Tax Heterogeneity and Misallocation

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1393 July 2024 Tax Heterogeneity and Misallocation Baris Kaymak and Immo Schott Please cite this paper as: Kaymak, Baris, and Immo Schott (2024). “Tax Heterogeneity and Misallocation,” International Finance Discussion Papers 1393. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2024.1393. NOTE: International Finance Discussion Papers (IFDPs) 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 International Finance Discussion Papers Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at www.ssrn.com.

Tax Heterogeneity and Misallocation∗ Barı¸s Kaymak† Immo Schott†‡ June 25, 2024 Abstract Thereissubstantialasymmetryineffectivecorporateincometaxrates across firms. While tax asymmetries would reduce productivity in frictionless economies, they can improve efficiency in a distorted economy if taxes alleviate other economic frictions. We develop a framework to estimate to what extent tax asymmetries affect productivity in distorted economies. Using US firm-level balance sheet data alongside measures of effectivemarginaltaxrates,wefindapositivecorrelationbetweentaxrates andfactorproductivity,suggestingthattaxasymmetryexacerbatesthedistortions from other economic frictions. Eliminating tax rate asymmetries would raise aggregate productivity by 3 to 4 percent if taxes distort capitalcostsalone. Modelswheretaxesalsodistortthemarginalcostoflabor predictpotentialgainsashighas9percent. Keywords: Business Taxation, Aggregate Productivity, TFP, Misallocation JELClassification: E23,H25,O47 ∗Theviewsexpressedherearethoseoftheauthorsanddonotnecessarilyreflecttheviews oftheFederalReserveBankofClevelandortheFederalReserveSystem. †DepartmentofEconomicResearch,FederalReserveBankofCleveland,1455E6thSt,Cleveland,OH44114,UnitedStates.E-mail:barkaymak@gmail.com ‡FederalReserveBoard.DivisionofInternationalFinance,20thandCStreets,NW,Washington,DC20551,UnitedStates.E-mail:immoschott@gmail.com 1

1 Introduction In an efficient economy, marginal products of inputs are equalized across firms. However,alargenumberofstudiesfollowingHsiehandKlenow(2009)hasdocumentedawidedispersioninmarginalproductivityacrossestablishments,suggesting that output can be improved by moving resources from firms with low marginalproductivitytofirmswithhighmarginalproductivity. Recentestimates suggestthattheUScouldraiseitsoutputbyasmuchas25percentifinputswere allocated efficiently (Bils et al., 2021). The sources of input misallocation, however, remain elusive, preventing policy guidance. This paper examines the role ofasymmetriccorporatetaxationasapotentialsourceofinputmisallocation. WedevelopaframeworktoestimatetheeffectoftaxheterogeneityonaggregateproductivityintheUS.Althoughthetaxcodedoesnotdistinguishbetween individual firms de jure, special provisions for deductions and allowances, such as imperfect loss-offsets or the favorable treatment of debt financing, can lead to a dispersion in effective marginal tax rates (EMTR) across firms. Estimates suggest that the resulting dispersion in marginal tax rates is large (Graham and Mills, 2008; Blouin et al., 2010). Figure 1a shows the variation in EMTR in our sample of publicly traded firms in the US between 1980 and 2021. On average, EMTR ranges from under 10 percent for the lowest third of the firms to over 30 percent for the highest third. The standard deviation of tax rates in the crosssectionvariesbetween13to17percentdependingontheestimateandyear. DifferencesinEMTRaresystematicallyrelatedtofirmcharacteristics. Figure 1b shows average EMTR by firm size, measured as total assets, employment, or sales. Larger firms are subject to higher tax rates. Because these firms representthemajorityofeconomicactivity,theeffectoftaxheterogeneityonoverall productivityispotentiallylarge,especiallyifsizeisanindicationofproductivity. Whetherthesedifferencesinmarginaltaxratesnecessarilyworsentheeconomy’sefficiencyisnotobvious. Whileheterogeneityinmarginaltaxrateswould lowerefficiencyincompetitive,otherwisefrictionlesseconomies,thesamecannotbesaidofeconomieswithdistortions(LipseyandLancaster,1956). Efficiency 1

(a)TaxRatesbyTaxTercile (b)TaxRatesbySizeClass Figure1: AsymmetryinEffectiveMarginalCorporateTaxRates Note.-Figureshowsaveragemarginalcorporatetaxratesbytercilesoftaxrates(panela),and by terciles of firm size as measured by assets, employment, or sales (panel b). The high and lowvaluesshownwithwhiskerscorrespondrespectivelytotaxrateestimatesfromBlouinetal. (2010)andGrahamandMills(2008).Barsshowtheiraverage.Source:Compustat.Sampleperiod is1980–2016. could in fact be improved by differential marginal tax rates if they helped offset otherdistortionsintheeconomy. Forinstance,thetaxadvantageofdebtlowers the marginal tax of more leveraged firms. This might ease credit frictions and improve investment. Or consider tax carry overs. Losses that are carried over frompreviousyearslowerafirm’scurrentmarginaltaxrate. Thismightalleviate liquidityconstraintsandpreventprematurefirmexit. Whetherthisisthecaseis anempiricalquestion. Inpursuitofananswer,wedevelopasimpletheoreticalframeworkthatfeatures heterogeneous firms and corporate taxation in a standard model of production. Importantly, while corporate taxes are modeled explicitly, the model includes other, unspecified distortions to factor allocation. We derive analytical formulas which predict the change in total factor productivity resulting from eliminating differences in marginal tax rates across firms. Our results highlight a key statistic which determines the effect of corporate tax policy on efficiency: the correlation between marginal tax rates and factor productivity in 2

the cross-section of firms. This correlation is informative about the interaction betweenvariousdistortions. Apositivecorrelationimpliesthatfirmswithhigher marginalproductivityaretaxedmoreheavily,weakeningoverallproductivityin theeconomy. To apply our formulas, we combine balance-sheet data on publicly listed companiesintheUnitedStatesfromCompustatwithfirm-levelestimatesofthe marginal tax rates on corporate income (Graham and Mills, 2008; Blouin et al., 2010). Our baseline calculations indicate that eliminating tax rate heterogeneity wouldraise aggregateTFPintheUSby3to4percent.1 Importantly, our results reflect a positive correlation between tax rates and estimated marginal products of capital and labor across firms. This contributes toourestimatesintwoways. First,eliminatingtaxasymmetrieslowerstaxrates forfirmswherecapitalismoreproductive. ThisimprovesTFPbymovingcapital to those firms. Second, because capital and laborare complementary in production, these firms also raise their employment. The accompanying movement of labor raises productivity even more, because EMTR and labor productivity are also strongly positively correlated in the data. Our calculations suggest that if taxrateswerenotcorrelatedwithotherdistortions,thenpotentialgainsinproductivity would be much smaller, less than 1 percent for most years, with the exceptionoftheperiodpriortothe1986taxreform. Thissuggeststhatcorporate tax policy has tended to exacerbate distortions to input allocation rather than offsettingthem. Thecorrelationbetweenlaborproductivityandtaxratesissomewhatsurprising. Because labor expenses can be deducted from net income, corporate taxes are thought to be non-distortionary to employment. Accordingly, our baseline analysis,wherecorporatetaxesonlyraisethemarginalcostofcapital,treatslabor distortions as exogenous to taxes. However, taxes can affect the marginal 1Following the literature, we focus on static productivity gains from reallocating inputs amongexistingproductionunits,holdingfirm-leveltechnologiesfixed. Indirectgainsfrompotentialimprovementsininnovationactivity,orintheefficiencyoffirmentryorexitwouldimply largergainsinthelong-run. 3

cost of labor in models with cash-in-advance requirements for wage payments, employment-based tax credits, or partial expensing of labor costs. In that case, eliminatingtaxasymmetriesmitigateslabordistortions,andraisestheaggregate TFPoverandaboveourbaselineresults. Assumingthatthecorrelationbetween labor distortions and tax rates is entirely endogenous, we estimate that tax rate homogenization could improve aggregate TFP by up to 9 percent. We consider thistobeanupperboundasthecorrelationbetweentaxratesandlaborproductivityislikelynotentirelyendogenous. This paper connects to the literature on the macroeconomic effects of factor misallocation(RestucciaandRogerson,2008;HsiehandKlenow,2009). Papersin thisliteraturetypicallyadoptoneoftwoapproaches. Thefirstapproachconsists of measuring the dispersion in marginal products of factors of production and then attributing this dispersion to firm-specific distortions. Comparing the distorted economy to a model-implied frictionless environment, papers following this approach typically find large potential gains from removing frictions (see e.g., Hsieh and Klenow (2009), Gopinath et al. (2017), and Adamopoulos et al. (2022)). Achallengeinthisliteraturehasbeentodistinguishbetweendifferences in marginal products and differences in production technologies and measurementerror(Bilsetal.,2021).2 The second approach focuses on measuring observable frictions at the firmlevelandcomputingtheassociatedreductionsinaggregateproductivity. ExamplesincludeGilchristetal.(2013),MidriganandXu(2014),DavidandVenkateswaran (2019), and Kim (2023). Because of computational and theoretical complexities, this approach is limited in its ability to model and compute a large number of distortionsandtheirinteractions. Becausespecific,observablefrictionsonlyexplainafractionoftheobservedheterogeneityinmarginalproductsacrossfirms, 2Hsieh and Klenow (2009) address these issues by benchmarking their misallocation measure to the US when assessing the extent of resource misallocation in India. Bils et al. (2021) usepaneldatatopurgethefirm-leveldispersioninproductivityofmeasurementerror.Because our findings rely on the covariance between tax wedges and productivity, errors in specificationormeasurementofmarginalproductsarelessofaconcern. Wediscusstheimplicationsof measurementerrorintaxwedgesindetailbelow. 4

by and large, these studies find the productivity gains from reallocation to be small. Thispapercombineselementsfrombothapproaches. Wefocusonaspecific friction–corporateincometaxes–whileexplicitlyallowingforother,moregeneral,distortions. AsinLipseyandLancaster’s(1956)analysisofthe‘secondbest’, removing differences in marginal tax rates across firms in an environment with frictionsneednotnecessarilyincreasetheeconomy’saggregateproductivity,in contrasttomostpreviouswork,whereeliminatingdistortionsimprovesproductivitybydesign. Theoutcome,instead,cruciallyreliesonthejointdistributionof taxratesandotherdistortions. Inthatsense,ourapproachisclosertoHarberger (1964), and, more recently, Baqaee and Farhi (2020), who study productivity effectsofmonopolisticpricesettingineconomieswithdistortions. Our paper is also related to the literature concerned with measuring the effects of corporate taxes on economic outcomes, such as investment or employment(Harberger,1962;HallandJorgenson,1967). Thisliteraturehasfocusedon the role of specific asymmetries in the tax code, such as those stemming from loss-offsetprovisions(Auerbach,1986;KaymakandSchott,2019),investmenttax credits Cummins et al. (1994), or tax jurisdictions Djankov et al. (2010); Slattery and Zidar (2020) among others. Whereas these papers focus on the effect of the level ofthecorporatetaxrateoneconomicoutcomes,westudythedispersionin taxratesanditsimplicationsforaggregateproductivity. Therestofthepaperisorganizedasfollows. Section2derivesourtheoretical results. Section 3 describes how we connect the theory to the data, presents the degreeoftaxheterogeneity,andshowshowtaxdistortionscanbemeasured. We presentourfindingsinSection4andconcludeinSection5. 2 Model Inthissectionwederiveageneralformulaforquantifyingthechangesinaggregate TFP from eliminating the heterogeneity in firm-level tax rates in the spirit 5

ofHsiehandKlenow(2009). Tofixideas,wefirstdevelopaninvestmentproblem with multiple distortions and show how the resulting optimality conditions can be generalized. We also allow for distortions to employment, but maintain an agnosticviewoftheirsources.3 Consider the investment problem of a firm that uses capital and labor to produceoutputwiththedecreasing-returns-to-scale(DRS)productionfunction, y = zF(k′,n),usingtechnologyz.4 Thefirmfacesaneffectivemarginaltaxrate on its income, τ, as well as other frictions, such as capital adjustment costs and credit constraints. Each period, the firm chooses capital investment and labor inordertomaximizethepayouttoshareholders,whichdependsoncurrentand expectedafter-taxprofits. Forsimplicity,assumethatthefirmknowstherealizationofthenextperiod’sproductivityz andtaxesτ atthetimeoftheinvestment decision. Thefirm’sproblemisgivenby (cid:18) (cid:19) i (cid:2) (cid:3) V(z,k) = max −i−Φ k+β (1−τ)[zF(k′,n)−ω n]+E V(z′,k′) n z′|z n,k′,i k (1) subjecttothelawofmotionforcapitalandacollateralconstraint k′ = i+(1−δ)k (2) i ≤ ζqk, (3) withassociatedmultipliersq andµ. The labor decision is not affected by the level of τ because wage payments 3InSection2.2,weconsidermodelswherecorporatetaxratesraiselaborcostsinadditionto thecostofcapitalanddiscusstheirimplicationsforaggregateproductivity. 4WhileweformulatetheprobleminaperfectlycompetitiveeconomywithfirmsfacingDRS in production, an equivalent setting would be one where firms have constant returns to scale production,butcompetemonopolisticallyasinHsiehandKlenow(2009). 6

aretax-deductible.5 Thefirst-orderconditionwithrespecttolaborisgivenby zF (k,n) = ω , (4) n n where ω denotes the effective user cost of labor. The optimality condition for n thechoiceofcapitalisgivenby (cid:20) (cid:18) i′(cid:19) (cid:18) i′(cid:19) i′ (cid:21) q = β (1−τ)zF (k′,n)−Φ +Φ′ +q′(1−δ)+µ′ζ′q′ , (5) k k′ k′ k′ with the familiar interpretation that at the optimal choice, the marginal cost of capital, q, equals the discounted future benefit of an additional unit of capital. This benefit consists of the marginal product of capital (net of expected future taxes),thevalueofnon-depreciatedcapital,andtheeffectsonthemarginalcosts ofinvestmentaswellasonthefinancialconstraint.6 Wedefinethefollowingtwotermsthatwillbeusedtosimplify(5). First,the taxwedgeω isdefinedas τ 1 ω ≡ . (6) τ 1−τ A higher effective marginal tax rate τ implies a higher value of ω . Second, the τ “residual”wedgeω isdefinedas R q (cid:20) (cid:18) i′(cid:19) (cid:18) i′(cid:19) i′(cid:21) ω ≡ −q′(1−δ)−µ′ζ′q′ +E Φ +Φ′ . (7) R β z′|z k′ k′ k′ Anyadditionalfrictionsafirmmightbefacingwouldbeincludedintheresidual wedge ω . In that sense, the particular distortions firms face other than differ- R entialtaxrates,beitadjustmentcostsorcreditconstraints,donotmatterforour resultsbelow.7 5The same is true for capital depreciation and eventual interest payments. Note, however, thatweareusingeffective marginaltaxratesinourestimationsbelow. Thesealreadytakeinto accountthetaxprovisionsfordepreciationanddebt-financing. 6ThefullderivationsarerelegatedtotheAppendix. 7Inwhatfollows,wetreatω asexogenous. Ifω isendogenoustotaxes,theneliminating R R tax rates would also reduce the dispersion in ω , and raise aggregate productivity, given the R 7

Usingtheexpressionforω andω ,wecanwrite(5)as τ R zF (k′,n) = ω ≡ ω ·ω , (8) k k τ R whereω denotestheeffectiveusercostofcapital,includingalldistortionssuch k as capital adjustment costs, financial constraints, and taxes. We decompose ω k into two parts. The first part, ω , stems from a directly observable distortion τ (effective marginal tax rates), the second is a residual term, ω , that captures all R otherfactorsthataffecttheuser-costofcapital. This formulation allows us to rewrite the firm’s problem in (1) as a static allocationproblem: max−ω k′ +zF(k′,n)−ω n (9) k n n,k′ The first-order conditions of (9) are consistent with the optimality conditions derivedin(4)and(8). 2.1 Tax heterogeneity and misallocation We now derive a formula to measure the effect on aggregate total factor productivity (TFP) stemming from heterogeneity in firm-specific effective costs of capital,ω ,andlabor,ω . Todoso,weassumeaCobb-Douglasproductionfunc- K N tion F(k,n) = zkαnβ. Let G(ω ,ω ) denote the joint distribution of distortions k n tocapitalandlaboracrossfirms. Our aim is to compare total output in the distorted economy with the allocation that a social planner would choose - using the same aggregate quantities (cid:82) (cid:82) of capital K = kdG and labor N = ndG as the competitive equilibrium of the distorted economy. Because total inputs are held constant between the two (cid:82) economies, any change in total output Y = ydG is equivalent to a change inaggregateTFP.Wefocusontheeffectofeliminatingtaxheterogeneityalone. Thereforeweassumethattheplannerdoesnot(orcannot)changeω andω . R n empiricalpatternsinthedatawedocumentbelow.Inthatsense,ourfindingsshouldbetakento beconservative. 8

ThefollowingpropositiongivesTFPinthedistortedcompetitiveequilibrium ofthiseconomy: Proposition1. Totalfactorproductivityinthedistortedeconomyis (cid:82) 1 − β − α Z = Y = z1−γω n 1−γω k 1−γdG . (10) KαNβ (cid:20) (cid:82) 1 − β −1−β (cid:21)α(cid:20) (cid:82) 1 −1−α − α (cid:21)β z1−γω n 1−γω k 1−γdG z1−γω n 1−γω k 1−γdG Eliminating tax differentials will generally alter the aggregate demand for capital and labor. We therefore introduce common tax rates (or subsidies) on capital and labor in order to keep the aggregate quantities unchanged. Therefore, the marginal products of labor and capital in the planner’s allocations are proportional to ω and ω , but not equalized across production sites. The opti- R n malityconditionsinthiscounterfactualscenarioaregivenby: zF (k,n) = ω′ = ω¯ ·ω and zF (k,n) = ω′ = ω¯ ·ω , (11) n n n n n k k R where ω¯ > 0 and ω¯ > 0 represent the planner’s tax or subsidy policy that is n k common across firms. The resulting optimality conditions for k and n coincide withthoseofaprofit-maximizingfirmthattakesthedistortionsandthecommon tax wedges ω¯ and ω¯ as given. Those wedges are chosen to satisfy the inputk n neutralityconstraintsontheallocationproblem: (cid:90) (cid:90) k(ω′,ω′)dG′ = K and n(ω′,ω′)dG′ = N n k n k where G′(ω′,ω′) denotes the distribution associated with the new distortions. k n Because wedges that are common to all firms do not distort relative marginal products, they do not cause a misallocation of inputs in the cross-section of firms.8 Consequently, G′(ω′,ω′) is equivalent to G′(ω ,ω ) in terms of its imk n R n 8Note that because this does not eliminate corporate taxation altogether, aggregate capital investmentremainssuboptimaloverall. 9

plicationsforTFPdistortions. ThecounterfactualTFPintheabsenceoftaxheterogeneitycanbeobtainedby settingω = 1(ortoanypositivescalar),andreplacingω byω inequation(10) τ k R as ω is the only remaining determinant of the marginal cost of capital. The R resultingcounterfactualTFPisgiveninthepropositionbelow. Proposition 2. Total factor productivity in the counterfactual economy with homogeneoustaxratesacrossfirmsis (cid:82) 1 − β − α α Z∗ = z1−γω n 1−γω k 1−γω τ 1−γdG . (12) (cid:20) (cid:21)α(cid:20) (cid:21)β (cid:82) 1 − β −1−β 1−β (cid:82) 1 −1−α − α α z1−γω n 1−γω k 1−γω τ1−γdG z1−γω n 1−γω k 1−γω τ 1−γdG TheratioofthecounterfactualTFPinequation(12)totheactualTFPinequation(10)givesthemarginaleffectofeliminatingtaxheterogeneityonaggregate productivity. From equation (12), Z∗ = Z when ω is constant across firms and τ Z∗ > Z whenever ω is heterogeneous but orthogonal to other distortions.9 τ More generally, however, Z∗ can be higher or lower than Z, depending on how taxratescorrelatewithotherdistortionsacrossfirms.10 To gain further insights, let us now consider an economy where the distortions are distributed jointly according to a log-normal density. The resulting formulashelpformanintuitionaboutthesourcesofmisallocationfromtaxheterogeneity. Theyshowhowinteractionsbetweentaxratesandotherdistortions can play an important role in assessing the allocative effects of tax distortions. Werelaxthelog-normalityrestrictioninourquantitativeanalysisbelow. Under thatassumption,TFPinthedistortedeconomyisequivalentto: (cid:90) 1 1 lnZ = ln z1− 1 γ − 21−γ (cid:2) α(1−β)σ k 2 +β(1−α)σ n 2 +2αβσ kn (cid:3) , (13) where σ2 and σ2 denote the variances of lnω and lnω respectively, and σ k n k n kn 9ThisfollowsfromJensen’sinequalitycombinedwiththefactthat1−β >α. 10Forinstance,Z∗ <Z whenω =1/ω andω ⊥ω . R τ τ n 10

is the covariance between them. Aggregate TFP reflects the underlying distributionofmicro-levelproductivitylevels,z,adjustedforefficiencylossescaused by input distortions. We are interested in the change in TFP from eliminating theheterogeneityintaxrates. Thisimpliessettingω′ toω¯ ·ω ,i.e.,eliminating k k R the tax wedge from the marginal product of capital in (8). The counterfactual TFP, lnZ∗, can be obtained by setting σ2 = σ2 and σ = σ in equation (14). k R kn Rn Takingdifferencesandrearrangingtermsgivesthenextproposition. Proposition 3. If ω ,ω , and ω are jointly log-normally distributed, then elimk n τ inating the heterogeneity in the marginal tax rates yields the following change in aggregateTFP: Z∗ 1α(1−β) α(1−β) αβ ln = σ2 + σ2(L −1)+ σ2L , (14) Z 2 1−γ τ 1−γ τ kτ 1−γ τ nτ whereσ2 isthevarianceoflnω andL = σ /σ2 andL = σ /σ2 denotethe τ τ kτ kτ τ nτ nτ τ slopecoefficientsfromalinearprojectionoflnω andlnω onlnω . k n τ Equation(14)presentsasimplewayofcapturingthetotalchangeinTFPfrom eliminating tax heterogeneity. It has three distinct components. The first one is apuremisallocationcomponent,representingthereductioninaggregateoutput caused by a dispersion in the marginal products of capital across firms. In the absenceofothereconomicdistortions,orifsuchdistortionswereorthogonalto taxrates,thiswouldbethetotalimprovementinTFPthatcanbeexpectedfrom equalizing marginal tax rates. The magnitude of the TFP gains is increasing in the variance of the tax rates, σ2, the span of control parameter, γ, and capital’s τ shareofincome,α.11 The second term in (14) captures the correlation of marginal tax rates with otherdistortionstocapital. ThecoefficientL islessthanoneiflnω andlnω kτ R τ arenegativelycorrelated. Thiscanariseiftaxesalleviateothercapitaldistortions. EliminatingtaxdifferentialsinthiscaseneednotleadtoTFPgains. Infact,inthe 11Toseethis,notethat α(1−β) =α+ α2 . 1−γ 1−γ 11

extreme case where tax rates fully offset other distortions, ω = ω−1, L = 0, τ R kτ whichimpliesthatthefirsttwotermscanceleachother. Of course, taxes could also exacerbate the existing distortions. If firms that have higher marginal costs of borrowing also have higher marginal tax rates, this would manifest as L > 1, and raise the potential gains from eliminating kτ taxdifferentials. The last term in (14) captures the correlation of marginal tax rates with distortionstolabor. Equalizationoftaxrateslowersthetaxratesforsomefirmsand raisestheirinputdemandresultinginareallocationoflabortowardthosefirms. This improves efficiency only if the marginal product of labor, ω , is higher at n thosefirmsonaverage,i.e.,ifL > 0. nτ 2.2 Alternative models of labor distortions In our equations above, we treated ω as exogenous to ω , because basic theory n τ suggests that corporate tax rate should not distort employment, conditional on capital and firm-level TFP. This follows from the fact that outlays on labor are typicallydeductedfromthetaxbase. Therearenonethelesssituationswherecorporatetaxratesmayhaveadirecteffectonemploymentdecisions,forinstance, when part of the labor cost cannot be deducted from income or when there are explicit employment-based credits and incentives, such as the recent employment retention credit provided by the CARES act. Similarly, models with cashin-advancerequirements,wherewageshavetobepaidbeforesalesarerealized, also lead to a tax-related wedge in the optimality condition for employment. In this subsection, we consider models with imperfect expensing of labor costs. In theAppendix,wepresentacash-in-advancemodelandillustratehowcorporate tax rates can directly affect employment decisions in addition to their indirect effectthroughinvestment. If there is an endogenous relationship between corporate taxation and the marginal cost of labor, then eliminating tax differentials would also affect labor distortions. This would potentially lead to larger TFP gains than implied by 12

Proposition (3) if taxes raise the marginal cost of labor. Ascertaining the causal effect of taxes on labor costs is not straightforward as it requires estimates of howtaxesalterfirm-specificlaborsupplyschedules. Someprogresscanbemade, however,onthepotentialroleofthesealternativemodelsbyinterpretingtheempirical correlation between labor productivity and tax rates as entirely endogenous. Aswedemonstratenext,thisprovidesanupperboundontheproductivity gainsfromhomogenizingtaxratesacrossfirmswhentaxesraisemarginallabor costs. Consider a scenario where a fraction λ ∈ [0,1] of labor costs are not deductible from the corporate tax base. Denoting the total cost per employee by ω ,theafter-taxincomeisnowgivenby(1−τ)[zF(k′,n)−(1−λ)ω n]−λω , l l l whichleadstothefollowingoptimalityconditionforemployment: zF (k,n) = (1−λ+λω )ω = ω (15) n τ l n When λ > 0, a higher corporate tax rate raises the marginal cost of labor. Importantly,heterogeneityintaxratescanleadtoadispersioninmarginalcosts of labor ω across firms, even when all firms face the same total cost per emn ployee ω .12 Unlike our baseline model above, eliminating tax heterogeneity in l this economy reduces the dispersion in marginal cost of labor, thereby leading tolargergainsinaggregateproductivity. In ourassociated calculationsbelow, we considerthe extreme caseofλ = 1, which implies ω = ω · ω . This is tantamount to interpreting the correlation n l τ betweenlaborproductivityandtaxratesasstructural. Thefollowingproposition givesthecounterfactualTFPfromeliminatingtaxheterogeneityinthatscenario: Proposition4. Inmodelswithimperfectlaborexpensing,totalfactorproductivity 12Asimilardistortioncanalsoarisewhenλ<0,i.e.,whenthereisataxcreditforemployment. Wefocusonλ>0heregiventhepositiveempiricalcorrelationbetweenlaborproductivityand taxratesbelow. 13

inthecounterfactualeconomywithhomogeneoustaxratesacrossfirmsis: (cid:82) 1 − β − α γ Z∗∗ = z1−γω n 1−γω k 1−γω τ 1−γdG . (16) (cid:20) (cid:21)α(cid:20) (cid:21)β (cid:82) 1 − β −1−β 1 (cid:82) 1 −1−α − α 1 z1−γω n 1−γω k 1−γω τ1−γdG z1−γω n 1−γω k 1−γω τ 1−γdG DividingZ∗∗abovewithZinequation(10)givestherelativeaggregatechanges in TFP from homogenizing tax rates across firms. When all distortions are distributed log-normally, the implied change in aggregate TFP can be simplified as follows. Proposition5. Supposeω = ω ·ω , ω = ω ·ω ,andω arejointlylog-normally k R τ n l τ τ distributed. Eliminatingtheheterogeneityinmarginaltaxrates(σ = 0)yieldsthe τ followingchangeinaggregateTFPinmodelswithimperfectlaborexpensing: Z∗∗ 1 γ α β ln = σ2 + σ2(L −1)+ σ2(L −1), (17) Z 21−γ τ 1−γ τ kτ 1−γ τ nτ whereσ2 isthevarianceoflnω andL = σ /σ2 andL = σ /σ2 denotethe τ τ kτ kτ τ nτ nτ τ slopecoefficientsfromalinearprojectionoflnω andlnω onlnω . k n τ Comparingequations(14)and(17)revealsthesignificanceofastructurallink betweentaxesandlaborcosts. Thefirstcomponent,attributabletothedispersion inthetaxratesislargerin(17),becauseitnowincludesthedirectcontributionof taxrateheterogeneitytothedispersioninmarginalcostoflabor,ω . Thesecond n component captures the correlation between tax rates and other distortions to capital. Because taxes now raise marginal costs of both capital and labor, they generate a positive correlation between the two. This exacerbates the distortionary effect of taxes (via σ in equation (13)). The last component in (17) can kn be smaller or larger than in equation (14) because it now captures the productivityimplicationsofthecorrelationbetweenthetaxwedge,ω ,andother labor τ distortions,ω . l In what follows, we present two sets of results: the baseline scenario, where 14

we interpret the empirical relation between labor distortions and tax rates as non-structural as in Section 2.1, and an alternative scenario, where we interpret itasstructural. Weconsiderthelatterasanupperboundontheallocativeeffects oftaxheterogeneity. Nextwedescribethedataandourmeasurementmethodology. 3 Data and methodology In this section we discuss the data sources and potential issues with the measurementofeffectivemarginalcorporateincometaxrates. Wethendescribeour methodology and examine the patterns of correlations between tax rates and firm-levelproductivity,whichserveasinputstoourformulasabove. 3.1 Data sources and definitions Our main data source is the Compustat database covering the years from 1980 to 2021. Compustat provides annual balance-sheet data on publicly listed companies. Toconductourcalculationsweuseinformationonoutput,employment, andthecapitalstock.13 Wedefineoutputasthesumofsalesandchangesininventories during the year.14 We measure labor input by employment. To construct a measure of a firm’s capital stock, we use a perpetual inventory method using investmentexpenditures. Thisallowsustocomputetheaverageproductivityof laborandcapitalforeachfirmandyear. Wesupplementthisdatawithestimatesoffirms’marginalcorporateincome tax rates, taken from two sources: Graham and Mills (2008) and Blouin et al. (2010). These studies take into account such factors as loss-offset provisions, depreciation allowances, and debt service when calculating an effective rate for each firm. Graham and Mills (2008) and Graham (1996) show that the simulated 13SeeAppendixBfordetailsonthedataused. 14Compustat does not contain information on the cost of intermediate inputs, preventing a measureofvalueadded. 15

tax rates provide a close approximation of the actual taxes paid as reported in taxrecords. Table1: Summarystatisticsofmarginaltaxrates Variable mean sd. p25 p50 p75 N τGM 0.169 0.171 0.007 0.070 0.342 125.048 τBCG 0.240 0.136 0.108 0.283 0.342 159.247 Note.–ThetwoeffectivetaxvariablesaretakenfromGrahamandMills(2008)andBlouinetal. (2010).SeeAppendixDforvariabledefinitionsandsampleselection. Summarystatisticsforthetwoeffectivemarginaltaxratemeasuresareshown in Table 1. The two tax measures differ somewhat in methodology. Rates estimated by Graham and Mills (2008) show more bunching at zero and at the top statutorymarginaltaxrate,whichhasvariedovertheyears. Ratesestimatedby Blouin et al. (2010) provide a smoother distribution, with a higher average rate andaslightlysmallervariance. Thetwotaxmeasuresarehighlybutimperfectly correlated(ρ = 0.61). 3.2 Measuring tax distortions Because we have two distinct tax rate measures that are correlated imperfectly, wetreateachmeasureasanerroneousestimateofthetruemarginaltaxrate. This allowsustoleveragetheempiricalcontentofeachmeasurebyfocusingontheir common component. Specifically, we interpret each measure as a combination ofthetruemarginaltaxrateandaclassicalmeasurementerror: lnω∗ = lnω +ϵ , iτ τ i whereϵ ismeasurementerrorwithvarianceσ andconditionalmeanE[ϵ |ω ] = i ϵ,i i τ 0 for i ∈ {1,2}. Replacing the tax wedges by their measured counterparts not only biases the estimates of the total allocative effect of tax heterogeneity, but 16

it can also lead to a misinterpretation of how tax rates interact with capital and labordistortions. Togainintuition,letusfirstconsiderequation(14),whichweuseforourdecompositionexercisesbelow,beforeweturntotheimplicationsofmeasurement error for the general, non-linear formula. Equation (14) has three empirical momentsthatdependonthetaxmeasure: thevarianceofthetaxwedge,σ2,aswell τ astheinteractionsoftaxwedgeswithcapitalandlaborproductivity,summarized bytheprojectioncoefficientsL andL . Whenω isreplacedbyitsmeasured kτ nτ τ counterpart,ω∗,allthreemomentsareestimatedwithabias. Thevarianceofω∗ τ τ is inflated relative to the variance of ω by a factor of (σ2 + σ2)/σ2. A larger τ τ ϵ τ measureddispersionintaxwedgestendstoexaggeratethemagnitudeoftheestimated change in TFP. On the other hand, the estimates of L and L , i.e., kτ nτ the projections of capital and labor productivity on tax wedges, are attenuated proportionally by σ2/(σ2 +σ2) when ω∗ is used. Lower measured correlations τ τ ϵ τ betweentaxwedgesandotherdistortionstendtoattenuatethemeasuredchange in TFP from eliminating tax heterogeneity. The net effect of these two forces is a downward bias in the estimated gains as summarized by the following proposition. Proposition 6. Assume that the tax wedge is measured with error, ω∗ = ω + ϵ τ τ withE(ϵ|ω ) = 0. Then,replacingtheω byω∗ inequation(14)underestimatesthe τ τ τ netTFPgainfromeliminatingtaxheterogeneity: σ2α(1−β) ln(Z∗/Z)|ω∗ = ln(Z∗/Z)|ω − ϵ . (18) τ τ 2 1−γ Additionally,theattenuatedestimatesofL andL resultinaninaccurate kτ nτ assessment of the interaction between tax wedges and other capital distortions. The capital component (second term in equation (14)) gets attenuated, and the directcomponent(firstterm)getsexaggerated. Thelaborcomponent(thirdterm) is unaffected because the attenuation bias when estimating L is offset by the nτ 17

upwardbiaswhenestimatingσ2.15 16 τ We address measurement error when we use equation (14) as follows. First, weestimatethevarianceoftaxwedgeswiththecovarianceofthetwomeasures: σˆ2 = cov(lnω∗ ,lnω∗ ). Second, we estimate L and L by regressing labor τ 1τ 2τ nτ kτ andcapitalproductivityonthemeasuredtaxwedgesusinganinstrumentalvariables approach, where each tax measure is used as an instrument for the other. This method is known to yield consistent estimates when the errors are uncorrelated across measures. Specifically, for each measure i,j ∈ {1,2} with i ̸= j, L ˆIV = cov(lnω∗ ,lnk)/cov(lnω∗ ,lnω∗ ). L ˆIV is defined similarly. We subi,kτ iτ iτ jτ i,nτ stitute these estimates in equation (14) to compute the change in aggregate TFP anditscomponents. However, because the distribution of tax rates shown in Table 1 is bimodal, itdepartsfromalog-normaldistribution. Therefore,wealsousethegeneralized formulas in equations (10), (12) and (16) to compute the potential productivity gains. Inparticular,wepartitionthefirmsintoequallysizedquantilebinsbased ontheir(measured)marginaltaxrateineachyear. Foreachgroup-yearcell,we then calculate the average tax wedge and compute the average firm-level TFP, along with capital and labor productivity as described above. In the Appendix, we show that the resulting bias for measurement error aligns with the error in equation (18) when the distribution of marginal products are log-normal, conditional on the tax rate, regardless of the marginal distribution of the tax rates. Accordingly, we adjust the resulting estimates of TFP gains for measurement error using equation (18). This requires an estimate for the variance of the measurement error, which we estimate by subtracting the covariance between the two measures, our estimate for the true variance, from the total variance of the measuredwedgeσˆ2 = var(lnω∗ )−cov(lnω∗ ,lnω∗ )forj ∈ {1,2}. Because ϵ,jt jτ 1τ 2τ we are interested in the cross-sectional dispersion in tax wedges, we repeat this 15Thisfollowsfromtheusualattenuationbiasformula:E[LˆOLS]×σ2 =L ×σ2 ,where nτ ω τ ∗ nτ ωτ LˆOLS istheOLScoefficientobtainedbyregressinglnω onlnω∗ nτ n τ 16Thecorrespondingbiasfromreplacingω withω∗inequation(17),i.e.,Whenthecorrelation τ τ betweenlabordistortionsandtaxratesiscausal,is− γ σ ϵ 2 . 1−γ 2 18

foreachyear. 3.3 Correlations between productivity and tax distortions Tomeasurethedistortionstocapitalandlabor,weusetheoptimalityconditions for factor demands, lnω = lnα + ln(y/k) and lnω = lnβ + ln(y/n), where k n factor shares α and β are common to all firms in an industry during a given year. Toestimatethecorrelationbetweentotaldistortionstocapitalandthetax wedge,weestimatethespecification ln(y/k) = Dk +L lnω∗ +ek, (19) it st kτ,t τ,it it where i denotes the firm, and t the year of observation. Dk are indicators for st a full set of sector and year interactions. These indicators capture variations in capital shares and average distortions across sectors and years. Therefore, L reflectsthecorrelationbetweenthetaxwedgeandothercapitaldistortions kτ,t acrossfirmsinagivenyear,thatis,ourestimateofL inequation(14). kτ Weestimatethecross-sectionalcorrelationbetweendistortionstolaborand taxwedgesusingasimilarspecification: ln(y/n) = Dn +L lnω∗ +en, (20) it st nτ,t τ,it it Because each tax estimate might contain measurement error, the OLS estimates of L and L are potentially attenuated. To remedy this issue, we estikτ nτ mateequations(19)and(20)withaninstrumentalvariablesapproach,whereone taxmeasureisusedasaninstrumentfortheother. We estimate separate values of L and L for each year to compute TFP kτ,t nτ,t gains or losses below. In Table 2 we summarize the patterns of correlations betweendifferentdistortionsusingacommonestimateforallyears. Thefirstthree columns show the OLS estimates of (19) and (20). The first row in each column shows the estimates obtained by tax measures provided by Graham and 19

Mills (2008), and the second row shows the corresponding estimate using the taxmeasuresfromBlouinetal.(2010). Bothmeasuressuggestastrongpositivecorrelationbetweentaxesandcapitalproductivity(column1),laborproductivity(column2),orfirm-levelTFP(column3),althoughtheysomewhatdisagreeonthestrengthofthatcorrelation. The two measures in the first column imply different correlation patterns between tax wedges and other distortions to capital. Recall that a value below (above)oneindicatesthatthetaxwedgeisnegatively(positively)correlatedwith other distortions to capital: cov(lnω ,lnω ) < 0 (> 0). Therefore while Gra- R τ ham and Mills’s estimates of the EMTR suggest a negative correlation between the tax wedge and capital distortions, Blouin et al.’s estimates suggest they are orthogonal. By contrast, both measures imply a positive correlation between distortionstolaborandthetaxwedgeincolumn2: cov(lnω ,lnω ) > 0). n τ Table2: Taxdistortionsandfactorproductivity (1) (2) (3) (4) (5) (6) lny/k lny/n lnz lny/k lny/n lnz PanelA lnω 0.67 0.55 0.65 1.26 1.61 1.72 1τ (0.04) (0.03) (0.02) (0.08) (0.06) (0.05) PanelB lnω 0.96 1.23 1.30 1.59 1.31 1.56 2τ (0.06) (0.04) (0.04) (0.09) (0.06) (0.06) Note.–Thetableshowstheresultsfromregressionsofproductivityonthetaxwedge(1/(1−τ)). Columns1to3reportOLSestimates. Columns4to6reportinstrumentalvariableestimatesto correctformeasurementerror.Allspecificationscontrolforafullinteractionofsectorandyear indicators. Data on productivity come from authors’ calculations from Compustat. Data on marginal tax rates come from Graham and Mills (2008) in Panel A and Blouin et al. (2010) in PanelB. 20

Correcting for the attenuation bias yields a more consistent picture across measures as shown in columns 4 to 6. Both estimates in column 4 indicate that otherdistortionstocapitalcorrelatepositivelywiththetaxwedgesacrossfirms, implying that the heterogeneity in tax rates exacerbates the existing distortions tocapital. Theestimatesincolumn5implyapositivecorrelationbetweenlabordistortionsandthetaxwedge. ThetwoalternativemodelspresentedinSection2interpret that correlation differently. From the perspective of our baseline model in Section2.1,thisissurprising. Becauselaborcostsaredeductedfromthetaxbase, employmentdecisionsshouldnotinprinciplebeaffectedbycorporatetaxes,and therelationshipbetweenthetwowedgesisthereforeconsideredspurious. Inthe modelpresentedinSection2.2,ontheotherhand,highertaxratesdirectlyraise themarginalcostoflabor. Therefore,apositivecorrelationisexpected. Columns 3 and 6 show the projections of firm-level TFP on the tax wedge, which we use below for some of our results. Consistent with the patterns from average labor and capital productivity, these estimates show that productive firmsonaveragefacehighermarginaltaxrates. Inourcalculationsbelow,wecomputetheIVestimatesforeachyear. Because from the two tax measures we obtain two estimates of the same underlying parameter,wecombinethembytakinganaverage,weightedbytheinverseoftheir variance. Forexample,usingtheestimatesfortheentiresampleperiod,reported in columns 4 and 5 of Table 2, we obtain a value of 1.41 (s.e. 0.04 ) for L and kτ 1.38(s.e. 0.02)forL fortheentiresampleperiod.17 nτ Before we turn to the implications of our estimates for aggregate TFP and output,weneedtosetvaluesfortheparametersoftheproductionfunction. For ourbaselineresults,wekeepthoseparametersfixedovertime. Thisallowsusto 17Specifically,thevarianceminimizingweightsareλ =var(bIV )/(var(bIV )+var(bIV )) 1 kτ,2 kτ,1 kτ,2 for bIV , and λ = 1 − λ for bIV . For L , for instance, the values in column (4) of kτ,1 2 1 kτ,2 kτ Table 2 imply a weight of 0.44 = 0.082/(0.082 + 0.092) for 1.59 and 0.56 for 1.26, giving a weighted average of 1.41. The standard error for the weighted estimate is given by var(bIV )×var(bIV )/(var(bIV )+var(bIV )). kτ,1 kτ,2 kτ,1 kτ,2 21

highlight the changes in the interactions between distortions when presenting the time trends. To that end, we set γ = 0.85, which implies a profit share of 15 percent in output. We set β = 0.85 × 2/3, which gives a labor share of 0.57. These two choices imply a capital share of α = 0.28. Given the downward trend in the labor share of income during our sample period, we also consider alternativescenariosfortheseparametersanddiscusstheirimplicationsforour findingsbelow. 4 Results Inthissection,wereportourestimatesfortheeffectofeliminatingcross-sectional differencesintaxwedgesontotalfactorproductivity. Ourprimaryfindingisthat eliminatingtaxheterogeneitywouldimproveTFPintheUnitedStates. Ourbaseline estimates put this gain between 3 and 4 percent. We find that this result is robusttoincludingmacroeconomictrendsinthedeclineofthelaborshareoran increaseinmarkups. WethendecomposethepotentialTFPgainsassociatedwith eliminating tax heterogeneity into its three components. The pure dispersion in taxratesexplainsasizeablepartoftheestimatedTFPgains,butthiscomponent became smaller after the tax reforms of the 1980s. The correlation of tax rates with capital and especially labor make up the largest component of projected gainsfromtaxmisallocation. 4.1 Aggregate productivity WebeginwiththeestimatesoftheoverallTFPgainsassociatedwitheliminating taxheterogeneityshowninFigure2. Thesolidblacklineshowsourbaselineestimate. ThechangeinTFPfromeliminatingtaxheterogeneityispositivethroughoutoursampleperiod. Thissuggeststhatdifferentialtaxratesdonotoffsetother distortions to capital and labor. On the contrary, our estimates imply that factorsarelikelymoreproductiveatfirmsthathavehighermarginaltaxrates. The average gain in TFP across all years is 3.3 percent. Given the TFP growth in the 22

US during our sample period, this corresponds to four years of average annual TFP growth. Over the sample period, the potential TFP gain varies between 2 percentand5percent,butthereisnodiscernibletimetrend. Figure2: TFPgainsfromtaxrateequalization Note.–ThefigureshowstheestimatedchangeinaggregateTFPifallfirmsweretofaceacommon corporatetaxrate. Baselinemodel(anditsapproximation)assumecorporatetaxesonlydistort investment.Thestructurallabormodeladditionallyallowstaxestodistorthiringdecisions. To understand the sources of the productivity gain, we now turn to our approximationoftheTFPgainsfromtaxhomogenizationinequation(14). First,we assesstheaccuracyoftheapproximationbycomparingtheimpliedtotalproductivitygainwithourfindingabove. The gray line in Figure 2 shows the estimated total TFP gains using the approximation formula. The shaded gray area represents error bands corresponding to two standard errors above and below the point estimate (associated with 23

thestandarderrorsofLIV andLIV). Usingtheapproximation,themagnitudeof kτ nτ thegainis4.6percentonaverage. Thisreinforcesourmainfindingthatthattax heterogeneityreducesaggregateTFP.Althoughslightlylargerthanthebaseline estimate, the estimates lie reasonably close to our baseline results. The two serieshaveaveryhighcorrelationcoefficientof(ρ = 0.81). Theapproximategains rangefromaround5percentduringtheearly1980stoaround3percentinrecent years,suggestinga2percentimprovementoveroursampleperiod. Next, we study the different components of the approximated gain in order to understand the interaction of tax heterogeneity with other distortions in the economy. From equation (14) the total TFP gains reflect not only the dispersion in tax rates,butalsotheestimatedcorrelationbetweenthetaxwedgeandotherdistortions to capital and labor. The stacked bars in Figure 3 decompose the total TFP gainsintothesethreecomponents. ThesolidlineinFigure3givesthetotalTFP gainandisidenticaltothegraylineinFigure2. The blue bars reflect the misallocation caused purely by tax heterogeneity. If tax wedges were uncorrelated with the marginal products of capital and labor, the blue bars would represent the total gains in TFP. They can therefore be interpreted as the TFP distortion caused by tax heterogeneity in an otherwise frictionless economy. From Figure 3 this component of the TFP gain was 1 to 2 percentpriorto1986,duemainlytothehigherstatutorycorporatetaxrate,and hasbeen under1 percentsince then. Overall,it representsless thana quarterof the total TFP gains. This highlights the importance of taking other distortions intoaccountwhenstudyingtheallocativeeffectsofaparticulardistortion. The red bars in Figure 3 represent the TFP gains that stem from how tax rates correlate with capital productivity. There are two hypothetical cases. If cov(ω ,ω ) < 0, or equivalently, L < 1, the heterogeneity in tax rate reduces R τ kτ the distortionary effects of other distortions. This could be the case if firms that facerelativelylargedistortions,forexample,duetocreditconstraintsoradjustment costs, face lower tax rates. In that situation, which is observed for several 24

Figure3: ComponentsofTFPgainsfromeliminatingtaxheterogeneity Note.– The figure shows the three components of TFP gains from tax rate equalization across firms(seeequation(14)). Thebluebarslabeled“Taxdispersion”representgainsinanotherwise frictionlesseconomy.Theredbarslabeled“Capital”showadditionalgains/lossesinaneconomy with capital distortions. The bars labeled “Labor” show additional gains in an economy with capitalandlabordistortions. yearsinthefigure,theredbarscontributenegativelytotheTFPgain. Thesecond case,i.e.,whencov(ω ,ω ) > 0isthemorecommoncase,however. Thisimplies R τ that tax rates are positively correlated with capital distortions. From the figure this correlation is not very strong, however, resulting in less than 1 percent of additionalTFPgains. Overtheyears,thepotentialgainsimpliedbythiscomponenthavebeenhighestduringthe1990sandearly2000sandhavediminishedin morerecentyears. Thissuggestsanimprovementfromanefficiencyperspective inthedistributionoftaxratesacrossfirmsovertime. The third component of the TFP gain comes from the correlation between labor distortions and tax wedges. This is shown as the yellow bars in Figure 3. 25

When that correlation is positive, equalizing taxes results in lower tax rates for firms where the marginal product of labor is typically higher. Because capital and labor are complementary in production, a lower tax rate also results in reallocation of employment toward high marginal product firms and creates an additional gain in TFP. Quantitatively, those gains represent a majority of the total gains depicted in Figure 3. This is partly because the share of labor in total incomeisroughlytwiceaslargeasthatofcapital.18 Overall, tax heterogeneity alone represents less than 1 percent of the total gainsonaverage,acrosstheyears. ThemajorityoftheprojectedgaininTFPfrom tax homogenization is due to the fact that tax wedges are correlated positively withotherlabordistortions. 4.2 Capital accumulation and potential output gains The estimated TFP gains above are defined as gains in total output for given quantities of aggregate labor and capital. In the long-run, however, the gain in productivity can cause additional capital accumulation and lead to additional output gains. To gauge the magnitude of this effect, consider the standard, representative agent growth model where labor is supplied inelastically. There, a 1 percentincreaseinTFPimpliesa1/(1−α)percentincreaseinthecapitalstock: 1 K = (αZ/r)1−α,whereZ isaggregateTFP.Thisraisestotaloutputbyα/(1−α) percent, because α is the capital share in production. This increase occurs in addition to the 1 percent increase in output due to higher TFP. In our baseline calibration, we assumed profits represent 15 percent of output and capital’s cost shareis1/3,implyingα = 0.85/3. Theseassumptionssuggestanadditionalgain of about 0.4 percent in total output from capital accumulation in the long run. Forourbaselineestimateof3.3percentTFPgainfromtaxhomogenization,this 18Moregenerally,capitalandlaborco-moveduringthereallocationfromeliminatingtaxheterogeneityaslongastheelasticityofsubstitutionbetweencapitalandlaborisnottoohigh(less than1/(1−γ)). 26

translatestoa4.6(= 3.3×1.4)percentlong-rungainintotaloutputpercapita.19 A related consequence of output growth is higher corporate tax revenue, which allows for a lower overall tax rate and further increases output growth through capital accumulation. Revenue-neutral gains in output are therefore largerthaninput-neutralgains. Specifically,revenueneutralityrequiresthatthe tax rate is reduced to offset the percent gain in output because net corporate income is proportional to output in our model: Π = (1 − γ)Y. Each percent decline in the tax rate raises the capital stockby 1 τ , and output by α times 1−α1−τ thecapitalstock.20 Additionaloutputallowsforevenlowertaxrates,andsoon. Theassociatedmultiplieris (cid:0) 1− α τ (cid:1)−1 ,whichisabout1.1whenα = 0.85/3 1−α1−τ and the (common) tax rate is 20 percent, roughly the average effective tax rate in our sample between the two estimates. Therefore, a revenue-neutral tax homogenization reform would raise output per capita by 5.1 percent (4.6×1.1) in thelong-run,oncecapitalaccumulationisaccountedfor. Selectionoffirmsthroughentryandexitisanotherimportantmarginwhereby tax homogenization can improve aggregate productivity. In standard models of industry dynamics without distortions (e.g. Hopenhayn (1992)), efficiency requiresthesurvivaloffirmswithhigherproductivity. Taxheterogeneitycandistortthatselectionbyallowinglessproductivefirmstosurvivelongerandpotentially pushing productive firms into premature exit because tax rates correlate positively with productivity. We are not able to measure the selection effects in ourdata,asexitsareuncommonamongpubliclylistedfirmsandentriesarenot observed until firms are publicly listed. Nevertheless, we think that tax homogenization would likely further raise productivity by improving the efficiency of firmselection. 19More generally, long-run output growth depends on the price elasticities of factor supply. Modelswithpositively-slopedcapitalsupplyschedules, suchasAiyagari(1994), wouldpredict smallergains,andthosewithpositivelyslopedlaborsupplyscheduleswouldpredictlargergains thanthefiguresreportedhere. 20Becauseω = 1 ,thepercentchangeinthetaxwedgeisrelatedtothepercentchangein τ 1−τ thetaxrateasfollows: dωτ = −dτ × τ . Multiplyingthatwiththecostelasticityofcapital ωτ τ 1−τ demand,1/(1−α)givesthetotaleffectoncapitalstock. 27

4.3 TFP gains in alternative models of labor distortions WenowturntoalternativemodelsdiscussedinSection2.2,wherethecorrelation between labor productivity and corporate tax rates arises structurally. Because that correlation is positive, eliminating tax heterogeneity reduces distortions to employment and improves aggregate TFP over and above what we have estimated so far. The resulting estimate for the TFP gains associated with eliminating tax heterogeneity is shown as the dashed red line in Figure 2. Overall, the estimated gains are considerably larger, averaging 9.1 percent over our sample period. RecallthattheaverageTFPgaininourbaselinescenariowas3.3percent. Gains are particularly large earlier in the sample, averaging around 10 percent. Thiswasatimewhentheaveragecorporatetaxratewashigher. Inrecentyears, theTFPgainstandsaround7percent,suggestinga3percentgainfromimprovementsinthedistributionoftaxasymmetryacrossfirms. 4.4 Macroeconomic trends and estimated TFP gains TheTFPgainsinFigure2appeartoberoughlystableovertime. Whencomputing these gains, we assumed constant values for the macroeconomic parameters of factorsharesandmarkups. Empirically,however,weobserveadownwardtrend inthelaborshareofincomeduringoursample. Recentworkhasarguedthatthe decline in the labor share is associated with a rise in price markups and/or an increaseinthecapitalshare. Inthissubsection,weinvestigatehowthesechanges mightaffectthetrendsinestimatedTFPgainsassociatedwithtaxheterogeneity. We take the decline of the labor share as given and benchmark its drop to the BEA’s measure for each year of our analysis. Of course, the shares of capital, labor and profits sum to one, and a change in the labor share necessarily changes at least one other parameter. While the evidence on the decline in the aggregate labor share is relatively well-accepted, how much of that decline was redistributed to capital versus profits is less clear. We therefore consider two alternative scenarios. First, we assume that the decline in the labor share was 28

matched one for one by a rise in the capital share of income, keeping the share ofprofitsconstantovertime. Second,weassumethatthelaborshareandcapital declinedproportionally,thusraisingtheprofitshare1−γ overtime. Itturnsout thatneitherofthesetwoscenarioschangesourfindingsverymuch. The resulting values for α, β, and γ are shown in Panel (a) of Figure 4. The blacksolidlineshowsthelaborshareofincomepublishedbytheBEA.Itdeclines from57.7percentin1980to53.0percentin2016. Inthefirstscenarioweconsider, thisismatchedbya4.7percentincreaseinthecapitalshareα,shownasthegray dashedlineinthefigure. Inthesecondscenario,wekeepthecostsharesoflabor andcapitalfixedat2/3and1/3,implyingtoariseintheprofitsharefrom13.5in 1980 to 20.5 in 2016, or, equivalently, a rise in the markup rate from 15.6 to 25.7 percent (shown as the red dashed line). The resulting capital share decline from 28.8percentto26.5percentisshownastheredsolidline. (a)Parameters (b)Misallocation Figure4: Macrotrendscenarios Note.–Panel(a)showsthelaborshareofincome(β)fromtheBEA,andtheassociatedchangesin thesharesofcapital(α)andprofits(1−γ)undertwoalternativescenarios.Panel(b)showsthe TFPgainsfromtaxrateequalizationineachscenario. Parametersareconstantinthebaseline scenario. Becauseourexperimentschangemultipleparametersatonceandbecausethe TFPequationin(10)isnon-linear,itisapriorinotclearhowthemacroeconomic 29

trends might change our estimates. However, we can obtain some insights by studyingitsapproximationinequation(14). Changes in the labor share of income have a ceteris paribus ambiguous effect on estimated TFP gains. Note that the labor share of income β acts as a weightinequation(14)whenconsideringdistortionsthatarerelatedtotheallocation of labor versus capital. A lower β shifts the weight from the correlation betweentaxdistortionsandotherlabordistortionstocapital. Becausetheeffect oftaxheterogeneityonallocativeefficiencyisgenerallyambiguousinadistorted economy - it depends on the correlations of tax rates with other distortions to capital and labor - the net effect of a change in the labor share is ambiguous as well. Forinstance,iflaborproductivityisgenerallyhighandcapitalproductivity isgenerallylowamongfirmsthatfacehighertaxrates,thenalowerlaborshare shouldbeassociatedwithsmallerTFPlossesfromtaxheterogeneity. We first consider the scenario of a higher capital share. A higher value of α raises the TFP gains, ceteris paribus. This effect is unambiguous from (14). Intuitively, the larger the importance of the distorted factor in production is, the largerarethelossesfromtaxdistortions. However,thedashedgraylineinpanel (b) of Figure 4 shows that the TFP gains from this scenario yield similar magnitudesasourbaseline,indicatingthattheroleofthecapitalshareisquantitatively small. Wenowconsiderthesecondscenario,underwhichmarkupsincrease,which isequivalenttoalowervalueofγ. Ceterisparibus,lowervaluesofγ areassociatedwithlowerTFPlossesfromtaxheterogeneityasindicatedbyequation(14). Therefore rising markups would tend to reduce the TFP gains over time. Intuitively, this is because lower values of γ bring the economy further away from a linear technology (or, equivalently, from perfect competition), where the best firm can absorb all the resources without facing diminishing returns to scale. The lack of that possibility lowers the total gains to reallocating inputs more efficiently. Looking at the red dashed line in panel (b) of Figure 4 once again shows 30

(a)RisingCapitalShare (b)RisingMarkups Figure5: SourcesofTFPgainsunderalternativemacroscenarios similarTFPgainsunderthisscenariorelativetothebaseline. Ourresultspointto an approximately 1 percentage point lower potential TFP gain from eliminating taxheterogeneityinrecentyears. Decomposition Figure 5 shows the decomposition of TFP gains under alternative macro scenarios where the labor share declines. The left panel attributes that decline to a higher capital share of income and the right panel to a rise in markups. The relative magnitudes of the interaction between tax wedges and capital or labor distortions are broadly similar across scenarios. Under rising markups,overallTFPgainsfromeliminatingtaxheterogeneitydeclinebymore, especiallytowardtheendofthesample. Thisisattributabletoalowervalueofγ, whichreducestheTFPlossesassociatedwitheachcomponent(seeequation(14)), althoughthedeclineinthelaborcomponentisthemostapparent. 5 Conclusion Ourfindingsshowthatpoliciesthatseektoreducedifferencesinmarginalcorporateincometaxrateswouldresultinsignificantgainsinaggregateproductivity. 31

Themajorityofthesegainsareattributabletotheempiricalcorrelationbetween factor productivity and marginal tax rates: firms that face higher tax rates are typicallythosewherecapitalandlaboraremoreproductiveonthemargin. These findings highlight the importance of accounting for other frictions whenstudyingtheimplicationsofaspecificdistortiontoaggregateefficiency. In a frictionless economy, or in a distorted economy where tax rates are orthogonaltoothereconomicfrictions,theproductivityeffectoftaxasymmetrieswould havebeenmuchsmallerinmagnitude. Theextentofpotentialgainsinproductivityalsodependsonthemodelused tointerprettheempiricalpatternsinthedata,rangingfromaround3percentin standardmodelswherecorporatetaxesdistortthemarginalcostofcapitalupto 9 percent in models where taxes additionally distort the marginal cost of labor. Empirical assessments of models of production where labor is chosen dynamically, or models with liquidity constraints where payments to labor are made prior to sales, are promising avenues for future research that seeks to ascertain whether and how hiring decisions are causally distorted by corporate tax rates, conditionaloncapital. It is also worth noting that although we estimate TFP losses associated with tax heterogeneity, eliminating the heterogeneity altogether is not necessarily productivity maximizing in distorted economies. Tax design that seeks to maximize aggregate productivity would aim to offset other distortions in the economybystrategicvariationsinthetaxrate. Efficientdesignofcorporatetaxation isanotherpromisingavenueforfutureresearch. References Adamopoulos, Tasso, Loren Brandt, Jessica Leight, and Diego Restuccia (2022). Misallocation, Selection, and Productivity: A Quantitative Analysis With Panel Data From China. Econometrica, 90(3), pp. 1261–1282. doi:https://doi.org/10.3982/ECTA16598. 32

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A Theoretical Appendix This appendix details the derivations in the text and gives the formal proofs for thepropositions. Firm’sproblemwithmultipledistortions Theoptimalityconditionsforinvestmentandfuturecapitalofthefirm’sproblemin(1)aregivenbythefirst-order conditionwithrespecttoinvestment: (cid:18) (cid:19) (cid:18) (cid:19) i i i : −1−Φ′ +q −µ = 0 ⇔ q = 1+Φ′ +µ. (A1) k k and (cid:2) (cid:3) k′ : β (1−τ)zF (k′,n)+E V (z′,k′) −q = 0, (A2) k z′|z k withtheenvelopecondition (cid:18) (cid:19) (cid:18) (cid:19) i i i V (z,k) = −Φ +Φ′ +q(1−δ)+µζq. (A3) k k k k Thisimpliesanoptimalityconditionforthechoiceofcapitalgivenby(5). Proposition1. Totalfactorproductivityinthedistortedeconomyis: (cid:82) 1 − β − α Z = Y = z1−γω n 1−γω k 1−γdG (A4) KαNβ (cid:20) (cid:82) 1 − β −1−β (cid:21)α(cid:20) (cid:82) 1 −1−α − α (cid:21)β z1−γω n 1−γω k 1−γdG z1−γω n 1−γω k 1−γdG Proof. Theprofit-maximizinglevelsofcapital,labor,andoutputare: (cid:18) (cid:19)1−α (cid:18) (cid:19) α 1 β 1−γ α 1−γ n = z1−γ (A5) ω ω n k (cid:18) (cid:19) β (cid:18) (cid:19)1−β 1 β 1−γ α 1−γ k = z1−γ (A6) ω ω n k 1

(cid:18) (cid:19) β (cid:18) (cid:19) α 1 β 1−γ α 1−γ y = z1−γ (A7) ω ω n k SubstitutinginthedefinitionofTFPgivesthefollowing: (cid:82) 1 − β − α Z = Y = z1−γω n 1−γω k 1−γdG KαNβ (cid:20) (cid:82) 1 − β −1−β (cid:21)α(cid:20) (cid:82) 1 −1−α − α (cid:21)β z1−γω n 1−γω k 1−γdG z1−γω n 1−γω k 1−γdG Proposition 2. Total factor productivity in the counterfactual economy with homogeneoustaxratesacrossfirmsis: (cid:82) 1 − β − α α Z∗ = z1−γω n 1−γω k 1−γω τ 1−γdG . (A8) (cid:20) (cid:21)α(cid:20) (cid:21)β (cid:82) 1 − β −1−β 1−β (cid:82) 1 −1−α − α α z1−γω n 1−γω k 1−γω τ1−γdG z1−γω n 1−γω k 1−γω τ 1−γdG Proof. In the counterfactual economy, ω′ = ω¯ ω = ω¯ ω /ω and ω′ = ω¯ ω . k k R k k τ n n n Prooffollowsfromsubstitutingtheseinequation(10). Thecommoncomponents ofdistortions,ω¯ andω¯ ,canceleachotherout. n k Proposition 3. If ω ,ω , and ω are jointly distributed log-normally, then elimk n τ inating the heterogeneity in the marginal tax rates yields the following change in aggregateTFP: Z∗ 1 1 α(1−β) αβ ln = α(1−β)σ2 + σ2(L −1)+ σ2L , (A9) Z 21−γ τ 1−γ τ kτ 1−γ τ nτ whereσ2 isthevarianceoflnω andL = σ /σ2 andL = σ /σ2 denotethe τ τ kτ kτ τ nτ nτ τ slopecoefficientsfromalinearprojectionoflnω andlnω onlnω . k n τ Proof. Let µ = E[lnx] and σ2 = V[lnx] be the mean and variance of the log of x x avariablex. Underjointlog-normality: 2

(cid:90) α β 1 ln y = lnα+ lnβ + (µ −αµ −βµ ) z k n 1−γ 1−γ 1−γ 1 1 + (σ2 +α2σ2 +β2σ2 −2ασ −2βσ +2αβσ ) 2(1−γ)2 z k n zk zn kn (cid:90) (1−β) β 1 ln k = lnα+ lnβ + (µ −(1−β)µ −βµ ) z k n 1−γ 1−γ 1−γ 1 1 + (σ2 +(1−β)2σ2 +β2σ2 −2(1−β)σ −2βσ +2(1−β)βσ ) 2(1−γ)2 z k n zk zn kn (cid:90) α (1−α) 1 ln n = lnα+ lnβ + (µ −αµ −(1−α)µ ) z k n 1−γ 1−γ 1−γ 1 1 + (σ2 +α2σ2 +(1−α)2σ2 −2ασ −2(1−α)σ +2α(1−α)σ ) 2(1−γ)2 z k n zk zn kn Usingtheseequations,theTFPinthedistortedeconomyis: 1 1 (cid:2) (cid:3) lnZ = µ + σ2 −α(1−β)σ2 −β(1−α)σ2 −2αβσ . (A10) z 21−γ z k n kn Whentaxdifferentialsareeliminatedcapitaldistortionsaregivensimplybyω , R whichgivestheTFPinthatcounterfactualas: 1 1 (cid:2) (cid:3) lnZ∗ = µ + σ2 −α(1−β)σ2 −β(1−α)σ2 −2αβσ . (A11) z 21−γ z R n Rn Note that σ2 − σ2 = σ2 + 2σ and σ − σ = σ . Rearranging the terms k R τ Rτ kn Rn nτ and netting out µ , σ2 and σ2 terms, the efficiency losses from distortions are z z n 3

equivalentto: Z∗ 1 1 (cid:2) (cid:3) ln = α(1−β)(σ2 −σ2)+2αβ(σ −σ ) Z 21−γ k R kn Rn 1 1 (cid:2) (cid:3) = α(1−β)(σ2 +2σ )+2αβσ 21−γ τ Rτ nτ σ2 1 (cid:20) σ σ (cid:21) = τ α(1−β)(1+2 Rτ )+2αβ nτ 2 1−γ σ2 σ2 τ τ σ2 1 = τ [α(1−β)(1+2(L −1))+2αβL ] kτ nτ 2 1−γ 1 1 α(1−β) αβ = α(1−β)σ2 + σ2(L −1)+ σ2L 21−γ τ 1−γ τ kτ 1−γ τ nτ The last two equalities substitute the linear projection coefficients for σRτ = σ2 τ L = L −1and σnτ = L . Rτ kτ σ2 nτ τ A.1 Adding cash-in-advance restrictions to the model Consider a version of the baseline model in Section (2), where labor costs are incurred before production and sales take place. For comparability, we change ournotationslightlytodenotethewagecostsbyω here,andreserveω forthe l n effectivemarginalcostoflaboroncetaxesandcash-in-advancerequirementsare takenintoaccount. Thefirm’soptimizationprobleminthiscasebecomes: (cid:18) (cid:19) i (cid:2) (cid:3) V(z,k) = max −i−ω n−Φ k+β (1−τ)zF(k′,n)+τω n+E V(z′,k′) l l z′|z n,k′,i k subjecttothelawofmotionforcapitalandacollateralconstraint k′ = i+(1−δ)k ω n+i ≤ ζqk, l 4

withassociatedmultipliersq andµ. Notethatwagepaymentsarealsosubjectto the collateral constraint as they need to be financed prior to production. These modificationsdonotaltertheoptimalityconditionforinvestment. Theoptimalityconditionforlaborisnowgivenby: 1−β +µ 1 zF (k,n) = ω +ω = ω n l l n β 1−τ (cid:124) (cid:123)(cid:122) (cid:125) ωτ The marginal cost of labor reflects two additional factors in addition to the usual wage cost. Suppose first that the collateral constraint is not binding for the firm: µ = 0. Because there is a lag between the labor outlay and the realization of sales, the cost of labor includes the opportunity cost of paying wages in advance, which is the foregone earnings on those funds that the firm could otherwise enjoy. This is represented by ω (1 − β)/β. Because this component l is not deducted from corporate income in the optimization problem above, the opportunity cost of paying labor outright, as opposed to investing those funds onthemarket,interactswiththetaxwedgeraisingthemarginalcostoflaborby ω = ω ω (1−β)/β. Thisformulationdefinesastructuralrelationbetweenthe n τ l marginal cost of labor ω and ω au. Higher values of ω au necessarily raise ω . n t t n Therefore,alteringthedistributionofω aualsoaltersthedistributionofω . We t n ignorethispossibilityinourbaselinemodel. The second factor originates from the collateral constraint. When the firm is financially constrained (µ > 0) the effective discount factor is higher than (1 − β)/β, because the opportunity cost of paying labor in advance is not to earn interest on those funds in the market, but to finance much needed capital on the margin. That the collateral constraint is binding implies that the firm’s return on capital is higher than the market. Therefore, constrained firms have a higher marginal cost of labor. Furthermore, tax wedges exacerbate any existing differencesinmarginalcostoflaborthatmightarisefromcollateralconstraints. σ2 = σ2 +σ2 +2σ wherex = ln(1+ 1−β+µω ) ≃ ln 1−β+µ +lnω ) n l x lx β τ β τ Proposition 4. If ω = ω ·ω ,ω = ω ·ω , and ω are jointly distributed logk R τ n l τ τ 5

normally, then eliminating the heterogeneity in the marginal tax rates yields the followingchangeinaggregateTFP: Z∗ 1 γ α β ln = σ2 + σ2(L −1)+ σ2(L −1), (A12) Z 21−γ τ 1−γ τ kτ 1−γ τ nτ whereσ2 isthevarianceoflnω andL = σ /σ2 andL = σ /σ2 denotethe τ τ kτ kτ τ nτ nτ τ slopecoefficientsfromalinearprojectionoflnω andlnω onlnω . k n τ Proof. Substituting ω = ω and ω = ω in equation (A10) for the TFP in the n l k R distortedeconomygives: 1 1 (cid:2) (cid:3) lnZ = µ + σ2 −α(1−β)σ2 −β(1−α)σ2 −2αβσ . (A13) z 21−γ z k n kn Whentaxdifferentialsareeliminatedcapitaldistortionsaregivensimplybyω , R whichgivestheTFPinthatcounterfactualas: 1 1 (cid:2) (cid:3) lnZ∗ = µ + σ2 −α(1−β)σ2 −β(1−α)σ2 −2αβσ . (A14) z 21−γ z R l Rl Notethatσ2−σ2 = σ2+2σ ,σ2−σ2 = σ2+2σ andσ −σ = σ +σ +σ2. k R τ Rτ n τ lτ kn Rl Rτ lτ τ Rearranging the terms and netting out µ and σ2 terms, the efficiency gains or z z lossesfromdistortionsareequivalentto: Z∗ 1 1 (cid:2) (cid:3) ln = α(1−β)(σ2 −σ2)+β(1−α)(σ2 −σ2)+2αβ(σ −σ ) Z 21−γ k R n l kn Rl 1 1 (cid:2) = α(1−β)(σ2 +2σ )+β(1−α)(σ2 +2σ )··· 21−γ τ Rτ τ lτ (cid:3) ··· +2αβ(σ +σ +σ2) Rτ lτ τ σ2 1 (cid:20) σ σ = τ α(1−β)(1+2 Rτ )+β(1−α)(1+2 lτ )··· 2 1−γ σ2 σ2 τ τ (cid:21) σ σ Rτ lτ ··· +2αβ(1+ + ) . σ2 σ2 τ τ 1 γ α β = σ2 + σ2(L −1)+ σ2(L −1) 21−γ τ 1−γ τ kτ 1−γ τ nτ 6

The last equality substitutes the linear projection coefficients for σRτ = L = σ2 Rτ τ L −1and σ lτ = L = L −1,andγ = α+β. kτ σ2 lτ nτ τ Proposition 5. Assume that the tax wedge is measured with error, ω∗ = ω + ϵ τ τ with E(ϵ) = 0. Then, replacing the ω by ω∗ in equation (14) underestimates the τ τ netTFPgainfromeliminatingtaxheterogeneity: σ2α(1−β) ln(Z∗/Z)|ω∗ = ln(Z∗/Z)|ω − ϵ , (A15) τ τ 2 1−γ Proof. Letσ2 = σ2+σ2 denotethevarianceofthemeasuredtaxwedge. Define τ∗ τ ϵ the projection x = L × lnω + e , where ω is the true tax wedge. The OLS xτ τ x τ estimateofL fromtheprojectionofxonlnω2 is: L ˆOLS = L × σ τ 2 . xτ τ∗ xτ xτ σ2 τ∗ α(1−β)σ2 α(1−β)σ2 αβ σ2 ln(Z∗/Z)|ω∗ = τ∗ + τ∗(L ˆOLS −1)+ τ∗L ˆOLS τ 1−γ 2 1−γ 2 kτ 1−γ 2 nτ σ2 +σ2α(1−β) α(1−β)σ2 αβ σ2 = − τ ϵ + τL + τL ˆ kτ nτ 2 1−γ 1−γ 2 1−γ 2 σ2α(1−β) = ln(Z∗/Z)|ω − ϵ . τ 2 1−γ A.2 Computationofthenon-lineargainsandmeasurement error correction Foreachx ∈ {ω ,ω z},definelnxˆ = b ×lnω ,whereb istheOLSestimator k n xτ τ xτ of L . We ignore the intercept term in that projection, because it cancels out xτ fromtheTFPequationsasitiscommontoallfirms. Notealsothatweareusing theOLSestimator,nottheconsistentestimator.A1 A1Because various biases from using the OLS estimator cancel each other out, the resulting formulaforerrorcorrectionissimplerandalignswiththatreportedinProposition6. Wealso consideredusingtheconsistent(IV)estimator,andanon-parametricestimatorforE[lnx|ω au]. t Bothyieldsimilarresults. 7

ThencomputecurrentTFPbysubstitutingωˆ ,ωˆ andzˆinequation(10),and k n theidealTFPbysubstitutingωˆ ,zˆ,andω′ = ωˆ /ω forω inthesameequation. n k k τ∗ k Thisyieldsthefollowingequations: ˆ (cid:82) (ω τ∗ )1− 1 γ (bzτ−βbnτ−αb kτ )dG τ∗ Z = τ∗ (cid:104) (cid:82) (ω τ∗ )1− 1 γ (bzτ−βbnτ−(1−β)b kτ )dG τ∗ (cid:105)α(cid:104) (cid:82) (ω τ∗ )1− 1 γ (bzτ−(1−α)bnτ−αb kτ )dG τ∗ (cid:105)β Z ˆ∗ = (cid:82) (ω τ∗ )1− 1 γ (bzτ−βbnτ−αbRτ)dG τ∗ , τ∗ (cid:104) (cid:82) (ω τ∗ )1− 1 γ (bzτ−βbnτ−(1−β)bRτ)dG τ∗ (cid:105)α(cid:104) (cid:82) (ω τ∗ )1− 1 γ (bzτ−(1−α)bnτ−αbRτ)dG τ∗ (cid:105)β where b = b − 1 is the projection coefficient of lnω on lnω and G is Rτ kτ R τ∗ τ∗ themarginaldistributionofthemeasuredtaxwedge. When ϵ is distributed independently log-normal, then for any scalar c > 0, E[ωc ] = E[ωcϵc] = E[ωc]·E[ϵc] = E[ωc]·exp(c2σ2/2). Replacing c with the τ∗ τ τ τ ϵ appropriatepowercomponentforeachtermgives: Z ˆ∗ Z ˆ∗ σ2α(1−β) ln τ∗ = ln τ − ϵ . (A16) Z ˆ Z ˆ 2 1−γ τ∗ τ Repeating these steps for the alternative formulation in Section 2.2 by substituting τ∗ for τ in the expression for Z ˆ∗∗ presented in equation (16) gives the τ∗ followingrelationbetweenthemeasuredTFPlossandtheactualTFPloss: Z ˆ∗∗ Z ˆ∗∗ σ2 γ ln τ∗ = ln τ − ϵ . (A17) Z ˆ Z ˆ 2 1−γ τ∗ τ B Data Appendix The firm-level data used in Section 3 were constructed as follows. We use the annualCompustatdatabase,whichprovidesbalance-sheetdataonpubliclylisted companiesintheUS.Oursampleincludestheyears1980–2021. Weperformthe followingsampleselectionanddata-cleaningsteps. Werestrictattentiontofirms 8

registered in the US. We exclude firms in the finance, insurance, and real estate sectors,aswellasinutilitiesandpublicadministration. Weremoveobservations withnegativesales. Weconstructfirm-levelcapitalstocksbyusingaperpetualinventorymethod. For each firm, we start with the year in which information on gross and net property, plant, and equipment (PPEGT and PPENT) is available. We then build thecapitalstockbyaddingthechangeinPPENTdeflatedbytheinvestmentprice deflatortothecalculatedcapitalstockforthatyear. We supplement these data with information on firms’ marginal tax rates, taken from two sources, i) Graham and Mills (2008), abbreviated as “GM” and ii) Blouin et al. (2010), abbreviated as “BCG”.A2 While the GM database covers the years 1980–2021, the BCG data are only available from 1980–2016. We link the Compustat data to the marginal tax rate data via the firm identifier GVKEY. Finally,weremovefirm-yearobservationsforwhichbothtaxratesaremissing. This results in a sample of 185,203 unique firm-year observations, averaging about 4,600 firms per year. Marginal effective tax rates are available for 70.3 percentofourobservations(90.2percentfortheBCGtaxrates). Estimationoffirm-levelTFP Weestimatefirm-levelTFPusingathree-step controlfunctionapproachfollowingOlleyandPakes(1996). Thekeyvariablesare value added, employment, and physical capital for each firm and factor shares in the production function. Value added is defined as sales plus the change in inventories. We begin by estimating factor shares at the two-digit NAICS level in three steps. First,weregresslogofoutputonsecond-orderpolynomialsinthelogsof the capital stock and investment expenditures, including an interaction term as well as log employment. We control for a full set of indicator variables for year and2-digitNAICSclassifications. Sectorswithfewerthan100observationswere droppedfromthisestimation. Second,tocorrectforsurvivalbias,weestimatea A2Eachstudycontainstwomeasuresofthemarginaltaxrates:beforeandafterinterestdeductionsareapplied.Themarginaltaxratesweuseinthispaperareafterinterestdeductions. 9

probitspecificationforfirmsurvivalintheCompustatdata(usingthesamepolynomials and year-industry dummies). In a third step, we estimate capital shares for each industry by regressing log output on the log capital stock, controlling forindustry-yeareffectsandthepredictedsurvivalprobabilityfromtheprevious step. We then compute log TFP assuming a Cobb-Douglas production function andnormalizeitsmeantozeroineachyearandindustry. 10