An equilibrium theory of wage and employment cyclicality by gender and by industry.

• Author: Shin, Donggyun

1. Introduction

   This paper explains how cyclical patterns of real wages and employment vary between genders and across industries and how these two factors are interrelated. More specifically, the main purpose of this paper is to develop an equilibrium model to account for the following five empirical regularities about the cyclicality of real wages and employment by gender and by industry in the United States:(1)

1. Both real wages and employment are more procyclical for men than for women.

2. The gap between genders is greater in real wage cyclicality than in employment cyclicality.

3. Within particular industries, employment is more procyclical for women than for men.

4. Real wages move more procyclically in the industries with more procyclical employment patterns.

5. Interindustry wage gaps based on aggregate time-series data are countercyclically biased.

   A great deal of effort has been made to explain disaggregate patterns of real wages and employment over the business cycle. For example, McDonald and Solow (1985), Bulow and Summers (1986), and Bils and McLaughlin (1992) developed various theories to explain the conventional wisdom that interindustry wage gaps move countercyclically. More recently, Solon, Barsky, and Parker (1994) adopted a basic labor demand-and-supply model to explain the observed gender wage and employment patterns over the cycle. Unlike these theories, the model developed in this paper accounts for a broader set of stylized facts. Not only gender and industry patterns but also wage and employment behaviors are jointly explained in one framework. Another feature of the current model is that all these empirical regularities are explained by the intersection of labor demand and labor supply. As will be explained in section 3, once the conventional competitive model is enriched to encompass cyclical mobility across industrial sectors, no further departures from the conventional model are needed to accord with the facts.

   This paper is organized as follows. Section 2 briefly summarizes recent empirical findings in the cyclicality literature and discusses how these observed patterns can be mutually consistent in a market-clearing framework. Section 3 develops an equilibrium model that jointly explains the five empirical regularities. The model generalizes Roy's (1951) two-sector equilibrium model of worker-sector matching by introducing a nonmarket sector and by dividing the entire population into two heterogeneous subpopulations: men and women. That is, although within each gender heterogeneity exists in comparative advantage among sectors, a gender difference also exists in the central tendency of comparative advantage, which makes the industry distribution of workers systematically different between genders. Under the assumption that aggregate shocks have a greater effect on the sector in which men have comparative advantage, labor demand moves more procyclically for men than for women.(2) With an additional assumption that the mean wage is higher in the sector subject to larger cyclical shocks, intersector wage gaps, by construction, move procyclically. However, heterogeneous workers change sectors following changed relative wages across sectors. When skill variances are similar across sectors,(3) each sector employs workers who are better in that sector than other workers would be even if skills are positively correlated across sectors. Because relatively low-skilled workers switch sectors, the inter-sector mean wage gap is observed to be smaller, in a cyclical upturn, than the would-be gap if within-sector skill composition were held constant. That is why intersector mean wage gaps based on aggregate time-series data are countercyclically biased. Numerical simulations demonstrate that reasonable parameter values exist under which the current model accords with all the empirical regularities. These parameter values are characterized most importantly by men's comparative advantage in the sector subject to larger cyclical demand shocks; that is, model assumptions are reinforced in numerical simulations. Section 4 concludes.

2. Review of Empirical Findings

   First, recent empirical findings summarized in Table 1 suggest that both employment and real wages are more procyclical for men than for women (regularity 1). For example, on the basis of the Panel Study of Income Dynamics (PSID) data (1969-1981), Blank (1989) estimated that the elasticity of average hourly earnings with respect to real GNP is -0.19 for nonwhite women, 0.48 for white women, 0.52 for nonwhite men, and 0.72 for white men. Finding similar patterns using total household income and head's labor income, she concluded that women's labor market earnings in general move far less with the general economy than do men's. On the basis of the National Longitudinal Survey (NLS) of labor market experience, Tremblay (1990) found a similar result. From data for young women (1966-1978), she found that a 1 [TABULAR DATA FOR TABLE 1 OMITTED] percentage point reduction in the national unemployment rate leads to a rise in real wages by 0.2% for nonwhites and 0.9% for whites. The comparable estimates for young men (1968-1978), were 1.6% for nonwhites and 1.5% for whites. Their findings were reconfirmed by Solon, Barsky, and Parker (1994). Using the PSID data (1967-1987), they found that a 1 percentage point reduction in the national unemployment rate is associated with a rise in real wages by 0.4% for women and 1.4% for men. As for employment, Clark and Summers (1981) estimated that when the unemployment rate of middle-aged males drops by 1 percentage point, per capita employment goes up by 1.4% for women and 1.7% for men. On the basis of the Current Population Survey (CPS) sample for the same period as their PSID sample, Solon, Barsky, and Parker (1994) estimated that a 1 percentage point reduction in the national unemployment rate leads to a rise in per capita hours of work by 1.4% for women and 1.8% for men. Shin's (1995) estimates over the period 1947-1993 show that the elasticity of per capita employment with respect to real GDP is 0.55 for men and 0.46 for women.

   Second, as noted by Solon, Barsky, and Parker, the gap between men and women is greater for wage cyclicality than for employment cyclicality (regularity 2).(4) They go on to explain that because women's short-run labor supply is more wage elastic (Killingsworth 1983), if the cyclical shifts in labor demand were gender neutral, a basic labor supply-and-demand analysis - shifting a labor demand curve along a stable short-run labor supply curve - would predict men's greater wage cyclicality but lesser employment cyclicality. Therefore, to derive greater employment as well as wage cyclicality for men, cyclical fluctuations in labor demand must be greater for men than for women. This explains why men's real wages are much more procyclical than women's and why men's employment is slightly more procyclical than women's.

   At first, it seems that greater labor demand cyclicality for men could be readily explained by men's greater representation in high-wage, cyclically volatile industries, such as construction and durable goods manufacturing. If both employment and wages in these industries were more procyclical, this could translate into greater employment and wage cyclicality for men. A consensus exists that employment is much more procyclical in male-intensive industries than in female-intensive ones.(5) On the contrary, however, it is commonly believed that interindustry wage gaps move countercyclically; that is, high-wage industries experience less procyclical real wage movement than low-wage industries do. For example, McDonald and Solow (1985, p. 1116) write,

   The test of success we have in mind is the ability of the enlarged model to give a plausible account of two more "stylized facts": that the wage differential between the primary and secondary sectors widens as the overall labor market weakens and narrows as it tightens; and that primary-sector employment fluctuates proportionally more than secondary-sector employment. . . . For the United States, we think of high-wage manufacturing, especially durable goods, as the prototype of the primary sector, and of trade and small-scale services as the prototype of the secondary sector.

   If real wages are less procyclical in the high-wage, cyclical industries in which men are overrepresented, how can we explain the greater wage procyclicality for men? Conversely, if real wages are more procyclical for men, why do those male-intensive industries show less procyclical wage movement?

   A series of recent studies by Wood (1992), Shin (1994), and Shin (1995) confront the puzzle with new empirical evidence on employment and real wage cyclicality by gender and by industry. First, as well discussed in Wood (1992), the conventional wisdom of countercyclical interindustry wage gaps is based on remarkably little evidence.(6) Using repeated cross-sectional data from the CPS to control for observable worker characteristics, he found that interindustry wage gaps are basically acyclical. His finding of acyclical rather than countercyclical wage gaps arose mainly from controlling for the workers' observable characteristics and therefore partially controlling for changing skill composition of within-industry workforces. His estimates (1992, table 3-4) show some evidence that not controlling for cyclical composition changes results in overestimation of the countercyclicality of the durables/retail and durables/services log wage gaps. In his conclusion, Wood speculated that, if he had been able to control more completely for worker quality, interindustry wage gaps would have been more procyclical.

   Because Wood controlled only for observable worker characteristics using data from repeated cross-sections, the estimates might still be subject to composition biases associated with unobserved worker characteristics. Therefore, Shin (1994) reestimated the...