Estimating Latent-Variable Panel Data Models Using Parameter-Expanded SEM Methods

This paper presents new estimation algorithms for three types of dynamic panel data models with latent variables: factor models, discrete choice models, and persistent-transitory quantile processes. The new methods combine the parameter expansion (PX) ideas in Liu et al. (1998) with the stochastic expectation-maximization (SEM) algorithm in likelihood and moment-based contexts. The goal is to facilitate convergence in models with a large space of latent variables by improving algorithmic efficiency. This is achieved by specifying expanded models within the M step. Effectively, we are proposing new estimators for the pseudo-data within iterations that take into account the fact that the model of interest is misspecified for draws based on parameter values far from the truth. We establish the asymptotic equivalence of the likelihood-based PX-SEM to an alternative SEM algorithm with a smaller expected fraction of missing information compared to the standard SEM based on the original model, implying a faster global convergence rate. Finally, in simulations we show that the new algorithms significantly improve the convergence speed relative to standard SEM algorithms, sometimes dramatically so, by reducing the total computing time from hours to a few minutes.