Public Sector Economics

Transcription

1 Public Sector Economics Munich, April Relocation of the Rich: Migration in Response to Top Tax Rate Changes from Spanish Reforms David R. Agrawal and Dirk Foremny

2 Relocation of the Rich: Migration in Response to Top Tax Rate Changes from Spanish Reforms David R. Agrawal University of Kentucky Dirk Foremny IEB and Universitat de Barcelona April 2017 Abstract A recent Spanish tax reform granted regions the authority to set income tax rates, resulting in substantial tax differentials. We use individual-level information from Social Security records over a period of one decade. Conditional on moving, taxes have a significant effect on the location choice. A one percent increase in the net of tax rate for a region relative to others increases the probability of moving to that region by 1.4 percentage points. Focusing on the stock of top-taxpayers, we estimate a mobility elasticity of Our model implies that the increase in tax revenue due to higher tax rates is larger than the loss in tax revenue from the out-flow of migration. Keywords: Migration, Taxes, Mobility, Rich, Decentralization JEL classification: H24, H31, H73, J61, R23 The foundations for this project were laid while David Agrawal was a guest researcher at the Universitat de Barcelona. He wishes to thank Universitat de Barcelona along with the people associated with this institution for their hospitality and support. The paper benefited from comments by José Maria Durán, Alejandro Esteller-Moré, Gabrielle Fack, William Hoyt, Jordi Jofre-Montseny, Camille Landais, Andrea Lassmann, Thomas Piketty, Kurt Schmidheiny, Albert Solé-Ollé, Juan Carlos Suárez Serrato, Johannes Voget, Daniel Waldenström, and David Wildasin as well as seminar participants at Centre for European Economic Research (ZEW), ETH Zurich, the Paris School of Economics, the Pontifícia Universidade Católica do Rio de Janeiro, Purdue University, the Universitat de Barcelona, the University of Kentucky, the University of Louisville, the University of Michigan, the MaTax Conference in Mannheim, Germany the PET 2016 Conference in Rio de Janeiro, and Universität Siegen. Dirk Foremny acknowledges financial support from projects ECO and ECO (Ministerio de Economía y Competitividad) and 2014SGR-420 (Generalitat de Catalunya). Any remaining errors are our own. University of Kentucky, Department of Economics and Martin School of Public Policy & Administration, 433 Patterson Office Tower, Lexington, KY ; dragrawal@uky.edu; phone: Agrawal is also an affiliate member of CESifo. Department of Public Economy, Political Economy and Spanish Economy, Universitat de Barcelona, Facultat d Economia i Empresa - Av. Diagonal, 690 (08034 Barcelona) Spain; foremny@ub.edu; phone

3 High-income taxpayers may be literally worth their weight in gold to the government where they reside. 1 As a means of tax avoidance, individuals may move in response to tax differentials resulting from residence based local income taxes. Tax avoidance typically arises when taxable income can be shifted in a way that it becomes subject to a favorable tax treatment (Piketty and Saez 2013), and mobile tax payers might simply relocate their tax residence and shift their taxable income abroad to reduce their income tax burden (Wilson 2009). As a result of tax induced mobility by high-income tax payers, governments may be unable to engage in redistribution (Epple and Romer 1991) and tax competition may intensify (Wildasin 2006). Despite the policy importance of analyzing taxation in an open economy setting, most studies have analyzed responses to taxation such as adjustment of taxable income (Saez, Slemrod and Giertz 2012) although a recent literature on tax-induced mobility has emerged following Bakija and Slemrod (2004). We provide evidence on migration using quasi-experimental evidence resulting from a Spanish tax reform. In the early 2000s, all regions in Spain had the same top marginal tax rate. In 2011, Spanish regions began changing their top marginal tax rates in response to a federal reform that gave the Autonomous Communities (regions or states) authority to adjust rates and the corresponding tax brackets. In 2014, top marginal tax rates diverged across regions by as much as 4.5 percentage points. For an individual in the top one percent of the distribution, this differential amounts to substantial differences in taxes 7500 Euro for the average person in the top 1% and much higher for those at the very top. These disparities led the popular press to dub low-tax regions as tax havens or one of several paradises on Earth. This quasi-experimental setting is unique. Research in this area requires linked data of individuals in the country of origin and destination, which is fairly complicated to obtain. 2 Exploiting sub-national variation is therefore an appealing alternative. However, personal income in most countries is taxed at the federal level and only a few countries tax personal income at the regional or local level (i.e., United States, Canadian provinces, Swedish municipalities, Italian regions and municipalities, Swiss cantons and localities). Given the expected mobility and avoidance responses, some of these countries only allow for small differentials across jurisdictions by limiting the tax-setting power of state and local governments. In countries with more substantial autonomy, regional personal income 1 The quoted phrase comes from Wildasin (2009), who writes: at current prices ($900/oz.), an average adult male s weight-equivalent (190 lbs.) of gold is worth around $2.7 million. Under conservative assumptions about life expectancy and discount rate, the present value of taxes paid by very high income taxpayers can easily exceed this amount. 2 Kleven, Landais and Saez (2013) and Akcigit, Baslandze and Stantcheva (2016) are notable exceptions. They focus on selected sub-groups of the population for which the authors have been able to assemble the information needed without access to individual income data linked across countries. Moretti and Wilson (2015) and Young et al. (2016) are also noteworthy state level examples, but as discussed below state level income taxation is not always residence based in the United States. 1

4 taxes have been implemented decades ago and large administrative data are not available for time periods before their implementation. Further, in the U.S., income taxes are often employment-based rather than residence-based (Agrawal and Hoyt 2014), which means that for local moves, individuals may change jobs rather than residence. 3 The reform in Spain granted substantial autonomy to the regions on a purely residence-based tax system. The tax administration, however, remains with the national authorities which facilitates access to good quality individual micro-data that is available before and after the decentralization of the tax. We use individual Social Security data for a random sample of the full population from 2005 to 2014 to study the migration decisions of the rich in response to this Spanish tax reform. Our paper is novel in several respects. First, we focus on all high income individuals rather than a select group of highly mobile individuals such as star scientists (Moretti and Wilson 2015; Akcigit, Baslandze and Stantcheva 2016), athletes (Kleven, Landais and Saez 2013), or foreigners subject to preferential taxation (Kleven et al. 2014; Schmidheiny and Slotwinski 2015). Detailed information on industry and occupation allows us to determine the external validity of this prior literature. Second, we study migration using a random sample of population level data for a complete panel of all regions in a country; single state analyses includes Young and Varner (2011) and population level U.S. studies include Young et al. (2016). 4 Third, we provide evidence on mobility in response to taxes in a country where mobility even among the rich is traditionally regarded as relatively low. 5 In particular, we find relatively large effects of taxes on location choices, but small stock responses. Finally, we develop a theoretical model of revenues to interpret these elasticities and to determine the revenue maximizing top tax rate on incomes with mobility. Discussion of taxing top incomes comes within the context of widening income inequality in many countries. Studying mobility in Spain is especially important given the implications for redistributive tax policy. Bonhomme and Hospido (fc) document that earnings inequality in Spain declined from about 1995 to 2007, but that it has risen dramatically since 2007 and is back to its 1995 level. Given these dramatic increases in earnings inequality, mobility in response to more progressive tax policy could threaten 3 In the United States, 5.3 million individual have an interstate commute. Approximately 75 million people live in metropolitan areas that cross state borders. Of these, approximately two-thirds live in MSAs that have an employment-based component to state and local income taxes. 4 Conway and Rork (2012) and Conway and Rork (2006) find no effect of state taxes on elderly migration. Brülhart and Parchet (2014) show that high-income retirees are relatively inelastic in response to estate taxes, but Eugster and Parchet (2011) provide evidence consistent with top-income taxpayers moving from high-tax to low-tax municipalities for local Swiss income taxes; Martínez (2016) finds estimates consistent with ours for Obwalden. We help reconcile these various estimates in our tax revenue model. 5 For this reason, our setting more closely resembles international migration, where mobility is still lower compared to internal migration in many other countries. 2

5 the ability to engage in redistribution given that the optimal degree of redistribution will decline as the mobility elasticity increases (Mirrlees 1982). One discussed policy response to widening inequality is changing top income tax rates. The paper proceeds as follows: we use administrative data to study tax-induced mobility. The individual Social Security return data contains information on each taxpayer s income that is not top coded. These data also contain information on the taxpayers declared location of residence in addition to certain characteristics reported to the Social Security administration. We merge these data to region level tax rates that we have assembled. We write our own tax calculator (similar to TAXSIM) that simulates average tax rates dating back to 2005 using regional tax codes; these average tax rates have some measurement error because our tax calculator misses some allowances. To address measurement error, we present results using marginal tax rates on top income as an instrument, which also has the advantage of generally being exogenous to the level of earnings (Kleven, Landais and Saez 2013). We first conduct an aggregated region pair level analysis. We calculate for each year in our data, the stock of top-taxpayers for every region pair combination in Spain and construct the log ratio of the stocks across regions; in addition, we calculate the net of tax rate differential between each of the region pairs. We then show that higher individual income taxes reduce the stock of top-taxpayers after accounting for destination fixed effects, origin fixed effects, and year fixed effects. The migration (stock) elasticity is approximately 0.25, which is generally smaller than estimates in the prior literature. Pre-reform migration stocks show no correlation with post-reform tax differentials. 6 Then, we turn to an individual level analysis that studies whether individuals are more likely to select low-tax regions, conditional on moving. Our empirical model allows us to account for region by year fixed effects and individual fixed effects across the alternatives so that all of our results are identified from within individual variation in tax rates. This approach has the advantage of allowing us to account for fixed characteristics of the taxpayer/mover that are constant across alternative regions in a given year as well as for other policy changes that affect all individuals in the top of the income distribution. A one percent increase in the net of tax rate for a region relative to others increases the probability of moving to that region by 1.43 percentage points. Although many things may matter for decisions on where to move, taxes appear to be important. These estimates suggest that the 4.1 percentage point top tax rate differential between Madrid and Cataluña in 2013 increases the probability of moving to Madrid by 5.1 percentage points. The effect of Madrid s 2014 tax cut of 0.4 percentage points further increases the probability of moving to Madrid by another 0.5 percentage points. This increase is 6 Such a stark placebo test is not often possible in other studies of migration. 3

6 relative to the baseline probability of a mover moving to Madrid in the pre-reform era, which was 30%. This analysis is motivated by Figure 1, which shows no correlation in the pre-reform period, but a strong correlation in the post-reform period between location choice and net of tax rates. In this analysis, we exploit novel data on occupation and industry to show that taxes play a stronger role for certain occupations and industries; these standardized data are not available in U.S. tax return data. This occupation and industry data allows us to verify the external validity of the prior literature that has focused on star scientists and athletes. Testing for heterogeneity across occupation and industry also helps to inform the recent policy debate on the efficiency of tax schemes for top earners in specific occupations. First, we replicate the result in the prior literature for scientists and find that those in the health industry have large migration effects; entertainers including athletes have large (but insignificant likely due to sample sizes) effects as well. Then we look at other occupations and industries to determine the external validity of the prior literature. Our results indicate that self-employed and higher-level occupations are more sensitive to taxes than lower-level occupations. Industry-level data demonstrates substantial heterogeneity with the largest effects emerging in the finance and real estate industry and the health industry. In so much as some of the individuals in the health sector may be star scientists, the results of this exercise suggest that the prior literature that has focused on particular industries may not generalize. Our analysis comes with one caveat: our data do not allow us to disentangle a real move from a fraudulent move where the taxpayer changes residence to a second home without actually changing where they spend the majority of the tax year. In so much as this is possible, the presence of such evasion implies that mobility includes both real responses as well as tax evasion responses. From a tax revenue perspective, it does not matter if the move is a real response or simple misreporting; from a labor supply perspective, real moves may be more important. We show results, to the best of our ability, that shed light on if the move is a real response or simply tax evasion by estimating the effect separately for groups which are more or less mobile (family and professional situation) and therefore respond by a real move. The prior literature does not always place the magnitudes of these elasticities into a formal model of tax revenues. As noted in Saez, Slemrod and Giertz (2012), absent both classic and fiscal externalities, the elasticity of taxable income suggests that the revenue maximizing tax rate on top incomes may be as high as 80% with a broad income tax base. However, changes resulting from mobility across regions are not generally captured in these estimates and therefore understanding mobility has important implications for understanding the optimal top income tax rate. In order to interpret the elasticities 4

7 that we estimate, we extend the classical revenue maximization model to incorporate migration. The model suggests that the effect of changes in taxes on revenue can be decomposed into a mechanical (tax rate) effect from higher taxes, the behavioral effect from changes in taxable income, and the behavioral migration effect. The last effect depends on the stock elasticity of migration rather than the flow elasticity. Using our stock elasticities, we find the mechanical effect dominates the behavioral effect for all regions in Spain, which has important implications for the position on the Laffer curve. For the region of Madrid, its lower rate relative to the central government tax rate in 2014 results in revenue falling by 52 million Euro due to the mechanical effect of the lower tax rate. Using our mobility estimates, new high taxpayers who migrate only contribute 7 million Euro more in revenue. In particular, we estimate that the revenue maximizing tax rate on top incomes above 94,000 Euro falls relative to what it would be with no migration, but is not statistically different. We conclude that, at least in the short-run, migration does not pose a large threat to redistributive taxation. 1 Institutional Details Spain consists of 17 autonomous communities (in Spanish: comunidades autónomas) which are comparable to states or regions in other federations. The autonomous communities are governed according to the Spanish constitution. Furthermore, the individual competences which each region assumes are regulated by a region specific organic law, known as Statute of Autonomy. 7 Since 1994, the regions receive a share of the Personal Income Tax (Impuesto sobre la Renta de las Personas Físicas) as part of their revenues, but it was only in 1997 that partial autonomy over marginal tax rates was delegated to the regions (see Durán and Esteller, 2005). Important for our purpose is that taxes are due at the place of residence (residencia habitual), which is declared in the local municipality of residence. However, initially regional autonomy was quite limited as regional level marginal tax rates applied only to 15% of the tax base and autonomous communities had little interest in changing marginal tax rates. Instead, they focused on setting tax credits, mostly for housing and renting as well as some personal circumstances such as ascendants and decedents. 8 In 2007, the regional-level individual tax rates still had to complement the common tax brackets set by the central level, but they were applied to a larger share 7 In general, the top spending categories by regions in Spain are education and health. These are services that are disproportionately consumed by lower-income groups. 8 Durán and Esteller (2006) show that those tax credits lower predominantly the effective tax burden for the poor, as many of them fade out with income. A prominent example are tax credits given to young individuals renting a flat in various regions. However, only young and low income individuals are eligible (for example below 35 years of age and 19,000 Euros in Extremadura, and 32 years and 20,000 in Cataluña). Madrid allows for a small deduction of school books for families with a tax base below 30,000 Euros, to give a further example of this type of deductions. 5

8 of their residents tax base. 9 Until 2009, 35% of income tax revenues raised within one region from the federal income tax was kept by the region with the remainder going to the federal government. Therefore, in 2007, Madrid was the first autonomous community which changed marginal tax rates, followed by La Rioja and Valencia in All of them implemented marginal tax rates which were slightly lower (less than 1 percentage point) than those in the remaining regions. Murcia followed in 2009, but returned to the common federal scheme thereafter. These initial reforms resulted in very small differences in taxes across regions. Another major wave of decentralization reforms followed this process in 2009 but these reforms were not implemented until The share of revenue that regions could keep was increased to half of all tax revenues collected in their territory. In addition, regions were also given the right to introduce new tax brackets on top of those implemented by the central government. In 2011, the regions could exercise this right as the last laws were approved in July In 2011, with both the ability to construct new brackets and top marginal tax rates in hand along with added incentives to retain more of the tax revenue, several regions increased marginal tax rates substantially, while the ones which decreased them previously maintained their lower rates (Bosch, 2010). This lead to substantial divergence of tax rates on top incomes. In all subsequent discussion when referring to the tax reform, we mean this 2011 implemented reform that gave regions more incentives to change tax rates. Any tax differences prior to this reform were trivial in comparison. Another reason for the immediate reaction of regional governments was that in 2011, the federal government raised marginal tax rates substantially and regions used this event to increase simultaneously their own tax rates, or decrease them to counteract the federal increase. In subsequent years, some further changes in regional top tax brackets were implemented, but the pattern of high-versus low-tax regions as of 2011 generally persists to the end of our sample in Given the immediate reaction of the autonomous communities to the tax reform, we believe this enhances identification of the migration elasticity. These reforms and tax changes have been widely talked about in the media (Figure A.3). Furthermore, as shown in Figure A.4, the regional tax rate in the place of residence is salient because the Spanish tax form computes an individual s average regional and federal tax liability separately, which makes the regional differences 9 c.f. Ley 35/2006, de 28 de noviembre, del Impuesto sobre la Renta de las Personas Físicas y de modificación parcial de las leyes de los Impuestos sobre Sociedades, sobre la Renta de no Residentes y sobre el Patrimonio. 10 A confounding factor could be the re-introduction of the wealth tax at the end of However, the decision was taken at the end of 2011, such that an immediate response in that year and even one in 2012 is unlikely to happen. Furthermore, the tax has been introduced as an explicitly temporary measure to reduce fiscal problems during the Great Recession. It was not until the end of 2012 that the government announced that the tax will also be applied in the following year, again without establishing the tax permanently. 6

9 very salient to tax payers. 11 When filling taxes in April, tax payers are also asked to state their place of residence. A change of their address can be done online at the same page where individuals submit their tax declaration and becomes effective immediately. 12 In Spain, the individual income tax system has separate tax systems for the labor income tax base and the capital income tax base. The reform only decentralized the labor income tax base to the regions, while the capital income tax base remained taxed only under the federal tax schedule. Given that we will use Social Security data to study migration, pure rentiers (individuals with capital income only) will be absent from the data. However, given that these rentiers face a common federal tax rate on capital income, the decentralization of the labor income tax base is irreverent for these individuals. The reform did not affect corporate taxes, so we do not have to worry about any correlation with corporate taxes, which remain the authority of the federal government. 1.1 Descriptive Figures of the Reforms In Figure A.1 we show the top marginal tax rates in 2010 (just prior to the reform) and in Notice that in 2010, all regions in our data set have tax rates that are within 0.10 percentage points of each other. But, by 2014, substantial spatial variation had emerged. Indeed, Figure A.2 shows a large jump on impact indicating that most of this variation was already in place by the first year of the reform Figure 2 shows the change by Spanish region. All tax rates increased over time in levels although some decreased relative to the federal rate. However, when considering the state reforms these changes differed by 5 percentage points across the regions. Figure 3 shows the changes for all regions and for all levels of income. In order to ease interpretation, we show the tax changes relative to what the tax rate would be if the region had simply adopted the federal tax rates. Relative to this standard, some regions decreased their tax rates while others increased their tax rates. The large tax changes occurred in the top 1% of the income distribution. Figure A.5 allows the reader to see how these tax rates evolved over time. Following the reform that substantially increased regional autonomy, tax rates diverged by four percentage points. This differentials persisted in subsequent years or sometimes widened. Given that many tax brackets change (and not just the top marginal tax brackets), we need to justify our focus on the top of the income distribution. Figure A.6/A.7 shows the marginal tax rates for Madrid (low-tax) and Cataluña (high-tax) overlayed on the 11 Although individuals know their average tax rate in the region of residence, it is unlikely they would know the exact average tax rate in all of the alternative regions within Spain. For this reason, highincome taxpayers may use the top marginal tax rate as a proxy for their expected tax liabilities in other regions. Gideon (2017) shows that many people think that all income is taxed at the marginal tax rate. 12 We do not observe the location of the individual declared. However, tax inspectors afterwards might double check any change of the fiscal residence with the data from the local register which we observe. 7

10 income distribution in Spain. The red vertical lines note the cutoffs for the top 5%, 3%, 2% and 1%, respectively. Notice that the top 1% incomes above 90,000 Euro approximately experienced the largest changes in tax rates across regions. The tax differences for individuals even in the top 2 to 5% were relatively small across regions. Focusing on this top income group, we calculate the transition matrix of individuals between regions (in our 4% random sample) and show this for the pre- and post-reform era in Table A.1 and A.2; Table A.3 also shows the transition matrix for the top 5%. 1.2 Who Changes By Larger Amounts? Regions that raise their tax rates by the largest amounts might be those regions where the mobility of top earners has been declining or where the stock of top earners is large or small. 13 Regions had little information about how individuals would respond to tax changes given the immediate decentralization and tax changes following the reform. In Table s A.4 and A.5 we show that characteristics of the region related to the top 1% seem to have very small effects on the predicted tax changes. Larger correlates with the tax changes are association with political, debt, and income conditions of the regions. Thus, the big bang nature of this decentralization seems to provide an ideal setting to study top tax rate changes on mobility. 2 Description of Data All data are taken from Spain s Continuous Sample of Employment Histories (Muestra Continua de Vidas Laborales, MCVL). The data is provided by the Ministry of Employment and Social Security (Ministerio de Empleo y Seguridad Social). This administrative data matches individual microdata from from social security records with data from the tax administration (Agencia Tributaria, AEAT), and official population register data (Padrón Continuo) from the Spanish national Statistical Office (INE). 14 The data consist of an approximately 4% non-stratified random sample (over 1 million observations each year) of the population of individuals which had any relationship with Spain s Social Security system in a given year due to work, receiving unemployment benefits, or receiving a pension. If an individual is in the data, they remain in the data as long as they have contact with the Social Security ministry, but new observations enter each year so that it remains representative. Those self-employed individuals that make contact with the 13 Policy responses are not accounted for when estimating the elasticity of taxable income. 14 The data we use are the Social Security data. Separate individual tax return data are available, however, these data have the disadvantage of being a stratified sample that is not representative across regions. Residence data in the Social Security data are less controversial; the tax return data often reports the location of work rather than the location of residence. Social Security data contains residence information based off local registers. 8

11 Social Security system do appear in our data; individuals with legal contracts are contributing to Social Security even if self-employed. Furthermore, most self-employment contracts will be reported to the authorities because the business client has incentive to ask for a VAT receipt in order to receive credits against the services purchased. An individual does not appear in the data if they have purely capital income, however, given that capital income taxes were not decentralized to the regions and face a common federal tax schedule, these individuals would not be affected by the decentralization of the labor income portion of the tax base. The observational unit of the raw data is based on each contact (for example, job) an individual had within a given year with Social Security. We aggregate this data at the individual level to obtain a panel data set which sums all individual incomes in a given year for a given tax payer. 15 We define the main work affiliation in each year as the one which was active for the longest time span since starting with this activity. One key is that from 2005 to 2014, the Social Security data are matched to income tax data. These income tax data are valuable because they are not subject to censoring; Social Security contributions are censored and do not contain some portions of income that are important for high income tax payers. Given we will focus on top income taxpayers it is important we have income data that is not censored and contains all sources of income. 16 Further, even for high-income tax payers, very little bunching is detected at the marginal tax rate kinks (Esteller-Moré and Foremny 2016), suggesting that income responses to the tax changes are not substantial. We construct the following main variables. First, we define a change of location if an individual changed his or her residence between t and t 1. Residence data of the current year is updated using residence of April in t + 1, which ensures that this period overlaps with the tax year as tax declarations are due in April to June. At this time, the data is crossed with the residence information from the official population registers. While residence information is available at much smaller spatial units, we are only interested in defining relocation across regions. As an example, an individual would be characterized as a mover in 2012 if he was living in a different region between April 2012 and April 2013 compared to his residence between April of 2011 and April In this way, his 2012 income is the relevant one for tax purposed in the region he moved to. 15 Only a small fraction of the sample are reported as married with a substantial fraction declaring their household status as other. Because of this limitation two individuals may move in our data when they are a common household. This complicates standard errors, but our results are robust to using only county pairs featuring only a single mover in a given year. 16 As noted in Bonhomme and Hospido (fc):... social security contributions exclude extra hours, travel and other expenses, and dismissal compensations. These differences seem more relevant for high skilled workers as the correlation in levels between contributions and taxable labor income is lower for the first group [high-skilled] (70%) than for the others (over 85%). Given our focus on high-income taxpayers we use the tax income data. 9

12 Second, we create an income variable which is the sum of all reported income by different employers within each year which is subject to the personal income tax (labor income, self employed income, and income in-kind). Given this information and other attributes, we simulate average and marginal tax rates for each individual in each year for each region using the information in the tax code provided by official documents. 17 This simulation takes into account the variation of marginal tax rates, their brackets, and basic deductions and tax credits for ascendants, decedents, and disabilities. We do not take into account any further region specific deductions or tax credits. However, given that we focus on high income individuals, this would almost never affect the marginal tax rate and the average tax rate only to a negligible amount as those omitted policies are targeted to low income individuals. 18 We use the tax calculator to simulate the tax rate in the region of residence and the tax rates in the alternative regions. Figure 4 shows the within individual variation across alternative regions that results from our calculator. We also use information on gender, age, education, as well as geographical information such as their first work affiliation or their place of birth from the MCVL. We merge data from 2005 until 2014 resulting in a panel of ten years. Some geographical restrictions apply to our sample. We do not observe individuals living in or moving to the Basque Country and Navarre as administration in these regions is independent. Summary statistics of our data are given in Table A.6. Table A.7 shows the top industries of movers in the top 1% and Table A.8 shows the occupation composition of movers. One interesting thing to note is that individuals in sports activities are one of the top groups both in terms of the absolute number of movers and the percent of individuals in that group that move. Over 8% of individuals in the top 1% that work in sports activities move following the tax reforms. Other industries include high-skilled individuals given the top occupation is engineers, graduates and seniors. This provides a nice parallel to the existing literature focusing on athletes and star scientists while also allowing us to look at a broader sample including all occupations. 3 Aggregate Analysis 3.1 Theory For simplicity consider a two region economy where r = o, d indexes the two regions. Assume the utility of top income individuals living in region r in period t is given by: V r,t = αu(c r,t ) + βv(g r,t ) + µ r γρ(n r,t ) (1) 17 We use the tax laws to write a tax calculator for Spain similar in spirit to TAXSIM. 18 Furthermore, these omissions from the tax calculator are common to all calculators. Even NBER s TAXSIM calculator does not present a complete set of tax rules for all states and years. Measurement error concerns are addressed via an IV procedure. 10

13 where c r,t is private consumption of the individual, g r,t is public services consumption, µ r,t is the value of other amenities that are specific to living in the origin region. The function ρ is a disultility that depends on population. The ρ(n r,t ) function allows us to indirectly bring in housing markets into the problem: a region becomes less attractive, the larger is its population perhaps because housing prices increase. In particular, fewer people in a region mean the cost of housing will be lower which raises utility relative to a region with more people and higher housing costs. 19 Each individual supplies a fixed unit of labor so that given the static nature of the problem, an agent consumes all of the after-tax income: c r,t = (1 τ r,t )w r,t where τ r,t is the tax rate. Following the standard in the literature, we assume that the separable utility functions u, v, and ρ each take on the log functional form. To close the model, we assume a simple model of production. Production in any given region is given by f(n r ) and satisfies the standard properties f Nr > 0 and f Nr < 0; the price of output is normalized to one Euro. With mobility, the equilibrium in the labor market requires the wage rate to equal the marginal product of labor w r = f Nr (N r ). Assuming that production is given by A r N θ r,t K η r where A r are fixed productive amenities in the region and K is the land/capital stock that is fixed in the short run, such as the stock of buildings. 20 Then we have in each r that w rt = Ar K r η. Nrt θ A locational equilibrium requires that V o,t = V d,t = V. Setting V o,t = V d,t, taking logs of the equilibrium wage equation and substituting implies ln( N d,t ) = 1 ( ) 1 τd,t π N o,t θ + γ ln + 1 τ α o,t α(θ + γ )ln α ( gd,t g o,t ) + ζ d ζ o (2) where ζ o and ζ d are defined to include the fixed productive amenities, fixed capital resources and consumption amenities across regions defined above. The above equation characterizes the equilibrium in the model Methods Denote the net of tax rate with respect to the top marginal rate by 1 mtr dt [1 mtr ot ] in the destination [origin] region. Then simplifying notation and generalizing to multiple 19 To see the idea of this function, consider an example. Suppose both regions were ex ante identical and had the same population. Then an individual who moves from region o to d will, all else equal, realize a lower level of utility in region d because after the move N d,t > N o,t. For this reason, we think this is an attachment to home model. 20 Of course, we can generalize the model to contain endogenous capital or housing for individuals. 21 The model can be derived without the ρ function using a fixed cost of moving by lowering utility in the destination region by that fixed cost. In this case, the only difference is the degree of capitalization into wages. Our model delivers partial capitalization into wages. 11

14 regions yields our estimating equation for the stock of individuals: ln( N d,t N o,t ) = βln[ln(1 mtr dt ) ln(1 mtr ot )] + ζ o + ζ d + ζ t + X odt π + ε od,t (3) The theory implies to estimate the model using the ratios of populations and taxes rather than the region s own population and own-tax rate only. In particular, we need to conduct this pairwise ratio because we have a small number of regions so that the tax differential matters for the stock. Only if the number of regions is large which is not the case in Spain would it be valid to estimate a regression of the population in one region on its own-tax rate. Another way of seeing this is to note that the number of people in a given region depends on the entire vector of net of tax rates in all of the regions. With a small number of regions, tax changes in region r r will have a non-negligible effect on N r, which means that we must consider the entire vector of alternative tax rates in our analysis. This is the purpose of estimating the stocks in pairwise ratios. Of course, this pairwise estimation complicates treatment of the standard errors. We cluster the standard errors three ways to account for correlation over time within region-pairs and to account for the common tax rates across origin and destination by year pairs. The the identification strategy fundamentally relies on a diff-in-diff. Given the set of fixed effects identification requires that, absent tax changes, region-pair stocks are fixed over time. Some notes concerning the empirical model are in order. First, we focus on the net of tax rate, which tells the researcher how much an individual will take home on the last Euro of their earnings. Use of the net of tax rate rather than the tax rate is common in the literature estimating behavior responses to taxes (Saez, Slemrod and Giertz 2012) and we follow this convention. For researchers unfamiliar with the net of tax rate, note that an increase in the tax rate will lower the net of tax rate. This means that the term in brackets informs the researcher of the differences in the net of tax rate between the destination and origin region and we expect the sign on the differential to be positive. Second, the use of the top marginal tax rate is valid if the the top marginal tax rate is more salient than the average tax rate and because individuals in the top marginal tax rate are likely the most responsive. The top marginal tax rate is likely to be most salient when determining the tax liability of the alternative regions; although individuals know the average tax rate in their region, they are unlikely to be able to calculate this across all of the alternative regions. The use of the top marginal tax rate also allows to avoid the problem of making assumptions about wages across the regions. Finally, going from equation 2 to 3 implies that all estimates should be thought of as the effect of tax changes inclusive of any spending changes. However, for the high income individuals, we expect tax increases correspond to increases in tax payments that are larger than any increase 12

15 in services. Alternatively, if tax changes on the top one percent do not result in changes in the government services provided to the top 1% (if they fund services for lower income households), then differences in government spending for the top 1% are subsumed in the region specific fixed effects. Estimates of β capture the reduced form elasticity rather than the structural parameters. With respect to the fixed effects, origin fixed effects capture amenities (both for households and firms) in the region of origin. Destination fixed effects capture such amenities in the destination region. These fixed effects also capture any time invariant policies of the region over our sample. Time fixed effects can be included in the model with covariates, but when no covariates are included do not need to enter the model because of the differencing across pairs. In some specifications, we control for time varying, region-pair specific shocks including economic shocks, demographic shocks, and industry composition shocks. We wish to derive the elasticity of the stock of top taxpayers. The estimating equation delivers the elasticity of the stock ratios. We can use the properties of elasticities and the symmetric effect of origin and destination top tax rates to define the stock elasticity of the population, ε, in a given region r as ε(n r ) = ε( N d N o ) 2 = β 2 ε. (4) We estimate a stock model rather than a flow model for several reasons. First, the stock elasticity is the parameter of interest in the revenue simulations we will conduct. Second, estimation in the flow model raises selection concerns because we do not observe migration between some regions and because a flow model would miss international migration, but the stock model will not. Finally, a flow model would rely on a model where utility of being in any location is always conditional on where individuals are located to start with in period t (the origin region); then identification requires region-pair migration flows are fixed over time. The stock model avoids all of these issues. In Appendix A.5 we further justify the use of a stock model. In the stock model we present, identification requires that, absent tax changes, region-pair stocks are fixed over time. This means that other regional changes over time are uncorrelated with the tax rate changes. This limitation of the aggregate analysis will be addressed in section 4 where we focus on individual movers and can control for time varying region-specific shocks using region by year fixed effects. 13

16 3.3 Results Given the simple panel data setting with fixed effects, we present our baseline results visually. To do this we regress the stock ratio on the fixed effects and predict the residuals. We then regress the net of tax rate variable on the fixed effects and predict the residuals. We then bin the residuals into twenty equally sized bins and fit a line of best fit through these data which allows us to non-parametrically see the relationship between taxes and migration. Figure 5 shows the baseline results using origin fixed effects and destination fixed effects; inclusion of year fixed effects does not change the results. Because all tax variables are in terms of the net of tax rate, when individuals keep more on the Euro in region d relative to region o, they are more likely to move to (or stay in) region d and the stock increases in d relative to o. As the differential increases in the upper panel of the figure, we see that it is consistent with β > 0, which confirms our theory. The bottom panels shows the effect of tax differentials on the log of the population; the left figure indicated that keeping relatively more in region d lowers the population in region o while the right panel indicates that keeping relatively more in region d raises the population in region d. One worry might be that the results could be driven by outliers. To account for this, we winsorize extreme values and verify the results are similar. While appealing, the graphical method is not transparent with respect to the magnitudes of the elasticities estimated and the standard errors. We present point estimates and standard errors for the aggregate analysis in table 1. Our preferred specification in column (2) contains both destination fixed effects, origin fixed effects, and time varying controls. Column (2) indicates the elasticity of the stock ratio. Dividing by two yields the elasticity of population in a given region r. This specification suggests the stock elasticity is approximately This estimate of the elasticity is lower than the estimates in Moretti and Wilson (2015), who estimate a stock elasticity of Our estimates of the elasticity are stable and are not sensitive to the inclusion of covariates, region specific time trends, or to the inclusion of region d by year fixed effects, which account for any other time varying policies in a given region. In particular, depending on the specification, the elasticity ranges between 0.21 and Given identification is based on a large reform, we wish to show a break in the patterns following the 2011 reform. To do this, for each region pair d and o, we calculate the net of tax differential between the regions in the post-reform period. If the net of tax differential increases in region d relative to region o, we classify that pair as one where the net of tax rate increases. The left panel in figure 7 shows the raw averages of the stock ratio for pairs where the region d gets to keep more income (taxes fall). For these 22 Moretti and Wilson (2015) do not directly estimate a stock elasticity. Rather, the paper estimates a flow elasticity and converts it to a stock elasticity. 14

17 observations, the stock ratio increases following the reform and remains higher. This suggest migration increases into regions that cut their taxes or migration decreases out of these regions. Of course, we can implement the analysis more formally. To do this, we implement an event study approach by estimating ln( N dt N ot ) = ln( 1 mtr d 1 mtr o )[ 2 y= 6 π y 1(t t = y) + 3 γ y 1(t t = y)] + ζ o + ζ d + ζ t + X odt π + v dot where ln( 1 mtr d 1 mtr o ) is the log ratio of the net of tax rates at the end of our sample. Then, 1(t t = y) are indicator variables relating to the time since the reform happened in period t = As such, π y show the evolution of the stock ratios prior to the reform and the γ y show the evolution following the reform. Multiplying by ln( 1 mtr d 1 mtr o ) captures the intensity of the treatment and allows us to jointly estimate the effect of relative increases and decreases in region d in one specification. The right panel of figure 7 shows no clear pre-trends, but a level increase in the stock ratio following the reform; given the large jump on impact this may suggest tax evasion rather than real moves. Again, this suggests that the regions that lowered rates allowing residents to keep more, saw an increase in the stock of top income taxpayers. Because of noise in the post-reform period, the the generalized event study design can also be presented as a simple dif-in-dif controlling for trends; the results are given in table A.9. Dividing these estimates by two confirms the stock elasticity of 0.25, which is significant across the post-reform period. y=0 One concern with the approach is that we might be picking up other time varying policies that are correlated with tax rates. To show that this is unlikely we conduct a placebo test using lower income groups. Our goal is to show that lower income groups do not respond to the top tax rate on individual income, which in turn, suggests that there are no time varying policy changes (to the extent that those time varying policies would influence both low- and high-income groups). In the upper panel of Figure 6 we present (using the same scale as the upper panel in the prior figure) results for the bottom 99% and the top 5% excluding the top 1%. No significant pattern emerges in response to top marginal tax rates for these groups, which suggest we are not picking up any time varying unobservable policies that also affected lower income groups. This strengthens the case for the exogeneity of the tax shocks. Finally, we conduct a placebo test using the pre-reform period. To do this, we take our measured tax differentials from and lag them by four years. We then match these post-reform tax rates to the four years prior to the reform. We show in the bottom panel of Figure 6 that no correlation between pre-reform stock ratios of the top 1% and post-reform tax rates exists. This suggests to us that the post reform tax rates were not driven by pre-reform conditions; we further (5) 15

18 explore this using an event study. A second concern with this model is that we may overestimate the stock elasticity due to migration because of taxable income responses. In particular, we might worry that the in regions lowering their tax rates, taxable income may rise resulting in more people moving into the top 1% of the income distribution in Spain. To address this concern, we implement several robustness checks. First, as noted in the prior paragraph, we do not see a change in the stock ratios for the top 5% (excluding the top 1%). If we were picking up taxable income responses, we would expect these individuals would come from lower percentiles and that the populations in these stocks would decline; they do not. Second, in Table 1 we show three checks. First, the results are robust to controlling for the (endogenous) ratio of taxable income reported by the top 1% in the region pairs. Second, we also adjust the population stocks accounting for movement within the income distribution. Let rt be the number of people who move in/out of the top percentile of the income distribution in region r. This number is calculated as the number of people who are in the top 1% this year but were not in it last year minus the number of people who were in the top 1% last year but are not this year. Then we calculate an adjusted stock ratio using Ñrt = N rt rt. We then run all specifications using ln(ñdt/ñot) as the dependent variable so that we are exploiting variation in the stock of people in the top 1% adjusted for any churn in the income distribution. 23 After doing this, we estimate an elasticity of 0.19, which falls slightly suggesting our prior estimates may capture some small taxable income responses. Finally, we estimate a taxable income elasticity directly by regressing the share of total earned income (individuals between 18 and 65 years, excluding pensions and unemployment benefits) in a region earned by the one percent on the net of tax rate, region and year fixed effects. This regression estimates a small and insignificant elasticity (0.137 with a standard error of 0.288) suggesting we are identifying mobility effects in our stock analysis. Figure A.8 shows a very small taxable income response that is not clearly evident. This is consistent with Rubolino and Waldenström (2017), which estimates a taxable income elasticity for the top percentile in Spain of 0.05; these estimates plus the 0.19 that we estimate for the stock elasticity sum to the results we obtained when not accounting for the taxable income response. The results of this exercise suggest that we are able to estimate the stock elasticity of population and are not identifying taxable income responses. However, to further address this issue, we now turn to an individual analysis where taxable income responses will not be a concern for identification. 23 An alternative might be to restrict the sample to individuals always in the top 1% of the income distribution. We tried doing this, but the sample of individuals satisfying this criteria becomes small given substantial churn in the income distribution. The results using this very restricted sample do not seem to address the concern. 16

19 4 Individual Analysis: Where to Move 4.1 Theoretical Motivation to Migration To consider an individual s choice to live, we modify the prior model to allow for individual specific consumption levels and we remove the ρ function and replace it with simple moving costs. The utility of individual i living in region o (for origin region) in period t is given by V i o,t = αu i (c i o,t) + βv i (g i o,t) + µ o,t where c i o,t is private consumption of the individual, g i o,t is public good services consumption, µ o,t is the value of other amenities that are specific to living in the origin region. Within the high income group it is likely that consumption of public services is similar across all individuals in the top percentile of the income distribution: g i o,t = g o,t. Each individual supplies a fixed unit of labor so that given the static nature of the problem, an agent consumes all of the after-tax income: c i o,t = (1 τ i o,t)w i o,t where τ i o,t is the average tax rate. If the individual moves, utility in region d (the destination region) given by Vd,t i = αui (c i d,t ) + βvi (gd,t i ) + µ d,t ρ i od,t where all parameters are similarly defined above except for ρ i od,t. In particular, this is the utility cost of moving from region o to region d. Note that that after-tax consumption can differ because of both tax differences and wage differences across regions. However, if the labor market is perfectly competitive, then wo,t i = wd,t i. An individual will move from region o to d if ( ) ( ) 1 τ i d,t w i d,t αln 1 τo,t i + αln wo,t i }{{}}{{} tax differentials ρ i od,t }{{} moving costs wage differentials + βln region by year effects ( ) gd,t {}}{ g o,t }{{} other policies + µ d,t µ o,t }{{} > 0. (6) location amenities If the model contains more than two regions, then for an individual to move to region d, Vd,t i must provide the highest level of utility among all possible regions. Then, it is clear that the all regional tax rates will matter for the individual s choice on where to migrate. This equation shows the challenges of studying the effect of taxes on migration, which we discuss in the subsequent section. 4.2 Probability of Moving In order to justify our subsequent focus on movers, we first study the probability of moving. Did the tax reforms implemented in 2011 have an effect on the overall probability of moving? Using the 2011 reform as an event, we use a generalized difference-in-differences with lower percentile individuals as a control group. Appendix A.6 shows the reforms had a small increase but statistically insignificant effect on the probability of moving. However, even though the probability of moving is not significantly changed relative to the pre-reform era, taxes may have large effects on the location choice conditional on moving (both on impact and throughout the reform). The prior aggregate analysis suggests that taxes matter for location choices. Thus, we focus on the location decision of 17

20 movers in the next section. Put differently, if an individual was planning to move, the Spanish reforms may influence the residence that they select conditional on moving. This is what we test in the subsequent section. 4.3 Methods and Identification Now we use disaggregated data with the observational level i being the individual taxpayer mover in year t if the individual relocated across regions between t and t 1. In particular, this means that we focus on movers in our estimating sample 2006 to 2011; the vast majority of individuals move only once over the course of our sample. A justification for focusing on movers is that local tax rates are likely a function of all indviduals location decision. Because movers are a relatively small share of the population of a given region, it is likely that the equilibrium tax rates selected following the fiscal decentralization are driven by the large share of the stayers (Schmidheiny 2006; Brülhart, Bucovetsky and Schmidheiny 2015). We denote the alternative residential options (different regions within Spain) as j in our model. The dependent variable d i,j,t is coded one for the chosen region of residence in year t and zero for all other region that are not selected. In its simplest form, we estimate the following linear probability model where tax rates are denoted by τ: d i,j,t = βpost t ln(1 τ) i,j,t + α i + ι j,t + ε i,j,t. (7) Because we use moves pre- and post-reform, we interact the net of tax rate with post t, which equals one for the years following the tax reform. 24 Our model contains individual fixed effects denoted α i and alternative by year fixed effects ι j,t. Note that the inclusion of α i is crucial because identification of our parameter of interest exploits the within individual variation in tax rates across regions. 25 In this way, we exploit the income tax differential of alternatives across regions for a given tax payer which relocated. The inclusion of alternative specific fixed effects implies that we include a dummy variable for each alternative j in each year t in the model. This captures any alternative region specific variable that would be constant across all top-earners, such as other regional taxes or wage differentials across regions and over time. The variation in tax rates across regions for the top 1% relative to other income groups is verified by looking at the within variation in Figure 4. It shows the standard de- 24 Results are robust to using the differential between the net of tax rate in the origin region and the destination alternative. Results are robust to excluding the interaction and simply using ln(1 τ) i,j,t given that taxes across regions were (almost) the same in the pre-reform era. The only differences that emerge were very small resulting from the three jurisdictions that changed their tax rates by less than a few tenths of a percentage point following the first wave of decentralization. 25 Technically, an individual i observation is an individual mover in a given year. Given very few individuals that move twice, we refer to these as individual fixed effects. 18

21 viation of marginal tax rates across alternative regions for individual observations (within group variation). Starting from this simple specification, we modify equation 7 to account for the effects given in equation 6. We discuss each of the terms in equation 6 in the order that they appear. First, we account for taxes in several different ways. In the baseline specification, we include the net of tax rate where we use the marginal tax rate. The marginal tax rate has the advantage of being exogenous to the level of earnings and for high-income tax payers the marginal tax rate is highly relevant. However, migration decisions are made off average rather than marginal tax rates. For this reason, we show the results are robust to using the average (net of) tax rate. Finally, we formalize the exogeneity of the marginal tax rate beyond simply using it as an exogenous proxy by using it as an instrument for the average tax rate. This has the advantage of reducing measurement error in the average tax rate, which might result from elements of the tax code not captured by our tax calculator. Second, equation 6 suggests that wage differentials across regions are also important. Although we observe wages is the region of residence, we do not observe counterfactual wages. Thus, equation 7 imposes that wages are equal across regions (perfectly competitive) or that all wage differentials are constant across all individuals. Although some of the wage effect could be picked up by the fixed effects, to relax this assumption, we include location specific dummies interacted with characteristics of the individuals that are correlated with wages (for example, age, age squared, male, and education). Denote the vector of characteristics interacted with region specific fixed effects as x i,t ι j. This allows the returns to education and the skill premium to vary by region; thus, ability affects the counterfactual wage depending on the region. We also include a dummy variable for the region of the workplace of the individual. 26 Third, public services across regions matter. If we did not include the region by year fixed effects, estimating equation 7 captures the effect of taxes inclusive of any endogenous change in spending. This would a lower bound on the pure tax effect because some of the tax increase funds public services for the wealth. However, the inclusion of region by year fixed effects (ι j,t ) captures any time varying policies such as changes in public services for the wealthy that are constant across all individuals. For high ability taxpayers it is likely that the public spending consumed in a given region is likely constant across individuals in that income group. In general, however, we note that tax increases on the rich are not likely to change public services for the rich as these taxpayers are net payers into the tax system. This is particularly the case given the major services provided by regions include education and health. 26 If the individual has multiple workplaces, we use the principle affiliation. 19

22 Fourth, equation 6 suggests that location specific amenities, µ d,t and µ o,t, also matter. To accounting for region specific policies, ι j,t also account for amenities in the alternative regions. Acknowledging the region of residence prior to moving may also play a special role, so we also include a dummy variable that equals one if the individual previously lived in the region. Finally, moving costs between regions, ρ od,t, also matter. To capture these moving costs, we include (z i,j,t ) a dummy variable that equals one if the region is the place of birth for the individual. We also include a dummy variable that equals one if the individual had their first job in that region. Following a standard gravity model of migration, we also include the log of distance between the region of prior residence and each of the alternative regions. 27 This captures the fact that nearby regions have lower moving costs because they allow individuals to maintain their social and family network. All of these additions imply that we estimate: d i,j,t = βpost t ln(1 τ) i,j,t + α i + ι j,t + ζ j x i,t ι j + γz i,j,t + ε i,j,t. (8) where x i,t ι j are individual characteristics interacted with region fixed effects and z i,j,t are individual characteristics specific to a particular region. 28 One important issues is the treatment of standard errors in this model. We adopt multiway clustering. First, we cluster over individual tax payers to allow for correlation across the regions within taxpayer and correlation over time for people who move twice. The second cluster is destination region by year clusters. This allows for an arbitrary error structure for all individuals that move to the same region within a given year. It allows for correlation in errors across all of the j alternatives conditional on the regionyear to which the individual moves. In the appendix, we show the results are robust to clustering over the destination region although the small number of clusters may lead to overrejecting the null hypothesis (see table A.11). Our analysis will focus on the sample of movers and not on individuals that do not move regions. To do this, we restrict the sample to individuals in the top 1% that move. Inclusion of the pre-reform years helps us to pin down our covariates, but results are robust to studying only the post-reform period. We focus on the sample of movers given we have already shown estimates of the stock elasticity and given the probability 27 For the origin region, we define distance as the natural log of one kilometer. 28 Following Bertoni, Gibbons and Silva (2015), we estimate our model using OLS. We do this because of the ease of the probability interpretation of the results. Further, we wish to do IV approaches and robustness checks using these data that are better suited for the linear model. It is not unprecedented to use OLS in the multi-nomial choice setting (for a recent example, see Bertoni, Gibbons and Silva 2015). The appendix shows the results are robust to non-linear model, but sometimes these models do not converge. 20

23 of moving analysis showed no increase on the odds of moving. Thus, all estimates that we derive should be viewed as estimates relating to the flow of migrants and not to the stock of individuals. The reason for the focus on movers is that we wish to study how taxes alter the place of residence conditional on moving in order to study where people move to. 4.4 Baseline Results Table 2 shows estimation of equation 7 and of the comprehensive equation 8. Column (1) shows the results including individual fixed effects and alternative by year fixed effects using the log of the net of marginal tax rate as the independent variable of interest. The coefficient, 0.521, is the expected sign and is statistically significant. Recall that when using the net of tax rate, a decrease in the tax rate increases the net of tax rate. Thus, a higher net of tax rate implies a higher probability of migrating to that region because the individual can keep more of what is earned. In terms of the magnitude, this coefficient implies that a one percent increase in the net of tax rate raises the probability of moving by or 0.5 percentage points. Given that these tax reforms were relatively large, the average tax change results in a substantial effect. This represents a substantial increase in the probability of moving to a region, which if random would have odds of 1/15. Subsequent columns of the table add various controls designed to be consistent with our theory: We control for factors that influence the cost of moving. We also add interactions of education, age and age squared with the alternative dummies to allow for possible differences in wages across regions. This helps with the precision of our estimates, but the coefficient on the net of tax rate only increases slightly. Critical to our analysis is that column (2) containing no wage controls and column (7) containing a complete set of wage controls (x i,t ι j ) are not different from each other in any meaningful way. In particular, the coefficient is One advantage of the regression procedure we use is its straightforward interpretation. In particular, these estimates suggest that for example the 4.1 percentage point differential between Madrid and Cataluña in 2013 increases the probability of moving to Madrid by 5.1 percentage points. The effect of Madrid s 2014 tax cut of 0.4 percentage points further increases the probability of moving to Madrid by another 0.5 percentage points. To get an idea of the relative magnitude of this effect, note that, in the pre-reform years 30.1% of movers decided to locate in Madrid. The control variables are of the expected sign. Conditional on being a mover, the home region dummy enters negatively. The location of the contract headquarters is positively associated with moving to a region. People are more likely to move to the place of birth or to the place of first job which is consistent with individuals having a home bias. Furthermore, distance enters negatively which is consistent with a gravity model of 21

24 migration where moving to more distant regions are more costly. A one percent increase in distance lowers the probability of moving to the region by.08 percentage points. This magnitude also helps benchmark the effect of taxes, which is about seven times larger. 4.5 IV Approach When using the marginal tax rate rather than the average tax rate, we are likely to underestimate the effect of taxes because the proxy variable might introduce measurement error concerns. In particular, unlike Kleven, Landais and Saez (2013), individuals in the top 1% in Spain may have a substantial portion of their income earned in lower brackets than the top brackets. This means that we can think of the marginal tax rate as a proxy given by ln(1 atr i,j,t ) = γ + δln(1 mtr i,j,t ) + ε i,j,t. Given the income distribution, δ is not as close to one as in the Kleven, Landais and Saez (2013) case. Thus, our results may be attenuated substantially. We can avoid this problem by using our tax calculator to construct the average tax rate assuming income is constant across the regions. This raises endogeneity concerns, but the marginal tax rate exogenous to earnings allows us to implement an IV strategy. 29 Table 3 shows results using the average net of tax rate where we instrument for it using the marginal tax rate used in the previous analysis. As expected, the results are larger in magnitude. This is expected because for a one percent increase in the marginal tax rate, the average tax rate increases by less than one percent. The IV approach reduces measurement error concerns that arise from simply using the marginal tax rate as a proxy for the average tax rate, which is presumed when we present results of the marginal tax rate directly. The first stage coefficient is the expected sign (positive), and is less than one as expected. The instrument is strong. After instrumenting, a one percent increase in the net of tax rate increases the probability of moving to a region by 1.43 percentage points in our most comprehensive estimating equation. 30 Table A.12 shows that without instrumenting for the average tax rate, the effect of the net of average tax rate is This downward bias is driven by endogeneity concerns that are resolved by instrumenting. 29 In our case we do not use the top marginal tax rate, but rather the person s marginal tax rate in the region of residence as an instrument. If changes in income across regions is small, this is not an issue because it will not change the bracket the individual falls into. However, if changes in income across regions is large (for that person), then this may potentially result in the individual changing tax brackets. This would make the marginal tax rate endogenous. We address this issue subsequently in the paper. 30 We control in our estimation for the existence of wealth taxes in different regions across time by region-year fixed effects. As our data does not include the level of wealth, we cannot control for differential effects of different levels of the wealth distribution across regions. As a proof that our results are not confounded by this, we re-estimated the model for years prior to and including 2012 when the wealth tax was initiated temporarily. This estimate, comparable to Column 7 of Table 4 confirms that income tax responses are even stronger in the first years (point estimate on the net of tax rate with a standard error of 1.002). 31 Table A.14 uses a nonlinear model to convert these to flow elasticities. Reassuringly, the elasticities match those in the aggregate analysis after we convert from a flow elasticity to a stock elasticity. 22

25 In Table 4 we show how the migration response varies across the income distribution for high-income taxpayers. The effects fall off substantially after the top 1% of the income distribution. This is expected given Figure 3, which shows the divergence of marginal tax rates is strongest in the top 1%. The divergence of tax rates across regions is not large outside of the top 1% and thus these lower income individuals are not influenced by the reform unless they expect to see large income increases in the future. The fact that we do not find effects for high income individuals that are not affected by the reform is reassuring as it suggests the effects on the top 1% are driven by tax changes and not other unobserved factors that may affect high-income individuals. We do not view this as an indication that these different groups have different tax elasticities. Given how small the tax differentials are outside of the top 1% of the distribution, a one percent change in taxes will have no salient effect on tax liability and likely would not change tax differentials more than the cost of moving. Thus, these smaller estimates verify the treatment groups are affected while other groups are not; these results do not indicate the elasticity varies across the income distribution. To test if the elasticity varied across the income distribution, we would need equally salient tax changes for lower income groups that exceed their moving costs. We realize that the marginal tax rate may not be exogenous to income if individuals change brackets across regions. Thus, the best instrument would account for the individual being within a fixed bracket. To address this issue, we remove any individuals from the analysis what are within χ% above or below all tax bracket thresholds (that affect the top 1%) for all regions. We show results for χ = {1, 2.5, 5}. Thus, for χ = 1, we remove anyone who is 3,000 Euro above or below the top tax bracket of 300,000 Euro, 1,750 Euro above or below the 175,000 Euro threshold, etc. Table A.13 shows that for χ = 1, 2.5, the results remain similar: a one percent change in the net of tax rate changes the probability of moving by 1.3 percentage points. For χ = 5, the results increase because such a large cutoff removes a substantial fraction of lower income individual in the top percentile, which leaves us with a sample of individuals that is higher income. 4.6 Placebo Test The reforms went into effect in 2011, but we have constructed data back until This allows us to conduct a placebo test to verify that post-reform tax rates are not correlated with unobservable characteristics of regions that are not accounted for by our fixed effects. Given that we have no tax differences in the pre-period, we need to use the post-reform data to construct a placebo measure of tax rates in the pre-period. To do this, for each individual i and region alternative j in the Social Security data, we 23

26 construct the mean tax rate in the post reform data (years 2011 to 2014). 32 We wish to see if these post-reform tax rates have any effect on the decisions of movers pre-reform. In Table 5 column (3), we show results for the IV approach using only the sample of movers in the post-reform era. We present this result to show that taking the mean across time for tax rates yields a very similar coefficient (1.39 versus 1.43 previously). In column (4), we restrict the sample to individuals that moved in the pre-reform period between 2005 and 2010 and implement the IV approach for these individuals using the placebo tax rates. The coefficient falls to 0.56 and is statistically insignificant with relatively large standard errors. Post-reform tax rates are not correlated with unobservable factors that may have influenced pre-reform migration. Other studies of migration exploiting state-level tax changes cannot construct such a placebo test. This placebo test is unique to our study given the the Spanish government decentralized taxes to the local regions starting in Heterogeneity Although we have identified significant location choice effects, we have yet to determine if the location choices reflect real moves or simply tax evasion by misreporting the primary residence (perhaps by households that have a second home). In order to shed light on this, we explore whether the tax changes have heterogeneous effects across different types of people within the top one percent by interacting the tax rates with indicator variables for various groups. 33 Table 6 presents the results using the average tax rates. In general, we do not find statistically significant differences across groups. This could be a result of the sample size that we have. However, we do find effects that are consistent with our expectations. For example, individuals with no kids have a stronger influence of taxes, which is consistent with these families having less costs of moving. 34 We also find larger effects for highly educated individuals in the top 1%. Very large effects emerge for younger workers (below age 40). In Table 7 we focus on heterogeneity by the job characteristic. In particular, we wish to see if the individual moves are driven by employment shocks or changes in the locations of firms. In column (1) and (1 ) we focus on individuals that had a nonvoluntary stop of their main contract in the previous year or in the year of the move. In column (2) we focus on individuals where the headquarter of the firm of their main contract moved. In column (3) we focus on individuals that changed their contract. In 32 We do not focus on the sample of people who moved post-reform. Rather we focus on the movers in the pre-reform compared to movers in the post-reform era. 33 Schmidheiny (2006) shows rich households are more likely to move to low-tax towns. 34 However, households without kids may also be able to engage in tax evasion more easily. The region of residence that an individual declares is the autonomous community where the children must attend school. But many of these households likely use private schools 24

27 general we find very similar point estimates across all of the categories, however, one category is insignificant in each case. In all columns, the insignificant category is the one with very few individual movers in it. Given that the estimates are not statistically different from each other, we conclude that the increases in the probability of moving are not being driven by firm-side responses. 4.8 Occupation and Industry The prior literature has been unable to answer the question whether policymakers can take the estimates derived for star scientists and athletes and apply these elasticities to the top of the income distribution more generally. The Spanish data we have access to is unique in that occupation and industry are reported in the data; this is not information that would be available when using U.S. tax return data. We test the external validity of focusing on star scientists and athletes using this occupation data. Although the number of athletes and star scientists are too small to focus on these groups specifically (see tables A.7 and A.8), we can aggregate to broader industry categories that allow us to study the heterogeneity across occupation and industry. This section also helps to inform the recent policy debate on the efficiency of tax schemes for top earners in specific occupations. Several OECD countries have preferential tax schemes for foreigners in high-income occupations. For example, Denmark has income tax exceptions for foreign scientists, Korea has exceptions for high-tech fields, Poland has exceptions for workers engaged in artistic, scientific, sport or expert activities, Switzerland has exceptions for managers and specialists. 35 In the United States, many states have aggressively passed jock taxes that target professional athletes, which enforce tax collections based on the number of duty days worked in a state. By focusing on the heterogeneity by occupation and industry, we can shed light on the efficiency of these tax schemes. To implement this, we estimate equation 8 with an interaction of ln(1 τ) i,j,t with dummy variables for occupation or industry categories. Table 8 shows the results by occupation. We present two set of results. In the first column for each occupation category listed, we show the effect on the probability of moving to a region relative to all other occupation categories. In the second column, we show the results in a particular occupation relative to all other occupations listed in only the lower panels in the table. In column (5), we present results from a single estimating equation where taxes are interacted with each of the occupation category dummy variables. When looking at this result, we identify the strongest effect for self employed occupations that are almost twice as large relative to all other occupations. This is consistent with these individuals being able to change their residence because their work location may also be flexible. Most 35 See OECD (2012) for a complete list of preferential tax rates for foreigners of particular occupations. 25

28 of the other three broad categories have similar degrees of responsiveness, but the lower level jobs in the other category seem to have less mobility. Although we have tried to group the occupations based on skill, the occupation categories do not follow a natural hierarchy. For this reason, we switch to industry classifications, where we use the one digit industry groupings in our data to break out the effects across fifteen industries. In table 9 we focus on the results by industry. We present two sets of results. In the upper panel, using a model that interacts the taxes with a particular dummy variable for industry k, we present the results in a particular industry relative to all other industries in the data. The second row showing the effects in all industries other than k has the flavor of a leave-one-out procedure that allows us to test the sensitivity of the estimates if we remove one industry. The results indicate that the coefficients generally remains stable. This is reassuring because it informs us that our results are not driven by a single industry. However, the first row, which represents the effect in industry k shows substantial heterogeneity. This is confirmed in the second panel of table 9 where we estimate a single estimating equation where taxes are interacted with dummy variables for each particular industry. We find the largest effects in the health, finance and real estate, and the other sector which includes high-ranking military officers. To compare this to the prior literature, athletes would fall under the category of arts and entertainment, while scientists could be under health or professional/scientific one of which exhibits a very high degree of tax-induced mobility. 36 Our general takeaway from these results is that the responsiveness to taxes varies substantially depending on occupation and industry. Thus, these results provide a cautionary tale that the prior literature focusing on star scientists and athletes may not generalize to other occupations. 5 Interpretation and Revenue Implications An important policy question is how this change affects tax revenue. For simplicity, and without loss of generality consider a two bracket tax system where all individuals in the top 1% are in the top bracket. Let τ be the lower bracket tax rate and τ be the top bracket threshold. Define N, which is a function of taxes, as the stock of individuals in the top 1%. Further define y, which is a function of taxes, as the average reported taxable income of each individual in the top bracket, y as the top bracket threshold, and R as revenue for a particular region. Revenue from the top taxpayers is equal to R = Nτy + Nτ(y y). Changing tax rates will have two effects: a mechanical effect as a result of the change in the tax rate and a behavioral effect resulting from migration and taxable income responses. Then we proceed by perturbing τ by totally differentiating the 36 We do not identify effects in the athletes category. This could be because this category includes other entertainers that may be less mobile because of specific productive amenities in particular cities. 26

29 revenue equation. The mechanical effect from the change in the top marginal tax rate is given by the formula dr m = N (y y) dτ (9) and the behavioral effect from a change in migration is given by dr b = dn [y τ + (y y) τ] (10) and the taxable income response is given by dr y = Nτ dy. (11) Thus, the total change in revenue is dr = dr m + dr b + dr y. Appendix A.9 shows that under relatively mild assumptions this reduces to: dr = N(y y)[1 (ɛ + ε)a τ ]dτ (12) 1 τ where a is the Pareto parameter for top income, ɛ is the taxable income elasticity and ε is the stock elasticity of migration with respect to the top marginal income tax rate. 37 We can calculate the revenue maximizing tax rate for the top marginal income tax bracket by setting expression 12 equal to zero. This yields: τ = (ɛ + ε)a (13) which differs from the standard formula in that it contains the stock elasticity. 5.1 Revenue Effect in Euros We estimate the revenue effects holding fixed the central government s tax rate at its 2014 level. Then we ask the question: at 2014 regional tax rates, how much does revenue change relative to if the region had simply mimicked the central government s tax rate on its tax base in 2014? Thus, for regions that raised their tax rate relative to the central government s tax rates, the mechanical effect is positive, but both the taxable income and mobility effect will be negative. For regions that decreased their tax rates relative to the central government tax rate, the effects will be opposite in sign. 38 Appendix 37 This also justifies our focus on the top marginal tax rate in the aggregate stock analysis. 38 This experiment is not designed to capture the effect of the changes in tax rates relative to Because the central government tax rate was also rising, this means all regional tax rates increased from 2010 to If this were the policy experiment, the taxable income response would be negative in all regions and the mechanical effect would be positive in all regions. When conducting the exercise this way, we similarly find the mechanical effect dominates. We want to calculate the revenue effects holding everything else constant including the federal tax rate. Further, we want to show the effect of 27

30 A.10 details how we implement this. Because we estimate the Pareto parameter and the mobility elasticity, all estimates have confidence bands. The presence of two estimated parameters means that we can estimate confidence bands using the parametric bootstrap. We assume the elasticity of taxable income is 0.15, which is slightly lower than the midpoint estimated in the literature in order to account for the Spanish tax base mainly being a tax on labor income. Table 10 shows the revenue effects on income above 94,000 Euro. The table shows that in all circumstances, the mechanical effect of higher or lower tax rates (column 1) is always the same sign as the total effect on tax revenue which includes all the behavioral effects (column 5). This means that governments are on the left side of the Laffer curve: raising tax rates relative to the central government rate increases tax revenue in the regions. For example, Madrid lowering its tax rate relative to the central tax rate corresponds to a decline of just under one percentage point on income above 94,000 Euro for the average person in the top 1%. This lower tax rate results in revenue falling by 52 million Euro. However, taxable income only rises by 4.5 million Euro and the additional new high taxpayers contribute 7 million Euro more. Thus, the behavioral effect from migration is only 13% of the mechanical effect and is comparable to the taxable income response. Column 6 shows that the total change in revenue from the reform lowers tax revenue by approximately one half of one percent of total personal income tax revenues in the region of Madrid. See figure A.11 for visual results. Comparing table 10 with simulations using a higher income threshold (not presented) it is interesting to note that the winners and losers are not always the same. This is because as shown in Figure 3 jurisdictions that raised their tax rate the most in the lower end of the top percentile are not always the regions that raised their top tax rates the most. Of course, the calculation of the revenue effects assumes that there are no fiscal externalities across various tax bases. For example, when Madrid lowers its tax rate, it obtains only a limited increase in income tax revenue from the increase in migration, but it likely also obtains additional revenue from other state and local tax sources such as the property tax (unless the vast majority of these moves are to a second home). While these additional revenue gains are likely going to increase the tax bases of other fiscal instruments, they are unlikely to outweigh the mechanical effect resulting from lower individual income tax rates. 5.2 Revenue Maximizing Tax Rates In table 11, we show the simulated revenue maximizing tax rate by state on top incomes, using equation 13. We define the top bracket as income above 94,000 Euro, which decentralization, which is a deviation from the counterfactual federal rate and not changes over time. 28

31 corresponds to the cutoff for the top 1%. We present 95% confidence bands using the parametric bootstrap. Column 1 shows that the revenue maximizing tax rate differs between 71% in Valencia and 76% in Madrid if individuals do not move and the elasticity of taxable income is We then can compare this to column 6, which uses our best estimate of the mobility elasticity and the same elasticity of taxable income as column 1. The revenue maximizing tax rate now ranges from 50% to 58%. This implies that mobility lowers the revenue maximizing tax rate by about 20 percentage points. However, for all regions, the confidence bands on these estimates are large enough that we cannot statistically reject the hypothesis that the revenue maximizing tax rate with no mobility is equal to the revenue maximizing tax rate in the presence of mobility. The remainder of the table shows the tax rates for other assumptions on the elasticity of taxable income. The fall in the revenue maximizing tax rates is larger than it would be in the United States because the Pareto parameter averages 2.4 across the regions in Spain and it is 1.4 in the United States. See figure A.12 for visual results. 6 Conclusion We find that individual income tax changes result in relatively small (stock) elasticities, but that the flow responses are relatively large. The flows of migrants are a relatively small fraction of the stock, so these large flow elasticities translate into relatively small changes in the stock of the rich in a given state. The revenue changes from increases or decreases in tax rates are small and the behavioral effects on tax revenue are much smaller than the mechanical effect resulting from a higher or lower tax rate. Although the recent economics literature has seen an increase in research on migration, we are the first study to focus in on individual level data in a country where mobility is reasonably low. Our elasticity estimates are large, but changes in the stock suggest the tax base effects are minimal. Thus, our results, at least in the short run, are consistent with Epple and Romer (1991) who show that local redistribution is feasible with migration. Despite this finding, if the Spanish nation is viewed as the common labor market for high-income Spanish taxpayers, then coordination of redistributive policy could result in welfare improvements (Wildasin 1991). In the long run, mobility is likely to rise over time given demographic shifts and technological innovations, which may in turn impose added constraints on the ability to engage in redistributive fiscal policy. References Agrawal, David R., and William H. Hoyt Commuting and Taxes: Theory, Empirics, and Welfare Implications. SSRN Working Paper. 29

32 Akcigit, Ufuk, Salome Baslandze, and Stefanie Stantcheva Taxation and the International Mobility of Inventors. American Economic Review, 106(10): Bakija, Jon, and Joel Slemrod Do the Rich Flee from High State Taxes? Evidence from Federal Estate Tax Returns. NBER Working Paper Bertoni, Marco, Stephen Gibbons, and Olmo Silva The Demand for Autonomous Schools. SOLE Working Paper. Bonhomme, Stéphane, and Laura Hospido. fc. The Cycle of Earnings Inequality: Evidence from Spanish Social Security Data. The Economic Journal. Bosch, Núria The Reform of Regional Government Finances in Spain. In IEB s World Report on Fiscal Federalism. IEB. Brülhart, Marius, and Raphaël Parchet Alleged Tax Competition: The Mysterious Death of Bequest Taxes in Switzerland. Journal of Public Economics, 111: Brülhart, Marius, Sam Bucovetsky, and Kurt Schmidheiny Taxes in Cities: Interdependence, Asymmetry, and Agglomeration. Handbook of Regional and Urban Economics, 5B. Conway, Karen Smith, and Jonathan C. Rork State Death Taxes and Elderly Migration - The Chicken or the Egg? National Tax Journal, 59(1): Conway, Karen Smith, and Jonathan C. Rork No Country for Old Men (Or Women) - Do State Tax Policies Drive Away the Elderly? National Tax Journal, 65(2): Durán, José María, and Alejandro Esteller Descentralización Fiscal y Política Tributaria de las CCAA: Un Primera Evaluación a Través de los Tipos Impositivos Efectivos en el IRPF. In La financiación de las comunidades aut nomas: Pol ticas tributarias y solidaridad interterritorial., ed. Núria Bosch and José María Durán. Universitat de Barcelona. Durán, José Maria, and Alejandro Esteller Exploring Personal Income Tax Diversity Among Spanish Regions. Tax Notes International. Epple, Dennis, and Thomas Romer Mobility and Redistribution. Journal of Political Economy, 99(4):

33 Esteller-Moré, Alejandro, and Dirk Foremny Elasticity of Taxable Income for Spanish Top Taxpayers. Working Paper2/2016. Eugster, Beatrix, and Raphaël Parchet Culture and Taxes: Toward Identifying Tax Competition. Discussion Paper no , Under Revision for Journal of Political Economy. Gideon, Michael Do Individuals Perceive Income Tax Rates Correctly? Public Finance Review, 45(1): Kleven, Henrik Jacobsen, Camille Landais, and Emmanuel Saez Taxation and International migration of Superstars: Evidence from the European Football Market. American Economic Review, 103(5): Kleven, Henrik J., Camille Landais, Emmanuel Saez, and Esben A. Schultz Migration, and Wage Effects of Taxing Top Earners: Evidence from the Foreigners Tax Scheme in Denmark. Quarterly Journal of Economics, 129: Martínez, Isabel Z Beggar-Thy-Neighbour Tax Cuts: Mobility after a Local Income and Wealth Tax Reform in Switzerland. Working Paper. Mirrlees, James A Migration and Optimal Income Taxes. Journal of Public Economics, 18(3): Moretti, Enrico, and Daniel Wilson The Effect of State Taxes on the Geographical Location of Top Earners: Evidence from Star Scientists. Federal Reserve Bank o San Francisco Working Paper OECD The Taxation of Mobile High-Skilled Workers. In OECD Tax Policy Study No. 21: Taxation and Employment OECD. Piketty, Thomas, and Emmanuel Saez Optimal Labor Income Taxation. Handbook of Public Economics, 5: Rubolino, Enrico, and Waldenström Trends and Gradient in Top Tax Elasticities: Cross-country Evidence, CEPR Discussion Paper Saez, Emmanuel, Joel Slemrod, and Seth H. Giertz The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1): Schmidheiny, Kurt Income Segregation and Local Progressive Taxation: Empirical Evidence from Switzerland. Journal of Public Economics, 90:

34 Schmidheiny, Kurt, and Michaela Slotwinski Behavioral Responses to Local Tax Rates: Quasi-Experimental Evidence from a Foreigners Tax Scheme in Switzerland. CESifo Working Paper Wildasin, David E Income Redistribution in a Common Labor Market. American Economic Review, 81(4): Wildasin, David E Global Competition for Mobile Resources: Implications for Equity, Efficiency, and Political Economy. CESifo Economic Studies, 52(1): Wildasin, David E Public Finance in an Era of Global Demographic Change: Fertility Busts, Migration Booms, and Public Policy. In Skilled Immigration Today: Prospects, Problems, and Policies., ed. Jagdish Bhagwati and Gordon Hanson, Oxford University Press. Wilson, John Douglas Income Taxation and Skilled Migration: The Analytical Issues. In Skilled Immigration Today: Prospects, Problems, and Policies., ed. Jagdish Bhagwati and Gordon Hanson. Oxford Scholarship. Young, Cristobal, and Charles Varner Millionaire Migration and State Taxation of Top Incomes: Evidence from a Natural Experiment. National Tax Journal, 64(2): Young, Cristobal, Charles Varner, Ithai Lurie, and Rich Prisinzano Millionaire Migration and the Demography of the Elite: Implications for American Tax Policy. American Sociological Review, 81(3):

35 Probability of Moving to Region Figure 1: Location Choice and Taxes: Individual Data Pre Reform log net of mtr Probability of Moving to Region Post Reform log net of mtr The figure shows the relationship between the probability of selecting to move to a given region and the log of the net of marginal (top income) tax rate. The unit of observation is mover-region. To construct the figure we regress a dummy variable for location choice (equals one if the movers selects that region and zero if the region is not selected) on a set of individual dummies and region dummies. Then we regress the log of the net of marginal tax rate on the same dummies. In the pre-reform period we use movers from 2005 to 2010 but use tax rates from 2011 to 2014 to see if post-reform tax rates have an effect on pre-reform migration. In the post-reform period we use movers from 2011 to 2014 and use the top tax rates for those years. After each regression, residuals are binned into twenty equally sized bins and a line of best fit placed through the binned data. Figure 2: Tax Rate Changes The figure shows top marginal tax rate changes (excluding federal rate changes) in percentage points from 2010 to (7,8] (6,7] (5,6] (4,5] (3,4] [2,3] No data 33

36 Figure 3: Tax Rate Changes Relative to Central Government Tax Rate (2014) mtr relative to central mtr in percentage points / income in tsd. of Euros The graph shows the change in the marginal tax rates for each state relative to what the tax rate would be if the regions just piggy backed on the federal tax rate in that same year. This shows the deviation in The vertical line shows the cutoff for the top 1%. Figure 4: Tax Rate Variation Over Time within std. dev Top 1% Top 2% Top 3% year The graph shows the standard deviation of marginal tax rates across alternative regions j for individual observations (within group variation) from 2005 to 2014 for different percentiles of the income distribution. Increasing variation indicates increasing dispersion of marginal tax rates across regions for a given tax payer. 34

37 Figure 5: Effect of Taxes on the Stock Ratio To construct the figure in the upper panel, we regress the log of the stock ratio in region d (called destination for convenience) relative to region o (called origin for convenience) on origin fixed effects and destination fixed effects. The same is done for the tax variable. The theoretically expected effect is positive as keeping more money in the destination state means tax rates are lower, which implies more migration to the destination, increasing the stock. The bottom panel, keeps the pairwise nature of the data, but only uses the log of population in a given region as the dependent variable and the log of the net of tax differential. In the left panel, and increase in what is kept at the destination region lowers the relative population of the origin region. In the right panel, an increase in what is kept in the destination region increases the relative population in the destination region. 35

38 Figure 6: Effect of Taxes on Stock Ratio: Placebo Tests Using Lower Income Groups To construct this figure in the upper panel, we regress the log of the stock ratio in region d (called destination for convenience) relative to region o (called origin for convenience) on origin fixed effects and destination fixed effects. The same is done for the tax variable, which is the log of the top bracket marginal net of tax rate in region d relative to region o. The only difference from the prior figure is that we use the stock ratios of individuals outside the top one percent and the stock ratios of other high-income earners not subject to top marginal tax rates (the top 5% excluding the top 1%). To construct the lower panel figure figure, we regress the stock ratio from pre-reform years ( ) on the fixed effects. The same is done for the tax variable, which is the top bracket marginal net of tax rate, but using post reform tax rates ( ) lagged back four years. Residuals are binned into twenty equally sized bins and the averages within the bins are plotted and a line of best fit placed through the binned data. The theoretically expected effect is zero given this is a placebo test. All figures use the same vertical scale as the first figure in Figure 5. Figure 7: Event Study of Stock Ratio Changes The left figure shows the raw averages of the stock ratios in region pairs where the net of tax rate increases in region d relative to region o following the reform. The stock ratio is the population in the top 1% n region d relative to region o. The right panel presents a formal event study where the treatment indicator is scaled by the average tax differential in the post-reform period between the regions. Thus, the vertical axis can be interpreted as the effect on the stock ratio of of a one percent increase in the net of tax rate in the destination region relative to the origin region.

39 Table 1: Aggregate Analysis: Effect on Stock Ratios of the Top 1% Baseline Specifications Addressing Changes to Taxable Income (1) (2) (3) (4) (5) (6) (7) (8) ln[(1 mtr d )/(1 mtr o )] 0.503* 0.482** 0.420* 0.524** * 0.539** 0.379* (0.288) (0.227) (0.247) (0.258) (0.337) (0.268) (0.258) (0.210) Origin FE? Y Y Y Y Y Y Y Y Destination FE? Y Y Y Y Y Y Y Y Year FE? N Y Y Y Y Y Y Y Demographic Controls? N Y Y Y Y Y Y Y Economic Controls? N N Y Y Y Y Y Y Industry Controls? N N N Y Y Y Y Y Destination By Year N N N N Y N N N Destination Time Trend N N N N N Y N N Robustness Check Control for Top Income Ratio Adjust Stock Ratio for Churn in Income Distribution Number of Observations The estimating sample focuses on the top 1 percent of the income distribution. The dependent variable is the log of the stock ratio, which is the number of individuals in the top 1% in region d relative to region o. The log of net of tax rate differential is the ratio of the net of tax rate in region d relative to region o and uses the top bracket marginal tax rate. The expected sign is positive. Each columns presents different specifications as noted in the rows below. The first set of specifications are the baseline specifications. The last two columns address potential taxable income responses by controlling for income in the top 1% and by adjusting the stock for the number of people that transition out of the top 1% relative to the prior year. The estimates represent the elasticity of the ratio. The elasticity of the stock in a given region can be obtained by dividing the point estimates by two. Standard errors allow for three-way clustering (state pair, origin-year, destination year). *** p<0.01, ** p<0.05, * p<0.1 Table 2: Baseline Individual Analysis: Marginal Tax Rates (1) (2) (3) (4) (5) (6) (7) ln(1 mtr i,j,t ) 0.521* 0.539* 0.584** 0.520* 0.531* 0.538* 0.555** (0.301) (0.277) (0.271) (0.278) (0.276) (0.277) (0.271) place of origin *** *** *** *** *** *** (0.060) (0.058) (0.060) (0.060) (0.060) (0.059) place of birth 0.192*** 0.190*** 0.193*** 0.193*** 0.193*** 0.190*** (0.026) (0.026) (0.027) (0.026) (0.026) (0.026) place of first work 0.188*** 0.180*** 0.188*** 0.188*** 0.187*** 0.180*** (0.019) (0.019) (0.019) (0.019) (0.019) (0.019) work place 0.249*** 0.216*** 0.251*** 0.253*** 0.247*** 0.222*** (0.041) (0.043) (0.041) (0.041) (0.040) (0.044) ln(distance) *** *** *** *** *** *** (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) individual fixed effects Y Y Y Y Y Y Y j by year fixed effects Y Y Y Y Y Y Y j by education N N Y N N N Y j by age N N N Y Y N Y j by age squared N N N N Y N Y j by male N N N N N Y Y controls N Y Y Y Y Y Y observations 14,775 14,775 14,775 14,775 14,775 14,775 14,775 R Column (1) estimates a variant of equation 7 while all remaining columns estimate variants of equation 8. In all specifications the estimating sample uses pre- and post-reform movers in the top 1% of the income distribution. The dependent variable equals one if the region is selected. The independent variable of interest is the log of the net of tax rate where the person specific marginal tax rate is used. Column (1) uses only alternative fixed effects by year and individual fixed effects. Column (2) adds the elements of z i,j,t listed in the table. Columns (4)-(8) add various variables interacted by the regions (age, age squared, education, and male), x i,t ι j, to account for counterfactual wages. All standard errors are clustered two-ways: region-year clusters and individual clusters. *** p<0.01, ** p<0.05, * p<0.1

40 Table 3: Baseline Individual Analysis: Average Tax Rates (1) (2) (3) (4) (5) (6) (7) ln(1 atr i,j,t ) 1.340* 1.384* 1.501** 1.337* 1.367* 1.382* 1.431** (0.784) (0.720) (0.704) (0.722) (0.718) (0.720) (0.705) place of origin *** *** *** *** *** *** (0.060) (0.058) (0.060) (0.060) (0.060) (0.059) place of birth 0.193*** 0.190*** 0.193*** 0.193*** 0.193*** 0.190*** (0.026) (0.026) (0.026) (0.026) (0.026) (0.026) place of first work 0.187*** 0.180*** 0.188*** 0.188*** 0.187*** 0.180*** (0.019) (0.019) (0.019) (0.019) (0.019) (0.019) work place 0.250*** 0.217*** 0.252*** 0.254*** 0.248*** 0.223*** (0.040) (0.043) (0.041) (0.041) (0.040) (0.044) ln(distance) *** *** *** *** *** *** (0.009) (0.009) (0.009) (0.009) (0.009) (0.009) individual fixed effects Y Y Y Y Y Y Y j by year fixed effects Y Y Y Y Y Y Y j by education N N Y N N N Y j by age N N N Y Y N Y j by age squared N N N N Y N Y j by male N N N N N Y Y controls N Y Y Y Y Y Y observations 14,775 14,775 14,775 14,775 14,775 14,775 14,775 R First Stage Coefficient 0.389*** 0.389*** 0.389*** 0.389*** 0.388*** 0.389*** 0.388*** (0.017) (0.017) (0.017) (0.017) (0.016) (0.017) (0.016) F-statistic Column (1) estimates a variant of equation 7 while all remaining columns estimate variants of equation 8. In all specifications the estimating sample uses pre- and post-reform movers in the top 1% of the income distribution. The dependent variable equals one if the region is selected. This table uses the person specific average tax rate rather than marginal tax rate. We instrument for the net of average tax rate using the net of marginal tax rate for the individual. All standard errors are clustered two-ways: region-year clusters and individual clusters. The bottom panel shows the first stage relationship between marginal and average tax rates. We present the Kleibergen-Paap rk Wald F statistic as a test of instrument strength. *** p<0.01, ** p<0.05, * p<0.1 Table 4: Individual Analysis: Different Percentiles Across the Income Distribution Using Average Tax Rates (1) (2) (3) Top 3% Top 2% Top 1% ln(1 atr i,j,t ) ** (0.398) (0.392) (0.705) individual fixed effects Y Y Y j by year fixed effects Y Y Y x i,t ι j Y Y Y controls: z i,j,t Y Y Y observations 42,690 29,445 14,775 F Statistic This table use the net of average tax rate. We instrument for the net of average tax rate using the net of marginal tax rate for the individual. We present the Kleibergen-Paap rk Wald F statistic as a test of instrument strength. Column (1) focuses on the top 3%, column (2) focuses on the top 2% and column (3) focuses on the top 1%. *** p<0.01, ** p<0.05, * p<0.1

41 Table 5: Placebo Test (1) (2) (3) (4) Marginal Tax Average Tax Post- Reform Pre- Reform Post- Reform Pre- Reform ln(1 t i,j,t ) 0.589** ** (0.276) (0.210) (0.653) (0.511) individual fixed effects Y Y Y Y j by year fixed effects Y Y Y Y x i,t ι j Y Y Y Y controls: z i,j,t Y Y Y Y observations 6,075 6,495 6,075 6,495 F-statistic This table constructs a placebo test by verifying that post-reform tax rates have no significant effect on pre-reform migration patterns. The post-reform sample is restricted to migrants in the post-reform period, while the pre-reform sample is restricted to individuals moving in the pre-reform period. To do this we construct the mean tax rate for each alternative and individual in the post-reform period Column (1) and (3) shows that even using this mean tax rate, we can reproduce our results using the annual tax rate. Columns (2) and (4) then use migration decisions in the period but using the mean tax rate constructed from the period Column (1) and (2) uses the person specific marginal tax rate. Columns (3) and (4) uses the average tax rate and instruments for it using the marginal tax rate. All standard errors are clustered two-ways: region-year clusters and individual clusters. We present the Kleibergen-Paap rk Wald F statistic as a test of instrument strength. *** p<0.01, ** p<0.05, * p<0.1 Table 6: Heterogeneity of Effects by Personal Characteristics ln(1 atr i,j,t ) (1) (2) (3) (4) Younger than ** (0.821) Older than (0.773) Kids (1.037) No Kids 1.709** (0.671) Men (0.784) Women 2.724** (1.066) University Degree 1.475* (0.789) No University Degree (0.970) individual fixed effects, j by year fixed effects, x i,t ι j, Y Y Y Y and controls: z i,j,t observations 14,775 14,775 14,775 14,775 F Statistic The tax rate is interacted with an indicator variable for the group category. This table presents results for the average tax rate. We instrument for the net of average tax rate using the net of marginal tax rate for the individual. The interaction term is instrumented for using the instrument interacted with the indicator variable for the group. All standard errors are clustered two-ways: region-year clusters and individual clusters. We present the Kleibergen-Paap rk Wald F statistic as a test of instrument strength. *** p<0.01, ** p<0.05, * p<0.1

42 Table 7: Heterogeneity of Effects by Job Characteristics ln(1 atr i,j,t ) (1) (1 ) (2) (3) Not Fired 1.630** 1.423** (0.695) (0.683) Fired (0.965) (1.032) No Firm Location Change 1.446** (0.703) Firm Location Change (1.227) No Contract Change 1.407** (0.713) Contract Change 1.659* (0.995) individual fixed effects, j by year fixed effects, x i,t ι j, Y Y Y Y and controls: z i,j,t observations 14,775 14,775 14,775 14,775 i observations (first group) i observations (second group) F-statistic The tax rate is interacted with an indicator variable for the group category. This table presents results for the average tax rate. We instrument for the net of average tax rate using the net of marginal tax rate for the individual. The interaction term is instrumented for using the instrument interacted with the indicator variable for the group. Fired / not fired means that the variable is equal to 1 if the individual had a non-voluntary stop of contract on the main contract. Column (1) is fired in the year prior to moving and column (1 ) is fired in the year of moving. Firm location change / no location change is equal to 1 if the headquarter of the firm of the main contract changes but the individual does not change firms in the year of moving. Contract change / no change is equal to 1 if the individual changes the firm of their main contract in the year of move. All standard errors are clustered two-ways: region-year clusters and individual clusters. We present the Kleibergen-Paap rk Wald F statistic as a test of instrument strength. *** p<0.01, ** p<0.05, * p<0.1

43 Table 8: Heterogeneity of Effects by Occupation ln(1 atri,j,t) (1) (1 ) (2) (2 ) (3) (3 ) (4) (4 ) (5) Self-Employed Not Self-Employed Engineers, college graduates and senior managers Not... Technical engineers and managers, graduate assistants, administrative managers Not... Other Not Other 2.501*** 2.501*** 2.495*** (0.934) (0.934) (0.968) (0.762) (0.762) * (0.759) (0.798) (0.787) 1.782** 1.871* (0.840) (0.991) (1.315) (2.213) (1.323) 1.406** (0.671) (1.533) (2.084) (3.018) (2.109) 1.434** (0.704) (1.273) individual fixed effects, j by year fixed Y Y Y Y Y Y Y Y Y effects, xi,t ιj, and controls: zi,j,t observations 14,775 14,775 14,775 11,895 14,775 4,725 14,775 1,980 14,775 F Statistic The tax rate is interacted with an indicator variable for the occupation category. In columns (1)-(4) without a prime, we show the effects for the category listed in a row relative to all other observations. In columns with a prime, we show the effect for the category listed relative to all other occupations not given in the rows above. For example, in column (2) we focus on engineers, college grads and senior managers relative to all other occupations including the self-employed. But, in column (2 ) all other occupations excludes the self-employed. In column (5) we show a single model estimating all the effects. This table presents results for the average tax rate. We instrument for the net of average tax rate using the net of marginal tax rate for the individual. The interaction term is instrumented for using the instrument interacted with the indicator variable for the group. The other category includes all occupations not in the previous three groups; these occupations include non-graduate assistants, administrative officers, subordinates, administrative assistants, first and second class officers, third class officers and technicians, and labourers. This category does not include missing observations, which represent the not other category in column (4 ). All standard errors are clustered two-ways: region-year clusters and individual clusters. We present the Kleibergen-Paap rk Wald F statistic as a test of instrument strength. *** p<0.01, ** p<0.05, * p<0.1

44 Table 9: Heterogeneity of Effects by Industry ln(1 atri,j,t) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Industry k versus All Other Industry Industry k Not Industry k ** *** * (1.506) (1.457) (3.063) (1.330) (1.145) (1.001) (2.119) (0.862) (0.889) (1.494) (1.875) (2.778) (1.152) (1.313) 1.373* 1.358* 1.466** 1.448** 1.495** 1.456** 1.492** 1.366* 1.475** 1.479** 1.458** 1.459** 1.408* 1.380* (0.706) (0.709) (0.708) (0.700) (0.725) (0.724) (0.704) (0.698) (0.743) (0.711) (0.704) (0.715) (0.741) (0.707) Single Regression Coefficients from a Single Regression With Taxes Interacted With a Dummies for Each Industry ** *** * (1.516) (1.479) (3.123) (1.317) (1.197) (1.049) (2.084) (0.906) (0.920) (1.505) (2.022) (2.723) (1.152) (1.327) Agriculture Manufacturing Electricity Construction Wholesale/Retail Transportation Information Financial Professional/Scientific Administrative Education Health Arts/Entertainment Other Short Industry Description individual fixed effects, j by year fixed effects, xi,t ιj, and controls: zi,j,t Y Y Y Y Y Y Y Y Y Y Y Y Y Y observations 14,775 14,775 14,775 14,775 14,775 14,775 14,775 14,775 14,775 14,775 14,775 14,775 14,775 14,775 The tax rate is interacted with an indicator variable for the industry category. In the upper panel, we show the effects for the category listed in a row relative to all other industries. In the second panel, we show a single model estimating all the effects for each industry; thus the row in the second panel represents a single regression. This table presents results for the average tax rate. We instrument for the net of average tax rate using the net of marginal tax rate for the individual. The interaction term is instrumented for using the instrument interacted with the indicator variable for the group. Detail industry categories are (1) Agriculture, forestry, and fishing, (2) Manufacturing, (3) Electricity, gas, steam, and air conditioning supply, (4) Construction, (5) Wholesale and retail trade, repair of motor vehicles and motorcycles; accommodation and food service activities, (6) Transportation and storage, (7) Information and communication, (8) Financial and insurance activities; real estate activities, (9) Professional, scientific, and technical activities, (10) Administrative and support service activities, (11) Education, (12), Human health and Social work activities, (13) Arts, entertainment, and recreation, and (14) Other, which includes all other industry codes that have only a small number of observations including water supply, sewage, waste management and remediation activities; and public administration and defense; compulsory social security. All standard errors are clustered two-ways: region-year clusters and individual clusters. *** p<0.01, ** p<0.05, * p<0.1

45 Table 10: Revenue Changes in Thousands of Euros Relative to Mimicking Central Government, Income Above 94,000 Euros (1) (2) (3) (4) (5) (6) Response dr m dr y dr b dr b (no aprox) dr percent Andalucía [-4567,-4121] [-15461,918] [-14357,856] [27400,43816] [.648,1.036] Aragón [203,258] [-44,826] [-40,729] [-2305,-1427] [-.203,-.126] Asturias, Principado de [-1018,-700] [-3125,175] [-2698,155] [4251,7612] [.478,.856] Balears, Illes [139,184] [-32,586] [-23,412] [-1388,-765] [-.169,-.093] Canarias [-256,-192] [-807,46] [-726,43] [1286,2149] [.115,.192] Cantabria [-291,-177] [-867,47] [-725,41] [973,1915] [.211,.414] Castilla y León [405,469] [-93,1562] [-84,1395] [-3962,-2303] [-.221,-.128] Castilla - La Mancha [240,292] [-55,954] [-51,884] [-2715,-1700] [-.244,-.153] Cataluña [-1482,-1359] [-5056,295] [-4276,250] [7211,12566] [.096,.168] Comunitat Valenciana Extremadura Galicia Madrid, Comunidad de Murcia, Región de Rioja, La [-517,-389] [-1633,95] [-1386,82] [2254,4001] [.452,.802] [330,398] [-74,1300] [-66,1136] [-3790,-2409] [-.21,-.133] [4315,4670] [-935,15922] [-827,14166] [-49269,- [-.588,-.387] 32393] [-168,-129] [-534,31] [-467,27] [1006,1578] [.131,.205] [29,51] [-8,150] [-6,109] [-328,-165] [-.135,-.068] This table calculates the changes in revenue in thousands of Euros realized by the region not mimicking the central government tax rate and assuming the federal tax rate did not change. We define the top tax rate on income above 94,000 Euro which is the top 1%, approximately. Column (1) shows the mechanical effect given by equation A.5; there are no confidence bands because no parameters are estimated to derive it. Column (2) shows the taxable income response given by equation A.13. Column (3) shows the mobility response given by equation A.12, while column (4) shows the mobility response given without approximation by equation A.8. Column (5) shows the total change in revenue given by equation A.14. Column (6) shows the total change in revenue as a fraction of regional revenue raised from the personal income tax (across all taxpayers). In all columns, we estimate the Pareto parameter for each region using the top 1% of the income distribution in Spain. We use our estimated mobility elasticity and standard error and assume the elasticity of taxable income is We present the change in revenue along with a 95% confidence interval, which is obtained using the parametric bootstrap.

46 Table 11: Revenue Maximizing Tax Rates, Income Above 94,000 Euros (1) (2) (3) (4) (5) (6) Formula Used Equation 13 Equation A.16 Mobility Elasticity 0 estimated estimated estimated estimated estimated ETI Andalucía [.739,.758] [.434,.965] [.395,.788] [.363,.671] [.335,.582] [.389,.778] Aragón [.725,.77] [.429,.963] [.39,.791] [.357,.671] [.33,.584] [.417,.777] Asturias, Principado de [.69,.764] [.399,.956] [.36,.771] [.328,.65] [.301,.562] [.383,.755] Balears, Illes [.693,.749] [.394,.949] [.356,.769] [.325,.644] [.299,.55] [.349,.752] Canarias [.714,.768] [.419,.953] [.38,.786] [.347,.662] [.321,.576] [.38,.771] Cantabria [.663,.764] [.377,.953] [.338,.762] [.307,.638] [.28,.55] [.342,.744] Castilla y León [.715,.744] [.409,.958] [.371,.772] [.34,.65] [.312,.56] [.362,.761] Castilla - La Mancha [.733,.77] [.434,.96] [.396,.791] [.363,.675] [.336,.588] [.396,.781] Cataluña [.717,.734] [.404,.954] [.366,.766] [.334,.641] [.309,.554] [.367,.754] Comunitat Valenciana [.692,.726] [.384,.946] [.347,.754] [.316,.626] [.29,.533] [.341,.737] Extremadura [.697,.754] [.399,.954] [.361,.768] [.329,.647] [.305,.557] [.359,.756] Galicia [.737,.772] [.439,.958] [.401,.795] [.368,.68] [.34,.593] [.406,.783] Madrid, Comunidad de [.755,.769] [.451,.965] [.412,.803] [.38,.688] [.351,.6] [.432,.789] Murcia, Región de [.735,.783] [.443,.962] [.404,.797] [.37,.684] [.342,.599] [.417,.789] Rioja, La [.657,.77] [.375,.948] [.335,.761] [.304,.638] [.277,.552] [.343,.746] This table calculates the revenue maximizing top tax rate. We define the top tax rate on income above 94,000 Euro which is the cutoff to be in the top 1%. In columns (1)-(5) we use equation 13 to estimate the revenue maximizing tax rate, while in column (6) we use equation A.16, which involves fewer assumptions. In column (1) we assume that the mobility elasticity is zero. In all other columns, the word estimated means we use the flow mobility elasticity and standard errors in Table A.9 Column 3, to obtain the stock elasticity. Columns (2) - (6) make different assumptions on the elasticity of taxable income. In all columns, we estimate the Pareto parameter for each region using the top 1% of the income distribution in each region in Spain. We present the revenue maximizing tax rate along with a 95% confidence interval, which is obtained using the parametric bootstrap.

47 A Appendices (Online Only) A.1 Additional Reform Figures Figure A.1 shows the region tax rates (inclusive of the federal rate) for 2010 and 2014; notice that in 2010 Madrid s tax rate was only slightly lower. Figure A.2 shows the level of top marginal tax rates in Spain for the years in between the prior figure. The reforms have been talked about substantially in the popular press as indicated by Figure A.3. Figure A.5 is analogous to Figure 3, except that it is given for the changes in 2011, 2012, and 2013; this figure shows the changes in the marginal tax rates across the income distribution relative to the scenario where the state would have just copied the federal marginal tax rates. Figure A.6 shows the income distribution of the top 1% using tax data. Figure A.7 shows the marginal tax brackets in Madrid and Barcelona overlayed on top of the income distribution; notice large differentials only really arise in the top percent of the distribution. A.2 Descriptive Evidence Tables A.1 and A.2 show the transition matrix between regions for individuals in the top 1% of the income distribution. The first table shows the transition matrix for the post-reform era and the second table shows the transition matrix for the pre-reform era. Table A.3 shows the pairwise migration flows between regions for the top 5% of the income distribution over the course of 2011 to These numbers represent the total number of migrants observed in our 4% random sample of the population. To obtain full population numbers multiply by 25. A.3 Correlation of State Characteristics and Tax Changes In this section, we show that the size of the state tax changes following the reform are not statistically associated with characteristics of the top 1% in the pre-reform period. In particular, the pre-reform in-migration rate, the stock of individuals in the top 1%, and the number of top 1% movers to not appear to predict the size of the tax change. Given that this analysis is limited to a cross-section of regions, this analysis is simply meant to be descriptive. Nonetheless, these types of variables also have small coefficients. The variables with large coefficients are the presence of a right wing government, debt per capita, and incomes in the region. Although not statistically significant, the large coefficients suggest these may be more important factors. This helps to allay concerns that governments changed their tax rates because they had expectations about how the migration rates of the top 1% or the stock of the top 1% in their region would respond. The results are shown in Table A.4 where the dependent variable is the size of the tax 45

48 change and in Table A.5 where the dependent variable is a dummy that equals one if the region became high-tax. A.4 Summary, Industry and Occupation Table A.6 shows summary stats for the top 1%. Tables A.7 and A.8 show the industry and occupation of the most common categories of migrants from the top 1% in the postreform period. Most industries and occupations are high-skill and previously studied subgroups such as athletes feature prominently in the distribution. Nonetheless, access to nationally representative Social Security data allows us to study a much broader set of occupations and industries than many studies in the prior literature. It also paints a picture of what the top 1% of the income distribution looks like in Spain. A.5 Justification of Stock Model of Migration Moretti and Wilson (2015) estimate a flow model of migration.lt o index the origin and d index the destination in year t. The reduced form is given by: ln(p odt /P oot ) = β[ln(1 mtr dt ) ln(1 mtr ot )] + ζ o + ζ d + ζ t + ν odt (A.1) where we have added time fixed effects to their model. The left hand side variable ln(p odt /P oot ) is the log odds ratio where P odt is the the share of the population that moves from state o to state d in year t and P oot is the fraction of the population that stays in state o in the same year. On the right hand side of the estimating equation are fixed effects given by ζ including: origin fixed effects, destination fixed effects, state pair (or origin by destination fixed effects) and time fixed effects. The net of tax rate with respect to the top marginal rate is given by 1 mtr dt [1 mtr ot ] in the destination [origin] region. Unlike Moretti and Wilson (2015), we prefer using a stock rather than flow model of migration in our aggregate analysis. In particular, notice that the log odds ratio will be missing whenever there is no migration between region. Given we only have a 4% sample of the full population this means we have a large number of missing observations which raises selection concerns. Second, our panel is much shorter than that of Moretti and Wilson (2015) which prevents us from being able to do important robustness checks like including region by year dummy variables. In addition, the identification strategy in Moretti and Wilson (2015) fundamentally relies on a diff-in-diff approach, but where the outcome is migration flows across regions rather than stocks of top earners across regions. Compared to a standard random utility model where individuals decide every period where to locate, irrespective of where they are, these flow specifications rely on a model where utility of being in any location is 46

49 always conditional on where individuals are located to start with in period t (the origin region). Identification relies on the assumption that moving costs ρ od are asymmetric across regions. This assumption has an important consequence: it generates some nonrandom permanent migration flows across regions that do not come from changes over time in amenities / characteristics across regions. In terms of identification, this means that the strategy is a little bit different from what is usually done in location choice models. Traditionally, the identification relies on the assumption that, absent tax changes, differences in stocks of individuals across regions are fixed over time. In the flow model, the assumption is that region-pair migration flows are fixed over time. For this reason, and given the large number of pairs with no observed migration flows and the length of our sample, we prefer the stock analysis. A.6 Probability of Moving (Anywhere) Model A.6.1 Methods We focus on the 2011 reform as the event because it is the year with the most variance in the state tax rates. As shown in Figure 4, earlier state changes were much less common and the later (2012) changes feature less variation across the regions. 39 Table A.10 presents a basic analysis where we estimate: m i,j,t = βln(1 mtr) j,t + α i + ι t + ε i,j,t (A.2) where m i,j,t is equal to 1 if an individual i moves from region j in year t and 1 mtr j,t is the net of tax rate in the origin region. For the marginal tax rate we use the top marginal tax rate in the region that the individual was living in (for movers this is the origin region and for stayers this is both the origin and destination region). We also include time and individual fixed effects. We focus on the top marginal tax rate to capture tax policy changes over time rather than tax changes due to changes in income. 40 results show small and generally statistically insignificant effects. In general, the To address issues of endogeneity, we also use a generalized difference-in-difference using an event study specification: m i,j,t = α i + ι t + T reat i [ 2 π y 1{t t i = y} + y= 4 ] 3 γ y 1{t t i = y} + ε i,t (A.3) where T reat i is equal to one if an individual is in the top one or two percent of the 39 The changes are larger in 2012 for each state, but this is because the federal tax rate also increased in Although we restrict our sample to individuals who stay in the top percent for the entire sample, we are still worried about income changes. y=0 47

50 income distribution in t i = 2011 and onward (the year of major tax changes) and 0 otherwise. 41 As a control group, we use individuals in the 90th to 95th percentiles of the income distribution that are not substantially affected by the reforms on very high income individuals. 42 When defining treatment, we run a split sample analysis where we estimate equation A.3 separately for individuals in regions that increased their taxes relative to the federal system and for individuals in regions that decreased their taxes relative to the federal system (see Figure 3). When doing this, we define the region based on where individuals lived one year prior to the reform (the origin region). The reason for this is that pooling these two regions would confound two different types of treatments: individuals living in regions that saw tax increases are more likely to move and regions that became the lowest tax regions are less likely to move. For example, in the most extreme case, an individual living in the lowest tax region should not increase the probability of moving at all. The dummy variables 1{t t i = y} measure the time relative tax reform change (thus the index y can be thought of as time since the event). The coefficients π y and γ y measure the relationship between the tax increases of 2011 and the probability of moving. The π y presents the coefficients in the four years prior to the event and the γ y presents the effect for the four years after the event. The year prior to the event (-1) is omitted from the regression so all coefficients are relative to that quarter. The generalized difference-in-difference method allows the researcher to have a direct test of the parallel trend assumption by verifying π y is around zero. Then, the γ y identify the treatment effect over time following the reform. We include individual and time fixed effects but do not include any controls, however, the results are robust to controlling for income. By creating the control group we remove the possibility that tax rates may have changed because of trends in a region. The control group of individuals in the 90th to 95th percentile are affluent enough that they are still mobile, but their incomes are low enough that they are not treated by the large tax rate changes in the top brackets. Nonetheless, the π y provide a direct test of whether they are a valid control group. 41 In the main analysis we do not want to define the treatment group as those in the top 1% in If defined this way, the effect of taxes on these individuals may decline over time simply because their incomes are likely to revert to the mean (and thus they are no longer affected by the tax reforms). To correct for this, we define the treatment group as entirely being composed of individuals that are always in the top 1% for every year after the reform and where the control group are individuals in the 90th to 95th percentile for every year after the reform. We also show the results when we define treatment simply based on being in the top 1% in the year of the reform. 42 If the control group perceives they will have higher income in the future, this group is partially treated and our effects represent lower bounds. To reduce this possibility we exclude the 96th to 98th percentile from our control group. 48

51 A.6.2 Results We show the baseline results in Figure A.9. Recall that the treatment group contains members of the 1% for all years following for the reform. In each figure, the upper panel uses people that resided in regions that lowered taxes relative to the federal average prior to the reform as the treatment group. In the lower panel, both the treatment and control group are restricted to people residing in regions prior to the reform that increased their tax rates relative to the federal average. The pre-trends are not statistically different from zero; if anything there is a slight downward trend in the second panel suggesting we may underestimate the effect. When looking at the upper panel, the probability of moving jumps up slightly in the year of the reform, but it is not statistically significant. When looking at the lower panel for residents of tax increasing regions, a small jump is evident that persists for three years. Theoretically, we might expect no effect on residents in regions that lower the tax rate, 43 but positive increases in mobility for individuals originating from regions that increased their tax rates. The second panel is consistent with this, but overall no statistically significant change in the probability of moving is detected. 44 In terms of the magnitude of the effect, the tax reforms appear to have an effect of less than one quarter of one percentage point. Figure A.10 shows similar effects when not addressing mean reversion and defining the treatment and control group based on their percentile in t i = We interpret these results as the tax reform having very mild effects that are statistically insignificant on the probability of moving. The results are similar if we use percentiles in the income distribution from 90% to 98% as controls. A.6.3 Probability Model Robustness Table A.10 shows the results estimating a panel data regression of the form given by equation A.2. This approach yields effects that are very small and not statistically significant. Theoretically, when you get to keep more money after-taxes in your origin region, you will be less likely to move. However, consistent with the results to follow, we find no effect in these simple panel data regressions. A.7 Individual Analysis Robustness Table A.12 shows results where the dependent variable is the net of average tax rate. In this table, however, we do not instrument for the average tax rate which is endogenous 43 However, we also may expect a small increase in the probability of moving in these regions because this set of regions contains regions other than the state with the lowest tax rate. Thus, although these regions all lowered their tax rates relative to the federal average, they are not all the absolutely lowest tax region and thus the presence of the tax differential with the lowest tax region may have some positive effect on migration. 44 One explanation could be that we do not observe migration outside of Spain. 49

52 to earnings. The results provide a useful benchmark to compare to the IV results. In general, these results are smaller in absolute value. This could be due to endogeneity of the average tax rate or because of measurement error in the average tax rate. Table A.13 shows a robustness check that removes individuals near the bracket thresholds of any state. The justification that the marginal tax rate is exogenous to income requires individuals do not change tax brackets across the various alternative regions. This could happen if an individual is close to any tax bracket across all of the j alternatives. Thus, to verify the instrument is robust to this possibility, we exclude individuals that could possibly change brackets because they are near any state level threshold. After doing this, the marginal tax rate is definitely exogenous to earnings and the results are very similar to our baseline IV estimates. Overall, our conclusion is that taxes have a significant effect on location choices and that this result is highly stable across various specifications, sample restrictions and robustness checks. A.8 Individual Analysis: Non-linear Models As an alternative to the linear probability model we estimate by OLS, equation 8 could be estimated by a multinomial logit model. This, however, only allows us to estimate the reduced form model with respect to the marginal tax rate and not to implement the previous IV strategy. Furthermore, interpretation of coefficients is less straightforward, in particular when we investigate heterogeneous effects with interaction terms. Nevertheless, apart from providing logit estimates as a robustness check, the previous literature (for example, Kleven, Landais and Saez (2013), Akcigit, Baslandze and Stantcheva (2016)) has shown that estimating the coefficient of interest in a non-linear fashion is extremely useful because the estimated coefficients can, under some assumptions, directly be interpreted as an approximation of the elasticity. If the error term is type I extreme value distributed, the flow elasticity can be computed as in equation the text. Given that P is relatively small in our case, e β and β is a direct estimate of this flow elasticity. To facilitate convergence, we focus on movers in post-period. Table A.14 is organized in the same fashion as Table 3 in the text, but estimates the coefficient by multinomial logit. 45 The estimated coefficients (flow elasticities) are in the range of 7 to 13.5 and therefore comparable to our aggregate elasticities estimated using the flow models. Our 45 An alternative to the alternative specific choice model implemented here is using a simple conditional choice model and forcing probabilities across cases (the j s) to sum up to unity as proposed by Bayer, Ferreira and McMillan (2007). Doing so results in slightly lower elasticities. This can partially be explained by the fact that this procedure ignores irrelevant alternatives, in our case the j s which have never been chosen as a region of destination. 50

53 preferred specification (7) controlling for all fixed effects and other variables obtains a value of This number can be converted to a stock elasticity. 47 Although the flow elasticity of 13 is very large (the prior literature estimates are between 1 and 3), converting to a stock elasticity yields an estimate that is near 0.20, which is smaller than the stock elasticity in Moretti and Wilson (2015) and consistent with our aggregate analysis. The reason for a larger flow elasticity, but a smaller stock elasticity is that the flow of migrants in Spain are much smaller than in U.S. data. For this reason, the response of the flows is large relative to the amount of flows, but this has a much smaller effect on the relatively large stock of the top 1%. A.9 Derivation of Revenue Response In this section, we derive the revenue response. The taxable income derivation follows Saez, Slemrod and Giertz (2012). Maintaining all other assumptions given in the text, we can write tax revenue as: R = Nτy + Nτ(y y). (A.4) Changing top tax rates will have two effects: a mechanical effect as a result of the change in the tax rate and a behavioral effect resulting from migration and responses of taxable income. We proceed by perturbing the top marginal tax rate τ by totally differentiating the revenue equation. As in the text, the mechanical effect from the change in the top marginal tax rate is given by the formula dr m = N (y y) dτ (A.5) and the behavioral effect from a change in migration is given by dr b = dn [y τ + (y y) τ]. (A.6) 46 Note that standard errors are smaller here because the estimation procedure does not allow for two-way clustering. We allow for correlation at the region-year level similar to Akcigit, Baslandze and Stantcheva (2016). 47 If the number of top income earners in period t is N t then the number of top earners in the next period is N t+1 = N t + where is the number of migrants (assuming the birth and death rates are equal). ε = 1 τ N Then the flow elasticity is given by e = 1 τ dn d(1 τ) d d(1 τ) > 0 and the stock elasticity is given by > 0. Noting that the change in the stock of top earners must equal the change in the number of migrants (d = dn), we can express ε S = e flows N where flows represents the gross flows. 51

54 The behavioral taxable income effect 48 arises of the form: dr y = Nτ dy. (A.7) Then, define the elasticity of taxable income, ignoring the possibility of shifting to a lower bracket, as ɛ = 1 τ y dy d(1 τ) respect to the top marginal tax rate as ε = 1 τ N can express equation A.6 as > 0 and define the stock elasticity of mobility with dn d(1 τ) > 0. Using these expressions, we εn( τy + τ(y y) )dτ < 0 1 τ (A.8) and equation A.7 as: τ ɛ(ny )dτ < 0. (A.9) 1 τ Notice that in the standard elasticity of taxable income model, summing A.7 and A.5 yields where a = y y y τ y N(y y)[1 ɛ 1 τ y y ]dτ (A.10) > 0 is the Pareto parameter if the top of the income distribution is Pareto distributed. In the presence of mobility, however, the total revenue effect is given by dr = N(y y)[1 ɛa τ 1 τ + τ(y y) ]dτ εn(τy )dτ. 1 τ (A.11) We can simplify the problem by assuming that the tax function is approximately continuous in the neighborhood of the top income tax bracket. In other words, we assume that τ was set approximately near τ such that τ τ is small. Doing so implies that the top tax rate is close to the lower tax rate and thus that the average tax rate approaches the top marginal tax rate. Then, equation A.8 simplifies to and the taxable income response is still given by τ εan(y y)( )dτ < 0 (A.12) 1 τ τ ɛan(y y) dτ < 0. (A.13) 1 τ This then means that we can rewrite the above equation A.11 as: dr = N(y y)[1 (ɛ + ε)a τ ]dτ (A.14) 1 τ 48 If a small fraction of individuals shift from the top bracket to the lower bracket, that effect will be second order and we can ignore it in our derivation. 52

55 In the text, we conclude that when there is no taxable income response that the mechanical effect dominates the behavioral effect. With taxable income responses, this will remain true so long as ɛ remains small. Given our estimates of the mechanical effect and estimates of the elasticity of taxable income, it appears the direction of our effects will be preserved. Then, we can calculate the often talked about revenue maximizing tax rate for the top marginal income tax bracket by setting expression A.14 equal to zero. Doing so yields the revenue maximizing tax rate of: τ = (ɛ + ε)a (A.15) which is different from the standard formula with no migration because it contains the additional term for the stock mobility elasticity, ε. 49 This suggests to us that when in an open economy setting, knowing the migration elasticity is equally important as knowing the elasticity of taxable income elasticity. Given that ε > 0 and a > 0, ignoring the migration elasticity will result in overestimating the revenue maximizing top Laffer tax rate. For example, using U.S. estimates, if a = 1.5 and ɛ =.25 (the mid point of the elasticity of taxable literature estimates) but the economy is closed so that no one migrates, then τ = 72.7%. If the economy is open and the stock migration elasticity is ε =.15, the τ = 62.5%. If ε =.25, the τ = 57.0%. The implication is that even a small migration elasticity can change the top marginal income tax rate by ten percentage points using the U.S. Pareto parameter. In the text we discuss the results using estimates for Spain. A.10 Empirical Estimation of Revenue Response To empirically estimate the revenue response we follow the following steps. This procedure accounts for the fact that the actual tax system contains many brackets, while our model only features two tax brackets. 1. We pick a value of y that we wish to focus on. We consider e94,000 which corresponds to the top 1% in We construct a dataset of individuals with incomes above this value of y and we calculate what their average tax rate would be in year t if they earned y using our 49 In order to relax the assumption that τ is set near τ, we can work with equation A.11 to derive the revenue maximizing tax rate. Doing so, yields τ = y y ετy (1 + ɛa + ε)(y y). (A.16) 53

56 tax calculator. Given we know what their total tax rate on their true income from our prior simulation of their tax rates, we use this to calculate what their average tax rate is on income above y. In particular, we calculate the average tax rate for each individual on income above the threshold as τ = T y T yy where y is true y y income, T is the average tax rate on their true income and T y is the average tax rate if they earned y. We then appropriately partition τ to its regional and central component. 3. Using the dataset we also calculate the total stock of individuals with income above the threshold in each region (and in all of Spain) along with the total out-flow from each region. 4. We fit the Pareto distribution separately for each region on the individuals with income above y and calculate the Pareto parameter and its corresponding standard error. 5. We then calculate the mean income and mean tax rates in each region of Spain, which is equivalent to collapsing our data at the region by year level. 6. We apply our theoretical model using: (a) y is 94,000 Euro (b) y is the average income of individuals above y in each state. We calculate this as the average income in the post-reform years in each region to minimize the threat of year specific shocks to income. The results are robust to using pre-reform numbers. (c) dτ is the regional tax rate minus the central government tax rate. To account for the fact that some small differences existed prior to the reform, we subtract off the regional tax rate net of the central government tax rate in 2010 for the few regions that had some differences prior to the reform. (d) τ is the tax rate the individual would have faced income of y (given by T y above). (e) N is the total stock of people above y. We calculate this as the average number of individuals in the state with income above y in the post reform years. The results are robust to using pre-reform numbers. (f) a and its standard error are estimated as above. (g) the stock elasticity ε and its standard errors comes from our empirical estimates. 54

57 (h) ɛ is set as 0.15 in our baseline simulation, but we show the results are robust for a range of values. 7. Given these values, we can simply apply the formulas in the appendix and use the parametric bootstrap to construct confidence bands. A.11 Works Cited in Appendix (and Not in Text) Bayer, Patrick, Fernando Ferreira, and Robert McMillan A Unified Framework for Measuring Preferences for Schools and Neighborhoods. Journal of Political Economy, 115(4):

58 Figure A.1: Tax Rates Over Time and Across Regions The top figure shows top marginal tax rates in The bottom figure shows top marginal tax rates in Notice the tax rates in 2010 differ only by 0.10 percentage points, so both figures are on different color gradients. Appendix Figure A.2 shows similar maps for

59 Figure A.2: Tax Rates Over Time and Across Regions The top figure shows top marginal tax rates in The middle figure shows top marginal tax rates in And the bottom figure shows tax rates in All figures are on different color gradients. 57

60 Figure A.3: News Article This newspaper article from June 2016 has a headline Madrid is a tax haven for the rich and big business. Figure A.4: Tax Declaration This is a blank tax declaration form. The line TBE reports the average tax rate to the federal government and the line TMA reports the average tax rate to the region. As is clear, the tax declaration delineates the payments to the state and federal government. 58