Corporate Tax Cuts and the Decline of the Manufacturing Labor Share

Board of Governors of the Federal Reserve System International Finance Discussion Papers ISSN 1073-2500 (Print) ISSN 2767-4509 (Online) Number 1379 August 2023 Corporate Tax Cuts and the Decline of the Manufacturing Labor Share Baris Kaymak and Immo Schott Please cite this paper as: Kaymak,BarisandImmoSchott(2023). “CorporateTaxCutsandtheDeclineoftheManufacturing Labor Share,” International Finance Discussion Papers 1379. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/IFDP.2023.1379. 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.

Corporate Tax Cuts and the Decline in the Manufacturing Labor Share Barıs¸ Kaymak* Immo Schott† August 29, 2023 Abstract We document a strong empirical connection between corporate taxation and the manufacturing labor share, both in the US and across OECD countries. Our estimates associate 30 to 60 percent of the observed decline in labor shares with the fall in corporate taxation. Using an equilibrium model of an industry where firms differ in their capital intensities, we show that lower corporate tax rates reducethelaborsharebyraisingthemarketshareofcapital-intensivefirms. Thetax elasticityofthelaborsharedependsonthejointdistributionoflaborintensitiesand value added at the micro level. Given the empirical distribution in the US manufacturing sector, our quantitative analysis suggests that corporate tax cuts explain a significant part of the decline in the manufacturing labor share since the 1950s. The shift away from traditionally large, labor-intensive production units raised the concentrationofmarketsharesandreducedtheconcentrationofemployment. JELclassification:E25,H32,L11,L60 Keywords: Labor share of income, corporate taxation, industry dynamics, firm size distribution * DepartmentofEconomicResearch,FederalReserveBankofCleveland. E-mail: barkaymak@gmail.com † Division of International Finance, Board of Governors of the Federal Reserve System. Email: immoschott@gmail.com

1 Introduction Labor’s share of income has been falling across the world, with the most striking declines observed in industries that have traditionally been capital intensive, such as manufacturing or mining (see, for instance, Elsby et al. (2013) or Karabarbounis and Neiman (2013)). In this paperweshowthatthedeclineofthelaborsharecoincideswithadownwardtrendincorporate tax rates and provide a framework to measure the marginal contribution of lower corporate tax ratestothedeclineofthelaborshare. The downward trend in the labor share of income in the US is shown in Figure 1. Since 1953theaggregatelaborsharefellbyapproximately7percentagepoints(pp),fromaround65 percent to 58 percent. This is shown as the dashed red line, plotted against the right y-axis in panel (a). This decline is driven primarily by the manufacturing sector. Manufacturing labor share measures from the Census and the BEA are shown as the solid black and grey lines in the same figure. While the two sources somewhat disagree on the level of the manufacturing labor share, they both show declines of over 20 pp between the 1950s and 2016.1 Because of the shift in the sectoral composition of US production away from manufacturing toward relatively labor-intensive sectors, such as services, the decline in the aggregate labor share has beenmuted. Figure1: Corporatetaxationandlabor’sshareofincomeintheUnitedStates (a)Laborshares(%) (b)Corporatetaxrates(%) Panel(a)showstheheadlineaggregatelaborsharemeasurefromtheUSBureauofLaborStatistics(righty-axis), together with manufacturing labor shares from the US Census and the National Income and Product Accounts providedbytheBureauofEconomicAnalysis(BEA)(lefty-axis). WecomplementthehistoricalBEAdatawith BEAKLEMSdatafrom1986onward. TheaverageeffectivecorporatetaxrateinPanel(b)istheratiooffederal corporatetaxrevenuetocorporateincome. Sources: FRED,TaxPolicyCenter,andGravelle(2004). 1InOnlineAppendixB,wecomparelaborsharemeasuresfromavarietyofdatasourcesanddiscussthedifferences. Thetotaldeclineinthemanufacturinglaborsharevariesbetween20to29percentagepointsdepending onthesourceanddefinition. 2

Over the same time period, business taxation has fallen. The average corporate tax rate measured as the ratio of federal corporate tax revenue to corporate income - shows a steady decline from 46 percent in the 1950s to 16 percent in 2016 (Figure 1-b). The secular decline over the years is the result of various tax reforms that reduced the effective marginal tax rate (MTR) either by directly lowering the statutory tax rate on corporations or by expanding regulatory exemptions and allowances, such as the depreciation allowance or the investment tax credit. Based on the statutory provisions, Gravelle (2004) estimates that the effective MTR on corporate income had declined from over 50 percent in the 1950s to 27 percent by 2003. Relativetotheheadlinestatutoryrate,theseaverageandeffectivemarginalratesbettercapture various provisions and exemptions in the tax code as well as efforts to minimize tax obligations. According to IRS statistics, C-corporations represented about 72% of business receipts on average between 1980 and 2015. The fact that C-corporations cover a large share of output intheeconomyisourmainmotivationforfocusingoncorporatetaxpolicy. However,asimilar trendisseenintaxratesonpass-throughentitiesduetothesecularfallintopmarginalincome tax rates since the 1950s and major tax reforms during the 1980s. The NBER’s tax calculator TAXSIM estimates that the MTR fell from 46 percent to 35 percent for partnerships and from 36percentto23percentforsole-proprietorsbetween1979and2008.2 These patterns are not unique to the United States. As we show below, there have been largedecreasesinlaborsharesamongOECDcountries,especiallyinmanufacturing,wherethe labor share declined by 0.34 pp per year on average between 1981 and 2007. Throughout this period, corporate tax rates in those countries dropped by 19 pp on average. More importantly, we find that the labor share fell by more in countries with larger declines in their corporate tax rate, with a correlation coefficient of 0.71 in our sample. Using the co-variation between these trends within countries and over time, we estimate that 30 to 60 percent of the decline in the manufacturinglaborshareisassociatedwiththefallincorporatetaxation. Motivated by these facts, we propose a model to study the impact of corporate taxation on the labor share. Our objective is to quantify the role of tax cuts, abstracting from other factors that might also impact the labor share. Our model is one of heterogeneous firms that differ in productivity as well as capital intensities. The aggregate industry labor share is given by an output-weighted average of firm-level shares. A reduction in the corporate tax rate lowers the cost of capital relative to labor. This disproportionately benefits capital-intensive firms and allows them to capture a larger share of the market. The ensuing reallocation of output toward capital-intensivefirmslowerstheaggregatelaborshare. The extent of this reallocation - and thereby the decline in the labor share in our model depends on the micro-level distribution of factor price elasticities and output in an industry. 2We abstract from organizational choices. If businesses reorganize to minimize tax obligations as in Dyrda andPugsley(2018),firms’taxliabilitiesmayhavefallenbymorethanwhatFigure1suggests. 3

Weshowthatthenet-of-taxelasticityoftheindustry’slaborshareisdeterminedbytheoutputweightedcoefficientofvariationoffirm-levellaborshares. Largerdispersioninlaborsharesor highercapitalintensityattheindustrylevelleadstolargerdeclinesintheindustry’slaborshare inresponsetotaxcuts. We apply the model to study the long-run decline in the manufacturing labor share. Due to the availability of micro-level data on value added and factor intensities for the universe of establishments,theUSmanufacturingsectoroffersauniqueopportunitytostudyawidesetof quantitativepredictionsaboutthemarginalimpactoftaxrates. Theseincludetheindustry’sdistributionsoffirmsizes,employment,andmarketshares,aswellasitslaborshare. Importantly, the distribution of output and factor intensities is itself endogenous to tax rates. Therefore, to assess the long-run effects of tax changes allowing for such variations in the capital-labor substitutability,we adoptacalibrationapproach wherewematchthe jointdistributionoflabor shares,valueadded,andemploymentatthefirmlevelin1967. Thisisessentialtopindownthe taxelasticityofthesectorallaborshare. Wethensimulatetwoeconomies: onewithaneffective corporate tax rate of 50 percent, as estimated for 1954, and one with a tax rate of 20 percent, the estimated rate for 2014. The difference in industry labor shares of the two economies is 12.6pp,whichisabouthalfoftheobserveddeclineinUSmanufacturing. Althoughwefocusonthemanufacturingsectorduetodataavailabilityoveralonghorizon, declinesinthelaborsharearealsoseentovaryingdegreesinmostotherUSsectors. Forexample, the mining sector experienced a similarly steep decline, whereas the wholesale and retail trade sectors show more modest reductions. Interestingly, the US service sector shows a slight upward trend in its labor share throughout our period of analysis.3 While a rise in the labor shareisdifficulttoreconcilewithlowercapitaltaxesinoursetup,ourmodeldoesofferanumberofreasonsforthesectoralvariationintheextentofthedeclineinthelaborshare. Section6 isdedicatedtoanalyzingthesesectoraldifferences. Todoso,wecombinethedifferenttaxelasticities that are implied by the sectors’ micro-level distributions of factor intensities with the evolution of each sector’s effective tax rate. The model’s predictions correlate positively with the realized changes in the labor share across sectors, largely reflecting sectoral differences in tax elasticities. Changes in sector-specific effective tax rates have also played a role, implying relatively larger declines in manufacturing and transportation, and smaller declines in services andmining. Inourmodel,areductionincorporatetaxationalsohasimplicationsforthedistributionsof employment and value added. The shift of production toward capital-intensive firms translates 3Acrossthecountriesinoursample, thelaborsharehasdeclinedinmostindustries, albeittoalesserdegree relative to manufacturing. The two exceptions are the service sectors in Denmark and the US, where we see slight increases in the labor share. In our analysis of the cross-country data below, we point to the relevance of counteractingtrendsintheservicesector,whichhavemorethanoffsetthedownwardpressureonthelaborshare fromtaxcuts. 4

into higher market concentration. However, because the expansion of output implied by lower corporatetaxratesisledprimarilybycapital-intensivefirms,theconcentrationofemployment declines. Labor-intensive firms, initially among the largest employers, shrink in size, in terms ofbothoutputandemployment. In Section 7, we test these predictions among US manufacturing industries. First, using thevariationinstate-leveleffectivecorporatetaxrates,wefindthatlowercorporateincometax ratesareassociatedwithadeclineinthestate’smanufacturinglaborshare. Second,inindustries wheretheeffectivetaxratedeclinedbymore,salesandvalueaddedbecamemoreconcentrated over time in line with the model’s predictions. Third, both employment concentration and average establishment size in manufacturing show a steady decline since the 1970s. Fourth, capital and investment per worker increased by more in manufacturing industries located in states that lowered their corporate tax rates. These patterns corroborate the theory that the declineinthelaborsharewascausedinpartbylowercorporatetaxrates. Themodel’spredictionsregardingthedistributionsoflaborsharesandvalueaddedareconsistentwithrecentempiricalfindings. Autoretal.(2020)showthatalargepartofthedeclinein the labor share took place within industries and that it was associated with rising market concentration in those industries. In their analysis of manufacturing establishments, Kehrig and Vincent(2021)showthatthecorrelationbetweenmarketsharesandlaborsharesdeclinedover time, resulting from a shift of market shares toward capital-intensive establishments. They document that the distribution of labor shares across establishments has otherwise remained stable. Ourpapercontributestotherecentliteratureonthecausesofthedeclineinthelaborshare. We focus on an institutional element, corporate taxation, however not to the exclusion of other proposedexplanations. Severalstudiesfocusonaspectsoftheproductionfunctionasanexplanation. Karabarbounis and Neiman (2013) argue that a decreasing price of capital equipment in recent decades has led to capital deepening and reduced the labor share of output, implying that capital and labor are substitutes in production (with an elasticity of substitution greater than one). Lawrence (2015) argues that capital and labor are complements and attributes the fall of the labor share to effective labor deepening that resulted from labor-augmenting technicalchange. GloverandShort(2019)findanelasticityofsubstitutionbetweencapitalandlabor near or below unity, implying that capital deepening cannot explain the decline in the labor share. Alvarez-Cuadrado et al. (2018) assume that labor and capital are gross complements, and argue that the fall in the labor share is a result of differences in the paces of capital-biased technical change in the service and manufacturing sectors. In Acemoglu and Restrepo (2018) the automation of tasks reduces the labor share as more and more tasks are completed by machines. Another strand of papers focuses on changes in the market structure to explain the fall in 5

thelaborshare. Autoretal.(2020)arguethattheincreaseinmarketconcentrationcouldresult from a rising price elasticity of demand that led to an increase in product competition among firms and resulted in the most efficient (and capital-intensive) firms grabbing a larger share of the market. On the other hand, De Loecker et al. (2020) find that firms’ market power has increased in the US, and argue that this raised the profit share at the expense of the labor and capitalshares.4 Broadly speaking, the literature has largely ignored institutional elements that may potentially be responsible for the decline in the labor share. One exception is Elsby et al. (2013), who consider deunionization in the US as a potential factor, but find little correlation between therateofunionizationandlaborsharesacrossindustries.5 In the next section, we document the link between corporate taxation and the labor share among OECD countries. In Section 3, we present our model and in Section 4, we provide a theoretical analysis of the effect of corporate taxation on the industry. Section 5 presents the quantitativeevaluationoftheimpactoflowercorporatetaxes. Section6examinesthevariation in the decline of the labor share across major sectors. Section 7 assesses the predictions of the model in regard to the distributions of employment and value added in the US manufacturing sector. Section8concludes. 2 Corporate taxes and the labor share in OECD countries In this section we empirically investigate the link between corporate taxation and the labor share at the country level. Our data cover the period 1981–2007 for a set of OECD countries. ThedataonlaborsharescomefromtheWorldKLEMSdatabase. Corporatetaxratesaretaken from the OECD and represent the combined central and sub-central statutory tax rates, where applicable.6 SeeOnlineAppendixBforthedetailsofourdatasets. Between 1981 and 2007 labor shares fell considerably. For the countries we observe throughout the sample period, the average fall in the aggregate labor share was 0.26 pp per year. This trend is more pronounced in the manufacturing sector, where the labor share fell by 4Theideathatproductivefirmshavegainedanadvantagevis-a`-vistherestoftheeconomyisalsoexpressed in Aghion et al. (2023) and Akcigit and Ates (forthcoming). In Aghion et al. (2023), productive firms expand intonewmarketsduetofallingcosts. Thisleadstohigherlong-runmarkupsandalowerlong-runlaborshare. In AkcigitandAtes(forthcoming),adeclineinknowledgediffusionacrossfirmsincreasesmarkupsoftop-firmsand therebyreducesthelaborshare. 5Severalpapersattributeasignificantfractionofthedeclineinaggregatelaborsharestomeasurementissues, coming from housing (Rognlie, 2015) and intellectual property products (IPP) (Koh et al., 2020). The latter authors show that IPP matters mainly outside of manufacturing, which is our focus. We rely on administrative dataforcalculatingmanufacturinglaborsharesanddonotusehousehold-leveldatathatmightbesusceptibleto, e.g.,changesinhouseprices. 6Weusestatutorytaxratesinourcross-countryanalysis. Theoperatingassumptionisthattherelativechanges inthestatutoryratesarerepresentativeofthoseintheeffectiveratesacrosscountries. 6

(a)Manufacturing (b)Aggregate Figure2: Corporatetaxrateandlaborshareacrosscountries Statutory corporate tax rate and labor shares of income in the manufacturing sector and the aggregate economy in 2007. The correlation coefficient is 0.60 (s.e. 0.14) for the manufacturing sector and 0.39 (s.e. 0.17) for the aggregateeconomy. Source: OECDandKLEMS. 0.34 pp per year. This pattern is shared by most countries. The largest declines occurred in Sweden, Austria, and Ireland, where manufacturing labor shares declined by well over 20 pp. ThesmallestchangesoccurredinSpain,Italy,andFrance. At the same time, there have been significant cuts to corporate tax rates. For the same set of countries, the average decline in the corporate tax rate between 1981 and 2007 was 19 pp, with substantial variation across countries. Among the countries with the largest cuts are Finland, Ireland, Austria, and Sweden with declines of over 30 pp (see Klein and Ventura (2021) for a detailed analysis of the business tax reform in Ireland). Almost no change in the corporatetaxratesoccurredinItalyandSpain. TheunderlyingtimeseriesareshowninOnline AppendixB.3. At a cross-sectional level, there is a strong correlation between corporate tax rates and labor shares of income. Figure 2 shows a scatter plot of the two variables in 2007, for both manufacturing and the aggregate economy. The correlation coefficient is 0.60 with a standard error (s.e.) of 0.14 for manufacturing and 0.39 (s.e. 0.17) for the aggregate economy. The fact that the correlation is higher for manufacturing is not surprising. Because labor costs are deducted from profits, the tax burden essentially falls on capital. As a result, capital-intensive sectorsaremoresensitivetothecorporatetaxrate. Figure3showsthecountry-levelchangesinthelaborsharebetween1981and2007against the changes in the corporate tax rate. There is a strong positive correlation between the two variables, especially in the manufacturing sector, where the correlation coefficient is 0.71 (s.e. 0.12). Countries that implemented larger cuts in corporate tax rates experienced a stronger fall inlabor’sshareofincome. Apositiverelationisalsoobservedfortheaggregateeconomy,with 7

(a)Manufacturing (b)Aggregate Figure3: Trendsincorporatetaxrateandlaborshare: 1981–2007 Changes(inpercentagepoints)instatutorycorporatetaxrateandlaborsharesofincomebetween1981and2007. Thecorrelationcoefficientis0.71(s.e. 0.12)forthemanufacturingsectorand0.41(s.e. 0.17)fortheaggregate economy. Source: OECDandKLEMS. acorrelationcoefficientof0.41(s.e. 0.17). To test the relationship between labor shares and corporate tax rates more formally, we regress the labor share on the corporate tax rate, controlling for fixed country and year effects. The results are reported in Table 1. In manufacturing, the coefficient on the corporate tax rate is 0.36 (s.e. 0.09). This suggests that a 10 pp drop in the corporate tax rate is associated with 3.6 pp decrease in a country’s manufacturing labor share.7 Given the observed declines in the tax rates, the estimates in columns 1 and 2 of Table 1 imply that, on average, the corporate tax cutsareassociatedwitha7.7ppdropinthemanufacturinglaborshareanda2.6ppdropinthe aggregate labor share throughout the sample period. These values correspond to 60 percent of theobserveddeclineinmanufacturingand30percentoftheaggregatedecline. One concern with these results may be the presence of other factors that lead to a decline in the labor share and that may be correlated with changes in the corporate tax rate during the sampleperiod. Toaddressthisconcern,weincludecountry-specifictrendsinthelaborsharefor eachsectorincolumns3and4ofTable1. Thecoefficientofthecorporatetaxrateistherefore identified by the accelerations and decelerations in the pace of the decline in the labor share. For the manufacturing sector, the coefficient on the corporate tax rate is somewhat smaller at 0.18(s.e. 0.06). Thislowercoefficientimpliesthatcorporatetaxcutsexplain31percentofthe declineinthemanufacturinglaborshareforthecountriesinoursample. Thecoefficientforthe aggregate economy remains almost unchanged at 0.10 (s.e. 0.05), and implies that corporate taxesareassociatedwith26percentofthedeclineintheaggregatelaborshare. 7To check the sensitivity of the results to specification, we regressed 10-year changes in the labor share on 10-yearchangesinthecorporatetaxrate. Thecoefficientsare0.36(0.18)formanufacturingand0.15(0.05)for theaggregateeconomy. TheseresultsarereportedinOnlineAppendixD.3. 8

Table1: Corporatetaxationandthelaborshare Manufacturing Aggregate Manufacturing Aggregate CorporateTaxRate 0.36 0.12 0.18 0.10 (0.09) (0.04) (0.06) (0.05) The depen- CountryTrends No No Yes Yes N 579 579 579 579 dentvariableislabor’sshareofincome.Allspecificationscontrolforfixedyearandcountryeffects.Specifications (3)-(4)controlforcountry-specificlineartrends.Standarderrorsareclusteredatthecountrylevel.Source:OECD andKLEMS. Itisimportanttonotethatthecoefficientsincolumns3and4areidentifiedbythedeviations from trend in one country relative to another. The assumption behind this approach is that the long-runassociationbetweenthetrendsincorporatetaxesandthelaborshareisacoincidence. As a result, the estimates represent a shorter-run elasticity of the labor share with respect to tax rates. Reflecting the Le Chatelier principle (Samuelson, 1947), the long-run elasticity is presumably larger if short-run adjustments to the factor intensity of production are costly. The estimates from the trend specifications can therefore be considered as a lower bound to the extent that the correlation between trends in fact reflects a causal relationship. We conclude that the fall in corporate taxes can explain between 31 to 60 percent of the decline in the manufacturinglaborshareacrosscountries. InOnlineAppendixD.2,weshowthatlowercorporatetaxrateswerealsoaccompaniedby a rise in capital investment across countries. A 10 percentage point reduction in the tax rate is associated with a 3 to 5 percent increase in the capital-to-labor ratio across specifications. Combined with the positive tax elasticity of the labor share in Table 1, our findings are consistentwiththesubstitutionofcapitalforlaborinresponsetoareductionincorporatetaxes. This isinlinewithKarabarbounisandNeiman(2019),whoalsoemphasizefactorsubstitutabilityin their analysis of the role of falling capital prices in the global decline in the labor share. Note, however,thatourfindingsinTable1arenotdrivenbyacorrelationbetweencorporatetaxrates and investment good prices. Controlling for the price of capital in our regressions does not significantly affect our results in Table 1. The coefficients on the corporate tax rate are 0.32 (0.09)and0.09(0.04)formanufacturingandtheaggregateeconomy.8 Our takeaway from the cross-country analysis is that falling corporate tax rates are an importantelementforunderstandingthedeclineinthelaborshare,especiallyinthemanufacturing sector. The results should nonetheless be interpreted with caution, as causality is hard to establish without truly exogenous shifts in corporate tax policy, which are hard to come by at a macro scale. We therefore develop a model to analyze, theoretically and quantitatively, the 8Thesearethelowestcoefficientsweobtainedacrossthreealternativemeasuresfortherelativepriceofcapital obtained from the Penn World Tables (version 9.1): the prices of capital stock, capital services, and investment goods, all relative to the price of household consumption. We have also controlled for labor costs using labor compensationperemployeeasaproxyforthewagerate. Thecoefficientsinthiscaseincreasefrom0.32to0.33 inmanufacturingand0.09to0.11intheaggregateeconomy. 9

effectofcorporatetaxesonthelaborshare. Themodelallowsustostudythiseffectinisolation byabstractingfromotherfactorsthatmightinfluencetheempiricaltrendsinthelaborshare. 3 An industry model with heterogeneous factor intensities We develop an industry equilibrium model that builds on Hopenhayn and Rogerson (1993), modifiedtoincludecorporatetaxesandheterogeneityinlaborintensities. Theresultingframework connects the production technologies at the firm level with the industry-level response to changes in factor prices, in the spirit of Houthakker (1955) and more recently Oberfield and Raval(2021). Thisallowsustoquantifytheimpactoftaxchangesonanindustry’slaborshare basedontheempiricaldistributionsofoutputandlaborsharesamongfirms. The model economy contains a mass of firms, a representative household, and a government. All firms produce a single good using capital and labor. Capital is managed by firms and laboris providedby thehousehold. Output canbe consumedor invested. Thegovernment taxes firms and redistributes the proceeds to the household in a lump-sum fashion, ensuring a balanced budget at all times. Time is discrete and the horizon is infinite. In what follows, we presentthedecisionproblemsoffirmsandthehousehold,describethecompositionoffirmsin theindustry,anddefinethestationarycompetitiveequilibrium. 3.1 Incumbent firms At time t there is an endogenous mass of incumbent firms, indexed by j. Firms differ in their capitalstocks,determinedbypastinvestmentchoices,andintheirproductiontechnologies,defined by efficiency, ε , and capital intensity, α . Technology is time-invariant.9 Given capital, j j k , each firm hires labor, n , to carry out production. Output is given by q = ε k αjn βj. jt jt jt j jt jt Theproductionfunctiondisplaysdiminishingreturnstoscale: α +β = γ < 1, ∀j,implying j j a unitary elasticity of substitution between capital and labor at the establishment level. Our choice of a Cobb-Douglas form at the micro level is motivated by empirical work that highlights roughly constant labor shares for a given establishment over time (Kehrig and Vincent, 2021). As we show below, the industry labor share depends on how output is allocated across establishments and can thus vary over time.10 We drop the firm subscripts j and t from hereon 9Asweshowbelow,theindustrylaborshareisdeterminedbythecross-sectionaldistributionoffirms’factor intensities. Foragivenstationarydistribution,temporalvariationsinfirm-levelcapitalintensitiesdonotchange theindustry’slaborshare. Weusethetermsfirmsandestablishmentsinterchangeablythroughouttheexposition ofthemodel. Notealsothatoutputandvalueaddedareidenticalinourmodel. 10As in Oberfield and Raval (2021), the elasticity of substitution between capital and labor is larger at the industrylevelthanattheplantlevelinourmodel. Whereastheyestimatealessthanunitaryelasticitybothatthe plantandindustrylevel,ourmodelfeaturesamorethanunitaryelasticityattheindustrylevelsincetheplantlevel 10

forbrevity. Firms produce and sell their output to maximize profits net of taxes. Formally, letting p denote the price of the output good and w the wage rate, we define a firm’s income before taxationasrevenueminuslaborexpenses:11 π (k,ε,α) = max pεkαnβ −wn, (1) b n where β = γ − α. Let n(k,ε,α) denote the associated labor demand. A fraction τ > 0 of π (k,ε,α) is taxed. The remaining income is distributed to shareholders and used to finance b capital investment, i, which determines next period’s capital stock : k′ = i+(1−δ)k, given a rateofdepreciationδ ∈ (0,1]. Incumbentfirmsmaystochasticallyexittheeconomyatanexogenousratexindependentof theirtechnologyorsize.12 Conditionalonsurvival,futureprofitsarediscountedwithρ ∈ (0,1). Theeffectivediscountrate,includingtheprobabilityoffirmsurvival,isρ˜= ρ·(1−x). Given its capital stock, k, and its technology, (α,ε), a firm chooses k′ to maximize its value, defined bythepresent-discounteddistributionstoshareholders. (cid:26) (cid:27) V(k,ε,α) = max (1−τ)π (k,ε,α)+pk(1−δ)−pk′ +ρ˜V(k′,ε,α) (2) b k′ Letk′(k,ε,α)denotetheassociatedcapitalpolicyfunction. 3.2 Entry and exit Once a firm exits, it cannot re-enter the market at a later period. It liquidates all remaining resources and distributes them to its shareholders. There is a large mass of ex-ante identical potential entrants who can join the industry anytime by paying an entry cost of c > 0 units e of output. This represents the cost of setting up shop, identifying a target customer group, etc. Once the entry cost has been paid, entrants draw a random efficiency level ε from the density H(ε),andcapitalintensityαfromthedensityG(α). Thetwodrawsareindependent. Thenew firmthenmakesaninvestmentforthefirstperiodofoperation. Potential entrants weigh the entry cost against the expected value of a firm before its technologyisrevealed. Freeentryimpliesthatthenetvalueofentrymustbezeroatanyequilibrium elasticityis1,asweshowinSection4. 11Forexpositionalsimplicity,wedonotallowfirmstowriteoffdepreciationexpensesordebtservice. Thishas nobearingonourquantitativeresultsbecausethesimulationsbelowarebasedoneffectivemarginaltaxratesthat alreadytakeintoaccountthetaxprovisionsfordepreciationanddebt-financing. 12ThisismotivatedbyempiricalworkinKehrigandVincent(2021),whodonotfindasignificantroleforentry andexitinthedeclineofthemanufacturinglaborshare. Amodelwithendogenousexitbehaviorwouldpredict largerdeclinesinthelaborsharethanwefindhere. 11

withpositiveentry,givingthefollowingequality. (cid:90) (cid:90) pc = V(0,ε,α)dH(ε)dG(α). (3) e Factorsthatraisethevalueofanincumbentfirmforagivenpricelevel,suchasadeclineinthe corporate tax rate, attract more entry. This triggers a change in the equilibrium price to ensure thatthefree-entryconditionissatisfied. 3.3 Distribution of firms The equilibrium distribution of firms is determined by entry and exit. The evolution of the distributionofincumbentfirms,denotedbyµ,isgivenby (cid:90) µ′(k′,ε,α) = (1−x)µ(k,ε,α)I(k′,k,ε,α)dk +Mh(ε)g(α)I(k′,0,ε,α), (4) k where the indicator function I(k′,k,ε,α) = 1 if k′(k,ε,α) = k′ and M denotes the mass of entrants. 3.4 Households There is a representative household with preferences over streams of consumption goods. The household is endowed with one unit of productive time each period. Labor is supplied inelastically to the production sector in return for wage income. The household owns all firms.13 Consumption expenditures are financed through disposable income, which consists of labor earnings,dividendsfromfirms,andtransfersfromthegovernment: p·C = w·1+D+T. 3.5 Competitive equilibrium Let s = (k,ε,α) denote the state of a firm. A stationary recursive competitive equilibrium consistsofnineendogenousobjects: apolicyfunctionforlabordemandn(s),apolicyfunction for capital demand k′(s), a value function for firms V(s), a positive mass of entrants M, a distribution of incumbent firms µ(s), aggregate consumption C, aggregate dividend payments 13Because we study steady-state equilibria, we abstract from the household’s portfolio choice problem for brevity. More generally, the household chooses a consumption stream C along with shares a (s) of each firm t t type s = (k,ε,α), to maximize lifetime utility (cid:80)∞ u(C ) subject to the sequential budget constraint C + (cid:82) (cid:82) t=0 t t ν (s)a (s)ds=w ·1+ (ν (s)+D (s))a (s))ds+T ,whereν (s)isthepriceofashareandD (s)denotes t t+1 t t t t t t t dividends. At the steady-state, C = C , implying the constant discount rate ρ˜in the firm’s problem; ν (s) t t+1 t equalsthevalueofafirmV(s),andthehouseholdholdstheentiretyofallfirmtypes: a (s)=µ (s). t t 12

tohouseholdsD,governmenttransferstohouseholdsT,andanoutputpricep,suchthati)n(s) solves the labor decision problem in (1), ii) k′(s) solves the investment problem in (2), iii) V is the value function (2) evaluated at the optimal policy functions, iv) the labor market clears (cid:82) n(s)µ(s)ds = 1, v) the distribution of incumbent firms is stationary: µ′(s) = µ(s), vi) the household’sbudgetconstraintholds: p·C = w·1+D+T,vii)dividendsequalnetaggregate (cid:82) profits D = [(1−τ)π (s)−pδk]µ(s)ds − Mpc , viii) the government budget is balanced b e (cid:82) T = τ π (s)µ(s)ds,andix)thefree-entrycondition(3)issatisfiedatpricep. b Thewagerateisthenume´raireand,hence,doesnotappearexplicitly. Theequilibriumdefinitionimpliesaggregatefeasibility,i.e.,totaloutputequalsthesumofaggregateconsumption, (cid:82) (cid:82) investment,andresourcesspentonentrycosts: qµ(s)ds = C + δkµ(s)ds+Mc . e Given the parameters, we compute the numerical solution to the stationary equilibrium as follows. Foragiventaxrateτ,weguessapricelevelpandcomputepolicyfunctionsforcapital andlaboralongwiththeassociatedvaluefunction. Ifthevaluedoesnotequaltheentrycostpc , e we adjust theprice guess. We continuethis guess-and-verify procedure via a bisection method until we find the equilibrium price at which the free-entry condition is satisfied. Because the distributionofincumbentfirmsishomogeneousofdegreeoneinthemassofentrants,M canbe pinned down through the labor market clearing condition. The stationary distribution of firms then determines aggregate dividends and taxes, which determine the steady-state consumption level. 4 Corporate taxes and the industry labor share In this section we analyze the stationary equilibrium of the model and demonstrate how corporate taxes affect factor demands and the labor share in the industry. To maintain tractability, we aggregate firms with different efficiencies, ε, but the same level of capital intensity α. This yields a representative firm for each type α with the production function q(k,n,α) = E[ε1− 1 γ]kαnβ. Without loss of generality, we normalize productivity such that E[ε1− 1 γ] = 1.14 WereturntotheoriginalformulationforthequantitativeanalysisinSection5. Inwhatfollows,wefirstestablishtherelationshipbetweenfactorpricesandthedistribution of output among firms with different capital intensities. This allows us to translate changes in relative factor prices into changes in industry factor shares. The partial equilibrium effects are analyzedfirst,followedbythegeneralequilibriumeffectsthatarisefromchangesintheindustry’s price level. We conclude by linking the effects of a change in the tax rate to equilibrium 14Weabstractfromlong-rungrowth.Balancedgrowth,wherefirm-leveldistributionsofemploymentandoutput arestable,requiresthatentrycostsrisewithoutput(KlenowandLi,2022). Inourmodel,thisisnecessarytokeep the labor share stable in a growing economy. By normalizing aggregate productivity, we implicitly assume that theentrycostsrisewithaggregateproductivity. 13

prices and establish our main result. Finally, we discuss the elasticity of factor substitution in ourframework. Theoptimallaborandcapitaldemandfunctionsimpliedbythefirm’sproblemin(2)are: (cid:18) (cid:19)1−α (cid:18) (cid:19) α (cid:18) (cid:19) β (cid:18) (cid:19)1−β β 1−γ α 1−γ β 1−γ α 1−γ n(α) = and k′(α) = , (5) w¯ r w¯ r τ τ (cid:16) (cid:17) where w¯ = w/p is the effective cost of labor and r ≡ 1 1−ρ˜ +δ is the gross user cost of τ 1−τ ρ˜ capitalasafunctionoftheeffectivediscountrate,thecorporatetaxrate,τ,andthedepreciation rate,δ. Notethatr isincreasinginτ,whilew¯ isdecreasinginthepricelevel,p. Labordemand τ isnotdistortedbythecorporatetaxratebecauselaborcostsaredeductedfromprofitsin(1). By contrast,corporatetaxesreducecapitaldemandbyincreasingthecostofcapitalr . Combining τ thefactordemandsin(5),outputisgivenby (cid:18) (cid:19) α (cid:18) (cid:19) β α 1−γ β 1−γ q(α) = , (6) r w¯ τ andthecorrespondingcapitalandlaborcostelasticitiesofoutputare α γ −α η = − η = − . (7) q,rτ 1−γ q,w¯ 1−γ Capital-intensive firms (higher α) are more sensitive to changes in the cost of capital and less sensitive to changes in the cost of labor. Similarly, changes in the real wage, w¯, generate a stronger output response among labor-intensive firms. As a result, the distribution of output acrossfirmsdependsontherelativecostofcapitalandlabor. ˆ The industry labor share, denoted by β , is the output-weighted average of firm-level labor q shares: (cid:90) (cid:90) ˆ β = λ(α)β(α)dG(α) = γ − λ(α)αdG(α) = γ −αˆ , (8) q q withoutputweightsλ(α)givenby q(α) λ(α) = . (9) (cid:82) q(α)dG(α) Because G(α) is fixed, changes in the industry labor share in the model are driven entirely by changes in the distribution of output. The following lemma establishes how a firm’s output weightλ(α)respondstoachangeinthecostofcapital.15 15AllproofscanbefoundintheAppendix. 14

Lemma1 Thepartialelasticityofoutputshareλ(α)withrespecttothecostofcapitalr is: τ α−αˆ q η = − λ,rτ 1−γ Lemma1showsthatthechangeinthemarketshareoftype-αfirmsdependsontheirrelative capital intensity. Following a drop in the cost of capital, firms with above-average capital intensities(α > αˆ )seeariseintheiroutputshares,whilethosewithbelow-averageintensities q see a decline. These changes reduce the industry’s labor share. The proposition below reports themagnitudeofthiseffectinpartialequilibrium. Proposition1 For a given price level p, a decrease in the cost of capital lowers the industry’s laborshare,withthemarginalchangegivenby: ∂β ˆ σˆ2(α) q q = , ∂logr 1−γ τ (cid:82) where σˆ2(α) = λ(α)(α − αˆ)2dG(α) is the output-weighted variance of capital intensity in q theindustry. When σˆ2(α) = 0, all firms in the industry have the same capital intensity regardless of the q relative factor price. However, when there is dispersion in capital intensities, a lower cost of capitalraisestheoutputshareofcapital-intensivefirms,resultinginafallintheindustry’slabor share. The larger the dispersion in factor intensities, the larger the reallocation of output, and, hence,thelargerthedeclineintheindustry’slaborshare. Next,wediscusstheimpactofthecorporatetaxrateontheequilibriumprice. Inthemodel, theequilibriumpriceisdeterminedbythefree-entrycondition,whichequatesthecostofentry totheexpectedvalueofthefirm. Ahighertaxrateτ lowersthevalueofthefirmwhileahigher pricelevelraisesthevalueofthefirmasstatedinLemma2. Lemma2 Firmvalueisdecreasinginτ andincreasinginp. A decrease in the tax rate raises the firm value, which encourages entry. To ensure that the free-entry condition is met, the price level p must fall. This result is obtained by combining Lemma2withthefree-entryconditioninthepropositionbelow. Proposition2 Withfreeentry,theequilibriumprice,p,isincreasinginthetaxrate,τ. Proposition 2 states that any additional profits from lower tax liabilities are passed on to consumers through lower prices. This results in a higher real wage w¯ = w/p (recall that the wage 15

rate serves as the nume´raire (w = 1)). As in Harberger’s (1962) seminal analysis, a fall in the price, p, amplifies the gains from lower corporate taxes to consumers and workers, partially offsetting the gains in profits.16 In industry equilibrium models, this is operationalized by the competitivepressureatthefirmentrymargin. A fall in the equilibrium price effectively raises the cost of labor by reducing the revenue perunitofoutputsoldrelativetothewagecostofproducingthatunit. Aslabor-intensivefirms aremoresensitivetolaborcosts,theiroutputsharefallsfurtherasestablishedbythefollowing lemma. Lemma3 Thepartialelasticityofoutputshareλ(α)withrespecttopricepis: α−αˆ q η = − . λ,p 1−γ Firms that are more labor intensive than the average firm in the industry, i.e. α < αˆ , see their q output shares fall following a decrease in the price level. This additional shift of production towardcapital-intensivefirmsresultsinafurtherdeclineinthelaborshareintheindustry. Proposition3 Adecreaseinthepricelevellowerstheaggregatelaborshare,withthemarginal changegivenby: ∂β ˆ σˆ2(α) q = . ∂logp 1−γ Together, Propositions 1 and 3 determine the total effect of a fall in the corporate tax rate on the aggregate labor share in equilibrium. The following proposition combines the partial and generalequilibriumeffectsandgivesthemainresultofthissection. Proposition4 The total (equilibrium) elasticity of the aggregate labor share with respect to thenet-of-taxrateisgivenby: (cid:32) (cid:33)2 1 σˆ2(α) q η = − < 0 βˆ q,(1−τ) 1−γ β ˆ q The overall decline in the aggregate labor share in response to lower taxes depends on i) the tax elasticity of the user cost of capital, ii) the cost elasticity of industry prices, and iii) the dispersion of factor intensities in the industry. Increases in either of these factors lead to larger declines in the industry’s labor share. Proposition 4 shows that these three factors can 16Recentempiricalpaperssuggestthatthetaxburdenissharedbetweencapitalandlabor. Fuestetal.(2018), for instance, find that in Germany the economic incidence on capital of corporate taxation is half the statutory incidence. SaezandZucman(2016)findthataboutathirdofstate-levelcorporatetaxesarepassedontolabor. 16

be summarized by the output-weighted coefficient of variation of micro-level labor intensities. A tax cut decreases the industry’s labor share by more, the larger is the dispersion of labor intensities and the lower is the initial level of the industry’s labor share. The span-of-control, γ,determineshowelasticproductioniswithrespecttofactorcosts. Higherγ generatesalarger shift in output toward capital-intensive firms, and result in a higher net-of-tax elasticity of the industry’slaborshare. The reallocation of output away from labor-intensive firms raises capital and lowers labor perestablishment. Thefollowingpropositionlaysouttherelevantelasticitieswithrespecttoto thenet-of-taxrate: ¯ Proposition5 The equilibrium elasticities of the average demand for capital, k, and labor, n¯, withrespecttothenet-of-taxrate(1−τ)are: (cid:32) (cid:33) (cid:32) (cid:33) ˆ ˆ ˆ 1 β 1 β −β k q n η = 1− > 0 and η = −1 < 0 k¯,(1−τ) 1−γ β ˆ n¯,(1−τ) β ˆ 1−γ q q ˆ ˆ Hereβ andβ arecapital-andemployment-weightedaveragesoffirm-levellaborshares. Bek n causeemploymentisskewedtowardlabor-intensivefirmsandcapitalisskewedtowardcapital- ˆ ˆ ˆ intensive firms, β < β < β in our model. Combining the two elasticities gives the response k q n ofaggregatecapitalperworkerintheindustry,asshowninthefollowingproposition. Proposition6 The equilibrium elasticity of aggregate capital per worker with respect to the net-of-taxrateis: (cid:34) (cid:35) ˆ ˆ β −β 1 n k η = 1+ · > 1 K/N,(1−τ) 1−γ β ˆ q (cid:124) (cid:123)(cid:122) (cid:125) (cid:124)(cid:123)(cid:122)(cid:125) η K/N,w¯/rτ η w¯/rτ,(1−τ) Thiselasticityhastwocomponents. Theterminbracketsistheelasticityoffactorsubstitution, ˆ ˆ η . It is above one because β < β . Because the micro-level production function is K/N,w¯/rτ k n Cobb-Douglas,theexcesssubstitutabilitycomesentirelyfromthereallocationofoutputacross firms. The extent of substitutability along this extensive margin reflects the heterogeneity in ˆ ˆ factor intensities in the industry. When all firms have the same factor intensity, β = β , and k n the industry level elasticity of substitution is equal to one.17 The second term in Proposition ˆ 6, 1/β , is the elasticity of the equilibrium factor price ratio with respect to the net-of-tax q rate. It exceeds 1 in equilibrium, because the direct effect of a tax cut on the cost of capital is 17Somealgebramakesthisexplicit: βˆ −βˆ = γ σˆ q 2(α) . Asσˆ (α)approaches0,sodoesβˆ −βˆ . n k γ−βˆ q βˆ q q n k 17

compounded by the equilibrium price response in the industry (Proposition 2). That response depends on the labor intensity of the industry. The more capital intensive it is, the larger the effectoftaxcutsonprofits,andthestrongerthepriceresponseinequilibrium. Combining Propositions 3 and 6 yields the following relation between the response of the laborshareandtheresponseofcapitalperworkertoachangeinthetaxrate: η η γ K/N,(1−τ) = − K/N,w¯/rτ · , (10) η βˆ q,(1−τ) η K/N,w¯/rτ −1 γ −β ˆ q whereη istheelasticityoffactorsubstitution. Itexceeds1ifandonlyifthelaborshare K/N,w¯/rτ declinesandthecapitalperworkerincreasesfollowingataxcut. Easiersubstitutability(higher η )isassociatedwithaweakerresponseincapitalperworkerrelativetothelaborshare K/N,w¯/rτ response. Conversely, larger increases in K/N are needed to lower the industry’s labor share, whensubstitutabilityislow. Notethattheindustry-levelelasticitiesreportedhereareendogenoustohowoutput,capital, and labor are distributed across firms with different factor intensities. These distributions are inturndeterminedbythelevelofthetaxrateand,morebroadly,bytherelativecostsofcapital and labor. For instance, changes in factor costs alter not only the level of the labor share, but alsoitssensitivitytothetaxrate. Attheextremes,e.g.,wherethecostofcapitalismuchlower thanthatoflabor,themarketsharesareheavilyconcentrated,leadingtoasmallertaxelasticity ofthelaborshare.18 In this sense, the elasticities above should be interpreted as local to the steady state. Measuresoftheelasticitiesbasedonpoint-in-timedataonmarketsharesandlaborsharesaretherefore suitable only if the market share distribution can be assumed to remain reasonably stable. For longer-run analyses, as in the case of a secular decline in the tax rate, model simulations arepreferableinordertocaptureendogenousvariationsincapital-laborsubstitutability. 5 Quantitative results In this section, we provide a measure of the effect of lower corporate taxes on the decline in the manufacturing labor share in the US. Proposition 4 showed how the tax elasticity of an industry’s labor share depends on the distribution of factor intensities and output at the micro level. We therefore calibrate the model to match the distributions of labor intensities, employ- 18Atthelimit,wheretheleastlabor-intensivefirmsproducetheentireoutput,theelasticityconvergestozero. Labor obsolescence, however, would not arise in our model at the limit, unless there is a mass of firms that exclusivelyusecapitalforproduction(β =0). 18

Table2: Calibrationsummary: Presetparameters Parameter Value Target δ 0.10 DepreciationRate γ 0.85 SpanofControl x 0.10 ExitRate,CensusBDS ρ 0.96 RealRateofReturnr ≈ 4% w 1 Nume´raire τ 0.40 CorporateIncomeTaxin1967 1967 τ 0.50 CorporateIncomeTaxin1954 1954 τ 0.20 CorporateIncomeTaxin2014 2014 ment,andvalueaddedinthemanufacturingsectorin1967.19 Wethensimulatetwoeconomies: one where the corporate tax rate is 50 percent, the effective marginal corporate tax rate estimatedbyGravelle(2004)for1954,andonewitha20percentcorporatetaxrate,theestimated marginal rate provided by the US Congressional Budget Office (2014).20 All other primitives are kept constant to focus on the marginal effect of corporate taxation. Throughout our analysis, we compare long-run equilibria associated with different tax policies. Each equilibrium hasastationarydistributionoffirmsintheindustryandfeaturesapositiveentryrate. 5.1 Model calibration A model period corresponds to one year. The discount rate ρ is set to 0.96. The capital depreciation rate is δ = 0.10. The span-of-control parameter is set to 0.85 as in Restuccia and Rogerson (2008) and implies that profits constitute 15 percent of income. The exogenous exit rateissetto10percent.21 Recallthatthewageisthenume´raire. Wesetthe1967corporatetax rate to τ = 0.40 based on Gravelle (2004). These parameter choices are summarized in Table 2. The remaining four parameters are jointly calibrated to four key moments that represent the distributions of employment, value added, and labor intensities in US manufacturing. A heuristic discussion of their connection to data moments can nonetheless provide some insight intotheiridentification. The first two parameters determine the heterogeneity in efficiency ε, which in turn affects the employment size distribution in the industry. We use average employment and concentra- 19Wecalibrateto1967databecausethisisthefirstyearforwhichCensusofManufacturesinformationonthe jointdistributionoflaborsharesandvalueaddedisavailable. 20Thestatutoryratein1954was52percent. Thehighesteffectivecorporatetaxratewas63percentin1953. 21TheexogenousexitratewechosecomesfromtheUSCensusBureau’sBusinessDynamicsStatisticsmanufacturingdataandreflectstheaverageratebetween1977and2004. 19

Table3: Calibrationsummary: Jointlyidentifiedparameters Parameter Value Targetsfrom1967 Data Model µ 0.767 Averageestablishmentsize 60.5 60.5 ε σ 0.290 Employmentshareoflargeestablishments(250+) 0.60 0.60 ε β 0.252 Manufacturinglaborshare 0.54 0.54 c 158.15 VA-weightedp50(LS)/median(LS) 0.89 0.89 e tion of employment as targets for the mean and the variance of logε. Specifically, we target the number of employees per establishment and the fraction of employment in establishments with more than 250 employees from the 1967 Census of Manufactures.22 To calibrate the distribution of labor intensities across firms in 1967, we follow the empirical evidence in Kehrig and Vincent (2021) and assume that labor shares β follow a symmetric triangular distribution acrossfirms. Thisdistributionischaracterizedbytwoparameters: anupperandalowerbound. Because β cannot exceed γ, the latter determines the upper bound. The lower bound, β, is calibratedbytargetingthemanufacturinglaborsharein1967,whichwasequalto53.9percent accordingtotheAnnualSurveyofManufactures(ASM).23 Finally,topindowntheentrycostc ,weuseaconcentrationmeasurefromthejointdistrie bution of manufacturing labor shares and value added. Specifically, we target the ratio of the value added (VA) weighted median labor share to the unweighted median labor share reported by Kehrig and Vincent (2021).24 A ratio of one corresponds to a symmetric distribution of value added over firms with different labor intensities. Ratios below one represent an output distribution biased toward capital-intensive firms. This ratio, which we denote by Λ, was 0.89 in 1967, implying a roughly symmetric distribution of value added across establishments with different labor intensities. The entry cost c determines the equilibrium price p in the industry e from the free-entry condition (3). As we showed above, changes in the equilibrium price in turn determine the real effective wage cost for the industry, w/p, and thereby the distribution ofoutputoverfirmswithdifferentlaborintensities. Thatishowc isidentified. e The resulting parameter estimates are shown in Table 3 along with the targeted moments. Theseestimatesminimizetheaveragepercentagedifferencebetweendataandmodelmoments at 0.3 percent. Table 4 compares the implied distributions of establishments, employment, and valueaddedacrossproductionsiteswiththecorrespondingdatafromthemanufacturingsector 22TheCensusBDSdataandtheCensusofManufacturesreportemploymentinvarioussize-classbins.In1967, establishmentswith250+employeesconstitutedthelargest4.25percentofallestablishmentsandrepresent60.05 percent of total employment. Below we compute Pareto indices to facilitate the comparison of concentration measuresovertime. 23Becausethereissomedisagreementonthemanufacturinglaborsharein1967acrossdatasources(seeOnline AppendixB.2),wereportresultsforalternativetargetvaluesbelow. 24Themedianvalueaddedweightedlaborsharesaysthat50percentofallvalueaddedisproducedbyestablishmentswithalaborsharelowerthanorequaltothisvalue. 20

Table4: Distributionsofestablishments,employmentandvalueadded. Data: 1967 EstablismentSize: <20 20-99 100-249 250-999 1,000+ Establishments 65.0 24.2 6.5 3.6 0.7 Employment 5.6 17.7 16.6 27.3 32.8 ValueAdded 5.1 14.9 14.9 27.1 38.0 Calibratedmodel EstablishmentSize: <20 20-99 100-249 250-999 1,000+ Establishments 65.7 23.2 6.8 3.5 0.8 Employment 5.9 16.8 17.2 26.6 33.5 ValueAdded 6.1 17.2 17.6 26.5 32.6 Thedatacomefromthe1967StatisticalAbstractoftheUnitedStates. DetailscanbefoundinOnlineAppendix B. reported in the 1967 Statistical Abstract of the United States. Even though only average establishmentsizeandoneemploymentconcentrationmomentweretargeted,themodelmatchesall threedistributionsverywell. Boththeshareofestablishmentsinthevarioussizebins,andtheir share of total employment and value added are close to their empirical counterparts. This is an encouraging sign of the model’s suitability for gauging the quantitative implications of tax changes,becausethesedistributionsdeterminetheindustry-levelelasticitiesinthemodel. 5.2 Corporate tax cuts and the labor share in manufacturing We now simulate two different economies: one with a corporate tax rate of 50 percent, as observed in 1954, and one with a corporate tax rate of 20 percent, as observed in 2014. The results are summarized in Table 5. The key finding is that a decrease in the corporate tax rate from 50 percent to 20 percent results in a decline in the labor share from 58.9 percent to 45.5 percent,i.e.,adeclineof13.4pp. This decline reflects partial and general equilibrium effects of roughly equal magnitude. In our simulations, holding the price level constant while lowering the corporate tax rate to 20 percent reduces the labor share by 6.9 pp. The general equilibrium effect comes from a lower price. This reduces profits per unit of output relative to the cost of labor and thereby offsets gains from lower taxation, especially among labor-intensive firms. Fixing τ = 0.5 whileloweringthepricetotheequilibriumlevelassociatedwithτ = 0.2givesa7.4ppdropin thelaborshareacrosssteadystates.25 Thetotaldeclineof13.4forthe30pointdropinthetaxratebetween1954and2014implies 25Theelasticityofthepricewithrespecttothetaxrateisslightlylowerwhenentrycostsaredenominatedin laborunitsversusoutputunits. Inthatalternativescenario,thelaborsharefallsby11.9ppinequilibrium. 21

Table5: Policyexperiment-Adropincorporatetaxes ModelSimulations Data Year 1967 1954 2014 1967 1954 2014 Corp. taxrate(τ) 0.40 0.50 0.20 0.40 0.50 0.20 Laborshare 0.54 0.59 0.46 0.54 0.61 0.34 MedianLSratioΛ 0.89 1.27 0.62 0.89 - 0.44 Column “1967” cor- InverseParetoIndex(250+) 0.84 0.88 0.80 0.84 0.84 0.77 AverageEstablishmentSize 60.5 103.6 23.8 60.5 54.5 44.4 PriceLevelp 1.00 1.18 0.71 - - - Costofcapitalr 1.00 1.20 0.75 - - - τ AggregateCapitalDemand 1.00 0.54 2.80 respondstothecalibratedbenchmarkeconomyforwhichthepricelevelandcostofcapitalhavebeennormalized tooneinthetable. Themodelsimulationsfor1954and2014useacorporatetaxrateofrespectively50percent and 20 percent. The “Data” columns use ASM and BDS data. The labor share ratio Λ is the output-weighted median divided by the unweighted median labor share. The output-weighted labor share moment is taken from KehrigandVincent(2021)andcorrespondstotheyear2012. Thismomentisunavailablein1954. Theinverse ParetoindicesrefertoemploymentconcentrationandarediscussedinSection5.5. a 0.45 point decline in the labor share per point drop in the tax rate in the long run. This is slightly above the 0.36 (0.09) estimate obtained in the cross-country data (Column 1 of Table 1). Considering the 27 point decrease in the US manufacturing labor share, from 61 percent in 1954 to 34 percent in 2014, observed in the Census data, our results imply that corporate tax cutsexplainabouthalfofthetotaldeclineinthemanufacturinglaborshareduringthisperiod. Recall from Proposition 3 that a lower industry labor share is associated with a larger sensitivity to tax rates for a given dispersion in factor intensities at the firm level. Because there is some disagreement across data sources on the level of the labor share in the 1960s, we performed model simulations with higher labor share targets for the 1967 economy. Raising the target to 70 percent, the highest estimate (reported by the BEA), results in an 8.7 point drop in thelaborsharebetween1954and2014. Thiscorrespondstoroughly40percentofthe21point decline observed in the BEA data. The implied rate of decline in the labor share is 0.29 point perpointdropinthetaxrate,whichisslightlybelowourcross-countryestimateof0.36(0.09). Thetaxelasticityofthelaborsharealsodependsonthespanofcontrolparameter,γ. Higher values of γ raise the cost elasticity of production and imply a larger output reallocation toward capital-intensive firms. Setting γ = 0.9, for instance, results in a decline of 26 pp whereas settingγ = 0.8impliesadeclineof8.1ppinthemanufacturinglaborshare. It is worth noting, however, that these alternative calibrations generate a poorer fit of the firm level distributions of employment and value added. Both the higher γ, and the higher initial labor share result in a counterfactually high concentration of employment among large employers relative to the data, whereas the benchmark calibration is consistent with the observeddistributionsofemploymentandvalueaddedasshowninTable4. 22

5.3 Implications for the output distribution The reallocation of production in response to the lower tax rate is shown in Figure 4, which groups firms according to their labor share on the horizontal axis. For each labor share type, the (red) line shows the frequency of firms and the (blue) bars show that group’s share of output. The benchmark economy with τ = 0.40 displays a roughly symmetric distribution of output, implying little cross-sectional correlation with labor share (panel a). Half of the output is produced by firms with a labor share lower than 49 percent, whereas the median labor share is 55 percent (recall that their ratio Λ = 0.89 is a calibration target). Following the decrease in the tax rate, production shifts toward capital-intensive firms (panel b). Half the output is nowproducedbyfirmswithlessthana34percentlaborshare,whereasthemedianlaborshare is still 55 percent, implying Λ = 0.62. An even greater reallocation can be seen in the US manufacturing data, where this ratio declines all the way to 0.44 at the end of our sample period(KehrigandVincent,2021). (a)BenchmarkEconomy,τ =40% (b)LowerCorporateTaxRateτ =20% Figure4: Jointdistributionoflaborsharesandvalueadded. The figures show distributions of value added (blue bars, left axes) and firm-level labor shares (red line, right axes). Panel(a)showsthecalibratedbenchmarkeconomy. Panel(b)showsthemodeleconomywithacorporate taxrateof20percent. From the theoretical analysis in Section 4, the model unambiguously predicts a decline in the cross-sectional correlation between output shares and labor shares in response to a lower tax rate. However, this does not necessarily imply an increase in the concentration in the unconditional output distribution as well. Had market shares before the corporate tax cut been highly concentrated among labor-intensive firms, then the relative decline in the output share of those firms would have led to a declining market concentration instead. The fact that the distribution of output shares was approximately symmetric across labor intensities in 1967 impliesthatmajorchangesinthetaxrateineitherdirectionwouldhaveresultedinanincrease inmarketconcentration. 23

To facilitate the comparison of concentration measures across time, we compute (inverse) Pareto indices implied by the output share of firms above a certain production level relative to theirshareinthefirmpopulation.26 Inoursimulations,theoutputconcentrationindex(implied by the output share of the largest 5 percent of firms, for instance) increases from 0.85 to 0.87 whenthetaxratedropsfrom0.5to0.2. Concentrationindicesbasedonsales(andmorerecently onvalueadded)showsimilarupwardtrends.27 5.4 Implications for capital investment Thereallocationofproductionawayfromlabor-intensivefirmsincreasestheoverallcapitalintensityoftheindustry. Comparingthe2014economywith1954inTable5,themodelpredicts a 3.5-fold increase in capital per worker. In comparison, the NBER manufacturing database shows a 4.6-fold increase in the capital-to-labor ratio in the US between 1958 and 2011, reflecting,inpart,aggregateTFPgrowth. The drop in the relative price of capital in the model, both directly from lower taxes and indirectly from the higher equilibrium real wage, implies a long-run average elasticity of substitution between capital and labor of 1.29 for the years 1954–2014. This value is consistent with the findings of Karabarbounis and Neiman (2019), who report the macro-level estimates to range between 1.17 and 1.49, with an average of 1.28. As we noted above, this elasticity is not constant in our model. The concentration of output among a smaller set of firms in lateryearsreducesthe(output-weighted)dispersioninfactorintensitiesintheeconomy,which lowers aggregate factor substitutability in the industry. The average model elasticity of factor substitutionbetween1967and2014is1.1instead. Recall from equation (10) that the relative tax elasticities of the labor share and of the industry’s capital per labor are informative of the elasticity of factor substitution. The relative responses of the labor share and capital investment in the model are similar to our estimates from the cross-country data. From Table 5, capital doubles and the labor share declines from 0.54 to 0.46 between 1967 and 2014, the period closer to our cross-country coverage. These give a log-ratio of -4.3 (= ln(2)/ln(0.46/0.54)). In comparison, the cross-country estimates imply a 0.1 percent drop in the aggregate labor share and a 0.3 to 0.5 percent rise in capital per worker (Tables D.1 and D.2), implying a log-ratio that is in the -3 to -5 range.28 Trends in US manufacturing suggest a similar ratio. In the NBER manufacturing database, the labor sharefellfrom0.54to0.34whilecapitalperworkerincreased4.6fold,implyingalog-ratioof 26Lettingq denotetheoutputshareoflargests percentoffirms,theParetoindexis: ι = logs /(logs − x x P x x logq ). x 27Theindicesbasedonthesalessharesofthetop4,8,20or50firmsincreasefrom0.74,0.79,0.85and0.89to 0.78,0.82,0.87and0.91between1972and2012,thefirstandlastyearsavailableinthedata. 28Theregressionofthelaborsharetonet-of-taxrateinlogsyieldsanestimateof0.10(0.04),similarto0.12in Table1Column1. 24

-3.3. The similarity of these ratios between the model and the data suggests that the extent of substitutabilityinthemodelisconsistentwiththatobservedacrosscountries. 5.5 Implications for the employment distribution Despite the rise in output concentration the model predicts a decline in employment concentration and a drop in average employment at the firm level (rows 4 and 5 of Table 5). In the benchmark economy, even though output is distributed symmetrically across firm types, employment is skewed toward labor-intensive firms because those firms require more labor per unitofoutput. Withalowertaxrate,moreoutputisproducedbycapital-intensivefirms,which need fewer units of labor per output. As the industry moves from a traditional labor-intensive structure to a capital-intensive structure, the correlation between labor intensity and market share declines. Labor-intensive firms, initially among the largest employers, shrink in terms of both output and employment. As a result, the concentration of employment decreases and averageemploymentfalls. Table 6 compares the employment distributions in the simulated 2014 economy with the data. Establishments with more than 250 employees, for instance, represented 4.3 percent of establishmentsandcaptured60.1percentofmanufacturingemploymentin1967. In2014,only 3.2 percent of establishments had more than 250 employees and they accounted for 46 percent of manufacturing employment. The associated concentration index, defined by the inverse of the Pareto index implied by the share of employment among the largest employers, fell from 0.84 to 0.77. The comparable employment concentration index falls from 0.84 to 0.80 in the model(Table5).29 Althoughnoneofthesemomentsweretargetedinthemodelcalibration,the modelcapturesthereallocationofemploymenttowardsmallfirminthedata. Theshiftinemploymenttowardsmallerfirmsalsoreducesaverageemployment. Themodel overstates the magnitude of this effect (average employment goes from 61 to 24 versus from 61to44inthedata),whichweattributetothelackoftechnologicalprogressinthemodel. An increase in industry TFP would raise the average establishment size in our model, mitigating thefallimpliedbytherisingmarketsharesofcapital-intensivefirms. Aswasthecasewithvalueaddedconcentration,itshouldbenotedthatthepredictedlower employmentconcentration dependson theindustry’s initialsize distribution. If employmentis initiallyconcentratedamonglabor-intensivefirms-asinthecaseofthemanufacturingsectorthenlowertaxescanbeexpectedtoreduceemploymentconcentration.30 29Online Appendix Figure D.1 shows a secular decline in all concentration indices based on alternative size classesofestablishmentsandoffirms. Comparingthetrendsinemploymentconcentrationacrossmajorsectors, wefindthatmanufacturingandminingstandoutinbothdimensions,whilesectorswithrelativelysmallerdeclines intheirlaborsharedonotshowadeclineinemploymentconcentration. 30Sectoral differences in the firm-level correlation between initial value-added shares and factor intensities 25

Table6: EmploymentDistributions Data: 2014 EstablishmentSize: <20 20-99 100-249 250-999 1,000+ Establishments 67.1 23.6 6.1 2.8 0.4 Employment 9.5 23.7 21.2 28.2 17.3 Model: Simulationwithτ = .2 EstablishmentSize: <20 20-99 100-249 250-999 1,000+ Establishments 82.1 13.5 2.9 1.3 0.2 Employment 13.8 24.0 18.5 23.6 20.1 Theupperpanelshowsthe2014CensusBDSdata. Thelowerpanelshowsmodelsimulationfromtheeconomy withthe20percentcorporatetaxrate. 6 Beyond the manufacturing sector Although we have focused our analysis on the manufacturing sector, it is reasonable to expect similar labor share declines in all sectors. After all, corporate taxes have declined for all corporations, which represent a large share of output in many sectors. Interestingly, however, with the exception of the mining sector, the decline in the labor share has been more moderate outside of manufacturing. In this section, we extend our quantitative analysis to other major sectors in the US and examine whether the relatively smaller declines in labor shares in other sectorsareconsistentwithourproposedmechanism. From the perspective of the model, two factors could lead to variation in the decline in the laborshareacrosssectors. First,thetaxelasticitiesofthelaborsharemaydifferacrosssectors, e.g., due to differences in the within-sector distributions of value added and factor intensities. This would lead to varying labor share responses to a given change in the tax rate. Second, reforms of the tax code can be reflected differently in the effective tax rates applicable to each sector. Such differences may arise from differences in capital composition, the size of fixed investment, or, simply, sector-specific allowances and exemptions. We illustrate the role of thesetwofactorsbelow. Inwhatfollows,wemaintainourcalibrationapproachtoquantifythemarginaleffectoftax cutsbymajorsector. Industry-leveldatamoments,suchastheexitrateoraverageemployment, areavailablefromtheBDSformajorsectors. Inregardstothejointdistributionoflaborshares and value added, we draw on firm-level data from Compustat because the Census coverage of the requisite data is limited to the manufacturing sector. Compustat only covers publicly listed firms. This could confound our findings if publicly listed firms were selected differently couldresultindivergenttrendsinemploymentconcentrationinreactiontofallingtaxrates. Thiscouldpotentially explainthelackofcorrelationbetweenthetrendsinemploymentconcentrationratiosandthelaborsharesacross narrowlydefinedindustries(Autoretal.,2020). 26

acrosssectorsinawaythatalsocorrelateswiththeirtaxelasticities.31 Becausethemodel’stax elasticity is based on the output-weighted dispersion of factor intensities, our concerns regardingnon-randomselectionaresomewhatmitigatedbythefactthatlistedcompaniesrepresenta large share of US output. Finally, we find that the distribution of factor intensities within the manufacturingsectorinCompustatisverysimilartowhatwasobtainedfromtheCensusdata. We compute the labor share for each firm as the ratio of its reported wage bill to its value added(definedbythesumofoperatingincomebeforedepreciation,changesininventories,and thewagebill). Manyfirmslackinformationonwagepayments,whichpresentsachallengefor calculatinglaborshares. FollowingDonangeloetal.(2019)and˙Imrohorog˘luandTu¨zel(2014), if the wage bill is not reported, we impute a value either by using reported values in adjacent years or by multiplying employment with the average wage in a firm’s 3-digit industry from the Quarterly Census of Employment and Wages (QCEW) during that year.32 This gives us a distribution of firm-level labor shares and value added by year. We exclude construction, agriculture, and financial services, each of which has fewer than 30 firms in our Compustat sample. Wefocusonthe10-yearperiodpriorto1985tocomputeourtargetmoments. Table7showsthedescriptivestatisticsfromCompustatforsixmajorsectors. Allmoments are weighted by value added. Recall from Proposition 3 that sectors with a larger dispersion in labor shares and those with lower overall labor shares can be expected to be more sensitive to tax rates. The manufacturing, mining, and wholesale trade sectors fall into this category. BycontrastTCPU(Transportation,CommunicationsandPublicUtilities)andretailtradeshow relatively little dispersion in labor intensities. The service sector shows a somewhat higher dispersion,butalsoahigheroveralllaborshare. Finally, our calibration requires a tax rate for each sector. Column 1 in Table 7 shows the average effective tax rates obtained from the IRS corporate tax statistics for 1985 - the benchmarkyearforourcalibration-andfor2013. ThedifferenceisshowninColumn3.33 The 1985 rates show substantial variation across sectors from 22 percent in services to 40 percent inmanufacturingandTCPU.Thetaxratesin2013aremoresimilartoeachother,varyingfrom 19 to 23 percent, with the exception of manufacturing, where the tax rate is 28 percent. This implies larger decreases in tax rates among sectors that had higher initial rates. Consequently, thelowestdropisseeninservices(3points)andthelargestdropsareseeninTCPU(19points) followedbymanufacturing(12points). 31Specifically,Compustatdatawouldunderstatetaxelasticitiesifpubliclylistedfirmsweredisproportionately selectedfromthemiddleoftheirsector’slaborintensitydistribution. If,inaddition,suchselectionwerestronger insectorswithlimiteddeclinesinthelaborshare,thenourfindingswouldfalselyattributethesectoraldifferences inthedeclineinthelaborsharetotaxcuts. Wedonotseeanapriorireasontosuspectthateitheristhecase. 32Amongfirmsthatexplicitlyreporttheirwagebill,thecorrelationbetweentheimputedandthereportedlabor share is 0.86, which gives us some confidence in the imputation procedure. Online Appendix C provides the details. 33IRS data do not distinguish between wholesale and retail trade. We assume that the tax rate is identical in thesetwosectorsandreportresultsforeachseparatelyandalsoforthecombinedtradesector. 27

Table7: Effectivetaxratesandthedistributionoflaborshareacrossmajorsectors Taxrate Laborshare Sector τ τ ∆τ mean median std. N 1985 2013 Manufacturing 0.40 0.28 -0.12 0.60 0.65 0.20 1,879 Mining 0.29 0.23 -0.07 0.41 0.30 0.22 203 TCPU 0.40 0.21 -0.20 0.71 0.70 0.11 117 Columns 1-3 show Trade 0.32 0.23 -0.09 0.61 0.62 0.14 427 WholesaleTrade - - 0.59 0.58 0.19 202 RetailTrade - - 0.61 0.62 0.12 225 Services 0.22 0.19 -0.03 0.69 0.70 0.17 355 average tax rates. Columns 4-6 show the mean, median, and standard deviation of the firm-level labor shares foreachsectorweightedbyvalueadded. Ndenotesthenumberoffirms. Sources: IRS(1985–2013)andCompustat(1975–1985). (a) (b) Figure5: Declinesinthelaborshareinmajorsectors: Modelversusdata Panel(a)contraststhedeclinesinthesectorallaborsharesinthedatabetween1985and2014(y-axis)withthe model predictions (x-axis). Dashed lines show the equality axis. The solid (red) line in Panel (a) shows the linearfit. Panel(b)addsmodelpredictionsassumingthatallsectorspaidthesametaxrates(whitecircles). The differencebetweenthetwopredictionsareattributabletosectoraldifferencesinthechangesineffectivetaxrates. To quantify the marginal impact of tax cuts on the labor share, we calibrate the model to match the sectoral labor shares given the tax rates in effect in 1985. We then simulate a new equilibrium using the 2013 tax rates. Details of our calibration, values for data moments, and calibratedparametervaluesforeachsectorcanbefoundinOnlineAppendixC.Wesummarize the results in Figure 5. Panel (a) compares the predicted changes in the sectoral labor share from tax changes (x-axis) with the actual decline in the sector’s labor share between 1987 and 2014 from the BEA.34 Because tax rates fall in all sectors, the predicted changes are negative throughout. With the exception of services, where the actual labor share increased, the predicted changes are smaller than the changes seen in the data. The dashed line represents the 45◦ lineonwhichthepredictedandactualchangeswouldbeequal. Giventheoutputsharesof 34BEAdataonsectorallaborsharesareavailablebeginningin1987. 28

these major sectors during the 1980s, the model attributes 36 percent of the observed decline to lower tax rates on average.35 Across sectors, the predictions correlate positively with the observed declines in the labor share with a coefficient of 0.89. This is encouraging, because it shows that the model gives a reasonable depiction of sectoral differences in labor share trends. Nonetheless, taxes only partially explain the sectoral differences in the decline in the labor share. The predicted sectoral variation in the decline in the labor share is driven mainly by differences in the sectoral tax elasticities. This is illustrated in panel (b). For each sector, the black dot corresponds to the predicted decline in labor shares using that sector’s specific tax rate (the same as in panel (a)). The white dots in panel (b) show the predicted changes assuming a uniform decline in their effective tax rates - taken to be the the change in the aggregate tax rate - starting from the initial sector-specific levels. These predictions are driven only by the differencesintaxelasticities,yettheyremainlarge. The(horizontal)differencesbetweenwhite and black dots for each sector are attributable to the differential effect of tax changes instead. TCPUshowsarelativelymuteddeclineinthiscounterfactualscenario,reflectingthemorethan averagedeclineinitseffectivetaxrate. Incontrast,servicesandminingwouldhaveseenlarger declineshadthefallintaxratesinthesesectorsbeencomparabletotheUSaverage. The labor share in the service sector presents a unique puzzle as it increases in the data despite the fall in the tax rate. The increase during the post-1986 period shown in Figure 5 is part of a longer-term upward trend in the US led by health care and education services prior to the 1986 tax reform (Elsby et al., 2013), which is likely to reflect factors outside of our model. Fromthatperspective,ourfindingssuggestthattheservice-sectorlaborsharewouldhaverisen fasterhaditnotbeenforthelowertaxrates. Cross-country data on the service-sector labor share shed some light on the importance of counteracting trends in the service sector. In our sample of OECD countries between 1981 and 2007, the service-sector labor share shows an upward trend only in Denmark and the US, and a downward trend in all other countries, albeit at a slower pace relative to manufacturing. To estimate the role of long-run trends for the service sector, we regress the labor share on the country’s corporate tax rate, controlling for fixed country and year effects as we did for manufacturing in Section 2. The marginal effect of corporate tax rates on the service-sector labor share is 0.13 (0.06) when country-specific trends are included in the regression and 0.04 (0.06) when they are not. That is, controlling for trends reveals a higher tax elasticity in the service sector. This suggests that the long-run trends in the service-sector labor share have tended to counter the downward pressure from lower tax rates. The prediction for the US servicesectorinFigure5isconsistentwithan0.18(= 0.55/3)pointdropinthelaborsharein 35Using1980s’outputweightstoaggregatesectorsinboth1985and2014,thetotalchangeis2.2pointsinthe model. Constant weights imply a 6.1 point drop in the data. Because the composition of output trends toward servicesduringthisperiod,theactualchangeinthedatais3.3points. 29

responsetoa1pointdeclineinthetaxrate,closetothe0.16estimatedfromcross-countrydata controllingforlong-runtrends. Thissuggestslowertaxesarelikelyassociatedwithadeclinein the labor share in services as well, albeit at a smaller rate than manufacturing, consistent with themodel’spredictions. Overall, we conclude that even though the corporate tax system applies to all entities in statute, the sensitivity of economic activity and output reallocation to tax rates depends on the distributionoffactorintensitiesineachsectorandontheeffectivecorporatetaxratethatapplies tothesector. 7 Evidence from state corporate taxes and patterns across US manufacturing industries In this section we empirically assess the relevance of the model’s mechanisms that link corporatetaxationtothelaborshare. Inparticular,weaskwhetherlowertaxratesareassociatedwith increased capital investment, higher market concentration, and firm entry across industries in theUSmanufacturingsector. Tothatend,weexploitdifferencesincorporatetaxpolicyacross US states to construct tax rates for each manufacturing industry based on where they are located. We then relate these tax rates to industry characteristics and test whether the evolution of labor shares, investment, value added, and market concentration is broadly consistent with themodel’simplications. 7.1 Corporate taxes and the labor share across US states We begin by discussing the cross-state patterns in the evolution of corporate tax rates and how they relate to changes in the manufacturing labor share in that state. Differences in tax policy across states are rather complex and stem not just from the headline statutory rate but also fromthegenerosityofexemptions,loss-offsetcarryhorizons,teasercreditsfornewbusinesses, etc. As a summary measure, we define each state’s effective corporate tax rate by the ratio of corporate tax revenue to profits, measured by the total gross operating surplus. The resulting rates are low relative to the federal tax rate ranging from 0 percent to 4.2 percent. Unlike the averagefederaltaxrate,whichshowsadownwardtrendovertime,averagestatetaxratesshow amoremixedpattern(seeOnlineAppendixB.3fordetailedgraphs). We relate these patterns in the tax rate to states’ labor shares in manufacturing, obtained fromtheCensusofManufacturesforeveryfiveyearsbetween1972and2007.36 Figure6plots 36In our analysis of the US manufacturing industry the labor share refers to the payroll share at operating 30

Figure6: CorporatetaxrateandmanufacturinglaborshareintheUS:1972–2007 Graphshowsthestate-levelchangesinthemanufacturingsectorlaborshareandtheaveragecorporatetaxratein percentagepoints. Thecorrelationcoefficientbetweenthetwovariablesis0.42(s.e. 0.11). thechangesinstates’laborsharesagainstchangesinaveragecorporatetaxratesbetween1972 and 2007. Reflecting the aggregate trend, manufacturing labor shares have fallen in all states. More importantly, there is a strong positive link between the two variables: states with larger decreases in the state-level corporate tax rate experienced a larger fall in the manufacturing laborshare. Table 8 shows the estimates from a regression of state-level manufacturing labor shares on thestate’saveragecorporatetaxrate. Thespecificationinthefirstcolumncontrolsforstateand year fixed effects. The coefficient implies that a 1 percentage point drop in a state’s average corporate tax rate is associated with a 2.35 pp drop in its manufacturing labor share. This is large relative to the cross-country estimates in Table 1. Note, however, that the average tax ratesarewellbelowthestatutoryrates,withanaverageratioof0.17amongstateswithpositive tax rates. This suggests a statutory tax elasticity of 0.39 (= 2.35∗0.17), which is closer to the 0.36fromthecross-countrydata. InColumn2,wereportestimatesfromaspecificationthatcontrolsforstate-specifictrends. The coefficient is 2.62 (s.e. 0.82), suggesting that the result is not driven by a spurious correlation between trends in labor shares and tax rates at the state level. The next two columns control for the changes in labor costs proxied by the state’s average wage and salary disbursementsduringtheyear. Thecoefficientonthecorporatetaxrateremainssimilar. manufacturingestablishmentsandisdefinedastheratiooftotalpayrolltototalvalueadded.SeeOnlineAppendix Bfordetaileddatadefinitions. 31

Table8: CorporatetaxationandthelaborshareacrossUSstates (1) (2) (3) (4) (5) (6) CorporateTaxRate 2.35 2.62 2.80 2.81 3.47 3.23 (0.74) (0.82) (0.69) (0.81) (0.77) (1.08) log Wage 0.08 0.08 0.12 0.12 (0.04) (0.05) (0.04) (0.07) The dependent variable Unemploymentrate 0.54 0.26 (0.21) (0.17) StateTrends no yes no yes no yes N 384 384 384 384 336 336 isthepayrollshareofvalueaddedinthemanufacturingsectorofastate. Corporatetaxratedenotestheaverage corporatetaxrateinastate.Allspecificationscontrolforyearandstatefixedeffects. Standarderrorsareclustered atthestatelevel.DatacomefromtheAnnualSurveyofManufactures1972–2012,theBEA,andSaezandZucman (2016). Thelasttwocolumnscoverthe1977to2012period. It is plausible that corporate tax rates react to economic conditions and are therefore not exogenous to the labor share. We think, however, that such endogeneity likely renders our estimates conservative. A procyclical tax policy, designed to smooth out cyclical fluctuations, would bias the estimates downward because the labor share is known to be countercyclical. Indeed, including the state unemployment rate as a control variable in columns (5) and (6) of Table8giveshighercoefficientestimatesforthetaxrate. These empirical patterns show that changes in corporate taxation are positively related to labor shares across US states, in line with the findings in Section 2 from cross-country data. Theestimatedcoefficientsvaryfrom0.39to0.58acrossspecificationsafteraccountingforthe differencebetweenaverageandstatutoryrates. Thesearesomewhatlargerthanthe0.18to0.36 range suggested by the cross-country data in Table 1. The state-level estimates likely reflect thehighmobilityofcapitalbetweenstatesandthereforedonotnecessarilyprovideanaccurate pictureofwhatmightbeexpectedattheaggregatelevel. 7.2 From states to industries To relate the trends in industry characteristics to changes in state-level corporate taxes, we compute industry-specific effective tax rates based on the location of establishments in each industry. In particular, we combine the state-level average corporate tax rates with data on the number of establishments by state and industry. In this way, we compute an establishmentweighted average of state-level tax rates for each 4-digit SIC industry available for the years 1974to2011. The differences in effective industry tax rates emerge from changes in state-level tax rates 32

given the location of establishments in each industry. The apportionment of a firm’s tax liabilities can be more complicated in reality, e.g., if a firm operates multiple establishments across state boundaries, or if it produces in one state, but markets its product in another state. To test the accuracy of our approach in capturing the industry-level variation in effective tax rates, we regress the industry’s labor share on the industry’s tax rate. The coefficient on the corporate taxrateis2.9(s.e. 1.2)percent,whichiscomparabletotheestimatesreportedinTable8. This givesusconfidenceintheempiricalresultsbelow,whichcomparesoutcomesacrossindustries. 7.3 Capital-labor ratio A key implication of the model is the reallocation of production away from labor-intensive firms,whichraisestheoverallcapitalintensityoftheindustry. WenowinvestigatethisrelationshipamongUSmanufacturingindustriesbytestingwhetherindustriesthatsawrelativelylarger increases in capital-labor ratios were those that experienced larger declines in labor shares and effective corporate tax rates. By comparing industries within the manufacturing sector we abstractfromaggregatetrendsininvestmentactivityintheUS.37 TheindustrydatacomefromtheNBERManufacturingDatabase,whichprovidesinformationonlaborcompensation,valueadded,andcapitalinvestmentinthemanufacturingsectorat the 4-digit SIC level. We measure the labor share by the ratio of total payroll to value added and the investment activity by the capital-labor ratio and investment expenditures per worker. Wefirstcheckwhetherthelaborsharedeclinewasaccompaniedbyanincreaseincapitalaccumulation by regressing the investment measures on an industry’s labor share while controlling for fixed year and industry effects. The results, presented in the first two columns in panel (a) of Table 9, show that industries where the labor share declined have experienced increased investment activity relative to other manufacturing industries. A 1 pp fall in the labor share is associated with a 0.33 percent increase in capital per worker and a 1.3 percent increase in investmentperworker. More importantly, the results presented in panel (b) of Table 9 show a significant tax response of capital investment. A 1 percentage point increase in the effective tax rate is associated with a 0.25 percent drop in capital per worker. This is qualitatively consistent with the model, but quantitatively much higher than our quantitative findings in Section 5 and our estimates from the cross-country data. This suggests a particularly high mobility of capital across industries in response to US state tax policies. Such mobility is limited at the aggregate level, whereadditionalcapitalhastobeeitheraccumulatedovertimeorfinancedbyanothercountry. 37Recent work by Gutie´rrez and Philippon (2017) points out an apparent disconnect between market-based profitability measures and net aggregate investment rates after 2000. This seems especially puzzling in light of declining capital costs (see, e.g., Barkai (2020)). Farhi and Gourio (2018) provide an evaluation of possible theories. 33

Table9: Capitaldeepening,sectorsize,andlaborshareinUSmanufacturing (1) (2) (3) (4) (5) (6) log(K/N) log(I/N) log(I/K) log(K/N) log(I/N) log(I/K) Panel(a) LaborShare -0.33 -1.25 -0.93 0.31 -0.80 -1.11 (0.15) (0.15) (0.14) (0.09) (0.12) (0.15) Panel(b) TaxRate(x100) -0.25 -0.26 -0.01 0.38 0.03 -0.34 (0.09) (0.09) (0.10) (0.08) (0.08) (0.12) IndustryTrends No No No Yes Yes Yes Standarderrorsinparenthesesareclusteredbyindustry. Allspecificationscontrolforfixedyearandsectoreffects (4-digitSIC).Columns4-6alsocontrolforindustry-specifictrends. DatacomefromtheNBERManufacturing IndustryDatabase1958–2011. Anindustry’scorporatetaxrateistheestablishment-weightedaverageofeffective statecorporatetaxrates. Column 2 projects investment per worker on the tax rates. A 1 percentage point increase in the tax rate is associated with a 0.26 percent drop in investment per worker, similar to the tax elasticity of capital per worker. This similarity is consistent with the long-run perspective ofthemodel. BecauseI/N = δK/N inthelong-runequilibrium,themodelpredictsthesame long-runtaxelasticityforI/N andK/N. The high sensitivity of investment to the labor share in panel (a) likely reflects a more mechanicalshort-runassociationbetweenthetwovariables,whichmightarisefromlumpiness of investment or cyclical factors. This view is consistent with the estimates in Columns 4- 6, which show results from a specification that includes industry-specific trends as controls. Relative to Columns 1 to 3, these specifications highlight the shorter-run dynamics in the data by controlling for the long-run associations between investment activity and tax rates. The taxelasticityofinvestmentperworkerisslightlylowerinabsoluteterms,butremainsstrongly negativeat-0.80(0.12),whereastherelationshipbetweencapitalperworkerandthelaborshare isnowpositivewithanelasticityof0.31(0.09)percent. Withrespecttotaxes,K/N risesinthe shorter-runwhereasI/N remainsunchanged. Theseresultssuggestthatashort-runreactionto a rise in corporate taxes occurs via reductions in employment and investment while the capital stock is relatively fixed. In the long run, capital declines. A similar result is obtained for I/K, which temporarily increases in response to tax cuts, but converges back to its initial level in the long-run steady state of the model. The estimates show a drop in I/K in the shorter run with an elasticity of -0.34 (0.12) and a recovery in the long run: the estimated response is 0.01 (0.10). 34

Table10: EstablishmentsinUSmanufacturing (1) (2) Panel(a) LaborShare -0.25 -0.27 (0.13) (0.08) Thedependentvariableislog-numberofestablishments. Bothspeci- Panel(b) TaxRate(x100) -0.31 -0.36 (0.12) (0.09) IndustryTrends No Yes ficationscontrolforfixedyearandsectoreffects(4-digitSIC).Column2alsoincludesindustrytrendsascontrols. Standarderrorsinparenthesesareclusteredbysector. Dataonthenumberofestablishmentsbyindustrycomes fromCountyBusinessPatternsandcoversthe1974to2011period. Anindustry’scorporatetaxrateistheestablishmentweightedaverageofeffectivestatecorporatetaxrates. Seetextfordetails. 7.4 Industry size Inresponsetolowertaxes,themodelpredictsatemporaryincreaseinentryratesandapermanent increase in industry size. The aggregate entry rate in the US, however, has seen a secular decline in recent decades (e.g., Decker et al. (2014)). In manufacturing, the total number of establishments in operation peaked during the mid-1990s, whereas the labor share continued to decline.38 To circumvent factors outside of our model, we test the model’s prediction using relativechangesinindustrysizeacrossindustrieswithinthemanufacturingsector. Table 10 shows the results from the regression of total number of establishments in an industry on that industry’s labor share. A decline in the labor share is associated with an increase in the number of establishments in operation across industries. There is a particularly strongnegativerelationshipbetweenthenumberofestablishmentsinoperationandthetaxrate facedbytheindustry. A1percentagepointdropinthetaxrateisassociatedwitha0.31percent increase in the number of establishments. Column 2 shows that this elasticity is similar when wecontrolforindustry-specifictrends. Theserelativepatternsarequalitativelyconsistentwith theeconomicmechanismshighlightedbythemodel. 7.5 Value added concentration in US manufacturing Anotherkeyquantitativepredictionofourmodelisthatcapital-intensivefirmsgrowrelativeto labor-intensivefirms,causingareallocationofmarketsharesthatresultsinhighervalueadded concentration. Totestthisprediction,wetestwhethermanufacturingindustriesthatsawlarger 38According to data from the BDS, the number of manufacturing establishments displays an inverse U-shape between1977and2013,withapeakat361,244in1996. 35

Table11: IndustryconcentrationandtaxesinUSmanufacturing DependentVariable con-8 con-20 con-8 con-20 con-8 con-20 Panel(a) LaborShare -0.16 -0.13 -0.12 -0.10 -0.06 -0.05 (0.07) (0.05) (0.05) (0.04) (0.04) (0.02) Panel(b) Themeasureofcon- Corporate -2.15 -5.14 -1.11 -4.05 -3.90 -4.26 TaxRate(x100) (3.05) (2.47) (2.83) (2.20) (1.52) (1.14) SamplePeriod 1997–2012 1997–2012 1972–1992 Concentrationof ValueAdded Sales Sales centrationistheinverseoftheParetoindeximpliedbytheshareofvalueadded(1997–2012)orsales(1972–1992) amongthetop8or20firmsintheindustry. Theexplanatoryvariableofinterestisreportedinthefirstcolumn. An industry’scorporatetaxrateistheestablishment-weightedaverageofeffectivestatecorporatetaxrates. Eachcell representsaseparateregressionandallspecificationsincludeindustryandyearfixedeffects. Standarderrorsare clusteredatthesectorlevel. decreasesineffectivecorporatetaxratesalsosawlargerincreasesinmarketconcentration. To that end, we combine 4-digit SIC-level concentration measures for manufacturing industries from the US Census with the NBER manufacturing database. Industry concentration is measured by the inverse of the Pareto index implied by the share of value added among the largest 4, 8, 20 and 50 firms, available every five years from 1997 to 2012. For earlier years, where value-added shares are not available, we construct similar measures based on the sales shares of the largest firms from 1972 to 1992. For brevity, we report results for the concentration measures based on the largest 8 or 20 firms. The measures using the largest 4 or 50 firms yieldsimilarresults(seeOnlineAppendixD). We first check if there is a negative relationship between an industry’s labor share and market concentration. Panel (a) of Table 11 reports results from regressing the industry valueadded concentration on that industry’s labor share between 1997 and 2012. All specifications include fixed effects for industry and year. The standard errors are clustered at the sector level as before. The results show that in industries where the labor share has fallen, market concentration has increased. Focusing on the concentration of value added among the top 8 firms, for instance, the estimate of -0.16 in the first column suggests that a 10 pp decrease in the labor share is associated with a 1.6 pp increase in the market concentration index. These resultsareconsistentwiththoseofAutoretal.(2020). In panel (b), we regress market concentration in an industry on that industry’s effective corporatetaxrate. Theresultsimplythatadropinthecorporatetaxrateofastateisassociated with an increase in the market concentration of industries that are heavily located in that state. 36

The estimated effects can be large. To put the numbers in context, consider the top 20 firms (in terms of value added) in an industry with a concentration index of 0.75 and a total of 241 firms in operation, roughly the median values in our sample. In this case, a 1 percentage point increase in the effective tax rate reduces the concentration index by 5.1 pp. Assuming a Pareto firm size distribution, this corresponds to roughly a 7 pp drop in the market share of the top 20 firms.39 This is a sizeable impact, but it should be noted that the interquartile range of 20-year taxchangesinoursampleisonly0.71pp. SimilarpatternsemergeinColumns3and4,wherewerepeattheregressionsforthe1997– 2012periodusingsalesconcentrationasaproxyforvalue-addedconcentration. Theelasticities are slightly lower in absolute terms when sales concentration is substituted for output concentration, likely due to variations in the share of intermediate goods in production. The general pattern remains comparable: higher tax rates are associated with lower market concentration, consistentwiththepredictionsofthemodel. Becausedataonvalueaddedconcentrationarenot available prior to 1997, we examine the patterns in sales concentration during the 1972–1992 period(Columns5and6). Wefindasomewhatweakercorrelationbetweenthelaborshareand thesalesconcentration,buttheeffectoftaxesonmarketconcentrationremainsimilar. InOnlineAppendixD.3,wereportalternativespecificationsrelatinglong-rundifferencesin marketconcentrationwithcorrespondingchangesinthelaborshareandtaxratesacrosssectors. The difference specifications point to size effects that are larger and more precise over longer horizons and for concentration measures that are based on a large number of firms, e.g., the largest50firms. Specificationsthatcontrolforindustry-specifictrendsgenerallyyieldqualitativelysimilarresults,butwithlowersizeeffects. Takentogether,thesealternativespecifications reflectthetensionbetweenthemodel’spredictions,basedonsteady-statecomparisons,andthe short- to medium-term fluctuations in market concentration especially as measured by a small numberoflargefirms. 8 Conclusion We highlight the role of an institutional factor, corporate taxation, for the global decline in the labor share. The evolution of market shares and the employment distribution in US manufacturingrelativetoothersectorscorroboratesthemodel’spredictions. Wefindthatthedeclinein corporatetaxationispartiallyresponsiblefortheshiftofproductionfromlabor-intensivefirms to capital-intensive firms over time. At the same time, the reallocation of production away fromtraditionallylarge,labor-intensivefirmsreducedtheoverallemploymentconcentrationin 39WithaParetodistribution,thevalue-addedshareofthetopx%offirmsisgivenbyx1−η,whereη ∈(0,1)is theconcentrationindex. Inthisexample,thevalue-addedshareofthetop20firmsfallsfrom0.54 = 20/2410.25 to0.47=20/2410.3,whereweassumethatthetotalnumberoffirmsremainsunchanged. 37

manufacturing. The key mechanism in our model is a fall in the relative cost of capital induced by a lower corporatetaxrate. Othertheoriesthatarebasedonchangesinrelativefactorprices,forinstance duetolowercapitalcosts(KarabarbounisandNeiman,2013;Barkai,2020)wouldoperateina waythatisqualitativelysimilartoafallinthetaxrate. Quantitatively,however,wesuspectthe impactissmallerforagivenchangeintherelativeprices. Inthecontextofourmodel,lowering the interest rate from around 4 percent toward zero has resulted in a 5.7 pp decline in the labor share since 1954.40 Since lower corporate taxes do not fully explain the decline in the labor shareandtheshiftofoutputtowardcapital-intensivefirms,wethinkthatotherfactorsmayalso beatplay.41 Recent legislation brought significant changes to business taxation in the US, including a dropinthestatutorycorporatetaxratefrom35percentto21percent. Oursimulationsindicate that the complete elimination of corporate taxes decreases the labor share by an additional 5 percentagepointsstartingfromthemodel’simplied2014values. While our paper focused on corporate taxation, labor taxation can be equally important. ThemaintaxesonlaborintheUSaretheindividualincometaxandpayrolltaxes. Theaverage individual income tax has been more or less stable in the US. Payroll taxes, on the other hand, increased significantly during the 1960s and 1970s, following the formation and expansion of the federal Social Security system and Medicare. Piketty and Saez (2007) report the average incomeandpayrolltaxratesbetween1960and2001. Thetotalrateincreasedfrom14.9percent to 22.9 percent, implying a 10.4 percent increase in the effective wage rate. Higher taxes on labor would reduce the labor share in our model in a way that is similar to that of corporate tax cuts. The model simulations predict a decline in the manufacturing labor share of 17.8 pp in response to changes in corporate and labor taxes combined, an additional drop of 4.3 pp attributabletolabortaxesalone. Ourexaminationoflaborsharepatternsacrossmajorsectorsrevealssignificantdifferences ineffectivetaxratesandintaxelasticities,stemmingfromthedistributionofvalueaddedwith respecttolaborintensity. Thesedifferencespartlyexplainthesectoraldifferencesinthedecline in the labor share. They do not, however, explain the rise in the US service-sector labor share during a period of declining corporate taxation. The diverging patterns in labor share between theservicesectorandtherestoftheeconomyremainsapotentialavenueforfutureresearch. 40Forthisexperimentweusetheparametersfromthebenchmarkeconomy,setτ =0.50andletρ→1. 41ThepositiverelationshipbetweencorporatetaxationandlaborsharesacrossUSstatessuggestsanon-trivial role for corporate taxation because firms in different states can be assumed to have access to similar prices for investmentgoods. 38

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A Theoretical Appendix This Appendix contains the derivations and proofs for the theoretical results mentioned in the paper. Factor Demands From (2) the first-order conditions for labor and capital demand, evaluated in the stationary distributionandforε = 1,are: w w¯ ≡ = βkαnβ−1 (A1) p (cid:18) (cid:19) 1 1−ρ˜ r ≡ +δ = αk′α−1n′β (A2) τ 1−τ ρ˜ Thestatementonpage14inthemaintext,thatforagivenlevelofcapital,labordemandis not distorted by the corporate tax rate, follows from (A1). On the other hand, (A2) shows that the presence of corporate taxes directly affects capital demand by increasing the effective cost ofcapitalr . τ Withfirmoutputevaluatedattheoptimallaborandcapitaldemandgivenby(6),theoutput elasticity of the real wage w¯ is η = ∂logq = − β , whereas η = ∂logq = − α , as was q,w¯ ∂logw¯ 1−γ q,rτ ∂logrτ 1−γ statedin(7)inthemaintext. Proof of Lemmas 1 and 3 The elasticity of the value-added share λ(α) with respect to the cost of capital r and with τ respecttotheequilibriumpricepis: α−αˆ α−αˆ q q η = − η = − . λ,rτ 1−γ λ,p 1−γ (cid:82) Proof. Let Q = q(α)dG(α) denote aggregate output. From (9), the elasticity of λ(α) w.r.t. a factor price x is η = η − η . The elasticity of aggregate output is η = ∂Q x = (cid:82) ∂q xdG(α) = λ,x q,x Q,x Q ∂x Q ∂xQ (cid:82) η qdG(α). Itfollowsthatη = η − (cid:82) η qdG(α). Thelemmathenfollowsbyreplacingη q,xQ λ,x q,x q,xQ λ,x withtheirdefinitionsin(7)andthedefinitionsofβˆ andαˆ . Forexample,tocomputetheelasticitywith q q respecttothecostofcapital,thesestepsyieldη = − α + (cid:82) α qdG(α) = − α−αˆq . λ,rτ 1−γ 1−γQ 1−γ 1

Proof of Proposition 1 For a given price level p, a decrease in the cost of capital lowers the aggregate labor share, withthemarginalchangegivenby: ∂β ˆ σ2(α) q q = . ∂logr 1−γ τ Proof. Following a change in factor price x, the change in the aggregate capital share is given by ∂αˆq = (cid:82) ∂λ(α) αdG(α) = 1 (cid:82) η λ(α)αdG(α). Using (cid:82) η fromLemma1,weobtain ∂x ∂x x λ,x λ,rτ ∂αˆ (cid:90) (α−αˆ )λ(α)αdG(α) (cid:82) λ(α)α2dG(α)−αˆ (cid:82) λ(α)αdG(α) −σ2(α) q q q q = − = − = . ∂r r (1−γ) r (1−γ) r (1−γ) τ τ τ τ Itfollowsthat ∂βˆ r = −∂αˆ r = σ q 2(α) . ∂rτ τ ∂rτ τ 1−γ Proof of Lemma 2 Firmvalueisdecreasinginτ andincreasinginp. Proof. Thefirm’svaluefunction(2),evaluatedatoptimalfactordemandlevelsis: (cid:32) (cid:33) 1 1−γ (cid:16)α(cid:17)α (cid:18) β (cid:19)β 1−γ V(α) = · (1−τ)1−β ·p1−α , (A3) 1−ρˆ r w Theelasticityoffirmvaluewithrespecttopriceis 1−α > 0,andtheelasticityoffirmvaluewithrespect 1−γ tothenet-of-taxrate(1−τ)is 1−β > 0. 1−γ Proof of Proposition 2 Withfreeentry,theequilibriumprice,p,isincreasinginthetaxrate,τ. Proof. The proof follows from combining Lemma 2 with the free-entry condition (3). Because the entrycostisconstant,adropinfirmvaluecausedbyhighertaxeshastobematchedwithanincreasein (cid:82) the price level to ensure that the free-entry condition holds. Formally, setting pc = V(α)dG(α) = e 1−γ (cid:82) (1−τ)pq(r ,w/p)dG(α), which is the discounted value of future profits net of taxes, and rear- 1−ρˆ τ ranginginflowtermsgivesthefollowingequationinoutputunits: (cid:90) (1−ρˆ)c = (1−γ) (1−τ)q(r ,w/p)dG(α) e τ Theimplicitfunctiontheoremgivesthederivativeofpwithrespectto(1−τ)as: 2

(cid:104) (cid:105) (cid:82) q(r ,w/p)+(1−τ) ∂q(rτ,w/p) dG(α) dp τ ∂(1−τ) = − , (A4) d(1−τ) (1−τ) (cid:82) ∂q(rτ,w/p) dG(α) ∂p Multiplyingbothsidesby(1−τ)/pgivestheelasticityofpricew.r.t. thenet-of-taxrateas: (cid:82) (1+η )q(r ,w/p)dG(α) 1−βˆ q,1−τ τ q η p,(1−τ) = − (cid:82) η q,p q(r τ ,w/p)dG(α) = − βˆ q , (A5) where η and η are partial elasticities of output with respect to (1−τ) and p. These elasticities q,1−τ q,p areα/(1−γ)andβ/(1−γ)respectivelyfromequation(6). Substitutingthemgivesthelastterminthe equalityabove,whichisnegativesinceβˆ ∈ (0,1). Notingthat(1−τ)decreaseswithτ concludesthe q proof. Proof of Proposition 3 A decrease in the equilibrium price level lowers the aggregate labor share, with the marginal changegivenby: ∂β ˆ σ2(α) 1 q = . ∂logp 1−γ Proof. Following a change in factor price x, the change in the aggregate capital share is given by ∂αˆq = (cid:82) ∂λ(α) αdG(α) = 1 (cid:82) η λ(α)αdG(α). Using (cid:82) η fromLemma1,weobtain ∂x ∂x x λ,x λ,p ∂αˆ (cid:90) −(α−αˆ )λ(α)αdG(α) (cid:82) λ(α)α2dG(α)−αˆ (cid:82) λ(α)αdG(α) σ2(α) q q q q = − = = . ∂logp logp(1−γ) logp(1−γ) logp(1−γ) Itfollowsthat ∂βˆ logp = − ∂αˆ logp = − σ q 2(α) . ∂logp ∂logp 1−γ Proof of Proposition 4 The equilibrium elasticity of the aggregate labor share with respect to the net-of-tax rate is givenby: (cid:32) (cid:33)2 1 σ (β) q η = − < 0 βˆ,(1−τ) 1−γ β ˆ q Proof. Recall that w¯ = w/p, where w = 1 is the nume´raire and p is pinned down from the free-entry condition. We demonstrate the proof by expressing the relevant comparative statics with respect to the realwage,w¯. 3

Usingthefirsttwopropositions,thederivativeofβˆ withrespectto(1−τ)is: (cid:32) (cid:33) dβˆ ∂βˆ dw¯ ∂βˆ dr σ2(α) 1 dr q q q τ q τ = + = (1−η ) , (A6) w¯,r d(1−τ) ∂w¯ dr ∂r d(1−τ) 1−γ r d(1−τ) τ τ τ whereη denotestheelasticityoftheequilibriumrealwageratewithrespecttotherentalrateofcapital w¯,r asimpliedbytheentrycondition. Becausew¯ = w/pwithw = 1normalizedandr = r/(1−τ)with τ r = (1−ρˆ)/ρˆ+δinalllong-runequilibria,(steady-state)equilibriumadjustmenttoachangeinthetax rate transpires solely through a change in the price level in our model. As a result, η = −η = w¯,rτ p,rτ η ,whichequals−(1−βˆ )/βˆ fromequation(A5). Equivalently,1−η = 1/βˆ . p,(1−τ) q q w¯,rτ q Substitutingthisresultbackintoequation(A6)givesthedesiredelasticity. Inparticular,notingthat dr /d(1−τ) = −r /(1−τ)fromthedefinitionoftheusercostofcapital,wehave: τ τ dβˆ σ2(α) 1 1 q q = − , d(1−τ) 1−γ βˆ (1−τ) q whichimplies (cid:32) (cid:33)2 dβˆ 1−τ 1 σ (α) q q = − d(1−τ) βˆ 1−γ βˆ q q notingthatσ (α) = σ (β)givestheresult. q q Proof of Proposition 5 Theequilibriumelasticitiesofaveragedemandforcapitalandlaborwithrespecttothenet-oftaxrate(1−τ)are: (cid:32) (cid:33) (cid:32) (cid:33) ˆ ˆ ˆ 1 β 1 β −β k q n η = 1− > 0 and η = −1 < 0, k¯,(1−τ) 1−γ β ˆ n¯,(1−τ) β ˆ 1−γ q q Before we begin the proof, we establish the partial elasticities of average capital and employment for a given price level p. Note that aggregate capital and labor in the industry are givenby: (cid:90) (cid:90) ¯ K = Mk = M k(α)dG(α) N = Mn¯ = M n(α)dG(α) (A7) ¯ withk andn¯ denotingindustryaveragesforcapitalandlabor. Lemma4follows: Lemma4 The partial equilibrium elasticities of average industry demands for capital and 4

laborwithrespecttofactorpricesare: ˆ ˆ 1−β β αˆ 1−αˆ k k n n η = − , η = − , η = − , η = − . k¯,rτ 1−γ k¯,w¯ 1−γ n¯,rτ 1−γ n¯,w¯ 1−γ where (cid:90) (cid:90) k(α) n(α) ˆ β = γ − αdG(α) and αˆ = αdG(α) k n K N are asset-weighted labor (cost-)share and employment-weighted capital (cost-)share respectively. Proof. Bydefinition, r ∂k¯ r (cid:90) ∂k (cid:90) k (cid:90) 1−βk 1−βˆ τ τ k η = = dG = η dG = − dG = − k¯,rτ k¯ ∂r k¯ ∂r k,rτk¯ 1−γ k¯ 1−γ τ τ Theproofsforotherelementsfollowsimilarly. Forinstance, (cid:90) (cid:90) (cid:90) w¯ ∂n¯ w¯ ∂n n 1−αn 1−αˆ n η = = dG = η dG = − dG = − . n¯,w¯ n,w¯ n¯ ∂w¯ n¯ ∂w¯ n¯ 1−γ n¯ 1−γ Next,weproveProposition5usingLemma4: Proof. AsintheproofforProposition4,notethat dk¯ = (cid:18) ∂k¯ dw¯ + ∂k¯ (cid:19) dr τ = k¯(cid:0) η η +η (cid:1) dr τ 1 . d(1−τ) ∂w¯dr ∂r d(1−τ) k¯,w¯ w¯,rτ k¯,rτ d(1−τ)r τ τ τ Substituting for partial elasticities η k¯,w¯ and η k¯,rτ from Proposition 4, for 1 − η w¯,rτ = 1/βˆ q as in the proofofProposition5andnotingthatdr /d(1−τ) = −r /(1−τ)fromthedefinitionoftheusercost τ τ ofcapital,wehave: (cid:32) (cid:33) dk¯ 1−βˆ βˆ −r 1 = k¯ − k η − k τ d(1−τ) 1−γ w¯,rτ 1−γ (1−τ)r τ (cid:32) (cid:33) dk¯ 1−τ 1 1 βˆ = (1−βˆ (1−η )) = 1− k d(1−τ) k¯ 1−γ k w¯,rτ 1−γ βˆ q Fortheelasticityofaveragelabor,wesimilarlyhave: dn¯ dr 1 τ = n¯(η η +η ) d(1−τ) n¯,w¯ w¯,rτ n¯,rτ d(1−τ)r τ (cid:18) (cid:19) dn¯ 1−αˆ αˆ −r 1 n n τ = n¯ − η − d(1−τ) 1−γ w¯,rτ 1−γ (1−τ)r τ (cid:32) (cid:33) dn¯ 1−τ 1 1−αˆ n = 1− d(1−τ) n¯ 1−γ βˆ q 5

Proof of Proposition 6 Theequilibriumelasticityofaggregatecapitalperworkerwithrespecttothenet-of-taxrateis: (cid:34) (cid:35) ˆ ˆ β −β 1 n k η = η −η = 1+ > 1 K/N,(1−τ) K,(1−τ) N,(1−τ) 1−γ β ˆ q Proof. TheprooffollowsfromProposition5andthefactthatη = η −η . K/N,(1−τ) K,(1−τ) N,(1−τ) B Data Appendix This appendix describes the data and presents some descriptive patterns. The first section lists the data sources, Section B.2 compares the manufacturing labor share obtained from different datasources,andSectionB.3presentstheunderlyingpatternsinthemanufacturinglaborshare andcorporatetaxratesacrosscountriesandUSstates. B.1 Description of Data Sources Data sources for cross-country analysis The OECD and KLEMS data used in Section 2 come from the following sources. Data on labor shares come from the World KLEMS website (worldklems.net). We use the 2011 update of the November 2009 release of the EU KLEMS database. Later releases do not include observations before 1996. We add to this the KLEMS data for Canada from the same website. The manufacturing sector is taken to be the timeseries“TotalManufacturingSector.” Thepre-2000OECDdataoncorporatetaxrateswerecollectedfromTableII.1athttp:// www.oecd.org/tax/tax-policy/tax-database.htm#C_CorporateCapital. Thepost-2000datacomefromTableII.1athttps://stats.oecd.org/index.aspx? DataSetCode=Table_II1%20. Weusethebasiccombinedcentralandsub-central(statutory) corporate income tax rate given by the adjusted central government rate plus the subcentralrate. Data sources for benchmark manufacturing calibration The data targets used in the calibrationofthemodelinSection5comefromthefollowingsources. 6

The entry rate was computed from the Census Bureau’s Business Dynamics Statistics releaseavailableathttps://www.census.gov/ces/dataproducts/bds/data.html. We use data from the manufacturing sector to compute the average exit rate targeted by the model. Thesamedatasetisusedtocomputetheemploymentdistributionsin2014. Targetsfortheaverageestablishmentsize,theconcentrationofemploymentinlargeestablishments, as well as the distributions of establishments across employment and value added are available in the 1970 Statistical Abstract of the United States and draw on the Census of Manufactures.A1 FromtheAnnualSurveyofManufactures(ASM)wefindthatthelaborshare inmanufacturingin1967was53.9percent. Thelaborshareisthesumofallformsofcompensation plus fringe benefits of all employees of operating manufacturing establishments divided by value added. For 1954 we impute fringe benefits using data from 1967. The benefit share of value added was 5.7 percent in that year. Employees comprise all full-time and part-time employees. Employees in administrative offices and auxiliary units are included. Employment in central administration - such as corporate headquarters, as well as proprietors and partners isexcluded. Datasourcesformajorsectorcalibration ToconstructoursampleoffirmsintheCompustatdatabase,weproceedasfollows. FromtheannualCompustatdatabaseweexcludefirm-year observations with an ISO Currency Code different than the US Dollar, firms in the finance, utilities, and government sectors, as well as observations with negative sales or negative total assets. We compute firm-level labor shares as the annual wage bill divided by value added. To compute the wage bill, we use the Compustat variable xlr whenever available. For the remaining observations, we compute the wage bill by multiplying the number of employees with an imputedwagerate. Formissingfirm-yearobservationsthathavenon-missingxlrvaluesforthe same firm in adjacent years, we impute a wage rate by inflating (or deflating) that firm’s wage rate in the adjacent year (xlr divided by number of employees) according to the average rate of wage growth from the QCEW in that firm’s sector. If a firm never reported its wage bill, thenweassignawagebillbymultiplyingthefirm’semploymentwiththeaveragewageratein thatsectorfromQCEW.A2 Valueaddedisdefinedasthewagebillplusearningsbeforeinterest (ebitda) plus the change in inventory (invt). We remove negative observations of value added and trim the resulting labor share at 150 percent following Kehrig and Vincent (2021). We A1The documents can be found at https://www.census.gov/library/publications/ time-series/statistical_abstracts.html. For later years we use data from the Census Bureau’s Annual Survey of Manufactures, available at https://www.census.gov/data/developers/ data-sets/Annual-Survey-of-Manufactures.html. A2If,forinstance,amanufacturingfirmreported40thousanddollarsaveragesalary(xlr/emp)in1980,butdid notreportanysalaryinformationin1981,wemultiply40thousanddollarsbytherateofwageinflationintheUS manufacturingsectorbetween1980and1981asreportedintheQCEW. 7

exclude firms in agriculture and construction because there are very few firms in those sectors intheCompustatdata. Theresultingsector-levellaborsharesarepresentedinTable7. Data sources for US state analysis The US state-level data used Section 7.1 come from the AnnualSurveyofManufactures1972–2012(laborshares),theBEA(unemploymentrates),and the data appendix of Saez and Zucman (2016) (income from corporate taxation). State-level corporate tax rates denote the average corporate tax rate in a state. We focus on mainland US states;thatis,weexcludeAlaskaandHawaii. DatasourcesforUSindustryanalysis TheUSindustry-leveldatacomefromthefollowing sources. Data from the County Business Patterns (CBP) comes from the US Census. Data prior to 1986 are available in the National Archives Catalog, while post-1986 data can be found at the Census website.A3 Our data-cleaning procedure follows that used in Autor et al. (2013),asdoestheconcordancebetweenthe1972and1987SICclassificationsystems. Forthe concordances between the 1997 and 2002 NAICS and the 1987 SIC classification systems, we usetheconcordanceprovidedontheNBER-CESManufacturingIndustryDatabasewebsite.A4 For the years 2007-2012 we use the concordances provided by the US Census.A5 To compute establishmentweights,weusetheestablishmentcountsfromtheCBPdatabase. From the US Economic Census, we obtain information on manufacturing concentration ratios at the four-digit SIC level.A6 We combine these data with state-level average corporate tax rates. We compute industry-specific tax rates by industry-state-time specific establishment shares from the County Business Patterns. Industry-specific tax rates are then computed by weightingstate-timespecificaveragetaxrateswiththeseestablishmentshares. For the regressions in Table D.8, we computed the 10-year differences in the labor share andthesalesconcentrationindicesfrom1972to2012. Thestatetaxdataareonlyavailablefor the years 1974 to 2011. We therefore replaced the differences at the two ends of the sample periodbythedifferenceintheeffectivetaxratefrom1974to1992andfrom1992to2011. A3https://www.census.gov/programs-surveys/cbp.html A4http://www.nber.org/nberces/ A5https://www.census.gov/eos/www/naics/concordances/concordances.html A6Manufacturing concentration data are available from the Census website. Data for years 1947-1992 is available in an Excel file at https://www.census.gov/data/tables/1992/econ/census/ concentraion-ratio-data.html while the post-1992 data are available from the Census’ FTP server athttps://www2.census.gov 8

FigureB.1: Comparisonofmanufacturinglaborsharemeasures B.2 US Manufacturing Labor Share: Definitions and Data Sources Labor share measures can differ across data sources due to differences in how compensation and value added are defined. In Section 5 we calibrated the model to fit key moments of the distribution of establishment labor shares computed from US Census data. In this section we compare the Census labor share to manufacturing labor shares from other data sources, namely the industry-level NIPA data produced by the Bureau of Economic Analysis (BEA), the industry-level data from the Major Sector Productivity and Costs program of the Bureau of Labor Statistics (BLS), and the NBER manufacturing database. The resulting series are compared in Figure B.1 and Table B.1 and are explained below. The upshot of our analysis is that while sources somewhat disagree on the level of the manufacturing labor share, they all showasubstantialdecline,varyingfrom20ppto29ppdependingonsourceanddefinition. The Census and BLS data show a secular decline throughout our sample period, whereas the BEA series show a later but faster decline. We show below that this stems mainly from differences inthedefinitionsofvalueadded. We define the labor share as the ratio of total labor compensation to value added, and the payroll share as the ratio of total payroll to value added, i.e. excluding fringe benefits. Figure B.1 shows the trends in payroll and labor shares from different sources. The left panel shows that while the NBER and Census payroll shares are virtually identical, the BEA measure is shiftedupwards. TherightpanelshowsthattheBLSmeasureofthemanufacturinglaborshare is lower than that of the Census, which in turn is lower than the BEA measure. All series display a large decline, which is summarized in Table B.1. Despite the level differences, all measures have in common a substantial decline by more than 20 percentage points since the 1950s. The BEA and the BLS both compute labor compensation based mainly on information 9

from the Quarterly Census of Employment and Wages (QCEW). Total labor compensation is defined as wages and salaries plus supplements to wages and salaries. Wages and salaries include wages, salaries, commissions, tips, bonuses, severance payments and early retirement buyout payments, supplementary allowances, the exercising of nonqualified stock options, inkind earnings, and supplements to wages and salaries. It specifically includes employees and corporate officers. Supplements to wages and salaries include employer contributions to employee pension and insurance funds and to government social insurance. The unit of analysis isafirm. FromtheBLS,onlytotallaborcompensationisavailable,whereastheBEAdataarebroken down into wages and salaries and supplements to wages and salaries. The BLS adds a fraction of proprietor’s income to total labor compensation. The compensation cost for labor services of proprietors is imputed based on the assumption that it is the same as that of the average employee in a sector. The BEA does not include earnings of the self-employed in total labor compensation.A7 TableB.1: Long-runchangesinvariouslaborsharemeasures NIPA/BEA BLS Census NBER Laborshare -21.3 -20.2 -29.1 Payrollshare -25.8 -29.4 -28.0 Changesareinpercentagepointsbetween1954and2011. TheNBERdatabeginin1958. Payrollsharemeasures fromtheBLSandlaborsharemeasuresfromtheNBERarenotavailable. Seedefinitionsinthetext. The Census data are based on mandatory report forms.A8 It includes each establishment’s total annual payroll, consisting of all forms of compensation paid, such as salaries, wages, tips and gratuities, commissions, bonuses, vacation allowances, sick leave pay, dismissal pay, and employee contributions to qualified pension plans. This measure excludes payments to proprietors. Fringe benefits are computed in a separate variable and include payroll taxes, employer-paid insurance premiums, pension plans, other employer-paid benefits, and profit or other compensation of proprietors or partners of unincorporated businesses. Stock options are included in fringe benefits in the manufacturing censuses. The unit of analysis is an establishment. This implies that compensation of employees in eventual separate headquarters is excluded.A9 Total payroll and total compensation are slightly higher in the BEA data compared to the otherdatasources,mainlyduetothedifferencesinindustrydefinitions. BecausetheBEA’sunit A7Forthemanufacturingsector,thetreatmentoftheself-employedisoflittleconsequenceinpractice. SectorleveltotalcompensationtimeseriesbasedonBLSandBEAdataarevirtuallyidentical. A8This applies to the Census of Manufactures (CMF) and the Annual Survey of Manufactures (ASM). It also appliestotheNBERmanufacturingdatabase,whichdrawsmainlyonvariablesfromtheASM. A9ThesamedatahaverecentlybeenusedinDeLoeckeretal.(2020)andKehrigandVincent(2021). 10

(a)BEAlaborsharemeasures (b)Purchasedservicesinvalueadded FigureB.2: Manufacturingvalueadded: Theroleofpurchasedservices Panel(a):Theblacklinesshowtheratioofcompensationtovalueadded. Theredlinesshowtheratioofcompensationtovalueaddedpluspurchasedservices. Theconnectedx-markersusetotalcompensationfromtheBEA’s industry-levelNIPAtables. TheconnecteddotsusetotalcompensationdatafromtheBEA’sKLEMSdata. Panel (b): DatacomefromtheBEAKLEMS. of analysis is a firm, not an establishment, remuneration to corporate headquarters is included in the BEA’s measure. In addition, the population of manufacturing production sites need not fully overlap with that of the Census, as some manufacturing plants that are part of a firm that isclassifiedinadifferentsectormightbeexcludedfromtheBEAdataandviceversa. The denominators of the labor and payroll share definitions differ across data sources, mainly due to the BEA’s treatment of purchased services, which are subtracted from its value added measures, but not from those of the Census (and NBER).A10 While the denominator in the BLS measure of the aggregate labor share is value added, to compute the manufacturing labor share, sectoral output (sales to final demand plus the intermediate goods sent to other industries)isused. Panel (a) of Figure B.2 shows versions of the BEA labor share measures that include purchased services in value added and compare it to the original series. Including purchased services lowers the labor share but hardly affects the substantial decline of slightly above 20 percentage points between 1963 and 2019. Panel (b) shows the share of purchased services in value added including purchased services. The relative share increases from the 1960s until 1990 and declines after 2000. This hump-shaped pattern results in a smaller decline in the BEA manufacturing labor share at the beginning of our sample and an acceleration after 2000 relativetotheCensusmeasure. Historical BEA data are based on the SIC industry classification system. The revisions to the historical series have, as of 2020, only been extended back to the year 1986. The revised A10SeealsoAppendixD.4inAutoretal.(2020). 11

data are part of the BEA KLEMS data set, which is fully consistent with the BEA’s industrylevelNIPAdatafrom1997on. B.3 Patterns in Corporate Taxation and Labor Shares across Countries and US States Trends in country-level statutory corporate tax rates together with manufacturing labor shares are shown in Figure B.3 for the countries in our sample. Countries with short panels (Estonia, Korea,Latvia,Lithuania,Luxembourg,Slovenia,andSlovakia)wereexcludedfromthefigure. ThesecountriesareincludedintheanalysisinSection2. Excludingthemfromourregressions doesnotaffectourresults. FigureB.3: Trendsinstatutorycorporatetaxratesandlaborsharesbycountry Trends in statutory corporate tax rate and labor’s share of income in the manufacturing sector for each country. Corporatetaxratesareshownontherighty-axis. Source: OECDandKLEMS. Trends in state-level effective corporate tax rates together with manufacturing labor shares areshowninFiguresB.4andB.5. 12

FigureB.4: Trendsineffectivecorporatetaxratesbystate: Alabama-Nebraska Effectivetaxratesarecalculatedastheratiooftotalcorporatetaxrevenueandgrossoperatingsurplusinastate andaretakenfromSaezandZucman(2016). 13

7.1 5.0 5.2 8.0 8.2 3.0 4.0 3.0 4.0 2.0 5.0 3.0 4.0 2.0 5.0 3.0 3.3 0.1 8.1 4.0 5.2 2.0 3.1 4.0 0.2 7.0 5.0 3.0 4.0 2.0 5.0 4.0 5.0 3.0 5.0 3.0 4.2 9.0 5.1 1.0 0.2 3.0 7.1 6.0 5.0 3.0 5.0 3.0 5.0 3.0 5.0 3.0 4.0 1.0 6.1 4.0 0.1 3.0 6.0 0.0 3.1 3.0 4.0 1.0 5.0 3.0 5.0 2.0 5.0 2.0 4.2 7.0 8.1 3.0 4.1 7.0 5.0 3.0 5.0 2.0 4.0 3.0 5.0 3.0 Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington 1970 1990 2010 1970 1990 2010 West Virginia Wisconsin Wyoming 1970 1990 2010 1970 1990 2010 1970 1990 2010 Year Corporate Tax Rate (left axis, %) Payroll Share (right axis) FigureB.5: Trendsineffectivecorporatetaxratesbystate: Nevada-Wyoming Effectivetaxratesarecalculatedastheratiooftotalcorporatetaxrevenueandgrossoperatingsurplusinastate andaretakenfromSaezandZucman(2016). 14

C Model Calibration: Details for Section 6 In Section 6, we calibrate the model for a number of major economic sectors. To do so, we constructsector-specificmomentsfromtheCensusBDSandCompustataroundtheinitialyear, 1985, when the sector-specific data on tax returns become available from the IRS. The Census BDSprovidesindustry-specificstatisticsonexitrates,averagefirmsize,andemploymentconcentration and is available starting in 1987. We use the reported values for 1987 as calibration targets. The targets for the average labor share and the ratio of the value added weighted median labor share to the unweighted median labor share are computed in Compustat using data forthe10yearspriorto1985. Wecombinemultipleyearstoensureasufficientlylargesample sizeforthecalculationofdistributionalmomentsofthefirm-levellaborshares. Next, we calibrate our model for each sector, using the appropriate sector-specific empirical targets. The discount rate, the capital depreciation rate, and the span-of-control parameters are kept at the levels reported in Table 2. In our benchmark analysis of the manufacturing sector, we assumed that labor shares follow a symmetric triangular distribution across firms. Because several of the non-manufacturing sectors display non-symmetric labor share distributions,weintroduceanewparameter,m,whichcontrolsthemodeofthetriangulardistribution. γ−β In the symmetric case, the mode is given by m = , where γ and β respectively define the 2 minimum and maximum of the distribution. To calibrate m, we target an additional empirical moment: theratioofthevalue-addedweightedstandarddeviationoflaborsharesoverthemedian value-added labor share. A lower mode m skews the distribution of labor shares toward low-labor-sharefirmsandincreasesthestandarddeviation.A11 TableC.1: Sector-specificcalibrationresults Sector Data Model (1) (2) (3) (4) (5) (6) (1) (2) (3) (4) (5) (6) Manufacturing 0.604 0.924 0.104 54.0 0.528 0.309 0.616 0.869 0.104 54.0 0.529 0.326 Mining 0.408 0.761 0.208 23.0 0.524 0.682 0.405 0.766 0.208 23.0 0.524 0.681 TCPU 0.706 0.986 0.129 24.0 0.537 0.191 0.712 1.00 0.129 24.0 0.537 0.191 WholesaleTrade 0.588 0.924 0.113 13.0 0.379 0.315 0.587 0.912 0.113 13.0 0.379 0.314 RetailTrade 0.610 0.950 0.135 13.0 0.370 0.200 0.644 0.937 0.135 13.0 0.370 0.209 Services 0.687 0.954 0.106 14.0 0.565 0.230 0.672 0.965 0.106 14.0 0.565 0.230 The moments are: (1) the average labor share, (2) the ratio of the value-added median labor shares over the unweightedmedianlaborshare,(3)theexitrate,(4)theaveragefirmsizein1987,(5)thefractionofemployment inthelargestfirms,(6)theratioofthevalue-addedweightedstandarddeviationoflaborsharesoverthemedian value-addedlaborshare. The sector-specific tax rates are available from the IRS website in SIC format for the years 1985,1990,1995,1996,and1997andinNAICSformatfrom1999–2013. Wemapthesingledigit NAICS values to single-digit SIC values. Each sector is calibrated using the respective A11For comparability, we also recalibrate the 1985 manufacturing sector level using the new empirical targets. Ourresultsarequantitativelyverysimilarifwedonotrecalibratethemodeofthetriangulardistributionforthe manufacturingsectorbutleaveitunchangedfromthesymmetriccase. 15

1985 tax rate. The IRS only reports tax rates for an aggregate trade sector. We apply the same taxratetofirmsinthewholesaleandretailtradesectors. To calibrate the model parameters for each sector, we minimize the difference between the sixdatamomentsinthatsectorandthecorrespondingvaluesimpliedbythemodel. Theresults are listed in Table C.1. The associated parameter values are shown in Table C.2. The fit of the modelisveryhighandiscomparabletotheresultsreportedinthemaintext. TableC.2: Sector-specificcalibrationresults: Parametervalues Sector Parameter µ σ x β m c ε ε e Manufacturing 0.860 0.270 0.104 0.301 1.379 115.62 Mining 0.901 0.260 0.208 0.164 3.261 92.90 TCPU 0.863 0.268 0.129 0.414 1.143 36.88 WholesaleTrade 0.699 0.207 0.113 0.312 1.827 32.00 RetailTrade 1.102 0.198 0.135 0.431 1.739 37.10 Services 0.451 0.276 0.106 0.382 1.291 26.36 Tableshowsthecalibratedparametervaluesformajorsectors. To construct Figure 5, we simulate a new steady state for each sector using its effective corporate tax rate in 2013 and compute the change in the labor share between steady states. Weplotthosechangesagainsttheactualdecline,asreportedbytheBEA.Toconstructthedata point for the actual change in the trade-sector labor share, we weight the wholesale and retail tradesectorsbytheirvalue-addedin1985. D Additional Results and Sensitivity D.1 Employment Concentration in the US FigureD.1showsthetrendsinmanufacturingemploymentconcentrationatthefirmlevel(panel a) and at the establishment level (panel b). The concentration measures at the firm level come from the BDS data, and show a downward trend regardless of the employment cutoff used to measure concentration. To compute the concentration measures for a longer horizon, we supplement the BDS data, available starting in 1977, with establishment-level data from the quinquennial Census of Manufactures for the years 1954–1972. The trends in manufacturing establishment-level employment concentration mirror those of firm-level concentration. Conditioning the concentration measures to establishments with at least 20 employees does not changethepatterns. 16

(a)Firm-level (b)Establishment-level FigureD.1: Manufacturingemploymentconcentration ConcentrationisdefinedbytheinverseoftheParetoindeximpliedbytheshareofemploymentamongthelargest firms (establishments). Letting s denote the share of firms (establishments) with more than x employees, and x e their share in total employment, the Pareto index is computed by ι = logs /(logs −loge ). Panel (a) x P x x x shows the concentration among firms with more than 1,000, 5,000, and 10,000 employees. Panel (b) shows the concentration among establishments with more than 250 and 1000 employees. The lines labeled (> 20) only showtherespectiveindicesconditioningonestablishmentswithatleast20employees. Sources:BDSandCensus ofManufacturers. D.2 Capital-Labor Ratios Across Countries WetestfortheeffectsofcorporatetaxesoncapitalinvestmentbylinkingaggregateK/N ratios from Penn World Table v9.1 to corporate tax rates for a subset of countries in our sample. We compute K/N by dividing the total capital services in a country by the total number of hours worked. Figure D.2 shows the changes in aggregate capital-labor ratios against the changes in the corporate tax rates between 1981 and 2007. The plot includes a fitted line from robust estimationandshowsanegativerelationship. TableD.1showsaformaltestofthisrelationship. ThedependentvariableisthelogofK/N andtheregressorsarelistedintherows. Column(1)showsthatcountrieswheretaxratesfellby more saw an increase in their aggregate capital intensity. Column (2) controls for capital costs andtotalfactorproductivity. BecausetheCzechRepublicandLuxembourgarevisibleoutliers in Figure D.2, we re-estimated these regressions using a robust estimation method in Columns (3)-(4). The results are broadly similar, with slightly lower but more precise tax elasticities.A12 Overall, the estimated tax elasticities are in the -0.3 to -0.5 range depending on specification. Columns (5)-(8) include controls for country-specific trends. These estimates assume that the long-run association between tax rates and the capital-labor ratio is attributable to factors outside the model that affect tax rates and capital per worker at the same time. As a result, they reflect a short-to-medium run response of the capital-labor ratio to taxes. The estimated size A12FollowingKarabarbounisandNeiman(2013),weusethe‘rreg’commandinStatatoperformtheseestimations. Thetwo-stepGLSestimatesyieldsimilarresults. 17

CCCZZZEEE HHHUUUNNN AAAUUUSSS DDDNNNKKK FFFIIINNN PPPOOOLLL IIIRRRLLL AAAUUUTTT GGGEEERRR SSSWWWEEE PPPRRRTTT JJJ UUU PPP SSS NNN AAA FFFRRRAAA CCCAAANNN UUUKKK GGGRRRCCC BBBEEELLL LLLVVVAAA EEESSSTTT EEESSSPPPIIITTTAAA NNNLLLDDD LLLTTTUUU KKKOOOSSSRRRVVVNNN LLLUUUXXX tnemyolpmE / latipaC Δ 1 8. 6. 4. 2. 0 -40 -30 -20 -10 0 Δ Corporate Tax Rate (%) FigureD.2: Corporatetaxesandcapital-laborratios: 1981–2007 Figure shows the change in aggregate log capital-labor ratio between 1981 and 2007 against the change in the corporatetaxrate(inpercentagepoints). Source. OECDandPennWorldTablev9.1. effects are qualitatively consistent with the model, but are quantitatively smaller. Considering thattime-to-buildcanbelongforcapitalstock,weviewtheseshorter-runresponsesasalower boundoncapital’sresponseinthelongrun. TableD.2showsresultsfromthedifferencespecificationusing10-yeardifferences(Columns 1and3)and20-yeardifferences(Columns2and4)controllingforfixedyeareffects. Columns 3 and 4 additionally include changes in the relative price of capital and TFP as control variables. Consistent with the levels specification, results show a negative association between the capital-laborratioandthetaxratewithanelasticityofaround0.5percentacrossspecifications. D.3 Difference Regressions This section presents estimation results from additional specifications. In the main text, we reportedresultsfromregressionsinlevelsofthevariablesofinterestwithfixedeffectsforstates (or industries) and years. Those specifications are superconsistent for long-run relationships between variables. Versions of those specifications with state-specific, or industry-specific trends are identified by shorter-run variations instead. They resulted in different coefficient estimates for variables that theoretically display different reactions in the long-run and the short-run. Forexample,theinvestment-to-capitalratiotemporarilyincreasesintheshort-runin response toa lower taxrate, but reverts backto its initiallevel in the long-run. Here, wereport 18

TableD.1: Corporatetaxcutsandcapital-laborratio: OECD1981–2007 (1) (2) (3) (4) (5) (6) (7) (8) Corporatetaxrate -0.48 -0.54 -0.34 -0.29 -0.18 -0.20 -0.07 -0.07 (0.16) (0.20) (0.04) (0.04) (0.12) (0.13) (0.03) (0.03) Priceofcapital -0.13 -0.09 -0.10 0.00 (0.09) (0.02) (0.11) (0.02) TFP -0.03 0.10 -0.14 0.00 (0.12) (0.03) (0.10) (0.02) N 579 579 579 579 579 579 579 579 The dependent variable is the aggregate capital-labor ratio. Standard errors are clustered at the country level in Columns (1)-(2). Columns (3)-(4) employ a robust estimation method to correct for outliers. All regressions controlforfixedcountryandyeareffects. TableD.2: Corporatetaxcutsandcapital-laborratio: OECD1981–2007 (1) (2) (3) (4) ∆TaxRate(x100) -0.50 -0.49 -0.54 -0.52 (0.20) (0.17) (0.23) (0.15) N 318 119 318 119 Thedependentvariableisthechangeintheaggregatecapital-laborratioover10yearsinColumns1and3, and over20yearsinColumns2and4. Allspecificationsincludefixedyeareffects. Columns2and4alsoincludethe changeinthepriceofcapitalandTFPascontrols. Standarderrorsareclusteredatthecountrylevel. 19

results from difference specifications. Note that difference regressions mechanically eliminate long-run, co-integrating relationships. Because our focus is on those long-run relationships, we try to circumvent this issue by taking differences over 10 years, which we assume are sufficientlylongforshort-rundynamicstohaveplayout. Tables D.3 to D.6 show the estimates from difference specifications for regressions in Tables 1, 8, 9, and 10 in the main text. The coefficient estimates are qualitatively consistent with the estimates reported in the main text. In most cases, the point estimates are close to those reported from the levels specifications, and, therefore, are statistically comparable. One exception is the tax elasticity of capital-per-worker in Table D.5, which is 0.02 (0.08) in 10-year differences, whereas the levels estimate in Table 9 is -0.25 (0.09). This is somewhat surprising given that the tax elasticity of investment is significantly negative, both in the level- and difference specifications. One would expect higher investment expenditures in response to lower taxes to manifest in a higher capital stock over time. A possibility is that 10 years may not be sufficientlylongtorecoverthelong-runrelationshipbetweentaxesandthecapitalstockindifferenceform. Indeed,becauseK/N ishighlypersistentinthedata,withanannualpersistence of 0.95, the half-life of a shock to the capital stock is about 20 years. Therefore, in Table D.6, wereportresultsfromadifferencespecificationover20years. Theestimatedcoefficientonthe corporatetaxrateis-0.30(0.12)inthiscase,closethe-0.25(0.09)inTable9. Table D.7 shows the estimates in Columns 1 and 2 of Table 11 for all concentration measures,definedbythevalueaddedsharesofthetop4,8,20and50firmsintheindustry. Concentration measures that rely on a larger number of firms generally yield smaller standard errors and larger size effects in response to tax changes. Table D.8 shows the same regressions estimated in difference form. The coefficient estimates are comparable to those from the levels specification in Table D.7. Table D.9 shows the difference specification results for sales-based concentration measures for varying sampling periods. The estimates are consistent with the estimatesfromthelevelsspecificationsreportedinTable11. In the main text, we did not report results from a specification that allows for industryspecific trends in value-added concentration. Because the underlying data is quinquennial, there are four data points for each industry during the 1997–2012 period, which is too few to estimate the fixed effects, trends and tax elasticities in a statistically robust manner. Here, we attempt to control for industry trends by combining sales-based measures of concentration at the SIC-4 level between 1972 and 2012, which gives 8 data points for each industry. All estimatesshouldbeinterpretedsubjecttothatcaveat. We start by revisiting the levels specifications (without industry trends) for the combined sample period. Columns 1 through 4 of Table D.10 shows the sales concentration regressions for the full sample for all sales-based concentration measures (top 4, 8, 20 or 50 firms). These estimates do not control for industry-specific trends and are comparable to the results reported 20

in Table 11 for all sales-based concentration measures. The results are qualitatively similar: lower effective tax rates in an industry are associated with higher market concentration. The coefficient estimates are somewhat lower in this combined sample (1972–2012 period) than in each of the sub-period reported in Table 11, namely the 1972–1992 period and the 1997–2012 period. A possible explanation for this is the change in the industrial classification system in the data between 1992 and 1997. The crosswalk we use between the two industrial classifications could be a source of measurement error in the combined sample, resulting in attenuated coefficientestimates. Toaccountforthatpossibility,Panelsc)andd)interactthefixedindustry effectswithanindicatorvariableforpost-1992data. Accountingfortheclassificationchanges resultsincoefficientestimatesthatarecomparableinmagnitudetothoseinTable11. The results from specifications with industry-specific trends in sales concentration are reported in Columns 5-8 of Table 11. Once again, the results are consistent with a negative relationship between the tax rates and concentration, as also indicated by the levels specifications reported in Columns 1-4. The point estimates are somewhat lower, suggesting that the responseofsalesconcentrationtotaxratesbuildsslowlyovertime,leadingtolargerelasticities inthelong-runthanintheshort-run. TableD.3: Changesincorporatetaxationandlaborshareacrosscountries (1) (2) (3) (4) Manufacturing Aggregate Manufacturing Aggregate ∆Corporatetaxrate 0.29 0.12 0.16 0.10 (0.09) (0.04) (0.07) (0.05) Countrytrendeffects no no yes yes N 309 309 309 309 The dependent variable is the change in labor’s share of income in a country over 10 years. All specifications control for fixed year effects. Specifications (3)-(4) control for fixed country (trend) effects. Standard errors in parenthesesareclusteredatthecountrylevel. Source: OECDandKLEMS. 21

TableD.4: ChangesincorporatetaxationandthelaborshareacrossUSstates (1) (2) (3) (4) (5) (6) ∆Corporatetaxrate 2.02 1.73 2.53 2.22 3.03 2.79 (0.79) (1.09) (0.79) (1.09) (1.01) (1.35) ∆logwage 0.12 0.17 0.12 0.16 (0.04) (0.05) (0.05) (0.08) ∆Unemploymentrate 0.36 0.24 (0.19) (0.20) Statetrendeffects no yes no yes no yes N 288 288 288 288 240 240 Thedependentvariableisthechangeinpayrollshareofvalueaddedinthemanufacturingsectorofastateover 10years. Corporatetaxratedenotestheaveragecorporatetaxrateinastate. Allspecificationscontrolforfixed yeareffects. Columns2,4and6includefixedstate(trend)effects. Standarderrorsinparenthesesareclusteredat thestatelevel. DatacomefromtheAnnualSurveyofManufactures1972–2012,theBEA,andSaezandZucman (2016). Thelasttwocolumnscoverthe1977to2012period. Standarderrorsinparentheses. TableD.5: Capitaldeepening,sectorsize,andlaborshareinUSmanufacturing (1) (2) (3) (4) ∆log(K/N) ∆log(I/N) ∆log(I/K) ∆log(estabs.) Panel(a) ∆LaborShare 0.17 -1.05 -1.22 -0.26 (0.08) (0.13) (0.16) (0.10) Panel(b) ∆TaxRate(x100) 0.02 -0.10 -0.12 -0.33 (0.08) (0.09) (0.12) (0.10) ∆ denotes differences over 10 years. All specifications control for fixed year effects (4-digit SIC). Standard errorsinparenthesesareclusteredbysector. DatacomefromtheNBERManufacturingIndustryDatabase1958– 2011. Dataonthenumberofestablishmentsbyindustry(specification(3))comefromCountyBusinessPatterns and covers the 1974 to 2011 period. An industry’s corporate tax rate is the establishment-weighted average of effectivestatecorporatetaxrates. Seetextfordetails. 22

TableD.6: Capitaldeepening,sectorsize,andlaborshareinUSmanufacturing (1) (2) (3) (4) ∆log(K/N) ∆log(I/N) ∆log(I/K) ∆log(estabs.) Panel(a) ∆LaborShare -0.09 -1.07 -0.98 -0.28 (0.15) (0.16) (0.17) (0.17) Panel(b) ∆TaxRate(x100) -0.30 -0.23 0.07 -0.46 (0.12) (0.10) (0.13) (0.13) ∆ denotes differences over 20 years. All specifications control for fixed year effects (4-digit SIC). Standard errorsinparenthesesareclusteredbysector. DatacomefromtheNBERManufacturingIndustryDatabase1958– 2011. Dataonthenumberofestablishmentsbyindustry(specification(3))comefromCountyBusinessPatterns and covers the 1974 to 2011 period. An industry’s corporate tax rate is the establishment-weighted average of effectivestatecorporatetaxrates. Seetextfordetails. TableD.7: ValueaddedconcentrationandtaxesinUSmanufacturing DependentVariable con-4 con-8 con-20 con-50 Panel(a) LaborShare -0.20 -0.16 -0.13 -0.08 (0.09) (0.07) (0.05) (0.03) Panel(b) TaxRate(x100) -0.77 -2.15 -5.14 -6.86 (3.40) (3.05) (2.47) (3.06) The measure of concentration is the inverse of the Pareto index implied by the share of value added among the top4,8,20or50firmsintheindustry. Anindustry’scorporatetaxrateistheestablishment-weightedaverageof effectivestatecorporatetaxrates. Eachcellrepresentsaseparateregressionandallspecificationsincludeindustry andyearfixedeffects. Standarderrorsareclusteredatthesectorlevel. 23

TableD.8: ValueaddedconcentrationandtaxesinUSmanufacturing DependentVariable ∆con-4 ∆con-8 ∆con-20 ∆con-50 Panel(a) ∆LaborShare -0.22 -0.19 -0.16 -0.11 (0.09) (0.07) (0.05) (0.04) Panel(b) ∆TaxRate(x100) 1.77 -0.42 -5.27 -7.72 (3.62) (3.33) (2.80) (3.75) ∆denotesdifferencesover10years. ThemeasureofconcentrationistheinverseoftheParetoindeximpliedby theshareofvalueaddedamongthetop4, 8, 20or50firmsintheindustry. Theexplanatoryvariableofinterest isreportedinthefirstcolumn. Anindustry’scorporatetaxrateistheestablishment-weightedaverageofeffective statecorporatetaxrates.Eachcellrepresentsaseparateregressionandallspecificationsincludeyearfixedeffects. Standarderrorsareclusteredatthesectorlevel. 24

TableD.9: SalesconcentrationandtaxesinUSmanufacturing DependentVariable ∆con-4 ∆con-8 ∆con-20 ∆con-50 Panel(a): 1972–1992 ∆LaborShare -0.05 -0.03 -0.04 -0.03 (0.05) (0.03) (0.01) (0.02) Panel(b): 1972–1992 ∆TaxRate(x100) -0.30 -2.24 -3.35 -3.56 (1.99) (1.53) (1.13) (0.80) Panel(c): 1997–2012 ∆LaborShare -0.17 -0.15 -0.12 -0.10 (0.07) (0.06) (0.04) (0.04) Panel(d): 1997–2012 ∆TaxRate(x100) 1.96 0.63 -4.02 -6.75 (3.23) (3.05) (2.44) (3.33) Panel(e): 1972–2012 ∆LaborShare -0.11 -0.10 -0.08 -0.06 (0.04) (0.03) (0.02) (0.02) Panel(f): 1972–2012 ∆TaxRate(x100) 1.08 -0.29 -1.73 -2.64 (1.36) (1.13) (0.91) (0.87) ∆ denotes differences over 10 years. The measure of concentration is the inverse of the Pareto index implied by the share of sales among the top 4, 8, 20 or 50 firms in the industry. The explanatory variable of interest is reported in the first column. An industry’s corporate tax rate is the establishment-weighted average of effective statecorporatetaxrates.Eachcellrepresentsaseparateregressionandallspecificationsincludeyearfixedeffects. Standarderrorsareclusteredatthesectorlevel. 25

TableD.10: Salesconcentration,laborshareandtaxesinUSmanufacturing con-4 con-8 con-20 con-50 con-4 con-8 con-20 con-50 Panel(a) LaborShare -0.11 -0.08 -0.06 -0.05 -0.08 -0.07 -0.06 -0.04 (0.04) (0.04) (0.02) (0.02) (0.04) (0.03) (0.02) (0.01) Panel(b) TaxRate(x100) 2.44 0.13 -1.02 -1.58 1.01 -0.58 -1.55 -2.23 (1.62) (1.42) (1.18) (0.99) (1.70) (1.44) (1.12) (0.90) Panel(c) LaborShare -0.11 -0.09 -0.07 -0.06 -0.07 -0.06 -0.05 -0.03 (0.04) (0.03) (0.02) (0.02) (0.04) (0.03) (0.02) (0.01) Panel(d) TaxRate(x100) -1.53 -3.21 -4.21 -4.19 0.89 -0.54 -1.52 -2.53 (1.50) (1.36) (0.98) (0.90) (1.73) (1.46) (1.14) (1.05) IndustryTrends no no no no yes yes yes yes ThemeasureofconcentrationistheinverseoftheParetoindeximpliedbytheshareofsalesamongthetop4,8, 20or50firmsintheindustry. Anindustry’scorporatetaxrateistheestablishment-weightedaverageofeffective statecorporatetaxrates. Eachcellrepresentsaseparateregressionandallspecificationsincludeindustryandyear fixedeffects. Panels(c)and(d)interactfixedindustryeffectswithanindicatorforpost-1992surveystoaccount for the change in industrial classification systems in the data. Columns (4)-(8) include industry-specific trends. Standarderrorsinparenthesesareclusteredatthesectorlevel. 26