Structural Analysis of Labor Market Transitions Using Indirect Inference

In the econometric analysis of labor market transitions, the data generating process is often specified as a continuous-time semi-Markovian process with a finite state space. With typically short panel data, analysts have long been concerned with the initial conditions problem--- a complication associated with the very first spells observed in the data which are typically left-hand censored or interrupted. For practical convenience, one may want to discard the left-hand censored spells altogether. When there is uncontrolled heterogeneity, this passive approach results in inconsistent parameter estimates for the structural model. It has been well documented that consistent estimation, based on the specification of the correct likelihood function, requires explicit functional forms for the density function of the left-hand censored spells. Such a requirement can not be met, except in very special cases. In this paper we investigate an estimation procedure using indirect inference (II). Our procedure consists of two easy steps. In the first step, a pseudo likelihood function is maximized. In the second, simulations are employed to eliminate the discrepancy of such a pseudo maximum likelihood estimator. We discuss the consistency and asymptotic normality of the II estimator. We describe in detail the pseudo maximum likelihood estimation, the auxiliary parameter estimates and the simulation algorithm. We also implement the procedure using a Dutch data set on labor market histories.