Rank regressions, wage distributions, and the gender gap.

I. Introduction

One of the most remarkable changes in the U.S. labor market during the 1980s has been the sharp reduction in the pay gap between men and women. In 1979, the ratio of the average hourly wage of women to that of men was 68.6 percent. By 1991, it had increased to 78.5 percent.(1)

By contrast, other wage differentials, such as the gaps between more- and less-educated workers and between more- and less-experienced workers, expanded significantly during the same period. Residual wage dispersion among workers with the same level of experience and education also expanded during the 1980s (Levy and Murnane 1992). In their influential study, Juhn, Murphy, and Pierce (1993) argue that these changes in the wage structure are primarily the result of an increase in the return to labor market skills.

Juhn, Murphy, and Pierce (1993) also make the more general point that in an era of rising skill prices like the 1980s, wage differentials between two groups of workers - such as men and women - should also have expanded. Their point is that if the wage gap between the two groups is due to skill differences between these groups, an increase in skill prices should expand the wage gap. For example, women have less actual labor market experience than men (O'Neill and Polachek 1993) and the returns to experience increased during the 1980s. The gender wage gap should, therefore, have expanded. It is quite remarkable that the gender wage gap actually decreased during the 1980s despite these countervailing forces.

In a recent study, Blau and Kahn (1997) estimate that the decline in the gender wage gap would have been five to six percentage points higher if the wage structure had remained stable. Similarly, Juhn, Murphy, and Pierce (1991) and Card and Lemieux (1996) argue that the wage gap between black and white men would have declined - instead of remaining constant - during the 1980s if the wage structure had remained stable. These studies show the importance of separating the effect of changes in the wage structure (or in skill prices) from true improvements in the position of one group vis-a-vis the other. The basic assumption common to all these studies is that wages essentially depend on skills and that changes in the wage structure should have the same effect on workers earning the same wages.(2) The impact of changes in the wage structure can vary considerably, however, at different points of the wage distribution. For example, DiNardo, Fortin, and Lemieux (1996) show that wage inequality expanded more dramatically at the lower end of the female wage distribution - because of the decline in the real value of the minimum wage - than elsewhere.

The first objective of this paper is to analyze the changes in the gender wage gap at each point of the wage distribution instead of focusing solely on what happens at the mean? To do so, we will decompose the changes in the gender gap at each point of the distribution into three components: changes in the skill composition of the workforce (education, experience, and so on), changes in the wage structure, and residual improvements in the relative position of women.

We propose a novel rank-based procedure to compute the first element of the decomposition - the effect of changes in the skill composition of the workforce on changes in the gender wage gap. This procedure is a flexible version of the standard human capital-competitive markets model of wage determination (Mincer equation). Once skill composition effects are accounted for, the remaining change in the gender gap depends on how the position of women in a given distribution of reference changes, and how this distribution of reference changes over time. These changes are called residual improvements in the relative position of women in the distribution of reference and wage structure effects, respectively. By assumption, the distribution of reference is a wage distribution that is unaffected by residual improvements in the relative position of women. This distribution of reference only depends on the wage structure and on the skill composition of the workforce.

The second objective of the paper is to show that the residual improvements in the relative position of women and the wage structure effects critically depend on which distribution is assumed to be the distribution of reference. For example, Blau and Kahn (1997) assume that the male wage distribution is the distribution of reference, that is the one not affected by improvements in the relative position of women. This assumption has long been challenged by authors, like Bergman (1971), who suggest that "privileged" groups may benefit from the lower wages accruing to "disadvantaged" groups.(4) In this paper, we consider the standard assumption that the male wage distribution is the distribution of reference, as well as the alternative assumption that the overall distribution of wages (men and women combined) is the distribution of reference. In other words, we compare the case where changes in the wage structure are identified from changes in the male wage distribution to the case where changes in the wage structure are identified from changes in the overall wage distribution.

The paper is organized as follows. Section II describes the data from the outgoing rotation group files of the Current Population Survey (CPS) and presents some descriptive evidence on how the male and female wage distributions and the gender gap have evolved over time. Section III presents the rank-based model of wage determination. We also discuss the normalization used to compensate for the fact that measures of actual labor market experience are not available in CPS data.

The estimation of the wage determination model and the estimation results are presented in Section IV. In Section V, these estimates are used to decompose the changes in the distribution of male and female wages into the three factors of interest. More specifically, we compute a series of counterfactual distributions to account for the effect of these factors under the two alternative assumptions about the distribution of reference. This provides a new way of decomposing the changes in wage inequality among both men and women. In particular, we can compute the effect of improvements in the relative position of women on male wage inequality under the assumption that the overall distribution of wages is the distribution of reference. In Section VI, the counterfactual distributions are used to perform a similar decomposition for changes in the gender gap at each point of the distribution. We conclude in Section VII.

II. Data and Descriptive Evidence

A. Data

This paper uses data from the 1979 and 1991 outgoing rotation group files of the CPS for wage and salary workers aged 16 to 65.(5) Our samples include all wage and salary workers, including agricultural workers, students, and part-time workers. The main advantage of these samples is their large size (around 170,000 workers in each year). Indeed, a detailed analysis of wage changes at each point of the distribution requires a large number of observations. We use the year 1979 as our base period because it is the first year in which these particular samples were collected. The end period is 1991 because the education variable is no longer comparable after that.

We restrict the samples to individuals reporting an hourly wage between $1 and $100 (in 1979 dollars).(6) Observations with allocated wages were not deleted from the sample; because of a coding error in the CPS, it is impossible to identify most workers with allocated wages in 1991. The GDP deflator for personal consumption expenditures was used to convert nominal wages into 1979 dollars.

Rather than focusing only on full-time workers, we include part-time workers but weight each observation by the number of weekly hours of work to better reflect the contribution of each worker to the labor market. Each observation is thus weighted by the product of the CPS weight and the usual hours of work per week. These hours-weighted estimates put more weight on workers who supply a large number of hours to the market.(7) They reflect the distribution of wages per hour worked in the economy rather than the distribution of wages per worker.

The explanatory variables used in the wage model ([X.sub.i]) are years of education, a quartic in years of potential experience (age - education - six), and a dummy variable for nonwhite. The means and standard deviations of the (log) wage and of the explanatory variables are reported separately for men and women in Table 1. One drawback of the CPS files is that they do not contain direct measures of actual labor market experience of workers. We discuss this issue in more detail in Section IIIC.

B. Descriptive Evidence on Changes in the Wage Distributions

Figure 1 presents kernel density estimates of the distributions of log wages for 1979 and 1991. These kernel density estimates can be thought of as smoothed histograms. The densities for men and women (solid and broken lines) are weighted by their respective shares of the total workforce. These two weighted densities therefore add up to the overall density of log wages for all workers (dotted line), which integrates to one.(8) The figure shows that the difference between the average log wages (indicated by a vertical line) of men and women - the unadjusted gender wage gap - shrank during this period. It also shows that both the male and the female wage distributions became increasingly unequal during this period. As noted by DiNardo, Fortin, and Lemieux (1996), the minimum wage has a clear visual impact on the shape of the 1979 distribution for both men and women.

 
Table 1 
 
Sample Means from the Current Population Survey 
 
                                 Men                 Women 
 
                           1979       1991       1979       1991 
 
Log wage                   1.863      1.794(a)   1.486      1.552 
                          (0.512)    (0.581)    (0.396)    (0.486) 
Education                 12.528     13.126     12.560     13.254 
                          (3.122)    (2.991)    (2.399)    (2.393) 
Experience                18.950     19.100     18.158     18.967 
                         (13.951)   (12.146)   (12.825)   (11.284) 
Nonwhite                   0.111      0.132      0.142      0.157 
                          (0.327)    (0.353)    (0.330)    (0.347) 
Number of observations    93,544     90,099     73,940     85,192 
 
Note: Figures in parentheses are standard deviations. 
 
a. In 1979 dollars. 

In addition to these well-known facts, two interesting patterns emerge from Figure 1. First, it is clear that the convergence between the male and female distribution of wages goes far beyond a simple convergence in means. The distribution of wages of women is clearly skewed to the right in 1979 (coefficient of skewness of 0.511) whereas the men's distribution is skewed to the left (coefficient of skewness …