Iterative estimation correcting for error auto-correlation in short panels, applied to lagged dependent variable models

Abstract

An iterative estimation procedure incorporating error serial correlation in short panels is presented. Neglecting serial correlation might both result in inconsistent variance estimates and in inconsistent parameter estimates, for example in (structural) models containing (functions of) lagged dependent variables. Lagged disturbances and/or lagged innovations are treated as unobserved or latent variables, and their estimates are included as supplementary regressors. Iterating until convergence results in consistent estimates of all model parameters. In addition, the asymptotic distribution of the proposed estimator, which can accommodate auto-regressive errors without any assumptions regarding starting values is presented. The main advantage of the proposed method is the maximal reuse of existing (cross-sectional) code, which can simply be adapted to serially correlated disturbances. As such, this “quick fix” estimator seems to be a promising avenue for applied researchers suspecting serial correlation in their data, but only willing to perform a moderate amount of coding (i.e. the iterative loop & the adaptation of the variance estimation), without having to develop, code and debug a full own model. The proposed method is applied to panel data models with lagged dependent variables with and without fixed effects.