Do Firms Share Their Success with Workers? The Response of Wages to Product Market Conditions

Do Firms Share their Success with Workers? The Response of Wages to Product Market Conditions Marcello Estev~ao and Stacey Tevlin(cid:3) March 23, 2000 Abstract Weprovidestrongnewevidencethatindustry(cid:12)nancialconditionsplayanimportantrole inwagedeterminationintheU.S.manufacturingsector. Ordinaryleastsquaresestimatesof thee(cid:11)ectofrentsperworkeronwagesarepositiveandsigni(cid:12)cant,butquitesmall. However, using two standard bargaining models, we illustrate that this may stem from a variety of econometricdi(cid:14)cultiesthatplaguetheOLSestimates. Inthispaper,weareabletoovercome these issues and identify the e(cid:11)ects of the industry (cid:12)nancial situation on wages. We do this using the U.S. input-output tables to isolate exogenous variation in an industry’s product market conditions. Our instrumental variable estimates reveal a substantial amount of rent sharing in U.S. manufacturing|much more than is consistent with a purely competitive labor market. (cid:3)Economists, Division ofResearch andStatistics, FederalReserveBoard. Email: stevlin@frb.gov. Thispaper is a substantially revised version of FEDs working paper #95-48. We bene(cid:12)ted from insightful discussions with Joshua Angrist, Olivier Blanchard, Ricardo Caballero, StevePischke, Robert Solow and Beth AnneWilson. We areverygratefultothevaluablesuggestionsprovidedbyLawrenceKatzandtwoanonymousreferees. Wewould alsoliketothankseminarparticipantsatMIT,UniversityofMaryland,IowaStateUniversity,andattheFederal Reserve Board for their comments. We are responsible for all remaining errors and the views expressed do not necessarily reflect theviews of theFederal Reserve Board or any other members of its sta(cid:11).

1 Introduction One of the central aims of theoretical work on wage formation is to understand why wages fail to clear the market for labor. Many of the theories that have been proposed to explain this phenomenon imply a positive correlation between pro(cid:12)ts and wages. However, although empirical studies on inter-industry wage di(cid:11)erentials provide indirect evidence that such a correlation may exist, direct tests of the e(cid:11)ect of industry rents on wages in the US economy have yielded very small estimates. The absence of direct empirical support casts doubt on the relevance of industry performance in wage determination. In this paper, we provide strong direct evidence that U.S. (cid:12)rms share rents with workers. Previous studies of the US economy have been unable to (cid:12)nd signi(cid:12)cant rent sharing because|lacking appropriate instruments|they failed to overcome the endogeneity of (cid:12)rm performance in a real wage equation. We use two simple bargaining models to illustrate that the degree of rent sharing can be identi(cid:12)ed using instruments that shift the demand curve for goods. Byfocusingonindustriesthataresuppliersofintermediateinputstootherindustries,we are able to isolate exogenous demandshocks for 62 four-digit sectors. Our instrumentalvariable analysis reveals that rent sharing is an important feature of the U.S. manufacturing sector. We (cid:12)nd an elasticity of wages with respect to (cid:12)rm performance that is ten times larger than OLS estimates. This result is robust to changes in the sample period, the group of industries, and the de(cid:12)nition of industry performance, as well as to controls for worker quality. This paper has (cid:12)ve other sections. In the next section, we review the theoretical and empirical literature on the relationship between wages and pro(cid:12)ts. Next, we present models that provide a framework for the empirical section and, in particular, organize the discussion on simultaneity and measurement error issues. Section 4 describes the empirical methodology to be used, including the choice of instruments, the way we control for changes in the industrymix of worker characteristics, and thespeci(cid:12)cation of each variable usedin the estimation. Section 5 reports results for di(cid:11)erent speci(cid:12)cations of the basic equation relating real wages and rents. The last section concludes. 2 The Literature Severaldi(cid:11)erenttheoriespredictapositivecorrelation betweenindustryperformanceandwages. E(cid:14)ciency-wage theories predict that (cid:12)rms will choose not to cut wages because of the nega- 1 tive impact on productivity, and therefore, on pro(cid:12)tability. Insider-outsider theories predict a positive relationship between rents and wages because incumbent workers, or \insiders", can be 1The e(cid:11)ect on productivity may stem from costly worker monitoring (Shapiro and Stiglitz (1984)) or labor turnover costs (Salop (1979)). Akerlof and Yellen (1988) emphasize sociological and psychological reasons for e(cid:14)ciency wages based on theidea of fairness. 2

uncooperative with new employees, or \outsiders", causing adverse e(cid:11)ects on overall produc- 2 tivity. These potential production disruptions are costlier to more pro(cid:12)table (cid:12)rms. A version of the implicit contract models of Azariadis (1975) and Baily (1974) can also generate a positive relationship between wages and pro(cid:12)ts: As long as (cid:12)rms are not risk neutral, a positive rent-sharing parameter is predicted because the derivative of wages with respect to pro(cid:12)ts is positive and equal to the ratio of the relative risk aversion of (cid:12)rms to the relative risk aversion 3 of workers. According to all of these theories, (cid:12)rm-speci(cid:12)c factors such as pro(cid:12)tability and workers’ bargaining power are important determinants of the real wage paid to a worker and can be 4 used to explain inter-industry wage di(cid:11)erentials. In contrast, under competitive labor market conditions, these variables should not have explanatory power. If labor markets were truly competitive, inter-industry wage di(cid:11)erentials would have to be explained by di(cid:11)erences in the mix of worker characteristics across industries and/or by job compensating premia. AseriesofstudiesusingdatafromtheU.S.,theU.K.,andCanada,hastestedtherelevanceof (cid:12)rm-speci(cid:12)cvariablesinanequationforrealwagedetermination. Ingeneral, thenullhypothesis ofjointsigni(cid:12)canceofthesevariablesisnotrejected,castingdoubtonapurelycompetitivelabor 5 market approach. Unfortunately, this approach yields results that are not robustto alternative speci(cid:12)cations. Each paper includes a di(cid:11)erent set of insider variables, and it is not clear what the interpretation for each coe(cid:14)cient is. An alternative approach is to align the equations with theory and provide a structural interpretation for the coe(cid:14)cient on sectoral rent in a wage determination regression. Previous authorsthathaveemployed thisapproachhavefoundthattherent-sharingcoe(cid:14)cientispositive 6 and signi(cid:12)cantly di(cid:11)erent from zero. Several of these papers use industry pro(cid:12)ts as a measure of performance and (cid:12)nd, in general, that the elasticity of real wages with respect to pro(cid:12)ts is quite small. Sanfey (1992) estimates an elasticity of wages with respect to pro(cid:12)ts-per-worker for the U.S. economy of :05, while Blanchflower et al (1996) estimate elasticities between :02 and :04. Studies that use data for other countries tend to (cid:12)nd similarly small estimates. 7 2SeeLindbeckandSnower(1987)foracollectionofpapersinthistradition. Thefundamentalsofthesemodels give a rationale for theexistence of unionsthat would betheinstitutional counterpart of insider power. 3SeeBlanchflower et al (1996). 4Nickelland Wadhwani(1990) and Nickelland Kong(1988) call thesefactors \insider variables". Theunemploymentrate,theaverageindustrialwage,andunemploymentinsurancebene(cid:12)tswouldbeexamplesof\outsider variables". 5Dickensand Katz (1987) and Layardet al (1991) describe these results in detail. 6For instance Blanchflower et al (1996), Carruth and Oswald (1990), Christo(cid:12)des and Oswald (1992), Currie and McConnell (1992), Denny and Machin (1991), Gardner (1999), Hildreth and Oswald (1993), Nickell and Wadhwani (1990), and Sanfey (1992). 7Weshouldnotethatsomeoftheseauthorsarguethattheseestimatesareactuallyquitesizable. Forinstance, Blanchflower et al (1996) point out that, according to their results, a 100 percent increase in pro(cid:12)tability in an industry would be associated with a pay rise of about 8 percent after some years. They argue that since pro(cid:12)ts are a volatile series, an economically signi(cid:12)cant portion of wage dispersion can beexplained byrents. 3

The main problem with these results is that they were produced without proper identi(cid:12)cation of the rent-sharing parameter. The simultaneity between wages and (cid:12)nancial conditions generates inconsistent estimates of the elasticity of wages with respect to pro(cid:12)tability measures. Controlling for this by using import and export prices as instrumental variables, Abowd and Lemieux (1993) estimate a much higher elasticity for Canada (0:20). Similarly, using a panel of U.K. (cid:12)rms and employing technological innovations as instruments, Van Reenen (1996) estimates a rent-sharing coe(cid:14)cient of 0:29. Although these two papers yield important evidence against the competitive labor market paradigm, theydosofor labor markets that are generally considered tobeless competitive than the U.S. market. Moreover, these studies use samples that are heavily unionized. (Indeed, the Abowd-Lemieuxsampleconsists entirely of collective bargainingagreements.) Inaddition, both studiesfailtocontrolforchangesintheindustrycompositionofindividualworkercharacteristics. The Van Reenen study also is unable to control for variation in the number of hours worked. In this paper, we extend this line of research to the U.S. labor market. We also control for variations in worker quality and present alternative results taking into account the variation in average hours worked. The main reason that the instrumental variable approach has not been applied to U.S data yet is that theinstruments used in previous studies are either notapplicable or unavailable for a large economy like the U.S. Therefore, we introduce instruments that are new to this literature: We use the input-output tables and the methods of Shea (1993) to select exogenous demand shocks for a representative sample of U.S. industries. This method yields an elasticity of wages per person with respect to rents per person (controlling for changes in labor quality) of about 0.29, implying that rent sharing is an important phenomenon in the U.S. economy. 3 Wages and rents 3.1 The basic estimation problem In this section, we describe the basic problem of estimating rent sharing with ordinary least squares. It is straightforward to show that OLS regressions of wages on various measures of industry performance yield inconsistent estimates. Consider the following equation: R W =γ +Z +(cid:17) (1) N where W is the real wage (per worker); R is real rents-per-worker; Z is a measure of the alter- N native wage a worker could expect to receive elsewhere; (cid:17) represents relevant omitted variables; andγ istherent-sharingparameter. Theestimation ofequation (1)canbemoreorlessproblematic dependingonthemeasuresofindustryperformanceused. Accountingpro(cid:12)tsarecommonly used in the literature. Economic pro(cid:12)ts, which take into account depreciation allowances and 4

8 the rental cost of capital, are a better measure. However, the calculation of both de(cid:12)nitions of pro(cid:12)ts|subtracting the wage bill from value added|imparts a direct downward bias in γ because W appears on both sides of the equation. In addition, the implicit assumptions underlying the calculation of economic pro(cid:12)ts lead to measurement error and inconsistent estimates of γ. We choose to bypass pro(cid:12)ts altogether and use value added to measure industry rents. As we will show, simple models of wage bargaining yield a structural relationship between value added-per-worker and wages. Unfortunately, value added may also be endogenous if, as seems likely, (cid:12)rms change labor inputs in response to autonomous variations in wages. Moreover, value added may serve merely as a proxy for the \true" (cid:12)nancial variable that (cid:12)rms and workers bargain over. In this case, a speci(cid:12)cation using value added could be plagued by measurement error. In the next section, we present simple models that help illustrate these econometric di(cid:14)culties and how we overcome them. Inparticular, wederive identi(cid:12)cation conditions for therent-sharingparameter usingtwo canonical bargaining models. 3.2 Bargaining models E(cid:14)cient bargaining. The (cid:12)rst model assumes that workers and (cid:12)rms bargain over wages and employment in order to maximize the joint surplus of their economic activity. If the parties do not reach an agreement, they receive fallback incomes. Workers maximize the surplus expected utility derived from their income (expected utility minus a threat point de(cid:12)ned by the fallback wage). The (cid:12)rm maximizes its surplus pro(cid:12)ts. We assume that the fallback or \strike" pro(cid:12)t is equal to zero. The source of workers’ bargaining power comes from their ability to act as a group and is represented by the parameter (cid:22). The Nash bargaining process is summarized by the maximization of: (cid:22) 1−(cid:22) Ω = (cid:8) (cid:5) (2) where (cid:5) is the pro(cid:12)t level of the (cid:12)rm. (cid:8) is the surplus expected utility of a representative worker, de(cid:12)ned as: (cid:8) = N(v(W)−v(Z)): (3) W is the real wage; N is the level of employment hired by the (cid:12)rm; Z is the alternative wage; and v(x) measures the utility derived by an individual from income x. Equation (3) assumes that the alternative wage received by a dismissed worker is also the fallback wage incase ofadisagreement. Additionally, wechoose theunitsof N sothatN can be interpreted as theprobabilityof employment. Theexpected alternative wage, Z, is afunctionof the representative worker’s characteristics{the \human capital" variables{and the state of the economy, such as the unemployment rate and the magnitude of unemployment bene(cid:12)ts. 8SeeBlanchflower et al (1996), for instance. 5

Let us write pro(cid:12)ts as: (cid:5)= Af(N)−WN where A is a revenue-shifting parameter. This parameter will, in general, be a function of the production technology and the demand for the (cid:12)nal good. Af(N) is a value-added function which here is assumed to be a function only of the amount of labor hired. Af(N) is the size of the \pie" to be divided between employees and employers. In other words, after production occurs and intermediate suppliers have been paid, the employer (who owns capital) bargains with a representative employee (who owns labor) to determine how value added will be divided between them. The (cid:12)rst-order conditions derived from maximizing (2) with respect to W and N are: Af(N) v(W)−v(Z) (cid:22) = (1−(cid:22)) +(cid:22)W (4) N v0(W) Af(N) W = (cid:22) +(1−(cid:22))Af0 (N) (5) N Linearizing v(Z) around W, omitting higher order terms, and rewriting both (4) and (5), yields: Af(N) W = (cid:22) +(1−(cid:22))Z (6) N Af0 (N) = Z (7) This is the \strongly e(cid:14)cient" bargaining case. Wages are a weighted average of labor Af(N) productivity, , andthe worker’s alternative market wage. Thelarger thebargaining power N of workers ((cid:22)) is, the larger wages are. When (cid:22) = 1, workers extract all the rents and (cid:12)rms make zero pro(cid:12)ts. In this model, (cid:12)rms hire workers until marginal labor productivity, Af0 (N), is equal to the wage a worker would receive if (cid:12)red, Z. Therefore, the level of employment does not depend on the contracted wage, implying that wage changes do not a(cid:11)ect value added per worker. Thus, in theory, equation (6) can be consistently estimated by ordinary least squares. However, empirically, it may be di(cid:14)cult to accurately measure the (cid:12)nancial conditions that workers care about. Indeed, measurement error may be part of the reason that most authors have found small estimates of the rent-sharing parameter. Fortunately, instrumental variables which are correlated to industry rents but uncorrelated to the measurement error, can help us uncover a consistent estimate of γ. A right-to-manage model. The assumption that workers and (cid:12)rms bargain over both wages and employment, as in the e(cid:14)cient bargaining model, has been criticized for being unrealistic. This assumption seems particularly heroic in the United States where wage negotiations 6

tend to be fairly decentralized. It seems likely that workers bargain over wages, but have no 9 voice in determining the overall level of employment. In the right-to-manage model, we allow bargaining between workers and (cid:12)rms to reflect this ine(cid:14)ciency. The Nash bargaining function to be maximized is now: Ω =(N(W)(v(W)−v(Z))) (cid:22) (cid:5) 1−(cid:22) (8) In (8), N(W) represents the optimal number of workers an employer will choose given the bargained level of wages. This function is obtained from the solution to the (cid:12)rm’s pro(cid:12)t maximization problem: Af0 (N) = W (9) Di(cid:11)erentiating (8) with respect to W, using (9), and linearizing v(Z) around W, gives: Af(N) W = γ +(1−γ)Z (10) N γ = γ((cid:22);(cid:15) fN ;(cid:15) WN) (11) According to equation (9), (cid:12)rms hire workers until the marginal product equals the contracted wage, W, rather than the alternative wage, Z. Thus, (cid:12)rms take wage changes into account when setting the level of employment, N. Therefore, this model points to an additional reason that OLS estimates are inconsistent: Rents per worker will be endogenously determined. Fortunately, as shown in equation (10), exogenous shifts in the revenue parameter, A|which does not vary with the level of employment|would enable us to identify the rent-sharing coe(cid:14)cient, γ. Instrumental variables that are correlated to A, but not to autonomous variation in wages, can help us with that task. It is also interesting to note that because the settled wage a(cid:11)ects the (cid:12)rm’s demand for labor, the rent-sharing parameter, γ, is not only a function of the workers’ bargaining power, but also of the elasticities of labor demand ((cid:15) WN) and the value added function ((cid:15) fN) with respect to employment|both of which we assume to be constant. Therefore, in contrast to the \e(cid:14)cient bargaining" model, γ is less than or equal to (cid:22), the parameter that represents 10 workers’ bargaining power. Consequently, instrumental variables estimation generates a lower bound for the parameter representing workers’ bargaining power. The larger the sensitivity of 9Layard et al (1991), among others, present some evidence that this might bethecase. 10After some algebra, it can be shown that γ = 1−(cid:22)(cid:15)NW(1 (cid:22) −(cid:15)fN)=(cid:15)fN < (cid:22), because (cid:15) NW < 0 and 0 < (cid:15) fN < 1 if the (cid:12)rm’s maximization problem has an interior maximum. If (cid:22) = 1, workers can set wages freely at a level, say, W. If the result of (cid:12)rms’ pro(cid:12)t maximization, taking W = W as given, generates positive pro(cid:12)ts, then γ < (cid:22) = 1. However, if (cid:12)rms make negative pro(cid:12)ts when W = W, then workers would choose wages such that pro(cid:12)tsarezero. Inthiscase, γ =(cid:22)=1. Seealso AbowdandLemieux(1993) foranalternativediscussion ofthe relationship between γ and (cid:22). 7

employment to changes in the contracted wage (i.e. the larger the magnitude of the elasticity of labor demand), the larger the di(cid:11)erence between γ and (cid:22) will be. To summarize this section and the preceding one, OLS estimates may beinconsistent dueto measurement error in the regressor. Furthermore, if (cid:12)rms set the level of employment without interference from workers, rents-per-worker will be highly endogenous. Fortunately, instrumental variables that shock the revenue parameter, A, help us overcome both problems and can be used to consistently estimate γ. 4 Empirical methodology and data description 4.1 Demand-shifters The last section made the case for the use of revenue-shifters as instruments for estimation of rent-sharing equations. Either technology shocks or exogenous variations in the demand for goods can be used as revenue shifters. We choose to use exogenous changes in demand for the output of a particular industry as our revenue shifters. We perform a panel data analysis for the four-digit sectors of U.S. manufacturing. One way of obtaining good demand shifters for this database is to use the input-output approach described in Shea (1993). Shea uses information from the input-output tables for two-, three-, and four-digit industries to choose variables that should be correlated with demand shifts of particular four-digit industries. Output of industry j is a good demand-shifter for industry i if industryj demandsalarge shareof industryi’s output, butindustryi, andother sectors closely related to it, comprise a small share of the production costs in industry j. The (cid:12)rst condition is to insure that output of industry j is relevant for identifying demand shifts. The second condition is to minimize the possiblesensitivity of theoutput of industryj to price variations in industry i. In other words, the second condition guarantees exogeneity. Let us call the demand share of industry j, DS, and the cost share of industry i, CS. An example may help here. Consider the explosives industry (SIC 2892). About 19 percent of the demand for explosives originates in the coal mining industry (SIC 12). However, the cost of explosives comprises only 1 percent of the input costs that the coal mining industry incurs. Thus, coal mining has the two characteristics that we want in an instrument: Movements in the output of coal shift the demand curve for explosives, but coal output is unlikely to be a(cid:11)ected by conditions in the explosives industry. Therefore, coal mining is a good exogenous demand shifter for the explosives industry. Shea (1993) shows that the asymptotic bias in the IV estimates of the supply elasticity obtained when using the input-output approach to select instruments is decreasing in the ratio, DS/CS. For a given ratio, increases in DS should increase the correlation between (cid:12)nal and intermediate output. UsingMonte-Carlo simulations, Sheashowsthatthis increasedcorrelation improves the small sample behavior of his estimates over some range. Therefore, variables with 8

high DS/CS ratios are good demand-shifters, in the sense that they identify a supply elasticity with small asymptotic bias. Since we need good demand-shifters, the same results apply to our 11 approach. This general rule is not enough to select potential instruments for industry i. It is also important to impose rules on the process of instrument selection that minimize the influence of common supply shocks between both the industrywe use as an instrument and the industryfor which we need an instrument. For instance, the cost share data we use in instrument selection is the cost share of the two-digit sector containing industry i. This guards against a situation where the cost share is small merely because the four-digit industry is much smaller than the two-digit instrument industry. In addition, we do not allow sectors with the same two-digit SIC codeasindustryitobeinstrumentsforindustryi. Thisprohibitionreflectstheassumptionthat supply shocks are highly correlated within a two-digit industry. For the same reason, industries belonging to di(cid:11)erent SIC groups that are subject to similar supply shocks were not used as 12 instruments for one another. Instruments chosen by this approach are good proxies for exogenous variation in A, the revenue-shifter: It is unlikely that variations in the price of sector i have a signi(cid:12)cant impact on the output of sector j because the share of sector i in sector j’s cost is small. Industries selected as demand-shifters according to this methodology tend to be more aggregated than the industryforwhichweareinstrumenting. Furthermore, someoftheinstrumentscouldhave been considered good demand shocks even before we imposed restrictions to guarantee exogeneity. Government defense spending is a good example. Changes in defense spending are primarily related to political and social events, not to speci(cid:12)c four-digit industry supply shocks. After choosing instruments based upon the above criteria, we then checked the list of potential instruments to make sure that the correlation between the instrumental variable candidate and the output of sector i was due to their input-output link. For instance, instrument candidates were rejected if they were too closely related to business cycle variations because costs in sector i could be correlated to the business cycle as well. To address this problem, we pretested thepotentialinstrumentsforrelevanceoncebusinesscyclevariations werepurgedfromthedata. First, we regressed the potential instruments on business cycle measures and saved theresiduals 13 from this equation. Then we regressed output growth on the residual instrument growth to check for instrument relevance. We discarded instruments which had low T (cid:3)R2 statistics or 14 were negatively correlated to the regressor. The 62 industries chosen after this (cid:12)nal check was concluded are reported in Appendix 1. 11Thethreshold values we used are DS=CS >3 and DS >15 percent,the same as Shea used. 12This is the case for the apparel and textile industries (SIC 23 and 22), the primary and fabricated metals industries (SIC 33 and 34), and theindustrial machinery and electrical machinery industries (SIC35 and 36). 13Di(cid:11)erentmeasureswereused. The(cid:12)nalregressionsusetotalmanufacturingpriceandproductionasbusiness cycle indicators. The results are insensitive to thechoice of other indicators. 14Although only a few instruments were negatively correlated to output, we discarded them since systematic demand shocks should be related to variations in outputin thesame direction. 9

Some sectors have only one good instrument, while others have more than one. In order to select one vector of instrumentsamong all the available possibilities, we maximized thecriterion which is used to guarantee instrument exogeneity. Hence, we chose the instrument with the highest ratio of DS to CS. These instruments are indicated by asterisks in the appendix. Using multiple instruments where they are available or using other criteria to generate the demandshift vector generated nearly identical results to those reported in the next section. 4.2 Data and basic speci(cid:12)cation Our dataset is drawn in large partfrom the NBER Productivity Database, which is constructed 15 using the Annual Survey of Manufactures. It includes annual data from 1958 to 1994. The wageinindustryiattimet,W it,iscomputedastheratiooftotalpayrolltoemploymentdivided by the consumer price index. The employment series, N it, includes both production and nonproduction workers. Real value added, R it, is de(cid:12)ned as the value of industry shipments plus 16 the change in inventories minus materials costs. Descriptive statistics for our key variables are shown in Appendix 1. We donot observe the alternative wage that a representative worker in a particular industry would receive if (cid:12)red and rehired in another industry. We assume that the alternative wage will depend on three components: First, it will reflect the state of the aggregate labor market. Second, it will depend on industry-speci(cid:12)c factors such as the nature of the work and the transferability of skills. These two components are easily controlled for using time dummies and (cid:12)xed e(cid:11)ects. However, the third component, the human capital of employees, may not be. Although a large portion of the di(cid:11)erences in human capital across industry is likely captured by(cid:12)xede(cid:11)ects, thecomposition of workers andskills in anindustrymay changeover time. This requires a measure of human capital that varies across time and industry. We construct our human capital measure, hc it, using household data from the Bureau of Labor Statistics. Ourmethod is described in detail in Appendix3. Briefly, there are three main steps: First using the outgoing rotation groups of the Current Population Survey, we ran wage regressions to get the predicted wage that each worker could expect to receive based solely on 17 education, experience, and other demographic characteristics. We then combined individual workers’ alternative wages into an aggregate alternative wage for each industry. Next, we mappedthose(Census)industriesintoSICcodesinordertomatchthemwithourmanufacturing data. 15The Annual Survey of Manufactures is conducted by the Census Bureau every year. Approximately 55,000 establishments respond to questions pertaining to payroll, shipments,materials costs, etc. 16We deflated shipments and inventories using the value-of-shipments deflator. Materials costs were deflated using the value-of-materials deflator. An alternative approach of deflating everything by the value-of-shipments deflator yields thesame basic results. 17Industrydummieswereincludedintheregressionforestimationpurposes,butwerenotusedintheprediction stage. 10

Our instruments (which are listed in Appendix 3) are constructed from a variety of sources. For industries with other two-, three-, and four-digit manufacturing industries for instruments, we used outputfrom the AnnualSurveyof Manufactures. For industries with the FIRE, health, and agriculture industries as instruments, we used gross product originating data from the National Income and Product Accounts (NIPAs). For the construction instruments, we used private residential and nonresidential structures investment, also from the NIPAs. Total construction is a chain-aggregate of residential and nonresidential construction. Our measure of defense spending is taken from the NIPA series for government consumption expenditures and gross investment. All of the NIPA data are in 1992 chain-weighted dollars. For (cid:12)shing, we used total landings of (cid:12)sh (in metric tons) from the Department of Commerce, National Marine and Fisheries Service. The empirical version of equation (10) is: r w it = (cid:11) i+γ n it +(cid:12) 0 hc it+(cid:17) it (12) it All variables are de(cid:12)ned in logarithms. (cid:17) it represents measurement error in our empirical de(cid:12)nition of sectoral rents and any remaining error. (cid:11) i represents industry-speci(cid:12)c e(cid:11)ects that do not vary over time. Taking the (cid:12)rst-di(cid:11)erence of (12) to control for these (cid:12)xed e(cid:11)ects and including time dummies to capture the time-speci(cid:12)c e(cid:11)ects in the alternative wage function, yields: r XT (cid:1)w it = γ(cid:1) n it +(cid:12) 0(cid:1)hc it+ (cid:12) j D j +(cid:1)(cid:17) it (13) it j=1 D j is the time dummy for the jth year. We run both OLS and IV versions of equation (13). 5 Results We discuss the basic results (cid:12)rst, then turn to how these results change when we adopt alternative speci(cid:12)cations. Table 1 shows the (cid:12)rst-stage regressions for real wages and value addedper-worker. It also reports regression results for other de(cid:12)nitions of industry rents that we will use in subsequent tables. Increases in demand have signi(cid:12)cantly positive e(cid:11)ects on pro(cid:12)tability and wages. Table 2 presents the basic OLS and IV results. The (cid:12)rst three columns show results with a sample period of 1960 to 1994. In these regressions, the alternative wage is assumed to be a function solely of time and sector-speci(cid:12)c e(cid:11)ects because our human capital variable only exists after 1979. The OLS estimate of the rent-sharing coe(cid:14)cient for our sample (column 2) is nearly identical to the OLS estimate for the entire sample of industries (column 1). Both estimates suggest that a 10 percent increase in value added-per-worker is associated with a 0.3 percent increaseinwages. AsinpreviousstudiesusingU.S.data, thiscoe(cid:14)cient issigni(cid:12)cantly di(cid:11)erent 11

from zero, but not particularly large. In contrast, the IV estimate of the rent-sharing coe(cid:14)cient 18 (column 3) is signi(cid:12)cantly di(cid:11)erent from zero and ten times larger than the OLS estimates. Remarkably, this elasticity is nearly identical to the results found by Van Reenen (1996) using a highly unionized sample of the U.K. labor market. In columns 4 through 8, we restrict the sample to 1980-94 in order to explore whether including a human capital variable changes the results. Our results are insensitive to both the inclusion of human capital controls and the change in sample period: Even though the OLS estimates for the shorter periodof time are a touch larger than theOLS estimates for thelonger time period, the IV estimates are identical. According to these (cid:12)gures, a 10 percent change in industry rents causes, on average, a 2.9 percent increase in wages. It is perhaps surprising that the human capital variable is insigni(cid:12)cant. However, this term merely reflects variations in human capital that are not captured by time dummies or (cid:12)xed e(cid:11)ects. We (cid:12)nd it plausible that the mix of worker characteristics in an industry does not vary substantially over time. As discussed earlier, for our purposes, value added-per-worker is a better measure of industry rents than accounting pro(cid:12)ts. However, in order to make our results comparable to earlier studies, estimates of the rent-sharing parameter using pro(cid:12)ts-per-worker are reported in Ta- 19 ble 3. The OLS estimates are a good deal smaller than the OLS estimates shown in Table 2. Using instrumental variables, we again (cid:12)nd substantially larger estimates of the rent-sharing coe(cid:14)cient. Indeed, the IV estimates are now about 15 times larger than the OLS (cid:12)gures. These results are robust to the use of other de(cid:12)nitions of industry pro(cid:12)ts such as those described in the appendix of Blanchflower et al (1996). An argument could be made that using variables that are not corrected for the number of hours each employee works may bias our IV estimates upward. Under this scenario, the wage variation we detect in response to changes in the product market could merely be capturing the fact that average hours of work are positively related to demand shocks. Table 4 presents estimates for wage equations using hourly variables. Both the total wage bill of production 20 workers and industry value added are divided by hours of production work. The results are qualitatively the same as the ones presented in Table 2, but the IV estimates are a bit smaller 18In section 3, we discussed the possible causes of the inconsistent OLS estimates: measurement error and simultaneity. We concluded that an IV approach would address both problems. However, knowing which type of bias dominates may also be interesting. If the problem were solely measurement error, as in the e(cid:14)cient bargaining model, less speci(cid:12)c instruments could be used. We experimented with using the output of a nearby sector as an instrumentand found that theresulting coe(cid:14)cient was about thesame as theOLSestimate. Thus, although measurement error is likely present, simultaneity appears to be a more important issue. Because our sample contains some non-unionized sectors, it is not surprising that the right-to-manage model is a better representation. 19Pro(cid:12)ts are de(cid:12)ned as the value of industry shipments plus the change in inventories minus materials costs andthewagebill. Allthetermsweredeflatedusingthevalue-of-shipmentsdeflatorexceptmaterialscosts,which were deflated using thevalue-of-materials deflator. 20Dataon hours of non-production workers are not available. 12

21 and less precise. This result gives some support to the view that movements in average hours ofworkmayexplainpartofthepositiverelationshipbetweenwagesandvalueadded-per-person. However, after controlling for hours, the rent-sharing parameter is still seven times larger than the OLS estimate, implying that procyclical hours are not the only factor at work. Most likely, variations in average hours of work are part of a broader bargaining process between (cid:12)rms and workers: When times are good, (cid:12)rms share pro(cid:12)ts, in part, by giving hours-constrained employees the opportunity to work longer and, therefore, to earn more per person. On the other hand, when times are tough, employees may be forced to work fewer hours. A quick glance at our list of instruments in Appendix 1 reveals that a number of industries we use have the same instruments; not surprisingly, an exogenous shock to one industry is often exogenous to another as well. However, we want to make sure that no one instrument is driving our results. For instance, if defense contractors tend to pay higher wages than other employers, an increase in defense spending could tend to shift the composition of industries toward higher-paying employers|leading to a spurious correlation. Alternatively, the mere fact that an industry instruments for many others could be a problem in and of itself. The cost share of vitreous plumbing (cid:12)xtures (SIC 3261) may constitute only a small share of the costs to the construction industry, but the costs of all 25 industries which use construction as an 22 instrument could be a large share. To address these issues, we also ran our OLS and IV regressions excluding the largest groups of industries that use common instruments. Table 5 contains these results. The (cid:12)rsttwo columns exclude industries where the instrument is Federal defense spending, and the other two columns exclude industries with construction spending as an instrument. Thecoe(cid:14)cients on value-added perworker in theIVregressions are signi(cid:12)cantly positive and more than twelve times the size of the OLS coe(cid:14)cients. Thus, our results are not 23 being driven by either of these instruments. As pointed out in Blanchflower et al (1996), a competitive labor market is not completely ruled out by our results so far. If labor mobility costs are sizable, the competitive model could 24 generate apositive relationship between rents-per-worker andwages intheshort-run. Inorder R to capture this dynamic e(cid:11)ect, we introduced lags of in our regressions. Table 6 shows that N the inclusion of these lags does not alter our results. The sum of the coe(cid:14)cients is essentially 25 the same as if the lags had been omitted. Additional speci(cid:12)cations with higher order lags 21Our point estimate is nearly identical to that of Abowd and Lemieux (1993), who use variables that are adjusted for hoursto estimate rent sharing in Canadian union contracts. 22As we pointed out in Section 4.1, for instrument selection, we use the cost share of the two-digit industry containing theindustry in question. Hence,we havealready circumvented this issue to some extent. 23The OLS and IV point estimates were also similar when both defense and construction were excluded from the instrument list. However, in that case, the sample is much smaller and the estimates are not as precisely estimated. The instrument that was used the most after defense and construction was primary metals, which was used for only (cid:12)veindustries. 24Thisresult isdriven bythefact that in theshort-run thelabor supply curveis not flat,as in thetraditional competitive model, but positively sloped. 25These results contrast with those of Blanchflower et al (1996). Using pro(cid:12)ts per worker, they found that 13

generate the same result. Because the competitive model with labor mobility costs predicts a long-run elasticity of zero, we can reject it in favor of a rent-sharing model. The estimates presented thus far assume that the rent-sharing parameter is the same across industries. As discussed in Abowd and Lemieux (1993), if this hypothesis is incorrect, OLS estimates of the rent-sharing parameter are inconsistent but IV estimates would still be valid. To shed some light on the possibility of heterogeneity by sector, we split the sample by union penetration and product market concentration. If the rent-sharing parameter varies substantially by industry, we would expect to see di(cid:11)erent coe(cid:14)cients across these groups. In addition, controlling for unionization and product market concentration may serve as robustness check for our basic results. As a measure of (cid:12)rms’ market power, we use an industry average of the Her(cid:12)ndahl concentration index published every (cid:12)ve years by the Bureau of Census. Table 7 breaks the sample in two: sectors that have market power below the median level and sectors that have market powerabovethemedianlevel. TheIVresultsshowthatthepro(cid:12)t-sharingcoe(cid:14)cientislargeand signi(cid:12)cant in both groups. Even though the IV estimate of the rent-sharing parameter for the high-concentration industries is larger than the estimate for the low-concentration industries, 26 the discrepancy between the two subsamples is not signi(cid:12)cantly di(cid:11)erent from zero. OurunionizationvariableistakenfromtheNBERtradedatabaseandisdescribedinAbowd (1990). Webreakoursampleintotwogroups: sectorsthathaveahighlevelofunionpenetration and sectors that have a low level of union penetration. Table 8 shows the OLS and IV results for both subsamples. Once again, the IV estimates are much larger than the OLS estimates. At (cid:12)rst glance, the IV results suggest that industries facing a more unionized labor force during the bargaining process share a smaller proportion of rents|a puzzling result. However, the IV estimate for the low unionization group is not precisely estimated. Thus, it is not surprising that we cannot formally reject the hypothesis that the two parameters are equal. In any case, a possibleexplanation fortheapparentpuzzlesuggested bythe(imprecise)pointestimates isthat a high sensitivity to (cid:12)rm performance generates excess wage variability, a feature that unions may (cid:12)nd undesirable. Taken together, the results in Tables 7 and 8 do not provide signi(cid:12)cant 27 evidence of sectoral heterogeneity. adding additional lags reduced the coe(cid:14)cients on the more recent terms. Moreover, the largest coe(cid:14)cient they found was on pro(cid:12)ts of three years earlier. As the authors noted, their results are consistent with simultaneity bias beingless important at longlags. Sinceweovercomethesimultaneity with instruments,includinglagsdoes not add much. 26We also re-ran these regressions using a four-(cid:12)rm concentration ratio as our index of market power. The results were similar: The coe(cid:14)cients were not signi(cid:12)cantly di(cid:11)erent across groups. 27Wealsocheckedforheterogeneitybyallowingtherent-sharingparametertovaryacrossindustries. Wecould notrejectthejointhypothesisofequalparameters. However,wearereluctanttomaketoomuchofthisevidence because theindividualindustry parameters were extremely imprecisely estimated. 14

6 Conclusions Our work sheds new light on tests of labor market competitiveness. Previous authors have estimated small elasticities of wages with respect to measures of industry performance for the Americanmanufacturingsector. Usinginstrumentalvariableanalysis,we(cid:12)ndanelasticity, 0.29, that is about ten times as large as the previous results and our own OLS estimates. Although, theoretically, thedi(cid:11)erencesbetweentheOLSandIVresultscouldstemfrommeasurementerror or sectoral heterogeneity, our results suggest that the more serious issue is the simultaneity between wages and (cid:12)nancial conditions. Our input-output approach to instrument selection overcomes the simultaneity. This result is robust to di(cid:11)erent speci(cid:12)cations and to controlling for changes in the mix of worker quality in each industry. Our results also provide further evidence against alternative explanations for the positive correlation between rents-per-worker and wages such as a neoclassical model with labor mobility costs. Thus, changes in industry rents appear to be a very important component of wage determination in U.S. manufacturing. Assuming our estimate of the rent-sharing parameter holds for the entire manufacturing sector, the results in this paperimplythat the majority (about 70 percent) of wage dispersionis explained by variations in industry rents. This remarkable result is in line with estimates found in similar studies using U.K. and Canadian data that were unable to control for the quality of the workforce. We (cid:12)nd that even after controlling for worker characteristics by industry, most of wage dispersion owes to di(cid:11)erences in industry (cid:12)nancial conditions. Thus, our results point to a less prominent role for human capital characteristics in wage determination than might have been expected. 15

Table 1: First-stage Regressions Value Added Value Added Pro(cid:12)ts Wage per Worker per Hour per Worker (cid:3) (cid:3) (cid:3) (cid:3) Demand .058 .209 .135 .386 Instrument (.013) (.066) (.066) (.121) R(cid:22)2 .23 .05 .04 .04 # obs. 2170 2134 2134 1999 Table 2: The E(cid:11)ect of Value Added per Worker on Wages 1960-94 1980-94 Entire Entire Sample Sample OLS OLS IV OLS OLS IV OLS IV Value .027 (cid:3) .029 (cid:3) .288 (cid:3) :045 (cid:3) .061 (cid:3) .292 (cid:3) .061 (cid:3) .290 (cid:3) Added (.001) (.004) (.103) (.003) (.010) (.132) (.010) (.129) Alternative -.016 .020 Wage (.045) (.061) R(cid:22)2 .19 .25 .15 .20 .20 # obs. 15339 2134 2134 6683 930 930 930 930 (cid:3) Statistically signi(cid:12)cant at a5percentlevel. (cid:3)(cid:3) Statistically signi(cid:12)cant at a10 percentlevel. Standarderrorsin parentheses. All regressions runin di(cid:11)erences of logs. 16

Table 3: The E(cid:11)ect of Pro(cid:12)ts per Worker on Wages 1960-94 1980-94 Entire Entire Sample Sample OLS OLS IV OLS OLS IV OLS IV (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3)(cid:3) (cid:3) (cid:3)(cid:3) Pro(cid:12)ts .009 .009 .143 .012 .010 .158 .010 .157 (.001) (.002) (.054) (.002) (.004) (.089) (.004) (.088) Alternative -.026 .013 Wage (.046) (.074) R(cid:22)2 .18 .24 .13 .17 .17 # obs. 14666 1999 1999 6638 924 924 924 924 Table 4: The E(cid:11)ect of Value Added per Hour on Wages 1960-94 1980-94 Entire Entire Sample Sample OLS OLS IV OLS OLS IV OLS IV Value .027 (cid:3) .043 (cid:3) .200 :044 (cid:3) .076 (cid:3) .208 .076 (cid:3) .200 Added (.001) (.005) (.141) (.003) (.012) (.187) (.012) (.184) Alternative .046 .052 Wage (.057) (.061) R(cid:22)2 .16 .18 .13 .15 .15 # obs. 15339 2134 2134 6683 930 930 930 930 (cid:3) Statistically signi(cid:12)cant at a5percentlevel. (cid:3)(cid:3) Statistically signi(cid:12)cant at a10 percentlevel. Standarderrorsin parentheses. All regressions runin di(cid:11)erences of logs. 17

Table 5: Regressions excluding certain instruments Excluding Excluding Defense Construction OLS IV OLS IV Value .028 (cid:3) .341 (cid:3) :026 (cid:3) :362 (cid:3)(cid:3) Added (.005) (.139) (.005) (.196) R(cid:22)2 .24 .20 # obs. 1819 1819 1345 1345 Table 6: Regressions including lagged value-added per worker OLS IV (cid:3) Value Added .039 .312 per Worker (.005) (.464) (cid:3)(cid:3) Value Added .008 -.082 per Worker (.005) (.574) (t−1) (cid:3) Value Added .018 .169 per Worker (.004) (.371) (t−2) R(cid:22)2 .26 # obs. 2005 2005 (cid:3) Statistically signi(cid:12)cant at a5percentlevel. (cid:3)(cid:3) Statistically signi(cid:12)cant at a10 percentlevel. Standarderrorsin parentheses. All regressions runin di(cid:11)erences of logs. 18

Table 7: Split by market concentration High Low Entire Entire Sample Sample OLS OLS IV OLS OLS IV (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) Value .022 .025 .382 .033 .038 .247 Added (.002) (.005) (.190) (.002) (.008) (.121) R(cid:22)2 .18 .28 .22 .25 # obs. 8216 1200 1200 7123 934 934 Table 8: Split by unionization High Low Entire Entire Sample Sample OLS OLS IV OLS OLS IV (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) Value .022 .052 .173 .032 .016 .501 Added (.002) (.007) (.090) (.002) (.005) (.352) R(cid:22)2 .22 .29 .17 .25 # obs. 7699 1085 1085 7640 1049 1049 (cid:3) Statistically signi(cid:12)cant at a5percentlevel. (cid:3)(cid:3) Statistically signi(cid:12)cant at a10 percentlevel. Standarderrorsin parentheses. All regressions runin di(cid:11)erences of logs. 19

Appendix 1 Demand-shifting instruments SIC Industry Instrument 2097 Manufactured ice Fishing 2291 Felt Goods Nonelectrical Equipment 2293 Padding & Upholstery Filling Transportation Equipment 2396 Automotiveand Apparel Trimmings Vehicles 2421 Sawmills and Planing Mills, general Residential Const. 2426 Hardwood Dimension and Floor Mills Construction 2431 Millwork Construction* Residential Const. 2434 Wood Kitchen Cabinets Construction* Residential Const. 2435 Veneerand Plywood Construction* Residential Const. 2439 StructuralWood Members, n.e.c. Construction Residential Const. Nonresidential Const.* 2452 Prefabricated Wood Buildings Construction* Residential Const. Nonresidential Const. 2492 Particleboard Construction* 2517 TV & Radio Furniture Electrical Equipment* Radios & TVs 2649 Miscellaneous Conv. Paper Construction 2753 Engraving and Plate Printing Finance, Insurance, Real estate 2874 Nitrogenous and Phosphatic Fertilizers Agriculture 2891 Adhesivesand Sealants Construction Residential Const.* 2892 Explosives Coal Mining 2893 Printing ink Publishing 2951 Paving Mixtures and Blocks Construction* Nonresidential Construction 2952 Asphalt Felts and Coatings Construction* Residential Const. One-unitConstruction 3251 Brick & StructuralClay Tile Construction* Residential Const. One-unitConstruction Nonresidential Const. 3253 Ceramic Wall and Floor Tile Construction* Residential Const. Nonresidential Const. 3259 StructuralClay Products, n.e.c. Construction* Residential Const. One-unitConstruction 20

Nonresidential Const. 3261 Vitreous Plumbing Fixtures Construction* Residential Const. One-unitConstruction Nonresidential Const. 3264 Porcelain Electric Supplies Nonresidential Const. Electrical Equip.* 3271 Concrete Block and Brick Construction* Residential Const. One-unitConstruction Nonresidential Const. 3272 Concrete Products, n.e.c. Construction* Nonresidential Const. 3273 Ready-mixedConcrete Construction* Residential Const. One-unitconstruction Nonresidential Const. 3274 Lime Primary Metals Basic Steel and Mills Iron and Steel* 3275 Gypsum Construction* Residential Const. One-unitConstruction 3291 AbrasiveProducts Nonelectrical equipment 3293 Gaskets, Packing and Sealing Devices Nonelectrical equipment* Transportation Equipment 3296 Mineral wood Construction* Residential Const. One-unitConstruction 3299 Nonmetallic Mineral Products, n.e.c. Primary Metals 3357 Nonferrous Wire Construction 3431 Metal Sanitary Ware Construction* Residential Const. One-unitConst. 3432 Plumbing FixtureFittings & Trim Construction* Residential Const. One-unitConst. 3441 Fabricated StructuralMetals Nonresidential Const. 3442 Metal Doors, Sash and Trim Construction* Residential Const. One-unitConst. 3449 Miscellaneous Metal work Nonresidential Const. 3463 Nonferrous Forgings Aerospace 3465 AutomotiveStampings Transportation Equipment* Autos 3482 Small Arms Ammunition Federal Defense Spending 3483 OtherAmmunition Federal Defense Spending 3489 OtherOrdnance Federal Defense Spending 21

3493 Steel Springs, except wire Transportation Equipment* Autos 3534 Elevators & Moving Stairways Nonresidential Const. 3547 Rolling Mill Machinery Primary Metals* Iron & Steel 3565 IndustrialPatterns Primary Metals* Iron & Steel Basic Steel and Mills 3567 IndustrialFurnaces Primary Metals 3624 Carbon and Graphite Primary Metals 3662 Radio & TV Communication Equipment Federal Defense Spending 3676 OtherElectronics Federal Defense Spending 3694 Engine Electrical Equipment Autos 3721 Aircraft Federal Defense Spending 3724 Aircraft & Missile Engines & Parts Federal Defense Spending 3761 Guided Missiles and SpaceVehicles Federal Defense Spending 3764 Guided Missile Propulsion Units Federal Defense Spending 3825 Mechanical Measuring Devices Electrical equipment 3843 DentalEquipment and Supplies Federal health spending 3996 Hard Surface and Floor Coverings Construction* Residential Const. One-unitConst. (cid:3)Anasterisk indicates which instrumentweused incases wherean industryhadmore thanonepotential instrument. 22

Appendix 2 Sample comparisons In thetext, westate thatour sampleis representative of the entireUS manufacturingsector. The table below shows the threshold values for the distribution of the key variables for both the entire sample of 450 industries and the smaller sample of 62 industries used in this paper. Wages and value added are in thousands of 1982 dollars per person. Value added-per-worker in the entire sample has a slightly larger right tail, but other than that, the distribution of wages and value added are very similar. We average the union penetration ratio across time to get a union variable for each industry. The Her(cid:12)ndahl index concentration numbers are industry averages of the 1982, 1987, and 1992 (cid:12)gures. Both of these variables are very similar across the two samples. Thus, the results in the text are not being driven by sample selection and they are representative of manufacturing in general. Wages Value Added Union Concentration Full Our Full Our Full Our Full Our Sample Sample Sample Sample Sample Sample Sample Sample 10% 12.4 15.2 15.8 18.9 23.2 25.9 121 92 30% 16.3 17.8 31.1 35.7 27.9 30.3 273 253 50% 19.1 20.2 42.7 45.0 32.1 34.1 509 675 70% 21.5 22.2 55.7 56.3 40.6 40.6 847 1151 90% 25.4 26.3 91.5 77.5 49.8 44.8 1536 1632 23

Appendix 3 Alternative wage construction Because pro(cid:12)table industries may attract higher quality workers, we need to make sure that any wage responsiveness to industry variables that we measure is not merely capturing the higher wages that high-quality workers earn. To the extent that labor quality varies across industry or time, our time and industry dummies will capture those movements. However, it is possible that worker quality varies systematically across time and industry. Our database cannot control for quality. Therefore, using data from the Current Population Survey from the Bureau of Labor Statistics, we have constructed measures of the wages that workers could be expected to earn based on their individual characteristics. Building this \alternative wage" consists of three major steps. First using CPS data, we predictthewage thateach worker could expecttoreceive given hisor hereducation, experience, and other demographic characteristics. We then combine individual workers’ alternative wages into an aggregate alternative wage for each industry. Next, we map those (Census) industries into SIC codes so that we can match them up with our manufacturing data. A.1 The CPS data and the basic regression 28 We use data from the CPS Outgoing Rotation Groups for 1979-1994. Our wage de(cid:12)nition is earnings per week, and our hourly wage de(cid:12)nition is earnings per week divided by hours per week. The log of each wage measure is regressed against the following variables: (cid:15) Education is grade attained or completed. Both the variable and its square are used. (cid:15) Age and its square are both included. (cid:15) Part time status is a dummy variable that is one if the person worked either part of the time, all year, or part of the year. (cid:15) Marital statusisadummythatisoneifthepersonismarried{whetherornotthespouse is present. (cid:15) There are (cid:12)ve race dummies. Some years have only three. (cid:15) Dummyvariablesforgeographiclocationareincluded. For1979-84, SMSAistherelevant area. For 1986-94, MSA Fips is used. (cid:15) State dummies are included in 1985, when the location variables are missing. (cid:15) Two-digit occupation dummies are used. 28We use outgoing rotation groups because the wage and hours series are more complete and consistent than in theMarch tapes. 24

(cid:15) Three-digit industry dummies are used for manufacturing. For non-manufacturing, 2digit industries are used. (cid:15) A gender dummy is included. (cid:15) Month dummies are included. In order to calculate what each individual could make regardless of industry, we want to take out the industry e(cid:11)ects from the prediction. Therefore, the regression is run using all the industry dummies, but the predicted wage is calculated by setting them equal to zero. We exclude a constant from the regression and drop one dummy from each of the other sets. This excluded group serves as a reference group. The alternative wage we predict can be thought of as a premium over and above (or below) what the excluded group earns. Our reference group is married, white, female, full-time schoolteachers who live in Washington, D.C. and were interviewed in December. This group was chosen because these categories stayed identi(cid:12)able across all the years, despite changing variable de(cid:12)nitions. We ran weighted regressions using the (cid:12)nal CPS weights. A.2 Aggregating predicted wages The predicted wages were then averaged within industries to obtain the alternative wage 29 estimateforworkersinthoseindustries. Wedidnotuseweighted averages becausetheweights represent the weight in the population, not the industry. This procedure yields an alternative wage measure for each Industry Classi(cid:12)cation Code for each year. The classi(cid:12)cation code is from the 1970 Census for years 1979-82 and from the 1980 Census for 1983-94. A.3 Matching Census industry de(cid:12)nitions to SICs TheassignmentofcensusindustriestoSICcodesisnotstraightforward. Forthe(CPS)years of 1983-92, census codes are based on the 1980 census which uses the 1972 SIC codes. Since we also use 1972 SIC codes, the mapping in the Appendix of the CPS documentation works (cid:12)ne. One SICindustry, 334, straddles two census industries. Therefore, we assign a weighted average of the alternative wages for those two census industries to SIC 334. For the CPS years of 1971-82, census codes are based on the 1970 census which uses 1967 SIC codes. There are many changes between 1967 and 1972 so that the CPS mapping appendix has to be altered according to the SIC revisions. There are also now many SIC codes that straddle census industries. These straddlers belong to 18 census industry ‘groups’. We created weighted averages of alternative wages for each group and assigned them to the ‘straddlers’. Once alternative wages have been calculated for each (1972 based) SIC code for each year, these are merged onto our basic dataset. 29Atthispoint,wealsocalculatedsomealternativewagesforgroupsofindustries. Thisfacilitatedthematching of Census industry codes to SICs in thenext section. 25

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