State Taxes and Spatial Misallocation

Transcription

1 State Taxes ad Spatial Misallocatio Pablo D. Fajgelbaum UCLA& NBER Eduardo Morales Priceto & NBER Jua Carlos Suárez Serrato Duke & NBER Owe Zidar Chicago Booth & NBER November 2015 Abstract We study the impact of the state tax distributio o aggregate real icome, welfare, ad the distributio of ecoomic activity across U.S. states. We build a spatial geeral-equilibrium model i which state govermets use tax reveue to fiace public services, ad estimate firm ad worker mobility elasticities ad prefereces for public services. We fid that a reveueeutral tax harmoizatio leads to a welfare gai of 0.7% ad to a similar icrease i real GDP. Additioally, state tax cuts lower ow-state ecoomic activity because of geeral-equilibrium effects o prices ad public services, ad impact other states differetly due to trade likages. We thak Costas Arkolakis, Domiick Bartelme, Lorezo Caliedo, Araud Costiot, Klaus Desmet, Cecile Gaubert, Erico Moretti, Nirupama Rao, Pat Klie, Ralph Ossa, Esteba Rossi-Hasberg, Aleh Tsyviski, ad Jo Vogel for helpful commets. Matt Pahas, Prab Upadrashta ad Joh Wieselthier provided excellet research assistace. Suárez Serrato gratefully ackowledges support from the Kauffma Foudatio. Zidar gratefully ackowledges support from the Kathry ad Grat Swick Faculty Research Fud ad Booth School of Busiess at the Uiversity of Chicago.

2 1 Itroductio Tax policy varies widely across coutries ad across regios withi coutries. I 2012, the U.S. states collected roughly $800 billio i tax reveue relyig o very differet levels of sales, persoal icome, ad corporate icome taxes. Recet research studyig dispersio i distortios across ecoomic uits across firms, as i Hsieh ad Kleow (2007), or across cities, as i Desmet ad Rossi-Hasberg (2013) suggests that this dispersio i tax rates may lower aggregate ecoomic activity; ideed, policies that would move the state tax structure towards greater tax harmoizatio have bee proposed i both academic ad policy discussios. 1 However, little is kow about the aggregate effects of elimiatig dispersio i tax rates, or, more geerally, about how the state tax distributio impacts the U.S. ecoomy. 2 What is the impact of the state tax distributio o aggregate real icome, welfare, ad the distributio of ecoomic activity across U.S. states? This questio is difficult to tackle because may geeral-equilibrium forces are at work chages i state taxes lead to reallocatios of workers, firms, ad trade flows across states, as well as to chages i the amout of public services provided by state govermets ad to the best of our kowledge, o existig aalysis has aswered it. To do so, we icorporate tools developed i recet trade ad ecoomic geography models ito a geeral-equilibrium model that accouts for several types of spatial iteractios amog states ad saliet features of the U.S. state tax system. We estimate key parameters elasticities of firm ad worker mobility across states ad prefereces for public services usig equilibrium relatioships implied by the model ad data o the spatial distributio of ecoomic activity ad govermet fiaces across states from 1980 to Usig the estimated model, we measure the effects of elimiatig tax dispersio. We also use the model to study the cosequeces of imposig other couterfactual distributios of state tax rates correspodig to policies that are ofte the subject of public debate. I our model, workers decide where to locate based o each state s taxes, wage, cost of livig, ad ameity level. I tur, firms decide where to locate, how much to produce, ad where to sell based o each state s taxes, productivity, factor prices, ad market potetial (a measure of other states market sizes discouted by trade frictios). Additioally, workers ad firms hold, respectively, idiosycratic preferece ad productivity draws across states, accordig to which they sort spatially. spedig i public services. The ameity ad productivity levels of each state partly deped o govermet I our model, this spedig is fiaced by sales, persoal icome, ad corporate icome taxes apportioed through both firm sales ad factor usage. 3 As a result, firm ad worker decisios deped o taxes both i partial equilibrium give relative prices ad 1 For a theoretical treatmet see Gordo (1983). For specific discussios see Shaviro (1993), Farber (2006), Sulliva (2014), ad Wilso (2015) for the U.S., ad Kee (1987), Devereux ad Pearso (1995), Béassy-Quéréa et al. (2014), ad Devereux et al. (2015) for Europe. 2 The March 24, 2015 poll of members of the IGM Ecoomic Experts Pael of Chicago Booth o Local Tax Icetives illustrates the disagreemet ad ucertaity amog ecoomists o questios related to this topic. 3 Our baselie aalysis focuses o these three types of taxes as they accout for the bulk of state tax reveue; see Sectio 2 for backgroud o the U.S. tax system. I the couterfactuals, we ispect alterative ways of measurig these tax rates. 1

3 state spedig ad i geeral equilibrium through the impact of taxes o prices ad publicservices provisio. Specifically, our model implies that state taxes impact the allocatio of firms, workers, ad goods through their effect o adjusted fudametals, defied as fuctios of actual state fudametals (productivity, ameity, ad trade costs), tax rates, ad govermet spedig. Give the level of govermet spedig, higher icome or sales taxes i oe state are equivalet to a lower ameity level i that state, higher corporate taxes are equivalet to lower productivity, ad chages i sales-apportioed corporate tax rates are equivalet to chages i trade costs. I geeral equilibrium, govermet spedig varies with the size of each govermet s budget; as a result, chages i tax rates i oe state impact the adjusted fudametals of every state. To measure the effects of alterative state tax structures we eed estimates of four structural parameters: the elasticities of worker ad firm mobility, ad the weight of public services i worker prefereces ad firm productivity. We idetify these parameters usig equilibrium relatioships from our model ad a logitudial dataset o the distributio of workers ad firms across states, state tax rates, ad state govermet reveue from 1980 to Specifically, our model geerates a worker-locatio equatio that predicts each state s employmet share as a fuctio of after-tax real wages ad govermet spedig, ad a firm-locatio equatio that predicts each state s share of establishmets as a fuctio of after-tax market potetial, factor prices, ad govermet spedig. Our estimatio strategy uses taxes i other states to istrumet for each state s factor prices ad govermet spedig. We estimate a partial elasticity of state employmet with respect to aftertax real wages of about 1, ad with respect to govermet spedig of about 0.2. Withi our model, the ratio betwee these reduced-form coefficiets idetifies the preferece for public services relative to private goods, ad their level idetifies the elasticity of worker mobility. 4 The remaiig parameters of the model (productio techologies ad state fudametals) are calibrated such that the model exactly reproduces as a equilibrium outcome the distributio of factor shares, wages, employmet, ad trade flows across states i 2007, the most recet year i which all the data we eed is available. We verify that the estimated model correctly predicts the distributio of variables ot targeted by the parametrizatio, such as the distributio of GDP ad of tax reveue shares i GDP across states. Usig the estimated model, we measure the effects of replacig the 2007 distributio of state tax rates with couterfactual distributios. Our mai couterfactuals assess the impact of tax reforms that elimiate dispersio i tax rates across states. We defie the spatial misallocatio caused by the state tax distributio as the welfare ad real-icome gais (if they exist) that would result from elimiatig the dispersio i each type of tax across states while keepig the size of state govermets costat. We udertake two types of couterfactuals that differ i the measure of govermet size that is kept costat: we udertake a reveue-eutral couterfactual by simultaeously brigig the commo tax rate for each type of tax to a level such that the tax reveue collectively raised by all states is the same as i the iitial sceario; ad we also uder- 4 These estimates are i the rage of existig work that has estimated similar specificatios, such as Boud ad Holzer (2000), Notowidigdo (2011), Suárez Serrato ad Wigeder (2011), Diamod (2015), ad Suárez Serrato ad Zidar (2014). See Sectio 4.3 for details. 2

4 take a spedig-eutral couterfactual by brigig the commo tax rate for each type of tax to a level such that the tax reveue collectively raised by all states joitly with a system of cross-state trasfers ca fiace the same level of govermet spedig as i the iitial sceario i every state. Dispersio i tax rates across states ca be show theoretically to reduce real icome ad welfare i restricted versios of our model that do ot feature some forces such as spatial exteralities through home-market effects ad govermet spedig. However, the model that we estimate ad use as basis for our couterfactuals accouts for these forces, ad therefore does ot ecessarily imply that elimiatig tax dispersio must lead to real-icome ad welfare gais. We fid that a reveue-eutral harmoizatio of sales, icome, ad corporate taxes leads to aggregate real-icome gais i the order of 0.7%, or roughly $110 billio i 2012, poitig to quatitatively importat effects from dispersio i these taxes relative to their reveue share i GDP, i.e., about 4%. Welfare gais are also i the order of 0.7%. The spedig-eutral elimiatio of tax dispersio leads to a 0.12% icrease i welfare ad to a similar icrease i real GDP, poitig to the existece of spatial misallocatio due to forces other tha the chages i state govermet spedig that a tax harmoizatio could imply. We ispect how these results would vary if the weight of govermet spedig i worker prefereces ad productivity was lower tha what our bechmark estimates imply, ad if we allowed for heterogeeity across states i workers prefereces for public services provided by state govermets. We cotiue to fid gais from elimiatig dispersio i icome, sales, ad corporate tax rates i these cases. For example, i a extreme parametrizatio that assigs zero weight to govermet spedig i prefereces ad productivity, both reveuead spedig- eutral couterfactuals lead to welfare gais of 0.2%. We also study couterfactuals uder parametrizatios correspodig to alterative estimatio strategies ad uder differet ways of measurig tax rates; e.g., adjustig corporate tax rates for state subsidies ad icorporatig progressivity i state ad federal icome tax schedules. We also use the estimated model to gauge the effects of other policies which are ofte subject to public debate. I some states, lower taxes are said to help create jobs or attract busiesses, 5 but also to erode the provisio of public services with little overall effect o employmet. 6 iform the ogoig debate o the effects of lowerig state taxes, we simulate a 1 percetage poit reductio i the idividual icome tax i each state at a time. O average, this policy causes a loss of ecoomic activity i the state eactig the tax chage. Geeral-equilibrium forces largely drive the effects: keepig goods prices, factor prices, ad govermet spedig costat, the tax reductio leads to a icrease i ecoomic activity i the state reducig taxes, but whe these variables are allowed to adjust, activity i that state decreases. We fid that this tax chage leads to heterogeeous impacts across other states, with the states who export or import relatively more from the state lowerig taxes experiecig a relatively smaller icrease i ecoomic activity. We also explore the implicatios of the sales apportiomet of corporate taxes; i.e., the fact that busiess profits are allocated to states proportioally to sales to determie each firm s effective corporate tax 5 E.g., see Gov Kasich s Wiig Proposal for Ohio: Lowerig Icome Taxes, Forbes, Arthur Laffer ad Nicholas Drikwater, May 15, E.g., see Kasas Ruious Tax Cuts, The New York Times, Editorial Board, July 13, To 3

5 rate. 7 I the model, the sales apportiomet distorts sales decisios, leadig firms to sell relatively more to states with lower sales-apportioed corporate taxes. We fid aggregate losses from fully apportioig corporate taxes through sales istead of employmet. We idetify a relevat role for trade i drivig this result: movig away from sales apportiomet implies smaller gais uder o heterogeeity i trade likages across states, suggestig a complemetarity betwee trade frictios ad the distortios caused by the sales apportiomet. To the best of our kowledge, this paper provides the first quatificatio of these ofte-debated policies usig a geeral-equilibrium model fitted to the actual distributio of ecoomic activity ad tax rates across all U.S. states. I terms of tools, the paper is related to a recet literature o quatitative ecoomic-geography models icludig Ramodo et al. (2012), Reddig (2012), Alle ad Arkolakis (2014), Caliedo et al. (2014), Bartelme (2014), ad Mote et al. (2015). 8 Our questio the impact of state taxes o the U.S. ecoomy distiguishes our paper from this previous literature. This focus drives our modelig choices, estimatio approach, ad couterfactuals. Our model combies a umber of igrediets already preset i existig studies, 9 plus a few ew oes dictated by our research questio. The ew igrediets are imperfect firm mobility (i the form of idiosycratic productivity draws across states), a tax structure that ecompasses the mai taxes used by U.S. states, ad a govermet sector that uses these taxes to fiace public services valued by workers ad firms. Relative to this literature, a cetral feature of our aalysis is the focus o performig couterfactuals with respect to policy variables that are directly observed (U.S. state tax rates) ad the estimatio of key parameters (elasticities of firm ad worker mobility ad prefereces for govermet spedig) usig chages over time ad space i those policies ad i ecoomic activity. 10 Our paper cotributes to the literature o the aggregate effects of misallocatio. A commo approach i the literature cosists i measurig distortios across firms as a implied wedge betwee a observed allocatio ad a model-implied udistorted allocatio, as i Hsieh ad Kleow (2007) ad Restuccia ad Rogerso (2008); a few papers have adopted a similar strategy to aalyze misallocatio across geographic uits, such as Desmet ad Rossi-Hasberg (2013), Hsieh ad Moretti (2015), or Bradt et al. (2013). These wedges capture distortios that may be due to mul- 7 See the discussio i Sectio 2.1. There is a substatial debate o state corporate tax apportiomet policy (e.g., ITEP (2012) ad Mazerov (2005)). Some (e.g., Zucma (2014)) have recetly advocated movig towards a system for corporate taxatio exclusively based o sales apportiomet. 8 These papers have i commo the itroductio of labor mobility ito quatitative trade models with CES prefereces such as Eato ad Kortum (2002) ad Aderso ad Va Wicoop (2003). 9 Specifically, our model icludes a edogeous umber of moopolistically competitive firms as i Krugma (1991) ad Helpma (1998), the use of differetiated products as itermediates as i Krugma ad Veables (1995), ad workers with idiosycratic prefereces across locatios as i Tabuchi ad Thisse (2002). These igrediets are preset i differet studies from the recet quatitative ecoomic-geography literature, e.g.. Reddig (2012) icludes free-etry ad idiosycratic prefereces of workers, Caliedo et al. (2014) allow for a full set of iput-output likages across sectors, ad Alle ad Arkolakis (2014) model exteralities which are isomorphic to some of these agglomeratio forces. 10 I this sese, our approach shares features with Caliedo ad Parro (2014), who, i a iteratioal trade cotext, estimate trade elasticities usig variatio i tariffs. A few recet papers are also cocered with the impact of policies i models with labor mobility. Gaubert (2014) studies subsidies i a model with with heterogeeous firms ad exteralities from city size, Ossa (2015) studies the Nash equilibrium i state subsidies i a spatial model with home market effects, ad Eeckhout ad Guer (2014) study optimal taxes across cities uder exteralities from city size. 4

6 tiple sources. Rather tha iferrig distortios from wedges, we focus o the spatial misallocatio geerated by oe specific type of distortio (state taxes) that we ca directly observe i the data. While this literature typically focuses o the impact of distortios o TFP, we study the impact o real icome ad welfare. 11 Fially, our paper is also related to the literature that has aalyzed the geeral equilibrium effects of tax chages. For example, Shove ad Whalley (1972), ad Ballard et al. (1985) emphasize the importace of geeral equilibrium effects whe aalyzig large chages i policy. Also i a geeral equilibrium, Albouy (2009) study the distortios i the allocatio of workers across U.S. cities caused by federal tax progressivity. The geeral-equilibrium effects implied by our aalysis deped o the elasticities of firm ad worker locatio with respect to taxes; evidece o the icidece of taxes o worker mobility icludes Bartik (1991) ad, more recetly, Moretti ad Wilso (2015); i terms of firm mobility, Holmes (1998) uses state borders to show that maufacturig activity respods to busiess coditios, ad a large literature studies the impact of local policies o busiess locatio. 12 Suárez Serrato ad Zidar (2014) provide evidece o the impact of corporate taxes o worker ad firm mobility, ad Suárez Serrato ad Wigeder (2011) show that local ecoomic activity respods to public spedig. While these papers quatify the local effects of actual policy chages, our framework allows us to quatify how couterfactual policy chages i oe or may states, such as tax harmoizatio, would impact outcomes i every state idividually ad i the U.S. ecoomy as a aggregate through both partial- ad geeral-equilibrium forces. The rest of the paper is structured as follows. Sectio 2 describes the U.S. state tax system. Sectio 3 develops the model ad describes its geeral-equilibrium implicatios. Sectio 4 describes our estimatio approach. Sectio 5 focuses o the spatial-misallocatio couterfactuals, ad Sectio 6 presets the results from additioal couterfactuals. Sectio 7 cocludes. Additioal derivatios ad figures, ad details o the estimatio ad o data sources, are show i a Olie Appedix. 2 Backgroud o the U.S. State Tax System Our bechmark aalysis focuses o three sources of tax reveue: persoal icome, corporate icome, ad sales taxes. The reveue raised by these taxes accouted, respectively, for 35%, 5%, ad 47% of total states tax reveue i 2012, ad collectively amouted to 4% of U.S. GDP. I this sectio, we first describe how we measure each tax rate. We the preset statistics that summarize 11 For ay observed distributio of taxes, the quatitative ecoomic-geography model that we adopt ca ratioalize the observed distributio of ecoomic activity (wages, prices, employmet, ad trade) as a equilibrium outcome correspodig to some joit distributio of productivity, ameities, ad trade costs. We do ot itroduce wedges i the model to save otatio, but we ote that, if itroduced, they would ot be separately idetified from these fudametals. 12 E.g., Devereux ad Griffith (1998) estimate the effect of profit taxes o the locatio of productio of U.S. multiatioals, Goolsbee ad Maydew (2000) estimate the effects of the labor apportiomet of corporate icome taxes o the locatio of maufacturig employmet, Hies (1997) exploits foreig tax credit rules to show that ivestmet respods to state corporate tax coditios, ad Giroud ad Rauh (2015) use establishmet-level data to show that multi-state C-corporatios reduce their activity o both the itesive ad extesive margis whe states icrease corporate tax rates. Chiriko ad Wilso (2008) ad Wilso (2009) also provide evidece cosistet with the view that state taxes affect the locatio of busiess activity. 5

7 the dispersio i tax rates across states. We coclude with evidece o the relatioship betwee state tax reveue ad govermet spedig. Appedix F details the sources of the data discussed i this sectio. 2.1 Mai State Taxes Persoal Icome Tax States tax the persoal icome of their residets. The base for the state persoal icome tax icludes both labor ad capital icome. I our bechmark aalysis, we use a flat state icome tax rate, ad we the explore how our couterfactual results chage if we accout for the progressivity of icome taxes at both the state ad federal levels. 13 We compute a icome tax rate for each state usig the average effective tax rate from NBER TAXSIM, which rus a fixed sample of tax returs through differet tax schedules every year ad accouts for most features of the tax code. 14 I 2010, the average across states was 3%; the states with the highest icome tax rates were Orego (6.2%), North Carolia (5.2%), ad Hawaii (5.0%), while seve states had o icome tax. Corporate Icome Tax States also tax busiesses. The tax base ad tax rate o busiesses deped o the legal form of the corporatio. The tax base of C-corporatios is atioal profits. 15 State tax authorities determie the share of a C-corporatio s atioal profits allocated to their state usig apportiomet rules, which aim to capture the corporatio s activity share withi their state. To determie that activity share, states put differet weight o three apportiomet factors: payroll, property, ad sales. Payroll ad property factors deped o where goods are produced ad typically coicide; the sales factor depeds o where goods are cosumed. 16 I 2012, the average corporate icome tax rate across states was 6.4%; the states with the highest corporate tax rates were Iowa (12%), Pesylvaia (10%), ad Miesota (10%), while six states had o corporate tax. Apportiomet through sales teds to be more prevalet: ietee states exclusively apportio through sales, while roughly half of the remaiig states apply either a 50% or 33% apportiomet through sales. Sice C-corporatios accout for the majority of et icome i the Uited States, i our bechmark aalysis we treat all busiesses as C-corporatios. 17 We also explore how our results chage whe we apply alterative corporate tax rates that adjust for the fractio of C-corporatios 13 The schedule of state icome tax rates teds to be progressive, but it is typically much flatter tha the federal icome tax schedule. We compare the progressivity of state ad federal icome tax rates whe we itroduce progressive icome taxes i Sectio The fixed sample correspods to actual 1984 tax returs. The features of the tax code take ito accout by NBER TAXSIM iclude maximum ad miimum taxes, alterative taxes, partial iclusio of social security, eared icome credit, phaseouts of the stadard deductio ad lowest bracket rate. State tax liabilities are calculated usig the data from the federal retur. All items o the retur are adjusted for iflatio, so differeces across tax years oly reflect chages i tax laws. 15 Most states limit the tax base to profits eared withi the water s edge, i.e. profits from domestic activity. 16 For example, a sigle-plat firm j located i state i with export share s j i to each state pays a corporate tax rate of t j = t corp fed + tl i + sj i tx, where t corp fed through sales i state (where t corp t l i = (1 θi x ) t corp is the federal tax rate, tx = θt x corp is the corporate tax apportioed is the corporate tax rate of state ad θ x is its sales apportiomet), ad i is the corporate tax apportioed through property ad payroll i state i. 17 C-corporatios accouted for 66% percet of total busiess receipts i 2007 (PERAB, 2010). 6

8 i total reveue i each state, or that accout for tax subsidies that some states grat to firms, reducig their effective corporate tax rate. Sales Tax Sales taxes are usually paid by the cosumer upo fial sale, ad states typically do ot levy sales taxes o firms for itermediate iputs or goods that they will resell. 18 I 2012, the average sales tax rate was 5%; the states with the highest sales tax rates were New Jersey (10%), Califoria (7.5%), ad Idiaa (7%), while five states had o sales taxes. I our bechmark aalysis, we defie the sales tax rate as the statutory geeral sales tax rate applied oly to fial cosumer sales. 2.2 Dispersio i Tax Rates ad i Tax Reveue across States Both the tax base ad the tax rates vary cosiderably across states. While most states collect both icome ad sales taxes, some rely almost exclusively o sales tax reveue, such as Texas ad Nevada, while others are sales-tax free, like New Hampshire ad Orego. Pael (a) of Figure 1 shows the 2010 distributio of sales, icome, corporate, ad sales-apportioed corporate tax rates. 19 For each tax, rates vary across states, corporate tax rates beig the most dispersed. For each type of tax, there are at least five states with 0% rates. 20 These differeces i tax structures across states are associated with differeces i total tax reveue collected. Pael (b) of the same figure shows the distributio i tax reveue as share of GDP across states. The share of the sum of icome, sales, ad corporate tax reveue i GDP varies across states betwee 2% ad 7%. Local (sub-state) govermets also tax residets. Overall, state taxes amout to roughly 60% of state ad local tax reveue combied. 21 Heterogeeity i tax rates across states is also preset whe both state ad local taxes are take ito accout. Figure A.1 i the olie appedix reproduces Pael (a) of Figure 1 usig the sum of state ad local tax rates. It shows that cross-state differeces i tax rates icrease whe local tax rates are take ito accout. 18 Most states make some kid of exceptio of sales tax for firms purchasig goods. These exemptios vary widely across states, but geerally, if a firm purchases material ad uses it as a iput i productio, it is exempt from the sales tax. For example i Alabama, property that becomes a igrediet or compoet part of products maufactured or compouded for sale costitutes a exempt wholesale sale. (Ala Code Sec (a)(6) ; Ala Code Sec (a)(9b) ; Ala Code Sec (4)(b) ; Ala Admi Code r ; Ala Admi Code r ). 19 The sales-apportioed corporate tax rate is the product of the sales apportiomet factor (which is betwee 0 ad 1) ad the corporate rate; i.e. the variable t x = θt x corp defied i footote Table A.2 i Appedix F.2shows the state tax rates i 2007 for persoal icome taxes, geeral sales taxes, statutory corporate taxes ad sales apportioed corporate taxes i all 50 states. Table A.1shows the federal icome, corporate ad payroll tax rates i Local govermets rely more heavily o property taxes tha icome, corporate, ad sales taxes. State tax reveue make up roughly 90%, 85%, ad 80% of cosolidated state ad local reveue from icome, corporate, ad sales taxes, respectively, but oly 3% of cosolidated property tax reveue. 7

9 Figure 1: Dispersio i State Taxes i 2010 (a) Distributio of Tax Rates Across States (b) Tax Reveue as Share of GDP Across States i 2010 Desity State Tax Rates i 2010 State Tax Reveue as Share of GDP i AK DE NH WY TX SD CO LA NV OR GA TN VA OK MT IL MO WA ND FL AZ NE UT SC AL OH IA NM MD NC PA KS IN ID NJ MA RI CA KY MI CT NY WI VT MN AR MS ME WV HI Sales Corporate Idividual Icome Sales Apportioed Corporate Icome Corporate Sales 2.3 Relatioship Betwee State Taxes ad Govermet Spedig State govermets typically have balaced budgets (Poterba, 1994), so we assume i our model that chages i state tax reveue traslate to chages i state govermet spedig. Figure 2 shows that there is ideed a high correlatio betwee the tax reveue from the taxes we cosider i the aalysis (i.e., persoal icome, corporate icome, ad sales taxes) ad direct state spedig durig both withi states over time ad across states i ay give year. Direct expeditures iclude all govermet expeditures other tha itergovermetal trasfers. 22 Pael A shows a bied scatter plot, which shows the mea of each bi, ad a regressio lie of states direct expeditures o states aggregate reveue from persoal icome, corporate icome ad sales taxes cotrollig for state fixed effects, ad Pael B shows a equivalet regressio but cotrollig for year fixed effects istead. Note that, i both cases, ot oly the R 2 is very close to oe, but also the slope is very close to oe. Therefore, a 1% icrease i tax reveue is early always expected to traslate ito a 1% icrease i state direct expeditures. 22 The mai direct-expediture items iclude educatio, public welfare, hospitals, highways, police, correctio, atural resources, parks ad recreatio, govermet admiistratio, ad utility expediture. 8

10 Figure 2: Comparig State Tax Reveue ad Spedig (a) State Fixed Effects (b) Year Fixed Effects Log State Direct Expeditures Log State Direct Expeditures Log State Tax Reveue i Model Note: Slope is 1.05 (0). Sample: R-squared is Log State Tax Reveue i Model Note: Slope is 1.01 (0). Sample: R-squared is 1. 3 Quatitative Trade Model with State Taxes ad Public Goods We model a closed ecoomy with N states idexed by or i. A mass M of firms ad L of workers respectively receive idiosycratic productivity ad preferece shocks, which gover how they sort across states. We let M ad L be the measure of workers ad firms that locate i state. We ormalize M = 1 ad L = 1, so that M ad L are the fractios of firms ad workers located i state. Each state is characterized by a edowmet H of fixed factors of productio (lad ad structures), a ameity level u, ad a productivity level z. There is a iceberg cost τ i 1 of shippig from state i to state (if oe uit is shipped from i to, 1/τ i uits arrive). Firms are sigle-plat ad sell differetiated products. To produce, they use the fixed factor, workers, ad itermediate iputs. Workers receive oly labor icome, which they sped i the state where they live. Firms ad fixed factors are owed by immobile capital owers exogeously distributed across states. State govermets collect persoal icome taxes t y, sales taxes t c, ad corporate icome taxes apportioed through sales, t x, or through payroll ad fixed factors, t l. Each state uses the tax reveue to fiace the provisio of public services, which eter as shifters of that state s ameity ad of the productivity of firms that locate i that state. The federal govermet collects persoal icome taxes t y fed, payroll taxes tw fed, ad corporate taxes tcorp fed. valued by cosumers or firms. 23 Federal public spedig is ot 23 We could impose the alterative assumptio that federal public spedig shifts the utility of cosumers idepedetly from where they locate. I this case, our aalysis would remai uchaged except that, for ay couterfactual chage i taxes, there would be a additioal aggregate welfare effect through its impact o the size of the federal budget. 9

11 3.1 Productio Techologies I each state, a competitive sector assembles a fial good from differetiated varieties through a costat elasticity of substitutio (CES) aggregator with elasticity σ, ( ˆ Q = i j J i ) σ ( ) q j σ 1 σ 1 σ i dj, (1) where J i deotes the set of varieties produced i state i ad q j i is the quatity of variety j produced i state i ad used i state. Lettig p j i be the price of this variety i state, the cost of producig oe uit of the fial good i state (equal to its price et of sales taxes) is ( ˆ P = i j J i ) 1 ( ) 1 σ p j 1 σ i dj. (2) Each variety j is produced by a differet firm; to produce q j i i regio i, firm j uses its ow productivity i that locatio, z j i, ad combies it with the fixed factor hj, workers l j ad itermediate iputs i j through a Cobb-Douglas techology: [ ( ) q j i = 1 h j βi ( ) l j 1 βi ] γi ( ) i j 1 γi zj i, (3) γ i β i 1 β i 1 γ i where γ i is the value-added share i productio of every firm i state i, ad where 1 β i is the labor share i value added i state i. The existece of a fixed factor is oe of the sources of cogestio i the model; the higher the umber of firms ad workers located i a give state, the higher the relative price of this fixed factor. Productio fuctios are allowed to vary by state; this flexibility is eeded to match the heterogeeity i the shares of total paymets to labor ad itermediate iputs expeditures i states GDP observed i the data. 24 The fial good Q is o-traded ad used by cosumers (workers ad capital-owers) for aggregate cosumptio (C ), by firms as a itermediate iput i productio (I ), by state govermets (G ) for public spedig, ad by the federal govermet (G fed ): 3.2 Workers ad Capital Owers Q = C + I + G + G fed. (4) A cotiuum of workers l [0, 1] decide i which state to work ad cosume. The idirect utility of worker l i state is v l = v ɛ l, where the vector { ɛ l N } captures worker l s idiosycratic =1 prefereces for livig i each state ad v is commo to all workers who locate i. This commo 24 This heterogeeity i the productio fuctio may be thought of as a way of capturig differeces i sectoral compositio across states; i the presece of multiple sectors, the labor ad itermediate-iput shares of each state would be edogeous ad chage i the couterfactuals, but abstract from this margi i our aalysis. 10

12 compoet is ( ) αw ( G v = u L χ (1 T W ) w ) 1 αw, (5) P where we defie workers keep-tax rate (i.e., the fractio of real icome kept by workers after payig sales ad icome taxes) as 1 T (1 ty fed )(1 ty ) t w fed 1 + t c. (6) Equatios (5) ad (6) imply that workers have prefereces over ameities ad fial goods. 25 The ameities of state have a edogeous part that depeds o the amout of public spedig ad a exogeous part u. The edogeous part equals real govermet spedig G ormalized by L χ W. The parameter χ W captures rivalry i public goods ad rages from χ W = 0 (o-rival) to χ W = 1 (rival). The exogeous part u captures both atural characteristics, like the weather, ad the rate at which the govermet trasforms real spedig ito services valued by cosumers, i.e., the quality or efficiecy i the provisio of govermet services. 26 The quatity of fial goods cosumed by a idividual equals after-tax wages, ((1 t y fed )(1 ty ) t w fed )w, ormalized by the after-tax price, (1 + t c ) P. 27 As a result, real cosumptio equals the pre-tax wage, w /P, adjusted by icome ad sales taxes, 1 T. The parameter α W captures the weight of state-provided ameities i prefereces. The idiosycratic taste draw ɛ l is assumed to be i.i.d. across cosumers ad states, ad it follows a Fréchet distributio, Pr ( ɛ l < x ) = e x ε W, with ε W > 1. A worker l locates i a state if = arg max v ɛ l. Remidig that we have ormalized the mass of workers to 1, the fractio of workers located i state is where v L = ( ( v ) εw, (7) v v ε W ) 1/εW. (8) Uder the Fréchet distributio, both the ex-ate expected utility of a worker before drawig { ɛ l } N =1 ad the average ex-post utility of agets located i ay state are proportioal to v; hece, we adopt it as our measure of worker welfare. 28 I the couterfactuals, we also report the chage i real cosumptio (of both mobile workers ad immobile capital-owers) ad real GDP; we preset the 25 Although we do ot allow for direct cosumptio of lad by workers, our model features cogestio forces through the price idex, as the fixed factor is used i productio. We could geeralize the framework to allow for a additioal source of cogestio by havig housig i equatio (5). 26 I.e., if we had a additioal variable z G represetig the efficiecy or quality of govermet spedig, it would eter multiplicatively with u. 27 Note that equatio 6 takes ito accout that state icome taxes ca be deducted from federal taxes. We abstract from the o-liearity of the federal icome tax scheme i the bechmark aalysis; empirically, we set the value of the federal icome tax rate t y fed to the average effective federal rate paid by U.S. residets. I sectio 5.4 we relax this assumptio ad allow the federal rate to be a fuctio of state wages. As the federal icome tax schedule is defied o omial wages, it may lead to spatial ( distortios, as aalyzed by Albouy (2009). 28 The costat of proportioality equals Γ εw 1 ε W ), where Γ ( ) is the gamma fuctio. 11

13 correspodig expressios i Sectio 5. A larger value of ε W implies that the idiosycratic taste draws are less dispersed across states; as a result, locatios become closer substitutes ad a icrease i the relative appeal of a locatio (a icrease i v /v) leads to larger respose i the fractio of workers that choose to locate there. From the defiitios of v ad L i (5) ad (7), it follows that ε W (1 α W ) is the partial elasticity of the fractio of workers who locate i state with respect to after-tax real wages, (1 T )(w /P ), while ε W α W is the partial elasticity with respect to real govermet services per worker, G /L χ W. We rely o these relatioships to estimate {ε W, α W } i sectio 4.3. Immobile capital owers i state ow a fractio b of a portfolio that icludes all firms ad fixed factors, idepedetly of the state i which they are located. Therefore, their icome is b (Π + R), where Π are atioal after-tax profits, R are the atioal returs to lad ad structures. We do ot eed to specify the umber of capital owers located i each state for our computatios. We calibrate the owership shares b to match the observed trade imbalaces across states. Capital owers sped their icome locally, ad pay sales taxes o cosumptio ad both federal ad icome taxes o their icome. 3.3 Firms A cotiuum of firms j [0, 1] decide i which state to locate ad produce ad how much to sell to every state. Each firm j produces a differetiated variety ad is edowed with a vector of { } N productivities z j i across states. Firms are moopolistically competitive; whe a firm j located i=1 i state i sets its price p j i i state, the quatity exported to state is qj i = Q (p j i /P ) σ. We first describe the profit maximizatio problem faced by firms located i a give state, ad the solve the firms locatio problem. We fially discuss some of the aggregatio properties of our model, which are commo with stadard models of iteratioal trade such as Melitz (2003). Profit Maximizatio give Firm Locatio i state i, its profits are π j i ( (z) = max 1 t j {qi} j i ) ( N If a firm j with productivity z decides to locate =1 x j i c i z ) N τ i q j i, (9) where t j i is the corporate tax rate of firm j i state i, xj i = P Q 1 σ (q j i )1 1 σ are its sales to state, ad c i = (w 1 β i i r β i i ) γ i P 1 γ i i is the the cost of the cost-miimizig budle of factors ad itermediate iputs, where r i stads for the cost of a uit of lad ad structures i state i. 29 All firms face corporate taxes apportioed through sales, payroll, ad lad ad structures. 30 A 29 Note that the defiitio of c i icorporates that, ulike cosumers, firms do ot face the sales tax whe purchasig the fial good to be used as a itermediate. 30 This assumptio implies that we treat all compaies as C-corporatios. I practice, may compaies are set up as S-corporatios ad parterships. These compaies are ot subject to corporate icome taxes. We igore them i our baselie model because they represet a small fractio of U.S. busiess reveues see our previous discussio i sectio 2.1. However, i Sectio 5.5 we perform a robustess check where corporate tax rates are adjusted by the =1 12

14 firm j located i state i whose share of sales to state is s j i pays sj i tx times the pre-tax atioal profits i corporate taxes apportioed through sales to state. Firms located i i also pay t l i times the pre-tax atioal profits i corporate icome taxes apportioed through payroll ad lad ad structures to state i, ad a rate t corp fed i federal corporate icome taxes. As a result, the corporate tax rate of firm j is: t j i = tcorp fed + tl i + N t x s j i. (10) Due to the sales apportiomet of corporate taxes, the decisio of how much to sell to each state i (9) is ot separable across states as i the stadard CES maximizatio problems with costat margial productio costs i Krugma (1980) or Melitz (2003). Whe a firm icreases the fractio of its sales to state (i.e., whe s j i icreases), the average tax rate chages depedig o the sales-apportioed corporate tax i state, t x, relative to that i other states. Sice the base of the corporate tax are atioal profits, firms trade off the margial pre-tax beefit of exportig more to a give state agaist the potetial margial cost of icreasig the corporate tax rate o its etire profits. Despite this iteractio i the sales decisio, the firm problem retais coveiet properties from the stadard CES maximizatio problem that allow for aggregatio; we describe these properties here ad refer to Appedix B.1 for derivatios. =1 Specifically, all firms located i a state i have the same sales shares across destiatios irrespective of their productivity, i.e., s j i = s i for all firms j located i i; from (10), this leads to a commo corporate tax rate across firms, t j i = t i. Additioally, firms set idetical costat markups over margial costs, but these markups vary bilaterally depedig o corporate taxes. The price set i by a firm with productivity z located i state i is: where σ σ c i p i (z) = τ i σ t i σ 1 z, (11) t i tx tx s i 1 t i. (12) The term t i is a pricig distortio created by heterogeeity i the sales-apportioed corporate tax rates. No dispersio i the sales-apportioed corporate tax rates (t x = t x for all ) implies t i = 0 for all i ad, ad the pricig decisio becomes the same as i the stadard CES maximizatio problem. The pricig distortio icreases with the sales tax i the importig state, t x, relative to other states, implyig higher prices for states with higher corporate taxes apportioed through sales. Firm Locatio Choice Firm-level productivity z j i ca be decomposed ito a term z 0 i which is commo to all firms that locate i i ad a firm-state specific compoet ɛ j i : zj i = z0 i ɛj i. The commo actual share of C-corporatios i each state. 13

15 compoet of productivity is: z 0 i = ( Gi M χ F i ) αf z 1 α F i. (13) As i the case of ameities, this commo compoet has a edogeous part that depeds o the amout of public spedig ad a exogeous part, z i. The edogeous part equals real govermet spedig G i ormalized by M χ F i, where the parameter χ F captures rivalry amog firms i access to public goods. The exogeous part captures both atural characteristics that impact productivity, like atural-resource availability, ad the rate at which the govermet trasforms real spedig ito services valued by firms. Usig (9), the profits of firm j whe it locates i i ca be expressed as the product of a commo ad a idiosycratic compoet: ) π i (z j ( ) ( ) σ 1 i = π i z 0 i ɛ j i. (14) The commo compoet, π i ( z 0 i ), is defied as the profit of a firm with productivity equal to z 0 i located i i. Firm j decides to locate i state i if i = arg max i π i (z j i ). The idiosycratic compoet of productivity, ɛ j i, is i.i.d. across firms ad states ad is draw from a Fréchet distributio, Pr(ɛj i < x) = e x ε F. This implies that firm-level profits, π i (z j i ), are also Fréchet-distributed with shape parameter ε F / (σ 1) > 1. As a result, ad remidig the reader that we have ormalized the mass of firms to 1, the fractio of firms located i state i is where π = M i = ( i ( πi ( z 0 i ) π ) ε F σ 1, (15) ) σ 1 ( ) π i z 0 ε ε F F σ 1 i. (16) Equatio (15) says that that the fractio of firms located i depeds o the commo compoet of profits i, π i ( z 0 i ), relative to that of other locatios. The distributioal assumptio o the idiosycratic productivity draw implies that both the ex-ate profits of a firm before drawig {ɛ j i }N i=1 ad the average ex-post profits of firms located i ay state are proportioal to π. 31 A larger value of ε F / (σ 1) implies that the idiosycratic productivity draws are less dispersed across states; as a result, locatios become closer substitutes, ad a icrease i the relative profitability of a locatio (a icrease i π i ( z 0 i ) / π) leads to a larger respose i the fractio of firms that choose to optimally locate i that locatio. Productivity Distributio Because firms self-select ito each state based o their productivity draws, the productivity distributio i each state is edogeous. However, as i Melitz (2003), ( 31 The costat of proportioality is Γ 1 σ 1 ε F ), where Γ ( ) is the gamma fuctio. 14

16 aggregate outcomes (i our case, at the state level) ca be formulated as a fuctio of a sigle momet z i of the the productivity distributio i each state i. This productivity level is edogeous ad ca be expressed as a fuctio of the umber of firms that optimally choose to locate i each state i: 32 z i = zi 0 M 1 ε F i. (17) The productivity of the represetative state-i firm z i is larger tha the ucoditioal average of the distributio of productivity draws, z i /zi 0 > 1, reflectig selectio. This equatio describes a additioal cogestio force i the model: because firms are heterogeeous ad self-select based o productivity, a higher umber of firms locatig i a state i is associated with a lower average productivity i state i. State Aggregates State-i outcomes ca be costructed as if i equilibrium all the M i firms located i state i had productivity z i. Specifically, the share of aggregate expeditures i state spet o goods produced i state i is ( ) pi ( z i ) 1 σ λ i = M i, (18) P where p i (z) is the pricig fuctio defied i (11). We costruct the sales shares s i, which are ecessary to compute the corporate tax rate t i i (10) ad the pricig distortio t i i (12), usig the idetity s i = λ i P Q /X i, where P Q are aggregate expeditures o fial goods i state. By defiitio, aggregate sales by firms located i state i are: X i = λ i P Q. (19) Because of Cobb-Douglas techologies ad CES demad, aggregate paymets to itermediate iputs, labor ad fixed factors i state i are costat fractios of X i. 33 As a result, spatial iteractios drive local effects: larger expeditures P Q i state act as a factor-demad shifter i state i through X i, ad its impact depeds o the itesity of the trade likage λ i. Aggregate pre-tax profits Π i are also proportioal to sales: implyig aggregate profits equal to Π i = ( 1 t ) Xi /σ. Π i = X i σ, (20) Cotrast with Models with Free Etry This structure has similar implicatios to stadard moopolistic competitio models with free etry, i the sese that i both types of models the 32 By defiitio, z i = ( j J i (z j i )σ 1 dj) 1 σ 1. To reach (17), we use that the Fréchet assumptio o the distributio of productivity draws implies π ( z i) = π i every state together with (15) ad the relatioship π i ( z 0 i ) /π ( z i) = ( z 0 i / z i ) σ 1, implied by (14). 33 See the expressios (A.6) to (A.8) i Appedix B.2. 15

17 umber of firms by locatio is edogeous ad proportioal to sales. From (20) ad the distributioal assumptio o the productivity draws, it follows that the umber of firms i state i ca be expressed as: M i = 1 t i π X i σ. (21) This coditio determies the umber of firms i each regio similarly to a stadard free-etry coditio i moopolistic competitio models such as Krugma (1980). 34 However, we prefer the micro-foudatio of equatio 21 described above for three reasos: first, it allows us to use data o patters of firm mobility to estimate the parameter ε F, see Sectio 4.3; secod, it is similar to existig work which has estimated elasticities of firm locatio with respect to taxes i the publicfiace literature such as Suárez Serrato ad Zidar (2014); third, it allows us to treat mobility of workers ad firms symmetrically State Govermet State govermets use tax reveue R to fiace spedig i public services. Total govermet spedig ad reveue i state is: P G = R = R corp + R y + R c, (22) where R corp, R, c ad R y, are govermet reveue from corporate, sales, ad icome taxes, respectively: R corp = t x s Π + t l Π, (23) R y = t y (1 t y fed ) [w L + b (Π + R)], (24) R c = t c P C. (25) The base for corporate tax profits are the pre-tax profits from every state, defied i (20), adjusted by the proper apportiomet weights. Equatio (24) shows that the base for state icome taxes is the icome of both workers ad capital-owers who reside i et of federal icome taxes. The base for the sales tax i (25) is the total persoal cosumptio expediture of workers ad capital owers, P C If, istead of firm mobility, we had assumed free-etry of homogeeous firms i each state with etry cost equal to f i uits of the factors ad iputs budle, the umber of firms i state i i our model would be: M i = 1 t i 35 c i f i The cost of ot usig the free-etry model is that chages i taxes do ot affect the total umber of firms i the ecoomy. We ote, however, that i both models the fractio of the total umber of firms located i each state is determied idepedetly from the total umber of firms (here ormalized to 1); as such, the aggregate-etry margi would ot affect the part of welfare chages that correspods to the spatial distributio of ecoomic activity which is the focus of our aalysis. However, it would be possible to carry out our aalysis usig the free-etry model to assess this additioal margi. 36 P C is defied i Equatio (A.11) i Appedix B.2. As metioed above, taxes are also collected by the federal govermet. Expressio (A.14) i Appedix B.2 shows the expressio for total taxes levied by the federal govermet i state. X i σ. 16

18 3.5 Geeral Equilibrium Defiitio A geeral equilibrium of this ecoomy cosists of distributios of workers ad firms { } N {L, M } N =1, aggregate quatities Q, C, I, G, G fed, wages ad rets {w, r } N =1, ad =1 prices {P } N =1 such that: i) fial-goods producers optimize, so that fial-goods prices are give by (2); ii) workers make cosumptio ad locatio decisios optimally, as described i Sectio 3.2; iii) firms make productio, sales, ad locatio decisios optimally, as described i Sectio 3.3; iv) govermet budget costraits hold, as described i Sectio 3.4; v) goods markets clear i every locatio, i.e. (4) holds for all ; vi) the labor market clears i every state, i.e. labor supply (7) equals labor demad (A.7) for all ; vii) the lad market clears i every locatio, i.e. (A.8) holds; ad viii) the atioal labor market clears, i.e. L = 1. Adjusted Fudametals Appedix B.3, presets a system of equatios that characterizes the geeral equilibrium solutio for wages ad employmet i every state, {w, L } N =1, ad welfare, v, as fuctio of the model s primitives. I this system, wages, employmet ad welfare are affected by state taxes { t c, t y, t x, t l N } oly through their impact o the adjusted fudametals i every { =1 {τ } } state, A N N i i=1, za, u A =1 : ( ) ( ) z A = (1 t ) 1 σ 1 1 +α ε F χ F P G αf F z 1 α F, (26) GDP τi A σ = τ i, (27) σ t i ( ) u A = (1 T ) 1 α W P G αw u, (28) GDP where P G /GDP is the share of state govermet spedig, defied i (22), to GDP. We ca express this share as ( P t G x PQ X + t l + 1 t y t c +t fed) y 1+t = c GDP ) b ((1 Π + t y t c +t y /(Π+R) fed 1+t c γ (σ 1) + 1 ) tc t w 1+t c fed (1 β ) γ (σ 1), (29) where P Q /X is the share of state expeditures to sales (i.e., a measure of state trade deficit). 37 The adjusted fudametals are fuctios of state fudametals (productivity z, ameity u, ad trade costs τ i ), tax rates ad govermet size. State- taxes impact the adjusted fudametals i state through their effect o the price distortio { t i } N i=1, the corporate tax rate t, the keep-tax rate 1 T, ad govermet size relative to GDP. State- taxes also affect the adjusted fudametals i states other tha through their impact o the price distortio, the corporate tax rate ad govermet size relative to GDP i these other states. Cosider the effect of sales-apportioed corporate taxes, {t x i }N i=1. These taxes impact the adjusted trade costs i state, τi A, through the pricig distortio { t } N i. Because of this distortio, i=1 37 Equatio (A.19) i Appedix B.2 shows the expressio for P Q /X. To reach (29), first replace P C from (A.11), R y from (24), ad R corp from (A.17) ito the govermet budget costrait (A.14), ad the ormalize by GDP usig (A.9). 17