Linear Dynamic Panel-Data Estimation using Maximum Likelihood and Structural Equation Modeling

Panel data make it possible both to control for unobserved confounders and to include lagged, endogenous regressors. Trying to do both at the same time, however, leads to serious estimation difficulties. In the econometric literature, these problems have been solved by using lagged instrumental variables together with the generalized method of moments (GMM). In Stata, commands such as xtabond and xtdpdsys have been used for these models. Here we show that the same problems can be addressed via maximum likelihood estimation implemented with Stata’s structural equation modeling (sem) command. We show that the ML (sem) method is substantially more efficient than the GMM method when the normality assumption is met and suffers less from finite sample biases. We introduce a command named xtdpdml with syntax similar to other Stata commands for linear dynamic panel-data estimation. xtdpdml simplifies the SEM model specification process; makes it possible to test and relax many of the constraints that are typically embodied in dynamic panel models; and takes advantage of Stata’s ability to use full information maximum likelihood (FIML) for dealing with missing data.