Modeling Dynamics in Time-Series–Cross-Section Political Economy Data

This article deals with a variety of dynamic issues in the analysis of time-series–cross-section (TSCS) data. Although the issues raised are general, we focus on applications to comparative political economy, which frequently uses TSCS data. We begin with a discussion of specification and lay out the theoretical differences implied by the various types of dynamic models that can be estimated. It is shown that there is nothing pernicious in using a lagged dependent variable and that all dynamic models either implicitly or explicitly have such a variable; the differences between the models relate to assumptions about the speeds of adjustment of measured and unmeasured variables. When adjustment is quick, it is hard to differentiate between the various models; with slower speeds of adjustment, the various models make sufficiently different predictions that they can be tested against each other. As the speed of adjustment gets slower and slower, specification (and estimation) gets more and more tricky. We then turn to a discussion of estimation. It is noted that models with both a lagged dependent variable and serially correlated errors can easily be estimated; it is only ordinary least squares that is inconsistent in this situation. There is a brief discussion of lagged dependent variables combined with fixed effects and issues related to non-stationarity. We then show how our favored method of modeling dynamics combines nicely with methods for dealing with other TSCS issues, such as parameter heterogeneity and spatial dependence. We conclude with two examples.