing rates are quite sensitive to this range of ETIs. 2/27/12 3:49 PM Literature, Vol. L (March 2012) change in the initial base z. The alternative tax base z′ can be a different tax base in the same time period or the same tax base in a different time period. The notion of fiscal externality is therefore dependent on the scope of the analysis both along the base dimension and the time dimension. In the limit, where the analysis encompasses all tax bases and all time periods (and hence focuses on the total present discounted value of total tax revenue), there can by definition be no fiscal externalities. To see the implication of income shifting, assume that a fraction s < 1 of the income Shifting that disappears from the individual income tax base following the tax rate increase dτ is shifted to other bases and is taxed on average at rate t. For example, if half of the reduc- tion in individual reported incomes is due to increased (untaxed) leisure and half is due to a shift toward the corporate sector, then s = 1/2 and t would be equal to the effective tax rate on corporate income.14 In the general case, a behavioral response dz now generates a tax revenue change equal to (τ − s · t) · dz. As a result, the change in tax revenue due to the behavioral response becomes: (8) dB = −N · e · zm  ·  _ τ   · dτ 1−τ s · t   · dτ. + N · e · zm  ·  _ 1−τ later date Therefore, formula (5) for the effect of a small reform on total tax revenue becomes: individual (9) dR = dM + dB [ ] τ − s · t   · e · a. = dM · 1 −  _ 1−τ to a shift 14 It is possible to have t > τ, for example if there are (nontax) advantages to the corporate form. If all the response is shifting (s = 1), dτ > 0 would actually then lead to behavioral responses increasing total tax revenue and hence reducing deadweight burden. 2/27/12 3:49 PM and Giertz: The Elasticity of Taxable Income 11 burden: (1) the extent to which individual income changes in the first tax base z shift to another form of income that is taxable, characterized by parameter s, and (2) the tax rate t at which the income shifted is taxed. In practice, there are many possibilities for such shifting and measuring empirically all the shifting effects is challenging, especially in the case of shifting across time. The recent literature has addressed several channels for such fiscal externalities. Alternatively, one could identify shifting by looking directly at the overall revenue from all sources. e · a · (τ − s · t) 2.2.1 Individual versus Corporate Income · a · (τ − s · t) Tax Base Most countries tax corporate profits with a separate corpor ate income tax.16 Unincorporated business profits (such as > τ*. sole proprietorships or partnerships) are in general taxed directly at the individual level. In the United States, closely held corpora- tions with few shareholders (less than 100 currently) can elect to become Subchapter S corporations and be taxed solely at the indi- vidual level. Such businesses are also called pass-through entities. Therefore, the choice of business organization (regular corporation taxed by the corporate income tax versus pass-through entity taxed solely at the indi- vidual level) might respond to the relative tax rates on corporate versus individual income. For example, if the individual income tax rate increases, some businesses taxed at the whether 16 Net-of-tax corporate profits are generally taxed again at the individual level when paid out as dividends to individual shareholders. Many OECD countries allevi- ate such double taxation of corporate profits by providing tax credits or preferential tax treatment for dividends. If profits are retained in the corporation, they increase the value of the company stock and those profits may, as in the United States, be taxed as realized capital gains when the individual owners eventually sell the stock. In general, the individual level of taxation of corporate profits is lower than the ordinary individual tax on unincorporated businesses t = 0.3 are realistic so that the combined tax on corporate profits and distrib- corporate to individual uted profits may be lower than the direct individual tax for individuals subject to high marginal individual tax rates. 2/27/12 3:49 PM of Economic Literature, Vol. L (March 2012) Carroll and David Joulfaian 1997, and Saez 2004b among others). 2.2.2 Timing Responses might If individuals anticipate that a tax increase will happen soon, such as when President Clinton was elected in late 1992 on a pro- gram to raise top individual tax rates, which was indeed implemented in 1993, they have incentives to accelerate taxable income real- izations before the tax change takes place.20 As a result, reported taxable income just after the reform will be lower than otherwise. In that case, the tax increase has a positive fis- cal externality on the pre-reform period that ought to be taken into account in a welfare analysis. As we will see below, this issue of reti- ming is particularly important in the case of realized capital gains21 and stock-option exercises (Goolsbee 2000b) because indi- viduals can easily time the realization of such income. Parcell (1995) and Sammartino and Weiner (1997) document the large shift of taxable income into 1992 from 1993 (even when excluding capital gains) in response to the tax increase on high-income earners promised by President-elect Bill Clinton, and enacted in early 1993. The labor supply literature started with a static framework and then developed a dynamic framework with intertemporal sub- stitution to distinguish between responses to temporary versus permanent changes in wage rates (MaCurdy 1981). In this frame- work, differential responses arise because, and only because, the income effects of and capital gains temporary versus permanent changes entirely escape the indi- 20 Anticipated tax decreases would have the opposite under which stock in effect. from the wealth tax for 21 A well-known example is the U.S. Tax Reform Act of of the business and 1986, which increased the top tax rate on realized long- term capital gains from 20 percent to 28 percent beginning because a change in the in 1987, and generated a surge in capital gains realizations would in general change at the end of 1986 (Auerbach 1988; Burman, Clausing, and O’Hare 1994). 2/27/12 3:49 PM and Giertz: The Elasticity of Taxable Income 13 As already noted, the ETI and MDWL concepts are relevant for the optimal design of the tax and transfer system, because they increase the economic cost of the higher mar- ginal tax rates needed to effect redistribu- tion. Importantly, though, they do not enter directly into an evaluation of deficit-financed tax cuts (or deficit-reducing tax increases). This is because, with a fixed time pattern of government expenditure, tax cuts now must eventually be offset by tax increases later. Ignoring the effects of one period’s tax rate on other periods’ taxable income, if the ETI is relatively large a current tax cut will cause a relatively large increase in current taxable income. Offsetting this, however, is the fact that when the offsetting tax increases occur later, the high ETI (and there is no reason to think it will go up or down over time) will generate relatively big decreases in tax- able income at that time. Accounting for the intertemporal responses, both of the real and income-shifting variety, to time-varying tax rate changes suggests that a deficit-financed tax cut that, by definition, collects no revenue in present value will cause deadweight loss by distorting the timing of taxable income flows. induces sole 2.2.3 Long-Term Responses One might expect short-term tax responses to be larger than longer-term responses because people may be able to easily shift income between adjacent years without alter- ing real behavior. However, adjusting to a tax responses to tempo- change might take time (as individuals might by the Frisch elastic- decide to change their career or educational elasticity with choices or businesses might change their workers can elec- long-term investment decisions) and thus earnings into pension the relative magnitude of the two responses or employers can pro- is theoretically ambiguous. The long-term at the expense of those pension contri- response is of most interest for policy mak- money is withdrawn. ing although, as we discuss below, the long- behalf of their share- term response is more difficult to identify dividend payments capital gains that are empirically. The empirical literature has pri- marily focused on short-term (one year) and 2/27/12 3:49 PM of Economic Literature, Vol. L (March 2012) the elasticity of reported income, but instead the elasticity of actual income. 2.2.5 Other Fiscal Externalities Changes in reported incomes might also have consequences for bases other than fed- eral income taxes. An obvious example is the case of state income taxes in the United States. If formula (6) is applied to the fed- eral income tax only, it will not capture the externality on state income tax revenue (as states in general use almost the same income tax base as the federal government). Thus our original analysis should be based on the combined federal and state income tax rates. Changes in reported individual income due to real changes in economic behavior (such as reduced labor supply) can also have con- sequences for consumption taxes. In par- ticular, a broad-based value added tax is economically equivalent to an income tax (with expensing) and therefore should also be included in the tax rate used for welfare computations. Finally, fiscal externalities may also arise due to classical general equilibrium tax inci- dence effects. For example, a reduced tax rate on high incomes might stimulate labor supply of workers in highly paid occupa- tions, and hence could decrease their pre- tax wage rate while reducing labor supply and thus increasing pretax wage rates of lower-paid occupations.26 Such incidence effects are effectively transfers from some factors of production (high-skilled labor in our example) to other factors of production (low-skilled labor). If different factors are taxed at different rates (due for example to increased expecta- 26 Such effects are extremely difficult to convincingly estimate empirically. Kubik (2004) attempts such an analy- sis and finds that, controlling for occupation-specific time trends in wage rates, individuals in occupations that expe- rienced large decreases in their median marginal tax rates due to the Tax Reform Act of 1986 received lower pre-tax expect this response is wages after 1986 as the number of workers and the hours worked in these professions increased. 2/27/12 3:49 PM and Giertz: The Elasticity of Taxable Income 15 not the extensive margin (home ownership) and that there is little evidence of externali- ties along the intensive margin. Moreover, granting the existence of such externalities does not imply that the implicit rate of sub- sidy approximates marginal social benefit. Theoretically, suppose a fraction s of the taxable income response to a tax rate increase dτ is due to higher expenditures on activities that create an externality with a social mar- ginal value of exactly t dollars per dollar of additional expenditure. In that case, formula (8) applies by just substituting the alternative tax base rate t with −1 multiplied by the per dollar social marginal value of the external- ity. For example, in the extreme case where all the taxable income response comes from tax expenditures (s = 1) with income before tax expenditures being unresponsive to tax rates, and if t = τ (the social marginal value of tax expenditures externalities is equal to the income tax rate τ) then there is zero mar- ginal excess burden from taxation as it is a pure Pigouvian tax.29 More generally, to the extent that the behavioral response to higher tax rates generates some positive externali- ties, formula (3) will overstate the marginal efficiency cost of taxation. Because the bulk of items that are deduct- ible from taxable income in the United States—state and local income taxes, mort- gage interest deductions, and charitable giving—may generate fiscal or classical exter- nalities, the elasticity of a broader, prededuc- tion, concept of income (such as adjusted gross income in the United States) is of inter- est in addition to a taxable income elasticity. That is why many conceptual and empirical analyses focus on adjusted gross income— which is not net of such deductible items— (1971) showed that rather than taxable income. The elasticity of in a model with fixed effects) and in a model taxable income and the elasticity of a broader measure of income may bracket the elasticity finding signifi- to individual marginal 29 Saez (2004a) develops a simple optimal tax model to capture those effects. 2/27/12 3:49 PM of Economic Literature, Vol. L (March 2012) the tax base choice affects the taxable income elasticity. Thus, as Slemrod and Kopczuk (2002) argue, the ETI can be thought of as a policy choice. The same logic applies to the enforcement of a given tax base, which can particularly affect the behavioral response to tax rate changes of avoidance schemes and evasion. To see this point, suppose that we estimate a large taxable income elasticity because the tax base includes many loopholes making it easy to shelter income from tax (we dis- cuss in detail such examples using U.S. tax reforms below). In the model of section 2.1, this suggests that a low tax rate is optimal. However, in a broader context, a much bet- ter policy may be to eliminate loopholes so as to reduce the taxable income elasticity and the deadweight burden of taxation.32 For example, Gruber and Saez (2002) estimate that the taxable income elasticity for upper income earners is 0.57, leading to a revenue maximizing rate of only 54 percent using for- mula (7) with a = 1.5. However, they find a much lower elasticity of 0.17 for a broader income definition for upper incomes, imply- ing that the revenue maximizing tax rate would be as high as 80 percent if the income tax base were broadened.33 Consider a simple example that illustrates this argument. As in our basic model, indi- viduals supply effort to earn income z. Now allow that individuals can, at some cost, shel- ter part of their income z into another form that might receive preferable tax treatment. Let us denote w + y = z, where y is shel- competition, execu- tered income and w is unsheltered income. pay at a different level Formally, individuals maximize a utility func- the marginal prod- observed, which tion of the form u(c, z, y) that is decreasing as discussed extensively in z (earning income requires effort) and y into the framework devel- (sheltering income is costly). Suppose we the analysis of Chetty produce an external- second-best Pareto effi- 32 This possibility is developed in the context of an opti- and large shareholders on mal linear income tax in Slemrod (1994). the best interests of 33 Both scenarios assume away fiscal and classical exter- nalities in behavioral responses. 2/27/12 3:49 PM and Giertz: The Elasticity of Taxable Income 17 concerns, and externalities such as charitable contributions, as discussed above.36 and provides 3. Empirical Estimation and y = 0, and Identification Issues is the elas- 3.1 A Framework to Analyze the to 1 − τ. Identification Issues is eroded To assess the validity of the empirical methods used to estimate the ETI and to explicate the key identification issues, it is useful to consider a very basic model of = uy . We can define the income reporting behavior. In year t, individ-   u(c′ + y, w + ual i reports income zit and faces a marginal tax rate of τit  = T′(zit ). Assume that reported income zitresponds to marginal tax rates with elasticity e so that zit  = z  0it  · (1 − τit )e , where z  0it  is income reported when the marginal tax rate is zero, which we call potential income.37 Therefore, using logs, we have: is higher (12) log zit = e · log(1 − τit ) + log z  0it  . taxpayers Note, in light of our previous preceding discussion, the assumptions that are embed- ded in this simple model: (a) there are no income effects on reported income (as vir- tual income E is excluded from specification (12), (b) the response to tax rates is immedi- ate and permanent (so that short-term and long-term elasticities are identical), (c) the elasticity e is constant over time and uniform across individuals at all levels of income,38 (d) individuals have perfect knowledge of the tax structure and choose z it after they know the model of 36 The public choice argument that narrow bases con- strain Leviathan governments would fall in that category, as a Leviathan government produces a negative externality. a separable model with 37 A quasi-linear utility function of the form = c − h1(z) − h2(y). u(c, z) = c − z0 (z/z0 )1+1/e /(1 + 1/e) generates such in- tax systems with a come response functions. value added tax) may be 38 This assumption can be relaxed in most cases, but it sometimes has important consequences for identification, as we discuss below. 2/27/12 3:49 PM of Economic Literature, Vol. L (March 2012) z  0it.  We Suppose that all tax rates change at time t = 1 because of a tax reform. Using repeated cross sections spanning the pre- and zit on post-reform periods, one can estimate the not identify the elasticity following two-stage-least-squares regression: (13) log zit = e · log(1 − τit ) + εit, 0it;  this occurs using the post-reform indicator 1(t ≥ 1) as an instrument for log(1 − τit). This regres- with τit, sion identifies e if εit is uncorrelated with 1(t ≥ 1). In the context of our simple model identify the elasticity e.39 The recent (12), this requires that potential log-incomes are not correlated with time. This assump- tion is very unlikely to hold in practice, as real economic growth creates a direct correlation between income and time. If more than two years of data are available, one could add a linear trend β · t in (13) to control for secu- lar growth. However, as growth rates vary year-to-year due to macroeconomic business cycles, the elasticity estimate will be biased if economic growth happens to be differ- ent from year t = 0 to year t = 1 for reasons unrelated to the level of tax rates; in this case the regression will ascribe to the tax change the impact of an unrelated, but coincident change in average incomes. In many contexts, however, tax reforms affect subgroups of the population differen- tially, and in some cases they leave tax rates essentially unchanged for most of the popu- lation. For example, in the United States during the last three decades, the largest absolute changes in tax rates have taken place at the top of the income distribution, with much smaller changes on average in the broad middle. In that context, one can use the group less (or not at all) affected by the tax change as a control and hence proxy where the effective unobserved income changes in the affected on the marginal contributions. In a case group (absent the tax reform) with changes is the marginal in reported income in the control group. of zero contributions, Such methods naturally lead to consider- rate. When the studied behav- is not helpful, as it is ation of difference-in-differences estimation methods discussed in section 3.4. 2/27/12 3:49 PM and Giertz: The Elasticity of Taxable Income 19 incomes of the high-income individuals are indeed responsive to marginal tax rates. Panel B of figure 1 shows the same income share and marginal tax rate series for the next 9 percent of highest-income tax filers (i.e., the top decile excluding the top 1 percent from panel A). Their marginal tax rate fol- lows a different pattern, first increasing from 1960 to 1981 due primarily to bracket creep (as the tax system in this period was not indexed for inflation), followed by a decline until 1988 and relative stability afterwards. In contrast to the top 1 percent, however, the share of the next 9 percent in total income is very smooth and trends slightly upward during the entire period. Most importantly,

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