Introduction (matching labor flows in search models with labor force participation)

The study of labor market participation and its interaction with labor market frictions has been focused on matching the patterns in labor market flows between employment, unemployment, and nonparticipation over the business cycle. Achieving this goal has been somewhat problematic, as it is difficult to get flows into and out of nonparticipation to match the data. These difficulties become compounded when also trying to account for business cycle fluctuations, as the relative magnitudes of each flow must be consistent with data. Even small discrepancies in flows have large implications for stocks if the errant flow rates occur for a large population such as employment or nonparticipation. Accordingly, before attempting to model the co­movement of worker flows with the business cycle, it seems natural to understand first how to match the flow data in a steady state environment: this is the goal of this paper.

The motivation for incorporating a participation margin in labor market search models is that flows in and out of nonparticipation are quite large. CPS data over 1968-2007 show that about 4.7% of nonparticipants move directly to employment in the average month (the N E flow) and 2.4% begin searching, becoming unem­ployed (the N U flow). Given the size of the inactive population, the flow from non-participation is quite large and accounts for more new hires than those who find work from unemployment. Another striking feature of these flows is that on aver­age, 23% of unemployed workers will quit searching in a given month, moving from unemployment to inactivity.

This paper shows that in order to match flows between employment, unemploy­ment, and nonparticipation in a search model, the transition process affecting workers’ search decisions must differ by employment state. A single, employment-independent transition process for workers’ search decisions will produce compositions of workers either in employment or nonemployment that will cause counterfactual flows. As this result comes from the identification of transition rates for participation and the stationary distributions they imply, it is not constrained to a particular model. The need for transitions to vary by employment state will be present in any three-state model of the labor market with search frictions, regardless of the mechanism used to create a participation margin. A better understanding of matching labor flows will help to guide future labor market models in matching these flows in both stationary and business cycle environments.

To illustrate this result, I introduce a general search model with three labor market states. The model provides an example for how transitions affecting labor force participation must depend on employment state, and will be convenient for identifying and estimating the shock process that affects a worker’s search decision. What governs a worker’s labor force participation status in this model is their ‘type,’ which determines whether they would choose to search when not employed. An interpretation of these types is a cost of searching. However, I allow for both ‘types’ of workers to reach employment, though at different arrival rates to reflect their respective search intensities. Because of this environment, both types of workers may move directly to employment. Workers’ idiosyncratic types are sub ject to a Markov transition process, producing the flows of workers between nonparticipation and unemployment. Finally, both types of workers separate from employment with some probability, returning to the nonparticipation or unemployed pool depending on their type.

Changes in a worker’s ‘Type’, whatever types may be, can be observed by changes in a worker’s reported job search decisions. This leads to a natural inter­pretation of type as heterogeneity in productivity, searching costs, or priors on such variables that would change a worker’s search behavior when out of employment. The key factor is that a change in this ‘type’ affects a worker’s search decision if not em­ployed, but not necessarily their willingness to participate in the labor market. The fundamental difficulty with identifying any transition process for these types is the fact that they are difficult to identify in employment when search decisions are not observed. To overcome this problem of identifying types in employment, I use the 48 month panel of the 1996 Survey of Income and Program Participants (SIPP) to observe workers’ search decisions prior to obtaining a job, and track their search deci­sions if they separate from the job during the survey. I estimate a Markov transition process for types from these employment spells. I find that the Markov process for employed workers I estimate from employment spells in the SIPP is consistent with what is needed in the model to match the average monthly flows in US labor market data.

Many of the three-state labor market models can be mapped to different inter­pretations of the types I described above. The labor market models in the literature consider the heterogeneity of agents to be in their desire to participate, only allowing for changes between being employed or unemployed (participation), and nonpartic­ipation to be driven by these transitions. If a participating ‘type’ of agent were to receive a transition shock, they would only move directly to nonparticipation from the change in ‘type’. Tripier (2004) and Veracierto (2008) find that in such a model, a positive aggregate shock causes a large spike in the unemployment rate through the N U flow as aggregate shocks move nonparticipants into unemployment, caus­ing counterfactual unemployment movements. Krusell et al. (2011, 2012) allow for sufficiently large idiosyncratic shocks to labor market productivity to affect agents’ participation decisions, which allows them to partially match the flow data while avoiding a procyclical unemployment rate through the N U flow. The specification of a type change affecting participation in their models requires the transition rate of employed workers from participating to inactive types to drive both the U N flow and the E N flow simultaneously, since the separation rate for an employed worker who receives a bad shock to labor market productivity is 1. Since only one transition process governs all agents, this results in being unable to match the large U N flow without causing a counterfactually high separation rate to inactivity, making the E N flow too large.

The reason that a single transition process fails to match labor flow patterns is due to the composition of worker types in employment that is generated from the transition process and flow probabilities. If the transition process is calibrated to match the flows to and from employment, that process will fail to match flows in nonemployment (namely, the large U N flow). If the transition process matches the observed transitions in search decisions in nonemployment, it will match the U N and N U flows but fail to match the composition of workers in employment. The transition process from matching the U N and N U flows results in a stationary distribution of workers with a ratio of 12 inactive types (who would choose not to search if out of employment) to 1 active type (who would search if out of a job). Although the number of workers moving to employment from nonparticipation and unemployment is roughly equal, having the same transition process as nonemployed workers, the employed converge to a similar ratio of types as in nonemployment. Since the separation rate of these workers is identical, this produces an E N flow that is about 10 times as large as the E U flow, which is at odds with the data. No matter how one chooses to identify the transition process, if it is assumed to affect all workers independent of employment status, it will always result in counterfactual flows either for the employed or the non-employed population. Allowing these transitions to be dependent on the worker’s employment status allows one to exactly match flows in steady state.

I purposefully abstract from modeling heterogeneity in the population outside of this participation decision to focus on the transition process in this search decision necessary to match labor flows. Although it is very likely that heterogeneity, for instance in the nonparticipant population plays a large role in the search and flow behavior of individuals, the goal is to understand what must change about the search behavior itself to match flows in the data. These changes could be driven by changes in heterogeneous characteristics of individuals. I provide evidence, however, from separation rates that workers seem to share the same separation rates regardless of their labor market status prior to a job or the labor market state they separate to. The only way for the employment to nonemployment (EU ,EN ) flows observed in the data to be consistent with a constant transition process would then require that the flows between nonemployment states such as the N U flow would be counterfactual.

The economic reasons for the difference in transition processes for employed versus nonemployed workers are difficult to identify, but have a natural interpreta­tion. Those who are employed may become attached to the labor force through some mechanism like experience or networks that make search less costly over time spent in employment. Alternatively, increasing one’s duration in nonemployment might make it tougher to search for a job because of discouragement or increasing costs of searching, and nonemployed agents increasingly choose not to search once out of a job.

In section 2.2, I introduce a simple model with participation and search, and outline how the model generates each of the monthly labor flows. I then show in sec­tion 2.3 that a transition process that is independent of an agent’s employment status will fail to match the average flows in the data. In section 2.4, I use the 1996 panel of the SIPP to estimate this transition process for types in employment, and show that allowing these transition processes to be employment-dependent allows one to match these flows in the data. In section 2.5, I show that this problem with matching flows with a single, invariant transition process is present in other specifications of search models with participation. Section 2.6 examines the model’s ability to match average flow rates in a business cycle setting. Section 2.7 discusses the plausible interpreta­tions of employment status affecting the transition process for agents as attachment to the labor force or a discouraged worker effect.