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 state taxes as a potetial source of spatial misallocatio i the Uited States. We build a spatial geeral-equilibrium model i which the distributio of workers, firms, ad trade flows across states respods to state taxes ad public-service provisio. We estimate firm ad worker mobility elasticities ad prefereces for public services usig data o the distributio of ecoomic activity ad state taxes from 1980 to 2010. A reveue-eutral tax harmoizatio leads to aggregate real-gdp ad welfare gais of 0.7%. Tax cuts by idividual states lower ow-state tax reveues ad ecoomic activity, ad geerate cross-state spillovers depedig o trade likages. We thak Costas Arkolakis, David Atki, Domiick Bartelme, Lorezo Caliedo, Araud Costiot, Klaus Desmet, Cecile Gaubert, Gordo Haso, David Lagakos, Erico Moretti, Nirupama Rao, Pat Klie, Ralph Ossa, Adrés Rodríguez-Clare, Esteba Rossi-Hasberg, Aleh Tsyviski, ad Jo Vogel for helpful commets, ad semiar participats at AEA, ASU, Be-Gurio U, Berkeley, Chicago, Chicago Booth, Columbia, Carlos III, Cowles, Duke, ERWIT, Haas, Hebrew U, Michiga, NBER, Priceto, SED, St. Louis Fed, Tel-Aviv U, UB, UCLA, UCSD, UNC, Upjoh, WEAI, Wiscosi, West Coast Trade Workshop, Yale, ad ZEW. Matt Pahas, Prab Upadrashta, ad Joh Wieselthier provided excellet research assistace. Fajgelbaum gratefully ackowledges support from the UCLA Zima Ceter. 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.
1 Itroductio Tax policy varies widely across coutries ad across regios withi coutries. I 2012, 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 (2009), or across cities, as i Albouy (2009) ad Desmet ad Rossi-Hasberg (2013) suggests that this dispersio i state tax rates may have a egative impact o 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 dispersio i state 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 aimed to aswer it. We icorporate tools developed i recet trade ad ecoomic geography models, such as Alle ad Arkolakis (2014) ad Reddig (2015), ito a geeral-equilibrium framework 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 distributio of ecoomic activity ad taxes across states from 1980 to 2010. Usig the estimated model we study the effects of elimiatig tax dispersio. We also 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 respectively draw idiosycratic prefereces ad productivities across states, accordig to which they sort spatially. The ameity ad productivity levels of each state partly deped o govermet spedig. 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 state spedig ad i geeral equilibrium 1 For specific policy discussios see Shaviro (1993), Farber (2006), Sulliva (2014), ad Wilso (2015) for the U.S., ad Kee (1987), Devereux ad Pearso (1995), Béassy-Quéré et al. (2014), ad Devereux et al. (2015) for Europe. See Gordo (1983) for a theoretical treatmet. 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. Our model does ot take a stad o how state taxes are determied. Doig so is ot ecessary to study the cosequeces of imposig couterfactual tax distributios, as we do i this paper. 1
through the impact of taxes o prices ad public-service provisio. Specifically, our model implies that state taxes impact the ecoomy through adjusted fudametals, defied as fuctios of exogeous state fudametals (productivity, ameity, ad trade costs), tax rates, ad govermet spedig. Give govermet spedig, higher icome or sales taxes i oe state are equivalet to a lower ameity level i that state i terms of their impact o the distributio of employmet ad wages. Similarly, higher corporate taxes are equivalet to lower productivity, ad chages i salesapportioed corporate tax rates are equivalet to chages i trade costs. Additioally, govermet spedig i ay state depeds o the whole distributio of state taxes ad, therefore, chages i tax rates i oe state also impact the adjusted fudametals of every other state. To measure the effects of alterative state tax structures, we eed estimates of four structural parameters: the elasticities of worker ad firm mobility with respect to after-tax real wages ad profits, respectively, ad the weights of public services i worker prefereces ad firm productivity. To estimate these parameters, we use equilibrium relatioships from our model ad a logitudial dataset o the distributio of workers, establishmets, tax rates, ad govermet reveue across states from 1980 to 2010. Our model geerates a worker-locatio equatio that predicts each state s employmet share as a fuctio of after-tax real wages ad state govermet spedig, ad a firmlocatio equatio that predicts each state s share of establishmets as a fuctio of after-tax market potetial, factor prices, ad state govermet spedig. Ituitively, higher partial elasticities of employmet ad firm shares with respect to govermet spedig i the data correspod to higher weights of public services i worker prefereces ad firm productivity i our model. We estimate these equatios usig taxes i other states to istrumet for each state s factor prices ad govermet spedig; this choice of istrumets is cosistet with our model, i which taxes i oe state impact ecoomic activity i other states oly through these geeral-equilibrium variables. This estimatio approach exploits the more tha 300 chages i tax rates that we observe over this time spa. We estimate a partial elasticity of state employmet with respect to after-tax real wages of about 1, ad with respect to govermet spedig of about 0.2. Our estimates of the firm-locatio equatio imply a higher elasticity of firm mobility with respect to taxes ad a smaller respose of firm locatio to govermet spedig. 4 We calibrate the remaiig parameters (productio techologies ad state fudametals) 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 are available. As a overidetifyig check, we compare the model s predictios for variables that are ot targeted by the parametrizatio agaist the data. We fid that the distributios across states of GDP ad of tax reveue shares i GDP implied by the estimated model are highly correlated with those observed i the data. 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 4 These estimates are i the rage of existig work that has estimated similar specificatios; e.g., Boud ad Holzer (2000), Notowidigdo (2013), Suárez Serrato ad Wigeder (2014), Diamod (2015), Suárez Serrato ad Zidar (2015), ad Giroud ad Rauh (2015). See Sectio 4.3 ad Appedix C.4 for details. 2
tax across states while keepig the size of state govermets costat. 5 We udertake two types of couterfactuals which differ i the measure of govermet size that is kept costat. First, we udertake a reveue-eutral tax harmoizatio by simultaeously brigig the commo tax rate for each tax to a level such that the tax reveue collectively raised by all states is held costat. We fid that a reveue-eutral harmoizatio of sales, icome, ad corporate taxes leads to aggregate real-icome gais of 0.7%, or roughly $110 billio i 2012, poitig to quatitatively importat realicome effects from dispersio i these taxes relative to their 4% reveue share i GDP. Welfare gais are also close to 0.7%. Secod, we udertake a spedig-eutral tax harmoizatio 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. The spedig-eutral tax harmoizatio leads to a 0.12% icrease i welfare ad to a similar icrease i real GDP. As i this couterfactual the distributio of real govermet spedig i each state is kept costat, this result idicates that there are gais from tax harmoizatio idepedetly from the chages i govermet spedig that a implemetatio of this policy could imply. We explore how these results deped both o the values of the parameters determiig the impact of public services o prefereces ad productivity, ad o alterative ways of measurig tax rates. First, we relax the assumptio that the weight of public services i prefereces is the same across all states. Heterogeeity i prefereces for public services may temper the gais from tax harmoizatio if tax rates are higher i states where these prefereces are stroger. Cosistet with this ituitio, we fid that the real-icome ad welfare gais from a reveue-eutral tax harmoizatio are 30% smaller tha i the bechmark if we parametrize the prefereces for public services so that they are proportioal to the tax reveue share i GDP of each state. However, spatial misallocatio cotiues to be preset i this case; moreover, i the spedig-eutral tax harmoizatio, assumig heterogeeous prefereces does ot alter the welfare ad real-icome gais relative to the bechmark. Secod, we aalyze how the results would vary if the weights of public services i prefereces ad productivity were cosiderably lower tha what our bechmark estimates imply. We fid that both the reveue- ad spedig- eutral tax harmoizatio cotiue to deliver welfare ad real-icome gais whe these weights are aywhere betwee zero ad our bechmark estimates; specifically, i the extreme case that assigs zero weight to public services i prefereces ad productivity, the welfare gais from tax harmoizatio are 0.2%. Fially, we also study couterfactuals uder alterative 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 cotiue to fid gais from elimiatig dispersio i icome, sales, ad corporate tax rates i all these cases. We also use the estimated model to gauge the effects of other policies that are ofte the subject 5 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 imply that elimiatig tax dispersio must lead to real-icome ad welfare gais. 3
of public debate. Lower state taxes are said to help create jobs or attract busiesses, 6 but also to erode the provisio of public services with little overall effect o employmet. 7 To 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. O average across states, this policy causes a loss of ecoomic activity i the state lowerig taxes. Geeral-equilibrium forces drive the result: the effect of lowerig taxes keepig goods prices, factor prices, ad govermet spedig costat is to icrease ecoomic activity; however, whe these variables adjust, activity decreases due to lower pre-tax real wages ad to lower tax reveue, which traslates ito lower provisio of public services. This tax chage has heterogeeous impacts across 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 chagig the sales apportiomet of corporate taxes. 8 I the model, this distortio leads firms to sell more to states with lower sales apportiomet. We fid aggregate losses from fully apportioig corporate taxes through sales, ad gais from movig away from sales apportiomet. We idetify a relevat role for trade i drivig this result, as these gais would be smaller uder lower trade costs, suggestig a complemetarity betwee trade frictios ad the distortios caused by the sales apportiomet. Our paper cotributes to the literature o the aggregate effects of misallocatio. A commo approach cosists i measurig distortios across firms as a implied wedge betwee a observed allocatio ad a model-implied udistorted allocatio, as i Restuccia ad Rogerso (2008) ad Hsieh ad Kleow (2009), ad the udertakig model-based couterfactuals to ispect the aggregate effects of dispersio i these wedges. Recet papers have adopted a similar methodology to aalyze misallocatio across geographic uits, such as Desmet ad Rossi-Hasberg (2013) ad Bradt et al. (2013). 9 These wedges capture distortios that may be due to multiple 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. 10 While this literature typically focuses o the impact of distortios o TFP, we study the impact o real icome ad welfare. Our framework builds o quatitative ecoomic-geography models that itroduce labor mobility ito quatitative trade models such as Eato ad Kortum (2002) ad Aderso ad Va Wicoop (2003), icludig Alle ad Arkolakis (2014), Caliedo et al. (2014), Ramodo et al. (2015), Reddig (2015), Bartelme (2015), ad Mote et al. (2015). Our research questio the impact of state taxes 6 See Gov Kasich s Wiig Proposal for Ohio: Lowerig Icome Taxes, Forbes, Arthur Laffer ad Nicholas Drikwater, May 15, 2015. 7 See Kasas Ruious Tax Cuts, The New York Times, Editorial Board, July 13, 2014. 8 See Sectio 2.1. There is a substatial debate o state corporate tax apportiomet policy (e.g., ITEP (2012) ad Mazerov (2005)). 9 See also Behres et al. (2011) ad Hsieh ad Moretti (2015). A related literature o spatial misallocatio cosiders rural-urba icome gaps; e.g., Golli et al. (2013) ad Lagakos ad Waugh (2013) fid productivity gaps betwee agricultural ad o-agricultural sectors which are suggestive of misallocatio, ad Brya ad Morte (2015) study whether these icome gaps reflect spatial misallocatio. 10 For ay observed distributio of taxes, our model 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. 4
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, 11 plus a few ew oes dictated by our questio; the ew igrediets are imperfect firm mobility i the form of idiosycratic productivity draws across states, 12 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 use of observed variatio i these same policies to idetify the key model parameters. 13 Recet papers cosiderig the impact of differet regioal policies usig related tools iclude Gaubert (2015) ad Ossa (2015). Our paper is also related to the literature that has aalyzed the geeral equilibrium effects of tax chages. Shove ad Whalley (1972) ad Ballard et al. (1985) poit out the importace of geeral equilibrium effects whe aalyzig large chages i policy. Albouy (2009) studies distortios i the allocatio of workers across U.S. cities caused by federal tax progressivity ad Eeckhout ad Guer (2015) study optimal icome taxatio across cities. 14 This literature aalyzes static eviromets i which taxes impact the allocatio across sectors or regios, as we do here. A large literature i macroecoomics studies the dyamic effects of taxes i the stadard growth ad real-busiess cycle model; Medoza ad Tesar (1998), amog others, study dyamic effects of taxes i a iteratioal settig. 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. 15 Suárez Serrato ad Zidar (2015) provide evidece o the impact of corporate taxes o worker ad firm mobility, ad Suárez Serrato ad Wigeder (2014) 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 state or i may states simultaeously, such as a tax harmoizatio, impact geeral-equilibrium outcomes i every state idividually ad i the U.S. ecoomy as a whole. 11 Specifically, our model icludes a edogeous umber of moopolistically competitive firms i each locatio similarly to Krugma (1991) ad Helpma (1998), the use of differetiated products as itermediates as i Krugma ad Veables (1995), ad workers with idiosycratic prefereces for locatio as i Tabuchi ad Thisse (2002). Similar igrediets appear i the recet quatitative ecoomic-geography literature refereced above. 12 I.e., i our model, there is imperfect mobility of two factors of productio (firms ad workers). For a quatitative setup also featurig imperfect mobility of several factors of productio see Galle et al. (2015). 13 Bartelme (2015) estimates labor ad wage elasticities with respect to market potetial usig Bartik istrumets. I a iteratioal-trade cotext, Caliedo ad Parro (2014) estimate trade elasticities usig variatio i tariffs. 14 Relatedly, Albouy (2012) studies optimal trasfer schemes i Caada i a Roback spatial-equilibrium settig. 15 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 (1996) exploits foreig tax credit rules to show that ivestmet respods to state corporate tax coditios, ad Giroud ad Rauh (2015) show that C-corporatios reduce their activity 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
The rest of the paper is structured as follows. Sectio 2 describes the features of the U.S. state tax system that motivate our aalysis. Sectio 3 develops the model ad describes its geeralequilibrium 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. Detailed derivatios, additioal figures, ad additioal details o both estimatio ad 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 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. 16 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 (see Appedix F.1 for details). 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. 17 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. 18 I 2012, the 16 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 5.5. 17 Most states limit the tax base to profits eared withi the water s edge, i.e., profits from domestic activity. 18 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 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 6
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. 19 We also explore how our results chage whe we apply alterative corporate tax rates that adjust for the fractio of C-corporatios 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. 20 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 tax rates ad tax bases vary cosiderably across states. Pael (a) of Figure 1 shows the 2010 distributio of sales, icome, corporate, ad sales-apportioed corporate tax rates. 21 For each tax, rates vary across states, corporate tax rates beig the most dispersed; the 90-10 percetiles of the distributios of sales, average persoal icome, ad corporate icome tax rates are 7%-1%, 5%-0%, ad 9%-0%, respectively. For each type of tax, there are at least five states with 0% rates. 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%. 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. t l i = (1 θi x ) t corp i is the corporate tax apportioed through property ad payroll i state i. 19 C-corporatios accouted for 66% percet of total busiess receipts i 2007 (PERAB, 2010). 20 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. 40-23-1(a)(6); Ala Code Sec. 40-23-1(a)(9b); Ala Code Sec. 40-23-60(4)(b); Ala Admi Code r. 810-6-1-.91; Ala Admi Code r. 810-6-1-.137). 21 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., it is t x = θt x corp defied i footote 18. Table A.2 i Appedix F.2 shows the state tax rates i 2007 i all 50 states. Table A.1 shows the federal icome, corporate, ad payroll tax rates i 2007. 7
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 0.1.2.3.4 0 5 10 State Tax Rates i 2010 Sales Corporate Idividual Icome Sales Apportioed Corporate State Tax Reveue as Share of GDP i 2010 0.02.04.06.08 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 Icome Sales Corporate WV HI Local (sub-state) govermets also tax residets. Overall, state taxes amout to roughly 60% of state ad local tax reveue combied. 22 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. 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 aggregate tax reveue from the taxes we cosider i the aalysis (i.e., persoal icome, corporate icome, ad sales taxes) ad direct state spedig durig 1980-2012, both withi states over time ad across states i ay give year. Direct expeditures iclude all govermet expeditures other tha itergovermetal trasfers. 23 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, while Pael (b) shows a equivalet regressio but cotrollig for year fixed effects istead. Note that, i both cases, ot oly is the R 2 is very close to 1, but the slope is also very close to 1. Therefore, a 1% icrease i tax reveue is early always expected to traslate ito a 1% icrease i state direct expeditures. 22 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. 23 The mai direct-expediture items are educatio, public welfare, hospitals, highways, police, correctio, atural resources, parks ad recreatio, govermet admiistratio, ad utility expediture. 8
Figure 2: Comparig State Tax Reveue ad Spedig (a) State Fixed Effects (b) Year Fixed Effects Log State Direct Expeditures 21.5 22 22.5 23 23.5 20.5 21 21.5 22 22.5 Log State Tax Reveue i Model Note: Slope is 1.05 (.001). Sample: 1980-2012. R-squared is 1. Log State Direct Expeditures 21 22 23 24 25 19 20 21 22 23 24 Log State Tax Reveue i Model Note: Slope is 1.01 (.005). Sample: 1980-2012. 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 has 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. 24 Federal public spedig is ot 24 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
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 (ad also its price before 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 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. 25 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 25 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
compoet is ( ) αw ( G v = u L χ (1 T W ) w ) 1 αw, (5) P where we defie the workers tax keep-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. 26 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. 27 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. 28 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 the reader that we have ormalized the mass of workers to 1, the fractio of workers located i state is L = ( v ) εw, (7) v where 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 26 The framework could easily be geeralized to allow for direct cosumptio of the fixed factor by workers i equatio (5) i the form of housig. I that specificatio, the price of lad would also eter as part of the cost of livig. Additioally, the effective tax keep-rate could be modified to also accout for average property taxes, ad housig supply could be allowed to be elastic. While extedig the model with these forces would be straightforward, quatifyig them would be less so because property taxes are largely imposed at the local (sub-state) level, ad housig supply elasticities vary cosiderably across cities withi states, as documeted by Saiz (2010). 27 I.e., if we had a additioal variable z G represetig the efficiecy or quality of govermet spedig, it would eter multiplicatively with u. 28 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 5.5 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). 11
it as our measure of worker welfare. 29 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 who 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. 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. 30 All firms face corporate taxes apportioed through sales, payroll, ad lad ad structures. 31 A 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 =1 ( 29 The costat of proportioality equals Γ εw 1 ε W ), where Γ ( ) is the gamma fuctio. 30 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. 31 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 5.6 we perform a robustess check where corporate tax rates are adjusted by the actual share of C-corporatios i each state. 12
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 corporate tax base is 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 sales-apportioed corporate taxes. 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 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 13
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 the profit of a firm with productivity 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 M i = ( πi ( z 0 i ) π ) ε F σ 1, (15) where the expected profits before drawig {ɛ j i }N i=1 are proportioal to32 π = ( i ) σ 1 ( ) π i z 0 ε ε F F σ 1 i. (16) Equatio (15) says that the fractio of firms located i depeds o the commo compoet of profits i, π i ( z 0 i ), relative to other locatios. A larger value of εf / (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 locate there. 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), 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: 33 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 (i.e., z i /zi 0 > 1), reflectig selectio. This equatio describes ( 32 The costat of proportioality is Γ 1 σ 1 ε F ), where Γ ( ) is the gamma fuctio. 33 By defiitio, z i = (z ( j J j i i )σ 1 dj) σ 1 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). 14
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 is the aggregate expediture 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. 34 As a result, spatial iteractios drive local effects: larger expediture P Q i state acts as a factor-demad shifter i state i through X i, with its impact depedig o the itesity of the trade lik, 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 a stadard ecoomic-geography model with free etry of homogeeous firms such as Helpma (1998) or Reddig (2015), i the sese that the umber of firms is edogeous ad proportioal to sales i each locatio. 35 We assume mobility of heterogeeous firms istead of free-etry of homogeeous firms 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 public-fiace literature, such as Suárez Serrato ad Zidar (2015); third, it allows us to treat mobility of workers ad firms symmetrically. 36 34 See the expressios (A.6) to (A.8) i Appedix B.2. 35 Specifically, 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 X i. If, istead, we had assumed free-etry of homogeeous firms π σ with etry cost equal to f i uits of the factors ad iputs budle of each state, the umber of firms i state i i our X i σ. model would be M i = 1 t i 36 c i f i The cost of assumig mobility of heterogeeous firms istead of free-etry of homogeeous firms is that, i the former, taxes do ot affect the total umber of firms i the ecoomy. We ote, however, that i both cases the fractio 15
3.4 State Govermet State govermets use tax reveue R to fiace spedig i public services. Motivated by the evidece discussed i Sectio 2.3, we assume that tax reveue traslates 1-to-1 ito govermet spedig. Total govermet spedig ad reveue i state is P G = R = R corp + R y + R c, (21) 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, (22) R y = t y (1 t y fed ) [w L + b (Π + R)], (23) R c = t c P C. (24) The base for corporate tax profits are the pre-tax profits from every state, defied i (20), adjusted by the proper apportiomet weights. Equatio (23) 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; i that expressio, Π = i Π i ad R = i r ih i are atioal after-tax profits ad returs to lad ad structures, respectively. The base for the sales tax i (24) is the total persoal cosumptio expediture of workers ad capital owers, P C. 37 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 (give by (A.7) i Appedix B.2) for all ; vii) the lad market clears i every locatio, i.e., equatio (A.8) i Appedix B.2 holds; ad viii) the atioal labor market clears, i.e., L = 1. of the total umber of firms located i each state is determied idepedetly from the total umber of firms (here ormalized to 1), i.e., the cross-sectioal distributio of firms is scale-idepedet. As such, allowig for free etry would ot affect the part of welfare chages correspodig to the spatial distributio of ecoomic activity, which is the focus of our aalysis. However, our aalysis could be carried out assumig free etry to assess this additioal margi. 37 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. 16