Bayesian approaches to the study of politics are increasingly popular. But Bayesian approaches to modeling multiple time series have not been critically evaluated. This is in spite of the potential value of these models in international relations, political economy, and other fields of our discipline. We review recent developments in Bayesian multi-equation time series modeling in theory testing, forecasting, and policy analysis. Methods for constructing Bayesian measures of uncertainty of impulse responses (Bayesian shape error bands) are explained. A reference prior for these models that has proven useful in short- and medium-term forecasting in macroeconomics is described. Once modified to incorporate our experience analyzing political data and our theories, this prior can enhance our ability to forecast over the short and medium terms complex political dynamics like those exhibited by certain international conflicts. In addition, we explain how contingent Bayesian forecasts can be constructed, contingent Bayesian forecasts that embody policy counterfactuals. The value of these new Bayesian methods is illustrated in a reanalysis of the Israeli-Palestinian conflict of the 1980s.

In the social sciences, randomized experimentation is the optimal research design for establishing causation. However, for a number of practical reasons, researchers are sometimes unable to conduct experiments and must rely on observational data. In an effort to develop estimators that can approximate experimental results using observational data, scholars have given increasing attention to matching. In this article, we test the performance of matching by gauging the success with which matching approximates experimental results. The voter mobilization experiment presented here comprises a large number of observations (60,000 randomly assigned to the treatment group and nearly two million assigned to the control group) and a rich set of covariates. This study is analyzed in two ways. The first method, instrumental variables estimation, takes advantage of random assignment in order to produce consistent estimates. The second method, matching estimation, ignores random assignment and analyzes the data as though they were nonexperimental. Matching is found to produce biased results in this application because even a rich set of covariates is insufficient to control for preexisting differences between the treatment and control group. Matching, in fact, produces estimates that are no more accurate than those generated by ordinary least squares regression. The experimental findings show that brief paid get-out-the-vote phone calls do not increase turnout, while matching and regression show a large and significant effect.

Multiplicative interaction models are common in the quantitative political science literature. This is so for good reason. Institutional arguments frequently imply that the relationship between political inputs and outcomes varies depending on the institutional context. Models of strategic interaction typically produce conditional hypotheses as well. Although conditional hypotheses are ubiquitous in political science and multiplicative interaction models have been found to capture their intuition quite well, a survey of the top three political science journals from 1998 to 2002 suggests that the execution of these models is often flawed and inferential errors are common. We believe that considerable progress in our understanding of the political world can occur if scholars follow the simple checklist of dos and don'ts for using multiplicative interaction models presented in this article. Only 10% of the articles in our survey followed the checklist.

Studies of voter turnout across states find that those with more facilitative registration laws have higher turnout rates. Eliminating registration barriers altogether is estimated to raise voter participation rates by up to 10%. This article presents panel estimates of the effects of introducing registration that exploits changes in registration laws and turnout within states. New York and Ohio imposed registration requirements on all of their counties in 1965 and 1977, respectively. We find that the introduction of registration to counties that did not previously require registration decreased participation over the long term by three to five percentage points. Though significant, this is lower than estimates of the effects of registration from cross-sectional studies and suggests that expectations about the effects of registration reforms on turnout may be overstated.

Testing the fit of competing equilibrium solutions to extensive form games crucially depends on assumptions about the distribution of player types. To illustrate the importance of these assumptions for differentiating standard statistical models of strategic choice, I draw on a game previously analyzed by Lewis and Schultz (2003). The differences that they highlight between a pair of perfect Bayesian equilibrium and quantal response equilibrium models are not produced by signaling and updating dynamics as claimed, but are instead produced by different assumptions about the distribution of player types. The method of analysis developed and the issues raised are applicable to a broad range of structural models of conflict and bargaining.

We welcome the opportunity to respond to Wand's careful and detailed analysis of our paper (Lewis and Schultz 2003). With the discipline's increasing inclination to move toward fully structural strategic choice models (e.g., Signorino 1999; Morton 1999), the issues that Wand raises are important to consider, as they bear on crucial questions of model construction and interpretation. Moreover, his work has allowed us to consider more carefully the properties of an estimator that we are in the process of applying to actual data.