Evidence on the Causes of the Rising Dispersion of Relative Wages

Evidence on the Causes of the Rising Dispersion of Relative Wages

EDWARD MONTGOMERY and DAVID STOCKTON*

In this paper, a neoclassical model of interindustry wage dispersion is derived and used to examine explicitly the fundamental role of microeconomic variables in determining relative wage movements. The empirical results demonstrate that the variance of labor quality and capital intensities across sectors are the primary determinants of the movement of the dispersion of relative wages within the manufacturing sector in the postwar period. Although the relative wage structure exhibits some response to unemployment, it is not sensitive to changes in inflation. The macro variables were also of limited quantitative importance in explaining changes in the relative wage structure.

Introduction Relative wages are a critical determinant of the allocation of labor re-

sources across sectors of a market economy. The rising dispersion of relative wages over the postwar period, and particularly during the 1970s, has led to suggestions that relative wages are being increasingly distorted by either a variety of macroeconomic factors or microeconomic market imperfections. Research pursuing macroeconomic explanations of rising relative wage dispersion has examined the roles of inflation and the business cycle in accounting for these movements. Microeconomic studies of

*The authors’ affiliations are, respectively, Department of Economics, University of Maryland, College Park, MD, and Board of Governors of the Federal Reserve System, Research Division, Washington, DC. We wish to thank Steven Garber, Daniel Hamermesh, Arnold Kling, Stephen Oliner, Kathryn Shaw, Charles Struckmeyer, and William Wascher for helpful comments. We also wish to thank an editor and an anonymous referee for suggesting numerous substantive improvements in this paper. Ashutosh Bhagwati and Robert Archacki provided excellent research assistance. The views and opinions expressed are those of the authors and not the Board of Governors or its staff.

INDUSTRIAL RELATIONS, Vol. 33, No. 2 (April 1994). 0 1994 Regents of the University of California Published by Blackwell Publishers, 238 Main Street, Cambridge, MA 02142, USA, and 108 Cowley

Road, Oxford, OX4 lJF, UK.

206

The Causes of the Rising Dispersion of Relative Wages I 207

relative wages, on the other hand, generally employ cross-section data and focus on explaining cross-industry wage differentials at a point in time. Consequently, both lines of research are not well suited for analyzing the role of neoclassical factors, such as underlying tastes and technology in explaining changes in the wage structure. This paper employs a simple neoclassical model of wage dispersion to explain the postwar evolution of relative wages. Our results indicate that nearly all of the movement in relative wage dispersion in the manufacturing sector of the U.S. economy can be explained by cross-industry differences in labor quality, capital intensity, and rates of technological change. Thus, market forces, rather than the macroeconomic environment or microeconomic distortions, appear to play the primary role in explaining movements in the relative wage structure.

The macroeconomic line of research has focused on whether aggregate economic forces, notably inflation, monetary disturbances, or the business cycle, have distorted the signaling value of the wage system, thus imposing real costs on the economy. Michael Wachter (1970a, 1970b, 1974, 1976), hypothesizing that within manufacturing the high-wage sector is less sensitive to cyclical influences than is the more competitive low-wage sector, consistently finds empirical support for the hypothesis that higher unemployment results in a widening of wage dispersion. In the early 1970s, Wachter (1970a, 1970b, 1974) found that inflation tended to compress the relative wage structure, presumably because of the relatively sluggish adjustment of wages to inflation in the high-wage sector, where long-term labor contracts are more important. However, in the latter half of the 1970s, Wachter and Wachter (1978) found that high inflation led to an increase in the dispersion of relative wages, which is attributed to the increasing prevalence of cost-of-living adjustment clauses in the contracts of the organized workers in the high-wage sector. The microeconomic determinants of relative wages receive little attention in these papers; the equilibrium dispersion of relative wages is modeled as either a constant term (Wachter, 1970a, 1970b, 1978) or as a constant term plus a trend (Wachter, 1974).

Hamermesh (1982) has applied the same general methodology used in the price-change dispersion studies to the labor market, investigating the dispersion of wage change, rather than the dispersion of wage levels.' In contrast to Wachter, he finds that inflation leads to more uniform in- dexation to inflation and less sensitivity to sector-specific excess demand.

'See Parks (1978) and Stockton (1983) for examples of studies that examined the relationship between inflation and price-change dispersion.

208 / EDWARD MONTGOMERY AND DAVID STOCKTON

The microeconomic variables in the Hamermesh model are limited to a term measuring variance of industrial output.

There is a large body of literature that has used cross-section data at the industry or individual level to estimate earnings equations in order to examine the sources of interindustry variations in wages. Works by Law- rence and Lawrence (1985), Kwoka (1983), and Pugel (1980) and numerous others have examined the importance of product and labor market imperfections such as unionism, plant size, and industry concentration.2 In addition, works by Dickens and Katz (1986) and Krueger and Summers (1986, 1988) have emphasized the importance of efficiency wage premia in certain industries in determining relative wages. Even after controlling for a wide range of individual and job characteristics, industry wage differences are large and do not appear to be explained fully by competitive factors. However, the results of Krueger and Summers (1986) indicate that the industry effects have remained relatively constant, at least between 1974 and 1984. This finding is of particular interest because it coincides with a period of rapidly rising interindustry wage dispersion and suggests that industry effects are not the primary explanatory factor behind the rise.

Our paper has little to contribute to explaining the apparent constant level of “noncompetitive” industry differentials, but focuses instead on the factors causing wage dispersion to change over time. In this effort, we have employed a neoclassical approach to modeling wage dispersion. The competitive model has the virtue that the motivations and constraints facing economic agents are straightforward and lead to testable hypotheses. As a consequence, it seems preferable to examine how far this approach can lead before adopting nonstandard explanations. However, we should make clear at the outset that there is nothing in our results that rules out constant noncompetitive industry wage premia. In the next section of this paper, we describe the general behavior of the relative wage structure in the postwar period. A simple neoclassical model is developed in the third section that derives real wages in each sector from a production technology, factor supply, and product demand. In the fourth section, the model is tested using time series and cross-section data on the manufacturing sector in the postwar period. We find that the neoclassical model is capable of explaining most of the postwar evolution of the relative wage structure. The fifth section extends the empirical model in order to assess the contribution of macroeconomic factors to an explanation of relative wage dispersion. We find that once the primary microeconomic determinants have

2See Parsley (1980) for surveys of the voluminous literature on unionism and relative wages.


FIGURE 1 Wage Dispersion

Twdigt t industries

- I) Coefficlent of Varlatlon - I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 0.26

- - 0.24

- - - - - - - 0.18

- - - 0.16

- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l l l l l l l l l l l l l 0.14

1951 1957 1963 1969 1975 1981

been explicitly included, the scope for macroeconomic factors to explain the movements in the relative wage structure is reduced greatly.

Trends in the Dispersion of Wages Figure 1 displays a plot of the coefficient of variation of wages of produc-

tion and supervisory workers for 20 two-digit manufacturing industries for the period 1948-81.3 In general, there has been a secular increase in the coefficient of variation of wages only interrupted by a period of relative stability during the 1960s. This secular rise in wage dispersion over the postwar period often has been overlooked in previous ~ t u d i e s . ~ Its pres-

3The wage series are the average hourly earnings for production and supervisory workers adjusted for overtime earnings.

4See Lawrence and Lawrence (1985) and Wachter and Wachter (1978). For the most part, these studies only have attempted to explain the rising dispersion of wages in the 1970s, using either noncompetitive arguments specific to that decade (Lawrence and Lawrence, 1985) or the macroeconomic influences of the business cycle and inflation (Wachter and Wachter, 1978). Nevertheless, as Figure 1 demonstrates, rising wage dispersion was not a phenomenon confined to the 1970s.


TABLE 1 RANKINGS AND PERCENT DEVIATIONS FROM THE AVERAGE MANUFACTURING

WAGE FOR TWO-DIGIT MANUFACTURING INDUSTRIES~ ~

Ranks Percent Deviations

Industry 1951 1961 1971 1981 1951 1961 1971 1981

Lumber Furniture Stone and glass Primary metals Fabricated metals Machinery Electrical machinery Transportation equipment Photographic equipment Misc. manufacturing Food and kindred Tobacco Textile mills Apparel Paper Printing Chemical Petroleum and coal Rubber Leather

13 14 1s 15 -.09 14 16 17 17 - . lo 11 11 9 8 -.oo 4 2 3 2 .17 6 7 7 9 .06 5 S S 6 .13

10 10 11 11 .01 3 3 2 3 .19 8 8 10 13 .03

1s 15 16 16 -.12 16 13 13 12 -.12 20 17 14 S -.26 17 20 19 18 -.1s 18 19 20 20 -.1s 12 12 8 7 -.02 2 4 4 10 .24 7 6 6 4 .05 1 1 1 1 .29 9 9 12 14 .03

19 18 18 18 -.19

-. 15 -.16

,021 .27 .09 .15 .03 .23 .04

-.16 - .05 - .22 - .29 - .28

.02

.20

.13

.32

.04 - .27

- . lo -.17

.05

.21

.07

.14 - .01

.27

. 00 -.15 - .04 - . lo - .27 - .29

. 0s

.20

.13

.30 -.03 -.26

-.11 - .2s

.06

.38

.05

.13 - .03

.33 -.05 -.24 - .05

.14 - .30 - .37

.10

.05

.16

.45 - .09 - .36

aThe percent deviation is the percentage difference between adjusted average hourly earnings in that industry and the mean value of average hourly earnings for manufacturing as a whole.

ence is not sensitive to the degree of aggregation of manufacturing industries; the same pattern also is observed when the coefficient of variation of wages is plotted for three- or four-digit manufacturing industries. Al- though there is evidence that there has been a secular increase in the dispersion of wages in the economy as a whole, we have chosen to focus on the manufacturing sector because detailed industry-level data are not available outside of man~facturing.~

The changing relative wage structure shown in Figure 1 has not resulted in a significant reshuffling of high- and low-wage industries. Table 1 presents the rankings and the percentage deviations from the mean wage for the 20 two-digit manufacturing sectors. The ranking of the sectors by mean wage rates presents a striking picture of stability across the postwar period. The rank correlation coefficient between 1951 and 1961 was .967, between

5Plots of the coefficient of variation of wages for three- or four-digit manufacturing industries or one- digit industries for the whole economy are available from the authors upon request.


1961 and 1971 was .962, and between 1971 and 1981 was .890. Even when viewed over the 30-year time span between 1951 and 1981, the rank correlation coefficient was .675, indicating that there has been only moderate change in the wage rankings of these sectors.

The structure of relative wages is less stable than the rankings of industries. In fact, relative wages, as measured by the percentage deviation from the mean wage, changed by greater than 10 percentage points between 1951 and 1981 in 13 of the 20 sectors. In most cases, high-wage industries tended to stay high or move higher, and low-wage industries tended to stay low or decline even further. Thus, the evidence suggests that the rise in the coefficient of variation of wages over the past 30 years was the result of a widening of the wage structure and did not reflect a substantial reordering of relative wages.

A Neoclassical Model of Wage Dispersion In this section, we first derive a neoclassical wage dispersion equation

under the assumption that the supply of capital is predetermined, but that labor is endogenous with respect to the current period wage. A second dispersion equation is then derived under the assumption that labor is inelastically supplied in each period. These wage dispersion equations are then estimated in the next section.

We assume that output in each industry can be described by a Cobb- Douglas production function with embodied technical progress in labor and disembodied neutral technical change. This production function is similar to that used in works by Lucas and Rapping (1969) and McGuire and Rapping (1968). In logarithmic form, the production function for industry i at time t is:

where Q, is output in industry i, Kit is the industry-specific level of capital stock, Zit is a measure of labor efficiency units, Oi captures the industry- specific rate of neutral technological progress, Ai is an industry-specific efficiency or technology parameter, and T is an index of time. The production function in equation (1) allows the rate of disembodied neutral technical change, labor-augmenting technical change, the level of the capital stock, man hours, and industry-specific efficiency to vary across industries. For analytical simplicity, we constrain the output elasticities or share parameter, a , to be constant across industries. The efficiency unit measure, Zit, reflects the presence of heterogeneous labor inputs that are used in different proportions in each industry and allows for the presence of em-


bodied technical change in labor. Labor efficiency units can be expressed as a function of the number of man hours, Lit, an index of labor quality, Sit, and a transformation parameter y6

zit = (Sit)YLit. (2) In the presence of heterogeneous workers, firms focus on the supply of efficiency units to an industry, which depends upon both the real wage and the relative wage paid in that sector. If we assume that workers observe their nominal wage but not the aggregate price level or the average wage before making their labor supply decisions, then we can express the supply in efficiency units as a function of the expected real wage, the expected relative wage paid in that industry, and an industry-specific intercept or scaling factor, Li:

log (Zit) = Li + P(l0g w;t - log P,) + g10g wrt - log q, (3) where w:~ is the wage per efficiency unit, P, is the expected price level, and t%i is the expected average wage per efficiency unit across all industries. The presence of the constant, Li implies that the supply of labor to industry i also may depend on factors like nonlabor income, the opportunity cost of work at home, noncompetitive constraints on labor supply, and the nonpecuniary characteristics of a specific ~ e c t o r . ~ The wage per efficiency unit, wR, can be expressed as a function of the observed industry-specific wage, wit, adjusted for the skill mix labor in industry i:

log [Wit/(Si,)Y] = log WIs. (4) To close the model, we assume that product demand in each industry can

be expressed as a function of relative prices and expected real income:

log QF = log Ci - $(log Pit - log P,) + vi log Q,, ( 5 ) where 9, is expected real income and Ci is an industry-specific constant. We have allowed the income elasticity of demand, vi, to vary across sectors so that changes in expected aggregate income need not shift demand equally in all industries.

Using equations (1) through ( 5 ) and the assumption of profit maximiza- tion, we can solve for the equilibrium nominal wage rate:

%ee Fallon and Layard (1975) for a discussion of the complementarity and substitutability of skills

T h e degree of risk or danger, location, and noise levels are only some nonpecuniary aspects of jobs and other labor.

that tend to vary across industries and could affect the supply of labor holding wages constant.


log wit = Di + a(+ - 1) Oi7 + aa(+ - 1) log Kit + a [ ~ + ( P a + a5 + 1) + (1 - a) (P + 01 log Sit

+ a[ag+ + (1 - a)[] log \^N: + aqi log P,, + a[++ + + + (1 - a)p] log PI

(6) where

Di = a(+ - 1) log Ai + a+log (1 - a) + a log Ci - a[a(+ - 1) + 11 Li

The wage rate paid by the industry is a function of the rate of disembodied neutral technical change, Oi, the level of skills, Si the capital stock Kit, the expected aggregate price level, Pi, the expected average skill adjusted wage, \̂ NS, and expected real income. If the change in the capital stock that occurs during a year is small relative to the total stock of capital, or if there are gestation lags and irreversibilities in capital acquisitions, then the capital stock may be treated effectively as exogenous in the wage determination process.8 In addition, it can be shown through some tedious algebraic manipulation that the sectoral wage is homogeneous to degree one in the aggregate price and wage levels.

The variance of the log of wages across sectors at time t, c& is a measure of the dispersion of wages. Using equation (4) to calculate the variance of the log of wages yields the following:

a = 1/[aY(P + +I(+ - 1) + + + (P + +)I.

4, = Po + PI&, + P2dt + P3q,,Iqt + P43 + P5T

+ &?: + &P, + PgqtT. (7) The dispersion of wages across industries thus can be expressed as a function of the variance of capital stocks, the variance of skills, the covariance of skills and capital, expected income, time, the interaction of expected income and time, and a constant. Under our simplifying assumptions of equal labor supply, technological, and product price elasticities across sectors, changes in the expected price level and the expected average wage have equiproportionate effects on sectoral wages and thus cancel out in the calculation of the dispersion of wages.

The presence of firm-specific human capital, pensions, and other institutional factors limit the within-period mobility of labor. Given the fact that most empirical studies have found only a negligible short-run elasticity of labor supply, we also examine the case where labor is inelastically supplied

8Since the technology, and hence the desired skill mix, within an industry is unlikely to change much over a year, we have assumed that workers and firms take the skill mix as given when determining their demand and supply of labor in each period.

214 I EDWARD MONTGOMERY AND DAVID STOCKTON

to each industry (p = 5 = O).9 Under this assumption, we can rewrite equation (4) in the following capital-intensive form:

log wit = Fi + a’eii7+ a’a($ - 1) log kit + a’ [y+ + (CC, - 1)al log sit + log PI + a’q log iT,, (8)

where

a’ = I/+ Kit = [Ki/SiLi], Fi = a’($ - 1) log Ai + log (1 - a ) + a’ log Ci - a’L,.

The variance of wages calculated for the capital intensive form of the model, equation (6), equals:

4, = Yo + ?Id, + 724 + Y,fl(S,k)t + Y4T2 + Y57

+ y,P: + y7iTt + y& t. (9) This version of the dispersion equation is virtually identical to equation (9, except that capital intensities replace capital stocks.

Data and Empirical Results of the Neoclassical Model In order to test empirically the neoclassical model, it is necessary to

construct a micro data set of wages, labor input, skills, and capital stocks. As mentioned above, data limitations force us to concentrate our analysis on the 20 two-digit industries composing the manufacturing sector. Wages are measured by average hourly earnings for production, and supervisory workers adjusted for overtime earnings. As suggested by the model, the wage dispersion measure is calculated as the variance of the log of wages. The weights used in calculating the variance of the log of wages are each sector’s share of total manufacturing employment.1O

To construct a measure of the interindustry dispersion of skills, we use a transformation of the Gollop and Jorgenson (1983) indexes of labor quality that are available for each of the two-digit manufacturing industries. These indexes are based on detailed information concerning the occupations,

9See Killingsworth (1983) for a review of the literature on labor supply. “The use of the weighted variance of the log of wages is similar to Krueger and Summers (1988) and

contrasts with Wachter’s use of the unweighted coefficient of variation, which is defined as the standard deviation of wages divided by the mean wage. Both measures attempt to eliminate the depen- dence of movements in the dispersion measure on the movement of the mean wage. The use of weighted moments prevents a relatively small sector from having a large influence on the movements of the relative wage structure. Despite differences in calculation and weighting, the movements in the two measures are nearly identical, with the correlation coefficient between the unweighted coefficient of variation and the weighted variance of the log of wages equaling ,998.


education, and demographic characteristics of the work force in each sector and how the usage of workers with these characteristics has changed over time. Chinloy (1980) and Jorgenson, Gollop, and Fraumeni (1987) found that shifts in the education mix across manufacturing industries is the single most important factor in explaining movements in our skill measure over the sample period as a whole and for all of the subperiods they examined except 1947-51. Shifts in the occupation mix also were found to be quite important, although less so in the 1970s when changes in the education and age distribution of the work force were found to be the most important factors in explaining sectoral changes in labor quality.11 Overall, shifts in the demographic characteristics and full-time status of the work force account for a part of the variance in the skill mix across industries, but the single most important factor is variation in schooling. A cross-section scaling procedure, described in appendix A, is implemented to make these indexes comparable both across sectors and across time.

Net capital stock series, published by the Department of Commerce for two-digit industries, are used to measure the flow of capital services to each sector. In some industries a substantial portion of the additions to the capital stock in the 1970s was devoted to pollution abatement equipment that was required by federal environmental regulations. This portion of the capital stock is not likely to raise the marginal product of labor in the manner assumed in the theoretical model, and hence is subtracted from the total to arrive at a net capital stock series that measures only capital available for the direct production process of that sector. The ratio of capital to effective labor inpute is derived by dividing the capital stock series, by the product of the sector-specific skill index and total annual hours of production workers.

Finally, expected income is estimated by using the fitted values of an autoregression of four lagged values of real GNP. Dummy variables are included for both the Korean War and the Nixon wage and price controls.'* The equations are estimated with annual data for the period 1948-81.

The results of estimating the models derived in the previous section are

"Bell and Freeman (1991) found that including a control for occupation mix had little effect on relative industry wage movements during the period 1972-80. This is consistent with the Chinloy (1980) findings that in the 1970s occupational shifts played only a minor role in explaining variations in skill levels across industries. Gender shifts were found to play a small role in both Bell and Freeman and in our skill series. It is important to note that our series does not restrict the role of occupation and gender to affect skills only linearly but allows a rich array of interaction effects between these variables and between schooling, part-time status, and age. Thus, it is not surprising that we find that variations in skills play a larger role in explaining relative wage movements than do Bell and Freeman (1991).

12The former is set equal to one in the years 1950-1953 and the latter is set equal to one in the years 1971-1974.


TABLE 2 THE NEOCLASSICAL EQUATIONS

Dependent Variable (Variance of Log Regression Average Hourly Earnings) 1 2 3 4 5 6

Constant

Variance of skills

Variance of capital stock

Covariance of skills and capital

Variance of capital/labor

Covariance of skills and capital/labor

Expected GNP

Expected GNP’

Expected GNP . Time

Time

Time2

Korean War controls dummy

Nixon price controls dummy

RZ Standard error (s.e.r.)

- 20.499 (- 1 .09)

(3.55) 4.287

0.74 (1.79) - ,897

(-2.86)

6.561 (1.08) - ,527

(-1.08) 3.265 (.96)

-20.114 (- .96) -5.077

(. 86) - .003

(- 1.55) - ,002

,931 ,0022

(.03)

Durbin-Watson (D.W.) 1.65 Sample period 1948-81

- 12.98 -35.690 1.537 ( - 1.15) (1.73) (2.90)

2.66 3.184 6.652 (3.78) (2.50) (4.63)

,062 (4.12)

-1.012 (-7.75)

4.244 (1.17) - .348

(-1.19)

(1.11) 2.261

- 13.67 (-1.09) -3.609 (1.02) - ,005 (4.96)

,001 (1.06)

,975 ,0013

2.29 1984-81

,029 (33) - ,655

(-2.50)

11.498 - .496 (1.73) (-3.00)

-9.29 ,038 (1.72) (3.05) 5.883

(1.57)

(1.58)

(1.40)

-36.489

-9.157

- ,002 - .006 (1.17) (-2.42) - ,001 - ,002 (W (. 69) .910 ,847 .0025 ,0033

1.08 1.05 1984-81 1984-81

.020 (13.07)

7.402 (9.89)

.746

.0043

.23 1948-81

-9.12 (- .58)

2.185 (1.82)

.038 (2.16) - ,786 (3.86)

2.983 (.58)

(-.59)

(.44)

(- .43)

(.33)

- .244

1.365

-7.935

- 1.750

- .005 (3.98)

,959 ,0014

2.34 1948-73

presented in Table 2. Column 1 corresponds to equation ( 5 ) , where the labor supply is assumed to be endogenous with respect to the current period wage. About 93 percent of the postwar movement in manufacturing wage dispersion can be explained by this relatively restrictive micro model of wage dispersion. As predicted by the theory, increases in the dispersion of both skills and capital stocks are found to increase the variance of wages. Only the sign of the coefficient on the covariance of skills and capital contradicts the theoretical model. This sign reversal on the covari-


ance term is not sensitive to changes in specification and appears in all versions of the models we test.13

As seen in equation (7), the model with perfectly inelastic labor supply leads to a formulation of the wage dispersion equation in terms of the dispersion of skills and the dispersion of effective capital intensities. The results of estimating this model (column 2) provide an even stronger re- inforcement of the basic predictions of the theory. As hypothesized, the dispersions of skills and capital intensities are significant factors in explaining the movement of the relative wage structure. Although the coefficients on the expected income terms are individually insignificant, a joint F-test rejects the hypothesis that they should be excluded from the regression.14 Furthermore, there is some evidence in the capital-intensive form of the model that the wage and price controls of the Korean War period acted to compress the relative wage structure; in other words, wages in the high- wage sector were held down relative to those in the low-wage sector. In contrast, the Nixon controls apparently had no significant effect on the relative wage structure.

If the capital stock is endogenous with respect to the current period wage, then the dispersion of capital intensities would drop out of the model and skills would be the primary explanatory factor describing wage dispersion. The results of estimating this version of the model are shown in column 3. This version of the model is capable of explaining 91 percent of the variation in the dispersion of wages. Moreover, the coefficient estimates are not particularly sensitive to the elimination of the capital terms. A final extreme, and less plausible, version of the neoclassical model would postulate complete within-period mobility of labor and capital, so that only the dispersion of skills influences the dispersion of wages. A simple regression of the dispersion of wages on the dispersion of skills (not shown in the table) indicates that the dispersion of skills can explain 53 percent of the year-to-year variation in the dispersion of wages. Neverthe- less, the statistical significance of the capital variables suggests their rele- vance in explaining wage dispersion.

In examining the models in columns 1 and 2, there is little evidence of serial correlation of the residuals in either formulation. The most significant difference between these two specifications is that the standard error

"Sign reversals in covariance terms have also been noted in the studies of price dispersion (Parks, 1978; Hercowitz, 1982). Furthermore, many studies in both the wage and price dispersion literature have simply ignored the interaction terms implied by the theoretical models, implicitly assuming the coefficients equal to zero (Hirsch, 1982).

I4An F-test of the restriction yields an F = 25.30, which is greater than the critical value of F(3,23) = 3.03 at the 5 percent level of significance.


TABLE 3 CORRELATION OF RELATIVE WAGES

WITH RELATIVE SKILLS~

SIC Industry Correlation

Lumber Furniture Stone, clay, glass Primary metals Fabricated metals Nonelectrical machinery Electrical machinery Transportation equipment Professional equipment Miscellaneous equipment Food Tobacco Textile mills Apparel Paper Printing Chemicals Petroleum and coal Rubber

.3?*

.91*

.88* -.45*

.40*

.48* - .24

.65* - .09

.56* -.95*

.9?*

.83*

.86*

.96*

.56*

.96*

.45*

.89*

*Significant at 5 percent level. aFor each sector i , the correlation between wI / w, and s / S ,

in the version of the model using the dispersion of capital intensities, column 2, is nearly one-half that of the version using the dispersion of capital stocks, column 1. In order to limit the number of permutations in subsequent exercises, we will concentrate on the capital-intensive version of the model, although the qualitative characteristics of the results reported below hold for both versions of the m0de1.l~

Although the dispersion of skills is positively related to wage dispersion, for our interpretation of this finding to be correct it must be the case that, at the industry level, movements in relative wages are positively correlated with movements in relative skill levels. As seen in Table 3, the simple

lsIt has been argued that the capitalilabor ratio may be correlated with interindustry wage dispersion for reasons other than those described in our model. The capital/labor ratio may proxy for unobserved labor quality. This, however, still would be consistent with a competitive explanation of wage dispersion. The capital/labor ratio also may serve as a proxy for the elasticity of labor demand and unions’ ability to extract rents or the costs of worker malfeasance, which are noncompetitive explanations. Our theoretically derived interpretation that the capitaYlabor ratio affects the marginal product of labor and hence wages when labor is not perfectly mobile seems preferable to the alternative interpretation in which the capital labor is a very indirect proxy for the elasticity of labor demand or costs of worker malfeasance.


correlations of relative wage and relative skills between 1948 and 1981 are positive and statistically significant in 16 of 20 industries. The two statistically significant exceptions are primary metals and foods, where rising relative skills were accompanied by declining relative wages. This pattern does not hold, however, in other heavily unionized industries; for example, in the auto industry rising relative skills were accompanied by rising relative wages, while in the rubber industry declining relative skills were accompanied by declining relative wages.

Another issue is whether the bulk of the explanatory power of this model results from either the inclusion of trend terms or a general trend in skills or capital intensities. In addressing this question, we first found that neither the dispersion of skills nor capital intensities are well represented by a simple time trend; a time trend explains only about 40 percent of the variation in the dispersion of skills and less than 70 percent of the dispersion of capital intensities. Second, we reestimate regression (2) without the three terms involving the time trend (column 4 in Table 2). An F-test indicates that the trend terms do form a statistically significant subset of variables in our micro model.16 Nevertheless, the model without the time trends is still capable of explaining 85 percent of the postwar variation in the relative wage structure, indicating that trend variables are not the primary source of the explanatory power of the model. A time trend alone can explain about 74 percent of the movement in wage dispersion (column 5 in Table 2), and thus the marginal contribution of the micro variables lies between about 24 and 85 percent. However, because trends are a measure of our ignorance, it seems preferable to start with economically plausible variables and then examine how much remains for the trends to explain. Regardless of the interpretation of the trends, the model has significant power for explaining deviations in wage dispersion around its trend; when all the variables are detrended and regression 2 is reestimated, we find that the model can explain about 85 percent of the deviation in wage dispersion from its trend. Thus, the performance of the basic model clearly captures something other than a common time trend in the data series.

Although when interpreted strictly in terms of the theoretical model, the trend terms represent the effect of the technical change, it should be recognized that these terms also may be capturing secular drift in factors other than the production function. For example, if unionization, product market concentration, or other noncompetitive factors were changing slowly over time in a way that affected the dispersion of relative wages,

16An F-test of the joint significance of the trend terms yielded on F(3,23) = 44.89, which was significant at the 5 percent level.


these influences would be captured by the trend terms. Unfortunately, the data are insufficient to allow us to directly specify these alternative secular influences. Consequently, some care must be exercised when interpreting the trend terms.17 It is interesting to note that the estimated trends are negative, suggesting that these secular influences were working to narrow wage dispersion in the postwar period.

Changes in the sample period are found to have little effect on the estimated equation. We estimated the model on data between 1948 and 1973, thus excluding the large macroeconomic disturbances that occurred later in the 1970s (see column 6 in Table 2). The signs and magnitudes of the coefficients are very similar to those estimated over the full sample.18 Furthermore, there is no evidence of parameter instability, as a Chow test could not reject the hypothesis that the coefficients were constant over the periods 1948-73 and 1974-81.19 As an additional check on the robustness of the relationship, the regression in column 6 is used out of sample to forecast wage dispersion between 1974 and 1981. The percentage root mean squared error is 5 percent, indicating that the out-of-sample errors are very small in relationship to the magnitude of the overall wage dispersion of this period. In addition, the mean percentage error of -2.2 percent suggests that the forecast errors are virtually unbiased.

As a final test of the underlying model, we estimate a wage equation, equation (8) from the previous section, for each of the 20 sectors over the period 1948-73 by the technique of seemingly unrelated regression.*O Each equation then was simulated outside of the sample for the period 1974- 1981, and the simulated values were used to calculate a wage dispersion series that was compared to the actual dispersion of wages over the same period.21 The root mean squared error for estimated wage dispersion over

"In addition, the appropriate specifications of these secular effects also is open to question; time trends are just one of many possible specifications. Nelson and Plosser (1982), for example, suggest that many nonstationary time series are better modeled as a random walk with drift. Nevertheless, a Box-Q statistic calculated for the first 10 sample autocorrelations of the residuals from regression 2 equals 13.62, which is autocorrelations of the residuals from regression 2 equals 13.62, which is below the critical value of ,$(lo) = 18.3 at the 5 percent level of significance. This suggests that the residuals ate close to a white-noise process, and thus our use of time trends does not appear to be unjustified.

1% contrast to Lawrence and Lawrence (1985), who, in general, do not find capital intensity to be a significant factor in explaining wage dispersion both prior to and including the 1970s. Additional support for the role of capital intensity in explaining wage dispersion prior to the 1970s can be found in Haworth and Rasmussen (1971); they find the capital/labor ratio to be highly significant in a cross- section wage equation for 1963.

T h e F-statistic was .74 and the critical value was 2.59 for the 5 percent level. *@This test was done at the suggestion of an anonymous referee. ZIIn contrast to the dispersion regression, multicollinearity among the regressors often hampered

accurate parameter estimates in the individual wage equations. Nevertheless, significant parameter estimates on the skills and capital variables had the correct sign in the majority cases. These results are available upon request.


this period is 9.1 percent. This error is larger than for the corresponding dispersion regression, but given the enormous shocks to the macroeconomic environment and productivity growth over this period the results of this very stringent test must be viewed as surprisingly favorable. More- over, these out-of-sample simulations account for the bulk of the rising dispersion of relative wages; actual wage dispersion rose by more than 33 percent, while the simulations expect a 20 percent increase in dispersion. In general, the neoclassical model presented in the second section is able to explain much of the postwar evolution of the relative wage structure and appears very robust to a wide range of specifications.

The Influence of Macroeconomic Factors in the Structure of Relative Wages

These findings do not preclude a possible role for macroeconomic factors in influencing relative wages. In this section several hypotheses about the channels through which the macroeconomic factors could affect the relative wage structure are delineated and tested.22 According to the Wachter hypothesis, unemployment is expected to increase wage dispersion, while increased inflation should lower wage dispersion. To test these hypotheses, the unemployment rate for prime age males (those 25-54 years of age) (UE) and annual changes in the consumer price index (INF) are added to our neoclassical model.

As seen in column 1 of Table 4, the inclusion of the macro variables leads to only a marginal improvement in the performance of these equations; the adjusted R2, the standard error of the regression, and the Durbin-Watson statistic are virtually unchanged. In addition, the point estimates and the significance levels of micro variables are largely unaf- fected by the inclusion of the macro variables. As hypothesized, the coefficient on the unemployment variable is positive and significant. The sign on the inflation term is negative, but insignificant. As was done above, regression 1 in Table 2 is reestimated from 1948 to 1973 and then used for forecast wage dispersion between 1974 and 1981. The root mean squared error is 6.1 percent and the percentage mean error is -4.7 percent, leaving both measures higher than those in the model neglecting the macro variables. The marginal contribution of inflation and unemployment to the explanatory power of the model, combined with the deterioration in the out-of-sample forecast performance, suggests that, while there may be

Wnlike cross-section microeconomic studies (Pugel, 1980; Kwoka, 1983; Lawrence and Lawrence, 1985), the use of both time series and cross-section data allows us to perform direct tests of the influence of macroeconomic variables on manufacturing wage dispersion.


TABLE 4 MACROECONOMIC VARIABLES IN THE NEOCLASSICAL EQUATIONS~

Dependent Variable Regression (Variance of Log Average Hourly Earnings) 1 2 3 4

Constant

Variance of skills

Variance of capital/labor

Covariance of skills and capitall

Expected GNP

Expected GNPZ

Expected GNP. Time

Time

Time2

Korean War controls dummy

Nixon price controls dummy

Unemployment rate

Inflation rate

Unanticipated inflation

Livingston unanticipated inflation

Inflation, 1948-69

Inflation, 1970-81

RZ Standard error (s.e.r.) Durbin-Watson (D.W.)

labor

rate

-18.18 (-1.66)

2.87 (4.35)

.059 (4.13) - ,935

5.91 (1.67) - .482

( - 1.68)

(- 7.44)

3.24 (1.62)

-19.79 ( - 1.60) -5.37

(-1.55) - .004

(-3.70) ,001

,669 (2.32)

(.92)

- ,007 (.53)

,978 .0013

2.31

-16.47 (-1.55)

2.85 (4.28)

,060 (4.19) - ,929

(-7.08) 5.36

(1.56) - ,437

( - 1.57) 2.90

(1.50) -17.67 ( - 1.48) -4.74

(-1.41) - ,004

(-3.81) ,001

(1.40) .675

(2.31)

,004 (.24)

,978 .0013

2.37

-18.89 (- 1.76)

2.86 (4.39)

,059 (4.17) - ,938

(-7.56) 6.14

(1.77) -so0

(-1.78) 3.33

(1.72) -20.40 (-1.69) -5.48

( - 1.63) - ,004

,001

.686 (2.40)

(-3.39)

(. 87)

1.853E. (. 90)

,978 ,0012

2.26

-18.63 (- 1.68)

2.95 (4.40)

,056 (3.78) - ,869

( -5.88) 6.05

(1.69) - ,493

(-1.71) 3.26

(1.62) -19.94 ( - 1.60) -5.34

( - 1.53) -.004

(-3.67) ,004

.479 (1.31)

(.43)

- .013

.010

,978 ,0013

(37)

(.42)

2.36

'All equations estimated from 1948 to 1981.


some cyclical effect on the relative wage structure, macroeconomic influences are not the primary determinant of postwar movements in relative wages.

In order to examine the sensitivity of these results to the specification of the inflation term, several alternative formulations are tested. One possible hypothesis is that, because of variations in the degree of explicit and implicit indexing, only the unanticipated portion of inflation causes distortions of the relative wage structure. To test this proposition, we use two different measures of unexpected inflation: the residuals from a four-year autoregression on inflation (INFU) and the forecast errors of the Living- ston survey data (INFU,,J. The result of reestimating the equations with these two measures of unanticipated inflation are shown in columns 2 and 3 in Table 4. Unexpected inflation is insignificant in both equations. As suggested by Wachter (1976), we also split the inflation variable into pre- 1970 (INF4869) and post-1970 periods (INF7081) in order to examine whether the increasing prevalence of cost-of-living clauses in the high- wage sector may have altered the relationship between inflation and wage dispersion. Although the coefficients on the split inflation terms, seen in column 4 in Table 4, have the signs predicted by Wachter, neither was statistically significant. These results again cast serious doubt on the proposition that inflation was a fundamental factor in explaining the sharp rise in relative wage dispersion in the 1970s.

Although inflation may not be related directly to the level of wage dispersion, it is possible that inflation may increase the noise in the relative wage structure. In this case, the error term in the neoclassical model would be heteroskedastic, with the error variance related to inflation. In the price dispersion literature this type of relationship has been shown to arise from nonsynchronous contracts (Stockton 1983), from variations in inflation expectations (Cukierman and Wachtel, 1982), or from an increase in the variance of unanticipated money (Hercowitz, 1982). We perform the Lagrang- ian multiplier test for heteroskedasticity suggested by Bruesch and Pagan (1979), using both actual and unexpected inflati0n.~3 In both cases the null hypothesis of homoskedasticity cannot be rejected at the 5 percent level of significance.24 Thus, these results provide no support for the hypotheses

ZThe estimated residuals from regression 2 in Table 4 are squared and then divided by the sample variance ( E * / ~ S ) . These transformed residuals are then regressed separately on inflation and unexpected inflation. Breusch and Pagan demonstrate that one-half of the explained sum of squares are distributed asymptotically chi-squared, ,$(s - l) , where s equals the number of estimated coefficients. Unexpected inflation was taken from the four-quarter autoregression described above, although the results are unchanged when the Livingston survey is used to calculate unexpected inflation.

UIn the case of actual inflation ,$ = .05 and for unanticipated inflation ,$ = .lo, both below the critical value of 3.84 at the 5 percent level of significance.


TABLE 5 THE CONTRIBUTIONS OF MICROECONOMIC AND MACROECONOMIC

VARIABLES TO CHANGES IN WAGE DISPERSION^

1948-60 1960-70 1970-81 1948-81

Change in Wage Dispersion ,0206 -.0071 ,0191 ,0325 Microeconomic contributionb (per- ,0212 - .0073 .0163 ,0301

Macroeconomic contributionc ,0015 -.0013 ,0015 ,0017

Change in residual (percentage - ,0021 ,0015 ,0014 ,0007

centage contribution) (1.0293) (1.0289) (3532) (.9262)

(percentage contribution) (.0738) (. 1759) (.0757) (.0523)

contribution) (-0.1031) (- ,2048) (.0711) (.0215)

BThe coefficient estimates used in the calculations are from regression (1) in Table 2. bContribution of the following variables: Constant, Variance of skills, Variance of capitalilabor, Covariance of skills

and capital/lahor, Expected GNP, Expected GNP2, Expected GNPTime, Time, Time2, the Korean War Controls Dummy, and the Nixon Price Controls Dummy.

cContribution of the following variables: Unemployment rate and Inflation Rate.

that inflation or unexpected inflation led to heteroskedastic disturbances in the basic neoclassical model of relative wage dispersion regression.

In order to assess the relative contribution of microeconomic and macroeconomic developments to explaining the persistent rise in wage dispersion in the 1950s and 1970s, and the falling wage dispersion of the 1960s, the change in wage dispersion can be partitioned into microeconomic, macroeconomic, and residual components. Table 5 presents the results of this partitioning for the time periods 1948-60, 1960-70, 1970-81, and 1948-81 using the coefficients from regression 1 in Table 4.25 As seen in column 4 in Table 5, the micro variables explain 93 percent of the rise in wage dispersion over the postwar period, while inflation and unemployment can account for only 5 percent of the total increase in wage dispersion. More- over, in each of the three decades examined, the changes in the neoclassical variables substantially overshadow the influence of changes in the macro variables. For example, the decline in wage dispersion that occurred over the 1960s is more than accounted for by movements in the micro variables. Even in the 1970s the secular evolution of the dispersion of relative wages primarily reflects changing skills of workers, capital intensities of production, technological progress, and income growth. The estimates indicate that less than 9 percent of the increase in wage dispersion

=We also performed this exercise using equation (4) from Table 4 which allows for a possible structural shift in the 1970s, as COLA clauses became more prevalent in the high-wage sector. Only for the period 1960-70 were there any differences between the results for this model and those reported in Table 5. For that period movements in the macro variables actually would have lead to an increase in wage dispersion. These results are available from the authors upon request.


over the decade of the 1970s can be accounted for by changes in inflation and unemployment. Thus, these findings suggest that, even if one dis- counts the marginal statistical significance of the macroeconomic variables, the quantitative magnitude of the contribution of these variables to the longer term movements in wage dispersion is still minimal.

Conclusions In this paper, we derive and estimate a simple neoclassical model of

wage dispersion. This model departs from previous efforts to explain movements in relative wages by explicitly modeling the fundamental role of tastes and technology in determining relative wage dispersion. The empirical results demonstrate that a basic microeconomic model can explain most of the postwar evolution in the measured relative wage structure, with the variance of labor quality and capital intensities across sectors being the primary determinants of the movements in relative wages within the manufacturing sector. The relative wage structure also is sensitive to changes in the expected level of income.

Having explicitly controlled for the microeconomic underpinnings of relative wages, the role of macro shocks appears to be more limited than indicated in previous research. Although the relative wage structure exhibits some response to cyclical changes in unemployment, we cannot find any consistent effect from changes in inflation. Furthermore, tests for heteroskedasticity fail to indicate any significant relationship between inflation and “noise” in the structure of relative wages. The results suggest that the effect of inflation on nominal wages has been sufficiently uniform across sectors so as to prevent changes in the aggregate price level from having substantial effects on the structure of relative wages.

Although this paper has demonstrated that market forces have played an important role in determining the movement in wage dispersion, as with much of the recent literature on interindustry wage dispersion, a number of important issues remain to be resolved. For example, it will be important to establish whether the apparent constancy of noncompetitive industry effects, found by Krueger and Summers (1986), holds for periods prior to 1974, as is implicitly assumed in this paper. This will require developing a much richer longitudinal cross-section data set than has been used in either time-series or cross-section studies to date. A second issue that needs further attention is the time dimension over which one should assume that capital and labor should be considered fully flexible and mobile. We have demonstrated that the dispersion of skills-the only variable that should affect wage dispersion in the very long run with fully mobile


factors-accounts for most of the change in wage dispersion over the postwar period. Nevertheless, product demand and capital intensities also appear to influence the year-to-year variation in wage dispersion. It would be interesting to know if and at what point in the frequency domain these intermediate-run explanatory factors fade, leaving skills as the only determinant of changes in the structure of relative wages.

Appendix A In order to incorporate the labor-augmenting technical change embod-

ied in the model, it is necessary to derive measures of the skills of the work force in each sector. The required index must track movements of skills over time, as well as differences in the absolute level of skills across the sectors at any point in time. To meet the first objective, we utilize time series indexes of labor quality at the two-digit level developed by Gollop and Jorgenson (1983). These indexes are based on detailed information concerning the occupation, education, and demographic characteristics of the work force in each sector.

These indexes compare skills in a single industry at different points in time, but they are not comparable across industries. To make them comparable, the indexes are rescaled in a base year. The scaling is based on a standard cross-section earnings equation (Mincer, 1974), estimated for the 20 two-digit industries using Census data for 1970:

log Ei = 5.672 + 0.048 TEN, - 0.002 TEN2, + 0.157 SCH, + 0.132 FULL,

+ 0.777 SEX, + 0.566 RACE, + 0.018 UNION, - 0.177 INT, (5.110) (1.743) (1.425) (7.709) (0.097)

(9.015) (1.781) (0.009) (0.081) R2 = .966 Standard error = 0.044, (A l l

where

Ei = total annual wages and salaries TEN, = median years on the job, TEN2, = TEN squared, SCH, = median school years completed, FULL, = percentage of total workers averaging 35 hours or

SEX, = percentage of total employees who are male, RACE, = percentage of total employees who are white, UNION, = percentage of production workers on payroll who

are union members, INT, = FULL, X UNION,.

more per week,

The Causes of the Rising Dispersion of Relative Wages 1 227

All the coefficients have the predicted signs (t-statistics are in parenthe- ses). The variation in earnings attributable to variations in tenure, schooling, and the percentage of full-time workers is assumed to be related to the variation of skills across sectors. The levels of skills for each of the 20 sectors are then measured as the fitted values of the regressions using just the skills variables; tenure, schooling, and full-time work. Having derived a scaler measure of the level of skills for each sector in 1970, these levels were extended forward and backward over time using the Gollop-Jorgenson time series of skill indexes. The final result was a complete time series-cross- section skills panel with labor quality comparable both across time and across sectors. The variance of the levels of skills is then calculated for each time period.26

As a check on the sensitivity of our results to the scaling procedure used, we also constructed our skill series using several different formulations of the earnings equation. For example, we found that the inclusion of a measure of the one-digit occupation mix of the industry had little effect on the scaling of skills. The occupation mix variable was not statistically significant when added to the cross-section earnings regression and the correlation between the scaling of skills in this augmented regression and that derived from equation A1 is r = ,997.

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Evidence on the Causes of the Rising Dispersion of Relative Wages