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Multivariate count models are rare in political science despite the presence of many count time series. This article develops a new Bayesian Poisson vector autoregression model that can characterize endogenous dynamic counts with no restrictions on the contemporaneous correlations. Impulse responses, decomposition of the forecast errors, and dynamic multiplier methods for the effects of exogenous covariate shocks are illustrated for the model. Two full illustrations of the model, its interpretations, and results are presented. The first example is a dynamic model that reanalyzes the patterns and predictors of superpower rivalry events. The second example applies the model to analyze the dynamics of transnational terrorist targeting decisions between 1968 and 2008. The latter example's results have direct implications for contemporary policy about terrorists' targeting that are both novel and innovative in the study of terrorism.

This article utilizes Bayesian Poisson changepoint regression models to demonstrate how transnational terrorists adjusted their target choices in response to target hardening. In addition, changes in the collective tastes of terrorists and their sponsorship have played a role in target selection over time. For each of four target types— officials, military, business, and private parties—the authors identify the number of regimes and the probable predictors of the events. Regime changes are tied to the rise of modern transnational terrorism, the deployment of technological barriers, the start of state sponsorship, and the dominance of the fundamentalists. The authors also include two sets of covariates—logistical outcome and victim's nature—to better explain the dynamics. As other targets have been fortified and terrorists have sought greater carnage, private parties have become the preferred target type. In recent years, terrorists have increasingly favored people over property for all target types. Moreover, authorities have been more successful at stopping attacks against officials and the military, thereby motivating terrorists to attack business targets and private parties.

Analyzing macro-political processes is complicated by four interrelated problems: model scale, endogeneity, persistence, and specification uncertainty. These problems are endemic in the study of political economy, public opinion, international relations, and other kinds of macro-political research. We show how a Bayesian structural time series approach addresses them. Our illustration is a structurally identified, nine-equation model of the U.S. political-economic system. It combines key features of the model of Erikson, MacKuen, and Stimson (2002) of the American macropolity with those of a leading macroeconomic model of the United States (Sims and Zha, 1998; Leeper, Sims, and Zha, 1996). This Bayesian structural model, with a loosely informed prior, yields the best performance in terms of model fit and dynamics. This model 1) confirms existing results about the countercyclical nature of monetary policy (Williams 1990); 2) reveals informational sources of approval dynamics: innovations in information variables affect consumer sentiment and approval and the impacts on consumer sentiment feed-forward into subsequent approval changes; 3) finds that the real economy does not have any major impacts on key macropolity variables; and 4) concludes, contrary to Erikson, MacKuen, and Stimson (2002), that macropartisanship does not depend on the evolution of the real economy in the short or medium term and only very weakly on informational variables in the long term.

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.

Time series of event counts are common in political science and other social science applications. Presently, there are few satisfactory methods for identifying the dynamics in such data and accounting for the dynamic processes in event counts regression. We address this issue by building on earlier work for persistent event counts in the Poisson exponentially weighted moving-average model (PEWMA) of Brandt et al. (American Journal of Political Science44(4):823–843, 2000). We develop an alternative model for stationary mean reverting data, the Poisson autoregressive model of orderp, or PAR(p) model. Issues of identification and model selection are also considered. We then evaluate the properties of this model and present both Monte Carlo evidence and applications to illustrate.