Unconditional Transformed Likelihood Estimation of Time-Space Dynamic Panel Data Models

I derive the unconditional transformed likelihood function and its derivatives for a fixed-effects panel data model with time lags, spatial lags, and spatial time lags that encompasses the pure time dynamic and pure space dynamic models as special cases. In addition, the model can accommodate spatial dependence in the error term. I demonstrate that the model-consistent representation of the initial-period distribution involves higher-order spatial lag polynomials. Their order is linked to the minimal polynomial of the spatial weights matrix and, in general, tends to infinity with increasing sample size. Consistent estimation requires an appropriate truncation of these lag polynomials unless the spatial weights matrix has a regular structure. The finite sample evidence from Monte Carlo simulations shows that a misspecification of the spatial structure for the initial observations results in considerable biases while the correctly specified estimator behaves well. As an application, I estimate a time-space dynamic wage equation allowing for peer effects within households.