Kleven & Schulz (2014) Estimating Taxable Income Responses - PDF

American Economic Journal: Economic Policy 2014, 6(4): 271–301 http://dx.doi.org/10.1257/pol.6.4.271 Estimating Taxable Income Responses Using Danish Tax Reforms † By Henrik Jacobsen Kleven and Esben Anton Schultz...

American Economic Journal: Economic Policy 2014, 6(4): 271–301 http://dx.doi.org/10.1257/pol.6.4.271 Estimating Taxable Income Responses Using Danish Tax Reforms † By Henrik Jacobsen Kleven and Esben Anton Schultz * This paper estimates taxable income responses using a series of Danish tax reforms and population-wide administrative data since 1980. The tax variation and data in Denmark makes it possible to overcome the biases from nontax changes in inequality and mean reversion that plague the existing literature. We provide compelling graphical evidence of taxable income responses, arguably represent- ing the first nonparametrically identified evidence of taxable income elasticities using tax reforms. We also present panel regression evi- dence that is extremely robust to specification, unlike previous results which have been very sensitive. (JEL D31, H24, H31, J22) T he modern literature on behavioral responses to taxes has shifted much of its focus from the elasticity of hours worked to the elasticity of taxable income. Effects on taxable income capture the full range of behavioral responses, including hours worked, unobserved effort, career choices, and tax avoidance and evasion, and therefore provide a more complete picture of the distortionary effects of taxation. Under certain conditions, as argued by Feldstein (1995, 1999), the elasticity of tax- able income provides a sufficient statistic for efficiency and optimal taxation, which places this parameter at the center stage of all the major normative questions in public finance.1 A large and growing literature estimates the elasticity of taxable income using tax return data, as recently surveyed by Saez, Slemrod, and Giertz (2012). Much of this work is based on the United States and uses as its source of identification a series of tax reforms in the 1980s and 1990s that were associated with substantial tax changes at the top of the income distribution (e.g., Feldstein 1995; Auten and Carroll 1999; Moffitt and Wilhelm 2000; Goolsbee 2000; Gruber and Saez 2002; Kopczuk 2005; * Kleven: London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom (e-mail: [email protected]); Schultz: Kraka, Kompagnistræde 20A, DK-1208 Copenhagen K (e-mail: [email protected]). We thank Raj Chetty, John Friedman, Hilary Hoynes, Niels Johannesen, Wojciech Kopczuk, Claus Kreiner, Tore Olsen, Emmanuel Saez, Monica Singhal, Joel Slemrod, and anonymous referees for helpful comments and suggestions. We are grateful to the Centre for Applied Microeconometrics (CAM) at the University of Copenhagen for data access, and to the Tuborg Foundation and the Economic Policy Research Network (EPRN) for financial support. † Go to http://dx.doi.org/10.1257/pol.6.4.271 to visit the article page for additional materials and author disclosure statement(s) or to comment in the online discussion forum. 1 The general condition for the elasticity of taxable income to be the (only) sufficient statistic for welfare analy- sis is that there exists a single wedge between the social marginal costs and benefits of any change in taxable income, independently of its source. This is unlikely to be fully satisfied as different types of taxable income responses (such as hours worked, wage bargaining, income shifting, and tax evasion) are associated with differ- ent wedges due to different fiscal and other externalities in which case some degree of decomposition is required. 271 272 American Economic Journal: economic policyNovember 2014 and Giertz 2007). In addition to the US literature, a number of recent studies esti- mate taxable income responses in other countries that have lowered m ­ arginal tax rates at the top of the income distribution, including the United Kingdom (Brewer, Saez, and Shephard 2010), Canada (Sillamaa and Veall 2001; Saez and Veall 2005), Norway (Aarbu and Thoresen 2001), Sweden (e.g., Hansson 2007; Blomquist and Selin 2010; Gelber 2012), and Poland (Kopczuk 2012).2 Reforms that target strongly the top of the income distribution provide interesting variation, but are also associated with some important empirical difficulties. Because the allocation of tax treatments is determined by pre-reform income level, we have to consider the possibility that different income groups differ in a number of non- tax dimensions that impact on taxable income and are correlated with the tax law changes. This problem is reinforced by the fact that tax return data contain typically very little information about taxpayers besides income variables and tax rates, mak- ing it difficult to control for any nontax differences across different taxpayers. Two key problems have been discussed extensively in the literature (e.g., Slemrod 1998; Saez 2004; Saez, Slemrod, and Giertz 2012). First, it is very hard to disen- tangle tax-driven changes in top incomes from changes that are driven by nontax factors such as skill-biased technical progress and globalization. This problem is particularly important in countries that have experienced strong secular increases in top income shares. When considering tax cuts at the top of the distribution, this may result in a substantial upward bias in the elasticity estimates. Second, defining treat- ments and controls according to pre-reform income level creates a mean-reversion problem, because a taxpayer with a positive income shock in the pre-reform year will tend to have a lower income in the following years, independently of the reform. For tax cuts at the top, this biases elasticity estimates downward. In order to cor- rect for the two biases mentioned above, the literature has attempted to control in a number of ways for pre-reform income levels. However, the richness of such income controls is constrained by the fact that the identification comes from different tax changes across pre-reform income levels, and in general the results turn out to be very sensitive to specification. This paper estimates taxable income responses using a series of Danish tax reforms and rich administrative data covering the full Danish population since 1980. Unlike US studies, the dataset combines tax return information with detailed labor market, education, and sociodemographic information. Besides the quality of the data, the Danish setting offers two important advantages allowing us to overcome the biases discussed above. First, the Danish income distribution has been much more stable than in most other countries, including English-speaking countries and other Nordic countries 2 Alongside the literature using tax reforms to estimate taxable income responses, a recent literature estimates taxable income responses using bunching at kinks or notches (Saez 2010; Chetty et al. 2011; Kleven and Waseem 2013). While bunching provides a compelling source of identification in theory, a key limitation in practice is that there tends to be very little bunching in empirical distributions and so the estimated elasticities are often tiny. The likely explanation is the presence of optimization frictions such as switching and attention costs combined with the fact that the utility gain of bunching in response to kinks is typically not very large (Chetty et al. 2011; Chetty 2012). Attenuation bias from frictions can be controlled for using notches (Kleven and Waseem 2013), but this source of variation is not always available. We come back to the question of frictions below. Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 273 25% Share (in %) of all taxpayers 20% 15% 10% 5% 0% 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Top 10% Top 5% Top 1% Top 0.5% Figure 1. The Evolution of Top Income Shares in Denmark Notes: The income shares are based on tax return information and a broad income measure including labor income, other personal income, and capital income (as defined in detail in Table 1). The sample includes all personal income tax filers aged 25–55. that have provided testing grounds for previous taxable income studies.3 To provide evidence on this, Figure 1 shows the evolution of Danish top income shares since the early 1980s based on a broad income measure including all labor income and capital income. We see that top income shares in Denmark have been remarkably constant over time. The stable income distribution in Denmark eliminates the threat to identification coming from nontax changes in inequality and therefore isolates mean-reversion as the key source of bias that must be controlled for. Second, we exploit a series of tax reforms that create large and compelling iden- tifying variation. In some years, the variation created by the Danish tax reforms is larger than the variation created by the major US tax reforms of the 1980s, and importantly the Danish variation does not feature the same strong correlation with income level as the US variation. The Danish reforms are associated with three main changes: (i) differential changes in marginal tax rates across different tax brack- ets, (ii) changes in bracket cutoffs that move large groups of taxpayers to different brackets, and (iii) a change from symmetric to asymmetric treatment of different income components (labor income, capital income, and deductions). The combina- tion of points (i) and (ii) create large and nonlinear tax variation through the income distribution in a way that is not systematically correlated with income level. Point (iii) implies that income composition, besides income level, plays a key role for the tax bill, thereby creating variation across individuals at the same income level. All three changes together therefore create very rich identifying variation. Because the tax system imposes differential treatment of different income types (labor income, capital income, and deductions), we estimate separately the 3 An international overview of the long-run evolution of top income shares in more than 20 countries (but not including Denmark) is provided by Atkinson, Piketty, and Saez (2011). 274 American Economic Journal: economic policyNovember 2014 e­ lasticities of taxable labor income and taxable capital income with respect to the marginal tax rate on each. In the presence of multiple tax bases with different tax rates, the overall taxable income elasticity is no longer a sufficient statistic for wel- fare ­analysis; one must in general estimate both own-tax and cross-tax elasticities for each base as we do here.4 Nevertheless, for comparability with the existing ­literature, we also present estimates of the overall taxable income elasticity with respect to a joint increase in the marginal tax rate on the underlying components. Our main findings are the following. First, considering a large and salient tax reform in the 1980s, we present compelling graphical evidence of behavioral responses for both labor and capital income. The evolution of labor and capital income in a treatment group (facing large tax cuts) and a control group (facing tax increases) are completely parallel in the pre-reform period and then diverge sharply just after the reform. A difference-in-differences approach based on the graphical analysis produces elasticities in the range of 0.2–0.3. We view these findings as a key contribution of the paper, especially considering that the previous taxable income literature has been unable to produce compelling nonparametric evidence of this kind. Second, turning to panel regressions using all tax reform variation over a long time period, we find that elasticities are in general quite modest. Labor income elas- ticities are around 0.05 for wage earners and 0.10 for self-employed individuals, while capital income elasticities are around two to three times larger than labor income elasticities. Third, behavioral elasticities are larger when estimated from large tax reform episodes than from small tax reform episodes, consistent with the general argument by Chetty et al. (2011) and Chetty (2012) that large tax changes are more likely to overcome optimization frictions and therefore reveal the struc- tural long-run elasticity. We find that the large tax reform variation in the 1980s is associated with a population-wide labor income elasticity of 0.12—and about twice as high when zooming in on the very largest tax variation in the data—whereas the smaller tax reform variation of the 1990s and 2000s is associated with a labor income elasticity of only 0.02. Interestingly, our labor income elasticity obtained from a large Danish tax reform is an order of magnitude larger than the labor income elasticity that can be obtained from the largest and most salient Danish tax kink (Chetty et al. 2011), suggesting that reform-based estimates are potentially more revealing of long-run (frictionless) behavior than bunching-based estimates. Finally, using the existence of sharp differential tax variation across income types, we are able to estimate separately own-tax and cross-tax elasticities of labor income and capital income. These estimates indicate that the two income types are substitutes, consistent with the presence of income-shifting behavior. Although the importance of shifting for estimating and interpreting taxable income responses has been dis- cussed extensively (e.g., Saez, Slemrod, and Giertz 2012), our study appears to be the first in the taxable income literature that tackles such cross-effects directly. 4 This general insight is relevant for most countries in the world, including the United States. As a specific example, consider the argument by Saez, Slemrod, and Giertz (2012) that the US elasticity of taxable income is not a sufficient statistic due to the presence of both personal and corporate tax bases with potential shifting (i.e., cross-tax effects) between the two. Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 275 Importantly, we show that the above findings are extremely robust to empirical specification, including socioeconomic controls and the specification of pre-reform income controls (which have been so crucial in previous work). The robustness of our findings is a result of the stable income distribution and the rich tax variation in Denmark. We therefore conclude that the Danish context offers a useful laboratory for a credible identification of taxable income responses. The paper proceeds as follows. Section I describes the Danish tax system and tax reforms. Section II describes the data and Section III sets out the empirical strategy. Section IV presents empirical results and Section V concludes. I. The Danish Tax System and Tax Reforms The Danish personal income tax treats different income forms in a partially separate fashion, as opposed to standard tax systems that apply a progressive rate structure to a single measure of taxable income. As shown in Table 1, the income concepts of the Danish income tax are labor income (LI ), personal income (PI = LI + other PI ), capital income exclusive of stock income (CI ), stock income (SI), deductions (D), and taxable income (TI = PI + CI + SI − D). These income concepts are aggregated into several different tax bases that are taxed at different rates. The definition of those bases as well as the associated tax rates have under- gone substantial changes over time due to a series of tax reforms, and this is the variation that we exploit to estimate behavioral elasticities. Taxes are divided into national and regional taxes, which are enforced and admin- istered in an integrated system. At the national level, a series of important tax acts have been implemented in recent decades. The tax acts analyzed here are the 1987 reform, the 1994 reform, the 1999 reform (called the Pentecost Package), and the 2004 reform (called the Spring Package). Most of these reforms were phased in over several years, which generates considerable tax variation in most years of the period we consider. We also exploit changes in tax schedules at the regional level, but those changes have been much smaller and are more uniform across taxpayers than the national changes. The national income tax is divided into three main brackets: a bottom bracket, a middle bracket, and a top bracket. The past 25 years of tax reform have been ­associated with three main changes. First, a lowering of marginal tax rates in each bracket, with larger cuts in the middle and top brackets than in the bottom bracket. Second, a substantial broadening of the tax base as negative capital income and deductions were prevented from offsetting positive income on a one-to-one basis. This change was implemented by changing the tax schedule from a function of total taxable income (TI) to a function of each of the underlying income components (LI, PI, CI, SI, D), with a higher marginal tax rate on labor income than on the other income components as well as a higher marginal tax on positive income than on neg- ative income (such as mortgage interest and deductions). With the exception of stock income, the taxation of the different income components is not fully separate and cross-effects in the tax function are therefore non-zero. Third, adjustments of bracket cutoffs that did not correspond to the base broadening, thereby pushing taxpayers into higher brackets. This bracket push combined with the fact that tax rates were 276 American Economic Journal: economic policyNovember 2014 Table 1—Income Concepts in the Danish Individual Income Tax Income concept Acronym Main items included 1. Labor income LI Salary, wages, honoraria, fees, bonuses, fringe benefits, business earnings 2. Personal income PI LI + transfers, grants, awards, gifts, received alimony − Labor Market Contribution, certain pension contributions 3. Capital income CI Interest income, rental income, business capital income − interest on debt (mortgage, bank loans, credit cards, student loans) 4. Stock income SI Dividends and realized capital gains from shares 5. Deductions D Commuting, union fees, UI contributions, other work expenditures, charity, paid alimony 6. Taxable income a TI PI + CI + SI − D a  The definition of taxable income in this table does not correspond to what is currently labeled taxable income in the Danish tax code, which excludes stock income as it is taxed on a separate schedule (see Table 2). reduced within each bracket imply substantial and very heterogeneous tax rate varia- tion through the income distribution. All of the changes together ­create strong varia- tion across taxpayers at different income levels, across taxpayers at similar income levels (but different income compositions), and across different income types. Table 2 shows tax rates and tax bases in four specific years: 1986 (before the 1987 reform), 1993 (before 1994 reform), 1998 (before the 1999 reform), and 2005 (after the 1999 and 2004 reforms). The tax system consists of a flat regional tax (shown for the average municipality) along with progressive national taxes levied on vary- ing tax bases. Besides the national bottom, middle, and top taxes that are present throughout the period, there are social security contributions, labor market contribu- tions, and an EITC (Earned Income Tax Credit) featured during different parts of the period. The tax rates shown in the table are cumulative such that a taxpayer in the top bracket is subject to the sum of the bottom, middle, and top taxes (along with the other flat taxes).5 The table shows the tax base changes mentioned above. In the mid-1980s, all tax rates applied to overall taxable income, whereas in the 1990s and 2000s no tax rate applies to this net income measure. In 2005, for example, tax liability is calculated from four different tax bases: taxable income exclusive of stock income (PI + CI – D), personal income plus positive net capital income (PI + [CI > 0]), labor income (LI), and stock income (SI). Two points are worth making regarding those tax base changes. First, when taxable income consists of subcomponents that are treated differently, the elasticity of over- all taxable income is no longer a sufficient statistic for welfare analysis. In this case, one must estimate elasticities of each underlying tax base, in principle including both own-tax and cross-tax elasticities. We therefore consider separately the e­ lasticities of 5 For example, in 1986, a taxpayer in the top bracket would face a marginal tax rate equal to 28.1 + 14.4 + 14.4 + 10.8 + 5.5 = 73.2 percent. However, a marginal tax ceiling is in place in all years, and this ceiling equals 73 percent in 1986 and is therefore binding for a taxpayer living in an average municipality. In 2005, the marginal tax ceiling has dropped to 59.0 percent and was indeed also binding for a taxpayer in the top bracket living in the average municipality. For labor income, there is a labor market contribution of 8 percent on top of the tax ceiling, but at the same time labor income enters all the other tax bases net of the labor market contribution. The effective tax ceiling on labor income in 2005 is therefore equal to 8.0 + (1 − 0.08) × 59.0 = 62.3 percent. Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 277 Table 2—Tax Bases and Tax Rates over Time in the Danish Individual Income Tax System 1986 1993 Tax type a Base Rate (%) Base Rate (%) Panel A Regional tax b TI 28.1 PI + CI − D 30.2 National taxes Bottom tax TI 14.4 PI + CI − D 22.0 Middle tax TI 14.4 PI + [CI > 0] 6.0 Top tax TI 10.8 PI 12.0 Social security contribution TI 5.5 — — Labor market contribution c — — — — EITC — — — — Tax on stock income d — — SI 30.0; 40.0 Marginal tax ceiling e TI 73.0 PI/CI/TI 68.0 1998 2005 Tax type a Base Rate (%) Base Rate (%) Panel B Regional tax b PI + CI − D 32.4 PI + CI − D 33.3 National taxes Bottom tax PI + CI − D 8.0 PI + [CI > 0] 5.5 Middle tax PI + CI 6.0 PI + [CI > 0] 6.0 Top tax PI + [CI > 21k] 15.0 PI + [CI > 0] 15.0 Social security contribution — — — — Labor market contribution c LI 8.0 LI 8.0 EITC — — LI 2.5 Tax on stock income d SI 25.0; 40.0 SI 28.0; 43.0 Marginal tax ceiling e PI/CI/TI 58.0 PI/CI/TI 59.0 Tax rates are cumulative. For example, the marginal tax rate in the top bracket in 1986 is equal to 28.1 + 14.4 + a  14.4 + 10.8 + 5.5 = 73.2 percent (but see footnote 4 regarding marginal tax ceiling adjustment). b  The regional tax includes municipal, county, and church taxes. The regional tax rate in the table is an average across all municipalities in Denmark in each year. c  After the introduction of the labor market contribution, labor income enters the other tax bases net of the labor market contribution. Hence, in those years, the effective tax rate on labor income equals the statutory tax rate times (1 − labor market contribution). d  After the 1987 reform, the taxation of stock income is completely separate from the rest of the income tax and follows a two-bracket progressive schedule with the marginal tax rates shown in the table. If the sum of all regional and national tax rates (excluding the stock income tax after the 1987 reform) exceeds e  the specified ceiling, the top tax is adjusted downward until the the marginal tax rate equals the ceiling. taxable labor income and taxable capital income.6 Second, by ­estimating elasticities of the underlying income components, we avoid the ­identification problems posed by base broadening that have been discussed extensively in the literature on taxable income responses (Slemrod 1998; Kopczuk 2005). The usual problem is that broad- ening of the dependent variable (taxable income) forces researchers to consider a constant-definition measure of taxable income in order not to confound behavioral and mechanical changes, but in so doing they are relating the tax rate to an artificial 6 Consistent with the income definitions in Table 1, we consider capital income (CI ) exclusive of stock income (SI). The latter is taxed on a completely separate schedule, which has remained relatively constant through most of the period and therefore offers less reform-based variation than the rest of the income tax code. The most useful quasiexperimental variation in stock income taxation is created, not by tax reforms, but by a sharp kink at the cutoff between two brackets in the stock income tax. Kleven et al. (2011) use bunching around this kink to estimate the elasticity of stock income and find evidence of strong behavioral responses driven by tax avoidance. 278 American Economic Journal: economic policyNovember 2014 Panel A. Marginal tax rate Panel B. Marginal tax rate on labor income on negative capital income 75 75 Marginal tax rate 70 70 Marginal tax rate 65 65 60 60 55 55 50 50 45 40 45 35 40 30 4 86 88 90 92 94 96 98 00 02 04 4 6 88 90 92 94 96 98 00 02 04 8 8 8 19 19 19 19 19 19 19 19 20 20 20 19 19 19 19 19 19 19 19 20 20 20 Panel C. Marginal tax rate Panel D. Share of taxpayers in positive capital income in the three tax brackets 75 60% Share of all taxpayers 70 Marginal tax rate 50% 65 60 40% 55 30% 50 20% 45 40 10% 35 0% 4 86 88 90 92 94 96 98 00 02 04 4 6 8 0 2 4 6 8 00 02 04 8 8 8 8 9 9 9 9 9 19 19 19 19 19 19 19 19 20 20 20 19 19 19 19 19 19 19 19 20 20 20 Bottom bracket Middle bracket Top bracket Figure 2. Two Decades of Danish Tax Reform Notes: The figure shows the evolution of marginal tax rates on labor income (panel A), negative capital income (panel B), and positive capital income (panel C) in each tax bracket (bottom, middle, and top) over time, along with the evolution in the share of taxpayers located in each bracket over time (panel D). tax base different from the one in the tax code in a given year. This is not an issue here as we consider the actual income subcomponents in the tax code, the definition of which has been (almost) constant and which are observed throughout the period. To put it differently, the empirical advantage of the Danish base broadening is that it does not consist in including previously untaxed (and therefore u­ nobserved) com- ponents in the tax system, but consists instead in reducing the tax rate associated with negative income and deductions that are in the tax code throughout the period. Figure 2 illustrates the implications of the tax rate and tax base changes described above for the effective marginal tax rates on labor and capital income in each bracket (bottom, middle, and top) over time. For labor income (panel A), the marginal tax rate in the top bracket has been declining from 73 percent to 62 percent, while the tax rate in the middle bracket has been declining from 62 percent to 49 percent. On the other hand, the bottom tax rate is increasing over the early part of the period and then declining over the later part of the period. Overall, the difference between the bottom tax and the middle/top taxes has been shrinking over this period, although the relative changes have not been dramatic. However, these graphs do not reveal the important implications of bracket push as we come back to below. For capital income, we distinguish between negative capital income (panel B) and positive capital income (panel C) as the two are taxed very differently. For nega- tive capital income, the three brackets have collapsed into one bracket, subject to the Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 279 bottom tax rate (as negative capital income was excluded from the middle and top tax bases). For taxpayers in the top bracket, the marginal tax rate associated with negative capital income has dropped from about 73 percent to 33 percent over the period, while for taxpayers at the bottom the drop has been much smaller. These dra- matic tax changes affect a very large number of taxpayers, because capital income is in fact negative for the majority of Danish taxpayers as a result of interest payments on loans (mortgage and other loans). For positive capital income, we also see very large changes as the band between the top and the bottom first narrows substantially (since all capital income is excluded from the top tax base) and then widens substan- tially (since positive capital income is reintroduced in the top tax base). Finally, to see the importance of bracket push due to underadjustment of bracket cutoffs as bases were broadened, panel D shows the evolution over time in the share of taxpayers located in each bracket. We see that the share of taxpayers liable to pay the top tax has increased dramatically from less than 10 percent of the population in the mid-1980s to almost 30 percent of the population in the mid-2000s. The share of individuals in the middle bracket has fallen from about 40 percent to slightly above 20 percent over the whole period, while the share of taxpayers in the bottom bracket falls from about 50 percent to 40 percent in the early part of the period and then rises back to 50 percent in the latter part of the period.7 These movements across brackets create substantial tax variation, especially for labor income. The combination of the tax rate changes for labor income in panel A and the bracket push in panel D create very strong and nonlinear tax variation through the income distribution. Overall, the reforms described in this section imply substantial tax variation over time and across individuals. Indeed, as we show in Section III when discussing the identification strategy, the variation in some years is comparable to the major tax acts in the United States in the 1980s. II. Data The dataset includes the full Danish population since 1980. It has been con- structed by Statistics Denmark based on several administrative registers, including the Income Tax Register and the Integrated Database for Labor Market Research (IDA). For each individual, the dataset contains detailed tax return information along with a large set of socioeconomic variables such as address, gender, age, mar- ital status, children, immigration status, ethnicity, employment status, job experi- ence, education, occupation, and industry. Marginal tax rates are not directly observed in tax return data, and we therefore have to simulate marginal tax rates for each taxpayer based on tax return information and a model of the Danish tax system. As there exists no publicly available tax simu- lation model for Denmark (such as the NBER TAXSIM model for the United States), we have constructed our own tax simulator accounting for all details of the Danish 7 The bottom, middle, and top bracket shares do not quite add up to 1, because a small amount of taxpayers below a basic exemption level are not liable to pay the bottom tax. 280 American Economic Journal: economic policyNovember 2014 tax system between 1984 and 2005.8 Based on this model and tax return data, we compute the marginal tax rate on a given income component by increasing income by DKK 100 (≃ US$18 as of August 2013). In particular, if tax liability T ​( · )​is a func- tion of n different income components z​ ​1​, … , ​z​  n​, we compute the marginal tax on z​ ​  j​ as ​τ​  j​ = ​[ T​( ​z1​​, … , ​z​  j​ + 100, … , ​z​  n​  )​ − (T​z1​​, … , ​z​  j​, … , ​z​  n​) ]​/100.9 Following Gruber and Saez (2002), the empirical strategy is to relate changes in taxable income over time to changes in marginal tax rates over time for individual taxpayers. We consider three-year intervals (1984–1987, … , 2002–2005), which correspond to the differencing in most US studies and more importantly fit the data in our context. In particular, we show graphically that three-year intervals are just enough to account for sluggishness in behavioral adjustments—long enough to cap- ture long-term effects, but not longer than that to avoid unnecessarily losing varia- tion and power. We denote the first year in any given three-year interval by s and the last year by s + 3. We include only taxpayers that are also observed in year s − 1, because this year is used to construct pre-reform income controls. The three-year differences are stacked to obtain a dataset with about 49 million observations. We impose the following restrictions on the estimation sample. First, we restrict attention to individuals aged 15–70 years. Second, individuals whose income in base year s comes primarily from welfare benefits are excluded, because including them would require us to account for the important incentive effects of the welfare system and model extensive responses. Third, we limit the sample to people who are fully tax liable in Denmark. These restrictions leave us with a sample of about 37 million observations, with summary statistics shown in Table A1 in the Appendix. III. Empirical Strategy A. Conceptual Framework The economic model underlying the taxable income literature is a simple exten- sion of the traditional labor supply model. It is assumed that each taxpayer maximizes a utility function u​( c, z, x )​, where c is consumption, z is reported taxable income, and x is a vector of individual characteristics. We may think of taxable income z as being generated by a number of underlying choices such as hours worked, unobserved effort, training, occupational choice, tax sheltering activities, etc. The implicit assumption in the literature is therefore that all those underlying activities are weakly separable from consumption in the utility function. Utility is maximized subject to a budget constraint c = z − T ​( z )​ = ​( 1 − τ )​  ⋅ z + y, where T ​( · )​ is tax liability, τ ≡ ​T ′​​( · )​is the marginal tax rate, and y ≡ τ ⋅ z − T​( z )​is virtual income. We may then write the optimal choice of taxable income as z = z​( 1 − τ, y, x )​. 8 We restrict the tax simulator to the period 1984–2005 (even though the dataset goes back to 1980) due mainly to difficulties of precisely measuring all the subcomponents of taxable income before 1984. But since we control for pre-reform income levels in the panel regressions, we will be using data from before 1984. 9 While the Danish income tax system is based on individual filing for married couples, it involves certain ele- ments of jointness due to the fact that some exemptions can be transferred across spouses. This implies that, for a married person, income tax liability depends on both individual incomes and on spousal incomes. Our TAXSIM model accounts fully for this jointness. Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 281 Consistent with the Danish setting, we extend the above model to account for the presence of multiple income types that are taxed differently. Consider therefore a consumer choosing incomes ​z​1​, … , ​z​  n​ under a tax schedule T ​( ​z1​​, … , ​z​  n​  )​. This consumer maximizes utility (1)  u = u​( c, ​z1​​, … , ​z​  n​, x )​, subject to a budget constraint n n (2)  ∑​ ​​z​  ​ − T​( ​z​​, … , ​z​  ​  )​ = ​∑​ ​​( 1 − ​τ​  j​  )​ ​z​  j​ + y, c = ​ j 1 n j=1 j=1 where ​τ​  j​  ≡ ∂ T/∂ ​z​  j​ is the marginal tax rate on income type j and y ≡ ​∑​  j=1​​τ​ ​  j​​z​  j​ − n T​( ​z1​​, …, ​z​  n​  )​ is virtual income. Our measure of virtual income is a generalization of standard virtual income to a situation with multidimensional income.10 As all z-variables in equation (2) are defined as income, if a given component z​ ​  j​ reflects a deduction in taxable income, then this component is defined as minus deductions. In this model, the optimal choice of income type j depends on all the net-of-tax rates and virtual income, i.e., (3)  ​z​  j​ = ​z​  j​​( 1 − ​τ​  1​, … , 1 − ​τ​  n​, y, x )​ ∀j. In general, an empirical specification for income type j should account for both ­own-price effects of the marginal net-of-tax rate on income type j as well as ­cross-price effects of the net-of-tax rates on all the other income types. In the empir- ical analysis, we first consider baseline specifications without cross-tax effects, and then turn to specifications that allow for cross-tax effects by exploiting the sharp tax variation across different income types in Denmark. The analysis of cross-tax effects enables us to evaluate the potential importance of income shifting between labor and capital income, an issue that has been much discussed in the literature. In the baseline model without cross-tax effects, expression (3) implies ​z​  is​​  = ​z​  j​​( 1 − ​τ​  jis​,​   ​yi​s​, ​xi​s​  )​for taxpayer i at time s. Adopting a log-linear specification, j we have (4) log ​( ​z​  jis​ ​  )​ = α + ε ⋅ log ​( 1 − ​τ​  jis​ ​  )​ + η ⋅ log ​( ​yi​s​  )​ + ​γ​  cs​  ​ ⋅ ​x​  ci​  ​ + ​γ​  v​ ⋅ ​x​  vis​​  + ​μ​i​ + ​ν​is​. In this specification, we distinguish between time-invariant individual characteris- tics ​x​  ci​  ​ whose effect may change over time and time-variant individual characteris- tics ​x​  vis​​  whose effect is constant over time. The effect of time-invariant individual characteristics whose effect is constant over time is subsumed in the individual fixed effect μ ​ ​i​. The key variables of interest are the uncompensated elasticity with respect 10 By modeling the income effect in terms of virtual income, we deviate from previous taxable income studies (such as Gruber and Saez 2002) where the income effect is specified simply in terms of after-tax income z − T​( z )​. Our virtual income specification keeps a clear link between the estimated coefficients and the compensated and uncompensated elasticities that represent sufficient statistics for welfare analysis. 282 American Economic Journal: economic policyNovember 2014 to the marginal net-of-tax rate (ε) and the income elasticity (η), the combination of which gives the compensated elasticity using the Slutsky decomposition.11 In first-differenced form, the model can be written as (5)Δ log ​( ​z​  jis​ ​  )​ = ε ⋅ Δ log ​( 1 − ​τ​  jis​ ​  )​ + η ⋅ Δ log ​( ​yi​s​  )​ + Δ​γ​  cs​  ​⋅ ​x​  ci​  ​ + ​γ​  v​ ⋅ Δ​x​  vis​​  + Δ ​νis​ ​. In the baseline specification, differences at time s are three-year differences from s to s + 3. B. Identification and Relationship to Previous Literature Because of the nonlinearity of the tax system, the marginal tax rate and virtual income are endogenous to the choice of taxable income, which creates a correlation between Δ log ​( 1 − ​τ​  js​ ​  )​, Δ log ​( ​ys​​  )​, and the error term. The usual way to construct instruments for these variables is to use mechanical tax changes driven by changes in tax laws. Hence, using the Danish tax simulation model described above, we sim- ulate post-reform marginal tax rates under pre-reform behavior, ​τ​  js+3​​(​ ​z​  1s​  ​, … , ​z​  ns​  ​  )​, where we account for the fact that the marginal tax rate on income j may depend not just on the level of income j but also on the levels of the other incomes. From the simulated marginal tax rates, we obtain mechanical net-of-tax rate changes, log ​( 1 − ​τ​  js+3(​​​ ​z​  1s​  ​, … , ​z​  ns​  ​  ))​  ​ − log ​( 1 − ​τ​  js(​​​  ​z​  1s​  ​, … , ​z​  ns​  ​  ))​  ​, which are used as instruments for the observed changes Δ log ​( 1 − ​τ​  js​ ​  )​. Analogously, we simu- late post-reform virtual incomes under pre-reform behavior, y​s​+3​​( ​z​  1s​  ​, … , ​z​  ns​  ​  )​ = ​∑​  j=1​​τ​ ​  js+3​​​( ​z​  1s​  ​, … , ​z​  ns​  ​  )​ ​z​  js​​  − ​Ts​+3​​( ​z​  1s​  ​, … , ​z​  ns​  ​  )​, and associated mechanical changes N in virtual income, log ​( ​ys​+3​​( ​z​  1s​  ​, … , ​z​  ns​  ​  ))​  ​ − log ​( ​ys​​​( ​z​  1s​  ​, … , ​z​  ns​  ​  ))​  ​, which are used as instruments for the observed changes Δ log ​( ​ys​​  )​. While the mechanical tax changes used as instruments are exogenous to post- reform incomes, they do depend on pre-reform incomes. Hence, the instruments may be correlated with the error term if the pre-reform income level is correlated with the error term. The literature has discussed two channels through which this may occur. First, taxpayers at different pre-reform income levels may experience dif- ferent income trends for nontax reasons. Indeed, many countries have experienced sharply increasing top income shares over the past few decades, and several studies have argued that these changes are driven by skill-biased demand shocks resulting from innovation and globalization. Unless skill can be directly controlled for, it would be captured by pre-reform income levels and skill-biased changes would then be absorbed in the estimated elasticity. Second, the pre-reform income level reflects both permanent and transitory income components, which creates a mean-reversion problem: a taxpayer with a very high income in the pre-reform year will tend to have a lower income in the post-reform year, other things being equal. In the absence of 11 The estimate ε is an uncompensated elasticity due to budget set linearization implied by the virtual income formulation. Under this formulation, the coefficient ε captures the effect of a proportional tax rate change on all units of earnings, holding constant virtual income (the linearized budget intercept with the consumption axis) and therefore not compensating for any income effects of the tax change. This is conceptually similar to a wage rate change in a standard labor supply function, which produces both substitution and income effects. Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 283 controls for transitory income components, they would be captured by pre-reform income levels and hence be absorbed by the estimated tax effect. The problems just described are particularly acute when considering tax reforms that are strongly targeted to certain income groups such as high-income earners (as in the case of the US tax reforms in the 1980s). In that case, the mechanical tax changes will be strongly correlated with income level and therefore with skill- dependent demand shocks and transitory income components. To deal with this problem, Auten and Carroll (1999), Moffitt and Wilhelm (2000), Gruber and Saez (2002), and Kopczuk (2005) propose to control in different ways for pre-reform income. For example, Kopczuk (2005) proposes a specification that includes the change in income in the year prior to the reform, z​ s​​ − ​z​  s−1​, as a proxy for transitory income components, along with the lagged income level ​z​  s−1​as a proxy for the per- manent income level. He allows for nonlinearity by experimenting with ten-piece splines in the logarithms of either of the two controls. He also explores a number of other specifications, including those adopted by Auten and Carroll (1999) and Gruber and Saez (2002). The results show that the elasticity estimates are extremely sensitive to the specification of pre-reform income controls. We consider the main pre-reform income controls that have been proposed in the literature. Unlike previous studies, we find that our results are extremely robust to the specification of income controls, which suggests that unobserved nontax factors impacting on taxable income do not pose a threat to identification here. There are two main reasons for the robustness of our findings. First, as discussed in the intro- duction and shown in Figure 1, the income distribution in Denmark has remained very stable over the period that we study, implying that bias from nontax changes in the income distribution is not a concern. This isolates mean-reversion as the only potential bias that the income controls have to correct for. Second, the biases dis- cussed above rely on the presence of a correlation between tax changes and pre- reform income level, which is not an important feature of the Danish reforms. As described earlier, the Danish reforms were not systematically targeted to certain income groups and created are lot of up-and-down movements in tax rates through- out the income distribution. In fact, the increasing asymmetry in the tax treatment of different income components creates variation even for taxpayers at the same income level (but with different income compositions). In the next section, we dem- onstrate the exact nature of the Danish variation around specific reform episodes. C. Mechanical Variation in Marginal Net-of-Tax Rates To give a clear sense of the identifying variation, Figure 3 shows the mechani- cal variation in marginal net-of-tax rates (i.e., the variation in the instrument) for different income types in panels A–C around the two largest reform episodes in our data, the 1987 reform (left side) and the 1994 reform (right side). Each figure shows three-year differences in percent, where we have split the sample into seven groups using base-year income variables: (i) individuals who are in the bottom bracket both before and after; (ii) individuals who are pushed from the middle to the bottom bracket; (iii) individuals who are pushed from the bottom to the middle bracket; (iv) individuals who are in the middle bracket both before and after; 284 American Economic Journal: economic policyNovember 2014 Panel A. Labor income 1987 Reform 1994 Reform (1986–1989 difference) (1993–1996 difference) Change in net-of-tax Change in net-of-tax taxpayers (percent) taxpayers (percent) 45% 35% 45% 35% 35% 35% 30% rate (percent) 30% rate (percent) Share of all Share of all 25% 25% 25% 25% 15% 20% 15% 20% 5% 15% 5% 15% −5% 10% −5% 10% −15% 5% −15% 5% −25% 0% −25% 0% To m le To m dle St mi m St o m m e e ay p ay p tto o b m M m e Bo to ttom M m e p p dl dl dl dl ay dd St to St to l l to to o to to p idd p idd Bo e t tto ay id m ott id id id id m ot to to o o tto b id y b id y b e e to to t a a e St St dl dl M M Panel B. Negative capital income 1987 Reform 1994 Reform (1986–1989 difference) (1993–1996 difference) Change in net-of-tax Change in net-of-tax taxpayers (percent) taxpayers (percent) 60% 35% 60% 35% rate (percent) 50% 30% 50% 30% rate (percent) Share of all Share of all 40% 25% 40% 25% 30% 20% 30% 20% 20% 15% 20% 15% 10% 10% 10% 10% 0% 5% 0% 5% −10% 0% −10% 0% To m le To m le St mi m St mi m e e ay p ay p tto o b m M m e tto o b m M m e p p dl dl dl dl ay dd ay dd St to St to l l to to to to to to p idd p idd Bo e t tto Bo e t tto id id id id m ot m ot to to o o id y b id y b e e to to a a St St dl dl M M Panel C. Positive capital income 1987 Reform 1994 Reform (1986–1989 difference) (1993–1996 difference) Change in net-of-tax Change in net-of-tax 50% taxpayers (percent) 50% 70% taxpayers (percent) 70% 40% rate (percent) rate (percent) 40% 60% 60% Share of all Share of all 30% 50% 30% 50% 20% 40% 20% 40% 10% 30% 10% 30% 0% 20% 0% 20% −10% 10% −10% 10% −20% 0% −20% 0% To m le To m le St mi m St mi m e e ay p ay p tto o b m M m e tto o b m M m e p p dl dl dl dl ay dd ay dd St to St to l l to to to to to to p idd p idd Bo e t tto Bo e t tto id id id id m ot m ot to to o o id y b id y b e e to to a a St St dl dl M M Share of taxpayers Mechanical change in marginal net-of-tax rate Figure 3. Mechanical Variation in the Marginal Net-of-Tax Rate Notes: The figure shows the mechanical variation in marginal net-of-tax rates (dashed lines) due to the 1987 reform and 1994 reform, respectively, on labor income (panel A), negative capital income (panel B), and positive capital income (panel C). Each panel shows three-year differences in percent, where we have split the sample into seven groups using base-year income variables: (i) individuals who are in the bottom bracket both before and after, (ii) indi- viduals who are pushed from the middle to the bottom bracket, (iii) individuals who are pushed from the bottom to the middle bracket, (iv) individuals who are in the middle bracket both before and after, (v) individuals who are pushed from the top to the middle bracket, (vi) individuals who are pushed from the middle to the top bracket, and (vii) indi- viduals who are in the top bracket both before and after. The figure also shows the size of each group as a share of all taxpayers (bars). Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 285 (v) individuals who are pushed from the top to the middle bracket; (vi) individuals who are pushed from the middle to the top bracket; and (vii) individuals who are in the top bracket before and after. Two aspects of the figure are worth noting. First, it is the combination of changes in tax bases and bracket cutoffs that makes it possible for a tax reform to push some taxpayers from a lower to a higher bracket (e.g., bottom to middle) and simulta- neously push other taxpayers in the opposite direction (e.g., middle to bottom). Second, the grouping of taxpayers in the figure is useful to make the identifying tax changes stand out. The grouping is different from one based on quantiles of the income distribution. Such a grouping would show much less average tax variation in each quantile group as it lumps together tax reductions for those who stay in a given bracket or move to a lower bracket with tax increases for those who are pushed into a higher bracket. Hence, an income quantile representation of tax changes would hide a lot of the identifying variation in the data. Each panel shows the mechanical change in the marginal net-of-tax rate in dif- ferent groups (dashed line, left y-axis) and the size of each treatment group (bars, right y-axis).12 Panel A shows the change in labor income taxation around the 1987 reform (1986–1989 difference) and around the 1994 reform (1993–1996 difference). For the 1987 reform, there are very large and strongly heterogeneous tax changes across taxpayers, with the percentage change in the net-of-tax rate varying between −20 percent and +42 percent. These differences in tax treatments across groups are larger than the tax treatment differences created by the Tax Reform Act of 1986 in the United States and the Tax Reform of the Century in Sweden in 1991, two reforms that have been extensively analyzed in the literature. For the 1994 reform, tax changes are also very large and heterogeneous, but not quite to the same degree as for the 1987 reform. Panels B and C show the variation in the taxation of negative and positive capital income around the same two reform episodes. For the 1987 reform, the tax variation on capital income, especially negative capital income, is even stronger than for labor income. The marginal net-of-tax rate for those in the top bracket increased by more than 50 percent (40 percent) in the case of negative (positive) capital income, while other groups of taxpayers experienced much smaller increases or reductions in the net-of-tax rate. The 1994 reform has much smaller effects than the 1987 reform and, importantly, the tax variation created by the 1994 reform is qualitatively very differ- ent. For positive capital income, for example, the net-of-tax rate is reduced at the top and increased at the bottom directly opposite the 1987 reform. Although the tax changes around 1987 and 1994 constitute the strongest varia- tion in the data, there is in fact a lot of variation throughout the period we consider. Importantly, the tax variation in other years is often qualitatively different in terms of who experience tax increases and who experiences tax cuts. 12 The population shares of the seven groups do not quite sum to 100 percent due to a small number of taxpayers below the exemption level for the bottom bracket. 286 American Economic Journal: economic policyNovember 2014 Panel A. Labor income 120 Treatment (tax cuts) 115 Control (tax increases) (index 1986 = 100) 110 Labor income 105 100 95 DD elasticity = 0.214 (0.011) 90 82 83 84 85 86 87 88 89 90 91 92 93 19 19 19 19 19 19 19 19 19 19 19 19 Panel B. Labor income: large versus small tax cuts 120 Treatment L (large tax cuts) 115 Control (tax increases) Treatment S (small tax cuts) (index 1986 = 100) 110 Labor income 105 100 DDL elasticity = 0.257 (0.013) 95 DDS elasticity = 0.186 (0.012) 90 2 3 4 5 6 7 8 9 0 1 2 3 8 8 8 8 8 8 8 8 9 9 9 9 19 19 19 19 19 19 19 19 19 19 19 19 Figure Panel4.C.Graphical Evidence Positive capital on Taxable Income Responses to the Danish 1987 Reform income 130 (Continued ) Treatment (tax cuts) 120 Control (tax increases) Positive capital income (index 1986 = 100) IV. Empirical Results 110 A. Graphical Evidence 100 This section presents graphical evidence on taxable income responses to the large 90 1987 reform. Figure 4 shows the evolution of labor income (panels A–B) and capital income (panel C) between 1982–1993 for groups thatDD were = 0.278differently affected elasticity (0.063) by the 1987 reform,80 demarcated by a vertical line.13 The figure is based on a b­ alanced 2 3 4 5 6 7 8 9 0 1 2 3 panel of individuals who are observed throughout the period. Panel A shows the 8 8 8 8 8 8 8 8 9 9 9 9 19 19 19 19 19 19 19 19 19 19 19 19 effect on labor income using a simple treatment-control assignment based on the reform-induced tax variation shown in Figure 3: the treatment group includes those who experience an increase in the marginal net-of-tax rate on labor income due to 13 The vertical line demarcates 1986, which is the last pre-reform year (as the reform was passed in parliament during 1986 and changed tax rates starting from 1987). Income levels in 1986 are normalized to 100 for all groups.  DDL elasticity = 0.257 (0.013) 95 DDS elasticity = 0.186 (0.012) 90 Vol. 6 No. 4 Kleven and Schultz: Taxable Income Responses in denmark 287 2 3 4 5 6 7 8 9 0 1 2 3 8 8 8 8 8 8 8 8 9 9 9 9 19 19 19 19 19 19 19 19 19 19 19 19 Panel C. Positive capital income 130 Treatment (tax cuts) 120 Control (tax increases) Positive capital income (index 1986 = 100) 110 100 90 DD elasticity = 0.278 (0.063) 80 82 83