Industry Evidence on the Effects of Government Spending

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Industry Evidence on the Effects of Government Spending Christopher J. Nekarda and Valerie A. Ramey 2010-28 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Industry Evidence on the Effects of Government Spending Christopher J. Nekarda Federal Reserve Board of Governors Valerie A. Ramey University of California, San Diego and NBER First version: December 2009 This version: February 2010 Abstract This paper investigates industry-level effects of government purchases in order to shed light on the transmission mechanism for government spendingontheaggregateeconomy. Webeginbyhighlightingthedifferent theoretical predictions concerning the effects of government spendingonindustrylabormarketequilibrium. Wethencreateapaneldataset thatmatchesoutputandlaborvariablestoshiftsinindustry-specificgovernment demand. The empirical results indicate that increases in government demand raise output and hours, but lower real product wages and productivity. Markups do not change as a result of government demand increases. The results are consistent with the neoclassical model of government spending, but they are not consistent with the New Keynesianmodeloftheeffectsofgovernmentspending. The views in this paper are those of the authors and do not necessarily represent the views or policies of the Board of Governors of the Federal Reserve System or its staff. ValerieRameygratefullyacknowledgesfinancialsupportfromNationalScience Foundation grant SES-0617219 through the National Bureau of Economic Research. WethankRobertBarro,MinOuyang,andGaryRichardsonforveryusefulcomments.

1 Introduction The recent debate over the government stimulus package has highlighted the lack of consensus concerning the effects of government spending. While most approaches agree that increases in government spending lead to rises in output and hours, they differ in their predictions concerning other key variables. For example, a key difference between the neoclassical approach and the New Keynesian approach to the effectsofgovernmentspendingisthebehaviorofrealwages. Theneoclassicalapproach predicts that an increase in government spending raises labor supply through a negative wealth effect.1 Under the neoclassical assumption of perfect competition and diminishing returns to labor, the rise in hours should be accompanied by a short-run fallinrealwagesandproductivity. Incontrast,thestandardNewKeynesianapproach assumes imperfect competition and either sticky prices or price wars during booms. This model predicts that a rise in government spending lowers the markup of price over marginal cost. Thus, an increase in government spending can lead to a rise in both real wages and hours, despite a decline in productivity.2 In alternate versions ofthisapproach,increasingreturnscanallowanincreaseingovernmentspendingto raiserealwage,hours,andproductivity.3 In this paper, we seek to shed light on the transmission mechanism by studying theeffectsofindustry-specificgovernmentspendingonhours,realwagesandproductivity on a panel of industries. As Ramey and Shapiro (1998) point out, an increase in government spending is typically focused on only a few industries. Thus, there is substantial heterogeneity in the experiences of different industries after an increase ordecreaseingovernmentspending. Thisheterogeneityallowsustostudythepartial equilibriumeffectsofgovernmentspendinginisolationsinceourpaneldatastructure permits the use of time fixed effects to net out the aggregate effects. Since the partial equilibrium effects are components of the overall transmission mechanism, it is instructivetostudytheseinisolation. Building on the ideas of Shea (1993), Perotti (2008), and Ouyang (2009), we use information from input-output (IO) data to create industry-specific government 1. See,forexample,BaxterandKing(1993). 2. See,forexample,RotembergandWoodford(1992). 3. See,forexample,Devereuxetal.(1996). 1

demand variables. We then merge these variables with the National Bureau of Economic Research (NBER) Manufacturing Industry Database (MID) to create a panel datasetcontaininginformationongovernmentdemand,hours,output,andwagesby industry. The empirical results indicate that increases in government demand raise output andhourssignificantly. Ontheotherhand,realproductwagesandlaborproductivity fall slightly. Markups are unchanged. We show that real product wages and labor productivitydonotfallmuchbecauseotherinputsalsorise. Alloftheresultsareconsistent with the neoclassical model. They are not consistent with the key mechanism oftheNewKeynesianmodel. 2 Relationship to the Literature Theexistingempiricalevidenceontheeffectsofgovernmentspendingonrealwages is mixed. Rotemberg and Woodford (1992) were perhaps the first to conduct a detailed study of the effects of government spending on hours and real wages. Using a vector autoregression (VAR) to identify shocks, they found that increases in military purchases led to rises in private hours worked and rises in real wages. Ramey and Shapiro (1998), however, questioned the finding on real wages in two ways. First, analyzing a two-sector theoretical model with costly capital mobility and overtime premia, they showed that an increase in government spending in one sector could easily lead to a rise in the aggregate consumption wage but a fall in the product wage in the expanding sector. Rotemberg and Woodford’s (1992) measure of the real wage was the manufacturing nominal wage divided by the deflator for private value added, which was a consumption wage. Ramey and Shapiro (1998) showed thattherealproductwageinmanufacturing,definedasthenominalwagedividedby theproducerpriceindexinmanufacturing,infactfellafterrisesinmilitaryspending. Second,RameyandShapiro(1998)arguedthatthestandardtypesofVARsemployed byRotembergandWoodfordmightnotproperlyidentifyunanticipatedshockstogovernment spending. With their alternative measure, they found that all measures of productwagesfellafterariseinmilitaryspending,whereasconsumptionwageswere essentially unchanged. Subsequent research that has used standard VAR techniques 2

to identify the effects of shocks on aggregate real consumption wages tend to find increasesinrealwages.4 ResearchthathasusedtheRamey-Shapiromethodologyhas tendedtofinddecreasesinrealwages.5 Barth and Ramey (2002) and Perotti (2008) are two of the few papers that have studied the effect of government spending on real wages in industry data. Barth and Ramey (2002) used monthly data to show that the rise and fall in government spendingonaerospacegoodsduringthe1980sCarter-Reagandefensebuildupledto a concurrent rise and fall in hours, but to the opposite pattern in the real product wageinthatindustry. Thatis,ashoursincreased,realproductwagesdecreased,and vice versa. Perotti (2008) used IO tables to identify the industries that received most of the increase in government spending during the Vietnam War and during the first partoftheCarter-Reaganbuildupfrom1977–82. Basedonaheuristiccomparisonof thechangeinrealwagesamonghisrankingofindustries,Perotticoncludedthatreal wages increased when hours increased. In the companion discussion, Ramey (2008) questionedseveralaspectsoftheimplementation,includingPerotti’sassumptionthat there had been no changes in capital stock and technology during each five year period. Asecondconcernwasthefactthatthesemiconductorandcomputerindustries wereinfluentialobservationsthatweredrivingthekeyresults. On the other hand, most research tends to find an increase in labor productivity attheaggregatelevel,althoughitisnotoftenhighlighted. Forexample,eventhough their different identification methods lead to fundamentally different results for consumption and real wages, the impulse response functions of both Galí et al. (2007) andRamey(2009b)implythataggregatelaborproductivityrisesafteranincreasein governmentspending. Insum,theevidenceforrealwagesisquitemixed,whiletheevidenceforproductivity is less mixed but often ignored. Therefore, it is useful to study the behavior of realwagesandotherlaborvariablesinmoredetail. 4. See,forexample,FatásandMihov(2001),Perotti(2004),Pappa(2005),andGalíetal. (2007). 5. See,forexample,Burnsideetal.(2004),Cavallo(2005),andRamey(2009b). 3

3 Industry Labor Market Equilibrium Inthissection,weconsiderhowgovernmentspendingcanaffectequilibriumemployment and wages in an industry under various model assumptions. We then use the theory to derive reduced-form predictions of the various models for the variables of interest. To begin, consider the first-order condition describing the demand for labor in industry i inyear t: W (1) A F (cid:0) H ,X (cid:1)=Mu it it H it it it P it The left hand side is the marginal product of labor, with Aas technology, H as hours, and X as a vector of other inputs, including capital. For a neoclassical production function, we require F > 0 and F < 0. The right hand side is the markup, Mu, H HH timestherealproductwage. The supply of labor to the industry depends on aggregate effects, and potentially on industry-level variables as well. The aggregate Frisch labor supply depends positively on the real consumption wage and the marginal utility of wealth, as in RotembergandWoodford(1991). Thus,wecanwritetheFrischlaborsupplyoflaboras (cid:18)W P (cid:19) (2) H =η it it ,λ . it t P P it Ct In this equation, W is the wage in industry i, P is the consumption goods price dei C flator, and λ is the marginal utility of wealth. Labor supply depends positively on both arguments. The first argument is just the consumption wage, which we have writtenastheproductwageinindustry i timestherelativepriceofindustry i. Potentially, we could include a third term as well, consisting of the industry relative wage. For example, if the expanding industry must pay an overtime premium, as in one of the models analyzed by Ramey and Shapiro (1998) or if there are adjustment costs of labor across industries, as in Kline (2008), then it is possible that the wage in an expandingindustryrisesrelativetowagesinotherindustries. Figure1combinesthesesupplyanddemandequationstoshowequilibriuminthe industry’slabormarket. Panel(a)considersthelabormarketeffectsofanincreasein 4

governmentspendingintheneoclassicalmodel. Theincreaseingovernmentspending raises the marginal utility of wealth, which shifts the aggregate labor supply curve out. Iftheindustryreceivesmoreofthegovernmentdemand,thentheindustryprice shouldriserelativetootherprices. Thus, P/P shouldrise,whichalsoshiftsoutlabor i C supply to this industry. As a result, equilibrium hours rise and the real product wage andproductivityfall. Incontrast,anindustrythatdoesnotreceiveanyincreaseingovernmentspending mayexperienceadeclinein P/P thatislargeenoughtocounteracttheriseinλ. In i C this case, labor supply curve shifts in. Thus, this industry would experience a decline inhours,anincreaseintherealproductwageandanincreaseinproductivity. Panel (b) considers the effects of countercyclical markups in the New Keynesian modelforanindustryreceivingpartoftheincreaseingovernmentspending. Because thenegativewealtheffectisstilloperativeinthestandardNewKeynesianmodel,the supplycurveshiftsout,butnowthedemandcurvealsoshiftsoutbecausethemarkup hasfallen. Thegraphmakesclearthattheexpansionaryeffectonequilibriumhoursis evengreater,buttheeffectontherealwageisambiguous. Nevertheless,productivity stillfalls. Panel(c)considerstheincreasingreturnsmodelofDevereuxetal.(1996). Intheir model,firm-levellabordemandcurvesslopedown,butifreturnstospecializationare sufficiently high, industry-level demand curves can slope upward. In this case, the shift out of labor supply to the industry can lead to a rise in hours, real wages, and productivity. To summarize, the neoclassical model predicts that an increase in government spending raises an industry’s hours, but lowers its real wage and labor productivity. ThestandardNewKeynesianmodelpredictsanincreaseinhours,adeclineinproductivity, and an ambiguous effect on real wages. The increasing returns model predicts ariseinhours,realwagesandproductivity. 4 Data and Variable Construction This section describes our data sources and explains how we construct the variables. Throughoutthepaper,uppercaselettersrepresentrealquantitiesandatildeindicates 5

a nominal quantity. Lowercase letters indicate the natural logarithm of a variable. The subscript i denotes industry and t denotes year. When possible, these subscripts areomittedinthetext;however,theyremaininallequations. 4.1 Industry-Specific Government Spending Our sources for constructing industry-specific government spending are the benchmark IO accounts, which are available roughly quinquennially, in 1947, 1958, 1963, 1967, 1972, 1977, 1982, 1987, 1992, 1997and2002. TheIOaccounts for1947and 1958donotcontaintheindustrydetailrequired,sowedroptheseobservations. The last two IO accounts, 1997 and 2002, are based on the North American industrical classificationsystem(NAICS)ratherthantheStandardIndustrialClassification(SIC). Because merging the NAICS with the SIC industries is difficult and fraught with potential error, we also drop 1997 and 2002. Thus, we use information from the 1963, 1967,1972,1977,1982,1987,and1992IOaccounts. Figure 2 shows real federal spending and real defense spending from 1958 to 1997. TheverticallinesindicatetheyearsforwhichtheIOaccountsareavailable. The figure makes clear that almost all fluctuations in federal government purchases are due to defense spending. Defense spending started increasing in 1965 after Johnson sent bombing raids over North Vietnam in February 1965. Defense spending peaked in 1968 at the height ofthe Vietnam War, and then fell until the mid-1970s. It began to rise in 1979, and then accelerated starting in 1980 after the Soviet Union invaded Afghanistan in December 1979. Spending peaked in 1987, fell gradually until 1990, andthenfellmoresteeply. We use the IO accounts to compute the sum of direct and indirect government spending. This comprehensive measure captures downstream effects of an industry’s spending. For example, an increase in government purchases of finished airplanes likelyalsoincreasesshipmentsofaircraftpartsindustriesthatsupplypartstotheaircraft industries. Because it is difficult to distinguish nondefense from defense spending when calculating indirect effects, we use total federal government spending. As the previous figure shows, using all federal spending rather than just defense should not be problematic because most of the level and variation in federal government purchases is defense spending. Moreover, some spending not classified as defense, 6

such as that for the National Aeronautics and Space Administration, is often driven bydefenseconsiderations. To compute federal government demand, we use the “Transactions” and “Total Requirements”tablesavailablefromtheIOaccounts. LetS˜IO bethenominalvalueof ijt inputsproducedbyindustry i shippedtoindustry j inyear t,measuredinproducers’ prices. Nominal direct government demand, G˜d, for industry i in year t is the value ofinputsfromindustry i shippedtothefederalgovernment(j= g): (3) G˜d =S˜IO . it igt Indirect government demand, G˜n, is calculated using commodity-by-commodity unit input requirement coefficients. Let r be the commodity i output required per ijt dollar of each commodity j delivered to final demand in year t. The indirect governmentdemandforindustryi’soutputisthedirectgovernmentpurchasesfromindustry j timestheunitinputrequirementofindustry i forindustry j’soutput: J (cid:88)t (4) G˜n = G˜d ×r . it jt ijt j=1 Total government demand for industry i in year t is the sum of direct and indirect demand: (5) G˜ =G˜d +G˜n. it it it Perotti (2008) defined his government demand variable as the change in an industry’sshipmentstothegovernmentbetweentwobenchmarkyearsdividedbytotal initial shipments of the industry, i.e., [G it −G i(t−5) ]/S i(t−5). His measure is potentially problematic, though, because it makes the questionable assumption that the distribution of government spending across industries is uncorrelated with industry technological change. As we will argue below, we have reason to believe that his measureiscorrelatedwithindustry-specifictechnologicalchange. We therefore construct an alternative measure of a government demand shock that should not be correlated with industry-specific technology. In particular, we de- 7

finethegrowthingovernmentdemandforindustry i,∆g ,as it (6) ∆g =θ ·∆g , it i t where θ is the average share of an industry’s total nominal shipments that go to i the government and g is log of aggregate real federal spending (based on national t incomeandproductaccounts(NIPA)data). Wecalculatetheshareofindustryi’stotal nominalshipmentsthatgotothegovernmentinyear t as G˜ (7) θ = it , it (cid:80)J S˜IO j=1 ijt We then calculate industry i’s average dependence on the government, θ , by averi aging over all IO years (1963–92). Table 1 shows the 15 industries with the largest shareofshipmentstothegovernment. Notsurprisingly,mostaredefenseindustries. Thus,ournewmeasureconvertstheaggregategovernmentdemandvariableinto anindustryspecificvariableusingtheindustry’slong-termdependenceonthegovernment as a weight. The idea behind this measure is that a given increase in aggregate government spending should have a bigger impact on an industry that, on average, sends a higher fraction of its output to the government. We could, in principle, use a time-varyingweightusingtheindividualIOtables. Wedecidedagainstthisapproach becauseofconcernthatchangesintechnologycoulddrivechangesinindustryshares over time. On the other hand, if there is a correlation between industry long-run average technology growth and the long-run average industry government shipment share,itwillbeaccountedforintheempiricalanalysisbyindustryfixedeffects. 4.2 Variables from the Manufacturing Industry Database TheManufacturingIndustryDatabase(MID),maintainedbytheNBERandCenterfor EconomicStudies(CES),containsannualdatafor4584-digitSICcodemanufacturing industries from 1958 to 1996.6 Most of the information is derived from the Annual SurveyofManufacturers(ASM).Weusetheversionbasedonthe1987SICcodes.7 6. Bartelsmanetal.(2000). 7. Throughoutthepaper,allSICcodesreportedarethe1987version. 8

The database provides information on hours only for production workers. We created two measures of total hours using two extreme assumptions: nonproduction workers always work 1,960 hours per year and nonproduction workers always work as much as production workers. This figure is slightly less than the usual 2000 hours per year because it allows for vacations and holidays, which are not included in production worker hours measures. The results were very similar, so we only report the results using the assumption that nonproduction workers always work 1,960 hours per year. The production worker product wage is the production worker wage bill dividedbyproductionworkerhourstimestheshipmentsdeflator. For one set of results, we construct share-weighted growth of inputs. The payroll data from the MID include only wages and salaries, and do not include payments for benefits, such as Social Security and health insurance. Thus, labor share estimates from this database are biased downward. Fortunately, Chang and Hong (2006) have compiled annual information for each 2-digit manufacturing industry from the NIPA of the ratio of total compensation to wages and salaries. We merge these factors to our 4-digit data and use them to magnify the payroll data to create more accurate laborshares. Weconstructrealshipmentsbydividingnominalshipmentsbytheshipmentsprice deflator. However,becausefirmsholdinventories,shipmentsarenotnecessarilyequal tooutput. Accordingtothestandardinventoryidentity,realgrossoutput, Y,isequal to real shipments, S, plus the change in real finished-goods and work-in-process inventories, IF. The MID database reports only the total value of inventories, I, at the endoftheyear;itdoesnotdistinguishinventoriesbystageofprocessinthereported stocks. Fortunately, we can back out the nominal change in materials inventories from other data in the MID. In particular, the measure of nominal value added, V˜, in the MIDisdefinedas: (8) V˜MID=S˜ −M˜ +∆˜IF, it it it it where M˜ isnominalmaterialscost. Since total inventories is the sum of finished-goods and work-in-process inventoriesandmaterialsinventories, IM,thechangeinmaterialsinventoriescanbeinferred 9

from the change in total inventories and the change in finished-goods and work-inprocess inventories: ∆˜IM =∆˜I −∆˜IF. Using this inventory relationship, we calcuit it it laterealgrossoutputas (9) Y (cid:117) S˜ it + (cid:150)˜I it − ˜I i(t−1) (cid:153) − ∆˜I i M t , it P it P it P i(t−1) P it where P isthepriceofoutput. Thisformulationforgrossoutputisnotexactbecause thelastterm,thechangeinrealmaterialsinventories,shouldbe ˜I i M t − ˜I i M (t−1) . P it P i(t−1) UnfortunatelytheMIDdoesnothavedataonthestockofmaterialsinventoriesateach point in time necessary. As a result, our measure of gross real output in equation 9 understatesproductionby (10) ˜I i M (t−1) × P it −P i(t−1) , P i(t−1) P it whichistheproductoftherealinitialstockofmaterialsinventories(valuedatoutput prices) and the rate of inflation of output prices. According to Bureau of Economic Analysis (BEA) estimates of inventories and sales in manufacturing, the real stock of materials inventories is about 50 percent of monthly sales, or about 4 percent of annualsales. Evenifannualinflationisashighas10percent,thebiaswouldonlybe −0.4percent. Many studies have used value added measures of output. However, Norrbin (1993) discusses the biases associated with using value added rather than gross output, and Basu and Fernald (1997) argue that value added is only valid with perfect competition and constant markups of unity. Thus, we do not use value added as a measureofoutput. We also use MID measures of total capital, plant, equipment, investment, materials usage and energy usage. The MID also includes price indexes for capital, investment, materials, and energy. We create real series from the nominal values by dividingbytheappropriatepriceindex. 10

We merge the MID data with the IO data by developing a correspondence between the 6-digit IO code–based IO data and the 4-digit SIC code–based MID data.8 Themergeddatabasecontains272industriesatthe4-digitSIClevel. Becausesomeof theindustrieswerecombinedinthemerge,wehadtoaggregatesomevariablesfrom theMID.Therealquantitiesweredefinedattheindustrylevelasthenominalquantitiesdividedbytherelevantpriceindex. Becausethepriceindicesinthisdatabaseare fixed-weightindices,itispossibletosumtherealquantities. Wethensummednominal and real quantities for the combined industries and used their ratios to construct priceindices. 5 Empirical Results 5.1 Properties of Industry-Specific Government Demand The usefulness of our government demand variable for distinguishing between the various theories depends on two key features. First, in order for it to represent only shiftsinindustrydemand,itmustbeuncorrelatedwithtechnology. Second,itshould berelevant,inthesensethatitissufficientlycorrelatedwithindustryoutputorhours. In this section, we assess how well the government demand variable satisfies these twoproperties. At the aggregate level, there is substantial evidence that fluctuations in military spending are mostly driven by geopolitical events and are for the most part exogenous to the currentstate of the economy.9 Since most variations infederal purchases are due to military spending, it is unlikely that aggregate shipments to the government are correlated with technology. That said, it is possible that the distribution of military spending across industries could be related to technological change. To see why technology might influence government spending at the industry level, consider the following example. Between 1972 and 1977, real federal spending declined by 3 percentandrealdefensespendingfellby9percent. Incontrast,totalrealfederalpurchases of computers (SIC 3571) rose by 219 percent over this period. This increase 8. Thecorrespondencetablesareavailableontheauthors’websites. 9. Forexample,Ramey(2009a). 11

was20percentoftheinitialvalueofshipmentsin1972,yetthefractionofshipments thatwenttothegovernmentroseonlyslightly,from7percentin1972to9percentin 1977 because industry shipments to nongovernment destinations also rose dramatically. Clearly, the increase in government spending on computers during this period wasnotduetoa“demandshift,”butratherbecausetechnologicalchangeinthecomputerindustryshiftedgovernmentdemandtowardthatindustryandawayfromother industries. In other words, it is likely that the rise in industry-specific government spendingwascorrelatedwithindustry-specifictechnologygrowth. It is for this reason that we do not adopt Perotti’s (2008) definition of shifts in government demand. Perotti (2008) compared the change in shipments to the government over a five-year period to the initial total shipments of the industry. By his definition,theincreaseincomputershipmentstothegovernmentwouldbeclassified asaverylargedemandshock,whereasitisclearthatitwaslinkedtoindustry-specific technologicalchange. The second desirable feature for our demand shifter is relevance. Is our government demand variable sufficiently correlated with output and hours? To investigate thisfeature,table2reportsreduced-formregressionsofthelogchangeoftwooutput measuresandthreelabormeasuresonthegovernmentdemandvariable. Thefirstrow reportstheresultsofasimpleregressionofthegrowthinrealgrossshipmentsonthe growth of our government demand variable (∆g). The coefficient is 1.84 (standard errorof0.16),implyingthata1-percentincreaseinaggregatefederalspendingcauses shipmentstorisebyalmost1percentinanindustrythatonaverageships50percent of its output to the government. The coefficient is estimated very precisely. Although the R2 is very low, the F statistic on the coefficient is 128, implying that our government demand variable is very relevant. The second row estimates this specification including year and industry fixed effects. The estimate is higher, at 2.46 (0.17), and ishighlysignificant. Thethirdrowoftable2showsthefixed-effectsregressionofthe growth in real gross output (which includes changes in work-in-process and finished goods inventories) on the growth of government demand. The estimated coefficient is 2.38 (0.18), statistically identical to that from the regression with shipments (line 2). Ineverycaseourgovernmentspendingvariableishighlyrelevant. Rows 4–6 of table 2 report the estimated effects of changes in government de- 12

mandonproductionworkerhoursandemployment. Allregressionsincludeyearand industry fixed effects. Row 4 shows the impact on production worker hours. The coefficient is 2.61 (0.16), which is somewhat above the coefficient for output. The government demand variable is also relevant for this variable, as evidenced by the implied F statistic. Rows 5 and 6 show that virtually all of the change is due to changesinemploymentratherthanaveragehoursperworker. To summarize the results of this section, the evidence shows that the new government demand variable we constructed is a very relevant instrument for shifts in output and hours. We have presented evidence that Perotti’s (2008) measure may be correlated with industry-specific technology. In contrast, we have constructed our demandmeasuresothatitisnotsubjecttothisproblem. 5.2 Government Demand Effects on Prices and Productivity 5.2.1 Wages and Prices Table 3 shows the results of instrumental variables (IV) regressions of wages and pricesontotalproductionworkerhours. Toisolatetheeffectofagovernment-demand inducedriseinhoursonwagesandprices,weinstrumentforhoursusingourgovernment demand variable. In particular, we regress the log change in product wages on the log change in hours, which is instrumented by the government demand variable. Row 1 shows that a government demand–induced increase in hours leads to a small decline in the relative real product wage. The estimate is statistically significant at the7percentlevel,butiseconomicallysmall. Row2showsthatanindustry’srelative wage does not change significantly, whereas row 3 shows that the relative price of an industry’s rises.10 Thus, the decline in the real product wage is mostly due to a rise in the relative product price. These results are qualitatively consistent with the competitivemodelshowninsection3. These results stand in contrast to Perotti’s (2008) conclusion that government spending raises real wages. Perotti used similar data sources, but based his analysis on ranking the top industries receiving government spending from 1963 to 1967 10. Theseresultspertaintorelativewagesandpricesbecausewehaveincludedtimefixed effects. 13

and from 1977 through 1982. Based on visual inspection of his table, he concluded that“thesectorsthatexperiencethelargestgovernmentspendingshocksarealsothe sectorsthatexperiencedthelargestpositivechangesintherealproductwage.”11 To determine the source of the differences in our conclusions, we construct Perotti’s (2008) government demand instrument, which is available only as five-year differences due to the frequency of the IO tables. We then regress the five-year log changeintherealproductwageonthefive-yearlogchangeinhours,instrumentedby this government demand variable. The coefficient is 0.15 (0.07), indicating a significantincreaseinrealwages. However,whenweincludetimeandindustryfixedeffects in the regression, we obtain a coefficient of −0.0005 (0.06). Thus, Perotti’s (2008) finding of a positive effect of government spending on real wages is due both to his definitionofthegovernmentspendingshock(withitspotentialcorrelationwithtechnology) and his failure to account for industry and time fixed effects. When we use our annual government spending shock and include industry and time fixed effects, wefindasmallnegativeeffectonrealproductwages. 5.2.2 Labor Productivity We next investigate the effects of a government demand–induced rise in hours on labor productivity. To understand the interpretation of the coefficient, consider the specialcaseofaCobb-Douglasproductionfunctionwheretheexponentonlaborisα. Thegrowthoflaborproductivityisgivenby (11) ∆(y −h p)=(α−1)∆h p +β·∆x +∆a , it it it it it where y is the log of real output, hp is the log of production-worker hours, x is the share-weightedlogofotherinputs,andaisthelogoftechnology. Ifthereisnochange inotherinputs,thenourgovernmentdemandinstrumentisvalidforestimatingα−1 since the instrument is uncorrelated with technology a. On the other hand, if other inputs are also increasing, then the demand instrument will be positively correlated withtheerrortermandtheestimateofα−1willbebiasedupward. Rows 4 and 5 of table 3 shows the effect of a government demand–induced rise 11. Perotti(2008),p. 208. 14

inhoursontwomeasuresofthegrowthinlaborproductivity. Ineachcase,wedivide an output measure by total hours of production workers. Both equations include year and industry fixed effects. The first measure uses real gross shipments and the second uses real gross output (equation 9). In both cases, the coefficient is small but negative, implying that a rise in hours leads to a slight decline in labor productivity. Ifwebelievethatotherinputsarefixed,thenthecoefficientimpliesahighvalueofα of 0.91 or 0.94. As we will show below, however, other inputs do rise in response to governmentspendingshock. Thus,thisestimateislikelyanupperboundonα. 5.2.3 Markup We can combine the results for productivity and real wages to determine the implications for the countercyclical markup hypothesis that is key to the New Keynesian explanation of fiscal policy. To see this, consider the definition of the log change in themarkup: (12) ∆µ =∆ (cid:128) y −h p(cid:138) −∆(cid:0) w −p (cid:1) , it it it it it where w isthelogofthenominalwageand p isthelogoftheoutputprice. Rows 6 and 7 of table 3 show IV regressions of the change in the markup on the change in total production worker hours. We calculate the markup with two output measures, one using real shipments and the other using real gross output. Both measures of the markup are essentially constant in response to an increase in hours. Inonecase,thecoefficientestimateis0.02(0.05)andintheotheritis−0.01 (0.04),butinneithercaseisitstatisticallydifferentfromzero. Thus,markupsappear tobeconstantinresponsetoashiftingovernmentdemand. 5.3 Effects of Government Demand on Other Inputs We now investigate the effects of government spending on several other key inputs. We begin by studying the responses of particular inputs. We then construct a shareweightedmeasureofinputsandestimatetheimpliedreturnstoscale. 15

5.3.1 Other Inputs Table 4 reports the reduced-form response of various inputs to industry-specific government spending changes. The first row reproduces the response of production workerhoursforcomparison. Supervisoryworkeremploymentincreasessignificantly (row 2), but the response, 2.33 (0.19), is smaller than for production workers hours (row 1), 2.61 (0.16). Thus, the ratio of supervisory workers to production workers declineswhengovernmentdemandincreases. Rows 3–5 investigate the response of various measures of capital inputs. Row 3 shows the response of the real capital stock. The response is positive and significant, but with a coefficient of 0.50 (0.06) it is much smaller than for labor. Thus, the increase in government spending leads to a decline in the capital-labor ratio. It is possible, however, that capital services could rise by more than the capital stock if capital utilization increases in response to government spending. To investigate this possibility,weconsidertwomeasuresofcapitalutilizationthathavebeenusedinthe literature. The first measure is energy usage. Numerous papers have used electricity consumptionasanindirectmeasureofcapitalutilization.12 Wedonothaveinformationinourdatasetonelectricityconsumption,butwedohaveinformationonoverall energy usage. Thus, the fourth row of table 4 reports the response of real energy usage. The coefficient estimate is 0.42 (0.21). If utilization is proportional to energy usage, then we can combine this estimate with the growth of capital of 0.50, to infer thatcapitalservicesriseby0.92. Whilelargerthanthebasicestimate,itisstillfarbelowtheriseinproductionworkerhours. Thesecondindicatorofcapitalutilizationwe consider is Shapiro’s (1993) measure of the workweek of capital, which is based on theCensusBureau’sSurveyofPlantCapacity. Thismeasurecountshoursperdayand days per week that a plant operates. Shapiro (1993) used this measure to show that the Solow residual is no longer procyclical once this utilization measure is included. Unfortunately,Shapiro’s(1993)measureisonlyavailablefrom1977to1987andonly for a subset of the industries. Row 5 reports the effects of government spending on thismeasure. Thecoefficientis−0.61(0.79)andisnotstatisticallysignificant. Thus, thisalternativesourcedoesnotraisetheestimateofthegrowthofcapitalservices. Row 6 shows the response of real materials inputs excluding energy. In this case, 12. See,forexample,JorgensonandGriliches(1967)andBurnsideetal.(1996). 16

theresponseis2.70(0.20),slightlylargerthanforhoursoroutput. Row7showsthe results for the ratio of real materials to output. The coefficient is 0.32 (0.13) and is statisticallysignificantfromzero. 5.3.2 Implications for Returns to Scale Tostudytheresponseofotherinputsmoresystematically,wecanestimatetheoverall returnstoscaleusingtheframeworkpioneeredbyHall(1990),andextendedbyBasu and Fernald (1997). In particular, we can estimate overall returns to scale from the followingequation: (13) ∆y =γ∆z +∆a , it it it where ∆z is the share-weighted growth of all inputs. The coefficient γ measures the returns to scale. If technology is the only source of error in this equation, then one canestimateγbyusingademandinstrumentthatiscorrelatedwithinputgrowthbut uncorrelatedwithtechnology. Consider a measure of share-weighted input growth treating energy as an input toproduction: (14) ∆z =s ∆k +s ∆h +s ∆m +s ∆e , it k it h it m it e it where k is the log of the real capital stock, his the log of total hours, m is the log of real materials usage, e is the log of real energy usage, and s is the share of input j. j Asdiscussedinsection4.2,weconstructthelaborshare(s )usingChangandHong’s h (2006) factors to inflate the observed labor share to account for fringe benefits. This raises the average labor share in the data set by 3 percentage points. Following Basu et al. (2006), we calculate the capital share as the residual from labor share and materialsshareandbyusingsharesaveragedovertheentiresample. We estimate the return to scale using an IV regression of the growth of log gross outputontheshare-weightedgrowthofinputsandonyearandindustryfixedeffects. We instrument for ∆z with our government demand variable (∆g). The first-stage regressionoftheshare-weightedinputsonourgovernmentvariablehasan F statistic that exceeds 200, indicating high relevance. The first row of table 5 reports the 17

IV regression. The estimated coefficient is 1.11 (0.05), indicating small, marginally statistically-significantincreasingreturnstoscale. However, as numerous papers have made clear, unobserved variations in capital utilizationorlaboreffortmaycontaminatetheerrorterm.13 Becausethesevariations are likely to be correlated with any instrument that is also correlated with observed input growth, estimates of γ are likely to be biased upward. We attempt to mitigate this bias in two ways. The first is to include a proxy for unobserved utilization. The secondistoconstruct∆z treatingenergyusageasaproxyforcapitalutilization. Basu et al. (2006) use the theory of the firm to show that, under certain conditions, unobserved variations in capital utilization and labor effort are proportional to the growth in average hours per worker. Row 2 of table 5 adds the growth of average hours per worker (∆¯h) to control for unobserved utilization. The estimate of the return to scale is little changed. Nevertheless, this specification is probably invalid because¯hisuncorrelatedwithtechnologyonlyunderrestrictiveassumptions. Although∆g ishighlyrelevantfor∆z,itisdifficulttofindadditionalrelevantinstrumentsfor∆¯h. Weattempttocreateextrainstrumentsbyusingseparatemeasures of direct and indirect government shipments and a quadratic in total government shipments as instruments for both variables. All statistics (such as Shea’s partial R2) suggest the instruments have low relevance for ∆¯h after being used for ∆z.14 Row 3 of table 5 reports the results of this IV regression. The estimate of the return to scale is little changed at 1.09 (0.06) and the coefficient on average hours per worker isnotsignificantlydifferentfromzero. Nonetheless,wearenotveryconfidentofthis specificationgiventheweakinstruments. A second approach to mitigate unobserved utilization is to construct ∆z treating capital utilization as proportional to energy usage. This alternate measure of shareweightedinputgrowthis (15) ∆z =s (cid:0)∆k +∆e (cid:1)+s ∆h +s ∆mxe, it ke it it h it mxe it where mxe is the log of real materials usage excluding energy. As before, we instrument for ∆z with ∆g. Row 4 of table 5 reports the regression using this alternate 13. See,forexample,Burnsideetal.(1996)andBasu(1996). 14. Shea(1997). 18

measure of input growth. The estimated coefficient, 1.07 (0.05), is not statistically differentfromunity,implyingconstantreturnstoscale. In sum, our results are completely consistent with the neoclassical assumptions concerning the effects of government spending. An increase in output induced by governmentspendingraiseshours,butlowersrealwagesandproductivity. Takingall inputsintoaccount,wecannotrejectconstantreturnstoscale. 6 Conclusion Ourstudyoftheeffectsofindustry-specificchangesingovernmentspendingindicates thatanincreaseingovernmentdemandraisesanindustry’srelativeoutputandhours. These increases are associated with small declines in its relative real wage and labor productivity, and a rise in its relative price. Its use of other inputs, such as capital, energy, and materials, rises as well. Our estimates of returns to scale are consistent with constant returns to scale. Thus, the results support the microeconomic assumptions underlying the neoclassical theory of the effects of government spending. In contrast,wefindnoevidenceoftherisingrealwagesorcountercyclicalmarkupsthat are central to the standard New Keynesian explanation for the effects of government spending. A key question, then, is why aggregate evidence indicates that an increase in government spending raises labor productivity whereas the industry-level evidence presented in this paper indicates that an increase in demand associated with higher governmentspendinglowerslaborproductivityslightly. BasuandFernald(1997)provideananswerbasedontheirextensivestudyoftheeffectsofaggregationonreturns to scale estimates. They show that durable goods manufacturers have higher returns toscalethanmanyotherindustries,someofwhichexhibitsharplydiminishingreturns to scale. Thus, anything that shifts output toward durable goods producers will lead to aggregate behavior that looks like increasing returns to scale. The 15 industries that depend most on government spending are all durable goods manufacturing industries. Thus,theincreaseinaggregatelaborproductivityinresponsetogovernment spending can be explained by reallocation rather than by firm-level or industry-level increasingreturns. 19

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Table 1. Industries with Largest Share of Shipments to the Government Rank SIC Industry θ i 1 3761 Guided missiles and space vehicles 0.920 2 3483 Ammunition, except for small arms, n.e.c. 0.807 3 3489 Ordnance and accessories, n.e.c. 0.769 4 3728 Aircraft and missile equipment, n.e.c. 0.628 5 3731 Ship building and repairing 0.626 6 3724 Aircraft and missile engines and engine parts 0.610 7 3663 Communication equipment 0.496 8 3721 Aircraft 0.491 9 3795 Sighting and fire control equip. 0.489 10 3812 Engineering and scientific instruments 0.435 11 3463 Nonferrous forgings 0.419 12 3482 Small arms ammunition 0.384 13 3339 Primary nonferrous metals, n.e.c. 0.321 14 3672 Other electronic components 0.294 15 3674 Semiconductors and related devices 0.282 Source: Author’scalculationsusingdatafromBEAbenchmarkIOtables. Notes: θ is the average share of industry i’s total nominal shipments that go to the federal i government. Calculated from a panel of 274 industries in 1963, 1967, 1972, 1977, 1982, 1987,and1992. 23

Table2. Reduced-FormRegressionsofIndustryOutputandLaboronGovernment Demand Independent variable Fixed Partial Dependent variable ∆g effects R2 it Output measures ∗∗∗ 1. Real shipments 1.836 No 0.013 (0.162) ∗∗∗ 2. Real shipments 2.464 Yes 0.020 (0.172) ∗∗∗ 3. Real gross output 2.376 Yes 0.017 (0.182) Production worker measures ∗∗∗ 4. Total hours 2.610 Yes 0.027 (0.155) ∗∗∗ 5. Employment 2.572 Yes 0.029 (0.149) ∗∗∗ 6. Average hours 0.038 Yes 0.000 (0.056) Source: Authors’regressionsusingdatafromtheNBER-CESMIDandBEAIOtables. Notes: Dependent variable isannual change inthe log ofthe output orlabor variable listed. Alllaborvariablesrefertoproductionworkers. ∆g istheindustry-specificchangeingovernit mentdemand(seeequation6). Allregressionshave10,135observationsfromapanelof274 industries over 1960–96; regressions include year and industry fixed effects when indicated. Standard errors are reported in parentheses. *** indicates significance at 1-percent, ** at 5-percent,and*at10-percentlevel. 24

Table 3. Instrumental-Variables Regressions of Wages, Prices, Labor Productivity and Markups on Total Production Worker Hours Independent variable Dependent variable ∆h p R2 it Wages and prices 1. Real wage −0.076 ∗ 0.170 (0.042) 2. Nominal wage −0.015 0.299 (0.026) ∗ 3. Price of output 0.061 0.335 (0.034) Productivity 4. Measured with real shipments −0.056 0.120 (0.047) 5. Measured with real gross output −0.090 ∗∗ 0.119 (0.049) Markup 6. Measured with real shipments 0.020 0.055 (0.045) 7. Measured with real gross output −0.014 0.064 (0.044) Source: Authors’regressionsusingdatafromtheNBER-CESMIDandBEAIOtables. Notes: Dependent variable is annual change of the log of the variable listed. Independent variableistheannualchangeofthelogoftotalproductionworkerhours(∆hp ),instrumented it bytheindustry-specificchangeingovernmentdemand(∆g ,seeequation6). Allregressions it have10,133observationsfromapanelof274industriesover1960–96andincludeyearand industryfixedeffects. Standarderrorsarereportedinparentheses. ***indicatessignificance at1-percent,**at5-percent,and*at10-percentlevel. 25

Table 4. Reduced-Form Regressions of Other Inputs on Government Demand Independent variable Partial Dependent variable ∆g R2 it ∗∗∗ 1. Production worker total hours 2.610 0.027 (0.155) ∗∗∗ 2. Supervisory worker employment 2.327 0.014 (0.194) ∗∗∗ 3. Real capital stock 0.497 0.007 (0.060) ∗∗ 4. Real energy 0.419 0.001 (0.205) 5. Workweek of capital −0.611 0.000 (0.789) ∗∗∗ 6. Real materials excluding energy 2.700 0.017 (0.204) ∗∗ 7. Real materials-output ratio 0.324 0.001 (0.128) Source: Authors’regressionsusingdatafromtheNBER-CESMIDandBEAIOtables. Notes: Dependent variable isannual change inthe log ofthe output orlabor variable listed. All labor variables refer to production workers. ∆g is the industry-specific change in govit ernmentdemand(seeequation6). Regressionshave10,135observationsfromapanelof274 industriesover1960–96; regressionwithworkweekofcapital(row5)hasonly1,793observations. Allregressionsincludeyearandindustryfixedeffects. Standarderrorsarereported in parentheses. *** indicates significance at 1-percent, ** at 5-percent, and * at 10-percent level. 26

Table 5. Instrumental-Variables Regressions of Output Growth on Input Growth Independent variable Input growth definition ∆z ∆¯h R2 it it ∗∗∗ 1. Energy as input 1.108 0.743 (0.049) 2. ¯has proxy for utilization, not 1.109 ∗∗∗ −0.013 0.743 instrumented (0.049) (0.025) 3. ¯has proxy for utilization, 1.093 ∗∗∗ 0.856 0.688 instrumenteda (0.066) (2.135) ∗∗∗ 4. Energy as proxy for utilization 1.065 0.692 (0.051) Source: Authors’regressionsusingdatafromtheNBER-CESMIDandBEAIOtables. Notes: Dependent variable is annual change of log real output. ∆z is annual growth of it share-weighted log inputs (including production worker hours); see equations 14 and 15. ∆¯h is annual growth of average hours per worker. Except for row 3, ∆z instrumented it it by industry-specific change in government demand (∆g , see equation 6). All regressions it have10,133observationsfromapanelof274industriesover1960–96andincludeyearand industryfixedeffects. Standarderrorsarereportedinparentheses. ***indicatessignificance at1-percent,**at5-percent,and*at10-percentlevel. a. Both ∆z and ∆¯h instrumented by direct shipments to government (∆gd), indirect it it it shipmentstogovernment(∆gn),andthesquareoftotalshipmentstogovernment. it 27

Figure 1. Labor Market Effects of An Increase in Government Spending (a)Competitivemodel W Pi i H i =η (cid:129) W Pi i P P C i,λ (cid:139) (cid:129) (cid:139) H(cid:48)=η Wi Pi,λ(cid:48) i Pi PC Wi=F ( H,X;A ) Pi H i i i H i (b)Countercyclicalmarkupmodel W Pi i H i =η (cid:129) W Pi i P P C i,λ (cid:139) (cid:129) (cid:139) H(cid:48)=η Wi Pi,λ(cid:48) i Pi PC Wi=F ( H,X;A )/µ(cid:48) Pi H i i i i Wi=F ( H,X;A )/µ Pi H i i i i H i (c)Increasingreturnsmodel W Pi i H i =η (cid:129) W Pi i P P C i,λ (cid:139) Wi=F ( H,X;A ) Pi H i i i (cid:129) (cid:139) H(cid:48)=η Wi Pi,λ(cid:48) i Pi PC H i 28

Figure 2. U.S. Federal Government Spending, 1958–1997 Chained2005dollars 800 Total Defense 700 600 500 400 300 1960 1965 1970 1975 1980 1985 1990 1995 Source: BEA. Notes: Verticallinesindicateyearswherebenchmarkinput-outputdataareavailable. 29