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http://clevelandfed.org/research/workpaper/index.cfm Best available copy Workinq P a w 8906 by Erica L. Groshen Erica L. Groshen is an economist at the Federal Reseme Bank of Cleveland. The author thanks Richard Freeman, John Ih~iLop, Katherine Bra-, John Bound, and seminar participants at l3oston and Stanford Universities for their valuable comments. Partial funding f m Social S c i m Research Council Grant No. SS-25-83-31 is gratefully acknowledged. Working papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical cconment. The views stated herein are those of the author and not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reseme System. June 1989 http://clevelandfed.org/research/workpaper/index.cfm Best available copy Recent interest in efficiency wage and insider/outsider models of wage determination has drawn attention to employer-based wage differences. Alternatively, these differences may simply reflect temporary, randm errors by wage-setters. This paper provides strong evidence against the possibility that employer wage variations are temporary or randm, along with additional verification of the existence of substantial employer wage differences within and between industries. The variance of wages is analyzed in a unique data set: wages paid to individual workers in selected blue- and white-collar occupations fram a sixyear panel of anployers within a single standard metropolitan statistical area. The most conservative estimate of establishment wage differentials in this sanple(controlling for very detailed job classification) yields a standard deviation of approxhmtely 12 percent within industry, or 18 percent, including interindustry differentials. Wage differences among employers are shown to be virtually stationary over time and related to establishment size, but not consistently to changes in establishment employment. http://clevelandfed.org/research/workpaper/index.cfm Best available copy The existence of l q e employer-based wage differences among apparently equivalent workers is often taken as supporting evidence for the existence of efficiency wages or implicit profitsharing (see Dickens and Katz [1987], for ample). 1 The two main alternative hypotheses that have been explored are sorting by worker-quality and by ampensating differentials, neither of which has found strong support in statistical tests. This paper tests a thin3 alternative, whether wage differences among qloyers are the result of randm, tmporary errors. If employer differentials are the result of errors, the efficiency of the labor market may be enhanced by their elimination, prhaps through government subsidies of information gathering and dissemination. On the other hand, if these differentials are efficient wages or profit-es, they may be ap- propriate second-best solutions to monitoring or agency problems endemic to the labor market, but have implications for other policy, such as trade or antidiscrimination policy, as demonstrated in FWlm and Summers (1986), or for macmewndc policy, as shm in Weitzman (1986). Efficiency wage aqnnents posit causality between workers' wages and on-the-job productivity (Yellen [1984], Stiglitz [I9841) ers may maximize profits by pay- . Thus, s a n e employ- a differential above the market~=learing wage, if resulting hxements in productivity exceed costs of the differential. At least five sources of inrreased productivity have been modeled: reduced monitoring (or shirking) costs (for exanple, Bulm and Summers [1986]), decreased turnover (Salop [1979]), sociological considerations (Akerlof [1982]), market insulation, and corporate consistency (keringer and Piore [1971]). http://clevelandfed.org/research/workpaper/index.cfm Best available copy 2 In contrast, implicit profi-ing models of wage variation (also called insider/outsider, rentsharing, and bargaining models) assum the ex- istence of variations in finns1rents and in employeestbargaining p e r (or agency costs). These conditions introduce the possibility of rentxapture by employees, although the models differ in the identity of agents and enforcementmechanisms. The players are clearest in the case of unionism; otherwise, the workerstbargaining agent is not obvious, although econdsts have long noted the existence of informal organization by nonunion workers ( m o p [I9571) , including uniorrthreat effeck versions (Dickens [I9861) and managerial capitalism/agency cost versions (Aoki [1984]). This paper focuses on the alternative explanation that wage differences among employers simply reflect randm errors by wage-setters. Seminal articles by Stigler(1962) and Rothschild and Stiglitz (1976) launched a family of pure information models that use costly job search to explain wage dispersion. Expensive job search allows the market to sustain a range of wages because a workertsgain from further search becanes uncertain, rather than a known quantity. While mean wages for a particular type of worker are equal to the workert s marginal product, the costs of information introduce an error term with a variance that is a positive function of the search and mobility costs for workers or employers. Thus, if employers adjust all workerst wages in tandem, errors may be correlated across occupations for an employer. Most previous empirical studies of interemployer wage differentials have focused on national interindustry differ-. 2 Because of data limita- tions, these studies have been unable to control well for local labor market conditions or detailed occupation, to oampare differentials between industries to those within industry, or to investigate the stability of employer differentials over time. http://clevelandfed.org/research/workpaper/index.cfm Best available copy 3 This paper provides new insight into establishment+ased wage variation, using a unique data set prepared for the author by the U.S. Wlreau of Labor Statistics. The wages of nonsupewisory white- and blue-collar workers in one city are examined to see whether employer differentials exist within a single labor market, whether they are stable aver the course of six years, and whether they are associated with growth or shrinkage of the establishment. Wage variation between industries is also canpared to that within industry. In addition, the results are ccrmpared to those in the Current Population Survey in order to estimate the m r a tn c e of interemployer wage variation as a source of wage variation in the econmy as a whole. The results cast light on the nature of wage differences among employers and on the plausibility of other propcsed sources of wage variation by employer. A number of previous studies find it unlikely that employer differentials arise fram systematic sorting of workers by measured or umeamred 3 ability within occupation. Even stronger empirical evidence tends to refute the hypothesis that wage differences among employers campensate for establish4 mentwide variations in working conditions. This paper provides evidence of substantial wage differences among employers within a single city. This finding greatly reduces the possibility that regionvide campensating differentials 5 for cost of living are the main source of employer differentials. The major contribution of this paper is the finding that interemployer wage differences, and rankings of employers by wage, are virtually stationary over six years. This result eliminates random variations (generated or perpetuated by costly information) as a likely s o u .of employer differentials. The persistence of establishment wage differentials is consistent with earlier http://clevelandfed.org/research/workpaper/index.cfm Best available copy 4 findings that employer wage differ- are associated with measurable charac- teristics of employers, such as establishment size and product market (Groshen [1988b]) . Process of elimination leaves the door open for the two provocative types of models of employer wage variation (efficiency wages and rentsharing) that have generated considerable interest. The conclusion identifies several key characteristics of interemployer wage differentials that need to be accounted for in any version of these models invoked. 11. The Data The data used in this study are a unique set canpiled for the author by the U.S. Wlreau of Labor Statistics, from Area Occupational Wage Surveys (AWS) for a single metropolitan statistical area (PEA) over the course of six years. The variables include the wage, sex, occupation, and establishment identifier of individual workers in nonsupemisory positions. Wages are the straight-time hourly wages (no overtime or shift premia included) of hourly workers, and the average hourly earnings of incentive workers. Although confidentiality restrictions prohibit the release of employers' names, the data include unique establishment identifiers and two plant characteristics: size class and two-digit Standard Industry Classification (SIC) code. This survey has the follming advantages: it allows control for %A, it includes many different industries, and it is longitudinal in establish- ments. In addition, the surveys cover a broad mix of occupations: w h i t e - and blue-collar, professional, skilled, and unskilled. The occupations surveyed belong to four major groups: clerical/office workers, professional personnel, custodial/materialwement workers, and maintenance/tool~powerplantoccu- http://clevelandfed.org/research/workpaper/index.cfm Best available copy 5 pations. ( m i x A presents a ccarp?letelist of the occupations covered in the survey.) An important feature of these data is specificity of the occupation definitions, which are actually job classifications and are more detailed than f d g i t Dictionary of Occupational Titles or Census codes. For example, secretaries are divided into five occupation classes, de- on their re- sponsibilities, and distinguished from other clerical occupations such as stenographers(three classes), typists (three classes), and file clerks (four classes). This level of detail pravides strong control for human capital as productively used. (Groshen [I988131 tests this assertion.) For brevity in the discussion that follaws, the term occupation will be used instead of AWS job classification, the more accurate term. In total, the particular survey analyzed below covers 88 occupations and 241 establishments in 42 two-digit SIC categories. Confidentiality re- strictions prevent the Wlreau of Labor Statistics fram releasing the identity of the MSA or the exact years covered. The MSA is described as located in the northeast region of the country and not widely dispersed geographically. The 6 six consecutive years fall between 1974 and 1981. Table 1 presents a summary of characteristics of the sample. Almost half (108) of the establidmmts are covered for the full six years; the re- mainder are fairly evenly split between those present for the first three years and the last three years, except for the few (7 percent) with missing data for one or more years. Thus, the data cover 1,008 establishmnt-year~. In any year, well over half of the establishments are among those covered for the full six years. Approximately 17,000 individuals are surveyed per year, for a grand total of 101,990 abservations. 6 http://clevelandfed.org/research/workpaper/index.cfm Best available copy Because the AWS occupations are found in many different industries and firms, the labor markets for such occupations may be more ccnnpetitive than the markets for more indus-ific or firmspecific occupations. Workers can be apected to be more mabile when their skills are readily transferable among many different employers. Thus, we would expect the wages of workers in AwS occupations to be more standard across qloyers than would the wages of workers in less cammon occupations. Hawever, because they are coaanon to most firms, AWS occupations gener- ally work outside the major productive activities of the establishments surveyed and capture a relatively mall proportion of the employees in most establishmmts. There are two alternatives to this approach. The first, analysis of industq-spcific surveys that include the occupations most prevalent in each industry, is taken by Grc6hen (198833). The second solution is to contract job classifications into broad occupational categories and survey all occupations and industries, as is done in household surveys. The analysis presented here includes a caparison of the results fram the AWS to those from industry surveys and f m the Current Population Survey. e r Differences 111. The Size and Stability of ~ l o ~ Wase A. Technicwe Of particular interest in the study of interemployer wage differences is a measure of their importance, that is, the relative contribution of employer wage differences to total wage variation. This &ion partitions the variance of wages into the portions associated with particular effects using analysis of variance (ANOVA) techniques. 7 http://clevelandfed.org/research/workpaper/index.cfm Best available copy At any time, wages are hypothesized to depend on an individual's occupation, employer, the interaction between employer and occupation, and an individual cmponent. If virtually all productive differences in human capital and working conditions are between, not within, nanmly defined occupations, then occupation dummies capture all significant differences in human capital and working conditions among jobs. GrOShen (1988b) examines this issue and finds that the standard human capital variables (age, education, and race) add little explanatory p e r to regressions with three-digit occupational dummies in the Current Population Survey. Given the detail of the occupation distinctions in these surveys, the human capital variables can be e x p c t d to explain even less of the remaining variation in these data. In order to control as fully as possible for differences in worker quality, the actual estimation includes dununies for sex and incentive pay along with occupation. For ease of expsition, this set of variables is referred to simply as ttoccupation.w The test for the importance of employer characteristics is to measure the size and significance of employer variables included in a wage equation with human capital variables. The first set of variables are establishment durmny variables, to capture the average deviation of employees f m their occupation means a - all occupations. This effect, the fixed effect of employer on wages, is the main focus of this analysis. Second, variations in employer differentials among occupations are captured by including variables for the interaction of occupation and establishment, which estimates an additional wage differential for each occupation in each plant. In this paper, this will be called an employee's lljob-cell.tt The equation estimated is as follaws: http://clevelandfed.org/research/workpaper/index.cfm Best available copy wijk = p + X ia + Y jp + x iYjr + Ei jkf (1) where wijk= ln(wage) of employee k in occupation i at employer p = mean wage for the population, Xi = vector of occupation dunmry variables, a = vector of occupation wage differentials, Yj = vector of establishment dummy variables, p = vector of employer wage differentials, XiYj= vector of job-cell dummy variables, r = vector of wage differentials for jab-cells, and eijk= randcarly distributed error term. Since all of the independent variables are dichotanous, equation(1) can be rewritten, and wages may be understood, as the sum of a series of differentials: w = p + a - + p +7..+E ijk 1 wherea-,8 , and r j 1 j th arethe i ij f ijk 11 , ,th 3 , and ijthelements ofthe a, 8, and r vectors, respectively, and p is the overall mean wage. Over time, any of these four capnents may change, htmducing coefficients on their interactions with year. These year-interaction coefficients capture trends or temporary deviations from average relative position aver the s i x years and may be estimated in an expanded version of equation (2) : t (3) t t t t w ijk = p + a1- + ai + p j + P j + ri j + T i j + E ijk The differentials can be understood as follows: 1) Occupation differential (ai)is an occupation's average deviation f m mean wages, across all establishments. Presumably, these premia reflect pmductivity and campensating differences among occupations. http://clevelandfed.org/research/workpaper/index.cfm Best available copy 2) Occupation-year differential (ati)is an occupationlsaverage deviation from its cswn mean wage in a particular year, across all establishments. These movements reflect responses to tmporary labor -ply shocks or adjustments t a m d new long-run positions. 3) Establishment differential (Pj ) is the employees' average deviation from occupation mean in an establishment, across all occupations. Thus, these encconpass many differentials proposed in earlier research: size of employer, h-dustry, penxntage female, union, etc. 4) Establishment-year differential (Pt) is the employees1 average deviation from establishment mean in a particular year, across all occupations. These movements reflect responses to temporary shocks or adjustments toward new long-run positions. 5) J-11 (interaction) differential (rij) is paid to a particular job-cell abwe the occupation and establishment differentials. High variance in this term indicates significantly different internal wage structures among employers. 6) Job-cell-year differential (rt j) is the job-cell deviation from mean in a particular year. High variance in this term indicates instability in the internal wage structures of employers. 7) Within job-cell (individual) differential (et jt) is an individual or residual deviation from the mean for an occupation in an establishment in a year, presumably the result of individual productivity differences or differing compensation strategies on the part of employers (for example, incentive versus day rates). The more that wages are tied to individuals or to short-run performance rather than to job, the larger is this cmponent. Note that equations(1) and (2) express the same model in different notation. Equation (3) estimates the same model as in equations (1) and (2), but is fully interacted with time. If the differentials in equation(3) are mutually independent(this issue will be considered belm), the total variance of wages may be partitioned as follows: The size of each variance cmponent estimate indicates its relative econdc hprtance. And, the variation associated with interactions between a cmpnent and year meafllres the stability of wage differentials associated 10 with the ccmpnent over time. Our http://clevelandfed.org/research/workpaper/index.cfm Best available copy interest is the economic and statistical significance of the differentials as groups, fllrm~lrizedby the relative size of the variance ccmpnents and their interactions, as follows: 1) 2 d and o a at measure the importance and stability of external occu- pational labor markets, respectively; measure the importance and stability of employer wage 2)<and$ Bt differentials in wage determination, -ively; 3) 2 d and o 7 7t measure the importance and stability of independent internal labor markets, respectively; and 4) dr measures the importance and stability of individual differt ences within job-cell. The essential complication to the discussion above is that varianceccmpnent deccanposition as shown in equation (4) is not straightforward when data are unbalanced. An unbalanced design produces multicollinearity between the vectors of dwany variables (X and Y ) in equation (I), w h i c h prevents a i j simple separation of the impacts of X and Y. If an establishment employs a relatively large number of workers in skilled occupations, we cannot distinguish whether a differential paid to those workers is due to their employer or 7 to their occupations. Thus, the technique applied is a decamposition of the sum of sqyares 8 of wages, rather than an explicit estimation of variance ccmpnents. This method provides a measure of the ambiguity arising f m design imbalance and does not require the imposition of structure on estimated differentials. The summary of the technique provided in table 2 shm huw a series of ordinary least squares (OLS) regressions is used to make the jump from equa- http://clevelandfed.org/research/workpaper/index.cfm Best available copy 11 tion (3) to equation (4). of regresors. Wages are regressed successively on different sets Cthanges in the coefficient of determination(that is, the sum of squares explained as a proportion of total) are used to partition the sum of squares of wages into aanponents comespriding to those in equation (4). 2 9 2 Use of the R standardizes a to a value of one. W First, in the pooled sample, log wages are regressed separately on vectors of occupation and establishment dummies and then on both sets of dum- . mies together (called the full mairreffects model) The marginal contribution of each set of dummies to the full main-effects model (over the equation with the other one alone) measures the portion of wage variation associated unambiguously with that factor. These correspond to minimum estimates of the relative size of the variance contributed by occupation and differentials, or 2 a . B 2 a and a 2 The difference between the R of each in the equation alone and their marginal contribution to the full main-effects equation is a measure of their joint (collinear,or ambiguous) explanatory p e r . To identify the industry effect, industry dummies are substituted for establishment durmnies. Next, the exercise is repeated with interactions between the main 2 effects and year, in order to estimate the relative size of a at and 2Pt, which indicate the stability of the main-effect estimates. The contribution 2 of all other interaction differentials, including job-cell(a ) and 7 job-cell-year differentials(a 2 7t ) , is the difference between the explanatory power of a regression on job-cellyear dummies and that of the full (time-interacted) main-effects model. The individual contribution(a 2 ct the variation unexplained by job-cell-year dummies. ) is http://clevelandfed.org/research/workpaper/index.cfm Best available copy 12 B. ANOVA of the Area Wase Survey Table 3 presents the ANOVA of wage data fram the area wage survey. The first column reports the degrees of freedom for each source of 10 variation. crement to The second column reports the percentage sum of squares, or in- <, captweii~eachmume. m e total sum of squares reported excludes the effect of annual means, which were extracted prior to the analysis presented. The third colunm records Fstatistics where appropriate. The top six raws fllmmarize the impact of the main effects: job clas11 sification, sex, incentive and establishment. Together, these factors ac- count for 90 percent of the observed variation in wages. The joint contribution of the ma& effects dominates, claiming 51 percent of total variation. This reflects an uneven distribution, or hmmplete overlap, of occupations among establishments in the sample. The marginal contributions of establishment over occupation, and vice versa, are 19.3 percent and 19.5 percent, respectively: about equal, and both highly significant statistically. Each acplains samewhere between 19 and 71 percent of total wage variation (71 percent is the marginal contribution plus the joint portion of variation). The fixed establishment cmponent of variation can be divided into the portions between industries and within industry. Betweerrindustry variation is 11.4 percent of total variation (almost 60 percent of the marginal establishment total), leaving 7.9 percent for within-industry variation. Both portions have significant Fstatistics. So, while industry captures a large part of the differences between establishment, it does not capture it all. These results indicate that larye establishment differentials exist within MSAs. The estimated establishment differentials have a l q e range: http://clevelandfed.org/research/workpaper/index.cfm Best available copy froan a minimum of -.81 to a maxirmrm of +.56, ccanpared to the mean. In fact, we cannot reject the possibility that employer differentials a .as important as occupation, sex, and incentive pay in the determination of wages. The importance of the interactions with time and between occupation and establishment are examined in depth below. The final category is individ- ual variation, which accounts for only 3 percent of total wage variation. This 12 suggests that individuals in the same j h l l are paid very similarly. C. The Uniformity of Establishment Differentials Across Oamational Groups The tenth raw of table 3, !la11 other interactions," masures the con- tribution of all interactions not explicitly listed in the raws above. These interactions include job-cell and j h l l y e a r interactions ( w h i c h 2 a 7 2 and a ): differences in age-earnings profiles, in the relative treat- 7t ment of job-cells by establishment, and changes in these over time. 'Ihis group of interactions is significant as a whole, but accounts for just 6.3 percent of total variation. That is, the most comemative estimate of the 19 pescent-is contribution of employer main effects- three times as large as the interaction contribution. The size of this term suggests that relative cccupational wage s t r u b are probably fairly similar among these establishments. Another way of examining the consistency of establishment differentials across occupational groups is to obtain and c a p r e independent estimates for the four general occupational groups in the sample. Correlations of the employer wage differ-across groups are shown in table 4. The upper panel lists correlations across groups when industry effects are included in establishment effects. For instance, the correlation between the establishment differentials of office workers and those of maintenance, 14 http://clevelandfed.org/research/workpaper/index.cfm Best available copy toolrooan and powerplant workers is .635. The correlations are similar in magnitude to those obtained in LeoaTd (1987) and Groshen and Krueger (1989). Rank order correlations(listed below the standard Pearson correlations) do not differ substantially. The lower panel shows the cross-occupational consistency of establishment effects within industry. Again, the correlations are generally quite high. In fact, the correlations involving professional and technical workers rise after controlling for industry. The smallest correlation (.306) occurs between office occupations and material movement and custodial workers. Apparently, interindustry differentials account for the bulk of the consistency in interesbblishment differentials between these two groups. In general, though, these results suggest that establishment differentials have consistent size and rank a m occupations, even within industry. D. The Stability of Establishment Wase Differentials The pattern of establishment and occupation wage levels in this survey remains'umhanged over six years. 'Ihiscan be inferred fram raws 7 through 9 of table 3, which suggest that occupation and establishment differentials are remarkably stable: occupation and establishment interactions with year con- tribute a total of less than 1 percent of observed variation. Rnployer differentials are only slightly less stable than occupation differentials. Another demonstration of the stability of establishment differentials is the lack of decay in y-ear correlations as the gap between obsema- tions lengthens. Table 5 p m t s correlation coefficients(both Speaman and Pearson) of estimated establishment differentials across t h . The correlation coefficients of estimated differentials for the same establishments in different years are strikingly high, starting at .99 for oneyear differences 15 http://clevelandfed.org/research/workpaper/index.cfm Best available copy and barely decaying to .97 for estimates six years apart. The picture for rank-order correlations is much the same: coefficients decline only to .95 13 after six years. The lower panel of table 5 shm the persistence of within-industry establishment differentials. Although somewhat lmer than the persistence of differentials that include imlustry effects, the correlations are still remarkably high: they decline only to .894 (. 856 in rank order) over the course of six years. So, not only are employer differentials stable in size over time, but the relative rank of employers by size of differential is also stationary for periods as long as six years. F'urthermre, the lack of any rapid decay over the period suggests that the patterns are probably stable for much longer than the six years included in the survey. E. Conversion into Standard Deviations Table 3 partitions the sums of squares, but does not indicate estimated variances for the components of interest. Table 6 presents results of multiplying the percmtage of the sum of squares due to each factor by the total variance of the sample, and then taking the square root to generate the suggested standard deviation. In order to stack the deck against the investigated effect, the joint effects from table 3 are allocated capletely to occupation. The results can be converted to standard deviations in two ways. First we see the entire establishment effect, including the imlustry effects. This generates a standard deviation of .18, which we can interpret as a percentage of the mean because wages were estimated in log fom. We can also extract two-digit industry effects fram the estimated establishment effects. http://clevelandfed.org/research/workpaper/index.cfm Best available copy 16 This leaves intra-industry variation with a standard deviation of 12 percent, strikingly similar to the estimate of 11 percent in the industry surveys in GrOShen (1988b). The similarity of these results, despite the very different sources, lends confidence to the findings. Huw big are these nwS3ers in practical tenns? The experiment that this research tries to simulate is the randm transfer of a worker in one establishment to a job in the same occupation at another establishment. What 14 is the expcted wage change from such a switch? Converting the suggested standard deviations in table 6 to e x p d e d wage changes, a random switch in establishment within industry (within job classification, sex, city, and incentive class) yields an e x p e c b d 12 percent Change (in absolute value) in wages; a switch that might be between indus- tries is expe&ed to g-te a 19 percent wage change. These differem=esare cconparable to average wage differences between union and nonunion employers, and correspond to differences of $2,100 and $3,300 per year, respectively, of the average wage of $17,000 earned by a blue-collar production worker in manufacturing in 1984. Switching employers within hdwtry results in a very larye e x p e c k d incame change, as larye as that from a switch in occupation within industry. In addition to the stability they shuw, the sheer size of these differentials makes it unlikely that they are caused by random variations. F. Ekwloyer Differentials and Wase Variation in the Current mulation Survey A large portion of current research in labor economics is based on log wage regressions of Current Population Survey (CPS) data, but at least half of 17 http://clevelandfed.org/research/workpaper/index.cfm Best available copy the wage variation in the CPS remains unexplained after inclusion of traditional measures of human capital. What portion of that Wnexp1ainedw1variation is actually due to employer differentials? B ampares variance canponents estimates for the s&industry Industry Wage Survey (IWS) average in Groshen (1988b), for the AWS, and for the May 1977 CFS. The IWS estimates are the simple means fmm ANOVA of the wages of production workers in six manufacturing industries. The AWS estimates are repeated from table 6, except that the effects of all interactions with time have been remved. Since these three data sources are quite different, adjustments for the differences are necessarily speculative. The conclusion reached is that, ccarrpared to total wage variation in the CPS, estimated variation due to estab- lishment differentials is larye, even by consemative measures. N. Establishment Size, Growth. and Shrinkage Differentials The employer wage differentials estimated above are presumably linked to characteristics of the employers, some of which have been identified, such as size of firm and size of establishment (Brawn and Medoff [1987]). This section investigates the link between wages and another characteristic of establishment-grwth or shrinkage of employment. In these data, grawth and shrinkage dummy variables can be created from dxqes over time in size class. Since Leonard (1989) finds that the size of establishment is surprisingly volatile, the first attempt to measure the influence of size change on wages uses net change in the size of employ- 18 http://clevelandfed.org/research/workpaper/index.cfm Best available copy ment at an establishment to measure grawth and shrinkage. Eunnnies for growth and shrinkage were entered separately in order to allow for lack of symn~try in lags or for stickiness in either direction. The upper panel of table 7 compares the contribution to explanatory power of size and the size change (m3 of the table) to that of establish- . ment dummies (m2), controlling for occupation and industry (row 1) The purpose is to measure h m much of employer variation within industry can be linked to size and size change. The results indicate that establishment size alone and dummy variables for establishment growth and shrinkage account for more than 19 percent of within-industry wage variation by employer in the AWS. Only 3 percent of this is contributed by the growth and shrinkage variables. The lower panel of table 7 presents the coefficient estimates for the regression equation in m 3 in the upper panel. Except for the smallest size class, wages increase monotonically with size, and we estimate a negative differential for growth and a negligible one for shrinkage. Table 8 presents the d t s of four other attempts to link estimated establishment differentials and changes in estimated differentials to growth or shrinkage of the establishment. The question is whether size change leads to greater or smaller wage changes than would be e x p c k d just f m the adjustment to wages of the new size class. If growth or shrinkage is exogenously determined and information is costly, then an employer's growth may raise its efficient wage under the turnover version of the efficiency wage hypothesis (see Salop [1979]). The wage increase is profiti~ximizingbecause, during growth, the employer needs to attract or retain a higher proportion of workers than it does in a steady 19 http://clevelandfed.org/research/workpaper/index.cfm Best available copy state. Similarly, an qloyer that needs to shrink its work force may allow relative wages to fall below previous levels. Attraction of new workers is unnecessary and quits are perhaps desirable. A second explanation for the same association canes f m the bargain- u s ing model. Suppose that establishment growth resulted frcnn t is, high profits--and shrinkage frm low profits. Then, gxuwth would indicate the presence of high wages because large rents were available for distribution. By the same logic, shrinkage would indicate lower wages. However, if grawth is endogenous, the zero-sum aspect of bargaining raises the possibility of the opposite relationship. If profits captured by workers would otherwise be used for expansion, then high-gmwth canpanies could be those with low wages. And shrinkers could be doing so because of their .highwages. This is the same prediction and causality generated by the simple campetitive model in the short run. I m wages lead to higher profits and, therefore, growth, unless the low wages induce quits, and thus, shrinkage; high wages should erode profits and cause shrinkage. Included here is the obsewation that since most hires are at the bottam of pay ranges, a hiring surge could appear to lower wages by lowering average tenure in a plant. To summarize, the turnover version of the efficiency wage hypothesis predicts a positive relationship between growth and wages. The bargaining model is ambiguous, depending on the exogeneity of growth, and the simple cmpetitive model predicts a negative relationship, or none at all. The first two columns of table 8 present regression coefficients for the effect of establishment growth and shrinkage on estimated establishment differentials, controlling for industry and size. The effect of shrinkage may be negative, occurring before the shrinkage takes place. The effect of growth http://clevelandfed.org/research/workpaper/index.cfm Best available copy 20 is also negative, but relative to the wages of establi-ts in the new size class, not the old one. 'Ihis suggests that wage changes may lag behind gmwth, but precede shrinkage. size change. S h That is, wages may be sticky uyxh.rards during the coefficient on growth is small and insignificant rela- tive to that on past size, and the coefficient on shrinkage is small and insignificant relative to that on current size, the mavement in wages is apparently not greater than that associated with a change of size category. However, the third column of table 8 diminishes confidence in the last point. In order to allow for more cmplete adjustment and to increase the signal-to-noise ratio, this column presents regressions of net changes in estimated differentials on net changes in size. Neither growth nor shrinkage has a large or significant impact on change in differentials. The sign of the coefficient on shrinkage m i m e s to positive but is small. Growth is esti- mated to reduce wages by 1 percent (with no controls for size), but the estimate is not significantly different fran zero. These data do not conclusively support any of the three hypotheses above. The first two columns suggest that wages are sticky upwards. If anything, wages are apparently lower for fi n n s that grow, but shrinkage has little or no effect. And, neither result is stable under alternative formulations (that is, relative to wages of employers of the same size). Thus, although size changes affect wages because wages hcrease with size, neither growth nor shrinkage appears to have a simple, consistent effect on wages, holding size constant. m e data reject the efficiency wage and the e x 0 g - bargaining predictions of a positive relationship between grawth and wages. m e correlation between wages and grawth, if there is one, http://clevelandfed.org/research/workpaper/index.cfm Best available copy 21 appears to be negative. It is even less likely that shrinkage is correlated with wages; but if so, shrinkage is also associated with (slightly) lmer wages. V. Conclusion A. flmaMlN of Findims The conclusions of this analysis are as follows: (1) Twenty to 70 percent of wage variance within this MSA is due to employerbased differences both between and within industry. The most conservative estimate of the standard deviation due to employer differentials within hdustry is 12 percent. Ccanbined with industry effects, this generates a standard deviation of approximately 18 percent: a major portion of the 50 percent total standard deviation of wages. (2) Establishment wage cliff- and rankings(even within industry) are virtually stationary for periods at least as long as six years, and probably for longer. (3) While establishment size can account for much of measured employer wage effects within industry, establishment growth and shrinkage do not have a simple, consistent relationship with employer wage levels or wage changes. Thus, even across occupations as diverse as those in the area wage survey, employer differentials are applied relatively uniformly. -ed to occupational means, employers tend to ampensate janitors as well (or as poorly) as they do industrial nurses, canputer programmers, millwrights, and stenographers. F'urthkre, employers are also very consistent in their patterns aver time. 22 http://clevelandfed.org/research/workpaper/index.cfm Best available copy Occupation (including sex and incentive) and employer differentials are clearly extremely important in wage determination. These factors, when well identified, as in these surveys, can explain more than 95 percent of wage variation. Thus, other characteristics of the individual (for exarrple, tenure, mrital status, or race) must operate through job classification or thmugh employer in order for them to have a large effect on wages. Otherwise, they are not highly influential in the determination of wages. In short, since a large impmement in earnings can be attained only through a pramotion or a change of employer, barriers to entry into highly remunerative occupations or establishments can have a devastating impact on the earnings of otherwise-cpalified workers. B. Irmlication for Sources of Establishment Waqe Differentials These results cast more light onto the nature of wage differences among employers and onto the plausibility of proposed sources of wage varia- tion by employer. Of the five sources of employer wage differentials that have been modeled (sorting by worker quality, ccrmpensating differentials, randam variations, efficiency wages, and insider bargaining), evidence in previous studies renders the first b o possibilities unlikely. The evidence presented above rejects the third possibility, random variations, as the source of employer differentials. The strong stability of establishment differentials over time provides canpelling evidence against the hypothesis that establishment differentials are tmporary fluctuations. If the differentials are random but not temporary, then they are extremely costly for high-wage employers, w h i c h suggests that labor-market information must be 23 http://clevelandfed.org/research/workpaper/index.cfm Best available copy even more costly. Wlt, the results of this survey and many other private substitutes are available to finns on a fairly timely basis at no cost (or at the cost of participation). Fbrthermore, the extent to which the differentials persistently (since at least the 1940s) depend on easily identified establishment characteristics, such as industry and size of establishment, makes the randrnn variations hypothesis unlikely. For instance, it is implausible that personnel officers of laqe f h have been consistently wrong, all mistakenly setting their wages too high for 40 years. Thus, the randrnn variation theory of establishment differentials may be ruled out. The finding of substantial wage differences among employers within a single city also argues against the possibility that regiomide capensating differentials for cost of living are the main source of employer differentials, although urban wage gradients within the city are still a possibility. Process of elimination also suggests the need for serious consideration of efficiency wage and rent-sharing (insider/outsider) models. This paper identifies several key characteristics of interemployer wage differentials that need to be present in any version of these models invoked. First, employer wage differentials are found among whitecollar work- ers, as well as blue-collar workers, in a nationally representative set of industries. The pewasiveness of these differentials q e s for explanations that apply a e e - b o a r d to all occupations in an establishment, and to the establishments in most industries. Thus, occupatiorrspecific difficulties in monitoring are not a likely source, because the occupations surveyed here are very diverse. Also unlikely are explanations that appeal to the characteristics of a single industry. http://clevelandfed.org/research/workpaper/index.cfm Best available copy 24 Second, although wages and size of establishment have a strong posi- tive correlation, plant size change has no sirnple, consistent relationship with wage level. Thus, the versions of efficiency wage and renkcharing models based on growth or shrinkage of establishment are unlikely sources of interemployer wage differences. M,since employer differentials are quite persistent on an annual basis, while annual profit rates of U.S. cmpmies are notoriously volatile, if these differentials are r e n t . ,they presumably reflect longrun, not short-run, rents. http://clevelandfed.org/research/workpaper/index.cfm Best available copy References Akerlof, George, I1LaborMarkets as Partial Gift Exchange, of Economics, vol. 97, November 1982, pp. 543-569. -1~ Joumal Aoki, Masahiko, The Coomtive Game Theom of the Firm, New York: Oxford University Press, 1984. Wrawn, Charles, lgEqualizing Differences in the Labor Market,'I guarterly Journal of Economics, Vol. 94, No. 1, February 1980. and James L. Medoff, The Employer Size Wage Effect, unpublished paper, September 1987. Ekuwn, William, John Hayles, Barry Iiughes and Lyndon Rme, Vrcduction and British JourLabor Markets in Wage Detemhation: Same Australian EvidencefV' n a l of Industrial Relations, Vol. 22, No. 2, July 1984. Wllaw, Jeremy I., and Lawrence H. Summers, I1ATheory of IXzal Labor Markets With Application to Industrial Policy, Discrimination, and Keynesian Unemp1oymentfwJournal of Labor Economics, Vol. 4, No. 3, Part 1, July 1986, pp. 376-414. Dickens, William, 'Wages, mloyment and the Threat of Collective Action by Workerf1I National Wlreau of E c o d c Research Working Paper No. 1856, March 1986. and Lawrence F. Katz, i industry Wage Patterns and Theories of Wage Determination,l1 National Wlreau of Economic F&sear& Working Paper No. 2271, July 1987. Doeringer, Peter, and Michael Piore, Internal Labor Markets and Manmwer Analysis, z-lexington,Mass.: D.C. Heath and Co., 1971. IXmlop, John T., llTheTask of Contemporary Wage Theory,I' in G. Taylor and F. Pierson, eds., New Conce~tsin Wase Determination, New York, 1957. Eberts, Randall W., "An Empirical Investigation of Intraurban Wage Gradients,I' Journal of Urban Economics, Vol. 10, 1981, pp. 50-60. Gibbons, Robert, and Lawrence F. Katz, llLearnhg, Mobility, and Inter-Industry Wage Differentials,I1Massachusetts Institute of Technology, unpublished paper, December 1987. Groshen, Erica L., Itsourcesof Wage,Dispersion: Does It Matter Where You Work?I1 Ph.D. Dissertation, Haward University, 1986. , 'Why Do Wages Vary Among Emp1oyers?l1Federal Fkserve Bank of Cleveland E c o d c Review, First Quarter 1988a. , I1Sourcesof Wage Dispersion: The Contribution of Interemployer Wage Differentials Within Industry,I1Federal Resewe Bank of Cleveland Working Paper No. 8802, 198813. http://clevelandfed.org/research/workpaper/index.cfm Best available copy and Alan B. Krueger, "The Structure of Supervision and Pay in Hospitalsttl Federal Reseme Bank of Cleveland Working Paper No. 8907, June 1989. Henderson, C.R., ItEstimationof Variance and Covariance Conpnents, ~iametrics, June 1953. Hocking, Ronald R., O.P. Hackney, and F.M. Speed, I1TheAnalysis of Linear Models with U n b d L a n c d Data," in H.A. David, ed., Contributions to Survey Samp l h and Amlied Statistics: Papers in Honor of H. 0. Hartlev, New York: Academic Press, 1978. Leonard, Jonathan S., ttOn the Size Distribution of Ehployment and Establishxmts,It Quarterly Journdl of Econdcs, 1989. , carrots and sticks: Pay, Supervision, and Turnaver,It Journal of Labor Econdcs, Vol. 5, No. 4, October 1987, pp. s136-s152. Mackay, Donald I., David Boddy, John Brack, John A. Diack and Norman Jones, Labour Markets Under Different Ewlovment Conditions, London: George Allen & Unwin Ltd., 1971. Nolan, Peter and William Ekwn, wCampetitionand Work Place Wage D e ~ t i o n Oxford , ~ Bulletin of Econdcs and Statistics, Vol. 45, No. 3, August 1983. R o ~ l d Michael, , and Joseph E. Stiglitz, ItEquilibriumin Ccanpetitive Insurance Markets: An Essay on the E c o d c s of linprfect Informationttl Quarterly Journal of Economics, Vol. 90, No. 4, November 1976. Salop, Steven, "A Model of the Natural Rate of Unemployment,Iv American Econ d c Review, Vol. 69, No. 1, Maxch 1979. Searle, S.R., Linear Models, New York: Wiley & Sons, 1971. Segal, Martin, llPost-Institutionalism in Labor Econdcs: The Forties and Fifties Revisited," Industrial and Labor Relations Review, Vol. 39, April 1986, pp. 388-403. Smith, Robert, ~ ~ ~ t i Wage . nDifferentials g and Public Policy: A Review,I1 Industrial and Labor Relations Review, Vol. 32, No. 3, April 1979. Stigler, George J., I1Informationin the Labor Market,81 Journal of Political Economy, Vol. 70, No. 5, Part 2, October 1962. Stiglitz, Joseph E., I1Theoriesof Wage Rigidities, National Wlreau of Ecod c Resear& Working Paper, 1984. , ItOnSearch and Equilibrium Price Distributionstwin Econdcs of Hirman Welfare, Michael J. Posken, ed., New York: Academic Press, Inc., 1979. Topel, Robert, Vquilibrium Earnings, Turnover and Unemployment, Journal of Labor Econdcs, Vol. 2, October 1984. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Weitman, Martin, ?he Share Economy: Conauerinu Staqflation, Cambridge, Mass.: Haward University Press, 1986. Yellen, Janet, Il~fficiencyWage Models of Unempl~yment,~ American ~conomic Review, Vol. 74, No. 2, May 1984. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Footnotes 1. Groshen (1988a) reviews the empirical and theoretical literature examining employer differentials. 2. Exceptions to this generalization are a g m u p of studies by ecodsts in the 1940s and 1950s summarized in Segal (1986). GrOShen (1988b) provides recent evidence of large establishment wage differentials among production workers in six manufacturing industries, using national industry wage surveys. 3. Groshen (1988b) finds it unlikely that intra-industry employer variations are due to sorting by termre, experience, education, or for variations in umeasured worker ability correlated with these meafllres of human capital. Dickens and Katz (1987) find that interindustry differentials cannot be explained by the three measures of human capital. And, Gibbons and Katz (1987) conclude that interindustry wage differences are not associated with unmeasured differences in productive abilities. 4. Attempts to identify the working conditions for which interindustry wage variations cmpemate have been notably unsuccessful, as have attempts to identify compensating variations in general (Elram [I9801 and Smith [1979]). 5. However, urban wage gradients within the city are still possible (Eberts [I9811) . 6. These years were characterized by historically high inflation rates, which might be a p c k d to result in more random behavior because of more costly information, and in more real downward wage flexibility on the part of employers. 7. Techniques for estimation of variance cmponents of a model of unbalanced design are detailed in Searle(1971) and Henderson (1953) Restricted maximum likelihood (Ill&) techniques are introduced in H o c h i n g , Hackney and Sped (1978). Ill& provides simple estimates of variance capnents and their standard errors at the expense of imposing a rigid structure on the distribution of level effects and errors. Because the appropriateness of the structure of this study is to imposed may vary among industries, and because the investigate the characteristics of establishment differentials, a nonparametric method was preferred for this analysis. Groshen (1986) provides a camplete discussion and examples of the application of alternative ANOVA techniques to similar data. . 8. The technique used here avoids the essence of ANOVA1sdifficulty with un- balanced data. A variance is a sum of squared deviations divided by the appropriate number of observations or degrees of freedom. In data with an unbalanced design, the correct number of degrees of freedom is unknam, so variance estimates must rely on estimates of the correct degrees of freedom. Such estimates require the impsition of structure on the data. 9. The following work concentrates attention on proportions of variance rather than on F-statistics for two reasons. First, because of the large sample sizes, all of the Fstatistics are strongly significant (the critical value is 1 in most cases), even if the economic significance is slight. Second, establishment identity is presumably an inefficient measure of the econcanically http://clevelandfed.org/research/workpaper/index.cfm Best available copy relevant differences between establishments. By construction, it captures all differences and thus identifies the maximum amount of variation that understanding of employer wage policy could explain. Hwever, as a measure of the source of employer differences, establishment may be finer than necessary. If so, the F-statistic can mislead because it averages out the inpact of all estimated levels. While the additional variation explained by unnecessary levels is negligible, the number of degrees of freedom used can be high, reducing the F-statistic. The inclusion of irrelevant levels washes out the significance of the relevant ones. The F-statistic of a factor X is defined as follows: where RRSS = restricted residual sum of squares, URSS = unrestricted residual sum of squares, k = number of restrictions or levels in parameter x, and n = degrees of freedom in unrestricted equation (that is, number of observations minus degrees of freedom used by other regressors) If k is the number of correctly specified levels of the factor X, then let 6 = measure of irrelevant fineness in another measure, say Y. That is, suppose instead of using k levels, we use the 6k levels of Y, where 6>1. Then, as long as the levels of X are a linear mination of the levels of Y, and n is large relative to 6k, the URSS of the equation will be almost the same, the RRSS will be the same, so the F-statistic of the inefficient parameter Y is as follows: . And, the ratio of Fy to Fx(for n large relative to k) is Fy/Fx (n-6k)k/ [(n-k) 61 = [ (w6)-k]/(n-k) 1 1/6. The maximum of the ratio is one (where X=Y, so 6=1); otherwise it decreases monotonically with increasing 6, -andapp&ches 1/6 for n large and k small. So the size of the F-statistic depends not only on the economic relevance of the parameter measured, but also on the inefficiency with which it is measured. Since the purpose of this work is to identify the potential explanatory p e r of variables based on establishment, I focus primarily on the percentage sum of squares explained by factors rather than t h m q h FLstatistics. 10. The number of degrees of freedom is determined by the number of dunnny variables used in the regressions. For example, in the case of establishments, the number of degrees of freedom is the number of establishments minus one. 11. The immtive dummy equals one when the worker in question has an incentive component to his or her earnings. These incentives may be in the form of individual or group piece rates, individual or group bonuses, or carmnissions. 12. This is the result for industries with a low proportion of incentive-based ccarpensation in Groshen (1988b). 13. These are quite similar to the results obtained by Mackay, et al. (1971) and Nolan and Brawn (1983) in England. http://clevelandfed.org/research/workpaper/index.cfm Best available copy 14. ?his question asks for the e x p e c b d absolute value of the difference between two identically distributed random variables. Assuming a normal distribution of differentials, the question reduces as follms: where d = randm differential, distributed N ( o , ~ ~ )and , @[0] and 9[0] are the normal density and the d a t i v e normal density functions, evaluated at zero. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Occupations Surveyed in the Area Wage Suwey Office Occupations Secretaries: Classes A, B, C, Dl E, and Not Classifiable By -el Staqraphers: Senior, General, and Not Classifiable By Level Transcribing-Machine Typists Typists: Classes A, B, and Not Classifiable By Level File Clerks: Classes A, B, C, and Not Classifiable By Level Switchboard Operators Switchboard Operator-Receptionists Order Clerks: No Level Distinctions, Classes A, B, and Not Classifiable Accounting Clerks: Classes A and B, and Not Classifiable By W e 1 Bookkeeping-Machine Operators: Classes A, B, and Not Classifiable By Level Me==wBilling-Machine ~illers Bookkeeping-Machine Billers Machine Billers, Not Classifiable By Level Payroll Clerks Key Entry Operators: Classes A, B, and Not Classifiable By Level Tabulating-Machine Operators: Classes A, B, and C Professional and Technical Ommations Canputer Systems Analysts (Wlsiness): Classes A, B, C, and Not Classifiable Cmpter Programmers (Wlsiness): Classes A, B, C, and Not Classifiable Cmpter Operators: Classes A, B, C, and Not Classifiable By Level Drafters: Classes A, B, C, and Not Classifiable By Level DraEter-Tracers Electronics Technicians: Classes A, B, C, and Not Classifiable By Level Peripheral Equipment Oprators Cmpter Data Librarians Registered Industrial Nurses Maintenance, Toolroam and Material Movement and Custodial EQwemlant Cccwations Ommations Main-Carpenters Truckdrivers: Light Truck, Medium Truck Maintenance Electricians Heavy Truck, Tractorlkztiler, and MainteMnce Painters Not Classifiable by Category Guards: No Level Distinction, Main-Mechanics (Machinery) Maintenance Mechanics (Motor Vehicles) Classes A, B, and Not Classifiable MainPipefitters Shippers Maintenance Sheet-Metal Workers Receivers Millwrights Shippers and Receivers Maintenan& Trades Helpers Warehousemen Machine-lbol Operators (Toolroam) Order-Fillers Tool and Die Makers Shipping Packers Stationary Engineers Material Handling Laborers Boiler Tenders Forklift Operators Pawer-TnlckOperators (Other Than Forklift) Janitors, Porters, and Cleaners Watchmen http://clevelandfed.org/research/workpaper/index.cfm Best available copy Deccanposition of the Variance of Wages in Three D a t a Sets 'Ihis appendix presents variance components estimates for the skhiiustq Industry Wage Survey ( I W S ) average in Groshen (1988b), for the Area Occupational Wage Surveys (AWS), and for the May 1977 Current Population Survey (CPS) . May 1977 was chosen as a year within the ranges of both the AWS and IWS. The q l e includes all priva-r, full-th employees between the ages of 18 and 65 with reported average hourly earnings of more than $1.75 per hour. The IWS estimates are the simple means fram ANOVA of the wages of production workers in six manufacturirq industries. The technique used in Groshen (1988b) is identical to that used here, except that all data are -ional, and so differentials are estimated without explicit interac- tions with year. The AWS estimates are repeated from table 5, except that the effects of all interactions with time have been removed. These three data sources are quite different, so adjustments for the differences are necessarily speculative. For instane, the standard deviation of wages in the AWS, (.20). .40, is double the mean for the six industry wage surveys As noted abave, area wage surveys cover a broader mix of occupations, both blue-collar and whitecollar. Moreover, area wage surveys include the effects of interindustry wage variation. The BS includes all of the sources of variation already mentioned, in addition to the full range of occupations in the econcnny. The first two raws of table B-1 present the least ccarparable rnrmbers across the three surveys: standard deviation estimates for total dispersion http://clevelandfed.org/research/workpaper/index.cfm Best available copy 33 and those due to occupation, sex, region, and kdustry differentials. Reported AWS and IWS figures allocate the entire joint occupation establishment effect to occupation. In the IWS, the variance in the first row includes regional variation, but not interindustry variation. In the AWS, the variation in the first row includes interindustry variation, but no regional variation. In the CPS, the first m captures both industry and regional sources of wage variation, in addition to occupation and sex. The level of detail of region, sex, and industry are roughly the same in the AWS and CPS, but CPS three-digit occupations lack the detail of the job classifications in the IWS and AWS. The CPS variation in the first mw is the same as that of the AWS, despite the higher total variance in the CPS. This suggests that variation within the CPS occupational categories is greater than the variation between regions in the country. Iack of occupational specificity leaves more wage variation unexplained than the addition of regional controls can capture. Another way to judge the impact of broad occupation data in the CPS is to note that in the plastics industry, contraction of the 42 BLS job classifi2 cations into 12 CPS occupational categories reduces the R of the equation by one half, frcnn 49 percent to 25 percent. In an ANOVA as shown, at least half of this differenrjudging frm the size of the contribution Itjoint"to occupation and establishment-might then be claimed by establishment differentials, raising the estimated employer effect in the CPS. The second row shows the remaining variation for each sample. These are quite similar for the AWS and IWS: a standard deviation of about .16. The CPS, however, retains a standard deviation of .31, almost twice as high. The next three rows present speculative estimates of the size of the within-industry establishment effect in the CPS, in order to provide bounds http://clevelandfed.org/research/workpaper/index.cfm Best available copy 34 for the probable contribution of establishment to CPS wage variation. The first method takes the point estimate of standard deviation fram the IWS and AWS: .11. Although this is a large portion of the unexplained standard devia- tion of .31, the estimate is conservative for two reasons. First, CPS occupations are very broad. The large joint cmponent of variation in the IWS and M S would shrink with these broad occupations, increasing the size of the estimated establishment impact on variation. Second, the I W S and PIWS oversam- ple large establishments and amit the smallest ones. In these data, estimated establishment variance is highest among the smallest establishments. Thus, the CPS should provide more establishment diversity because it samples evenly fram all sizes of employer. The second estimate assigns the AWS establishment percentage of total wage variation to establishment in the CPS, and comerts this to a standard deviation of .13. The result is very similar to the first estimate and has the same limitations. The third method is less conservative and assigns to establishment the same percentage of remaining variation (after occupation, industry, etc.) as is found in the AWS. That converts to a standard deviation of .20. In order to see if the limited number of occupations surveyed in the AWS accounted for these results, the last column of table 6 presents the same exercises on the subsample of CPS obsewations for workers in AWS occupations. (They totalled 24 percent of the CPS sample.) The variance of wages is lower in the subsample, but the entire decrease in variance is in the betweenoccupation portion of variance. This leaves the estimates of establishment effect virtually the same, increasing confidence in them. 35 http://clevelandfed.org/research/workpaper/index.cfm Best available copy Eiut how mu& of the remaining variation is actually noise? The rea- sons CPS wage reports may have a larger noise+o-signal r a t i o than BLS wage surveys are as follaws: 1) CPS average hourly earnings are t imprecisely defined (they include e a m h g s f m overtime o r shift p d a o r froan second jobs); 2) CPS respondents1 memories are probably subject t o more error than are the establishment records used by t h e BLS; 3) CPS data-cleaning is f a r less thorough 4) CPS occupations than BLS efforts; and are subject t o large reporting error. So, the nonoccupation variation in the CPS is probably biased ulJwards. Thus, campared to total wage variation in the CPS, estimated variation due t o establishment differentials is large, even by conservative IIEISW~S. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 1 Characteristics of Area Wage Survey Sample Mean Wage Vari- $5.68 of In (Wage) 1 .I74 Standard Deviation of In(Wage) Number of Observations 1 .42 101,990 Nuniber of Occupations 88 Number of Establishments Male 59.3% Receive Incentive Pay Establishment Size Percent of obsewations 2.2% Major Industry Group (1-DisitSIC) 2. 3. 4. 5. 6. 7.& 8. Year of Observation 241 Percent of Obsewations Nondurable Manufacturing IXlrable Manufacturing Transport. and Utilities Wholesale and Retail Trade Financial Services Fersonal and Wzsiness Services 10.0% 28.8% 11.0% 17.3% 12.8% 19.7% Number of Years Observed '~etof annual effects. Source: Tabulations from the BLS Area Wage Survey, unidentified area in the Northeast for s i x consecutive years between 1975 and 1982. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 2 Tkchicpe for Partitioning Sum of Squares in Unbalanced Data Source of Variation FEEent of Total Sum of squares' 1. Occupation, Sex, Incentive(controlling for estab.) 2. Joint Occupation and Establishment 3. Establishment and -try 4. - *B *c (controlling for occup., etc.) - *A - *A - *c *c Industry (controlling for occupation, etc.) *c 5. Establishment Within Industry *c 6. Total Main Effects *c 7. Occupation, etc., -Year Interactions 8. Joint Occupation, etc., and Establishment 9. Establishment Year-Interactions 10. All Other Interactions(controlling for main effects) 11. Total Between Job-Cell-Years 12. Individual 'IWI'AL - SC + $A - *BT *CT *AT + *cT *D *BT - *CT - *AT - *c R', 100% - $, 100% 'The subscripts on the coefficients of determination correspond to the regression models listed below. Occupation, sex, and inoentive are listed as occupation, for ease of exposition. AT. w..I l kt = p + ?a + ?tat + eijrt + $a + eijkt B. WI-l -k' = p + Yip + eijk t wi jkt = p + Yip + yjtpt + Ei jkt C. wijtf = p + ?a + Yip + eijtf C. wijtf = p + %a + l(i@ + eijC cr. wijtf = p + %a + %'at + yjp + yjtpt + eijk t t eijkt D. WI l-k. t = p + ?a + xitat + Y i p + yjtpt + 3 Y j r + ? t ~ j t r+ A. wijtf = p where wi -tf = In wage of individual k in occupation, establishment j, and year t = vector of occupation dummy variables for occupation i Y. = vector of establishment dummy variables for establishment j $ = vector of ittiustry dummy variables for industry -j XiYj = durmnies for occupation i in establishment j, i.e., for job-ell ij, a, p, ,gl r = vectors of estimated parameters, and the superscript t denotes variables and parameters that vary over time. 4 http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 3 Analysis of Sources of Wage Variation Within an Area1 Degrees Saurce of Variation of Totalsum M a n of squares 89 1. Occupation, Sex and Incmtivd - 2. Joint Occupation, etc., and Establishment 3. Establishment and Percent of Industry3 240 4- Industry3 41 5. ~stablishmentWithin Industrf' 199 6. Total Main Effects 329 7. Occupation, etc. -Year Interactiod 436 - 8. Joint Occupation, etc. and Establishment 9. ~stablishment-Year~nteractiod 767 10. AI.~other ~nteractions~ 11,230 11. Total Between Job-Cell-Years 12,762 12. Individual 89,222 m Total Sum of Squares 'All reported figures are net of main annual effects. 2Controllingfor industry and establishment. 3Controllingfor occupation, sex, and incentive. 4Controllingfor occupation, sex, irmentive, and industry. 5~ntrolling for main effects and establishment-year interactions. 6Controllingfor main effects and occupation, sex, incentive-year interactions. 7Controlling for main effects and their interactions with year. 8All I?-statisticsare significant at well above the 1% level. Source: Tabulations f m BIS Area Wage Survey. Fstatistis http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 4 Correlations of Estimated Establishment Wage Differentials over p our Occupational ~roupsl A. Including Industry Effects' TYPE OF Professiondl CORRELATION and Technical Pearson Rank Office Maintenance, Tool- Material Movement Room and Ewerplant and Custodial .854 .788 Professional Pearson andTechnical Rank Maintenance, Toolroam, and Pearson Ewerplant Rank B. Controlling for Industry Effects1 - - TYPE: OF Professional Maintenance, Tool- Material Movanent CORRELATION and 'lkdmical roam and Powerplant and Custodial Office Pearson Rank .886 .892 Professional Pearson and'l'khical Rank Maintenance, Toolrwmand Powerplant Pearson Rank 'Results weighted by nunker of observations in establishment. Estimated establishment differentials are average differentials(taken from independent regressions for each occupational group) over period in which the establishment was observed. Source: Tabulations from BLS Area Wage Survey. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 5 Correlations of Estimated Establishment Differentials Over Six Years Including Industry ~ffectsl A. TYPE OF CmFEmTION 1 Year 2 4 5 4 5 3 6 Pearson Rank Year 2 Pearson Rank 3 Pearson Rank 4 Pearson Rank 5 B. Pearson Rank Controlling for Indusby ~ f f d TYPE OF (30RREXATION Year 2 3 -- 1 Pearson Rank 2 Pearson Rank Year 3 - - 6 - .975 .970 .968 .962 .909 .891 .904 .869 .894 .856 - .974 .969 .925 .909 .924 .897 .906 .871 - .959 .969 Pearson Rank 4 Pearson Rank 5 Pearson Rank 'Results weighted by number of observations in establishment. 2F&ultsweighted by number of observations in establishment. Industry-year effects are excluded. Establishments in industries with only one establishment are also omitted. Source: Tabulations f m BLS Area Wage Survey. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 6 Sqgested Standard Deviations for Area Wage Survey Source Sugyested Standard Deviation1 Occupation Establishment (Including Industry) Establishment (Within Industry) Interactions Individual 'IwTm '~uggestedstandard deviation=[(category proportion of CSS)x(total variance)1". Joint contribution is allocated to occupation. Source: Tabulations from BLS Area Wage Survey. http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 7 Camparison of Regression on Establishment IMmtnies with Regressions on Establishment Size in the Area Wage Survey A. Eq. Cumparison of Explanatory F k x e r AF# F# Independent Variables (1) Occupation, Sex, Incentive and 2-Digit SIC fram Eq. 1 81.8 (2) Occupation, etc. and Establishment Ikmmies (3) Occupation, etc., SIC, Establishment Size Category and Net Size Change 83.3 RATIO OF EXPLANAKIRY POWER OF FSTABLISIZE TO ESTABLISHMENT IXlMMIES +1.5 .I90 B. Coefficients fram Regression of In (Earnings) on Establishment Size Variable Coefficient or Number of txmmlies Occupation Male Receive Incentive Pay 2-Digit SIC Establishment Size 20-49 50-99 100-249 250-499 500-999 1,000-2,499 2,500-lNet Shrinker Net Grower Source: Tabulations fram BLS Area Wage Suwey. (Std. Error) http://clevelandfed.org/research/workpaper/index.cfm Best available copy Table 8 Effect of Establishment Size Change on Estimated Establishment Differentials in the Area Wage Survey merit Variable Current Estimated Establishment Differential (1) (2) Coefficient on Establishment Shrinkage DUIUIIY (std. error)l -0.005 (0.024) Coefficient on Establishment Growth r~many (std. error)l -0.04g2 (0.024) Other Controls 2-Digit SIC, Current Estab. Size Net Change in Estimated Establishment Differential Over Survey Period (3) -0.052~ (0.023) -0.011 (0.025) 2-Digit SIC, Previous Estab. Size $ 0.712 0.711 F-Stat. for Size Changes 2.02 2.67 Sample Size 767 767 Weight Mrmber of observations in establishment 0.513 0.28 231 Average nmber of observations in establishment '~rawthand shrinkage are defined as positive or negative changes (respectively) in the establishment size category. For Equations 1 and 2, the change is frcan the last year to present. For Equation 3, it is net change over the survey period. 'significant at the 5% level. 3~ntrol for years spanned is necessary because the calculation and elimination of annual effeck may intmluce bias (due to sample variations) in year-to-year caparisons of wage effects. Source: Tabulations fram BLS Area Wage Survey. http://clevelandfed.org/research/workpaper/index.cfm Best available copy - Table B-1 Industry and Area Wage Survey Standard Deviation Conpnents Ccanparea to Current Population Survey Log Wage Variation wage Survey Source of Variation of Log Wage Total Std. Dev. % K I M Area Wage Survey f w 5 J - Standard Standard Deviation ~eviatiod auTent Population Y May 1977~ All AWS o~cup-~ Occup- .20 occupation, Sex, Region, and/or -try1 .12 Total Remaining Establishment (known) .16 .ll Establishment (Estimated) 1)AWS & I W S Point Estimate 2)AWS % of Total 3)AWS % of Remaining Occupation-Establishment Interaction .06 Individual .09 . or For IWS IWS and CPS, includes SMSA durrony and region (4 regions for CPS) and AWS includes incentive durrany and joint effects. In CPS, uses 3 t occupation. CPS and AWS tatals include 2-digit i d u s t r y . 2~ffects of interactions with year have been excluded frcnn AWS results. 3The CPS saqle includes all priva'kssecbr fulltime workers between the ages of 18 and 65 with reported average hourly earnings of more than $1.75. 41ncludingonly observations for occupations included in the AWS saqle. Source: Tabulations f m BLS Area Wage Survey, BLS Industry Wage Surveys (see Groshen 1988b), and May 1977 CPS.
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