I simulate the model with aggregate uncertainty to evaluate its ability to produce cyclical volatility in vacancies, unemployment, and part-time work over the business cycle. To evaluate the business cycle properties of the model, I focus on the relative volatility of part-time utilization, unemployment, vacancies, and worker flows in comparison to aggregate output. Two primary results arise from the business cycle analysis. First, the model is able to match the volatility and cyclical properties of P T E relative to U found in the data. That is, unemployment and part-time are countercyclical and similar in their relative volatility, as highlighted in Section 1.2.2. Second, the volatility of unemployment and vacancies is increased relative to the model without an operative part-time margin. Table 1.7 shows the business cycle moments for the model with and without part-time employment relative to the data. For the model without part-time labor, the model is recalibrated to the same target moments, but with £ = 0. The primary change in parameter values between the two calibrations is the idiosyncratic shock parameters x and nx, which are .312 and 0.973 in the case without part-time (compared with x = .288 and nx = .933 with a part-time margin). The results displayed are the standard deviation and correlation of the cyclical component of the logged and detrended variables relative to aggregate output (Y ).
The model with an operative part-time margin improves the fit of the model to business cycle properties substantially. Unemployment becomes more volatile and countercyclical, though it is still not as volatile as it is in the data. The volatility of vacancies and the job-finding rate double. While the volatility in unemployment and vacancies increase, the separation rate remains close to the value in the data. Additionally, although the total volatility in PTE is higher in the data than in the model, the model matches quite well the relative volatility of PTE and U . The model also matches the strong negative correlation of PTE with aggregate output.
The change caused by part-time utilization on the business cycle properties in the model is twofold. First, the part-time margin changes the movement of measured labor productivity in reaction to a shock. A fundamental productivity shock causes changes along the part-time margin for firms, which stabilizes the change in labor productivity for the firm because of decreasing returns to scale in the production function. This decrease in utilized labor means that output is more volatile for a given shock. The increase in volatility of output is similar to the effect of varying effort in real business cycle models with labor-hoarding, such as in Burnside et al. (1993). Similar to their model, productivity shocks are realized after employment is fixed. In the labor-hoarding literature, however, hours per worker are fixed during a period since workers supply a constant number of hours, and firms adjust utilization by contracting with workers over effort when the shock is realized. This produces procyclical movements in labor productivity and increases the volatility of output from a shock. In this model, variation in labor utilization occurs in the hours margin through part-time employment rather than in unobservable effort. Firms adjust to productivity shocks using part-time employment, changing the amount of output per worker. Productivity varies less than output since decreasing returns to scale increases the average productivity of firms when labor utilization decreases.
The second effect of part-time utilization is in the volatility of the model, and comes from the effect of part-time employment on the separation rate. Firms with the option of using part-time labor use fewer layoffs in the event of a large idiosyncratic productivity shock. Since the calibrated idiosyncratic shock process matches the average monthly separation rate, when firms use part-time instead of layoffs, a less persistent shock is needed to produce the same average monthly separation rate. This increases the volatility of unemployment and vacancies over the business cycle as well, since aggregate shocks primarily change the magnitude of job destruction and creation in adjusting firms. More firms adjusting labor produces a larger response to aggregate changes in productivity. One interesting point to note is that the volatility of the separation rate remains low as a result of the part-time margin being used instead of layoffs, so that the increase in volatility affects job creation more than job destruction.
It should be noted that this increased volatility arises even with a conservative value of leisure. The volatility of unemployment and vacancies can also be increased by raising the value of leisure b to be close to the value of working, as in the recalibration of the model of Mortensen and Pissarides (1994) by Hagedorn and Manovskii (2008). The reason volatility increases with an increase in b is that the surplus created by a filled vacancy decreases as workers become indifferent between leisure and work. This makes vacancies and the job-finding rate very sensitive to changes in productivity. However, raising the benefit from non-market work in this model will also result in a counterfactually high volatility of the separation rate.