Working Papers
2003
27 records found
Estimating incumbency advantage and its variation, as an example of a before/after study
Gelman, Andrew, Huang, Zaiying
Submitted: 2003-02-07
Keywords: Bayesian inference, before-after study, Congressional elections, Gibbs
Abstract: (click to show/hide) Incumbency advantage is one of the most studied features in American legislative elections. In this paper, we construct and implement an estimate that allows incumbency advantage to vary between individual incumbents. This model predicts that open-seat elections will be less variable than those with incumbents running, an observed empirical pattern that is not explained by previous models. We apply our method to the U.S. House of Representatives in the twentieth century: our estimate of the overall pattern of incumbency advantage over time is similar to previous estimates (although slightly lower), and we also find a pattern of increasing variation. In addition to the application to incumbency advantage, our approach represents a new method, using multilevel modeling, for estimating effects in before/after studies.
Gelman, Andrew, Huang, Zaiying
Submitted: 2003-02-07
Keywords: Bayesian inference, before-after study, Congressional elections, Gibbs
Abstract: (click to show/hide) Incumbency advantage is one of the most studied features in American legislative elections. In this paper, we construct and implement an estimate that allows incumbency advantage to vary between individual incumbents. This model predicts that open-seat elections will be less variable than those with incumbents running, an observed empirical pattern that is not explained by previous models. We apply our method to the U.S. House of Representatives in the twentieth century: our estimate of the overall pattern of incumbency advantage over time is similar to previous estimates (although slightly lower), and we also find a pattern of increasing variation. In addition to the application to incumbency advantage, our approach represents a new method, using multilevel modeling, for estimating effects in before/after studies.
Bayesian exploratory data analysis
Gelman, Andrew
Submitted: 2003-02-11
Keywords: bootstrap, Fisher's exact test, graphics, mixture model, model checking, multiple imputation, prior predictive check, posterior predictive check, p-value, u-value
Abstract: (click to show/hide) Exploratory data analysis (EDA) and Bayesian inference (or, more generally, complex statistical modeling)---which are generally considered as unrelated statistical paradigms---can be particularly effective in combination. In this paper, we present a Bayesian framework for EDA based on posterior predictive checks. We explain how posterior predictive simulations can be used to create reference distributions for EDA graphs, and how this approach resolves some theoretical problems in Bayesian data analysis. We show how the generalization of Bayesian inference to include replicated data $y^{\rm rep}$ and replicated parameters $\theta^{\rm rep}$ follows a long tradition of generalizations in Bayesian theory. On the theoretical level, we present a predictive Bayesian formulation of goodness-of-fit testing, distinguishing between $p$-values (posterior probabilities that specified antisymmetric discrepancy measures will exceed 0) and $u$-values (data summaries with uniform sampling distributions). We explain that $p$-values, unlike $u$-values, are Bayesian probability statements in that they condition on observed data. Having reviewed the general theoretical framework, we discuss the implications for statistical graphics and exploratory data analysis, with the goal being to unify exploratory data analysis with more formal statistical methods based on probability models. We interpret various graphical displays as posterior predictive checks and discuss how Bayesian inference can be used to determine reference distributions. The goal of this work is not to downgrade descriptive statistics, or to suggest they be replaced by Bayesian modeling, but rather to suggest how exploratory data analysis fits into the probability-modeling paradigm. We conclude with a discussion of the implications for practical Bayesian inference. In particular, we anticipate that Bayesian software can be generalized to draw simulations of replicated data and parameters from their posterior predictive distribution, and these can in turn be used to calibrate EDA graphs.
Gelman, Andrew
Submitted: 2003-02-11
Keywords: bootstrap, Fisher's exact test, graphics, mixture model, model checking, multiple imputation, prior predictive check, posterior predictive check, p-value, u-value
Abstract: (click to show/hide) Exploratory data analysis (EDA) and Bayesian inference (or, more generally, complex statistical modeling)---which are generally considered as unrelated statistical paradigms---can be particularly effective in combination. In this paper, we present a Bayesian framework for EDA based on posterior predictive checks. We explain how posterior predictive simulations can be used to create reference distributions for EDA graphs, and how this approach resolves some theoretical problems in Bayesian data analysis. We show how the generalization of Bayesian inference to include replicated data $y^{\rm rep}$ and replicated parameters $\theta^{\rm rep}$ follows a long tradition of generalizations in Bayesian theory. On the theoretical level, we present a predictive Bayesian formulation of goodness-of-fit testing, distinguishing between $p$-values (posterior probabilities that specified antisymmetric discrepancy measures will exceed 0) and $u$-values (data summaries with uniform sampling distributions). We explain that $p$-values, unlike $u$-values, are Bayesian probability statements in that they condition on observed data. Having reviewed the general theoretical framework, we discuss the implications for statistical graphics and exploratory data analysis, with the goal being to unify exploratory data analysis with more formal statistical methods based on probability models. We interpret various graphical displays as posterior predictive checks and discuss how Bayesian inference can be used to determine reference distributions. The goal of this work is not to downgrade descriptive statistics, or to suggest they be replaced by Bayesian modeling, but rather to suggest how exploratory data analysis fits into the probability-modeling paradigm. We conclude with a discussion of the implications for practical Bayesian inference. In particular, we anticipate that Bayesian software can be generalized to draw simulations of replicated data and parameters from their posterior predictive distribution, and these can in turn be used to calibrate EDA graphs.
Empirical Social Inquiry and Models of Causal Inference
Yang, David
Submitted: 2003-03-05
Keywords: causal inference, method nesting, small-N research
Abstract: (click to show/hide) This essay examines several alternative theories of causality from the philosophy of science literature and considers their implications for methods of empirical social inquiry. In particular, I argue that the epistemology of counterfactual causality is not the only logic of causal inference in social inquiry, and that different methods of research appeal to different models of causal inference. As these models are often philosophically inter-dependent, a more eclectic understanding of causation in empirical research may afford greater methodological versatility and provide a more complete understanding of causality. Some common statistical critiques of small-N research are then considered from the perspective of mechanistic causal theories, and alternative strategies of strengthening causal arguments in small-N research are discussed.
Yang, David
Submitted: 2003-03-05
Keywords: causal inference, method nesting, small-N research
Abstract: (click to show/hide) This essay examines several alternative theories of causality from the philosophy of science literature and considers their implications for methods of empirical social inquiry. In particular, I argue that the epistemology of counterfactual causality is not the only logic of causal inference in social inquiry, and that different methods of research appeal to different models of causal inference. As these models are often philosophically inter-dependent, a more eclectic understanding of causation in empirical research may afford greater methodological versatility and provide a more complete understanding of causality. Some common statistical critiques of small-N research are then considered from the perspective of mechanistic causal theories, and alternative strategies of strengthening causal arguments in small-N research are discussed.
The Statistical Analysis of Roll Call Data
Clinton, Joshua, Jackman, Simon, Rivers, Doug
Submitted: 2003-05-07
Keywords: spatial voting model, item response theory, roll call voting, Bayeisan simulation
Abstract: (click to show/hide) We develop a Bayesian procedure for estimation and inference for spatial models of roll call voting. Our appraoch is extremely flexible, applicable to any legislative setting, irrespective of size, the extremism of legislative voting histories, or the number of roll calls available for analysis. Our model is easily extended to let other sources of information inform the analysis of roll call data, such as the number and nature of the underlying dimensions, the presence of party whipping, the determinants of legislator preferences, or the evolution of the legislative agenda; this is especially helpful since it is gernally inappropriate to use estimates of extant methods (usually generated under assumptions of sincere voting) to test models embodying alternative assumptions (e.g., log-rolling). A Bayesian approach also provides a coherent framework for estimation and inference with roll call data that eludes extant methods; moreover, via Bayesian simulation methods, it is straightforward to generate uncertainty assessments or hypothesis tests concerning any auxiliary quantity of interest or to formally compare models. In a series of examples we show how our method is easily extended to accommodate theoretically interesting modesl of legislative behavior. Our goal is to move roll call analysis away from pure measurement or description towards a tool for testing substantive theories of legislative behavior.
Clinton, Joshua, Jackman, Simon, Rivers, Doug
Submitted: 2003-05-07
Keywords: spatial voting model, item response theory, roll call voting, Bayeisan simulation
Abstract: (click to show/hide) We develop a Bayesian procedure for estimation and inference for spatial models of roll call voting. Our appraoch is extremely flexible, applicable to any legislative setting, irrespective of size, the extremism of legislative voting histories, or the number of roll calls available for analysis. Our model is easily extended to let other sources of information inform the analysis of roll call data, such as the number and nature of the underlying dimensions, the presence of party whipping, the determinants of legislator preferences, or the evolution of the legislative agenda; this is especially helpful since it is gernally inappropriate to use estimates of extant methods (usually generated under assumptions of sincere voting) to test models embodying alternative assumptions (e.g., log-rolling). A Bayesian approach also provides a coherent framework for estimation and inference with roll call data that eludes extant methods; moreover, via Bayesian simulation methods, it is straightforward to generate uncertainty assessments or hypothesis tests concerning any auxiliary quantity of interest or to formally compare models. In a series of examples we show how our method is easily extended to accommodate theoretically interesting modesl of legislative behavior. Our goal is to move roll call analysis away from pure measurement or description towards a tool for testing substantive theories of legislative behavior.
Spatial Voting Theory and Counterfactual Inference: John C. Breckenridge and the Presidential Election of 1860
Jenkins, Jeffery A., Morris, Irwin
Submitted: 2003-07-02
Keywords: spatial voting theory, counterfactual inference, presidential election
Abstract: (click to show/hide) One important catalyst for the onset of the Civil War was the presidential election of Abraham Lincoln in 1860. Lincoln, competing against three other candidates, won election with the smallest percentage of the popular vote in American history. Given the circumstances, a slightly different electoral slate might have engineered his defeat. We examine this possibility by focusing on the candidacy of John C. Breckinridge, the final entrant into the race. Historians disagree over the rationale behind Breckinridge's candidacy. Some argue that it was a desperate effort to defeat Lincoln; others suggest that it was designed to insure Lincoln's victory. Using election counterfactuals and applying spatial voting theory, we examine these arguments. Our evidence suggests that Breckinridge had no reasonable chance to win. Support for Breckinridge's candidacy was only reasonable if the intention were to elect Lincoln.
Jenkins, Jeffery A., Morris, Irwin
Submitted: 2003-07-02
Keywords: spatial voting theory, counterfactual inference, presidential election
Abstract: (click to show/hide) One important catalyst for the onset of the Civil War was the presidential election of Abraham Lincoln in 1860. Lincoln, competing against three other candidates, won election with the smallest percentage of the popular vote in American history. Given the circumstances, a slightly different electoral slate might have engineered his defeat. We examine this possibility by focusing on the candidacy of John C. Breckinridge, the final entrant into the race. Historians disagree over the rationale behind Breckinridge's candidacy. Some argue that it was a desperate effort to defeat Lincoln; others suggest that it was designed to insure Lincoln's victory. Using election counterfactuals and applying spatial voting theory, we examine these arguments. Our evidence suggests that Breckinridge had no reasonable chance to win. Support for Breckinridge's candidacy was only reasonable if the intention were to elect Lincoln.
Agglomerative Clustering of Rankings Data, with an Application to Prison Rodeo Events
Zorn, Christopher
Submitted: 2003-07-03
Keywords: Cluster analysis, ordinal data, classification, rankings, dissimilarity
Abstract: (click to show/hide) This paper considers the problem of assessing item similarity on the basis of rankings data, that is, data on ordinal outcomes. I discuss a modification to the standard dissimilarity measure used in agglomerative clustering which addresses the ordinal nature of ranking data. I then apply this alternative to cluster nine events comprising the Angola, Louisiana prison rodeo.
Zorn, Christopher
Submitted: 2003-07-03
Keywords: Cluster analysis, ordinal data, classification, rankings, dissimilarity
Abstract: (click to show/hide) This paper considers the problem of assessing item similarity on the basis of rankings data, that is, data on ordinal outcomes. I discuss a modification to the standard dissimilarity measure used in agglomerative clustering which addresses the ordinal nature of ranking data. I then apply this alternative to cluster nine events comprising the Angola, Louisiana prison rodeo.
Presidential Elections and the Stock Market: Comparing Markov-Switching and (FIE)GARCH Models of Stock Volatility
Leblang, David, Mukherjee, Bumba
Submitted: 2003-07-07
Keywords: Volatility, Markov-Switching, ARCH, Political Business Cycle, Stock Markets
Abstract: (click to show/hide) Existing theoretical research on electoral politics and financial markets predict that when investors expect left parties Democrats (US), Labor (UK), to win elections market volatility increases. In addition, current econometric research on stock market volatility suggests that Markov-Switching models provide more accurate volatility forecasts and fit stock price volatility data better than linear or non-linear GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models. We take issue with both of these claims. We construct a formal model which predicts that if traders anticipate that the Democratic candidate will win the Presidential election stock market volatility decreases. Using two data sets from the 2000 Presidential election we test our claim by estimating several GARCH, Exponential-GARCH (EGARCH), Fractionally Integrated Exponential-GARCH (FIEGARCH) and Markov-Switching models. We also conduct extensive out-of-sample forecasting tests to evaluate these competing statistical models. Results from the out-of-sample forecasts show^×in contrast to prevailing claims that GARCH and EGARCH models provide substantially more accurate forecasts than the Markov-Switching models. Estimates from all the competing statistical models support the predictions from our formal model.
Leblang, David, Mukherjee, Bumba
Submitted: 2003-07-07
Keywords: Volatility, Markov-Switching, ARCH, Political Business Cycle, Stock Markets
Abstract: (click to show/hide) Existing theoretical research on electoral politics and financial markets predict that when investors expect left parties Democrats (US), Labor (UK), to win elections market volatility increases. In addition, current econometric research on stock market volatility suggests that Markov-Switching models provide more accurate volatility forecasts and fit stock price volatility data better than linear or non-linear GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models. We take issue with both of these claims. We construct a formal model which predicts that if traders anticipate that the Democratic candidate will win the Presidential election stock market volatility decreases. Using two data sets from the 2000 Presidential election we test our claim by estimating several GARCH, Exponential-GARCH (EGARCH), Fractionally Integrated Exponential-GARCH (FIEGARCH) and Markov-Switching models. We also conduct extensive out-of-sample forecasting tests to evaluate these competing statistical models. Results from the out-of-sample forecasts show^×in contrast to prevailing claims that GARCH and EGARCH models provide substantially more accurate forecasts than the Markov-Switching models. Estimates from all the competing statistical models support the predictions from our formal model.
Causal Inference with General Treatment Regimes: Generalizing the Propensity Score
Imai, Kosuke, van Dyk, David A.
Submitted: 2003-07-08
Keywords: causal inference, income, medical expenditure, non-random treatment, observational studies, schooling, smoking, subclassification
Abstract: (click to show/hide) In this article, we develop the theoretical properties of the propensity function which is a generalization of the propensity score of Rosenbaum and Rubin (1983). Methods based on the propensity score have long been used for causal inference in observational studies; they are easy to use and can effectively reduce the bias caused by non-random treatment assignment. Although treatment regimes need not be binary in practice, the propensity score methods are generally confined to binary treatment scenarios. Two possible exceptions were suggested by Joffe and Rosenbaum (1999) and Imbens (2000) for ordinal and categorical treatments, respectively. In this article, we develop theory and methods which encompass all of these techniques and widen their applicability by allowing for arbitrary treatment regimes. We illustrate our propensity function methods by applying them to two data sets; we estimate the effect of smoking on medical expenditure and the effect of schooling on wages. We also conduct Monte Carlo experiments to investigate the performance of our methods.
Imai, Kosuke, van Dyk, David A.
Submitted: 2003-07-08
Keywords: causal inference, income, medical expenditure, non-random treatment, observational studies, schooling, smoking, subclassification
Abstract: (click to show/hide) In this article, we develop the theoretical properties of the propensity function which is a generalization of the propensity score of Rosenbaum and Rubin (1983). Methods based on the propensity score have long been used for causal inference in observational studies; they are easy to use and can effectively reduce the bias caused by non-random treatment assignment. Although treatment regimes need not be binary in practice, the propensity score methods are generally confined to binary treatment scenarios. Two possible exceptions were suggested by Joffe and Rosenbaum (1999) and Imbens (2000) for ordinal and categorical treatments, respectively. In this article, we develop theory and methods which encompass all of these techniques and widen their applicability by allowing for arbitrary treatment regimes. We illustrate our propensity function methods by applying them to two data sets; we estimate the effect of smoking on medical expenditure and the effect of schooling on wages. We also conduct Monte Carlo experiments to investigate the performance of our methods.
Primaries and Turnout
Kanthak, Kristen, Morton, Becky
Submitted: 2003-07-09
Keywords: primaries, turnout, bivariate probit, selection model, treatment effects
Abstract: (click to show/hide) We consider the effects of differences in primary systems on voter turnout in primaries as well as the effect of holding primaries on general election turnout and support for candidates chosen in primaries. The analysis is based on a group majority voting model of turnout where candidates from two major parties simultaneously make strategic entry decisions and mobilize voters strategically in primaries and general elections if they choose to enter. We evaluate the model's predictions using data from midterm Congressional primaries and general elections in the 1980s. We use a two-stage estimation process. First, the model's predictions concerning the effects of primary system differences on whether primaries occur and the vote totals in primaries is estimated using a maximum likelihood bivariate probit selection model. We find that primary system variables do have significant effects on whether primaries are held and to some extent affect vote totals in primaries, although there are interesting party specific differences suggesting that Republicans see advantages from mobilizing voters in open primary systems while Democrats benefit in semi-closed primary systems. Second, the estimated vote totals in the primaries are used as treatment variables via an instrumental variables approach in a simultaneous equation system with two dependent variables general election vote totals and the vote share of the Democratic party's candidate. We find that voting in primaries has a positive and significant effect on voting in general elections and significantly increase the vote share of the party holding the primary, suggesting that the arguments that primaries by their existence decrease voter turnout and hurt parties holding them have no support.
Kanthak, Kristen, Morton, Becky
Submitted: 2003-07-09
Keywords: primaries, turnout, bivariate probit, selection model, treatment effects
Abstract: (click to show/hide) We consider the effects of differences in primary systems on voter turnout in primaries as well as the effect of holding primaries on general election turnout and support for candidates chosen in primaries. The analysis is based on a group majority voting model of turnout where candidates from two major parties simultaneously make strategic entry decisions and mobilize voters strategically in primaries and general elections if they choose to enter. We evaluate the model's predictions using data from midterm Congressional primaries and general elections in the 1980s. We use a two-stage estimation process. First, the model's predictions concerning the effects of primary system differences on whether primaries occur and the vote totals in primaries is estimated using a maximum likelihood bivariate probit selection model. We find that primary system variables do have significant effects on whether primaries are held and to some extent affect vote totals in primaries, although there are interesting party specific differences suggesting that Republicans see advantages from mobilizing voters in open primary systems while Democrats benefit in semi-closed primary systems. Second, the estimated vote totals in the primaries are used as treatment variables via an instrumental variables approach in a simultaneous equation system with two dependent variables general election vote totals and the vote share of the Democratic party's candidate. We find that voting in primaries has a positive and significant effect on voting in general elections and significantly increase the vote share of the party holding the primary, suggesting that the arguments that primaries by their existence decrease voter turnout and hurt parties holding them have no support.
States as Policy Laboratories: Experimenting with the Children's Health Insurance Program
Volden, Craig
Submitted: 2003-07-09
Keywords: diffusion, federalism, dyad-year, event, history, learning
Abstract: (click to show/hide) For more than a decade, scholars of policy diffusion across the states have relied on state-year event history analyses. Such work has been limited by: (1) focusing mainly on neighbor-to-neighbor diffusion paths, rather than other similarities across states; (2) neglecting the role of the success or failures of policies in their diffusion; (3) studying singular specific policy adoptions rather than the choice among policy variants; and (4) setting aside questions about how diffusion mechanisms vary across different policies and different political processes. This paper proposes the alternative approach of dyad-year event history analysis, commonly used in international relations, and applies it to the study of policy diffusion in Children's Health Insurance Program from 1998-2001. This approach uncovers strong evidence of the emulation of states with similar political, demographic, and budgetary characteristics, and those with successful policies. Moreover, the diffusion mechanisms differ substantially across different policy types and political processes.
Volden, Craig
Submitted: 2003-07-09
Keywords: diffusion, federalism, dyad-year, event, history, learning
Abstract: (click to show/hide) For more than a decade, scholars of policy diffusion across the states have relied on state-year event history analyses. Such work has been limited by: (1) focusing mainly on neighbor-to-neighbor diffusion paths, rather than other similarities across states; (2) neglecting the role of the success or failures of policies in their diffusion; (3) studying singular specific policy adoptions rather than the choice among policy variants; and (4) setting aside questions about how diffusion mechanisms vary across different policies and different political processes. This paper proposes the alternative approach of dyad-year event history analysis, commonly used in international relations, and applies it to the study of policy diffusion in Children's Health Insurance Program from 1998-2001. This approach uncovers strong evidence of the emulation of states with similar political, demographic, and budgetary characteristics, and those with successful policies. Moreover, the diffusion mechanisms differ substantially across different policy types and political processes.
Political Preference Formation: Competition, Deliberation, and the (Ir)relevance of Framing Effects
Druckman, Jamie
Submitted: 2003-07-09
Keywords: framing effects, experiments, rational choice theory, political psychology
Abstract: (click to show/hide) A framing effect occurs when different, but logically equivalent, words or phrases such as 95% employment or 5% unemployment cause individuals to alter their preferences. Framing effects challenge the foundational assumptions of much of the social sciences (e.g., the existence of coherent preferences or stable attitudes), and raise serious normative questions about democratic responsiveness. Many scholars and pundits assume that framing effects are highly robust in political contexts. Using a new theory and an experiment with more than 550 participants, I show that this is not the case framing effects do not occur in many political settings. Elite competition and citizens inter- personal conversations often vitiate and eliminate framing effects. However, I also find that when framing effects persist, they can be even more pernicious than often thought not only do they suggest incoherent preferences but they also stimulate increased confidence in those preferences. My results have broad implications for preference formation, rational choice theory, political psychology, and experimental design.
Druckman, Jamie
Submitted: 2003-07-09
Keywords: framing effects, experiments, rational choice theory, political psychology
Abstract: (click to show/hide) A framing effect occurs when different, but logically equivalent, words or phrases such as 95% employment or 5% unemployment cause individuals to alter their preferences. Framing effects challenge the foundational assumptions of much of the social sciences (e.g., the existence of coherent preferences or stable attitudes), and raise serious normative questions about democratic responsiveness. Many scholars and pundits assume that framing effects are highly robust in political contexts. Using a new theory and an experiment with more than 550 participants, I show that this is not the case framing effects do not occur in many political settings. Elite competition and citizens inter- personal conversations often vitiate and eliminate framing effects. However, I also find that when framing effects persist, they can be even more pernicious than often thought not only do they suggest incoherent preferences but they also stimulate increased confidence in those preferences. My results have broad implications for preference formation, rational choice theory, political psychology, and experimental design.
Demographic Forecasting
Girosi, Federico, King, Gary
Submitted: 2003-07-10
Keywords: forecasting
Abstract: (click to show/hide) We introduce a new framework for forecasting age-sex-country-cause-specific mortality rates that incorporates considerably more information, and thus has the potential to forecast much better, than any existing approach. Mortality forecasts are used in a wide variety of academic fields, and for global and national health policy making, medical and pharmaceutical research, and social security and retirement planning. As it turns out, the tools we developed in pursuit of this goal also have broader statistical implications, in addition to their use for forecasting mortality or other variables with similar statistical properties. First, our methods make it possible to include different explanatory variables in a time series regression for each cross-section, while still borrowing strength from one regression to improve the estimation of all. Second, we show that many existing Bayesian (hierarchical and spatial) models with explanatory variables use prior densities that incorrectly formalize prior knowledge. Many demographers and public health researchers have fortuitously avoided this problem so prevalent in other fields by using prior knowledge only as an ex post check on empirical results, but this approach excludes considerable information from their models. We show how to incorporate this demographic knowledge into a model in a statistically appropriate way. Finally, we develop a set of tools useful for developing models with Bayesian priors in the presence of partial prior ignorance. This approach also provides many of the attractive features claimed by the empirical Bayes approach, but fully within the standard Bayesian theory of inference. The latest version of this manuscript is available at http://gking.harvard.edu.
Girosi, Federico, King, Gary
Submitted: 2003-07-10
Keywords: forecasting
Abstract: (click to show/hide) We introduce a new framework for forecasting age-sex-country-cause-specific mortality rates that incorporates considerably more information, and thus has the potential to forecast much better, than any existing approach. Mortality forecasts are used in a wide variety of academic fields, and for global and national health policy making, medical and pharmaceutical research, and social security and retirement planning. As it turns out, the tools we developed in pursuit of this goal also have broader statistical implications, in addition to their use for forecasting mortality or other variables with similar statistical properties. First, our methods make it possible to include different explanatory variables in a time series regression for each cross-section, while still borrowing strength from one regression to improve the estimation of all. Second, we show that many existing Bayesian (hierarchical and spatial) models with explanatory variables use prior densities that incorrectly formalize prior knowledge. Many demographers and public health researchers have fortuitously avoided this problem so prevalent in other fields by using prior knowledge only as an ex post check on empirical results, but this approach excludes considerable information from their models. We show how to incorporate this demographic knowledge into a model in a statistically appropriate way. Finally, we develop a set of tools useful for developing models with Bayesian priors in the presence of partial prior ignorance. This approach also provides many of the attractive features claimed by the empirical Bayes approach, but fully within the standard Bayesian theory of inference. The latest version of this manuscript is available at http://gking.harvard.edu.
A Reassessment of Presidential Campaign Strategy Formation and Candidate Resource Allocation
Reeves, Andrew, Chen, Lanhee, Nagano, Tiffany
Submitted: 2003-07-11
Keywords: comments greatly appreciated, presidential campaign strategy
Abstract: (click to show/hide) Daron Shaw (1999) argues in "The Methods behind the Madness: Presidential Electoral College Strategies, 1988-1996" that candidates formulate state-level general election campaign strategies based on a number of predictable and exogenous factors, such as the cost of television advertisements and electoral vote share. Shaw (1999) further asserts that these strategies are strong independent predictors of candidate resource allocation. His article supports these conclusions with what are claimed to be results from ordered probit and two-stage least squares (2SLS) regressions, but we demonstrate that both are in fact ordinary least squares (LS) regressions. When we implement the methods that Shaw (1999) claims to use, we find that all key substantive conclusions in the article vanish. We show that the factors attributed to the formation of electoral college strategy are insignificant and that whether these strategies have any independent effect on the allocation of campaign resources cannot be ascertained from his (claimed or actual) methods and data.
Reeves, Andrew, Chen, Lanhee, Nagano, Tiffany
Submitted: 2003-07-11
Keywords: comments greatly appreciated, presidential campaign strategy
Abstract: (click to show/hide) Daron Shaw (1999) argues in "The Methods behind the Madness: Presidential Electoral College Strategies, 1988-1996" that candidates formulate state-level general election campaign strategies based on a number of predictable and exogenous factors, such as the cost of television advertisements and electoral vote share. Shaw (1999) further asserts that these strategies are strong independent predictors of candidate resource allocation. His article supports these conclusions with what are claimed to be results from ordered probit and two-stage least squares (2SLS) regressions, but we demonstrate that both are in fact ordinary least squares (LS) regressions. When we implement the methods that Shaw (1999) claims to use, we find that all key substantive conclusions in the article vanish. We show that the factors attributed to the formation of electoral college strategy are insignificant and that whether these strategies have any independent effect on the allocation of campaign resources cannot be ascertained from his (claimed or actual) methods and data.
Imitative and Evolutionary Processes that Produce Coordination Among American Voters
Mebane, Walter R.
Submitted: 2003-07-11
Keywords: imitation, evolutionary game, strategic coordination, voting
Abstract: (click to show/hide) I examine the extent to which evolutionary game models based on the idea of pure imitation may help to explain recent empirical findings that the American electorate is involved in a situation of large-scale strategic coordination. Pure imitation in this context is the idea that some voters who are dissatisfied with their current strategy look around and adopt the strategy of the first voter they encounter who has attributes similar to theirs. The current analysis is part of a plan to use evolutionary models to motivate simulations based on National Election Studies data. The model implies that all voters ultimately use strategic coordination, although competing strategies disppear at different rates, depending on the voter's partisanship.
Mebane, Walter R.
Submitted: 2003-07-11
Keywords: imitation, evolutionary game, strategic coordination, voting
Abstract: (click to show/hide) I examine the extent to which evolutionary game models based on the idea of pure imitation may help to explain recent empirical findings that the American electorate is involved in a situation of large-scale strategic coordination. Pure imitation in this context is the idea that some voters who are dissatisfied with their current strategy look around and adopt the strategy of the first voter they encounter who has attributes similar to theirs. The current analysis is part of a plan to use evolutionary models to motivate simulations based on National Election Studies data. The model implies that all voters ultimately use strategic coordination, although competing strategies disppear at different rates, depending on the voter's partisanship.
Negotiated Compliance: Social Solutions to the 'Principal's Problem'
Whitford, Andrew B., Miller, Gary J., Bottom, William P.
Submitted: 2003-07-11
Keywords: principal-agency theory, experiments, incentives, trust, hierarchical logit
Abstract: (click to show/hide) Principal-agency theory has typically analyzed the principal's problem1: how to write a contract with incentives that will induce an agent to provide the principal with the maximum feasible expected gain. In practice, principal-agent contracts are typically negotiated, not imposed. Experiments indicate that agent compliance is determined less by the negotiated terms of the contract than by expectations created by the negotiation process itself. We interpret this as justification for a renewed interest in the politics of negotiation and bureaucratic politics.
Whitford, Andrew B., Miller, Gary J., Bottom, William P.
Submitted: 2003-07-11
Keywords: principal-agency theory, experiments, incentives, trust, hierarchical logit
Abstract: (click to show/hide) Principal-agency theory has typically analyzed the principal's problem1: how to write a contract with incentives that will induce an agent to provide the principal with the maximum feasible expected gain. In practice, principal-agent contracts are typically negotiated, not imposed. Experiments indicate that agent compliance is determined less by the negotiated terms of the contract than by expectations created by the negotiation process itself. We interpret this as justification for a renewed interest in the politics of negotiation and bureaucratic politics.
Space Is more than Geography
Beck, Nathaniel, Gleditsch, Kristian
Submitted: 2003-07-11
Keywords: spatial econometrics, time-series--cross-section data
Abstract: (click to show/hide) Most spatial models use some measure of distance in the spatial weighting matrix. But this is not required: any measure of "similarity" that has the mathematical properties of distance will work well. Here we use spatial methods to allow for dyads which share a common partner to be similar (and a directed dyad and its reverse to be especially similar). While we find evidence of spatial effects in a model with a spatially lagged error, we note that the substantive conseequences of taking this into account are not great. We then use various measures of "community" to assess the impact of similarity in models of democracy and development; the three similarity measures are physical distance, cultural (religious) similarity and trade. In a simple cross-sectional model the spatial lag has large consequences; however, when we move to time-series--cross-section data the impact of the spatial lag is very small. We also argue that one can simplify estimation in many time-series--cross-sectional data sets with temporally independent errors by using the first temporal lag of the spatial lag, which makes for simple estimation.
Beck, Nathaniel, Gleditsch, Kristian
Submitted: 2003-07-11
Keywords: spatial econometrics, time-series--cross-section data
Abstract: (click to show/hide) Most spatial models use some measure of distance in the spatial weighting matrix. But this is not required: any measure of "similarity" that has the mathematical properties of distance will work well. Here we use spatial methods to allow for dyads which share a common partner to be similar (and a directed dyad and its reverse to be especially similar). While we find evidence of spatial effects in a model with a spatially lagged error, we note that the substantive conseequences of taking this into account are not great. We then use various measures of "community" to assess the impact of similarity in models of democracy and development; the three similarity measures are physical distance, cultural (religious) similarity and trade. In a simple cross-sectional model the spatial lag has large consequences; however, when we move to time-series--cross-section data the impact of the spatial lag is very small. We also argue that one can simplify estimation in many time-series--cross-sectional data sets with temporally independent errors by using the first temporal lag of the spatial lag, which makes for simple estimation.
Lagging the Dog?: The Robustness of Panel Corrected Standard Errors in the Presence of Serial Correlation and Observation Specific Effects
Kristensen, Ida, Wawro, Gregory
Submitted: 2003-07-13
Keywords: time-series cross-section data, serial correlation, fixed effects, panel data, lag models, Monte Carlo experiments
Abstract: (click to show/hide) This paper examines the performance of the method of panel corrected standard errors (PCSEs) for time-series cross-section data when a lag of the dependent variable is included as a regressor. The lag specification can be problematic if observation-specific effects are not properly accounted for, leading to biased and inconsistent estimates of coefficients and standard errors. We conduct Monte Carlo studies to assess how problematic the lag specification is, and find that, although the method of PCSEs is robust when there is little to no correlation between unit effects and explanatory variables, the method's performance declines as that correlation increases. A fixed effects estimator with robust standard errors appears to do better in these situations.
Kristensen, Ida, Wawro, Gregory
Submitted: 2003-07-13
Keywords: time-series cross-section data, serial correlation, fixed effects, panel data, lag models, Monte Carlo experiments
Abstract: (click to show/hide) This paper examines the performance of the method of panel corrected standard errors (PCSEs) for time-series cross-section data when a lag of the dependent variable is included as a regressor. The lag specification can be problematic if observation-specific effects are not properly accounted for, leading to biased and inconsistent estimates of coefficients and standard errors. We conduct Monte Carlo studies to assess how problematic the lag specification is, and find that, although the method of PCSEs is robust when there is little to no correlation between unit effects and explanatory variables, the method's performance declines as that correlation increases. A fixed effects estimator with robust standard errors appears to do better in these situations.
Noncommutative harmonic analysis of voting in small committees
Lawson, Brian, Orrison, Michael, Uminsky, David
Submitted: 2003-07-13
Keywords: spectral analysis, noncommutative harmoinc analysis, voting analysis, supreme court
Abstract: (click to show/hide) This paper introduces a new method, noncommutative harmonic analysis, as a tool for political scientists. The method is based on recent results in mathematics which systematically identify coalitions in voting data. The first section shows how this new approach, noncommutative harmonic analysis is a generalization of classical spectral analysis. The second section shows how noncommutative harmonic analysis is applied to a hypothetical example. The third section uses noncommutative harmonic analysis to analyze coalitions on the Supreme Court. The final section suggests ideas for extending the approach presented here to the study of voting in legislatures and preferences over candidates in multicandidate mass elections.
Lawson, Brian, Orrison, Michael, Uminsky, David
Submitted: 2003-07-13
Keywords: spectral analysis, noncommutative harmoinc analysis, voting analysis, supreme court
Abstract: (click to show/hide) This paper introduces a new method, noncommutative harmonic analysis, as a tool for political scientists. The method is based on recent results in mathematics which systematically identify coalitions in voting data. The first section shows how this new approach, noncommutative harmonic analysis is a generalization of classical spectral analysis. The second section shows how noncommutative harmonic analysis is applied to a hypothetical example. The third section uses noncommutative harmonic analysis to analyze coalitions on the Supreme Court. The final section suggests ideas for extending the approach presented here to the study of voting in legislatures and preferences over candidates in multicandidate mass elections.
Identification of Multidimensional Spatial Voting
Rivers, Doug
Submitted: 2003-07-15
Keywords: Identification, Multidimensional Spatial Models
Abstract: (click to show/hide) No abstract provided.
Rivers, Doug
Submitted: 2003-07-15
Keywords: Identification, Multidimensional Spatial Models
Abstract: (click to show/hide) No abstract provided.
Discriminating Methods: Tests for Nonnested Discrete Choice Models
Clarke, Kevin A., Signorino, Curtis S.
Submitted: 2003-07-15
Keywords: discrete choice, nonnested testing, strategic choice, Vuong test, nonparametric test
Abstract: (click to show/hide) We consider the problem of choosing between rival models that are nonnested in terms of their functional forms. We discuss both a parametric and distribution-free procedure for making this choice, and demonstrate through a monte carlo simulation that discrimination is possible. The results of the simulation also allow us to compare the relative power of the two tests.
Clarke, Kevin A., Signorino, Curtis S.
Submitted: 2003-07-15
Keywords: discrete choice, nonnested testing, strategic choice, Vuong test, nonparametric test
Abstract: (click to show/hide) We consider the problem of choosing between rival models that are nonnested in terms of their functional forms. We discuss both a parametric and distribution-free procedure for making this choice, and demonstrate through a monte carlo simulation that discrimination is possible. The results of the simulation also allow us to compare the relative power of the two tests.
Selection Bias and Continuous-Time Duration Models: Consequences and a Proposed Solution
Boehmke, Frederick, Morey, Daniel, Shannon, Megan
Submitted: 2003-07-15
Keywords: duration, selection bias, exponential, monte carlo
Abstract: (click to show/hide) In this paper we explore the consequences of non-random sample selection for continuous time duration analysis. While the consequences of selectivity are reasonably well-understood in linear regression and common discrete choice models, we have little or no understanding of how it affects duration models. In this paper we study this issue by conducting a series of Monte Carlo analyses that estimate common duration models on data that suffer from selectivity. Our findings indicate that the consequences are severe: both coefficients and standard errors may be biased in an unknown direction. In addition, we find that selection bias may create the appearance of (non-existent) duration dependence. Given these difficulties, we develop a solution for self-selectivity bias in duration models and present evidence that demonstrates its superiority to models that ignore the problem.
Boehmke, Frederick, Morey, Daniel, Shannon, Megan
Submitted: 2003-07-15
Keywords: duration, selection bias, exponential, monte carlo
Abstract: (click to show/hide) In this paper we explore the consequences of non-random sample selection for continuous time duration analysis. While the consequences of selectivity are reasonably well-understood in linear regression and common discrete choice models, we have little or no understanding of how it affects duration models. In this paper we study this issue by conducting a series of Monte Carlo analyses that estimate common duration models on data that suffer from selectivity. Our findings indicate that the consequences are severe: both coefficients and standard errors may be biased in an unknown direction. In addition, we find that selection bias may create the appearance of (non-existent) duration dependence. Given these difficulties, we develop a solution for self-selectivity bias in duration models and present evidence that demonstrates its superiority to models that ignore the problem.
Estimation of Equations with Ordered Categorical Variables
Franklin, Charles, Jackson, John
Submitted: 2003-07-16
Keywords: ordered variables, measurement error, macropartisanship
Abstract: (click to show/hide) Ordered categorical variables frequently appear on both the right- and left-hand side of statistical models. We discuss the problems that measurement error, induced by categorization of continuous latent variables, introduces to these models. We show the nature of the bias and demonstrate its consequences by both Monte Carlo simulation and applications to data on partisanship at the individual and macro levels.
Franklin, Charles, Jackson, John
Submitted: 2003-07-16
Keywords: ordered variables, measurement error, macropartisanship
Abstract: (click to show/hide) Ordered categorical variables frequently appear on both the right- and left-hand side of statistical models. We discuss the problems that measurement error, induced by categorization of continuous latent variables, introduces to these models. We show the nature of the bias and demonstrate its consequences by both Monte Carlo simulation and applications to data on partisanship at the individual and macro levels.
Democracy as a Latent Variable
Treier, Shawn, Jackman, Simon
Submitted: 2003-07-16
Keywords: democracy, Polity, measurement, latent variables, Bayesian statistics, item-response model, ordinal data, latent class analysis, democratic peace, Markov chain Monte Carlo
Abstract: (click to show/hide) Measurement is critical to the social scientific enterprise. Many key concepts in social-scientific theories are not observed directly, and researchers rely on assumptions (tacitly or explicitly, via formal measurement models) to operationalize these concepts in empirical work. In this paper we apply formal, statistical measurement models to the Polity indicators of democracy and autocracy, used widely in studies of international relations. In so doing, we make explicit the hitherto implicit assumptions underlying scales built using the Polity indicators. We discuss two models: one in which democracy is operationalized as a latent continuous variable, and another in which democracy is operationalized as a latent class. Our modeling approaches allow us to assess the measurement error in the resulting measure of democracy. We show that this measurement error is considerable, and has substantive consequences when using a measure of democracy as an independent variable in cross-national statistical analysis. Our analysis suggests that skepticism as to the precision of the Polity democracy scale is well-founded, and that many researchers have been overly sanguine about the properties of the Polity democracy scale in applied statistical work.
Treier, Shawn, Jackman, Simon
Submitted: 2003-07-16
Keywords: democracy, Polity, measurement, latent variables, Bayesian statistics, item-response model, ordinal data, latent class analysis, democratic peace, Markov chain Monte Carlo
Abstract: (click to show/hide) Measurement is critical to the social scientific enterprise. Many key concepts in social-scientific theories are not observed directly, and researchers rely on assumptions (tacitly or explicitly, via formal measurement models) to operationalize these concepts in empirical work. In this paper we apply formal, statistical measurement models to the Polity indicators of democracy and autocracy, used widely in studies of international relations. In so doing, we make explicit the hitherto implicit assumptions underlying scales built using the Polity indicators. We discuss two models: one in which democracy is operationalized as a latent continuous variable, and another in which democracy is operationalized as a latent class. Our modeling approaches allow us to assess the measurement error in the resulting measure of democracy. We show that this measurement error is considerable, and has substantive consequences when using a measure of democracy as an independent variable in cross-national statistical analysis. Our analysis suggests that skepticism as to the precision of the Polity democracy scale is well-founded, and that many researchers have been overly sanguine about the properties of the Polity democracy scale in applied statistical work.
Erratum for 'The Method Behind the Madness: Presidential Electoral College Strategies, 1988-96,' JOP Vol. 61, No. 4, November 1999: 893-913.
Shaw, Daron
Submitted: 2003-07-30
Keywords: elections, campaigns, strategy, advertising
Abstract: (click to show/hide) A recent analysis of my 1999 JOP article on Electoral College strategies identifies two important errors. In both cases, tables containing critical multivariate analyses erroneously report preliminary and methodologically inappropriate estimations that I conducted for an earlier version of the paper. The corrected results are presented here, along with some further clarifications about the variables and estimation techniques. These corrected results continue to support the central arguments of the article, although one discrepancy between the old and new findings is worth noting.
Shaw, Daron
Submitted: 2003-07-30
Keywords: elections, campaigns, strategy, advertising
Abstract: (click to show/hide) A recent analysis of my 1999 JOP article on Electoral College strategies identifies two important errors. In both cases, tables containing critical multivariate analyses erroneously report preliminary and methodologically inappropriate estimations that I conducted for an earlier version of the paper. The corrected results are presented here, along with some further clarifications about the variables and estimation techniques. These corrected results continue to support the central arguments of the article, although one discrepancy between the old and new findings is worth noting.
The Macro Mechanics of Social Capital
Keele, Luke
Submitted: 2003-10-15
Keywords: social capital, time series, public opinion
Abstract: (click to show/hide) Interest in social capital has grown as it has become apparent that it is an important predictor of collective well-being. Recently, however, attention has shifted to how levels of social capital have changed over time. But focusing on how a society moves from one level of social capital to another requires that we alter current theory. In particular, by moving to the context of temporal change, we must not treat it as a lumpy concept with general causes and effects. Instead, we need a theory that explains the macro mechanics between civic activity and interpersonal trust. In the following analysis, I develop a macro theory of social capital through a careful delineation of the social capital aggregation process which demonstrates that we should expect civic engagement to affect interpersonal trust over time with the reverse not being true. Then, I develop and use new longitudinal measures of civic engagement and interpersonal trust to test the direction of causality between the two components of social capital. Finally, I model civic engagement as a function of resources and demonstrate how the decline in civic engagement has adversely affected levels of interpersonal trust over the last thirty years.
Keele, Luke
Submitted: 2003-10-15
Keywords: social capital, time series, public opinion
Abstract: (click to show/hide) Interest in social capital has grown as it has become apparent that it is an important predictor of collective well-being. Recently, however, attention has shifted to how levels of social capital have changed over time. But focusing on how a society moves from one level of social capital to another requires that we alter current theory. In particular, by moving to the context of temporal change, we must not treat it as a lumpy concept with general causes and effects. Instead, we need a theory that explains the macro mechanics between civic activity and interpersonal trust. In the following analysis, I develop a macro theory of social capital through a careful delineation of the social capital aggregation process which demonstrates that we should expect civic engagement to affect interpersonal trust over time with the reverse not being true. Then, I develop and use new longitudinal measures of civic engagement and interpersonal trust to test the direction of causality between the two components of social capital. Finally, I model civic engagement as a function of resources and demonstrate how the decline in civic engagement has adversely affected levels of interpersonal trust over the last thirty years.
Forming voting blocs and coalitions as a prisoner's dilemma: a possible theoretical explanation for political instability
Gelman, Andrew
Submitted: 2003-10-27
Keywords: coalitions, cooperation, decisive vote, elections, legislatures, prisoner's dilemma, voting power
Abstract: (click to show/hide) Individuals in a committee can increase their voting power by forming coalitions. This behavior is shown here to yield a prisoner's dilemma, in which a subset of voters can increase their power, while reducing average voting power for the electorate as a whole. This is an unusual form of the prisoner's dilemma in that cooperation is the selfish act that hurts the larger group. Under a simple model, the privately optimal coalition size is approximately 1.4 times the square root of the number of voters. When voters' preferences are allowed to differ, coalitions form only if voters are approximately politically balanced. We propose a dynamic view of coalitions, in which groups of voters choose of their own free will to form and disband coalitions, in a continuing struggle to maintain their voting power. This is potentially an endogenous mechanism for political instability, even in a world where individuals' (probabilistic) preferences are fixed and known.
Gelman, Andrew
Submitted: 2003-10-27
Keywords: coalitions, cooperation, decisive vote, elections, legislatures, prisoner's dilemma, voting power
Abstract: (click to show/hide) Individuals in a committee can increase their voting power by forming coalitions. This behavior is shown here to yield a prisoner's dilemma, in which a subset of voters can increase their power, while reducing average voting power for the electorate as a whole. This is an unusual form of the prisoner's dilemma in that cooperation is the selfish act that hurts the larger group. Under a simple model, the privately optimal coalition size is approximately 1.4 times the square root of the number of voters. When voters' preferences are allowed to differ, coalitions form only if voters are approximately politically balanced. We propose a dynamic view of coalitions, in which groups of voters choose of their own free will to form and disband coalitions, in a continuing struggle to maintain their voting power. This is potentially an endogenous mechanism for political instability, even in a world where individuals' (probabilistic) preferences are fixed and known.
Unanticipated Delays: A Unified Model of Position Timing and Position Content
Boehmke, Frederick
Submitted: 2003-12-09
Keywords: duration, discrete choice, seemingly unrelated, position taking, NAFTA
Abstract: (click to show/hide) On potentially contentious votes or when the margin of an upcoming vote is expected to be small, public position announcements by elected representatives may be strategically linked to position content and ultimately, to vote choice. Strategic position timing may occur when legislators announce early in order to sway others' vote choice; it may occur late when legislators stall in order to gain more information or are hoping that a close margin will make their vote valuable to participants willing to make side payments. Since intentions behind delay may often be unobserved or even unobservable, existing empirical analyses are unable to capture them. In this paper I argue that unobserved factors that influence position timing are related to unobserved factors influencing position content. To test this prediction, I develop a seemingly unrelated discrete-choice duration model that estimates the relationship between unobserved factors in the two processes. I then estimate this model using data on position timing and position content from the vote for the North American Free Trade Agreement. The results provide clear evidence that the two processes are linked and are consistent with my arguments about the sources of unanticipated delay.
Boehmke, Frederick
Submitted: 2003-12-09
Keywords: duration, discrete choice, seemingly unrelated, position taking, NAFTA
Abstract: (click to show/hide) On potentially contentious votes or when the margin of an upcoming vote is expected to be small, public position announcements by elected representatives may be strategically linked to position content and ultimately, to vote choice. Strategic position timing may occur when legislators announce early in order to sway others' vote choice; it may occur late when legislators stall in order to gain more information or are hoping that a close margin will make their vote valuable to participants willing to make side payments. Since intentions behind delay may often be unobserved or even unobservable, existing empirical analyses are unable to capture them. In this paper I argue that unobserved factors that influence position timing are related to unobserved factors influencing position content. To test this prediction, I develop a seemingly unrelated discrete-choice duration model that estimates the relationship between unobserved factors in the two processes. I then estimate this model using data on position timing and position content from the vote for the North American Free Trade Agreement. The results provide clear evidence that the two processes are linked and are consistent with my arguments about the sources of unanticipated delay.
