Now that it is shown that employment-dependence of the transition process over types can produce aggregate monthly flows consistent with data, I show that the need for different transition processes by employment state is robust to the specific characteristics of the model. It is necessary to show that the reason for the initially poor matching of flows in this model when all types have the same transition process independent of employment status is not a result of using a participation margin based on search decision only. Using standard alternatives where participation transitions
affect both search and employment will generate a similar result. This issue that flows out of employment conflict with the stationary distribution of worker types is robust to other specifications of labor force participation, and will result in poor matching of flows with any model with labor frictions.
To illustrate this, consider an alternative specification of labor force participation using a mechanism that affects both the employment and search decision, such as shocks to labor market productivity coupled with some disutility of working. In such a model, job offers arrive for all nonemployed individuals at the same rate, so the N E flow is the percentage of nonparticipants who receive a shock to become participants times the percentage of workers who receive a job offer. The remaining workers to receive the participation shock but do not receive a job offer comprise the N U flow. A shock to productivity inducing nonparticipation would show up as a flow from E to N or from U to N , depending on the employment status of the worker.
While the EU flow only comes from the separation rate Ỗ, the EN flow comes from the participation shock hitting employed workers, causing them to drop out. This environment is similar to the one used in Krusell et al. (2011), but without assets. I abstract from assets for simplicity. The flows in their calibrated model are reported in Table 2.8:
The mapping of model elements to flows using similar notation to Section 2.2 is displayed in Table 2.9.
If these flows were only accounted for by a shock to productivity such that high productivity workers choose to participate and low productivity workers choose inactivity, the transition process can be identified by the NE and NU flows and a population weighted average of the EN and UN flows. Doing so produces the following transition matrix: This matrix produces the stationary distribution of participants to nonparticipants at a ratio of 2 to 1. However, doing so makes the size of the U N flow constrained to being too small at 0.066 in order to maintain the appropriate sizes of the EU and E N flows in the data. The point of this exercise is not to delve into a critique of their paper, but to outline that these tensions are present in any model with 3 labor market states. To generate any higher of a U N flow rate in this model in an attempt to match the data would require the increase of the rate that high productivity types become low productivity agents, but this would also generate counterfactually high separation rates from employment to nonparticipation. Even with the use of additional idiosyncratic shocks and considerable success in matching the comovement of flows over the business cycle, it is difficult for such a model to match the levels of the flows in the data.