Interpreting Dynamic Space-Time Panel Data Models

There is a great deal of literature regarding the asymptotic properties of various approaches to estimating simultaneous space-time panel models, but little attention has been paid to how the model estimates should be interpreted. The motivation for use of space-time panel models is that they can provide us with information not available from cross-sectional spatial regressions. LeSage and Pace (2009) show that cross-sectional simultaneous spatial autoregressive models can be viewed as a limiting outcome of a dynamic space-time autoregressive process. A valuable aspect of dynamic space-time panel data models is that the own- and cross-partial derivatives that relate changes in the explanatory variables to those that arise in the dependent variable are explicit. This allows us to employ parameter estimates from these models to quantify dynamic responses over time and space as well as space-time diffusion impacts. We illustrate our approach using the demand for cigarettes over a 30 year period from 1963-1992, where the motivation for spatial dependence is a bootlegging effect where buyers of cigarettes near state borders purchase in neighboring states if there is a price advantage to doing so.