Estimating Latent-Variable Panel Data Models Using Parameter-Expanded SEM Methods
为三类含潜变量的动态面板数据模型（因子模型、离散选择模型、持久-暂时分位数过程）提出了新估计算法，结合参数扩展与随机期望最大化方法，显著提升收敛速度，将计算时间从数小时缩短至几分钟。
This article 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 of Liu, Rubin, and Wu 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.