The Elasticity of Taxable Income in Spain: 1999-2014

We study how taxable income responds to changes in marginal tax rates, using as a main source of identifying variation three large reforms to the Spanish personal income tax implemented in the period 1999-2014. The most reliable estimates of the elasticity of taxable income (ETI) with respect to the net-of-tax rate for this period are between 0.45 and 0.64. The ETI is about three times larger for selfemployed taxpayers than for employees, and larger for business income than for labor and capital income. The elasticity of broad income (EBI) is smaller, between 0.10 and 0.24, while the elasticity of some tax deductions such as the one for private pension contributions exceeds one. Our estimates are similar across a variety of estimation methods and sample restrictions, and also robust to potential biases created by mean reversion and heterogeneous income trends.

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Introduction
The impact of personal income taxes on the economic decisions of individuals is a key empirical question with important implications for the optimal design of tax policy. Not surprisingly, the modern public finance literature has devoted significant efforts to study behavioral responses to changes in taxes on reported taxable income, as reviewed by (Saez, Slemrod and Giertz, 2012). Most of this work focuses on the elasticity of taxable income (ETI), which captures a broad set of real and reporting behavioral responses to taxation. Indeed, reported taxable income reflects not only individuals' decisions on hours worked, but also work effort and career choices as well as the results of investment and entrepreneurship activities. Besides these real responses, the ETI also captures tax evasion and avoidance decisions of individuals to reduce their tax bill.
In this paper, we estimate the elasticity of taxable income in Spain, an interesting country to study because during the last two decades it has implemented several major personal income tax reforms, plus a variety of smaller legislative changes, including the ability of regional governments to modify the tax schedule. Due to data availability, we focus on the reforms implemented in the period 1999-2014, which provide useful variation to identify the ETI. We consider all legislative changes in the personal income tax, although identification mainly comes from three major reforms. In particular, the 2003 reform lowered the top marginal tax rate (45 to 43 percent) and also reduced the marginal rate for the bottom bracket (18 to 15 percent). The 2007 reform was an overhaul of the income tax system, turning the standard personal deduction into a tax credit, which increased the progressivity of the tax. It also modified the definition of tax bases, shifting a substantial part of capital income from the "general" to the "savings" tax base and thereby lowering the marginal rate on capital income. Finally, the 2012 reform, introduced in the middle of a severe recession, increased tax rates across the board, pushing the top marginal rate up to 52 percent (further increased to 56 percent in some regions, like Andalusia and Catalonia).
The empirical literature on the ETI has stressed two challenges that could prevent obtaining consistent estimates of this parameter: mean reversion and heterogeneous income trends. Mean reversion is due to transitory shocks to income. When taxpayers receive a transitory income shock in a given year, they tend to revert to their permanent income in subsequent years. This makes it difficult to disentangle changes in reported income due to mean reversion from changes induced by tax reforms. Moreover, the potential bias due to mean reversion has opposite signs for tax cuts and tax increases.
The impact of mean reversion is particularly acute in the top and bottom tails of the income distribution, affecting taxpayers with low and high permanent income, who are precisely the groups often targeted by tax reforms.
Electronic copy available at: https://ssrn.com/abstract=3422056 Heterogeneous income trends across groups of taxpayers differently affected by tax reforms are problematic for similar reasons. Much of the discussion in the literature has centered around the increase in income inequality in the US in the 1980s (documented by Piketty and Saez, 2003), because many papers in this literature evaluate the reduction in the top marginal rate in the 1986 Tax Reform Act. In that setting, it is hard to disentangle whether increases in taxable income by top earners are caused by the tax reform or by the underlying trend toward higher inequality. In the case of Spain, the existence of secular income trends seems less problematic for the estimation of the ETI, as there has been no comparable increase in income inequality over the period under study.
However, the asymmetric impact of the Great Recession across groups of taxpayers could also create challenges for identification.
In the empirical anlysis, we use an administrative panel dataset of income tax returns compiled by the Instituto de Estudios Fiscales (IEF) with information provided by the Spanish Tax Agency (AEAT). The panel is a random stratified sample with 8.1 million observations over the period 1999-2014 (about 3 percent of each year's income tax returns). It contains detailed information on the main components of each income source (labor, capital and self-employment), income-related deductions, the legal tax bases, details on a broad range of tax credits and the overall tax liability for each taxpayer. We use this information to construct a stable definition of taxable income over time. This homogenization is necessary to provide consistent estimates of the ETI for a long period such as 1999-2014 during which significant tax base changes were introduced (e.g. 2007 reform). Since the marginal tax rate (MTR) is not contained in the data, we construct our own tax calculator (in the spirit of the NBER's TAXSIM for the US) to calculate the MTR for each taxpayer, and also to build the predicted-tax rate instruments described below. We calculate the MTR as a weighted average of the MTR applicable to each income source (labor, financial capital, real-estate capital, business income and capital gains).
We use various panel-based two-stage least squares (2SLS) diff-in-diff estimators to obtain consistent estimates of the ETI. The baseline instrument is the predicted change in the net-of-tax rate, defined assuming that income stays constant (in real terms) between a pair of years. This instrument has been used extensively in the literature dating back to Gruber and Saez (2002). Identification comes from heterogeneous changes in the personal income tax schedule across groups of taxpayers due to tax reforms. In all regressions, we control for socio-demographic characteristics of taxpayers (e.g., age, gender, geographic location and indicators for joint filing, children and old-age dependents) that proxy for their permanent income. The presence of mean reversion and heterogeneous income trends in the data motivates the inclusion of nonlinear functions of base-year income, aiming to resolve the potential biases introduced in the estimates. As we discuss in more Electronic copy available at: https://ssrn.com/abstract=3422056 detail below, we also use state-of-the-art estimation methods proposed by Kleven and Schultz (2014) and Weber (2014) to deal with these identification challenges.
We begin the empirical analysis by examining the existence of mean reversion and heterogeneous income trends in Spain over the 1999-2014 period. Mean reversion is present at the bottom and top tails of the income distribution, which makes it essential to account for mean reversion in the regression analysis. Regarding changes in the income distribution, we show that top income shares have been relatively stable in Spain.
This suggests that the existence of secular income trends across groups of taxpayers differentially affected by tax reforms is not a first-order concern in this context. In addition to the average estimates of the ETI, we analyze heterogeneous responses across groups of taxpayers and sources of income. The results on the anatomy of the response are in line with the predictions from the literature. As expected, stronger responses are documented for groups of taxpayers with higher ability to respond. In particular, self-employed taxpayers have a higher ETI than wage employees, while real-estate capital and business income respond more strongly than labor income. The elasticity of broad income (EBI) is between 0.10 and 0.24, substantially lower than the ETI, indicating that deductions play a significant role in taxpayers' responses. Indeed, we find large responses on the tax deductions margin, especially private pension contributions.
Nevertheless, the EBI is relevant in quantitative terms, particularly for self-employed taxpayers, suggesting that there may be real labor supply responses to taxation or evasion behavior that go through reported broad income.
The paper proceeds as follows. Section 2 briefly reviews the large literature on the ETI, including earlier estimates for Spain. Section 3 describes the Spanish personal income tax and the main tax reforms in the period 1999-2014, and also describes the administrative panel dataset used in the empirical analysis. Section 4 provides a sim-Electronic copy available at: https://ssrn.com/abstract=3422056 ple conceptual framework and discusses our estimation strategy to obtain consistent estimates of the ETI. Section 5 reports the main empirical results and the sensitivity analysis. Section 6 concludes.

Relation to the Existing Literature on the ETI
A large body of research has attempted to estimate the elasticity of taxable income.
Although the most influential works focus on the US personal income tax, there are estimates available for an increasing number of advanced economies. As a result of this body of research, meta-analyses of the ETI estimates for a variety of countries have been conducted by Neisser (2017) and Klemm et al. (2018).
In one of the seminal papers in this literature, Feldstein (1995) used a sample of US income tax returns from 1985 and 1988 to study responses to the 1986 Tax Reform Act (TRA). He estimated a very large elasticity, between 1 and 3, which would put the US on the wrong side of the Laffer curve. Later studies, using an extended dataset for the period 1979-1990 in the US and more sophisticated regression techniques, revised these estimates downward to about 0.4 (Auten and Carroll, 1999;Gruber and Saez, 2002). These studies take into account two econometric challenges largely ignored in Feldstein (1995): a trend towards higher income inequality that was unrelated to tax reforms and the existence of substantial mean reversion in taxable income over time.
This literature has been extensively summarized by Saez, Slemrod and Giertz (2012), concluding that the "best available estimates [of the ETI in the US] range from 0.12 to 0.40" (p. 42). The literature also examined the anatomy of the response in the US, which results in small elasticities of broad income (EBI), around 0.1, indicating that most of the taxpayers' reaction is through itemization rather than real or reporting responses in gross income. Furthermore, the empirical literature documents a much stronger response of taxpayers with a broader scope to react (e.g., self-employed vs. wage employees) and larger reactions in specific sources of income such as capital and business income.
Regarding the intepretation of the ETI, Feldstein (1999)  In an early critique of this literature, Slemrod (1992Slemrod ( , 1998 pointed out that the ETI is not a stable parameter (neither over time nor across countries), and stressed the idea that government policy can have an effect on the ETI. For example, wide availability of tax deductions and exemptions is likely to lead to a larger elasticity of taxable income, all else equal. Similar arguments are made by Kopczuk (2005), who also warns about focusing only on marginal tax rate changes, when most reforms simultaneously modify the definition of the tax base. Taking these insights together, the literature highlighted the need to provide estimates on both the anatomy and the heterogeneity of the response of taxpayers, keeping a definition of taxable income stable over the period under analysis.
Some recent work has challenged the "consensus" empirical strategies from Saez, Slemrod and Giertz (2012), proposing alternative estimation techniques. Weber (2014) shows that the Gruber-Saez instrument is endogenous because it is correlated with recent income shocks. She proposes using further lags of taxable income to construct the predicted net-of-tax rate instrument, as these lags are less correlated with current income shocks and provide more credible identification. Applying her method to the same dataset used by Gruber and Saez (2002), she estimates a larger elasticity in the range between 0.68 and 0.86. This elasticity is similar in order of magnitude to the baseline ETI estimate for Germany obtained following Weber's proposal in Doerrenberg, Peichl and Siegloch (2017) which is in the range of 0.54 to 0.68. In contrast, the estimate of the EBI (0.47) reported in Weber (2014) is larger than the EBI estimates obtained in Doerrenberg, Peichl and Siegloch (2017), with estimates between 0.16 and 0.28. Using time-series methods and a "narrative" approach to describe post-war tax reforms in the US, Mertens and Olea (2018) estimate a substantially larger ETI of around 1.2, with an even larger elasticity for high-income earners and a positive and significant elasticity elsewhere in the income distribution.
In another influential study, Kleven and Schultz (2014) apply a refinement of the Gruber-Saez estimation strategy, adding an instrument for virtual income to separately estimate income effects. They analyze a series of income tax reforms in Denmark, arguing that estimating the ETI using a longer period and the variation of multiple tax reforms is a more reliable empirical strategy to identify causal effects of taxes than the usual onereform analysis. Additionally, the authors stress the suitability of examining economies less affected by the ususual empirical challenges to identify the ETI such as Denmark where income distribution has been stable over time and tax changes affected different Electronic copy available at: https://ssrn.com/abstract=3422056 parts of the income distribution, reducing the potential bias from mean reversion. They estimate the ETI and EBI for overall income, and also separately for labor and capital income, finding consistently small values between 0.05 and 0.2.

Existing Estimates of the ETI for Spain
in contrast with the standard three-year interval used in the literature to avoid capturing income-shifting responses that bias estimates. Therefore, these estimates should be interpreted with caution. 1 Our paper departs from the earlier literature on the ETI in Spain by considering a much longer time period (1999-2014) over which multiple tax reforms took place, including both tax cuts and tax increases. This provides much richer identifying variation, allowing us to obtain more consistent estimates of the ETI. Besides the longer period of analysis, we adopt state-of-the-art methodological approaches to estimate the ETI, simultaneously dealing with the multiple threats to identification. In particular, we present estimates using the Gruber and Saez (2002) three-year difference estimator as a baseline, and compare them to the results obtained with the methods proposed by Kleven and Schultz (2014) and Weber (2014). In addition to this, we present evidence on 1 Other estimates of the ETI in Spain are available in working paper form or published as think tank reports (Badenes, 2001

The Spanish Personal Income Tax
During the period analyzed in this paper, 1999-2014, the Spanish personal income tax (PIT) has been structured in two separate tax bases: a "general" tax base comprising a broad definition of taxable income taxed with a progressive schedule, and a "special" tax base comprising specific income sources taxed with a flat-rate schedule. Until 2006, the special tax base included only some types of capital gains. In 2007, it was renamed the "savings" tax base and additional components of capital income were added, as explained in more detail in Section 3.2.
Taxable income in the general tax base is computed in several steps. The first step is to sum the gross income from each income source. 2 Second, the income-related expenditures (required to earn that income) are subtracted from each income source, resulting in the adjusted gross income (AGI). Third, income-specific deductions are subtracted from each AGI to obtain the taxable income for each source.
As an example, taxable labor income results from adding the gross income earned by workers (e.g., wages and salaries, bonus, in-kind payments) and subtracting incomerelated expenditures, such as payroll taxes for wage employees, and then substracting income-specific deductions (e.g., the general reduction for labor income). The process is the same for other income sources. 3 After computing taxable incomes from all sources and adding them up, a set of general deductions is subtracted to obtain the general taxable income, which is taxed with a progressive tax schedule. 4 The special (savings, since 2007) tax base is taxed at a preferential tax rate, targeted at particular components of capital income. 5 In the period 1999-2006, the preferential 3 Other relevant income-related expenditures are the reported inputs acquisitions for entrepreneurs or housing expenses for landlords. Each income source has its own set of deductions and implementation rules. For instance, deductions for irregular financial capital, the deduction for home rentals or the deductions desinged to promote entrepreneurial activity and employment.
4 Some examples of general deductions are those associated to personal and family circumstances (individual allowance, joint filing, number of children and dependents), the deduction for contributions to private pension plans and allowances related to past negative tax liabilities.  Electronic copy available at: https://ssrn.com/abstract=3422056 tax rate was applied only to long-term capital gains, while in 2007-2014 special taxable income included capital gains derived from the transmission of assets as well as the main component of financial capital income (i.e., income from interests and dividends).
Taxable income in this case results from subtracting the remnant of deductions not applied in the general tax base, as well as allowances for past capital losses.
The application of the progressive tax schedule to the general tax base and the flat rate to the special/savings tax base yields, respectively, the general and the special/savings tax liability. The aggregate tax liability from these two tax bases is further reduced by the application of several tax credits, resulting in the tax due. The most relevant tax credits in quantitative terms are the mortgage interest tax credit for primary dwellings, the tax credit for the birth or adoption of children, the e400 stimulus tax The legislative power to rule and reform the personal income tax law has traditionally been assigned to the Spanish parliament, which designs the structure and main features 6 Apart from these, there is a broad set of smaller (in revenue terms) tax credits for house renting, double taxation, business investment and charitable donations. A complementary discussion of the structure of the Spanish PIT and its main components can be found in García-Miralles, Guner and Ramos (2019).
of the tax (often following the initiative of the central government). However, since 1997 regional parliaments have progressively obtained legislative capacity (extended in 2002 and 2010) to introduce changes in the tax schedule for the general base, modifications in the personal and family deductions, and also the ability to introduce new tax credits. In spite of the regional dimension of the tax, the PIT is administered at the national level in a unique tax return by the Spanish Tax Agency. 7

Tax Reforms
The specific definition of the components that determine tax bases as well as the tax rates applied to taxable income have been subject to substantial modifications over time.
These changes are due to major reforms of the PIT but also to significant changes passed in the annual Budget Law and measures included in other bills. 8 The core reforms of the PIT that provide us with useful identifying variation were put into force in 2003,2007 and 2012 fiscal years (note that the fiscal year coincides with the calendar year). We also consider changes in the general tax schedule at the regional level. These regional changes were modest until 2010, when in the context of the European Sovereign Debt 7 For historical reasons, the autonomous communities of the Basque Country and Navarre (which account for six percent of Spain's population), have the power to design, collect and enforce their own PIT. For this reason, they are not included in this study.
8 See online Appendix A for references to the bills that introduced the major tax reforms in the Spanish personal income tax as well as a simplified description of other relevant legislative tax changes also considered in the empirical analysis.
Crisis regional parliaments became more active in creating new brackets with higher marginal tax rates for top-income earners (see discussion in Tax Reforms Appendix).
These two sets of changes in the PIT constitute the identifying variation that we use to estimate the elasticity of taxable income for the period 1999-2014.
The 2003 Reform reduced the top marginal tax rate from 48 to 45 percent (a 6.25percent cut) and the lowest marginal rate from 18 to 15 percent (a 20-percent cut).
The top panels of Figure 1 depict the changes in the marginal tax rate (MTR, left) and average tax rate (ATR, right) by levels of taxable income. The reform reduced the number of tax brackets (from six to five) and was particularly beneficial for taxpayers with taxable income between e40,460 and e45,000, as they experienced a 16.7 percent reduction in their marginal tax rate (from 45 to 37 percent). The tax rate on capital gains was also reduced from 18 to 15 percent. Besides the lower marginal tax rates, the The 2007 Reform was a significant overhaul that modified both the definition of taxable income in the two tax bases and the overall tax structure. The two most relevant changes were (i) moving most financial capital income from the general to the savings tax base, and (ii) converting the personal and family exemptions (with the exception of the deduction for joint filing) into a tax credit from the general tax liability, rather than a deduction from the tax base. Regarding (i), income from interest and dividends went from being taxed at 45 percent in the general base to being taxed at the 18 percent flat rate in the savings base (a 60-percent reduction in the MTR). This implied a dramatic reduction in the marginal tax rate for medium and high-income taxpayers with substantial financial income. Notice that this modification could also imply lower marginal rates for additional income obtained from other sources such as labor, real-estate or business income. The reform also expanded the definition of capital gains taxed under the savings tax base, including all gains from the transmission of assets regardless of the period over which the gain was generated. 10 Regarding (ii), the new way to calculate tax liability consisted of applied the progressive tax schedule to general taxable income and the personal and family exemption separately, and then subtracting the two resulting amounts. 10 Before this reform, capital gains derived from the transmission of assets whose generation period was inferior to one year (two years in 1999-2000) were included in the general tax base. From 2007 to 2012, only residual capital gains not associated to the transmission of assets, e.g., net changes in wealth, were included in the general tax base. In 2013, short-term capital gains (up to one year) derived from assets transmission were include again in the general tax base.
Notice that this change increased the progressivity of the tax schedule, because in the new system all taxpayers with the same personal and family characteristics obtain the same reduction in tax liability, while in the case of a deduction tax liability decreases in proportion to each taxpayer's marginal tax rate.
It the 2007 reform, the number of brackets in the progressive tax schedule for the general tax base was reduced from five to four. For example, a small bracket with a 15percent rate that applied to incomes up to e4,161.6 in 2006 was eliminated and replaced by a larger bracket for incomes up to e17,700 taxed at a 24-percent rate. The reform also expanded a tax bracket for middle income, reducing the marginal tax rate in the

Data
We use an administrative panel dataset of income tax returns compiled by the 11 Except for those from the Basque Country and Navarre, as explained in footnote 7.
The dataset contains more than 8.1 million tax returns (about 500,000 per year, on average), with a larger sample in the more recent years reflecting the increase in the total number of taxpayers. Each tax return is associated with a sampling weight that represents the inverse of the probability of being selected. Using these weights, the yearly aggregates of the main gross income and tax base and liability magnitudes are representative of the ones reported in the universe of the population (see Onrubia, Picos and Pérez, 2011, for more details).
The dataset contains detailed information on the main components of all income sources, income-related deductions of type of income, the rights and effective tax exemption of each deduction, the legal tax bases, disaggregated information on a broad range of tax credits and the overall tax liability. In terms of socio-demographic characteristics, we observe gender, date of birth, province and city of residence. Besides, the information in the tax return data allows us to infer the number of children and dependents that each taxpayer is responsible for. Table 1 in the online appendix reports the share of income due to each income source (left panel) and the share of income received by each category of taxpayer (right panel). About 80 percent of income reported in the Spanish PIT is labor income, 8.9 percent capital income, 8.3 percent business income and 3.9 percent capital gains. If we classify taxpayers into different categories based on their most important source of income, we observe that wage employees account for 82 percent of the tax returns analyzed. Self-employed taxpayers represent 7.8 percent of the sample, although it is worth noting that only two-thirds of these (5.2 percent of the total) are under the direct estimation regime. The rest of self-employed taxpayers are in the "objective estimation" or agricultural regimes, where the tax liability is determined based on observable features of each business, rather than actual income. For this reason, in the analyses performed below we will only consider the first group as self-employed. 12 The remaining 10 percent of taxpayers are almost equally split into the "saver" and "investor" categories, where the most relevant income sources are capital income or capital gains, respectively.
The marginal tax rate (MTR) is not directly observed in the tax return data. Thus, we use the available information on income and regional location, as well as the main tax base parameters, to calculate the MTR with a self-constructed tax calculator in the spirit of the NBER TAXSIM used in studies about the US. Building this tax calculator is critical for our empirical strategy, as it is needed to calculate the predicted net-of-tax In most of our regression analysis, we estimate the elasticity of taxable income with respect to the net-of-tax marginal rate. Therefore, we need a measure of the "overall" marginal tax rate faced by each taxpayer. To do this, we construct a weighted marginal tax rate on all taxable income, where the weights correspond to the relative importance of each income source in each tax return. 14 Let the share of income due to source j be denoted by s j it ≡ z j it /z it . 15 Then the overall marginal tax rate for taxpayer i in year t is given by:

Sample Selection and Homogeneous Definition of the Tax Base
We follow the existing literature to apply some sample restrictions to arrive at the estimation sample. First, we exclude taxpayers with negative taxable (or gross) income.
This is important because the main outcome variable is defined as the change in log taxable income, which would not be properly defined if income in one of the periods is negative. Since joint filing is only preferable for households in which the second earner has very low income, we consider the tax declaration the unit of analysis. Moreover, we 13 We describe the tax calculator in more detail in online Appendix B, and the full code is available from the authors upon request. Table A.1 reports the percentage of observations in which taxable income and tax liability calculated with our tax calculator is within two percent of the actual values recorded in the administrative panel dataset of tax returns. The accuracy rates are always above 97.5 percent, and in many years they reach 100 percent.
14 This approach was first implemented in the literature on the Spanish ETI by Onrubia and Sanz-Sanz (2009), and a similar method is also used by Kleven and Schultz (2014) for Denmark. 15 In less than two percent of observations, income is negative for at least one source (often business income). To ensure that the weights in the formula add up to one for these observations, we apply a normalization. We redefine the income shares for these observations as follows: drop year-pair observations where taxpayers change their filing status between the base year (t) and t + s. Further, we exclude pensioners, identified as taxpayers aged 65 and rate instrumental variable used to identify causal effects. 13 We calculate the marginal tax rate separately for each income source, following Kleven and Schultz (2014). We first calculate the tax liability for the observed taxable income, and then re-do the calculation adding e10 to that amount. Then, we divide by 10 the difference between the two tax liabilities, to obtain the marginal tax rate for each income source: above with positive labor income but zero social security contributions. The reason for excluding pensioners is because their main source of income is determined mechanically by public pension rules. Note that our main results are robust to including pensioners in our estimation sample.
Contrary to common practice in the literature (e.g., Gruber and Saez, 2002, and followers), we do not exclude observations below a certain threshold of gross income in the base-year. Instead, we carefully document and quantify the existence of mean reversion in each period. Then, in the regression analysis, we test different specifications of nonlinear controls for base-year income to find an econometric solution to this potential bias. In a robustness test, we check that our results are not affected by dropping taxpayers with broad income below e5,000 or e10,000 in the base year (see Section 5 for details). In

Summary Statistics
Electronic copy available at: https://ssrn.com/abstract=3422056 restrictions described above plus the fact that we take 3-year differences of the data in each period (which means we "lose" three years of observations), result in a baseline panel dataset with 4.02 million observations.
Real average gross income in 2012 euros is e36,200, and real average taxable income is e23,392, both with high dispersion and highly skewed to the right (i.e., the median is lower than the average in both cases). The average net-of-tax rate is 0.71, corresponding to a marginal tax rate of 29 percent. The average change in log real taxable income is −0.02, although there is substantial heterogeneity in this variable, which can take large values both positive and negative. The average change in the log net-of-tax rate is also close to zero (−0.01), with substantial variation on both sides of its distribution.
Finally, the average taxpayer is 46.6 years old, 42 percent of taxpayers are female and 17 of households file jointly (in the latter case, the dataset records the gender and age of the primary earner).

Estimation Strategy
We follow the previous literature and estimate a model in differences, using the predicted change in the net of tax rate as an instrument for the actual change. To address the identification challenges of mean reversion and heterogeneous income trends, we employ a variety of nonlinear controls for base-year income as well as modifications of the baseline instrument that have been poposed in the literature.
compared to a linear tax system with a tax rate equal to τ . Graphically, virtual income can be depicted by extending the part of the budget set where the taxpayer is located and finding its intersection with the vertical axis. Given this setup, we can write the optimal choice of taxable income as z = z(1 − τ, y).
Following Kleven and Schultz (2014), we write the following log-linear specification: Consider the taxable income model used in the literature, which is an extension of the traditional labor supply model. Taxpayers maximize a utility function u(c, z), where c is consumption and z is reported taxable income. This function is increasing in consumption and decreasing in taxable income, because generating income is costly. The budget constraint is given by c = z − T (z), where T (·) represents tax liability, which is the result of applying the tax schedule (a potentially nonlinear function) to a given taxable income.
Note that this budget constraint may also be written as is the marginal tax rate and y ≡ τ z − T (z) is virtual income. The latter can be thought of as the reduction in tax liability that results from the progressivity of the tax schedule,

Conceptual Framework
where μ i is an individual fixed effect that absorbs all time-invariant individual characteristics. We include two sets of controls: x c i includes time-invariant characteristics whose effect may change over time (e.g., gender or joint vs. individual filing) and x v i,t includes time-varying characteristics assumed to have a stable effect over time (e.g., age, region). The term ε can be interpreted as the elasticity of taxable income with respect to the net-of-tax-rate, while η is the elasticity with respect to virtual income. Notice that, in this formulation, ε is the uncompensated elasticity, because the inclusion of virtual income implies a linearization of the budget set around the optimal income choice. 16 As is standard in the literature, we estimate a model in differences: After taking differences, the individual fixed effect μ i drops out of the model. Notice that in this specification, each observation consists of two tax returns from different years.
With this notation, the base year in each observation is denoted as year t.

Identification Strategy
Estimating equation (2)   In practice, we calculate this predicted net-of-tax rate, τ p using the following expression: Electronic copy available at: https://ssrn.com/abstract=3422056 Then, the instrument is defined as the (log) change between the marginal tax rate faced in t and the tax rate they would have faced in year t + s keeping their real income from year t. The first-stage relationship can be written as follows: (3) The literature has extensively discussed two challenges to the empirical identification of the ETI: mean reversion and heterogeneous income trends unrelated to tax changes Notice that, with a progressive tax schedule, virtual income is by definition non-negative.
To construct the instrument for the change in log virtual income, we use the predicted marginal tax rate that we calculated to construct the net-of-tax rate instrument. Then, the instrument is given by: 17 tax liability. That is: As we show below, this instrument yields a very strong first-stage relationship. Therefore, we can safely conclude that the instrument is relevant. However, it is not guaranteed that the exclusion restriction holds if base-year income is a good predictor of future income change, potentially making the instrument invalid. For example, the influential paper by Weber (2014) argues that the instrument may violate the exclusion restriction when taxable income features substantial serial correlation because shocks to z t are correlated with shocks to z t+s . We explore the implications of this issue in the following subsection.
In the regressions following the estimation method of Kleven and Schultz (2014) where the subscript in T t+s indicates that we calculate the tax liability using the tax schedule of period t + s. We can then easily construct the instrument for the change in the log net-of-tax rate as follows:

Mean Reversion and Heterogeneous Income Trends
Electronic copy available at: https://ssrn.com/abstract=3422056 (Saez, Slemrod and Giertz, 2012). We discuss them in detail here, and describe some potential solutions that have been proposed.

Mean reversion arises because taxpayers with a positive (negative) income shock in
year t tend to have, on average, lower (higher) income in year t + s (s = 1, 2, 3...) as they return to their permanent income. In our specific context, Figure

Results
We first present our main estimates of the elasticity of taxable income for the period 1999-2014, using the longest panel dataset available in a consistent format. We present results for the three alternative estimation methods described in the previous section:

Main Elasticity Estimates
The first three columns in Table 3  The estimated elasticity of taxable income is 0.356. Column 6, includes a five-piece Electronic copy available at: https://ssrn.com/abstract=3422056 linear spline of log taxable-income, yielding a point estimate of 0.343. All estimates are highly statistically significant, thanks to the large sample size of more than four million observations. One caveat to the interpretation of these results is that the p-value for the diff-in-Sargan test statistic, used to determine whether the instrument is exogenous, is close to zero in all three specifications. This implies rejecting the null hypothesis of exogenous instruments, in line with the results from Weber (2014). Therefore, the ETI estimates in columns 4-6 should be interpreted with caution. Table 4 reports ETI estimates for the same period (1999-2014) using the two alter-

Anatomy of the Response
In this subsection, we explore the anatomy of the aggregate taxable income responses documented above. Table 5 reports estimates of the ETI for employees (columns 1-4) vs.
Electronic copy available at: https://ssrn.com/abstract=3422056 self-employed taxpayers (columns 5-8). In each case, we present two specifications using the Gruber-Saez method (with cubic and log splines), one using Kleven-Schultz's method (with cubic splines) and one using Weber's method (with lagged cubic splines). The ETI estimate for employees is between 0.23 and 0.47. In contrast, the ETI for self-employed taxpayers is 0.65 with the Gruber-Saez method, 0.93 with Kleven-Schultz's and above In Table 6, we focus on the elasticity of different types of income to the same tax We then turn to studying whether taxpayers' responses are due to real labor supply changes, tax avoidance or tax evasion. To do this, Table 7 reports estimates of the elasticity of broad income (EBI), defined as the sum of all income sources subtracting only income-related deductions (e.g., social security contributions paid by employees). 19 The EBI provides a measure of the real (e.g., labor supply) and evasion (e.g., income underreporting) responses to taxation, whereas the ETI also accounts for avoidance reponses (e.g., taking advantage of more tax deductions). As in previous tables, we report results for three different estimation methods: Gruber-Saez (columns 1-2), Kleven-Schultz (columns 3-4) and Weber (columns 5-6). The estimates of the EBI are between 0.10 and 0.24 in all specifications, suggesting that real and evasion responses account for about one-third of the total taxable income response to taxation. However, the relevance of reporting responses is heterogeneous across types of taxpayers. Indeed, Table 8 further explores whether wage employees and self-employed taxpayers have a different EBI.
Indeed, wage employees have a very low EBI (below 0.10 across all specifications), while self-employed have an EBI around 1. These results confirm the intuition that reported income of the self-employed is much more responsive to taxation either through a real We conduct a number of additional empirical exercises to check the robustness of our results. In Table 10, we report estimates of the ETI restricting the sample to taxpayers with base-year broad income above e5,000 (Panel A) and e10,000 (Panel B), respectively. This is an often-used restriction in the literature, where it is justified as a way to deal with intense mean reversion at the bottom of the income distribution (Gruber and Saez, 2002). Comparing the results in Table 10 to those in columns 5-6 in Table 3 and columns 1-2 and 5-6 in Table 4, we find that the ETI estimates are very similar. These or an evasion response.
In Table 9, we shift the focus to examine the responses of reported tax deductions to changes in marginal tax rates. We follow the approach of Doerrenberg, Peichl and Siegloch (2017) and use the same identification strategy as in previous tables, but with the log change in tax deductions as the dependent variable. In these specifications, we expect to find negative point estimates because the outcome variable is the log change in deductions, which are subtracted from taxable income: if the net-of-tax rate decreases (tax increase), taxpayers will tend to claim higher deductions to lower their tax liability. Panel A of Table 9

Robustness Checks
Electronic copy available at: https://ssrn.com/abstract=3422056 results are reassuring because they indicate that, despite the massive mean reversion at the bottom of the distribution documented in Figure 2, the inclusion of non-linear controls for base-year income (cubic and log splines) is enough to make the estimates stable for all three estimation methods.
In Table 11, we present results using two-year and one-year differences to assess how our main estimates change under different time horizons. Up until this point, we have followed the ETI literature's convention of analyzing three-year differences. The rationale for this is to avoid capturing mostly anticipation responses (in the form of re-timing of reported income or deductions across years) instead of the medium-term response to tax changes. The top panel of Table 11 shows the results with two-year differences and the bottom panel with one-year differences. The results for the Gruber-Saez method (columns 1-2) and Weber's method (columns 5-6) are similar to the baseline estimates from Tables 3 and 4. In contrast, the estimates using the Kleven-Schultz method are lower, between 0.14 and 0.17, although still statistically different from zero.
In the online Appendix, we report additional robustness checks, showing: estimates of the Gruber-Saez and Kleven-Schultz methods with lagged base-year income splines (Table A.2), ETI estimates from a balanced panel of taxpayers present in the sample for all years between 1999 and 2014 (Table A.3), ETI estimates including pensioners (Table A.4) and, finally, ETI estimates excluding taxpayers who moved across regions within Spain during the period under analysis (Table A.5). In all four cases, we report the results for the three estimation methods with cubic and log splines (lagged in the Weber specifications). We generally obtain ETI estimates very similar to those obtained in Tables 3 and 4, providing further support to the robustness of our results.
As a final exercise we examine the distribution of taxable income around kinkpoints of the income tax schedule to obtain alternative estimates of the ETI using bunching methods (Saez, 2010). We find very almost no bunching evidence in any period, consistent with an existing working paper by Esteller-Moré and Foremny (2016). All the histograms with the distribution of taxable income around kinks are shown in online Appendix Figures A.1 and A.2. Note that the lack of bunching evidence does not necessarily imply that our panel-based estimates are biased, as there are well-known reasons for the bunching estimator to be biased towards zero, such as optimization frictions, inattention and career concerns (for a detailed discussion, see Kleven, 2016).

Discussion of Results
We conclude from these results that Spanish taxpayers' response to tax changes are moderate, with significant heterogeneity in the response across groups of taxpayers and types of income. Given the well-known limitations of the Gruber-Saez estimator (potential endogeneity, weak controls for heterogeneous income trends and exclusion of Electronic copy available at: https://ssrn.com/abstract=3422056 income effects), and the results of the diff-in-Sargan test of instrument exogeneity, we consider that the most reliable estimates are those obtained using the Kleven-Schultz and, especially, Weber methods. In Table 4, we obtain point estimates between 0.52-0.54 (Kleven-Schultz method) and 0.62-0.64 (Weber method). In the robustness tests of Tables 10 and A.2-A.5 the ETI estimates using these two methods (with cubic or log splines) are all between 0.45 and 0.64. Therefore, we conclude that the most reliable Regarding the anatomy of the response, we highlight two important results. First, the larger ETI estimates for self-employed taxpayers and business income confirms the intuition that responses to taxation depend both on tax enforcement intensity and the availability of reaction margins (e.g., fixed-hours contracts vs. independent work). Second, the high elasticity of tax deductions indicates the relevance of avoidance responses to taxation. They also contribute to rationalizing the small estimated EBI compared to the higher ETI estimates. Nevertheless, the significant EBI estimates for self-employed taxpayers suggests that reporting responses (possibly due to real and evasion responses) are relevant for that group.

Concluding Remarks
In this paper, we have estimated the elasticity of taxable income (ETI) using a panel of However, we document significant heterogeneity in the response to tax changes across groups of taxpayers and for different sources of income. In particular, estimates of the ETI for self-employed taxpayers are on average three times larger than the estimates for wage employees. Consistent with that, business and real-estate capital income exhibit Electronic copy available at: https://ssrn.com/abstract=3422056 stronger responses to taxation than labor income, which is subject to both stricter tax enforcement and market rigidities. In terms of the anatomy of the response, we find smaller elasticities of the broad income, in the range between 0.10 and 0.24, although they are quantitatively relevant, particularly for self-employed taxpayers. The differences in magnitude between the estimated ETI and EBI indicates the relevance of tax deductions in taxpayers' responses. Indeed, we document an elasticity exceeding one for some tax deductions, such as the one for private pension plan contributions.
As stressed by the long-standing literature on the ETI, this elasticity is not a structural parameter and its identification is subject to multiple econometric challenges, which often result in unstable estimates. Considering these limitations, this paper presents a broad set of sensitivity analyses in order to test the robustness of our estimates. Adapting recent methodological approaches, we show that our estimates are robust to potential biases created by mean reversion and heterogeneous income trends across groups of taxpayers unrelated to tax reforms.
Electronic copy available at: https://ssrn.com/abstract=3422056 García-Miralles, Esteban, Nezih Guner, and Roberto Ramos.       Notes: each dot in these figures represents the average of the vertical axis variable over bins of the horizontal axis variable, where the each bin contains a similar number of observations. Panel (a) represents the OLS relationship between the outcome variable of interest Δ ln(z) and the endogenous covariate Δ ln(1 − τ ). Panel (b) represents the first-stage relationship between the endogenous covariate Δ ln(1 − τ ) and the predicted tax rate instrument Δ ln(1 − τ p ). Panel (c) represents the reduced-form relationship between the outcome variable Δ ln(z) and the instrument Δ ln(1 − τ p ), where the latter has been computed using one, two and three lags of taxable income. The regression lines depicted are estimated using the same number of observations as in the regressions in columns 1-3 of Table 3, without including any controls or fixed effects.
Notes: this table reports the share of broad income due to each income source (left panel) and the share of income received by each category of taxpayer (right panel). The definition of the categories is given in Section 3.3. All results based on data for the period 1999-2014 from the administrative panel dataset of income tax returns provided by the Instituto de Estudios Fiscales (Pérez, Villanueva and Molinero, 2018) and applying the sampling weights contained in the dataset. Notes: this table reports summary statistics for observations included in the panel dataset covering the period 1999-2014, used in the main regression analysis, e.g. Table 3. Monetary values are reported in real 2012 euros. Averages are calculated taking into account the sampling weights assigned to each observation. The total number of observations reported is unweighted. See discussion in sections 3.3 and 5 for details on the sample restrictions imposed by both data analysis and the methodological approach.

Tables
using the predicted tax rate instrument standard in the ETI literature, as in Gruber and Saez (2002). The F-statistic corresponds to testing the null hypothesis that the coefficient on the instrument is equal to zero. Column 3 reports the reduced-form estimator, i.e. Δ ln(z it ) = θΔ ln 1 − τ p + w i,t . Columns 4 through 6 report the secondstage of the 2SLS estimator using three-year differences, again following the standard specification in the literature. Column 4 does not include any controls for base-year income. Column 5 includes a five-piece cubic spline of log base-year income. Column 6 includes a five-piece spline of log base-year income. Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children, ascendants and the type of taxpayer according to her main source of income (employee, self-employed, saver or taxpayers with other main source of income such as capital gains). Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%.  (2014), which uses the same instrument as Gruber and Saez (2002), but also includes the change in log virtual income, Δ ln(v), to capture income effects. Column 1 includes a cubic spline of log base-year income, whereas column 2 includes a spline of log base-year income. Columns 3-6 report the results of applying the estimation method proposed by Weber (2014), where the instrument is based on further lags of taxable income. Columns 3 and 4 include a cubic and log spline of base-year income, respectively, while columns 5 and 6 include lagged versions of those splines. Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children, ascendants and the type of taxpayer according to her main source of income (employee, self-employed, saver or taxpayers with other main source of income such as capital gains). Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. Notes: this table reports elasticity estimates for two groups of taxpayers: employees (columns 1-4) and self-employed workers (columns 5-8), defined based on the main source of income, as explained in Section 3.3. All regressions include data for the period 1999-2014. Columns 1 and 2 report the ETI estimates for employees using the Gruber and Saez (2002) method, with cubic and log splines of base-year income. Column 3 reports the estimates using the method from Kleven and Schultz (2014) with a cubic spline, and column 4 reports the estimates using the method from Weber (2014), with a lagged cubic spline. Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children and ascendants. Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. , real estate capital income (Panel C) and business income (Panel D), as explained in Section 3.3. All regressions include data for the period 1999-2014. Columns 1 and 2 report the ETI estimates for employees using the Gruber and Saez (2002) method, with cubic and log splines of base-year income. Column 3 reports the estimates using the method from Kleven and Schultz (2014) with a cubic spline, and column 4 reports the estimates using the method from Weber (2014), with a lagged cubic spline. Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children and ascendants. Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. Notes: this table reports the elasticity of broad income (EBI), defined as the sum of income from all sources, without subtracting deductions but excluding capital gains for the reasons stated in Section 3.3. All regressions include data for the period 1999-2014. Columns 1-2 report the estimates of the EBI applying the Gruber-Saez estimation method under two alternatives: lagged cubic splines (column 1) and lagged log splines (column 2). Columns 3-4 report the estimates of the EBI using the method from Kleven and Schultz (2014) under two alternatives: lagged cubic splines (column 3) and lagged log splines (column 4). Columns 5-6 report the estimates of the EBI using the method from Weber (2014) under two alternatives: lagged cubic splines (column 5) and lagged log splines (column 6). Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children, ascendants and the type of taxpayer according to her main source of income (employee, self-employed, saver or taxpayers with other main source of income such as capital gains). Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. , defined based on the main source of income, as explained in Section 3.3. All regressions include data for the period 1999-2014. In each Panel, columns 1-2 report the estimates of the EBI applying the Gruber-Saez estimation method under two alternatives: lagged cubic splines (column 1) and lagged log splines (column 2). Columns 3-4 report the estimates of the EBI using the method from Kleven and Schultz (2014) under two alternatives: lagged cubic splines (column 3) and lagged log splines (column 4). Columns 5-6 report the estimates of the ETI using the method from Weber (2014) under two alternatives: lagged cubic splines (column 5) and lagged log splines (column 6). Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children and ascendants. Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. In each panel, we report the elasticity of deductions under different estimation models: Gruber-Saez in columns 1-3, Kleven-Schultz in columns 4-5 and Weber in columns 6-7. Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children and ascendants. Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. Notes: this table reports the elasticity of taxable income for the period 1999-2014 using alternative sample restrictions to exclude taxpayers with base-year taxable income below a certain threshold: e5,000 in the top panel and e10,000 in the bottom panel. The ETI estimates can be compared to those in tables 3 and 4, where the base-year income restriction is zero (i.e., only include taxpayers with positive taxable income). The specifications follow the same sequence as table 11 above: Gruber-Saez method in columns 1-3, Kleven-Schultz method in columns 4-5 and Weber method in columns 6-7. Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children and ascendants. Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. These estimates can be compared to the main estimates from tables 3 and 4 that use three-year differences. The specifications follow the same sequence as Table 10 above: Gruber-Saez method in columns 1-3, Kleven-Schultz method in columns 4-5 and Weber method in columns 6-7. Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children and ascendants. Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. The flat tax rate applied to the savings tax rate was modified along the Great Recession in order to increase both its average effective taxation and its progressivity. In A.2.1 Regional Tax Schedules

A.2 Other Tax Reforms
Regional governments started to slightly modify the marginal tax rates in 2007 (the first to do so was the Madrid Region) with very modest reductions across the full tax schedule. pp higher than the pre-reform tax rate). 21 Besides of changes in the tax rate structure, regional governments introduced since the 1990s several tax credits that either complement the ones included in the central level (e.g., investment in habitual housing) or create new ones (e.g., education and kindergarten expenditures). The total amount of these tax credits have progressively increased over time but it is still quantitatively tiny reaching an estimated impact of 0.03 percent of GDP in 2014 (Dirección General de Tributos, 2019). Finally, since 2010 several regional governments (Madrid, Cantabria and Castilla-La Mancha) have introduced enhancements in the tax credits associated to personal and family circumstances. 21 Other regional governments also created additional tax brackets with higher marginal rates as Andalusia (top rate of 56 percent), Asturias (top rate of 55.5 percent) or Extremadura and Cantabria (top rates of 55 percent). 22 We omit other income sources, called imputations and attributions, from the formulas below for simplicity, as they are distributed across the two tax bases but they represent small amounts for most taxpayers. However, we do incorporate them in the tax calculator to compute taxable income and tax liability. Tax liability is calculated in two steps. In the first step, the income tax schedule of each tax base is applied to the taxable incomes defined above. Whenever tax liability is negative, the losses are carried out to the following year as tax credits (which can reform introduced more progressivity in the tax schedule. In the second step to calculate tax liability, we subtract all tax credits, denoted by Notes: these figures show the taxable income distribution (in nominal euros) around several kinks at low and middle income levels created by the Spanish personal income tax schedule over the period 2000-2014. A kink is defined as the taxable income threshold where taxpayers face a change in their marginal tax rate. The distributions pool yearly data for different periods of time when the tax schedule is identical across these fiscal years. To compute the share of taxpayers in each bin of taxable income, we elevate each observation included in the sample using the sampling weight reported in the data. The bins of taxable income are e200 wide. The graphs show that there is no significant bunching at any of the kinks in the taxable income distribution over the period 2000-2014.   Notes: these figures show the taxable income distribution (in nominal euros) around several kinks at middle and high income levels created by the Spanish personal income tax schedule over the period 2000-2014. A kink is defined as the taxable income threshold where taxpayers face a change in their marginal tax rate. The distributions pool yearly data for different periods of time when the tax schedule is identical across these fiscal years. To compute the share of taxpayers in each bin of taxable income, we elevate each observation included in the sample using the sampling weight reported in the data. The bins of taxable income are e200 wide, except for panel (e) where the bin width is e500 and panel (f) where it is e1,000. The graphs show that there is no significant bunching at any of the kinks in the taxable income distribution over the period 2000-2014.
Appendix Tables   Table A.1: Tax Calculator Accuracy Rates   General Tax Base  Special or Savings Tax Base Year Taxable Income Tax Liability  Taxable Income Tax Liability Notes: this table reports the elasticity of taxable income (ETI) for the period 1999-2014 including lagged splines in order to capture potential heterogeneous trends in income across groups of taxpayers during the sample period. Columns 1-2 report the estimates of the ETI applying the Gruber-Saez estimation method under two alternatives: lagged cubic splines (column 1) and lagged log splines (column 2). Columns 3-4 report the estimates of the ETI using the method from Kleven and Schultz (2014) under two alternatives: lagged cubic splines (column 3) and lagged log splines (column 4). Columns 5-6 report the estimates of the ETI using the method from Weber (2014) under two alternatives: lagged cubic splines (column 5) and lagged log splines (column 6). Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children, ascendants and the type of taxpayer according to her main source of income (employee, self-employed, saver or taxpayers with other main source of income such as capital gains). Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%.   Notes: this table reports the elasticity of taxable income (ETI) for the period 1999-2014 using the balanced panel of taxpayers included in the sample. Columns 1-2 report the estimates of the ETI applying the Gruber-Saez estimation method under two alternatives: cubic splines (column 1) and log splines (column 2). Columns 3-4 report the estimates of the ETI using the method from Kleven and Schultz (2014) under two alternatives: cubic splines (column 3) and log splines (column 4). Columns 5-6 report the estimates of the ETI using the method from Weber (2014) under two alternatives: lagged cubic splines (column 5) and lagged log splines (column 6). Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children, ascendants and the type of taxpayer according to her main source of income (employee, self-employed, saver or taxpayers with other main source of income such as capital gains). Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%.
Notes: this table reports the elasticity of taxable income (ETI) for the period 1999-2014 considering pensioner taxpayers included in the sample. Columns 1-2 report the estimates of the ETI applying the Gruber-Saez estimation method under two alternatives: cubic splines (column 1) and log splines (column 2). Columns 3-4 report the estimates of the ETI using the method from Kleven and Schultz (2014) under two alternatives: cubic splines (column 3) and log splines (column 4). Columns 5-6 report the estimates of the ETI using the method from Weber (2014) under two alternatives: lagged cubic splines (column 5) and lagged log splines (column 6). Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children, ascendants and the type of taxpayer according to her main source of income (employee, self-employed, saver or taxpayers with other main source of income such as capital gains). Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%. Notes: this table reports the elasticity of taxable income (ETI) for the period 1999-2014 excluding taxpayers that changed their regional fiscal residence in any year included in the sample period. Columns 1-2 report the estimates of the ETI applying the Gruber-Saez estimation method under two alternatives: cubic splines (column 1) and log splines (column 2). Columns 3-4 report the estimates of the ETI using the method from Kleven and Schultz (2014) under two alternatives: cubic splines (column 3) and log splines (column 4). Columns 5-6 report the estimates of the ETI using the method from Weber (2014) under two alternatives: lagged cubic splines (column 5) and lagged log splines (column 6). Standard errors clustered by taxpayer are reported in parentheses. All specifications include regional and year fixed-effects as well as controls for age, age squared, gender and indicators for joint filing, children, ascendants and the type of taxpayer according to her main source of income (employee, self-employed, saver or taxpayers with other main source of income such as capital gains). Observations in all regressions are weighted by log base-year taxable income. Significance levels: *** = 1%, ** = 5%, and * = 10%.