Introduction part-time employment and firm-level labor demand over the business cycle

Part-time employment for economic reasons (P T E ) has recently attracted at­tention from policy-makers as an indicator of weakness in the aggregate labor market due to its unprecedented size during the last recession. P T E reached 7% of employ­ment at its peak, affecting roughly 9 million workers in the US. Like the unemployment rate, the share of employment in P T E is volatile and countercyclical. Our under­standing of part-time labor and its relation to the aggregate economy, however, is lacking relative to our knowledge of unemployment. This paper focuses on examining the changes in the population of P T E over the business cycle and developing a search model of involuntary part-time work.

I begin by using data from the Current Population Survey to document three important facts about P T E : first, more full-time workers become part-time employed for economic reasons each month than become unemployed, and this inflow is more volatile than is the flow of full-time workers to unemployment. During the last reces­sion and subsequent recovery, the decrease in aggregate hours caused by individuals moving from full-time to P T E is on average 77% of the loss in hours caused by full­time workers separating to unemployment. Second, P T E is not a persistent state, and is characterized by high flow probabilities to full-time employment and unem­ployment. Workers in PT E are three times as likely as the unemployed to return to full-time work, and about seven times as likely as full-time workers to separate to unemployment. Lastly, PT E fluctuates due to within-job changes in hours rather than to changes in unemployment status.[1] Using the dependent interview structure of the CPS as in Fallick and Fleischman (2004) to look at job transitions, I find that 82% of the transitions of employed workers into or out of P T E are due to within-job changes in hours.

I build upon the framework of Kaas and Kircher (2015) on the basis of these facts to model firm-level labor demand with a part-time employment margin in a frictional labor market. This focus on firm-level demand is appropriate because the movement of workers with respect to P T E is primarily within-job. Firms are het­erogeneous in productivity, and firm size is determined through a decreasing returns to scale production technology in labor. Firms expand and contract their respective workforces in response to idiosyncratic and aggregate shocks, while facing frictions due to costly vacancy postings and competitive search. Firms can use part-time labor when facing a negative productivity shock in order to lower wage costs temporarily and reduce layoffs, avoiding the costly recruitment necessitated by future hiring when productivity increases.

Given that the facts outlined in CPS data concern worker flows and the model is about firms, I focus on the ability of the model to reproduce the qualitative fea­tures of PT E observed in the CPS data. Part-time utilization within firms is volatile in the model, implying that the flows of workers between full-time and part-time employment are large relative to the movement of workers between full-time employ­ment and unemployment. This matches the first fact I outlined

previously: workers in full-time employment are more likely to move to part-time than to separate to unemployment. The volatility also reflects the finding that workers in part-time em­ployment have a high probability of returning to full-time work. Firms use part-time labor in conjunction with separation, so that workers placed in P T E also experience higher separation rates than do full-time workers. The high respective probabilities of either returning to full-time or separating to unemployment are consistent with the lack of persistence in P T E indicated by the CPS data. Just as in the data, the aggregate stock of P T E is as volatile as unemployment and negatively correlated with output over the business cycle.

In quantitative exercises, I investigate the distribution of part-time usage across firms of varying growth rates and age, and within different size categories. I find that part-time utilization is correlated with employment growth for shrink­ing firms, reflecting firms’ usage of P T E along with layoffs in response to negative shocks. The model is consistent with the positive cross-sectional correlations of em­ployment and hours growth outlined in empirical work by Cooper et al. (2004, 2007) and Trapeznikova (2014) at the aggregate level. Consistent with their empirical find­ings on firm-level correlations of hours and employment growth, firm-level usage of part-time leads employment growth in my model. To extend the analysis of part-time usage to observable firm characteristics, I calibrate the model to match the firm size and age distribution found in Business Dynamics Statistics data from the Bureau of Labor Statistics. Heterogeneity in a permanent component of firm-level productivity matches the firm size distribution in the data, while the entrant share of firm produc­tivity types and firm exit probabilities match the age distribution of firms. Very young firms use less part-time employment due to high employment growth, and part-time usage increases with firm age. Heterogeneity in the exit rates of firms plays a key role in the distribution of part-time utilization. If exit rates were equal for all firms, part­time use would decrease with permanent productivity (and, therefore, size). Lower exit probabilities for high-productivity firms increase the value of future labor in the same manner as does a lower discount rate, incentivizing productive (and large) firms to use part-time employment instead of layoffs. Part-time utilization increases by about 40% for the largest firms once exit rates are allowed to vary.

Over the business cycle, the model generates countercyclical and volatile move­ments in both part-time employment and unemployment. The incorporation of a part-time employment margin increases the volatility of both unemployment and vacancies relative to the case with only an employment margin. Part-time employ­ment affects the cyclical properties of the model through two mechanisms. First, part-time utilization increases the volatility of output relative to average labor pro­ductivity. Aggregate shocks cause a reduction in output from firms’ immediate use of part-time employment. Due to decreasing returns to scale in labor, this decrease in labor utilization is accompanied by an increase in productivity per hour of labor. This effect is similar to that caused by time-varying effort in the labor-hoarding and factor-utilization literature, as exemplified by Burnside et al. (1993), Burnside and Eichenbaum (1996), and Bils and Cho (1994). Burnside et al. (1993) assume fixed hours per worker prior to the realization of productivity shocks in addition to fixed employment. Firms vary labor-utilization by demanding varying levels of effort, pro­ducing volatility in output and procyclical labor productivity. My model achieves similar effects by allowing for the adjustment of hours through the use of part-time employment by firms.

The second effect of the part-time margin in the model is an increase in the volatility of unemployment and vacancies from changes in the use of layoffs by firms. Firms use fewer separations in reaction to negative shocks when there is an operative part-time margin. Because idiosyncratic shocks generate the ma jority of endogenous worker separations, a model with part-time labor requires a less persistent shock pro­cess to generate the same unemployment rate as does a full-time only model. This increase in the prevalence of firm-level shocks produces more employment adjustment, increasing the volatility of unemployment and vacancies over the business cycle. The increased volatility in unemployment and vacancies is not accompanied by an in­crease in the volatility of the separation rate because layoffs are decreased in favor of part-time employment. The amplification of unemployment and vacancies over the business cycle in a model with large firms is also found in Elsby and Michaels (2013), but through a different mechanism. In their model, decreasing returns and the Stole-Zwiebel bargaining process for wages implies that workers and firms split the marginal and infra-marginal surplus of a match, resulting in a low surplus for the marginal worker, akin to the recalibration of the standard search model in Hagedorn and Manovskii (2008).

Section 1.2 describes and reports the facts I outline in CPS data. Section 1.3 presents a search model which is consistent with the documented data on part­time work. In section 1.4, I characterize the dynamics of the firm through its policy functions on hiring, part-time utilization, and layoffs. In Section 1.5, I calibrate the model to match aspects of the aggregate labor market as well as the size distribution of firms. Section 1.6 discusses the implications of the calibrated model for part-time use over the firm size and age distribution, as well as the business cycle properties of the model. Section 1.7 outlines ongoing work using US Census Bureau data to document the co-movements of hours and employment growth over the distribution of firms and concludes.