The items on this page are grouped in reverse chronological order and include both talks, workshops, and published papers that I can release. If you are looking for the code or data for any of these papers (published or unpublished) check the Code & Software or the Replication pages.  For a full list of my publications, see my CV on the Homepage of this site.

Event Count Time Series Models

Brandt, Patrick T. and Todd Sandler. 2012. A Bayesian Poisson Vector Autoregression Model. 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. Replication zip file  (This is the code for the BaP-VAR model!  BUGS / JAGS / R code is included for the examples in this paper here.)

Brandt, Patrick T. July 2010. Slides from talks at Academia Sinica: Basic Event Counts I and II.  Worked examples in RProposed extensions.  These slides and examples give an overview of the state of the art in PAR(p), PEWMA, and some recent Bayesian count models.  You might be interested in the R code for the examples on the Code and Software link.

Brandt, Patrick T., and John T. Williams. 2001. A Linear Poisson Autoregressive Model: The Poisson AR(p) ModelPolitical Analysis 9(2): 164-84. 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 Science 44(4):823–843, 2000). We develop an alternative model for stationary mean reverting data, the Poisson autoregressive model of order p, 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.

Brandt, Patrick T.,  John T. Williams, Benjamin O. Fordham and Brian Pollins. 2000. Dynamic Modeling for Persistent Event-Count Time SeriesAmerican Journal of Political Science 44(4): 823-843. We present a method for estimating event-count models when the data is generated from a persistent time- series process. A Kalman filter is used to estimate a Poisson exponentially weighted moving average (PEWMA) model. The model is compared to extant methods (Poisson regression, negative binomial regression, and ARIMA models). Using Monte Carlo experiments, we demonstrate that the PEWMA provides significant improvements in efficiency. As an example, we present an analysis of Pollins (1996) models of long cycles in international relations.

Forecasting Methodology and Evaluation

Brandt, Patrick T., John R. Freeman and Philip A. Schrodt. 2011. Racing Horses: Constructing and Evaluating Forecasts in Political Science  Presented at the Society for Political Methodology 28th Annual Summer Meeting, Princeton University, Princeton, NJ, July 2011. 

Brandt, Patrick T., John R. Freeman, Tse-Min Lin and Philip A. Schrodt. 2013. Forecasting Conflict in the Cross-Straits: Long Term and Short Term Predictions How are conflict forecasts affected by the choice of the training set? Remarkably, as many forecasts as are currently being produced using such data, there has been little discussion of this issue. A forecast validation is conducted using data from the Global Dataset on Events, Location and Tone (GDELT) for the Cross-Straits. Across several forecasting models, the size of the training set is varied and rolling and cumulative samples are used. The forecast densities produced are then scored using a continuous rank probability score to determine forecast quality. The results show that shorter rolling training sets can perform as well as or better than longer training sets that use all of the available data. For the Cross-Straits, a Markov-switching Bayesian vector autoregression (MS-BVAR) model outperforms several other forecasting models. The use of these shorter, rolling samples reduces the computational burden of produc- ing forecasts, which is particularly important when using non-linear, computationally intensive methods such as MS-BVARs.  Prepared for the 2013 American Political Science Association Meeting, Chicago, IL.


Brandt, Patrick T. and John R. Freeman. 2013. Why (Not to) Filter or Pre-Whiten the GDELT Time Series.  Some commentary on our experience with dealing with trends and filtering the GDELT data for China and Taiwan.  And why you will likely get the same answers if you do not filter or pre-whiten, since there are no obvious trends for this sub-sample.

Inter- and Intra-state Conflict

Brandt, Patrick T. John R. Freeman, Tse-min Lin and Phillip A. Schrodt. 2012. A Bayesian Time Series Approach to the Comparison of Conflict Dynamics. Prepared for APSA 2012.  Despite the apparent decline in interstate war and some other kinds of conflicts since the middle of the last century, the world continues to be plagued by lethal, politically motivated violence. We address major deficiencies in the rationalist accounts of this violence. Using time series data from the Event Data Project (EDP) at Pennsylvania State University and a Markov-switching, Bayesian multivariate time series model, we produce novel test of rationalists’ theoretical expectations and of empiricists’ stylized facts. We show that there are significant differences in the dynamic structure (mechanisms) of conflicts in the Levant, Cross Straits, and Indian subcontinent. In particular, the number of conflict phases and the lag structures of these conflicts are not the same. Moreover the regimes in the Levant are best conceived in terms of different variances while those in the other two cases in terms of different intercepts. These differences translate into different short and long term patterns of (non) reciprocity and of conflict phase shifts. Hence the evolutionary—non-equilibrating—behaviors of the belligerents in the three conflicts are distinct (Diehl, 2006). The actual patterns are different than those reported recently by Zeitzoff (2011) for the Levant but they appear consistent with some commentaries on Pakistani policymaking (Tremblay and Schofield, 2005). There is little evidence that succession processes or changes in the type of government are the source of conflict phase shifts. The exception is the change in the regime type of Pakistan in the late 1990s; this change does appear to have caused a conflict phase shift. Empirically, conflict dynamics across rivalries differ greatly. There are major differences in the patterns of verbal and material behavior in the Cross Straits and Indian Subcontinent as well as between the conflict dynamics in these two rivalries and the conflict dynamics between the the Israelis and Palestinians. As regards the idea of conflict phase shifts, we find, contrary to many works in the literature, that there are a relatively small number (2-3) in each of our cases. The propensity of some scholars to find 4 or more phases seems to be due to post hocpattern hunting of the kind that Taleb (2010) and others criticize.

Brandt, Patrick T., John R. Freeman and Philip A. Schrodt. 2011. Real TIme, Time Series Forecasting of Inter- and Intra-State Political ConflictConflict Management and Peace Science 28(1):41-64. We propose a framework for forecasting and analyzing regional and international conflicts. It generates forecasts that (1) are accurate but account for uncertainty, (2) are produced in (near) real time, (3) capture actors’ simultaneous behaviors, (4) incorporate prior beliefs, and (5) generate policy contingent forecasts.We combine the CAMEO event-coding framework with Markov-switching and Bayesian vector autoregression models to meet these goals. Our example produces a series of forecasts for material conflict between the Israelis and Palestinians for 2010. Our forecast is that the level of material conflict between these belligerents will increase in 2010, compared to 2009.

Brandt, Patrick T., Michael Colaresi and John R. Freeman. 2008. Dynamics of Reciprocity, Accountability, and Credibility.  Journal of Conflict Research 52(3):343-374.  Web Appendix.  Replication files.  Do public opinion dynamics play an important role in understanding conflict trajectories between democratic governments and other rival groups? The majority of previous research has assumed either that public opinion is irrelevant to conflict processes or that the relationships are one-way causal chains. In this paper, we argue that neither of these assumptions are theoretically or empirically necessary. Instead, we interpret several theories of opinion dynamics and government behavior as particular causal links in models of reciprocity, accountability and credibility relationships. Theoretical expectations about the character of these linkages are translated into four distinct Bayesian structural time series models. These models allow us to include novel domestic public information where available, as well as relax the strict recursive structure that previous time series models have assumed. The models are fit to events data from the Israeli-Palestinian conflict with provisions for U.S. intervention and public support for peace. We find that a credibility model, which allows domestic public opinion to influence U.S., Palestinian and Israeli behavior within a given month, fits the data best. This credibility model supports research that predicts asymmetric reciprocity between democratic and non-democratic belligerents. For the credibility model there is evidence that more pacific Israeli opinion leads to more immediate hostility by the Palestinians toward the Israelis. The direction of this response suggests a negative feedback mechanism where low level conflict is maintained and momentum toward either all out war or dramatic peace is slowed.

T. David Mason, Mehmet Gurses, Patrick T. Brandt, and Jason Michael Quinn. 2011. When Civil Wars Recur: Conditions for a Durable Peace After Civil Wars?  International Studies Perspectives. 12(2): 171--89. Evidence from civil war data sets indicate that once a civil war ends in a nation, that nation is at risk of experiencing another one at a later date. We estimate a series of survival models in an effort to model the factors that influence the duration of the peace following the conclusion of a civil war. The theoretical framework that informs the analysis suggests that the outcome of the previous civil war, its duration and deadliness should affect the duration of the peace. In addition, characteristics of the post-civil war environment -- the extent of democracy, the level of economic development, and the degree of ethnic fractionalization -- should also affect the duration of the peace. Finally, the introduction of peacekeeping forces should make the peace more durable. Findings indicate that long wars create a war weariness effect while high casualty rates make the recurrence of civil war more likely. Highly democratic and highly autocratic post-war regimes are less likely to experience a peace failure, and nations that have moderate levels of ethnic fractionalization are also more likely to experience a new civil war than are nations that are ethnically homogeneous or fragmented among a large number of relatively small ethnic groups. Finally, peacekeeping does make the peace more likely to endure.

Patrick T. Brandt, T. David Mason, Mehmet Gurses, Nicolai Petrovsky, and Dasha Radin. 2008.  When and How the Figthing Stops: Explaining the Duration and Outcome of Civil WarsDefence and Peace Economics 19(6): 415-434.  Replication data and code. A number of recent studies have explored the question of what factors explain variations in the duration of civil wars. The factors that predict the termination of a civil war event (and, therefore, explain variation in the duration of the war) are different from those that predict whether or not a war will occur in the first place. We argue, instead, that the duration of a civil war is a more nearly a function of the factors that predict how it ends: in government victory, rebel victory, or negotiated settlement. After discussing the logic by which protagonists in a civil war choose to stop fighting, we derive a set of hypotheses on the characteristics of the conflict itself and the conflict environment that should affect the outcome of the civil war and, therefore, explain a substantial portion of the variation in the duration of civil wars. We test these hypotheses with a competing risk model using Fearon and Laitin’s (2003) data on 109 civil wars that occurred between 1945 and 1997. Our results show that there are substantial differences in the factors that predict the duration of civil wars across the different outcomes.

International and Comparative Political Economy

Sattler, Thomas, Patrick T. Brandt and John R. Freeman. 2010. Democratic Accountability in Open EconomiesQuarterly Journal of Political Science 5(1):71-97.  We analyze democratic accountability in open economies based on different hypotheses about political evaluations and government responsiveness. Specifically, we assess whether citizens primarily rely on government policies or if they focus on economic outcomes resulting from these policies to evaluate governments. Our empirical analysis relies on Bayesian structural vector autoregression models for the British economy, aggregate monthly measures of public opinion, and economic evaluations from 1984 to 2006. We find that voters continuously monitor and strongly respond contemporaneously to changes in monetary and fiscal policies, but less to changes in macroeconomic outcomes. Voters also respond to policies differently when institutions change. When the Bank of England became politically independent, citizens shifted their attention toward fiscal policy, and the role of monetary policy in their evaluations decreased significantly. Finally, politicians respond to voting behavior by adjusting their policies in a sensible way. When vote intentions and approval decrease, the government reacts to the public by adjusting fiscal policy and, before the Bank of England became independent, also monetary policy. Presented at the Conference on the Political Economy of International Finance (PEIF), Emory University and the Federal Reserve Bank of Atlanta, February 9, 2007. 

Sattler, Thomas, John R. Freeman and Patrick T. Brandt. Political Accountability and the Room to Maneuver. 2008. Comparative Political Studies 41(9): 1212-1239; Erratum, Comparative Political Studies 42(1): 125-131. (The version linked here is the correct one, not the one that was published incorrectly by Sage in 2008.) Most scholars now agree that, despite economic globalization, national governments retain substantial room to maneuver in terms of policy and hence welfare outcomes. By implication, popular sovereignty over national life continues to exist. Through voting and other forms of political participation, citizens evaluate the policy decisions of their public officials and hold them accountable for those choices. In fact, this wisdom rests on very weak footings. Many studies of the room to maneuver make no provision for popular evaluation of policy; they assert rather than demonstrate popular satisfaction with policy choices and economic outcomes. Most omit channels for popular preferences to feedback into policy choice and policy outcomes. For these reasons we lack a good understanding of the causal chains that connects policy choice to policy outcomes to popular evaluations, and then again to policy choices. In addition, extant research fails to draw meaningful distinctions between short and long-term consequences of policy choice (dynamics), and concomitantly to provide any precise measures of the magnitudes of policy outcomes. But without scientifically sound measures of these magnitudes we have no idea how much, if any, room to maneuver democratic governments actually retain. We develop a framework that addresses these issues. The framework is genuinely interdisciplinary insofar as it endogenizes both the open economy and the polity. We use current published research-especially the work in new open macroeconomics, government approval research and the political economy of financial markets-to identify this model. From it we extract three competing arguments about the causal chains that connote popular sovereignty over the economy. Then using a Bayesian structural time series model we test the competing arguments. The testbed for our analysis is the U.K., a political economy that is distinctive for being both highly open to trade and finance and, at the same time, producing a high degree of clarity of responsibility for its governments. Our results do not support the Room to Maneuver thesis in general or as it applies to the UK. And they are only partly consistent with those of previous research about the existence of political accountability in open economies. On the one hand, in our sample period (1981-1997) the British government was responsive to changes in political evaluations, specifically sociotropic economic expectations. And its policy changes effectively fed back into popular evaluations of government policy particularly into vote intentions. Hence, a visible link from popular evaluations to policy and back to popular evaluations existed. On the other hand, this accountability mechanism worked outside the real economy. The changes in policy induced by shifts in popular evaluations of the British government had no impact on inflation and economic growth.  Presented at the International Political Economy Society Meeting, Princeton University, Princeton, New Jersey, November 2006 and the Midwest Political Science Association Meeting, Chicago, IL, April 2006. Winner of the Robert H. Durr Award for the best methodology paper the the 2006 Meeting of the Midwest Political Science Association. 


Brandt, Patrick T. Justin George, and Todd Sandler. 2016. "Why concessions should not be made to terrorist kidnappers.European Journal of Political Economy. September. 44: 41-52. This paper examines the dynamic implications of making concessions to terrorist kidnappers. We apply a Bayesian Poisson changepoint model to kidnapping incidents associated with three cohorts of countries that differ in their frequency of granting concessions. Depending on the cohort of countries during 2001–2013, terrorist negotiation successes encouraged 64% to 87% more kidnappings. Our findings also hold for 1978–2013, during which these negotiation successes encouraged 26% to 57% more kidnappings. Deterrent aspects of terrorist casualties are also quantified; the dominance of religious fundamentalist terrorists meant that such casualties generally did not curb kidnappings. See the press release.

Santifort, Charlinda, Todd Sandler and Patrick T. Brandt. 2013. “Terrorist attack and target diversity: Changepoints and their drivers.” Journal of Peace Research. 50(1): 75-90. Terrorists choose from a wide variety of targets and attack methods. Unlike past literature, this article investigates how diversity in target choice and attack modes among domestic and transnational terrorists has evolved and changed over the past 40 years. Changes in the practice of homeland security, which affects the marginal costs of target–attack combinations, and changes in the dominant terrorist influence at the global level, which affects the marginal benefits of target–attack combinations, drive the changepoints. Our empirical analysis relies on count data drawn from the Global Terrorism Database (GTD) for 1970–2010 that distinguishes between domestic and transnational terrorist incidents. Given the data-intensity requirements of our methods, the study is necessarily from a global perspective. A Bayesian Reversible Jump Markov chain Monte Carlo (RJMCMC) changepoint analysis is applied to identify arrival rate changes in both domestic and transnational terrorism. The changepoints in these aggregate series are then matched with those of the subset time series for attack modes (e.g. assassinations and bombings) and target types (e.g. officials and private parties). The underlying drivers of these changepoints are then identified. The article also calculates a Herfindahl index of attack diversity for the aggregate and component domestic and transnational terrorism time series for the entire period and during four subperiods. The variation in both domestic and transnational terrorist attacks has generally fallen over the last four decades; nevertheless, this diversity still remains high. Bombings of private parties have become the preferred target–attack combination for both transnational and domestic terrorists. This combination is the hardest-to-defend target–attack combination and requires the most homeland security resources. Policymakers can use these and other results to focus their counter-terrorism measures.

Brandt, Patrick T. and Todd Sandler. 2010. What do Transnational Terrorists Target? Has i Changed? Are we Safer?  Journal of Conflict Resolution 54(2): 214-236. This paper 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 --- we 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.  We also include two sets of covariates --- logistical outcome and victim's nature --- to better explain the dynamics.  As other targets were fortified and terrorists 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.

Brandt, Patrick T. and Todd Sandler. 2009. Hostage Taking: Understanding Terrorism Event Dynamics.  Journal of Policy Modeling 31(5): 758-778. This paper employs advanced time series methods to identify the dynamic properties of three hostage taking series. The immediate and long run multipliers of three covariates — successful past negotiations, violent ends, and deaths — are identified. Each hostage series responds differently to the covariates. Past concessions have the strongest impact on generating future kidnapping events, supporting the conventional wisdom to abide by a stated no-concession policy.  Each hostage series has different changepoints caused by a variety of circumstances. Skyjackings and kidnappings are positively correlated, while skyjackings and other hostage events are negatively correlated. Policy recommendations are offered. 

Vector Autoregression: VAR, SVAR, BVAR

Brandt, Patrick T. and John R. Freeman. 2009. Modeling Macro Political DynamicsPolitical Analysis. 17(2):113-142.  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 Erikson, MacKuen and Stimson’s model of the American macropolity (2002) with those of a leading macroeconomic model of U.S. (Sims and Zha 1998 and Leeper, Sims, and Zha 1996). This structural model, with a loose informed prior, yields the best performance in terms of model fit and new insights into the dynamics of the American political economy. The model 1) captures the conventional wisdom 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 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.  Originally prepared for the 2005 APSA Meeting.

Brandt, Patrick T. and John T. Williams. 2007. Multiple Time Series Models. Sage Publications, Thousand Oaks, California. Series: Quantitative Applications in the Social Sciences. Many analyses of time series data involve multiple, related variables. Modeling Multiple Time Series presents many specification choices and special challenges. This book reviews the main competing approaches to modeling multiple time series: simultaneous equations, ARIMA, error correction models, and vector autoregression. The text focuses on vector autoregression (VAR) models as a generalization of the other approaches mentioned. Specification, estimation, and inference using these models is discussed. The authors also review arguments for and against using multi-equation time series models. Two complete, worked examples show how VAR models can be employed. An appendix discusses software that can be used for multiple time series models and software code for replicating the examples is available.

Key Features:

  1.  Offers a detailed comparison of different time series methods and approaches.
  2.  Includes a self-contained introduction to vector autoregression modeling
  3.  Situates multiple time series modeling as a natural extension of commonly taught statistical models.

Patrick T. Brandt and John R. Freeman. 2006. Advances in Bayesian Time Series Modeling and the Study of Politics: Theory Testing, Forecasting, and Policy Analysis. Political Analysis. 14(1): 1-36. 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.



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