Tax Policy Endogeneity: Evidence from R&D Tax Credits

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Tax Policy Endogeneity: Evidence from R&D Tax Credits Andrew C. Chang 2014-101 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Tax Policy Endogeneity: Evidence from R&D Tax Credits Andrew C. Chang∗ November 21, 2014 Abstract Because policymakers may consider the state of the economy when setting taxes, endogeneitybiascanariseinregressionmodelsthatestimaterelationshipsbetweeneconomicvariables and taxes. This paper quantifies the policy endogeneity bias and estimates the impact of R&D tax incentives on R&D expenditures at the U.S. state level. Identifying tax variation comesfromchangesinfederalcorporatetaxlawsthatheterogeneouslyimpactstate-levelR&D taxincentivesduetothesimultaneityofstateandfederalcorporatetaxes. Withthisexogenous variation,mypreferredestimatesindicatea1%increaseinR&Dtaxincentivesleadstoa2.8- 3.8%increaseinR&D.Alternatively,estimatesthatignoreendogenouslydeterminedpolicies indicatethata1%increaseinR&Dtaxincentivesleadstoa0.4-0.7%increaseinR&D.These resultsareconsistentwithtaxpoliciesthatareimplementedbeforeaneconomicdownturn. Keywords: CorporateTax;FiscalPolicy;R&DPriceElasticity;TaxCredits;PolicyEndogeneity JELCodes: H20;H25;H32;H71;K34;O38 ∗Federal Reserve Board. Constitution Ave., Washington DC 20551 USA. +1 (657) 464-3286. a.christopher.chang@gmail.com. https://sites.google.com/site/andrewchristopherchang/. Thisresearchwassupported byagrantfromtheDepartmentofEconomicsattheUniversityofCalifornia-Irvine.However,theviewsexpressedin thispaperaremineandarenotnecessarilythoseoftheuniversity,theFederalReserveBoard,ortheFederalReserve System. I thank several anonymous referees, the editor Kenneth A. Couch, Ryan Baranowski, Marianne P. Bitler, DavidBrownstone,ChristopherS.Carpenter,LindaR.Cohen,TheodoreF.Figinski,BreeJ.Lang,SarahB.Lawsky, DavidLicata,DavidNeumark,GeorgeC.Saioc,ManishaShah,andseminarparticipantsattheAllCaliforniaLabor Conference,APPAM,BatesWhite,CalPoly-SLO,CFPB,CLEA,DOJ,FDIC,FRB,GeorgiaTech,HKU,NTU,OregonState,RAND,RPI,UB,UBC,UC-Irvine,andWEAIforvaluablecomments. IalsothankAnthonyMarcozzifor valuableresearchassistance,EllenAugustiniakandJennyChangforaidininterpretingtaxlaws,JonahB.Gelbachfor assistancewithbootstrapping,DanielJ.Wilsonforinformationontaxdata,andNirmalaKannankuttyandRaymond WolfeforsupportwithNationalScienceFoundationdata. Iamresponsibleforanyerrors. 1

1 Introduction Governments use the tax system to encourage long-run economic growth, promote investment, andsmoothbusinesscyclefluctuations. Forexample,theUnitedStateshasrepeatedlyadjustedits corporate income tax rate and built up corporate income tax credits to attain favorable economic outcomes (Goolsbee, 1998). These tax incentives are a cost for the government. The economic rationale behind tax incentives is that they correct for market failures. For example, in the case of the research and development (R&D) tax credit, because of moral hazard in the financing market for R&D projects and due to the positive technological spillovers from R&D, the level of R&D in theeconomywithoutgovernmentinterventionisbelowtheefficientlevel(Arrow,1962;Griliches, 1992). Therefore, a tax incentive to promote additional spending on R&D would help move the economytowardtheefficientlevelofR&D. Policymakersandmanyeconomistsholdadeep-rootedbeliefabouttheefficacyoffiscalpolicy. A necessary condition to evaluate whether tax incentives are an effective use of revenues is to estimatewhethertaxincentivespromotetheirtargetedeconomicactivity. Unfortunately,economic research estimating the real effects of tax incentives must overcome the inherent endogeneity of taxpolicies.1 Amongotherfactors,thestateoftheeconomyaffectstaxpolicies. Endogeneity bias may lead regression models to either overestimate or underestimate the efficacy of tax policies. For example, suppose that the true effect of tax policies on the economy is zero and that governments change tax incentives while the economy is in a trough. This timing of the tax policies could come about with or without the government actively using taxes to respond to the trough. In this scenario, as the true impact of the tax policies is zero, a revitalized economy afterpolicymakersimplement taxincentivescouldsimplybe mean ortrendreversion(or both). A difference-in-differencesapproachthatcomparesaggregateactivitybeforeandafterthetaxpolicy changes and ignores the endogenously determined timing of the policies would attribute mean or 1PreviousstudiesthatinvestigatetheimpactoftaxpoliciesincludeEasterlyandRebelo(1993);Goolsbee(1998); Ramey and Shapiro (1998); Burnside, Eichenbaum, and Fisher (2004); Mountford and Uhlig (2009); Romer and Romer(2010);Ramey(2011). 2

trendreversiontoaneffectoftaxpoliciesontheeconomy.2 Regressionestimateswouldbebiased towardfindinganeffect. As an alternative scenario, suppose instead that tax incentives affect the economy and that, in terms of timing, tax incentives change just prior to when a downturn would occur without the tax incentives. As in the previous scenario, this timing of tax incentives could be with or without government foresight of the pending downturn. Such a downturn could be a general economic downturncausedbybusinesscyclefluctuationsoralargefirmthatisplanningonhaltingoperations to relocate to a different geographic region. If lawmakers change tax policies just prior to when a downturn would occur, and the true effect was that the tax incentives prevented the downturn, theneconometricianswouldobservenoeffectofthetaxpolicieswhenthetrueeffectwaspositive. In this second case, the bias in a regression model would be toward finding no effect (also called attenuationbias). To quantify the endogeneity bias driven by the timing of tax policies and to evaluate the efficacy of a particular targeted tax incentive traditionally supported by the market failures argument, thispaperestimatestheelasticityofresearchanddevelopment(R&D)withrespecttoR&Dtaxincentives. I use the setting of U.S. states and their R&D tax incentives due to an exogenous source of variation in state-level R&D tax incentives: variation driven by changes in federal corporate tax laws. State policymakers give special attention to their own state’s economic conditions when tailoring their state-level tax policies. However, the federal government arguably pays less attention to state-level conditions when it forms uniform federal tax policies. If variation in state-level R&D tax incentives driven by federal corporate tax laws is uncorrelated with state-level factors that would otherwise drive state corporate tax policy and R&D, then using this variation mitigates endogeneityconcernsandmaygenerateunbiasedestimates. In addition, when a federal tax law changes, preexisting state tax laws determine the federal law’s effect across states. Because these preexisting state laws differ by state, changes in federal corporate tax laws have different effects on state-level R&D tax incentives across states. This 2Ifthemarginaltaxratebythefirmisconstant,thenregressionsusingfirm-leveldatacouldlessenthisendogeneity bias. 3

feature of state tax codes allows this paper to disentangle the effects of the federal tax policies fromothermacroeconomicshocks. The general identification strategy of using federal laws for policy variation across states has been used in other ways, such as analyzing minimum wages (Card, 1992). I follow the personal incometaxliteraturetoisolatetheexogenousvariationinstate-levelR&Dtaxincentivesdrivenby federal corporate tax laws (Gruber and Saez, 2002). In the literature on R&D tax incentives, this paperisclosesttoWilson(2009).3 With corporate tax variation from only changes in federal laws, this paper estimates models that indicate an elastic response of R&D to R&D tax incentives. My preferred estimates indicate that if governments were to increase R&D tax incentives by 1%, then R&D would increase by 2.8-3.8%. My estimates are large relative to results from previous literature on R&D tax incentives. Hall and Van Reenen (2000), Table 2, reviews studies of U.S. data and suggests existing research finds anaverageelasticityof1.0witharangeof[0,1.6]. Tobecomparabletopreviousstudies,thispaper alsoestimatesmodelsusingcorporatetaxvariationfrombothstateandfederallaws. Thesemodels should give biased estimates because states choose their tax incentives. Models with corporate tax variation from both state and federal laws give estimates consistent with existing literature in the range of [0.4, 0.7]. Comparing the estimates from using exogenous federal law variation to estimatesusingendogenousstatelawvariationsuggestsseriousbiastowardsfindingtaxincentives are ineffective when ignoring the endogenous determination of tax policies, which is consistent with Yang (2005); Romer and Romer (2010).4 This attenuation bias supports the story that tax incentives offset future economic downturns, either policymakers have foresight about downturns ormerelythroughfortunatetimingofthetaxes. 3ForotherstudiesonR&Dtaxincentives,seethereviewbyHallandVanReenen(2000)andsubsequentworkby Bloom, Griffith, and Van Reenen (2002); Paff (2005); Wu (2005); Rao (2010); Czarnitzki, Hanel, and Rosa (2011); LokshinandMohnen(2012). ThemaincontributionoverWilson(2009)isIabandontheassumptionthatstate-level R&Dtaxpoliciesareexogenous. Idiscussotherdifferencesintheresultssection. 4Yang(2005)simulatesgrowthmodels. Thepapershowsthatcalibratedmodelsthatomitpreemptivetaxpolicies are misspecified. Romer and Romer (2010) use narrative information on federal taxes to separate endogenously determinedtaxesfromexogenouslydeterminedtaxes. Withvectorautoregressions,RomerandRomer(2010)findthe endogenoustaxvariationleadstounderestimatesoftheimpactoftaxesontheeconomy. 4

2 Data and Estimation InordertoquantifytheeffectofR&DtaxincentivesonR&Dexpenditures,Iestimatethefollowing accelerator-typemodelthattakesintoaccountpartialadjustmentofR&Dexpendituresandallows forothermacroeconomicshocks: (cid:48) ln(RD )=πln(RD )+ϕ +λ +γln(RDTaxIncentiveRate )+ln(X )β +ε (1) it it−l i t it it it where subscript i represents a state, subscript t is time, ln() is the natural log operator, X is a matrix of controls, and the key regressor, RDTaxIncentiveRate, is the proportion of R&D that the government pays for through tax incentives. This model is analogous to the panel data models of Bloom, Griffith, and Van Reenen (2002); Wilson (2009). With state fixed-effects ϕ and time dummies λ, ordinary least squares applied to equation (1) amounts to using the standard within estimator. TheprimarysourceofdataonstatecorporatetaxpoliciesthatIusetoconstructstate-levelR&D taxincentiveratesarethevolumesoflawsthateachstatepassesinagivenyear,calledstatesession laws.5 When available, I also capitalize on state statutes, Commerce Clearing House’s (CCH’s) U.S. Master Multistate Corporate Tax Guide (Various Years), CCH’s IntelliConnect, CCH’s State TaxHandbook(VariousYears),anddatafromWilson(2009). The dependent variable RD is state-year company-financed R&D expenditures from 1981- 2006. This variable excludes federally-financed R&D, income taxes, and interest on tax. These datacomefromtheNationalScienceFoundation’s(NSF’s)SurveyofIndustrialResearchandDevelopment (SIRD).6 These data are biennial (odd year) observations of company-financed R&D up to 1997 and annual from 1997-2006. I focus on spending for four reasons: 1) a tax incentive’s 5SessionlawsareprintedbyeachstateandareaccessibledigitallythroughHeinOnline. 6R&Ddataareavailablesince1963,butIfocusontheperiodsincetheintroductionofthefederalR&Dtaxcredit following previous studies of state R&D tax incentives (Paff, 2005; Wu, 2005; Wilson, 2009). The introduction of thefederalR&Dtaxcreditin1981createdstrongincentivesforfirmstorelabelexpendituresasR&Dandcreatesa potential measurement break between the pre-credit era and the post-credit era (Eisner, Albert, and Sullivan, 1986; Hall and Van Reenen, 2000). While subsequent revisions increasing the generosity of the federal R&D tax credit couldstrengthentherelabelingincentive,startingin1981firmsalreadyhadtheincentivetorelabeltheirexpenditures asR&D. 5

first-order effect is on spending, 2) other measures of innovative output are noisy, 3) identification of the causal effect of tax incentives on innovative output is even more problematic given the lags ininnovation,and4)theadditionalprojectsthatthefirmwouldundertakewithmoregeneroustax incentives likely have a different marginal private and social products than projects that would be undertakenwithouttaxincentives. TheNSFcensorsobservationswhenthedisclosureofastate’sR&Dinaparticularyearwould revealinformationaboutanindividualfirm’sR&D.Thiscensoringtendstoeliminateobservations from low R&D states and states where R&D is concentrated among a few firms. Therefore, I analyzethe21highR&DstateswhereIobserveR&Dexpendituresconsistentlywithoutimputationin the 1980s and 1990s. Observing states in the 1980s and 1990s is necessary because federal R&D taxincentivelawswerepassedinthe1980sand1990s.7 Because I observe states on a yearly basis, the controls capture state-level factors that could affect R&D. As R&D is procyclical, the model incorporates gross state product (GSP) from the BureauofEconomicAnalysis(BEA)andtheunemploymentratefromtheBureauofLaborStatistics as proxies for business cycle effects.8 Federal funding for R&D can either complement or substituteforcompany-financedR&D.Forexample,ifafirmreceivesafederalR&Dcontractthen it may undertake complementary R&D investments to help fulfill the contract. Conversely, firms may simply substitute the acquired public funds for private funds.9 I control for federal funding with federally-financed R&D expenditures from the NSF’s SIRD and data on federal obligations for R&D from the NSF’s WebCASPAR database.10 To control for other unobserved factors that could influence innovative activity, the model uses state expenditures on academic R&D. Data on 7For 2000-2006 the NSF provides imputed observations of R&D for states that are not in the data for the 1980s and1990s. Thestatesinmysamplearethe21withfewornoimputedobservations: Alabama,Arizona,California, Colorado, Connecticut, Florida, Illinois, Indiana, Maryland, Massachusetts, Michigan, Minnesota, NewJersey, New York,NorthCarolina,Ohio,Oregon,Pennsylvania,Texas,Virginia,andWisconsin. ThissampleofhighR&Dstates comprises80-90%ofR&Dafter2000. TwopercentofdatafromthissampleofstatesareimputedbyNSF.Dropping theimputedobservationshasnoeffectontheresults. 8SeeBarlevy(2007),Ouyang(2011),orChang(2013)forresearchintomacroeconomicdeterminantsofR&D. 9Thereisalargeliteraturedebatingwhetherpublicfundscomplementorsubstituteforprivatefunds. SeeDavid, Hall,andToole(2000)forareview. 10See the review in Brown, Plewes, and Gerstein (2005) for details on the differences between these two sources ofdata. Theresultsreportestimatesusingobligationdatatomaximizethesamplesize. Theresultsareinsensitiveto bothmeasurementsoffederalR&Dexpenditures. 6

academic R&D expenditures come from the NSF’s WebCASPAR database. I convert all variables fromnominaltorealvalueswiththeBEA’sGDPdeflator.11 I estimate specifications both with and without the lagged dependent variable. The lagged dependent variable captures the adjustment costs of R&D. To incorporate this lag, I impose a biennial structure over the entire sample period and use the first available lag of R&D (t −2). Imposing a biennial structure on the data drops observations when R&D data are available on an annualbasis,buthasnoeffectontheresults.12 Thewithinestimatorappliedtoequation(1)isconsistentforalargetimedimension. However, forasmalltimedimensionthecoefficientonthelaggeddependentvariableestimatedbythewithin estimator is biased downward (Nickell, 1981). For the panel in this paper, I have data with a time dimension similar to Bloom, Griffith, and Van Reenen (2002); Wilson (2009) of between 12-19 observations,whichshouldreducethebiasfromthewithinestimator.13 3 R&D Tax Incentive Rates Thissectiondescribesthecalculationofstate-levelR&Dtaxincentiveratesandshowspre-treatment plotsthatsupportthispaper’sidentificationstrategy. 3.1 Computation of R&D Tax Incentive Rates Because of the deductibility of R&D expenditures and R&D tax credits, a firm’s marginal dollar of R&D reduces the firm’s tax liability.14 The decrease in tax liability from a marginal dollar of 11The raw data for most of the variables are non-stationary. However, the time dummies and state fixed effects detrendallofthevariables(CameronandTrivedi,2005). Panelunitroottests(SaidandDickey,1984;Levin,Lin,and Chu,2002)onthedetrendedvariablessupportstationarityforallvariablesexceptGSP,andGSPhasnoeffectonthe mainresults. 12AppendixAconductsarobustnesscheckthatusestheannualdatafrom1997-2006. 13As a robustness check, I also attempt to correct for potential Nickell bias with both the one-step and two-step BlundellandBond(1998)GMMestimators,transformingtheinstrumentingequationusingtheorthogonaldeviations transformation(ArellanoandBover,1995)tomaximizethesamplesize,andalsothethreebias-correctionsofthebiascorrected least squares (LSDVC) estimators of Bruno (2005a,b). Unfortunately, both the Blundell and Bond (1998) andBruno(2005a,b)LSDVCestimatorsgenerateimpreciseestimates. 14Firms above their minimum taxable income amount can reduce their tax liability by increasing R&D because R&Disfullydeductible. 7

R&Disthegovernment’sR&Dtaxincentiverate. LetFT denotefederaltaxes,ST denotestatetaxes,RDtot betotalR&Dexpenditures,andr be thediscountrate. ImodeltheR&Dtaxincentiveratefortherepresentativefirm,15RDTaxIncentiveRate as: (cid:32) (cid:33) ∂(ST +FT ) M 1 ∂(ST +FT ) RDTaxIncentiveRate =− it it + ∑ it+m it+m (2) it ∂RDtot ∏ m (1+r ) ∂RDtot it m=1 s=1 t+s−1 it which is the reduction in taxes at time t for state i due to R&D at time t, plus the discounted changes in taxes for future periods.16 I set the discount rate as the dividend-price ratio of the S&P 500 plus its long-term growth rate of 2.4%, following Chirinko, Fazzari, and Meyer (1999); Wilson (2009) with data from Shiller (2005).17,18 To construct RDTaxIncentiveRate, I only use assumptions that are either the same as or weaker than existing studies. Appendix B describes the computationandtheassumptionsindetail. Equation (2) incorporates tax variation from both state and federal laws.19 The variation from state laws is likely endogenous to R&D expenditures at the state level. This endogeneity might arise because state policymakers may set R&D tax incentives as a function of unobserved state economic or political conditions. For example, if a firm threatens the state legislature that it will close down its operations and move to a different state, then the threat of relocation by the firm maycausethelegislaturetopassataxincentivepolicythatbenefitsthefirm. 15ImodeltherepresentativefirmbecausetheNSF’sR&Ddataareatthestatelevel. 16Taking into account the discounted sum of future changes in taxes is necessary because R&D tax credits are occasionallycalculatedasacreditamountoveraM-yearmovingaveragebaseofpreviousR&Dexpenditures. This calculationimpliestakingR&Dtaxcreditsinperiodt canaffecttheabilityofafirmtotakeacreditinfutureperiods. The model only takes into account future changes in taxes when they would be affected by a moving average base, whichisatmost4yearsintothefuture. 17ThetheoreticalrationalebehinddiscountingfutureperiodswiththeS&P500istheopportunitycostofafirm’s funds. AfirmdecidingtoundertakeR&Dcouldinsteadfundsomeoutsideinvestment,withtheS&Pbeingarepresentativeindicatoroftheavailablemarketrateofreturn. 18Equation (2) discounts changes in the tax liability of future periods using the actual realized interest rate. The assumption behind this formulation is firms correctly anticipate the interest rate with certainty and follows Wilson (2009). Asarobustnesscheck,Ialsodiscountfutureperiodsbyassumingfirmsinperiodt usetheinterestratefrom periodt−1toformfutureexpectationsoftheinterestrate. Thisalternativeformulationgivessimilarresults. 19Thetaxratesdescribedbytaxlawsarecalledstatutoryrates. 8

A large body of research from economists and political scientists finds that observed state characteristics influence tax policy changes: tax policies are not randomly changed. These state characteristics range from business cycle measures, such as the unemployment rate, to political variables,suchasbalancedbudgetrules.20 SpecifictoR&Dtaxincentives,thegenerosityofstatelevel R&D tax incentives may be affected by politician’s concerns over revenue loss (Kim, 2010). Astate’sinitialadoptionofaR&Dtaxcreditisalsocorrelatedwithobservedstate-leveleconomic conditions(MillerandRichard,2010). Of course, if observable characteristics were all that drive tax policy changes, then a model couldcontrolfortheseobservables. Theconcernisthatunobservablevariablesinfluencetaxpolicies. A direct test for unobservable characteristics that affect tax polices is impossible. However, an abundance of anecdotal evidence documents that state lawmakers respond to state economic conditions when formulating tax policies. Many of these conditions are probably unobservable to econometricians. For example, Arizona Senator Barbara Leff, one of the sponsors of a bill to increase Arizona’s R&D tax credit, wrote: “We should be the leader in manufacturing, research and development and headquarters but we are not. These jobs are going elsewhere because Arizonadoesnothavespecificincentivesinplacetoattractthesecompanies.” (Leff,2009). Similarly, when California was plagued with high unemployment in 1993, California Governor Pete Wilson made job creation the center of his political platform. In the Governor’s 1993 State of the State address he asserted: “If we are to create jobs, we have to cut taxes... I ask this new legislature to create new jobs. To put Californians back to work by enacting tax incentives and other changes to create jobs... I ask you to invest in the jobs of the future by enhancing the tax credit for research anddevelopmentofnewtechnologies,andIaskyoutomakeitpermanent.” In addition to explicit economic conditions, passing bills through informal political coalitions is another unobserved variable that affects the passage of tax policies.21 For example, a lawmaker 20ExamplesofstudiesthatresearchhowstatecharacteristicsaffecttaxesincludeBerryandBerry(1992,1994)for electoralcycles,Stratmann(1992,1995)forstrategiccoalitionsamongpoliticians,Poterba(1994)forbalancedbudget rules,CrainandMuris(1995);GilliganandMatsusaka(2001)forlegislativestructure,SwankandSteinmo(2002)for unemploymentandcapitalmobility,andAidtandJensen(2009)forfiscalspendingpressureandtaxcollectioncosts. 21Thispracticeisalsocalledlogrolling. 9

may vote to pass a R&D tax credit tax bill for high-tech companies with the sole purpose of securing another vote for a bill on highway construction. To the extent that firms take into account the state’s provision of public goods when making their R&D decisions, this unobserved coalition would be correlated with both R&D expenditures and R&D tax policies, biasing regression estimates. Furthermore,thesecoalitionsbetweenpoliticiansarecommonplace(Tullock,1959). TogetameasureofR&Dtaxincentiveratesfreefromthebiasthatarisesbecausestateschoose their own R&D tax incentives, I isolate the variation in equation (2) from only federal laws. Table 1liststhelawsthispaperusesforfederally-drivenvariationinstate-levelR&Dtaxincentiverates. Thisvariationshouldbeexogenoustounobservedstate-levelconditionsthataffectstate-levelR&D and state-level policies. State governments can tailor tax policies to respond to their own idiosyncraticstateeconomicconditions. However,thefederalgovernmentsetsuniformnationalR&Dtax policiesandislessattentivetoidiosyncraticstateconditions. Let∆RDTaxIncentiveRatefed bechangesintheR&Dtaxincentiveratedrivenbyfederallaws. Theexpressionfor∆RDTaxIncentiveRatefed is: fed ∆RDTaxIncentiveRate =RDTaxIncentiveRate(ST , FT )−RDTaxIncentiveRate(ST , FT ) it it−1 it it−1 it−1 (3) which is the change in the R&D tax incentive rate from a given change in federal tax laws holding state tax laws fixed. This strategy of isolating only the exogenous variation in R&D tax incentivesisanalogoustotheGruberandSaez(2002)methodofconstructingexogenouspersonal income tax rates.22 The R&D tax incentive rate at time t from only federal laws is the sum of all previouschangesinR&Dtaxincentivesdrivenbyfederaltaxlaws: 22GruberandSaez(2002)isolateexogenouschangesinpersonalincometaxratesarisingfromvariationintaxlaws attimetbyconditioningonthepreviousperiod’sincome.Theirexogenouschangesinpersonalincometaxratesreflect policydecisionsatahigherlevel(federalgovernment)thantheunitofobservation(individual). Itaketheanalogous approachandcreateexogenousR&Dtaxincentivesfromvariationinfederaltaxlawsattimet byconditioningonthe previousperiod’sstatetaxlaws. Myexogenouschangesalsoreflectlawchangesatahigherlevel(country)thanthe unitofobservation(state). 10

t RDTaxIncentiveRate fed = ∑ ∆RDTaxIncentiveRate fed +RDTaxIncentiveRate (4) it in i0 n=1 AresearchermaybeconcernedthatregressionmodelsthatuseRDTaxIncentiveRatefed might still be biased because state tax policies may respond endogenously to federal corporate tax policies. Another worry is equation (3) may miss the effects of contemporaneous changes in state and federal corporate tax laws. If state laws change contemporaneously with federal laws, then anestimatedcoefficientonRDTaxIncentiveRatefed mayactuallybepickinguptheeffectsofcontemporaneous state and federal tax law changes instead of the variation in only exogenous federal taxlaws. Tomitigatetheseconcerns,asarobustnesscheckIdropthetwostates(IllinoisandMassachusetts) that enacted R&D tax credits within one year after a change in the federal R&D tax credit. Droppingthesestatesgivessimilarresults.23 Additionalevidenceagainstthehypothesisthatstatesarerespondingendogenouslytochanges in federal tax laws come from the session law data. The R&D tax credit laws for some states contain a preamble that describes the rationale behind why the law was passed. The preambles championgoalssuchasjobcreation,businessexpansion,andbeingtheleaderininnovation. None ofthepreamblesmentionchangesinfederaltaxlawsasmotivation.24 Figure 1 plots summary statistics of per-dollar state-level R&D tax incentive rates, calculated withbothstateandfederallawsdrivingthevariation(equation2). Federallawsinducelargeshifts in state-level R&D tax incentive rates. The figure’s vertical lines denote the effective dates for the federal tax laws. For example, the phase-in of the federal R&D tax credit caused the large increase in rates from 1981 to 1982. Similarly, a reworking of the federal R&D tax credit caused the second large increase in rates from 1989 to 1990. On net, federal laws place the average R&D tax incentive rate at around 0.5 over the last 30 years. In addition, the introduction of state R&D tax incentives (the first state R&D tax credit was introduced in 1981, effective in 1982) increased 23AppendixApresentstheresults. AppendixAalsopresentsoveridentificationtestsfollowingaformatsimilarto Weber(2014). Withtheseoveridentificationtests,Iamunabletorejectthevalidityofmyinstrument. 24AppendixCgivesexamplesofthesepreambles. 11

the across-state variation in state-level R&D tax incentive rates over time.25 Figure 2 plots rates for a few individual states. Aside from 1999, between zero and two states in my sample pass an R&D tax credit bill that affects the state’s R&D tax incentive rate in each year, whereas in 1999 fourstatespassedsuchabill. Figure 3 plots summary statistics of per-dollar state-level R&D tax incentive rates with only federallawsdrivingthevariation(equation4). Figure4plotsthesamevariableforfourindividual states. Again, vertical lines show the effective dates for the federal tax laws. The removal of variation from state laws decreases the across-state variation over time. However, because of the heterogeneous effects of federal laws on state-level R&D tax incentive rates, the across-state variationinratescontinuestoincreaseovertime. 4 Institutional Details of the Interactions Between Federal and State Tax Law The computations of federal and state corporate taxes are interdependent. A firm’s federal tax liability depends on the firm’s state tax liability and vice versa. The simultaneity between federal and state corporate taxes contributes to differential effects of federal laws on state-level R&D tax incentive rates across states. I model the heterogeneous changes in R&D tax incentive rates from federal laws by taking into account two broad classes of incentives: 1) incentives relating to deductionsforcorporateincometaxespaidand2)incentivesrelatingtoR&Dtaxcredits.26 The federal government allowed a deduction for state corporate income taxes starting in 1954. At the same time, some states allow deductions for federal or state corporate income taxes (or both). Other states allow neither type of deduction. This between-state variation in tax policies implies any change in federal tax law that affects a firm’s federal income tax liability will have 25Withstatefixedeffectsandtimedummies,identifyingvariationcomesfrommeandeviationsinR&Dtaxincentive rates, notfromlargeshiftsthataffectallstatesequally. Therobustnesscheckssectionconfirmsthemainresultsare notsensitivetothelargeincreaseinratesfromtheintroductionofthefederalR&Dtaxcreditin1981. 26Thesetwoclassesarethemselvesinterdependent,butIseparatethemforexposition. SeethemodelinAppendix B. 12

differentialeffectsontotaltaxliabilityacrossstates. For example, changes in the federal corporate income tax rate directly affects total taxes for all states. For states that allow federal corporate income taxes paid as a deduction, changes in the federal corporate income taxrate aredampened. Thevalue of thisdeduction isproportional tothe state corporate income tax rate. Suppose the federal government increases the federal corporate income tax rate from 0.4 to 0.5 and that there are no R&D tax credits or state deductions for state corporate income taxes.27 If a state does not allow a deduction for federal corporate income taxes paid,thentheincreaseintaxesforfirmswouldbetencentsperdollaroftaxableincome. Ifastate with a five percent corporate income tax allows a deduction for federal corporate income taxes paid,thentheincreaseintaxesforfirmswouldbe9.5centsperdollaroftaxableincome. Forevery dollar of additional federal corporate income tax, firms can take an additional dollar of deduction on their state taxes. With a five percent state corporate income tax rate, each dollar of deduction from state taxable income is worth five cents. Therefore, changes in the federal corporate income taxratehaveheterogeneousimpactsonthevalueofdeductions,andhenceR&Dtaxincentiverates duetothedeductibilityofR&Dexpenditures,asafunctionofstatecorporateincometaxratesand whatproportionoffederalcorporatetaxesstatesallowasadeduction. VariationinthefederalR&Dtaxcreditalsocontributestodifferentialeffectsoffederallawson state-level R&D tax incentives. The largest source of variation comes from the passage of Public Law (PL) 101-239 on December 19, 1989. Public Law 101-239 increased the effective federal R&D tax credit and reduced allowable deductions for R&D expenditures starting on January 1, 1990. In 1989, the federal R&D tax credit was 20% of qualified research expenditures (QREs) above a three-year moving average base amount of QREs.28 In addition, in 1989 firms could deduct 50% of their QREs claimed for computing the federal R&D tax credit from their federal taxableincome. PL101-239changedthebaseamounttoafixedbaseanddisallowedthededuction forQREsusedtocalculatethecredit.29 27ThepresenceofR&Dtaxcreditsandstatedeductionsforstatecorporateincometaxescomplicatestheintuition, butthemainpointisthesame. 28SeeGuenther(2006)forareviewofthefederalR&Dtaxcredit. 29Treatingtaxcreditsastaxableincomeiscalledcreditrecapture. 13

Changingthebaseamountfromathree-yearmovingaveragebasetoafixedbasedramatically increased the effective R&D credit rate (Hall, 1993; Wilson, 2009). Under the three-year moving average base, for each dollar of credit claimed a firm had to lower its future claimed credit by a third of a dollar for each of the next three years. With the fixed base, PL 101-239 eliminated this opportunity cost. At the same time, the disallowance of the 50% QRE deduction decreased the effective credit rate because firms could no longer take both a deduction and a credit for the same QREs. The heterogeneous effects on state-level R&D tax incentive rates from PL 101-239 came from two factors: 1) how states structured their R&D tax credits and 2) how states computed state taxableincome(statetaxableincomebasis). A two common features of state tax policy are: 1) offering a state R&D tax credit computed withthesamemethodasthefederalR&Dtaxcreditand2)havingthiscomputationmethodlinked directlytotheInternalRevenueCode(IRC),thedocumentthatgovernsU.S.federaltaxlaw. These two combined features of state tax policy are called piggybacking. For example, Oregon Revised Statues § 317.152, which authorizes a R&D tax credit for Oregon QREs, states “A credit against taxesotherwisedueunderthischaptershallbeallowedtoeligibletaxpayersforincreasesinqualifiedresearchexpenses... thecreditshallbedeterminedinaccordancewithsection41oftheInternal RevenueCode.” Piggybacking implies any change in the computation of the federal R&D tax credit automatically updates how piggybacking states calculate their R&D tax credits: changes in federal tax law cause changes in effective state tax law and state policymakers do not dictate these changes. In 1989, California, Indiana, Iowa, Minnesota, North Dakota, Oregon, and Wisconsin piggybacked onthefederalR&Dtaxcredit. Allelseequal,forthesesevenstatesPL101-239increasedboththe effective federal R&D tax credit and the effective state R&D tax credit. Therefore, for these states PL 101-239 caused a disproportionally large increase in R&D tax incentive rates relative to states without piggybacked R&D tax credits. For states without piggybacked R&D tax credits, PL 101- 239causedanincreaseinR&Dtaxincentiveratesofbetweennineandthirteencentsperdollarof R&D. The increase in rates for states with piggybacked R&D tax credits was approximately 50% 14

greaterthantheincreaseinratesforstateswithoutpiggybackedR&Dtaxcredits. The basis for state taxable income also helped foster heterogeneous effects of PL 101-239 on state-level R&D tax incentive rates. In general, states either use income from all sources (gross receipts) or federal taxable income as a starting point for computing state taxable income. States that incorporate federal taxable income as a starting point automatically apply federal-specific deductions and exemptions to form state taxable income. For these states, changes in the IRC cause automaticupdatesinstatetaxcodes. Ontheotherhand,statesthatformstatetaxableincomestartingwithincomefromallsourcesdonotincorporatefederal-specificdeductionsandexemptionsso that alterations to the IRC have no effect on their state tax codes. Public Law 101-239 disallowed the 50% QRE deduction allowed prior to 1990 when taking the federal R&D tax credit (IRC § 280C(c)). For states with federal taxable income as a base, PL 101-239 caused an automatic increaseinthestateincomebase(thatis,adecreaseintheeffectivefederalR&Dtaxcredit)andhad noeffectforstatesthatusedincomefromallsourcesasabase. Thisfeatureofstatetaxcodesalso contributestodifferentialeffectsoffederallawsonstate-levelR&Dtaxincentiverates. Appendix Dgivesadetailedexampleofhowafederaltaxlawpassesthroughtotheconstructionofequation (4).30 5 Pre-treatment Plots Separating the effect of R&D tax incentives on R&D from other macroeconomic shocks relies on heterogeneous effects of federal tax laws on state-level R&D tax policies. One concern with this strategy is that the effects of federal laws on state-level policies are non-randomly assigned. If states receive disproportionate tax incentives from federal laws because of unobserved state-level factorsthatalsoaffectR&D,thenevenfederalvariationintaxeswouldgivebiasedestimates. Tocheckforbiasfromfederallaws,Iperformastandardcheckinthedifference-in-differences framework and plot the levels and trends of R&D for each state prior to the introduction of the 30In the interest of brevity I simplified this discussion slightly. Some states have specific provisions that override whatthebasewouldpredict. SeeAppendixBfordetails. 15

federal R&D tax credit in 1981 (the first treatment law). If the levels and the trends of R&D for the treatment and control groups appear similar prior to the introduction of the federal R&D tax credit,thenthesegraphsbolsterthecaseforrandomassignmentofthetreatment. Aslightcomplicationwiththeseplotsarisesbecausethetreatmentisaseriesoflawsthateach treats all states, not just a single standard binary treatment and control setup. Federal laws affect somestatesmorethanothers,buteachfederallawimpactseverystate. Tomakeresultscomparable toastandardgraph,Igroupstatesintoabove/belowmedianrategroupsandplottheaverageR&D foreachofthesetwogroups. Figure 5 groups states into above/below median R&D tax incentive rates based on variation from both state and federal laws (equation 2). The dashed line represents average nominal R&D forthesetofstateswithanabovemedianaveragevalueofR&Dtaxincentivesfrom1981-2007.31 The solid line is the set of states with a below median average value of incentives over the same time period. From 1963-1971, the trends look parallel, although the level of R&D for states with abovemediantaxincentivesishigherineachyear. From1971-1979,agapemergesbetweenthese two groups of states, with nominal R&D growing faster for states that implement more generous taxincentivesfrom1981-2007. Figure 6 instead groups states into above/below median average values in R&D tax incentive rates with the rates calculated from only federal law variation (equation 4). Again, the dashed line represents states above the median.32 From 1963-1977, the trends and levels of R&D for the two groups are close. A small gap opens up in 1979, with the above median group showing higherR&D.However,thepre-treatmentlinesmatchmoreclosely,inbothlevelsandtrends,when groupingstatesaccordingtoratescalculatedfromonlyfederallawvariation. 31Thisgroupofstatesis: Arizona, California, Connecticut, Indiana, Massachusetts, Minnesota, NewJersey, New York,Pennsylvania,andWisconsin. 32Thisgroupis: California,Colorado,Connecticut,Indiana,Minnesota,NewYork,NorthCarolina,Pennsylvania, Oregon,andWisconsin. 16

6 Results This section presents my main specifications and a robustness check involving the user cost of capital. AppendixAconductsadditionalrobustnesschecks. 6.1 Main Specifications Table 2 presents instrumental variables estimates with RDTaxIncentiveRatefed instrumenting the statutorytaxincentiverateRDTaxIncentiveRate. Thetablereportscoefficientsaselasticitiesfrom natural log-natural log specifications. All specifications indicate an elastic response of R&D to tax incentives of at least 2.0. Columns (1) and (2) present results from static specifications that omit the lagged dependent variable. Column (1), a specification that only includes the R&D tax incentive rate with state fixed effects and time dummies, indicates an elasticity (standard error) of 4.51 (1.59). Column (2) adds lagged federal R&D following Wilson (2009) as well as academic R&D and the unemployment rate as controls. The coefficient (standard error) of the rate term remains elastic at 5.06 (2.02). Among the control variables, only federal R&D is statistically significant. The positive coefficient on federal R&D suggests complementarity between federal R&Dandcompany-financedR&D. If the lagged dependent variable belongs in the model, then omitting it leads to inconsistent estimates. I prefer to include the lagged dependent variable due to R&D’s high adjustment costs. Dynamicspecificationsalsoallowmetobackoutanimpliedlong-runelasticity,γ/(1−π),where γ is the coefficient of the key regressor and π is the coefficient on the lagged dependent variable. Columns(3)-(5)representmypreferredestimatesthatincludethelaggeddependentvariable. The lagged dependent variable attenuates the elasticity estimate of R&D to tax incentives, but improves the precision.33 Furthermore, the results continue to indicate a 1% increase in R&D tax incentives leads to at least a 2% increase in R&D. The estimates are also statistically significant at standard levels. Column (3) of Table 2, which uses only the instrumented tax rate, the lagged 33Attenuated estimates with improved precision when including the lagged dependent variable is consistent with Bloom,Griffith,andVanReenen(2002)’scross-countrystudyofR&Dtaxcredits. 17

dependent variable, and fixed effects implies an elasticity estimate (standard error) of 2.89 (1.14). The coefficient (standard error) on the lagged dependent variable is 0.46 (0.10), confirming the presence of adjustment costs for R&D and implying a long-run elasticity (standard error) of 5.38 (1.74). Column (4) of Table 2 includes a full set of control variables. The coefficient (standard error) of the instrumented ln(RDTaxIncentiveRate) is still large at 3.69 (1.59). GSP enters the model as positive and large, consistent with the procyclicality of R&D. The coefficients on the other controlvariableshaveasimilarinterpretationtothestaticspecificationincolumn(2),althoughthe coefficientonacademicR&Disnownegative. Column(5)removesGSPsothatthemodelincludes only stationary variables. This specification gives similar results to column (4) and continues to indicateanelasticresponseofR&Dtotaxincentives. AcademicR&Dincolumn(5)isonceagain insignificant. Table3presentsresultsfromequation(1)withthekeyregressorasthepotentiallyendogenous R&D tax incentive rate (state and federal laws driving the tax variation) estimated with ordinary least squares (OLS). The lack of an instrument makes Table 3’s specifications analogous to specificationsfromtheexistingliteratureonR&Dtaxincentives. TheestimatesfromTable3shouldbe biasedduetostateschoosingtheirR&Dtaxpolicies. With OLS, all specifications in Table 3 indicate a smaller response of R&D to tax incentives than the response from models that instrument the tax rate. Columns (1) and (2) present results from static models, which omit the lagged dependent variable. The specification in column (1) includes only the endogenous tax incentive rate, ln(RDTaxIncentiveRate), and fixed effects. This specification indicates a 1% increase in the R&D tax incentive rate causes a 1.66% increase in company-financed R&D. In column (2), I retain the static model and add control variables. The responseofR&Dtoitstaxrateremainsalmostunchanged. Table 3, columns (3) - (5) present results from my preferred dynamic specifications. The estimatesfromthesedynamicspecificationsindicateaninelasticresponseofR&Dtoitstaxrate,with a range between 0.37 and 0.65. These estimates are well within the range of estimates provided 18

by the existing literature. The precision of the dynamic specifications continues to be superior to the static specifications and the control variables have the same interpretation as the controls from Table2.34 ThesepointestimatesaresmallerthanthecomparablespecificationfromWilson(2009)(Table 1, column 1), although they fall within the range of estimates reviewed by Hall and Van Reenen (2000). The difference from Wilson (2009) is primarily due to the fact that this paper uses large R&D states without imputed observations while Wilson (2009) uses all available states and also imputed observations. I am restricted to large R&D states because these states are the ones I observe during the period when federal tax laws were changing (1980s and 1990s). Observations for smaller R&D states are not available before 2000 and after 2000 many observations for these smallstatesareimputed. SeeAppendixEforadditionaldetails. The difference between the results in Tables 2 and 3 suggests ignoring the endogeneity of tax policies leads to attenuated estimates of the response of R&D to tax incentives. Because the estimates of the response of R&D to tax incentives with exogenous variation in incentives are larger than the estimates with endogenous variation, the results are consistent with policymakers implementing R&D tax incentives to offset the future loss of R&D expenditures. For example, if firms plan to relocate R&D activity to another region, then lawmakers may offer the firm tax incentives to keep the firm’s R&D activity from changing location. This preemptive offering of R&D tax incentives would cause researchers to observe no effect of the endogenously determined tax policies when their true effect was to prevent a drop in R&D. Therefore, the presence of this prevention mechanism would bias regression models towards finding no effect of tax policies on R&D. 34Apossibilitywhytheestimatesbetweenendogenousandexogenousvariationaredifferentisbecauseofdifferent treatment effects across states. Unfortunately, this possibility is not testable. The treatment variable’s magnitude is onlysomewhatrelated(non-linearly)totheendogenousRDTaxIncentiveRate. Twoofthefivestateswiththehighest averageRDTaxIncentiveRatearealsointhetop5impactedbyfederaltaxlaws,whilethesameistrueforsevenofthe topten. 19

6.2 User Cost of Capital Robustness Check In this subsection, I present results from a robustness check involving the user cost of capital. Appendix A presents a variety of additional robustness checks that show the paper’s results are insensitivetovariousmodelanddataspecifications. Following Chirinko and Wilson (2008) and Wilson (2009), I form the user cost of R&D capital RDUserCost as an extension of Hall and Jorgenson (1967). The user cost is the ratio of the R&D tax incentive rate, RDTaxIncentiveRatefed, to the tax incentive rate of output, OutputTaxIncentiveRate,whereoutputisafullydeductibleexpensethatdoesnothaveanassociatedtaxcredit,35 adjustedfordepreciationδ ofR&Dandthediscountrater: fed RDTaxIncentiveRate RDUserCost = it [r +δ ] (5) it t t OutputTaxIncentiveRate it Equation (5) captures the fact that the opportunity cost of investment in R&D is an investment in some other good, such as output. Rewriting equation (1) with the natural logarithm of the user costasthekeyregressoryields: fed ln(RD ) = πln(RD )+ϕ +λ +κln(r +δ )+γln(RDTaxIncentiveRate ) it it−l i t t t it (6) (cid:48) −υln(OutputTaxIncentiveRate )+ln(X )β +ε it it it Under depreciation and discount rates that are uniform across states, the time dummies absorb ln(r +δ ) so that equation (6) amounts to the original model with a new term for the tax incent t tiverateofoutput,ln(OutputTaxIncentiveRate ). Includingln(OutputTaxIncentiveRate )inthe it it model continues to indicate an elastic response of R&D to R&D tax incentives. For example, the specification in column (5) of Table 2 yields a R&D tax incentive rate estimate (standard error) of 3.68 (1.74). The control variables have similar point estimates and the tax incentive rate of output 35Specifically,IcomputeOutputTaxIncentiveRatewiththemodelinAppendixBwithoutthetermsforR&Dspecifictaxincentives. 20

isinsignificantatstandardlevels.36 7 Conclusion Policymakers form tax policies based on the state of the economy. This characteristic leads to endogeneity bias in regression models that estimate the effect of taxes on economic variables. To determine this endogeneity bias and the real effects of tax incentives, this paper estimates the elasticityofR&DwithrespecttoR&Dtaxincentives. This paper improves on previous studies by using identifying tax variation in state-level R&D tax incentives from changes in federal corporate tax laws. Because the federal government sets uniform national tax policies and is less attentive than state governments to idiosyncratic statelevel economic conditions, using variation from federal tax laws reduces concerns over biased estimates stemming from states choosing their own tax polices. This paper finds R&D is sensitive totaxincentives,withmypreferredestimatesindicatingthata1%increaseinR&Dtaxincentives wouldleadtoa2.8-3.8%increaseinR&Dexpenditures. This paper also estimates models with R&D tax incentive rates calculated using tax variation from both state and federal laws. These models are similar to those from previous studies and should give biased estimates because states choose their own R&D tax incentives. My models with endogenous tax variation in R&D tax incentive rates produce much smaller estimates of the elasticity of R&D with respect to tax incentives, with an average estimate of 0.5. The difference between the estimates from uncorrected endogenous tax variation and only exogenous federal tax variation indicates serious attenuation bias from the endogenous tax variation. The direction of this bias suggests that tax incentives may offset future economic downturns, which is consistent withYang(2005);RomerandRomer(2010). Couldpolicymakersbepurposelydesigningoffsettingtaxincentives? Ifso,thenpolicymakers may see a downturn is beginning or predict one will happen and change policies to offset the 36Calculating OutputTaxIncentiveRate by isolating only state-level tax variation from federal laws in the cost of outputwiththeanalogousdefinitionfromequation(3)givessimilarresults. 21

upcoming downturn. Another story is that policymakers could simply be adopting tax incentives whenfundsareavailable,whichmaybejustbeforeadownturnstarts. Several mechanisms may contribute to the elastic response of R&D to tax incentives that my models find. Because of the state fixed effects and time dummies, my models identify coefficients based on deviations from mean levels of R&D and R&D tax incentives. Increases in R&D for statesthatimplementincentivesanddecreasesinR&Dforstatesthatdonotimplementincentives wouldbothcontributetothemagnitudeofmyestimates. A large elasticity could be due to low adjustment costs of R&D across state borders. There may be low adjustment costs because firms may relocate R&D between their establishments to maximizetaxincentives. ThepresenceofmobileR&Dcouldbeanincentiveforstatestocompete strategically with tax incentives. Depending on the slope of state reaction functions, strategic competition can lead to either too generous tax incentives (relative to the efficient level) or some stateswithgenerousincentivesandotherswithminimalincentives(BruecknerandSaavedra,2001; Brueckner,2003;DeckerandWohar,2007;ChirinkoandWilson,2008,2011). MyelasticityestimatescouldalsobeexplainedbyfirmsraisingtheirtotalR&Dinresponseto beingofferedtaxincentives. Thisexplanationseemsplausiblewhenthefirm’sgeneralinvestments have strong complementarities or even when just the firm’s R&D-specific projects have strong complementarities. For example, suppose that R&D and non-R&D investment are complements. If a tax incentive lowers the price of R&D, then the firm will respond by undertaking additional non-R&Dinvestment. However,thisadditionalnon-R&Dinvestmentwillalsoincentivizethefirm totakeonadditionalR&DandpotentiallyleadstoalargeresponseofR&Dtotaxincentives. References Aidt, Toke S., and Peter S. Jensen, “The Taxman Tools Up: An Event History Study of the IntroductionofthePersonalIncomeTax,”JournalofPublicEconomics93:1-2(2009),160-175. 22

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Ramey, Valerie A., “Identifying Government Spending Shocks: It’s All In the Timing,” Quarterly JournalofEconomics126:1(2011),1-50. Ramey,ValerieA.,andMatthewD.Shapiro,“CostlyCapitalReallocationandtheEffectsofGovernment Spending,” Carnegie-Rochester Conference Series on Public Policy 48 (1998), 145- 194. Rao,Nirupama,“DoTaxCreditsStimulateR&DSpending? RevisitingtheEffectoftheR&DTax CreditinitsFirstDecade,”WorkingPaper(2010). Romer, Christina D., and David H. Romer, “The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks,” American Economic Review 100:3 (2010), 763-801. Roodman, David, “How to do xtabond2: An Introduction to Difference and System GMM in Stata,”StataJournal9:1(2009),86-136. Said, Said E., and David A. Dickey, “Testing for Unit Roots in Autoregressive-Moving Average ModelsofUnknownOrder,”Biometrika71:3(1984),599-607. Shea, John, “The Input-Output Approach to Instrument Selection,” Journal of Business & EconomicStatistics11:2(1993),145-155. Shiller,RobertJ.,IrrationalExuberance(Princeton: PrincetonUniversityPress,2005).Dataavailableathttp://www.econ.yale.edu/~shiller/data.htm Stratmann, Thomas, “The Effects of Logrolling on Congressional Voting,” American Economic Review82:5(1992),1162-1176. Stratmann,Thomas,“LogrollingintheU.S.Congress,”EconomicInquiry33:3(1995),441-456. Swank, Duane, and Sven Steinmo, “The New Political Economy of Taxation in Advanced CapitalistDemocracies,”AmericanJournalofPoliticalScience46:3(2002),642-655. 28

Tullock, Gordon, “Problems of Majority Voting,” Journal of Political Economy 67:6 (1959), 571- 579. Weber, Caroline E., 2014, “Toward Obtaining a Consistent Estimate of the Elasticity of Taxable IncomeUsingDifference-in-Differences,”JournalofPublicEconomics117(2014),90–103 Wilson, Daniel J., “Beggar Thy Neighbor? The In-State, Out-of-State, and Aggregate Effects of R&D Tax Credits,” Review of Economics and Statistics 91:2 (2009), 431-436. Also as Federal ReserveBankofSanFranciscoWorkingPaper2005-8(2007). Wu, Yonghong, “The Effects of State R&D Tax Credits in Stimulating Private R&D Expenditure: A Cross-State Empirical Analysis,” Journal of Policy Analysis and Management 24:4 (2005), 785-802. Yang, Shu-Chun Susan, “Quantifying Tax Effects Under Policy Foresight,” Journal of Monetary Economics52:8(2005),1557-1568. Zodrow,GeorgeR.,“CapitalMobilityandCapitalTaxCompetition,”NationalTaxJournal63:4-2 (2010),865-902. A Appendix: Robustness Checks A.1 Additional Controls and Sample Restrictions AresearchermaybeconcernedthecontrolvariablesinTables2and3areinsufficientlyrich. Therefore, I experiment with a more saturated specification of controls that utilizes contemporaneous, one lag, and two lags of all control variables. The R&D tax incentive rate driven only by federal laws generates an elasticity estimate (standard error) of 4.60 (1.82). This estimate continues to indicate a large response of R&D to tax incentives consistent with the more simple specifications of Table 2. This more saturated specification gives an elasticity estimate (standard error) of 0.53 29

(0.77) for the endogenous R&D tax incentive rate driven by both state and federal laws, which is inlinewiththeparsimoniousspecificationsinTable3.37,38 Table 4 considers models subject to various sample modifications. Starting with the specification in column (5) of Table 2, in column (1) of Table 4 I trim the 2% of observations with the largest residuals, removing 1% of the sample from each tail.39 I conduct this robustness check to see if the results are driven by only a few observations that the model does not explain well. Column(2)estimatesthemodelwithdatastartingin1985toremovetheeffectoftheintroduction of the federal R&D tax credit, which causes the large increase in R&D tax incentive rates from 1981-1982 in Figures 1 and 3. In column (3), I estimate the model only with data up to 1999 because the variation in R&D tax incentive rates driven by federal laws comes exclusively from the 1980s and 1990s. In column (4), I use all of the available R&D data by abandoning the biennial structure used so far. This strategy changes the model from biennial to annual observations from 1997-2006 and addresses concerns over potential loss of precision from dropping observations in thelatterpartofthesample.40 The models subject to these sample modifications continue to suggest an elastic response of R&D to tax incentives. The smallest estimate comes from removing outliers in column (1), which indicates if governments were to increase R&D tax incentives by 1%, then R&D would increase by2.9%. Estimatingthemodelwithdatastartingin1985yieldsanestimatesimilartothemainresultin Table2. Therefore,themainresultisnotdrivenbythephase-inofthefederalR&Dtaxcreditthat causesthelargeincreaseinR&Dtaxincentiveratesfrom1981to1982shownbyFigures1and3. Droppingobservationsafter1999incolumn(3)imposesthelargestsamplereductionandalso has the largest effect on the estimates. The estimate of the price elasticity (standard error) is now much more elastic at 6.29. This large increase in magnitude is likely due to the increased 37Theresultsarealsorobusttoaddingstate-specificlineartimetrends,therateofgrowthofGSP,andthefirstlag oftherateofgrowthofGSPascontrols. 38The endogenous R&D tax incentive rate driven by both state and federal laws gives inelastic to approximately unitelasticpointestimatesforallrobustnesschecks. 39A5%sampletrim(2.5%fromeachtail)yieldssimilarestimates. 40WeightingstatesbyaverageGSPfrom1981-2006alsogivessimilarresults. 30

downward bias on the lagged dependent variable from the within estimator. The coefficient on the lagged dependent variable is down to 0.09 from 0.39 in Table 2, column (5). This bias on the laggeddependentvariablerenderstheothercoefficientsinconsistent,sotheestimatesfromcolumn (3)shouldbetakenwithadoseofsuspicion. The final sample modification in column (4), using annual observations from 1997-2006 insteadofbiennialobservations,givesasimilarestimatetothemainresultsofTable2. Forallspecifications subject to sample modifications, federal R&D complements company-financed R&D. AcademicR&Dandtheunemploymentrateareinsignificant.,41 Finally,asanadditionalcontrol,Iestimatespecificationsthatincludeageographicallyweighted out-of-state tax incentive rate following Wilson (2009). I add this control to investigate potential relocationeffects. Table 5 shows the results. Column (1) presents the result from Table 2, column (5) for comparison. Columns (2) - (4) of Table 5 add the weighted out-of-state tax incentive rate. Table 5 inoutofstate cludestheweightedout-of-statetaxincentiverate,RDTaxIncentiveRate ,astheinverselyit geographically-weighted R&D tax incentive rate of the closest three states, with state locations determinedby2000USCensuspopulationcentroidsanddistancesbetweenstatescomputedusing the great circle formula (similar results hold using the weighted average of the closest five states). The table instruments the out-of-state tax incentive rate using an analogously weighted version of theinstrumentforthein-statetaxincentiverate. First-stageF-statisticsontheexcludedinstruments arebetweenthreeandthirteen,dependingonthespecification. The takeaway message from Table 5 is that the effect of the instrumented out-of-state tax incentiverateisimpreciselymeasured. Thecoefficientisneverstatisticallydifferentfromzero,but the standard errors are quite large (between 4 and 6). The coefficient on the in-state tax incentive 41The clustered standard errors imply rejection at the 5% level or lower for the key coefficient in the preferred models. I also check the rejection rates, following the recommendation of Cameron, Gelbach, and Miller (2008), by bootstrapping the t-statistic using the wild cluster bootstrap-t procedure (Brownstone and Valletta, 2001). I use Rademacherweightswith1000replicationsforeachtestandimposethenullhypothesisthatthetaxpolicyvariableis zeroasadvocatedbyDavidsonandMacKinnon(1999);Cameron,Gelbach,andMiller(2008). Thebootstrapblocks are states. The hypothesis test of H :γ =0 vs. H :γ >0 yields p-values between 0.03 and 0.09 for the preferred 0 A model’skeyregressors. 31

rate is still approximately three and is significant at the 5% level or better in all specifications. While I would like to be able to identify a R&D relocation effect, the data do not allow me to eithersupportarelocationeffectorruleoneout. A.2 Other Dynamic Forms and Alternative R&D Tax Incentive Rates Table 6, columns (1) - (2) present robustness checks with alternative formulations of the lagged dependent variable. Following Wilson (2009), in column (1) I continue to make use of the entire R&D sample and instead incorporate the lagged dependent variable as the most recent available lagofR&D:t−2forthebiennialperiod(1981-1995)andt−1fortheannualperiod(1997-2006). This specification allows the coefficient on the lagged dependent variable to vary between the biennial and annual periods. Column (1) gives a larger response of R&D to tax incentives, but the resultsarequalitativelysimilartothemainresultsfromTable2. In Table 6, column (2) I return to the biennial data structure and use ln(RD ) instead of the it−4 most recent available lag, ln(RD ). If R&D tax policy is contemporaneously determined with it−2 lagged R&D, then instrumenting with ln(RDTaxIncentiveRatefed) and including lagged R&D in the model will lead to inconsistent estimates. Incorporating a deeper lag of R&D in the model instead of the most recent lag ameliorates concerns over contemporaneously determined lagged R&D and R&D tax incentives. Using ln(RD ) instead of ln(RD ) causes the coefficient on it−4 it−2 ln(RDTaxIncentiveRatefed) to increase to 7.11. The estimate on ln(RD ) decreases to 0.10. it−4 These results are similar to the static specifications that omit the lagged dependent variable and Table4,column(3). Table6,column(3)calculatestheinstrumentusingonlythesinglelawthatgeneratesthelargest source of variation across states: public law (PL) 101-239, which was passed on December 19, 1989andeffectivein1990. Thetabledenotesthisinstrumentasln(RDTaxIncentiveRatePL101−239). Instrumenting RDTaxIncentiveRate with ln(RDSubsidyRatePL101−239) makes the model analogoustoabinarytreatmentandcontrolsetupwherethetreatmentlawisPL101-239andthepre/post treatmentperiodsarebefore/onorafter1990. Thecostofthissetupisremovingpotentiallyexoge- 32

nous variation and increasing measurement error in the key right-hand side variable. A benefit is thisformulationonlyusesvariationfromR&Dtaxcreditsandnotvariationfrommoregeneralincometaxdeductions. Incometaxdeductionsareapplicabletoothertypesofinvestmentsavailable toafirm. Changesinincometaxdeductionsmightelicitcomplementary/substitutableinvestments for R&D and would imply the response of R&D to changes in these more general tax deductions might be different than the response of R&D to R&D specific changes in the tax incentive rate (forexample,R&Dtaxcredits). However,calculatingR&Dtaxincentiverateswithonlyvariation fromPL101-239continuestosuggestanelasticresponseofR&Dtotaxincentives(standarderror) of3.14(1.39).42 Theestimateswithln(RDTaxIncentiveRatePL101−239)aresmallerthanthosethat useallavailablevariation,suggestingsomeattenuationbias. Table6,column(4)usesln(RDTaxIncentiveRatePL101−239)anddropsstatesthatchangedtheir R&D tax credits between 1990-1991 (Illinois and Massachusetts) to avoid confounding the effect of PL 101-239 with changes in state R&D tax credits around the same time period. These states mighthaveendogenouslyrespondedtothelargechangeinthefederalR&Dtaxcreditbyenacting theirownR&Dtaxincentives. However,droppingIllinoisandMassachusettshasalmostnoeffect ontheestimates. A researcher may be concerned about selection between states that chose to have laws that bound themselves to PL 101-239 and those that did not enact such laws. Therefore, I estimate models with separate policy variables for states that had and did not have R&D tax credits piggybacked to PL 101-239 that give similar results. The coefficients (standard errors) on ln(RDTaxIncentiveRatefed) for the specification in column (5) of Table 2 are 4.15 (2.07) for piggybackedstatesand4.35(2.23)fornon-piggybackedstates. Anotherselectionconcernisifcertaingeographicregionschoosetoimplementcertainpolicies. 42Researchers may be concerned that firms anticipated PL 101-239. However, anticipation of PL 101-239 would bias the elasticity estimates toward zero. In 1989 the federal R&D tax credit was a credit amount for R&D over a 3-yearmovingaveragebaseofR&D.ThemovingaveragebasecreatedadisincentiveforfirmstoclaimtheR&Dtax creditastakingacreditinagivenyearwouldreducetheallowablecreditforthenext3years.PL101-239removedthe movingaveragebaseamountandtheopportunitycostofclaimingtheR&Dtaxcredit. Iffirmsanticipatedthispolicy changein1989,thenmorefirmswouldhaveclaimedtheR&Dtaxcreditin1989,perhapsattheexpenseofR&Dthey wouldhaveclaimedin1990,whichwouldbiastheestimateoftheeffectofPL101-239in1990towardzero. 33

However, estimating models with separate policy variables by census region (West, South, Midwest,Northeast)alsogivessimilarresults. Thecoefficients(standarderrors)onln(RDTaxIncentiveRatefed) for the specification in column (5) of Table 2 are 3.73 (1.77) for West, 3.74 (1.82) for South, 3.02 (1.92)forMidwest,and3.28(2.04)forNortheast.43 A.3 Overidentification Tests As a final type of robustness check, I run specifications with an overidentified first-stage and run Difference-in-Sargan tests to check for instrument validity. Table 7 runs Difference-in-Sargan overidentificationtestsfollowingaformatsimilartoWeber(2014),Table2. Iconstructthechanges inmyinstrumentbyconditioningondifferentlagsofstatetaxpolicy: fed,l ∆RDTaxIncentiveRate =RDTaxIncentiveRate(ST , FT )−RDTaxIncentiveRate(ST , FT ) it it−l it it−l it−1 (7) for l =1,2,3,4. I then test the validity of my instrument by running the Difference-in-Sargan testbyexcludingtheinstrumentconstructedbyconditioningontheshortestlaglengthofstatetax policy, which presumably would be most susceptible to endogeneity bias. Column (1) displays the baseline specification from the paper (one instrument, constructed by conditioning on l = 1), while columns (2) - (5) display results using an overidentified first-stage and corresponding Difference-in-Sargan tests. For all overidentified specifications, I am unable to reject the validity of the baseline instrument from the paper at standard significance levels. The elasticity estimates of the tax incentive rate using multiple instruments are a bit smaller than when using a single instrument,butarestillinexcessof2.5. 43Estimatingseparatepolicyvariablesandseparatecontrolsforeachcensusregiongivesimpreciseestimates. 34

B Appendix: R&D Tax Incentive Rate Model ThisappendixprovidesdetailsoncomputingtheR&Dtaxincentiverateinequation(2). Let FTI denote federal taxable income, I indicate income, k be the R&D credit rate for establishedfirms,subscriptiindicateastate-levelvariable,subscript f indicateafederal-levelvariable, subscript t be time, χ be the proportion of the federal R&D credit the Internal Revenue Code (IRC) disallows as a deduction, RDfedCR symbolize the amount of R&D claimed for the federal R&D credit, and RDtot be total R&D expenditures. Because the federal government allows both state corporate income taxes and R&D expenditures as deductions from FTI,44 the expression for FTI follows(8): FTI =I −ST −RDtot+χ k RD fedCR (8) it it it it ft ft it Federaltaxes,FT,aresimplythecorporateincometaxrateτ timesFTI,lessthefederalR&D credit. TheexpressionforFT is: fedCR FT =FTI τ −k RD (9) it it ft ft it After a transitional period from 1981-1982, the federal R&D credit was a percentage of qualified research expenditures (QREs) over the greater of 50% of a firm’s QREs or a 3-year moving average of QREs. Assuming firms are not constrained by the base,45 the 3-year moving average makesRD fedCR =RDtot−1 ∑ 3 RDtot andtheexpressionforFT: it it 3 m=1 it−m 1 3 FT =FTI τ −k (RDtot− ∑ RDtot ) (10) it it ft ft it it−m 3 m=1 Since 1990 the federal R&D credit is a percentage of QREs above a fixed base instead of a 3-yearmovingaveragebase. WithQREsunconstrainedbythisfixedbase,RD fedCR =RDtot and: it it 44The federal government has allowed these deductions since prior to the beginning of the R&D data from the NationalScienceFoundation. 45Hall(1993)notesthemajorityofR&DfirmshaveR&Dlevelsabovetheirbaseamounts. MamuneasandNadiri (1996)andWilson(2009)alsoemploytheassumptionofR&Dlevelsoverthebaseamount. 35

FT =FTI τ −k RDtot (11) it it ft ft it Comparing equations (10) and (11), the 3-year moving average formulation directly increases federal taxes paid by k 1 ∑ 3 RDtot . There are also indirect effects on the federal tax burden ft3 m=1 it−m becausefederaltaxesdependonstatetaxesandviceversa. In computing state taxable income STI, states generally start with federal taxable income or income from all sources, then add state-specific modifications to form state taxable income. Let ξ be the proportion of state i’s income taxes required to be added back to federal taxable income, φ be the proportion of state i’s federal taxes deductible from state taxable income, ω indicate the proportion of state i’s R&D credit recaptured, α represent the proportion of federal recaptured credit allowed as a state deduction, and RDstateCR be the amount of R&D claimed for state i’s R&Dcredit. TheexpressionforSTI is: STI =FTI +ξ ST −φ FT +ω k RDstateCR−α χ k RD fedCR (12) it it it it it it it it it it ft ft it whichgiveswaytoastatetaxburdenST of: ST =STI τ −k RDstateCR (13) it it it it it For the corporate income tax rate τ I follow Shea (1993) and Wilson (2009) and use the toptiercorporaterateswithoutalternativeminimumtax. Forstateswithonlyataxongrossincomeor statedcapitalinsteadofnetincome,Isetτ astherateongrossincomeorstatedcapital. Iaccount it for temporary taxes and surcharges in τ . In the R&D sample, 2/3 have a single corporate income it taxrate forthe entiresample period. The remaining1/3 levythe highest-tiercorporate incometax at very low levels of taxable income. For example, among states with graduated rates, in 2000 the averagehighesttierwasonlyonehundredandfortysixthousanddollarsoftaxableincome. I model firms as filing based on the calendar year to keep the timing consistent with the other annual variables. If states change a law midway through the year and specify an explicit proration 36

for a calendar year, then I prorate accordingly. For example, if a state has τ = 0.1 for 6 months of 1990, then implements an increase to τ =0.2 for 1990, I code 1990 as τ =0.2 if no proration clauseexistsandτ =0.15ifaprorationclausedoesexist. States generally compute their R&D credits in one of three ways: 1) a non-incremental credit, where the credit is calculated as a percentage of QREs, 2) a credit for QREs above a fixed base (following the federal credit formula in place since 1990), or 3) a credit for QREs above a Myear moving average of QREs.46 With QREs above the fixed base or for the non-incremental credit case, RDstateCR = RDtot. For the years a state employed a M-year moving average base, it it RDstateCR =RDtot− 1 ∑ M RDtot . Following Wilson (2009), I do not consider state R&D tax it it M m=1 it−m creditsspecifictoagivenindustry,foragivenareawithinastate,orforaspecificfirmsizebecause theNSFR&Ddataareatthestatelevel. The federal R&D credit and approximately 2/3 of states use a single R&D credit rate k for all applicable R&D expenditures (i.e., no credit tiers). The remaining 1/3 of states have tiered credit amounts and are divided between offering higher credit amounts for higher tiers of R&D expenditures and offering lower credit amounts for higher tiers of R&D expenditures. I report resultsusingthehighesttierofR&Dexpendituresaslargecorporations,whichconstitutethebulk of R&D spending, are likely to be in the top tier.47 I also check the results with the median tier, whichgivessimilarresults. These formulations can accompany both states that base STI on FTI and those that start with income from all sources in calculating STI. To see this point, substituting the expression for FTI 46IntheR&Dsample,ConnecticutandMarylandareexceptions. ConnecticuthashadtwoR&Dcreditssince1993: a20%creditforQREsovera1-yearmovingaverage(ConnecticutGeneralStatutes§12-217j)andalevelcreditfor QREsbelowthemovingaverage(ConnecticutGeneralStatutes§12-217n). Thelevelcreditistieredat1%,2%,4%, and6%basedonthefirm’slevelofQREs. Inaddition,thefirmmayonlytake1/3ofthelevelcreditinthetaxyear thatitincurstheR&Dexpenditures. Theremaindermustbedeferreduntilthenexttaxperiod. Transitionalprovisions wereinplacefrom1993-1994. LikeConnecticut,MarylandhastwoR&Dcreditsthatworkintandemandhavebeen inplacesince2000(MarylandTax-GeneralCode§10-721). Thefirstcomponentisa10%creditforQREsabovea 4-yearmovingaverageofQREs.Thesecondcomponentisa3%creditforQREsthatdonotqualifyforthe10%credit component. Imodelbothofthesealternativemechanisms. 47Somestatesimposeamaximumcreditamountafirmcanclaimthatisnotdependentonthefirm’staxableincome and/orastatewidelimitontheamountofR&Dtaxcreditthatcanbeclaimedbyallfirmsinthestateeachyear. The firm-specificlimitonR&Dtaxcreditsisequivalenttoamarginalrateofzeroforthetoptier. Iassumethestatewide limitprovisionisnotbinding,followingWu(2005);Wilson(2009). 37

in equation (8) into equation (12) and setting α =1 (since states that base STI on income from it allsourcesdonotconsidertherecaptureprovisionsofthefederalR&Dcredit)yields: STI = I −ST −RDtot+χ k RD fedCR +ξ ST −φ FT it it it it ft ft it it it it it +ω k RDstateCR−α χ k RD fedCR (14) it it it it ft ft it = I +ST (ξ −1)−RDtot+χ k RD fedCR (1−α )−φ FT +ω k RDstateCR it it it it ft ft it it it it it it it = I +ST (ξ −1)−RDtot−φ FT +ω k RDstateCR it it it it it it it it it whichisasufficientlygenericexpressionforSTI forstatesthatuseincomefromallsourcesas astartingpointintheirSTI computation. SolvingthesystemofequationsdepictingFTI,FT,STI, ST, and differentiating with respect to total R&D expenditures RDtot (the choice variable) yields it the expression for the R&D tax incentive rate in equation (2).48 The system of equations for FTI, FT, STI, ST takes into account a broader range of deductions that is found in previous literature and models the simultaneity of state and federal taxes, allowing this paper to compute state-level R&D tax incentive rates with weaker assumptions than previous studies (Paff, 2005; Wu, 2005; Wilson, 2009). In addition, because of the large number of tax parameters captured by the model andthattheeffectiveR&Dtaxincentiverateisacontinuousvariable,inmysampleeachstatehas adifferenteffectiveR&Dtaxincentiverate. Computing the discounted changes in taxes for all future periods requires assumptions about how firms form expectations about future tax law. Because the tax data are available at a higher frequency (annually) than the R&D data are (biennially), minor changes to the timing of forming expectations in the tax data give the same results. Following Romer and Romer (2010), I treat simple extensions of R&D credits as anticipated. I also treat state IRC conformity updates as anticipated. ExtensionstoR&Dcredits,whicharealmostuniversallyenactedonatemporarybasis 48Equation(2)assumesfirmshavesufficienttaxableincometoclaimR&Dtaxincentives,consistentwithprevious studiesofR&Dtaxincentives. AdummyvariableforifastatehasarefundableR&Dtaxcredit(taxcreditsthatcan beclaimedforanyleveloftaxableincome)orallowsfirmstoselltaxcreditstootherfirmshasnoeffectontheresults. 38

withbuilt-inexpirationdates(sunsetprovisions),areextremelycommon. IntheR&Dsample,only one state (Illinois) allowed its R&D credit to lapse for a year before reactivating its R&D credit. Similarly, most state legislatures tend to enact IRC conformity updates during each legislative session. For other tax laws, I assume firms in year t have access to laws in effect through November of year t, form expectations based on these laws, and take into account the laws that will change taxes in future periods. To my knowledge, no hard data exist on the precise timing of firm’s expectations of future taxes. However, large corporations with dedicated accounting resources shouldbeanticipatingfuturetaxchangesthatwilloccurduetolawsonthebooks. Iconfirmedthis assumption through correspondence with a tax lawyer who worked for a large corporation. The session law data allow me to pinpoint how laws will change taxes in future periods, which allows thispapertocalculateRDTaxIncentiveRatewithaweakerassumptionthanpreviousstudies. C Appendix: R&D Tax Credit Law Preambles ThisappendixgivesexamplesofpreamblesfromstateR&Dtaxcreditlaws. Thetextsareallfrom sessionlawsaccessiblefromHeinOnline. Theportioninitalicsmotivatesthelaw. Michigan Public Acts 2007 No. 145, “An act to meet deficiencies in state funds by providing fortheimposition,levy,computation,collection,assessment,reporting,payment,andenforcement oftaxesoncertaincommercial,business,andfinancialactivities;toprescribethepowersandduties of public officers and state departments; to provide for the inspection of certain taxpayer records; to provide for interest and penalties; to provide exemptions, credits, and refunds; to provide for the disposition of funds; to provide for the interrelation of this act with other acts; and to make appropriations.” NewYork,2010RegularSession,Chapter55,PartMM,§1,“Itishere-byfoundanddeclared that New York state needs, as a matter of public policy, to create competitive financial incentives for businesses to create jobs and invest in the new economy. The excelsior jobs program act is 39

created to support the growth of the state’s traditional economic pillars including the manufacturing and financial industries and to ensure that New York emerges as the leader in the knowledge, technologyandinnovationbasedeconomy. Theprogramwillencouragetheexpansioninandrelocation to New York of businesses in growth industries such as clean-tech, broadband, information systems,renewableenergyandbiotechnology.” North Carolina, 1996 Second Extra Session, Chapter 13, House Bill 18, “An act to reduce taxesforthecitizensofNorthCarolinaandtoprovideincentivesforhighqualityjobsandbusiness expansioninNorthCarolina.” D Appendix: Example Effect of Federal Tax Law on Treatment Variable This appendix details how the treatment variable, equation (4), is affected by PL 101-239 for the stateofWisconsin. In1989,whichwastheyearpriortothepassageofPL101-239,thefederalR&Dtaxcreditwas a20%incrementalcreditforR&Dexpendituresovera3-yearmovingaveragebaseand50%ofthe granted credit was treated as federal taxable income for the firm. Wisconsin had a 5% state R&D taxcreditthatwascomputedinthesamemannerasthefederalcredit. Inaddition,thecomputation method for the Wisconsin R&D tax credit was linked to federal tax law. Therefore, any change in the computation method for the federal R&D tax credit would pass through automatically to the state R&D tax credit. Wisconsin also treated half of state tax credits as state income for the firm, disallowedthefederaldeductionforstatetaxespaidwhencomputingstatetaxableincome,anddid not allow a state income deduction for federal taxes paid. Using the notation from Appendix B, these tax features correspond to state parameters of ξ =1, φ =0, α =0.5, k =0.05, M =3, it it it it and τ = 0.079. PL 101-239 removed the moving average base computation and started to treat it the entire federal R&D tax credit as income, thereby changing M to zero and α for Wisconsin to onein1990. WisconsindidnotchangeanyofitsR&Dtaxcreditlawsfrom1989to1990. 40

To compute the change in the treatment variable from 1989 to 1990, I take the difference betweenwhattheR&Dtaxincentiveratewouldbepost-federallawchangeconditionedon1989’s statetaxlaws,lesswhatthestateR&Dtaxincentiveratewasin1989. Becausein1989Wisconsin’s R&D tax credit law was linked to the federal tax law, I compute the former piece as if firms in Wisconsin were subject to both state and federal R&D tax credits that did not use a moving averagebaseandasifboththestateandfederaltaxcreditsweretreatedasordinaryincome. E Appendix: Wilson (2009) Replication and Comparison This appendix compares the results from Wilson (2009) with a replication and highlights key differences between Wilson (2009) and this paper, particularly the comparable specifications using state-leveltaxvariationinTable3. Forthereplicationexercise,DanWilsonprovidedmewiththetaxdataforhisusercost. However,inreplicatinghisresultsIdonothavethenon-taxvariablesorthecode. Table 8, column (1) reports the results from Table 1, column (1) of Wilson (2009). The key regressor, ln(RDTaxRateWilson), is the tax user cost from Dan Wilson’s data.49 To compare reit sults with this paper, I switch the sign of ln(RDTaxRateWilson), as Wilson (2009) reports the key it coefficient as the negative of the tax incentive rate, while this paper reports the tax incentive rate. Column (2) of Table 8 is my replication of Table 1, column (1) of Wilson (2009). I report replicationresultsusingthecreditratefor thehighesttierofR&Dexpendituresandthegeneralizedleast squares (GLS) estimator.50 Although it is unclear from Wilson (2009) which credit tier the results are based on, the 2007 working paper version (pg. 37) specifies that results are for the highest tier of R&D expenditures. In addition, the 2007 working paper version (pg. 19) adds that the results areobtainedwiththeGLSestimator,althoughthiscontradictsthepublishedpaper’saccountofestimationwithordinaryleastsquares(OLS)(pg. 433). However,theresultsfromthe2007working paper, Table 2, column (2) match Table 1, column (1) of the published version exactly. I also find 49ThiscoefficientisρininWilson(2009). it 50SeeAppendixBforadditionaldetailsonR&Dtaxcredittiers. 41

thatreplicationwiththeGLSestimatormorecloselymatchesthepublishedpaper’sresults. FromTable8,column(2)wecanseethereplicationresultsareclosetothepublishedestimates. Thecoefficient(standarderror)ofln(RDTaxRateWilson)fromthereplicationis1.13(0.43)vs. 1.21 it (0.44)asthepublishedestimateincolumn(1). Replicationwiththecreditrateforthelowesttierof R&D expenditures gives results closer to Wilson (2009), with the key coefficient (standard error) as 1.23 (0.42). The other replication coefficients are similar to those in Wilson (2009). Since I do not have the original data from Wilson (2009) (other than the tax user cost), the non-tax variables subjecttodatarevision(e.g.,GSP)willbedifferentinmyreplicationsosomedifferenceinresults isexpected. Column(3)restrictsWilson’sspecification,whichusesall50statesplustheDistrictofColumbia, toonlyincludethesampleof21highR&Dstatesfromthispaper.51 These21statesarethosewhere IobserveR&Dinthe1980sand1990s,whichiswhenthevariationinfederaltaxlawstakesplace. Also, since these are the higher R&D states, they have few or no imputed observations (2% of the sample from the high R&D states is imputed, but the table drops these observations). The estimate of ln(RDTaxRateWilson) drops from slightly above unit elastic to an inelastic 0.20 and is it insignificant from zero. In column (4), I replace Wilson’s key coefficient with my measured tax rate ln(RDTaxIncentiveRate ), which also gives an inelastic estimate of 0.15.52 Therefore, the it differenceinestimatesbetweenTable3andTable1,column(1)ofWilson(2009)isnotduetomy data or my calculation of ln(RDTaxIncentiveRate ), although ln(RDTaxIncentiveRate ) tends to it it givemorepreciseestimatesthantheusercostfromWilson(2009).53 Wilson(2009)’suseofimputedobservationsdrivessomeofthedifferenceinestimatesbetween columns (3) - (4) and column (2). In Table 8, column (5) I again use Wilson (2009)’s sample and key coefficient but drop imputed observations. The estimate of ln(RDTaxRateWilson) drops it from 1.13 to 0.79, suggesting that about 1/3 of the difference comes from imputation, while the 51These states are: Alabama, Arizona, California, Colorado, Connecticut, Florida, Illinois, Indiana, Maryland, Massachusetts, Michigan, Minnesota, New Jersey, New York, North Carolina, Ohio, Oregon, Pennsylvania, Texas, Virginia,andWisconsin. 52Changing the estimator from GLS to OLS gives an estimate (clustered standard error by state) for ln(RDTaxIncentiveRate )of0.48(0.64). it 53Betterprecisionisduetomoredetailedmodelingandhigh-qualitydata. SeeAppendixB. 42

remaining 2/3 comes from sample state composition. A researcher may be concerned that the composition of my sample may be driving some of the difference between my estimates using fed exogenous variation, ln(RDTaxIncentiveRate ) (e.g., in Table 2) and previous literature. While it I cannot rule out this possibility, my estimates with comparable specifications and variation in Table3usingln(RDTaxIncentiveRate )stillproducesimilarresultstopreviousstudies. Also,my it sample of states is arguably the relevant sample to use as these states are doing most of the actual innovating. 43

Figure1: R&DTaxIncentiveRate-StateandFederalVariation 0.7 0.6 0.5 0.4 0.3 1981 1986 1991 1996 2001 2006 Year Average Endogenous Tax Incentive Rate Min and Max Endogenous Tax Incentive Rate This figure plots summary statistics of state-level R&D tax incentive rates, calculated using variation from both state and federal laws, over time. Vertical lines indicate the dates that federal tax lawswereeffective. Sources: statesessionlaws,InternalRevenueCode. 44

Figure2: R&DTaxIncentiveRate-StateandFederalVariation-SelectStates 0.7 0.6 0.5 0.4 0.3 1981 1986 1991 1996 2001 2006 Year Arizona Endogenous Tax Incentive Rate California Endogenous Tax Incentive Rate Indiana Endogenous Tax Incentive Rate Texas Endogenous Tax Incentive Rate Thisfigureplotsstate-levelR&Dtaxincentiverates,calculatedusingvariationfrombothstateand federal laws, for Arizona (solid line), California (dashed dotted line), Indiana (long dashed line), and Texas(short dashed line). Vertical lines indicate the dates thatfederal tax laws wereeffective. Sources: statesessionlaws,InternalRevenueCode. 45

Figure3: R&DTaxIncentiveRate-OnlyFederalVariation 0.7 0.6 0.5 0.4 0.3 1981 1986 1991 1996 2001 2006 Year Average Exogenous Tax Incentive Rate Min and Max Exogenous Tax Incentive Rate This figure plots summary statistics of state-level R&D tax incentive rates, calculated using variation from only federal laws, over time. Vertical lines indicate the dates that federal tax laws were effective. Sources: statesessionlaws,InternalRevenueCode. 46

Figure4: R&DTaxIncentiveRate-OnlyFederalVariation-SelectStates 0.7 0.6 0.5 0.4 0.3 1981 1986 1991 1996 2001 2006 Year Arizona Exogenous Tax Incentive Rate California Exogenous Tax Incentive Rate Indiana Exogenous Tax Incentive Rate Texas Exogenous Tax Incentive Rate This figure plots state-level R&D tax incentive rates, calculated using variation from only federal laws,forArizona(solidline),California(dasheddottedline),Indiana(longdashedline),andTexas (short dashed line). Vertical lines indicate the dates that federal tax laws were effective. Sources: statesessionlaws,InternalRevenueCode. 47

Figure 5: Nominal R&D Prior to Federal R&D Credit - Endogenous R&D Tax Incentive Rate Grouping 1500 1000 Nominal RD (millions) 500 0 1963 1965 1967 1969 1971 1973 1975 1977 1979 Year Above Median Below Median Tax Incentive States Tax Incentive States This figure groups states into above/below median average R&D tax incentives from 1981-2007 usingvariationfrombothstateandfederallawsinstate-levelR&Dtaxincentives. Thedashedline representsaveragenominalR&DforstateswithhigherthanthemedianaveragevalueofR&Dtax incentives. ThesolidlineisforstateswithbelowthemedianaveragevalueofR&Dtaxincentives. Sources: NSF’sSIRDandstatesessionlaws. 48

Figure 6: Nominal R&D Prior to Federal R&D Credit - Exogenous R&D Tax Incentive Rate Grouping 1500 1000 Nominal RD (millions) 500 0 1963 1965 1967 1969 1971 1973 1975 1977 1979 Year Above Median Below Median Treatment States Treatment States This figure groups states into above/below median average R&D tax incentives from 1981-2007 usingvariationfromonlyfederallaws. ThedashedlinerepresentsaveragenominalR&Dforstates withhigherthanthemedianaveragevalueofincentivesfromfederaltaxlaws. Thesolidlineisfor states with below the median average value of incentives from federal tax laws. Sources: NSF’s SIRDandstatesessionlaws. 49

Table1: FederalLawsAffectingR&DTaxIncentiveRates PublicLaw TaxCodeChange EffectiveYear 97-34 R&DCreditImplementedat25% 1981 99-514 R&DCreditReducedto20% 1986 CorporateIncomeTaxReducedto34% 1987/1988 100-647 R&DCreditRecaptureIncreasedto50% 1989 101-239 R&DCreditRecaptureIncreasedto100% 1990 R&DCreditBaseComputationChanged 1990 103-66 CorporateIncomeTaxIncreasedto35% 1993 104-188 R&DCreditRenewedAfterExpiration 1996 Source: InternalRevenueCode(LexisAnnotations). 50

Table2: InstrumentalVariablesEstimatesIndicateElasticResponse DependentVariable: ln(RD ) it (1) (2) (3) (4) (5) fed ln(RDTaxIncentiveRate ) 4.51 5.06 2.89 3.69 3.78 it (1.59)*** (2.02)** (1.14)*** (1.59)** (1.69)** ln(RD ) 0.46 0.38 0.39 it−2 (0.10)*** (0.10)*** (0.11)*** ln(GSP ) 0.58 it (0.31)* ln(Federal RD ) 0.39 0.20 0.22 it−2 (0.12)*** (0.07)*** (0.07)*** ln(AcademicRD ) 0.07 -0.31 -0.15 it (0.29) (0.24) (0.21) Unemployment Rate -0.69 -1.27 -1.14 it (3.27) (2.67) (2.69) ImpliedLong-Run 5.38 6.00 6.23 TaxIncentiveElasticity (1.74)*** (2.00)*** (2.09)*** First-stageF-statistic 2.28 2.50 2.14 1.78 1.84 StateFixedEffects X X X X X TimeDummies X X X X X Observations 226 226 206 206 206 The key regressor RDTaxIncentiveRate is instrumented with RDTaxIncentiveRatefed. The estimatoris2SLS.First-stageF-statisticisfortheexcludedinstrument. Thistablereportscoefficients as elasticities except for the unemployment rate, which is a semielasticity. Clustered standard errorsbystateinparentheses. Theimpliedlong-runelasticityisthecoefficientofthetaxratedivided by one minus the coefficient on the lagged dependent variable with the standard errors calculated withthedeltamethod. *,**,***: significantat10%,5%,1%. 51

Table3: R&DTaxIncentiveRateComparabletoPreviousStudiesIndicatesInelasticResponse DependentVariable: ln(RD ) it (1) (2) (3) (4) (5) ln(RDTaxIncentiveRate ) 1.66 1.74 0.58 0.37 0.65 it (1.00) (1.11) (0.73) (0.73) (0.76) ln(RD ) 0.53 0.49 0.49 it−2 (0.11)*** (0.09)*** (0.11)*** ln(GSP ) 0.89 it (0.20)*** ln(Federal RD ) 0.37 0.13 0.16 it−2 (0.11)*** (0.07)* (0.06)*** ln(AcademicRD ) 0.08 -0.44 -0.18 it (0.30) (0.22)* (0.20) Unemployment Rate 2.31 0.85 0.94 it (2.87) (1.84) (1.78) ImpliedLong-Run 1.21 0.72 1.29 TaxIncentiveElasticity (1.40) (1.37) (1.38) StateFixedEffects X X X X X TimeDummies X X X X X Observations 226 226 206 206 206 Thekeyregressorln(RDTaxIncentiveRate)istheR&Dtaxincentiveratecalculatedusingchanges in both state and federal laws (the statutory rate). The estimator is OLS. This table reports coefficients as elasticities except for the unemployment rate, which is a semielasticity. Clustered standard errors by state in parentheses. The implied long-run elasticity is the coefficient of the tax ratedividedbyoneminusthecoefficientonthelaggeddependentvariablewiththestandarderrors calculatedwiththedeltamethod. *,**,***: significantat10%,5%,1%. 52

Table4: SampleModifications DependentVariable: ln(RD ) it (1) (2) (3) (4) fed ln(RDSubsidyRate ) 2.96 3.21 6.29 3.41 it (1.25)** (1.82)* (1.74)*** (1.66)** ln(RD ) 0.48 0.31 0.09 0.44 it−2 (0.11)*** (0.15)** (0.10) (0.11)*** ln(Federal RD ) 0.24 0.24 0.36 0.20 it−2 (0.06)*** (0.07)*** (0.12)*** (0.06)*** ln(AcademicRD ) -0.22 -0.25 0.15 -0.20 it (0.17) (0.20) (0.27) (0.19) Unemployment Rate -1.68 1.59 -5.18 -0.62 it (2.31) (2.85) (2.99)* (2.46) ImpliedLong-Run 5.69 4.70 6.88 6.14 TaxIncentiveElasticity (1.62)*** (1.97)*** (1.45)*** (2.29)*** StateFixedEffects X X X X TimeDummies X X X X Observations 202 199 143 287 SampleModification TrimOutliers Post-1984 Pre-2000 AnnualData Post-1997 Thistablereportscoefficientsaselasticitiesexceptfortheunemploymentrate,whichisasemielasticity. Clustered standard errors by state in parentheses. The implied long-run elasticity is the coefficient of the tax incentive rate divided by one minus the coefficient on the lagged dependent variable with the standard errors calculated with the delta method. *, **, ***: significant at 10%, 5%,1%. 53

Table5: IncludingWeightedOut-of-StateTaxIncentiveRate DependentVariable: ln(RD ) it (1) (2) (3) (4) ln(RDTaxIncentiveRate ) 3.78 2.91 3.60 3.88 it (1.69)*** (1.08)*** (1.50)** (1.57)** outofstate ln(RDTaxIncentiveRate ) 1.89 -1.12 1.36 it (4.63) (5.51) (4.24) ln(RD ) 0.39 0.45 0.39 0.38 it−2 (0.11)*** (0.09)*** (0.10)*** (0.10)*** ln(GSP ) 0.66 it (0.38)* ln(Federal RD ) 0.22 0.18 0.23 it−2 (0.07)*** (0.08)** (0.07)*** ln(AcademicRD ) -0.15 -0.35 -0.13 it (0.21) (0.31) (0.22) Unemployment Rate -1.14 -1.23 -1.21 it (2.69) (2.68) (2.55) ImpliedLong-Run 6.23 5.34 5.93 6.28 TaxIncentiveElasticity (2.10)*** (1.62)*** (1.98)*** (1.99)*** StateFixedEffects X X X X TimeDummies X X X X Observations 206 206 206 206 Eachcolumnestimatedwith2SLS.First-stageF-statisticfortheexcludedinstrumentsarebetween three and thirteen. All columns include state fixed effects and time dummies. Clustered standard errorsbystateinparentheses. Theimpliedlong-runelasticityisthecoefficientofthetaxincentive ratedividedbyoneminusthecoefficientonthelaggeddependentvariablewiththestandarderrors calculatedwiththedeltamethod. *,**,***: significantat10%,5%,1%. 54

Table6: AlternativeSpecifications DependentVariable: ln(RD ) it (1) (2) (3) (4) fed ln(RDTaxIncentiveRate ) 5.25 7.11 it (2.75)** (2.84)*** ln(RDTaxIncentiveRatePL101−239) 3.14 2.89 it (1.39)** (0.91)*** ln(RD(Biennial) ) 0.42 t−2 (0.11)*** ln(RD(Annual) ) 0.31 it−1 (0.15)** ln(RD ) 0.41 0.44 it−2 (0.10)*** (0.10)*** ln(RD ) 0.10 it−4 (0.13) ln(Federal RD ) 0.13 0.34 0.21 0.17 it−2 (0.09) (0.11)*** (0.06)*** (0.05)*** ln(AcademicRD ) -0.23 -0.03 -0.15 -0.24 it (0.20) (0.35) (0.19) (0.21) Unemployment Rate -1.87 -2.99 -0.71 -0.15 it (3.12) (4.22) (2.40) (2.11) ImpliedLong-Run 7.58 7.90 5.35 5.15 TaxIncentiveElasticity (2.49)*** (2.42)*** (1.82)*** (1.14)*** StateFixedEffects X X X X TimeDummies X X X X Observations 306 202 206 188 SampleModification AnnualData None None DropIL,MA Post-1997 Column (1) uses all available data and divides the coefficient on the lagged dependent variable intoseparatecoefficientsforthebiennial(1981-1996)andannual(1997-2006)R&Ddataperiods. Columns(2)-(4)usethedefaultbiennialdatastructureovertheentiresample. Incolumns(3)and (4), ln(RDTaxIncentiveRatePL101−239), only uses variation from Public Law 101-239 in R&D tax incentive rates. Column (4) drops Illinois and Massachusetts due to contemporaneous changes in stateR&DcreditswithPublicLaw101-239. Thistablereportscoefficientsaselasticitiesexceptfor theunemploymentrate,whichisasemielasticity. Clusteredstandarderrorsbystateinparentheses. Theimpliedlong-runelasticityisthecoefficientofthetaxincentiveratedividedbyoneminusthe coefficient of the dependent variable (annual lag for column 1) with the standard errors calculated withthedeltamethod. *,**,***: significantat10%,5%,1%. 55

Table7: Difference-in-SarganOveridentificationTests DependentVariable: ln(RD ) it (1) (2) (3) (4) (5) ln(RDTaxIncentiveRate ) 3.78 3.13 3.55 2.59 2.55 it (1.69)*** (1.44)** (1.70)** (0.84)*** (0.85)*** ln(RD ) 0.39 0.42 0.40 0.43 0.43 it−2 (0.11)*** (0.11)*** (0.11)*** (0.10)*** (0.10)*** ln(Federal RD ) 0.22 0.21 0.22 0.20 0.19 it−2 (0.07)*** (0.06)*** (0.07)*** (0.05)*** (0.05)*** ln(AcademicRD ) -0.15 -0.16 -0.15 -0.16 -0.16 it (0.21) (0.20) (0.21) (0.19) (0.19) Unemployment Rate -1.14 -0.71 -0.99 -0.34 -0.32 it (2.69) (2.43) (2.73) (2.04) (2.00) ImpliedLong-Run 6.23 5.35 5.92 4.55 4.50 TaxIncentiveElasticity (2.10)*** (1.75)*** (2.14)*** (0.94)*** (0.98)*** InstrumentLags 1 1,2 1,2,4 1,3,4 3,4 Difference-in-Sarganp-value 0.26 0.25 0.54 0.19 First-stageF-Statistic 1.84 2.11 3.51 12.94 19.1 Observations 206 206 206 206 206 Each column estimated with 2SLS. First-stage F-statistic tests the excluded instruments. All columns include state fixed effects and time dummies. Clustered standard errors by state in parentheses. Instrument lags refers to instruments constructed with the referenced lags of state tax policy. For example, in column (2) the endogenous RDTaxIncentiveRate is instrumented with RDTaxIncentiveRatefed constructed by conditioning on the first lag of state tax policy and RDTaxIncentiveRatefed created by conditioning on the second lag of state tax policy. The table calculates the Difference-in-Sargan test by excluding the instrument computed with the shortest listed lag length. The implied long-run elasticity is the coefficient of the tax incentive rate divided by one minus the coefficient on the lagged dependent variable with the standard errors calculated withthedeltamethod. *,**,***: significantat10%,5%,1%. 56

Table8: Wilson(2009)Comparison DependentVariable: ln(RD ) it Wilson(2009) Wilson(2009) Reported Replication (1) (2) (3) (4) (5) ln(RDTaxRateWilson) 1.21 1.13 0.20 0.79 it (0.44)*** (0.43)*** (0.43) (0.40)** ln(RDTaxIncentiveRate ) 0.15 it (0.30) ln(RD(Biennial) ) 0.49 0.43 0.56 0.56 0.49 t−2 (0.04)*** (0.04)*** (0.05)*** (0.05)*** (0.04)*** ln(RD(Annual) ) 0.45 0.39 0.48 0.48 0.43 it−1 (0.05)*** (0.04)*** (0.05)*** (0.06)*** (0.04)*** ln(GSP ) 0.73 0.67 0.73 0.75 0.55 it (0.18)*** (0.18)*** (0.20)*** (0.19) (0.17)*** ln(Federal RD ) -0.05 -0.01 -0.02 -0.02 -0.01 it−2 (0.01)*** (0.01) (0.01) (0.01) (0.01) ImpliedLong-Run 2.18 1.83 0.38 0.28 1.37 TaxIncentiveElasticity (0.81)*** (0.69)*** (0.83) (0.55) (0.70)* StateFixedEffects X X X X X TimeDummies X X X X X OnlyLargestR&DStates X X DropImputedObservations X X X Observations 365 366 232 232 336 Column (1) is the reported values of Table 1, column (1) of Wilson (2009). Column (2) is my replication of Table 1, column (1) ofWilson (2009). Columns (3) and (4) restrict thesample to 21 highR&Dstatesusedinthispaper. Column(5)usesallstates,includingtheDistrictofColumbia, and drops observations where ln(RD ) is imputed. For all columns, the estimator is GLS with it standarderrorsthatallowofAR(1)serialcorrelationandwithin-stateheteroskedasticity,following Wilson (2009). The implied long-run elasticity is the coefficient of the tax incentive rate divided by one minus the coefficient on the annual period’s lagged dependent variable with the standard errorscalculatedwiththedeltamethod. *,**,***: significantat10%,5%,1%. 57