Taking Time Seriously: Dynamic Regression Models ⁄

Dramatic change in the world around us has stimulated a wealth of interest in research questions about the dynamics of political processes. At the same time, we have seen increases in the number of time series data sets and the length of typical time series. While advances in time series methods have helped us to think about political change in important ways, too often published time series analysis displays shortcomings in three areas. First, analysts often estimate models without testing the restrictions implied by their specification. Second, applied researchers link the theoretical concept of equilibrium with the existence of cointegration and use of error correction models. Third, those estimating time series models have often done a poor job of interpreting their statistical results. The consequences, at best, are poor connections between theory and tests and thus a limited cumulation of knowledge. Often, the costs include biased results and incorrect inferences as well. Here, we outline techniques for the estimation of linear models with dynamic specification. In general, we recommend that analysts start with a combination of general dynamic models and test for restrictions before adopting a particular specification. Finally, we recommend that analysts make use of the wide array of information that can be gleaned from dynamic specifications. We illustrate this strategy with data Congressional approval and tax rates across OECD countries. Theoretical and empirical research in all subfields of political science is devoted in large measure to understanding the causes and consequences of events, opinions, behavior, and institutional change as they unfold over time. In recent years, we have seen a dramatic increase in the range of data available over time and with it increasing interest in and application of time series analysis. The proliferation of federal statistical databases and survey data on Americans’ attitudes to include data at high frequency and among subgroups has added geometrically to the available time series data in American politics. Modern international relations scholars have access to data on trade, foreign direct investment, capital flows, economic sanctions, and military expenditures for (increasingly) long stretches of consecutive years. Along with cabinet durations and economic data, the field of comparative politics is now seeing time series of pre and post communist opinion and behavior that are long enough to draw inferences about important research questions in that field. Once primarily limited to the analysis of the few time series in American politics that span significant amounts of political time, scholars of international political economy and comparative politics are increasingly conducting time series analysis. The interest in dynamics and the data needed to tackle these research questions can only continue to grow. Political scientists have done a good job introducing and developing methods appropriate for different types of dynamic political data. Statistical models appropriate for durations (Box-Steffensmeier & Jones 2004, Box-Steffensmeier & Zorn 2002, Box-Steffensmeier & Boef 2005), counts (Brandt & Williams 2001), panels of time series (Stimson 1985, Beck & Katz 1995, Beck & Tucker 1996, Beck & Katz 1997, Beck, Katz & Tucker 1998), unit, near unit, and fractional roots (Ostrom, Jr. & Smith 1993, De Boef & Granato 1997, Box-Steffensmeier & Smith 1998), and endogenous time series (Freeman, Williams & Lin 1989), for example, have appeared in political science journals.1 This body of research recommends classes of estimators and provides advice for estimation to ensure that the dynamic model is consistent with the empirical properties of the data. Debate over unit and fractional root characterizations of political time series continues (Beck 1993, Williams 1993, De Boef & Granato 1997, Box-Steffensmeier & Smith 1996, Box-Steffensmeier & Tomlinson 2000, Freeman, Houser, Kellstedt & Williams 1998). We do not enter this important debate here. We focus instead on the important and common case where data is stationary and regressors are weakly exogenous for the parameters of interest.