Title and Abstract
Unconditional transformed likelihood estimation of time-space dynamic panel data models
Panel data sets allow to account for unobserved unit-specific heterogeneity, as well as time-series and cross-sectional dependence. 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. Consistent estimation in short panels requires proper allowance for the influence of the initial observations. 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. An appropriate truncation of these lag polynomials becomes necessary unless the spatial weights matrix has a regular structure. The finite sample evidence from Monte Carlo simulations shows that the proposed estimator performs well in comparison to a bias-corrected conditional likelihood estimator if parameter proliferation is kept under control. As an application, I use data from the Panel Study of Income Dynamics to estimate a time-space dynamic wage equation that I derive from a bargaining model. I find significant spillover effects among household members that give rise to a positive cohabitation premium. Furthermore, the theoretical bargaining model justifies a particular nonlinear restriction on the spatial time lag that simplifies the analytical derivations considerably and is also empirically supported.
Kripfganz, S. (2020). Unconditional transformed likelihood estimation of time-space dynamic panel data models.
Manuscript, University of Exeter.