Some scholars build models to classify documents into chosen categories. Others, especially social scientists who tend to focus on population characteristics, instead usually estimate the proportion of documents in each category – using either parametric “classify-and-count” methods or “direct” nonparametric estimation of proportions without individual classification. Unfortunately, classify-and-count methods can be highly model dependent or generate more bias in the proportions even as the percent of documents correctly classified increases. Direct estimation avoids these problems, but can suffer when the meaning of language changes between training and test sets or is too similar across categories. We develop an improved direct estimation approach without these issues by including and optimizing continuous text features, along with a form of matching adapted from the causal inference literature. Our approach substantially improves performance in a diverse collection of 73 data sets. We also offer easy-to-use software software that implements all ideas discussed herein.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/AVNZR6.

Existing research on the extensive Chinese censorship organization uses observational methods with well-known limitations. We conducted the first large-scale experimental study of censorship by creating accounts on numerous social media sites, randomly submitting different texts, and observing from a worldwide network of computers which texts were censored and which were not. We also supplemented interviews with confidential sources by creating our own social media site, contracting with Chinese firms to install the same censoring technologies as existing sites, and—with their software, documentation, and even customer support—reverse-engineering how it all works. Our results offer rigorous support for the recent hypothesis that criticisms of the state, its leaders, and their policies are published, whereas posts about real-world events with collective action potential are censored.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/26212.

We offer the first large scale, multiple source analysis of the outcome of what may be the most extensive effort to selectively censor human expression ever implemented. To do this, we have devised a system to locate, download, and analyze the content of millions of social media posts originating from nearly 1,400 different social media services all over China before the Chinese government is able to find, evaluate, and censor (i.e., remove from the Internet) the large subset they deem objectionable. Using modern computer-assisted text analytic methods that we adapt to and validate in the Chinese language, we compare the substantive content of posts censored to those not censored over time in each of 85 topic areas. Contrary to previous understandings, posts with negative, even vitriolic, criticism of the state, its leaders, and its policies are not more likely to be censored. Instead, we show that the censorship program is aimed at curtailing collective action by silencing comments that represent, reinforce, or spur social mobilization, regardless of content. Censorship is oriented toward attempting to forestall collective activities that are occurring now or may occur in the future — and, as such, seem to clearly expose government intent.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN1/22691.

In response to the data-based measures of model dependence proposed in King and Zeng (2006), Sambanis and Michaelides (2008) propose alternative measures that rely upon assumptions untestable in observational data. If these assumptions are correct, then their measures are appropriate and ours, based solely on the empirical data, may be too conservative. If instead and as is usually the case, the researcher is not certain of the precise functional form of the data generating process, the distribution from which the data are drawn, and the applicability of these modeling assumptions to new counterfactuals, then the data-based measures proposed in King and Zeng (2006) are much preferred. After all, the point of model dependence checks is to verify empirically, rather than to stipulate by assumption, the effects of modeling assumptions on counterfactual inferences.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/VL7QMO.

Inferences about counterfactuals are essential for prediction, answering “what if” questions, and estimating causal effects. However, when the counterfactuals posed are too far from the data at hand, conclusions drawn from well-specified statistical analyses become based on speculation and convenient but indefensible model assumptions rather than empirical evidence. Unfortunately, standard statistical approaches assume the veracity of the model rather than revealing the degree of model-dependence, and so this problem can be hard to detect. We develop easy-to-apply methods to evaluate counterfactuals that do not require sensitivity testing over specified classes of models. If an analysis fails the tests we offer, then we know that substantive results are sensitive to at least some modeling choices that are not based on empirical evidence. We use these methods to evaluate the extensive scholarly literatures on the effects of changes in the degree of democracy in a country (on any dependent variable) and separate analyses of the effects of UN peacebuilding efforts. We find evidence that many scholars are inadvertently drawing conclusions based more on modeling hypotheses than on their data. For some research questions, history contains insufficient information to be our guide.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/EK886K.

Inferences about counterfactuals are essential for prediction, answering “what if” questions, and estimating causal effects. However, when the counterfactuals posed are too far from the data at hand, conclusions drawn from well-specified statistical analyses become based on speculation and convenient but indefensible model assumptions rather than empirical evidence. Unfortunately, standard statistical approaches assume the veracity of the model rather than revealing the degree of model-dependence, and so this problem can be hard to detect. We develop easy-to-apply methods to evaluate counterfactuals that do not require sensitivity testing over specified classes of models. If an analysis fails the tests we offer, then we know that substantive results are sensitive to at least some modeling choices that are not based on empirical evidence. We use these methods to evaluate the extensive scholarly literatures on the effects of changes in the degree of democracy in a country (on any dependent variable) and separate analyses of the effects of UN peacebuilding efforts. We find evidence that many scholars are inadvertently drawing conclusions based more on modeling hypotheses than on their data. For some research questions, history contains insufficient information to be our guide.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/O2NXPE.

We address the problem that occurs when inferences about counterfactuals – predictions, “what if” questions, and causal effects – are attempted far from the available data. The danger of these extreme counterfactuals is that substantive conclusions drawn from statistical models that fit the data well turn out to be based largely on speculation hidden in convenient modeling assumptions that few would be willing to defend. Yet existing statistical strategies provide few reliable means of identifying extreme counterfactuals. We offer a proof that inferences farther from the data are more model-dependent, and then develop easy-to-apply methods to evaluate how model-dependent our answers would be to specified counterfactuals. These methods require neither sensitivity testing over specified classes of models nor evaluating any specific modeling assumptions. If an analysis fails the simple tests we offer, then we know that substantive results are sensitive to at least some modeling choices that are not based on empirical evidence.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/MJ1YCL.

This talk summarizes a paper – Gary King and Richard Nielsen. 2015. “Why Propensity Scores Should Not Be Used for Matching” – with this abstract: Researchers use propensity score matching (PSM) as a data preprocessing step to selectively prune units prior to applying a model to estimate a causal effect. The goal of PSM is to reduce imbalance in the chosen pre-treatment covariates between the treated and control groups, thereby reducing the degree of model dependence and potential for bias. We show here that PSM often accomplishes the opposite of what is intended — increasing imbalance, inefficiency, model dependence, and bias. The weakness of PSM is that it attempts to approximate a completely randomized experiment, rather than, as with other matching methods, a more powerful fully blocked randomized experiment. PSM, unlike other matching methods, is thus blind to the often large portion of imbalance that could have been eliminated by approximating full blocking. Moreover, in data balanced enough to approximate complete randomization, either to begin with or after pruning some observations, PSM approximates random matching which turns out to increase imbalance. For other matching methods, the point where additional pruning increases imbalance occurs much later in the pruning process, when full blocking is approximated and there is no reason to prune, and so the danger is considerably less. We show that these problems with PSM occur even in data designed for PSM, with as few as two covariates, and in many real applications. Although these results suggest that researchers replace PSM with one of the other available methods when performing matching, propensity scores have many other productive uses.

See also related work.

We discuss a method for improving causal inferences called “Coarsened Exact Matching’’ (CEM), and the new “Monotonic Imbalance Bounding’’ (MIB) class of matching methods from which CEM is derived. We summarize what is known about CEM and MIB, derive and illustrate several new desirable statistical properties of CEM, and then propose a variety of useful extensions. We show that CEM possesses a wide range of desirable statistical properties not available in most other matching methods, but is at the same time exceptionally easy to comprehend and use. We focus on the connection between theoretical properties and practical applications. We also make available easy-to-use open source software for R and Stata which implement all our suggestions.

See also An Explanation of CEM Weights.

Matching is an increasingly popular method of causal inference in observational data, but following methodological best practices has proven difficult for applied researchers. We address this problem by providing a simple graphical approach for choosing among the numerous possible matching solutions generated by three methods: the venerable “Mahalanobis Distance Matching” (MDM), the commonly used “Propensity Score Matching” (PSM), and a newer approach called “Coarsened Exact Matching” (CEM). In the process of using our approach, we also discover that PSM often approximates random matching, both in many real applications and in data simulated by the processes that fit PSM theory. Moreover, contrary to conventional wisdom, random matching is not benign: it (and thus PSM) can often degrade inferences relative to not matching at all. We find that MDM and CEM do not have this problem, and in practice CEM usually outperforms the other two approaches. However, with our comparative graphical approach and easy-to-follow procedures, focus can be on choosing a matching solution for a particular application, which is what may improve inferences, rather than the particular method used to generate it.

Please see our follow up paper on this topic: Why Propensity Scores Should Not Be Used for Matching.

We introduce a new “Monotonic Imbalance Bounding” (MIB) class of matching methods for causal inference with a surprisingly large number of attractive statistical properties. MIB generalizes and extends in several new directions the only existing class, “Equal Percent Bias Reducing” (EPBR), which is designed to satisfy weaker properties and only in expectation. We also offer strategies to obtain specific members of the MIB class, and analyze in more detail a member of this class, called Coarsened Exact Matching, whose properties we analyze from this new perspective. We offer a variety of analytical results and numerical simulations that demonstrate how members of the MIB class can dramatically improve inferences relative to EPBR-based matching methods.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/OMHQFP.

Although published works rarely include causal estimates from more than a few model specifications, authors usually choose the presented estimates from numerous trial runs readers never see. Given the often large variation in estimates across choices of control variables, functional forms, and other modeling assumptions, how can researchers ensure that the few estimates presented are accurate or representative? How do readers know that publications are not merely demonstrations that it ispossibleto find a specification that fits the author’s favorite hypothesis? And how do we evaluate or even define statistical properties like unbiasedness or mean squared error when no unique model or estimator even exists? Matching methods, which offer the promise of causal inference with fewer assumptions, constitute one possible way forward, but crucial results in this fast-growing methodological literature are often grossly misinterpreted. We explain how to avoid these misinterpretations and propose a unified approach that makes it possible for researchers to preprocess data with matching (such as with the easy-to-use software we offer) and then to apply the best parametric techniques they would have used anyway. This procedure makes parametric models produce more accurate and considerably less model-dependent causal inferences. Winner of the Warren Miller Prizefor the best article published in Political Analysis. Also winner of the Fast Breaking Paper, for the article with the largest percentage increase in citations among those in the top 1% of total citations across the social sciences in the last two years by Thomson Reuters’ ScienceWatch, 2008.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/RWUY8G.

Designing Social Inquiry presents a unified approach to qualitative and quantitative research in political science, showing how the same logic of inference underlies both. This stimulating book discusses issues related to framing research questions, measuring the accuracy of data and the uncertainty of empirical inferences, discovering causal effects, and getting the most out of qualitative research. It addresses topics such as interpretation and inference, comparative case studies, constructing causal theories, dependent and explanatory variables, the limits of random selection, selection bias, and errors in measurement. The book only uses mathematical notation to clarify concepts, and assumes no prior knowledge of mathematics or statistics.

See the 2021 edition.

MatchingFrontier is an easy-to-use R Package for making optimal causal inferences from observational data. Despite their popularity, existing matching approaches leave researchers with two fundamental tensions. First, they are designed to maximize one metric (such as propensity score or Mahalanobis distance) but are judged against another for which they were not designed (such as L1 or differences in means). Second, they lack a principled solution to revealing the implicit bias-variance trade off: matching methods need to optimize with respect to both imbalance (between the treated and control groups) and the number of observations pruned, but existing approaches optimize with respect to only one; users then either ignore the other, or tweak it, usually suboptimally, by hand.

MatchingFrontier resolves both tensions by consolidating previous techniques into a single, optimal, and flexible approach. It calculates the matching solution with maximum balance for each possible sample size (N, N-1, N-2,…). It thus directly calculates the entire balance-sample size frontier, from which the user can easily choose one, several, or all subsamples from which to conduct their final analysis, given their own choice of imbalance metric and quantity of interest. MatchingFrontier solves the obvious joint optimization problem in one run, automatically, without manual tweaking, and without iteration. Although for each subset size k, there exist a huge (N choose k) number of unique subsets, MatchingFrontier includes specially designed fast algorithms that give the optimal answer, usually in a few minutes.

MatchingFrontier has officially been “Qualified for Scientific Use” by the U.S. Food and Drug Administration.

Does the U.S. Supreme Court curtail rights and liberties when the nation’s security is under threat? In hundreds of articles and books, and with renewed fervor since September 11, 2001, members of the legal community have warred over this question. Yet, not a single large-scale, quantitative study exists on the subject. Using the best data available on the causes and outcomes of every civil rights and liberties case decided by the Supreme Court over the past six decades and employing methods chosen and tuned especially for this problem, our analyses demonstrate that when crises threaten the nation’s security, the justices are substantially more likely to curtail rights and liberties than when peace prevails. Yet paradoxically, and in contradiction to virtually every theory of crisis jurisprudence, war appears to affect only cases that are unrelated to the war. For these cases, the effect of war and other international crises is so substantial, persistent, and consistent that it may surprise even those commentators who long have argued that the Court rallies around the flag in times of crisis. On the other hand, we find no evidence that cases most directly related to the war are affected. We attempt to explain this seemingly paradoxical evidence with one unifying conjecture: Instead of balancing rights and security in high stakes cases directly related to the war, the Justices retreat to ensuring the institutional checks of the democratic branches. Since rights-oriented and process-oriented dimensions seem to operate in different domains and at different times, and often suggest different outcomes, the predictive factors that work for cases unrelated to the war fail for cases related to the war. If this conjecture is correct, federal judges should consider giving less weight to legal principles outside of wartime but established during wartime, and attorneys should see it as their responsibility to distinguish cases along these lines. Winner of the McGraw-Hill Awardfor the best journal article on law and courts written by a political scientist and published during the previous calendar year; Law and Society Association Prize, Runner up, to “recognize exceptional scholarship in the field of sociolegal studies for an article published in the previous two years”;Pi Sigma Alpha Award, for the best paper delivered at the previous year’s MWPSA Conference; the Robert H. Durr Award, for “the best paper applying quantitative methods to a substantive problem” at the previous year’s MWPSA Conference; and the American Judicature Society Award, Honorable Mention, for the best paper presented at the previous year’s meetings of the American, Midwest, Northeastern, Southern, Southwest, or Western Political Science Associations.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/OLD7MB.

Binary, count and duration data all code discrete events occurring at points in time. Although a single data generation process can produce all of these three data types, the statistical literature is not very helpful in providing methods to estimate parameters of the same process from each. In fact, only single theoretical process exists for which know statistical methods can estimate the same parameters - and it is generally used only for count and duration data. The result is that seemingly trivial decisions abut which level of data to use can have important consequences for substantive interpretations. We describe the theoretical event process for which results exist, based on time independence. We also derive a set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of understanding and avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical models and theoretical processes that are not constrained by the particular forms of data that happen to be available. We discuss these issues and suggest an agenda for political methodologists interested in this very large class of aggregation problems.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/UDRSQ6.

The literature on cabinet duration is split between two apparently irreconcilable positions. The attributes theorists seek to explain cabinet duration as a fixed function of measured explanatory variables, while the events process theorists model cabinet durations as a product of purely stochastic processes. In this paper we build a unified statistical model that combines the insights of these previously distinct approaches. We also generalize this unified model, and all previous models, by including (1) a stochastic component that takes into account the censoring that occurs as a result of governments lasting to the vicinity of the maximum constitutional interelection period, (2) a systematic component that precludes the possibility of negative duration predictions, and (3) a much more objective and parsimonious list of explanatory variables, the explanatory power of which would not be improved by including a list of indicator variables for individual countries.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/CVJPAN.

This software is no longer being actively updated. Previous versions and information about the software are archived here.

A stand-alone, easy-to-use program for running event count and duration regression models, developed by and/or discussed in a series of journal articles by Gary King. (Event count models have a dependent variable measured as the number of times something happens, such as the number of uncontested seats per state or the number of wars per year. Duration models explain dependent variables measured as the time until some event, such as the number of months a parliamentary cabinet endures.) Winner of the APSA Research Software Award.

Ecological inference (EI) is the process of learning about individual behavior from aggregate data. We relax assumptions by allowing for “linear contextual effects,” which previous works have regarded as plausible but avoided due to non-identification, a problem we sidestep by deriving bounds instead of point estimates. In this way, we offer a conceptual framework to improve on the Duncan-Davis bound, derived more than sixty-five years ago. To study the effectiveness of our approach, we collect and analyze 8,430 2x2 EI datasets with known ground truth from several sources — thus bringing considerably more data to bear on the problem than the existing dozen or so datasets available in the literature for evaluating EI estimators. For the 88% of real data sets in our collection that fit a proposed rule, our approach reduces the width of the Duncan-Davis bound, on average, by about 44%, while still capturing the true district level parameter about 99% of the time. The remaining 12% revert to the Duncan-Davis bound.

Easy-to-use software is available that implements all the methods described in the paper.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/8TB7GO.

The enormous Nazi voting literature rarely builds on modern statistical or economic research. By adding these approaches, we find that the most widely accepted existing theories of this era cannot distinguish the Weimar elections from almost any others in any country. Via a retrospective voting account, we show that voters most hurt by the depression, and most likely to oppose the government, fall into separate groups with divergent interests. This explains why some turned to the Nazis and others turned away. The consequences of Hitler’s election were extraordinary, but the voting behavior that led to it was not.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/OMYW0P.

Binary, count and duration data all code discrete events occurring at points in time. Although a single data generation process can produce all of these three data types, the statistical literature is not very helpful in providing methods to estimate parameters of the same process from each. In fact, only single theoretical process exists for which know statistical methods can estimate the same parameters - and it is generally used only for count and duration data. The result is that seemingly trivial decisions abut which level of data to use can have important consequences for substantive interpretations. We describe the theoretical event process for which results exist, based on time independence. We also derive a set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of understanding and avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical models and theoretical processes that are not constrained by the particular forms of data that happen to be available. We discuss these issues and suggest an agenda for political methodologists interested in this very large class of aggregation problems.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/UDRSQ6.

The program EI provides a method of inferring individual behavior from aggregate data. It implements the statistical procedures, diagnostics, and graphics from the book A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data (King 1997).

Ecological inference, as traditionally defined, is the process of using aggregate (i.e., “ecological”) data to infer discrete individual-level relationships of interest when individual-level data are not available. Ecological inferences are required in political science research when individual-level surveys are unavailable (e.g., local or comparative electoral politics), unreliable (racial politics), insufficient (political geography), or infeasible (political history). They are also required in numerous areas of major significance in public policy (e.g., for applying the Voting Rights Act) and other academic disciplines ranging from epidemiology and marketing to sociology and quantitative history.

Survey researchers have long sought to protect the privacy of their respondents via de-identification (removing names and other directly identifying information) before sharing data. Although these procedures can help, recent research demonstrates that they fail to protect respondents from intentional re-identification attacks, a problem that threatens to undermine vast survey enterprises in academia, government, and industry. This is especially a problem in political science because political beliefs are not merely the subject of our scholarship; they represent some of the most important information respondents want to keep private. We confirm the problem in practice by re-identifying individuals from a survey about a controversial referendum declaring life beginning at conception. We build on the concept of “differential privacy” to offer new data sharing procedures with mathematical guarantees for protecting respondent privacy and statistical validity guarantees for social scientists analyzing differentially private data. The cost of these new procedures is larger standard errors, which can be overcome with somewhat larger sample sizes.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/X4Y2FL.

We offer methods to analyze the “differentially private” Facebook URLs Dataset which, at over 40 trillion cell values, is one of the largest social science research datasets ever constructed. The version of differential privacy used in the URLs dataset has specially calibrated random noise added, which provides mathematical guarantees for the privacy of individual research subjects while still making it possible to learn about aggregate patterns of interest to social scientists. Unfortunately, random noise creates measurement error which induces statistical bias – including attenuation, exaggeration, switched signs, or incorrect uncertainty estimates. We adapt methods developed to correct for naturally occurring measurement error, with special attention to computational efficiency for large datasets. The result is statistically valid linear regression estimates and descriptive statistics that can be interpreted as ordinary analyses of non-confidential data but with appropriately larger standard errors.

We have implemented these methods in open source software for R called PrivacyUnbiased. Facebook has ported PrivacyUnbiased to open source Python code called svinfer. We have extended these results in Evans and King (2021).

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/UDFZJD.

Venerable procedures used for privacy protection in sharing data within individual companies and governments, within academia, and between sectors have recently been proven massively inadequate (e.g., respondents in de-identified surveys can usually be re-identified). Furthermore, the benefits of getting our data sharing act together go far beyond the university, since unprecedented quantities of data that could help social scientists understand and ameliorate the challenges of human society are presently locked away inside companies, governments, and other organizations, in part because of worries about privacy violations. We address these problems with a general-purpose data access and analysis system with mathematical guarantees of privacy for individuals who may be represented in the data, statistical guarantees for researchers seeking insights from it, and protection for society from some fallacious scientific conclusions. We build on the standard of “differential privacy’’ but, unlike most such approaches, we also correct for the serious statistical biases induced by privacy-preserving procedures, provide a proper accounting for statistical uncertainty, and impose minimal constraints on the choice of data analytic methods and types of quantities estimated. Our algorithm is easy to implement, simple to use, and computationally efficient; we also offer open source software to illustrate all our methods.

Based on papers (each joint with subsets of Georgie Evans, Meg Schwenzfeier, Adam Smith, and Abhradeep Thakurta) available at GaryKing.org/privacy.

Conjoint survey designs are spreading across the social sciences due to their unusual capacity to estimate many causal effects from a single randomized experiment. Unfortunately, by their ability to mirror complicated real-world choices, these designs often generate substantial measurement error and thus bias. We first present a simplified statistical framework for conjoint designs that also enables researchers to study a wider array of substantive questions. We then replicate both the data collection and analysis from eight prominent conjoint studies, all of which closely reproduce published results, and show that a large amount of observed variation in answers to conjoint questions is effectively random noise. We then discover a common empirical pattern in how measurement error appears in conjoint studies and, with it, we introduce an easy-to-use statistical method to correct the bias.

Based on joint work available at GaryKing.org/conjointE by Katherine Clayton, Yusaku Horiuchi, Gary King, Aaron Kaufman, and Mayya Komisarchik.

Venerable procedures used for privacy protection in sharing data within individual companies and governments, within academia, and between sectors have recently been proven massively inadequate (e.g., respondents in de-identified surveys can usually be re-identified). Furthermore, the benefits of getting our data sharing act together go far beyond the university, since unprecedented quantities of data that could help social scientists understand and ameliorate the challenges of human society are presently locked away inside companies, governments, and other organizations, in part because of worries about privacy violations. We address these problems with a general-purpose data access and analysis system with mathematical guarantees of privacy for individuals who may be represented in the data, statistical guarantees for researchers seeking insights from it, and protection for society from some fallacious scientific conclusions. We build on the standard of “differential privacy’’ but, unlike most such approaches, we also correct for the serious statistical biases induced by privacy-preserving procedures, provide a proper accounting for statistical uncertainty, and impose minimal constraints on the choice of data analytic methods and types of quantities estimated. Our algorithm is easy to implement, simple to use, and computationally efficient; we also offer open source software to illustrate all our methods.

Based on papers (each joint with subsets of Georgie Evans, Meg Schwenzfeier, Adam Smith, and Abhradeep Thakurta) available at GaryKing.org/privacy.

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model specifications and estimation procedures, and analyses to assess the approach’s robustness to correlated measurement errors and to errors in categorical variables. These results support using the technique to reduce bias and increase efficiency in a wide variety of empirical research.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/29610.

Although social scientists devote considerable effort to mitigating measurement error during data collection, they often ignore the issue during data analysis. And although many statistical methods have been proposed for reducing measurement error-induced biases, few have been widely used because of implausible assumptions, high levels of model dependence, difficult computation, or inapplicability with multiple mismeasured variables. We develop an easy-to-use alternative without these problems; it generalizes the popular multiple imputation (MI) framework by treating missing data problems as a limiting special case of extreme measurement error, and corrects for both. Like MI, the proposed framework is a simple two-step procedure, so that in the second step researchers can use whatever statistical method they would have if there had been no problem in the first place. We also offer empirical illustrations, open source software that implements all the methods described herein, and a companion paper with technical details and extensions (Blackwell, Honaker, and King, 2017b).

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/29606.

Applications of modern methods for analyzing data with missing values, based primarily on multiple imputation, have in the last half-decade become common in American politics and political behavior. Scholars in these fields have thus increasingly avoided the biases and inefficiencies caused by ad hoc methods like listwise deletion and best guess imputation. However, researchers in much of comparative politics and international relations, and others with similar data, have been unable to do the same because the best available imputation methods work poorly with the time-series cross-section data structures common in these fields. We attempt to rectify this situation. First, we build a multiple imputation model that allows smooth time trends, shifts across cross-sectional units, and correlations over time and space, resulting in far more accurate imputations. Second, we build nonignorable missingness models by enabling analysts to incorporate knowledge from area studies experts via priors on individual missing cell values, rather than on difficult-to-interpret model parameters. Third, since these tasks could not be accomplished within existing imputation algorithms, in that they cannot handle as many variables as needed even in the simpler cross-sectional data for which they were designed, we also develop a new algorithm that substantially expands the range of computationally feasible data types and sizes for which multiple imputation can be used. These developments also made it possible to implement the methods introduced here in freely available open source software that is considerably more reliable than existing strategies.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/GGUR0P.

Katz and King (1999) develop a model for predicting or explaining aggregate electoral results in multiparty democracies. This model is, in principle, analogous to what least squares regression provides American politics researchers in that two-party system. Katz and King applied this model to three-party elections in England and revealed a variety of new features of incumbency advantage and where each party pulls support from. Although the mathematics of their statistical model covers any number of political parties, it is computationally very demanding, and hence slow and numerically imprecise, with more than three. The original goal of our work was to produce an approximate method that works quicker in practice with many parties without making too many theoretical compromises. As it turns out, the method we offer here improves on Katz and King’s (in bias, variance, numerical stability, and computational speed) even when the latter is computationally feasible. We also offer easy-to-use software that implements our suggestions.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/F06OSQ.

We propose a comprehensive statistical model for analyzing multiparty, district-level elections. This model, which provides a tool for comparative politics research analagous to that which regression analysis provides in the American two-party context, can be used to explain or predict how geographic distributions of electoral results depend upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or aggregate areas. We also provide new graphical representations for data exploration, model evaluation, and substantive interpretation. We illustrate the use of this model by attempting to resolve a controversy over the size of and trend in electoral advantage of incumbency in Britain. Contrary to previous analyses, all based on measures now known to be biased, we demonstrate that the advantage is small but meaningful, varies substantially across the parties, and is not growing. Finally, we show how to estimate the party from which each party’s advantage is predominantly drawn. Winner of the Pi Sigma Alpha Awardfor the best paper at the previous year’s meetings of the Midwest Political Science Association, 1998.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/NDS9AT.

Amelia II is a complete R package for multiple imputation of missing data. The package implements a new expectation-maximization with bootstrapping algorithm that works faster, with larger numbers of variables, and is far easier to use, than various Markov chain Monte Carlo approaches, but gives essentially the same answers. The program also improves imputation models by allowing researchers to put Bayesian priors on individual cell values, thereby including a great deal of potentially valuable and extensive information. It also includes features to accurately impute cross-sectional datasets, individual time series, or sets of time series for different cross-sections. A full set of graphical diagnostics are also available. The program is easy to use, and the simplicity of the algorithm makes it far more robust; both a simple command line and extensive graphical user interface are included.

Amelia II software web site

Amelia II is a complete R package for multiple imputation of missing data. The package implements a new expectation-maximization with bootstrapping algorithm that works faster, with larger numbers of variables, and is far easier to use, than various Markov chain Monte Carlo approaches, but gives essentially the same answers. The program also improves imputation models by allowing researchers to put Bayesian priors on individual cell values, thereby including a great deal of potentially valuable and extensive information. It also includes features to accurately impute cross-sectional datasets, individual time series, or sets of time series for different cross-sections. A full set of graphical diagnostics are also available. The program is easy to use, and the simplicity of the algorithm makes it far more robust; both a simple command line and extensive graphical user interface are included.

Amelia II software web site

“The classic work on qualitative methods in political science”

Designing Social Inquiry presents a unified approach to qualitative and quantitative research in political science, showing how the same logic of inference underlies both. This stimulating book discusses issues related to framing research questions, measuring the accuracy of data and the uncertainty of empirical inferences, discovering causal effects, and getting the most out of qualitative research. It addresses topics such as interpretation and inference, comparative case studies, constructing causal theories, dependent and explanatory variables, the limits of random selection, selection bias, and errors in measurement. The book only uses mathematical notation to clarify concepts, and assumes no prior knowledge of mathematics or statistics.

Featuring a new preface by Robert O. Keohane and Gary King, this edition makes an influential work available to new generations of qualitative researchers in the social sciences.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/YHZG5M.

Designing Social Inquiry presents a unified approach to qualitative and quantitative research in political science, showing how the same logic of inference underlies both. This stimulating book discusses issues related to framing research questions, measuring the accuracy of data and the uncertainty of empirical inferences, discovering causal effects, and getting the most out of qualitative research. It addresses topics such as interpretation and inference, comparative case studies, constructing causal theories, dependent and explanatory variables, the limits of random selection, selection bias, and errors in measurement. The book only uses mathematical notation to clarify concepts, and assumes no prior knowledge of mathematics or statistics.

See the 2021 edition.

Some of the most important phenomena in international conflict are coded as “rare events data,” binary dependent variables with dozens to thousands of times fewer events, such as wars, coups, etc., than “nonevents”. Unfortunately, rare events data are difficult to explain and predict, a problem that seems to have at least two sources. First, and most importantly, the data collection strategies used in international conflict are grossly inefficient. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all available events (e.g., wars) and a tiny fraction of non-events (peace). This enables scholars to save as much as 99% of their (non-fixed) data collection costs, or to collect much more meaningful explanatory variables. Second, logistic regression, and other commonly used statistical procedures, can underestimate the probability of rare events. We introduce some corrections that outperform existing methods and change the estimates of absolute and relative risks by as much as some estimated effects reported in the literature. We also provide easy-to-use methods and software that link these two results, enabling both types of corrections to work simultaneously.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/RNSU7V.

We study rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, such as wars, vetoes, cases of political activism, or epidemiological infections) than zeros (“nonevents”). In many literatures, these variables have proven difficult to explain and predict, a problem that seems to have at least two sources. First, popular statistical procedures, such as logistic regression, can sharply underestimate the probability of rare events. We recommend corrections that outperform existing methods and change the estimates of absolute and relative risks by as much as some estimated effects reported in the literature. Second, commonly used data collection strategies are grossly inefficient for rare events data. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables, such as in international conflict data with more than a quarter-million dyads, only a few of which are at war. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all variable events (e.g., wars) and a tiny fraction of nonevents (peace). This enables scholars to save as much as 99% of their (nonfixed) data collection costs or to collect much more meaningful explanatory variables. We provide methods that link these two results, enabling both types of corrections to work simultaneously, and software that implements the methods developed.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/SPAFJK.

We offer the first independent scholarly evaluation of the claims, forecasts, and causal inferences of the State Failure Task Force and their efforts to forecast when states will fail. State failure refers to the collapse of the authority of the central government to impose order, as in civil wars, revolutionary wars, genocides, politicides, and adverse or disruptive regime transitions. This task force, set up at the behest of Vice President Gore in 1994, has been led by a group of distinguished academics working as consultants to the U.S. Central Intelligence Agency. State Failure Task Force reports and publications have received attention in the media, in academia, and from public policy decision-makers. In this article, we identify several methodological errors in the task force work that cause their reported forecast probabilities of conflict to be too large, their causal inferences to be biased in unpredictable directions, and their claims of forecasting performance to be exaggerated. However, we also find that the task force has amassed the best and most carefully collected data on state failure in existence, and the required corrections which we provide, although very large in effect, are easy to implement. We also reanalyze their data with better statistical procedures and demonstrate how to improve forecasting performance to levels significantly greater than even corrected versions of their models. Although still a highly uncertain endeavor, we are as a consequence able to offer the first accurate forecasts of state failure, along with procedures and results that may be of practical use in informing foreign policy decision making. We also describe a number of strong empirical regularities that may help in ascertaining the causes of state failure.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/BS4236.

Binary, count and duration data all code discrete events occurring at points in time. Although a single data generation process can produce all of these three data types, the statistical literature is not very helpful in providing methods to estimate parameters of the same process from each. In fact, only single theoretical process exists for which know statistical methods can estimate the same parameters - and it is generally used only for count and duration data. The result is that seemingly trivial decisions abut which level of data to use can have important consequences for substantive interpretations. We describe the theoretical event process for which results exist, based on time independence. We also derive a set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of understanding and avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical models and theoretical processes that are not constrained by the particular forms of data that happen to be available. We discuss these issues and suggest an agenda for political methodologists interested in this very large class of aggregation problems.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/UDRSQ6.

Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that your vote will be decisive in a U.S. presidential election, a problem that has been studied by political scientists for more than two decades. The exact value of this probability is of only minor interest, but the number has important implications for understanding the optimal allocation of campaign resources, whether states and voter groups receive their fair share of attention from prospective presidents, and how formal “rational choice” models of voter behavior might be able to explain why people vote at all. We show how the probability of a decisive vote can be estimated empirically from state-level forecasts of the presidential election and illustrate with the example of 1992. Based on generalizations of standard political science forecasting models, we estimate the (prospective) probability of a single vote being decisive as about 1 in 10 million for close national elections such as 1992, varying by about a factor of 10 among states. Our results support the argument that subjective probabilities of many types are best obtained through empirically based statistical prediction models rather than solely through mathematical reasoning. We discuss the implications of our findings for the types of decision analyses used in public choice studies.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/0FT6ZL.

“Robust standard errors” are used in a vast array of scholarship to correct standard errors for model misspecification. However, when misspecification is bad enough to make classical and robust standard errors diverge, assuming that it is nevertheless not so bad as to bias everything else requires considerable optimism. And even if the optimism is warranted, settling for a misspecified model, with or without robust standard errors, will still bias estimators of all but a few quantities of interest. The resulting cavernous gap between theory and practice suggests that considerable gains in applied statistics may be possible. We seek to help researchers realize these gains via a more productive way to understand and use robust standard errors; a new general and easier-to-use “generalized information matrix test” statistic that can formally assess misspecification (based on differences between robust and classical variance estimates); and practical illustrations via simulations and real examples from published research. How robust standard errors are used needs to change, but instead of jettisoning this popular tool we show how to use it to provide effective clues about model misspecification, likely biases, and a guide to considerably more reliable, and defensible, inferences. Accompanying this article is open source software that implements the methods we describe.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/26935.

Last year was difficult for Google Flu Trends (GFT). In early 2013, Nature reported that GFT was estimating more than double the percentage of doctor visits for influenza like illness than the Centers for Disease Control and Prevention s (CDC) sentinel reports during the 2012 2013 flu season (1). Given that GFT was designed to forecast upcoming CDC reports, this was a problematic finding. In March 2014, our report in Science found that the overestimation problem in GFT was also present in the 2011 2012 flu season (2). The report also found strong evidence of autocorrelation and seasonality in the GFT errors, and presented evidence that the issues were likely, at least in part, due to modifications made by Google s search algorithm and the decision by GFT engineers not to use previous CDC reports or seasonality estimates in their models what the article labeled algorithm dynamics and big data hubris respectively. Moreover, the report and the supporting online materials detailed how difficult/impossible it is to replicate the GFT results, undermining independent efforts to explore the source of GFT errors and formulate improvements.

See our original paper, “The Parable of Google Flu: Traps in Big Data Analysis”

Large errors in flu prediction were largely avoidable, which offers lessons for the use of big data.

In February 2013, Google Flu Trends (GFT) made headlines but not for a reason that Google executives or the creators of the flu tracking system would have hoped. Nature reported that GFT was predicting more than double the proportion of doctor visits for influenza-like illness (ILI) than the Centers for Disease Control and Prevention (CDC), which bases its estimates on surveillance reports from laboratories across the United States ( 1, 2). This happened despite the fact that GFT was built to predict CDC reports. Given that GFT is often held up as an exemplary use of big data ( 3, 4), what lessons can we draw from this error?

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/24823.

See also “Google Flu Trends Still Appears Sick: An Evaluation of the 2013‐2014 Flu Season”.

WE THANK BRONIATOWSKI, Paul, and Dredze for giving us the opportunity to reemphasize the potential of big data and make the more obvious point that not all big data projects have the problems currently plaguing Google Flu Trends (GFT), nor are these problems inherent to the field in general.

See our original papers: “The Parable of Google Flu: Traps in Big Data Analysis,” and “Google Flu Trends Still Appears Sick: An Evaluation of the 2013‐2014 Flu Season”

Social Scientists rarely take full advantage of the information available in their statistical results. As a consequence, they miss opportunities to present quantities that are of greatest substantive interest for their research and express the appropriate degree of certainty about these quantities. In this article, we offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a reader-friendly manner. Using this technique requires some expertise, which we try to provide herein, but its application should make the results of quantitative articles more informative and transparent. To illustrate our recommendations, we replicate the results of several published works, showing in each case how the authors’ own conclusions can be expressed more sharply and informatively, and, without changing any data or statistical assumptions, how our approach reveals important new information about the research questions at hand. We also offer very easy-to-use Clarify software that implements our suggestions.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/BDWIC3.

Political scientists forecast elections, not primarily to satisfy public interest, but to validate statistical models used for estimating many quantities of scholarly interest. Although scholars have learned a great deal from these models, they can be embarrassingly overconfident: Events that should occur once in 10,000 elections occur almost every year, and even those that should occur once in a trillion-trillion elections are sometimes observed. We develop a novel generative statistical model of US congressional elections 1954-2020 and validate it with extensive out-of-sample tests. The generatively accurate descriptive summaries provided by this model demonstrate that the 1950s was as partisan and differentiated as the current period, but with parties not based on ideological differences as they are today. The model also shows that even though the size of the incumbency advantage has varied tremendously over time, the risk of an in-party incumbent losing a midterm election contest has been high and essentially constant over at least the last two thirds of a century.

Please see “How American Politics Ensures Electoral Accountability in Congress,” which supersedes this paper.

A recent article by the Open Science Collaboration (a group of 270 coauthors) gained considerable academic and public attention due to its sensational conclusion that the replicability of psychological science is surprisingly low. *Science *magazine lauded this article as one of the top 10 scientific breakthroughs of the year across all fields of science, reports of which appeared on the front pages of newspapers worldwide. We show that OSC’s article contains three major statistical errors and, when corrected, provides no evidence of a replication crisis. Indeed, the evidence is consistent with the opposite conclusion – that the reproducibility of psychological science is quite high and, in fact, statistically indistinguishable from 100%. (Of course, that doesn’t mean that the replicability is 100%, only that the evidence is insufficient to reliably estimate replicability.) The moral of the story is that meta-science must follow the rules of science.

Replication data is available in this dataverse archive. See also the full web site for this article and related materials, and one of the news articles written about it.

What should a researcher do when statistical analysis software terminates before completion with a message that the Hessian is not invertable? The standard textbook advice is to respecify the model, but this is another way of saying that the researcher should change the question being asked. Obviously, however, computer programs should not be in the business of deciding what questions are worthy of study. Although noninvertable Hessians are sometimes signals of poorly posed questions, nonsensical models, or inappropriate estimators, they also frequently occur when information about the quantities of interest exists in the data, through the likelihood function. We explain the problem in some detail and lay out two preliminary proposals for ways of dealing with noninvertable Hessians without changing the question asked.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/0LRZN6.

“Politimetrics” (Gurr 1972), “polimetrics” (Alker 1975), “politometrics” (Hilton 1976), “political arithmetic” (Petty [1672] 1971), “quantitative Political Science (QPS),” “governmetrics,” “posopolitics” (Papayanopoulos 1973), “political science statistics (Rai and Blydenburgh 1973), “political statistics” (Rice 1926). These are some of the names that scholars have used to describe the field we now call “political methodology.” The history of political methodology has been quite fragmented until recently, as reflected by this patchwork of names. The field has begun to coalesce during the past decade and we are developing persistent organizations, a growing body of scholarly literature, and an emerging consensus about important problems that need to be solved. I make one main point in this article: If political methodology is to play an important role in the future of political science, scholars will need to find ways of representing more interesting political contexts in quantitative analyses. This does not mean that scholars should just build more and more complicated statistical models. Instead, we need to represent more of the essence of political phenomena in our models. The advantage of formal and quantitative approaches is that they are abstract representations of the political world and are, thus, much clearer. We need methods that enable us to abstract the right parts of the phenomenon we are studying and exclude everything superfluous. Despite the fragmented history of quantitative political analysis, a version of this goal has been voiced frequently by both quantitative researchers and their critics (Sec. 2). However, while recognizing this shortcoming, earlier scholars were not in the position to rectify it, lacking the mathematical and statistical tools and, early on, the data. Since political methodologists have made great progress in these and other areas in recent years, I argue that we are now capable of realizing this goal. In section 3, I suggest specific approaches to this problem. Finally, in section 4, I provide two modern examples, ecological inference and models of spatial autocorrelation, to illustrate these points.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/TTW7YI.

The financial stability of four of the five largest U.S. federal entitlement programs, strategic decision making in several industries, and many academic publications all depend on the accuracy of demographic and financial forecasts made by the Social Security Administration (SSA). Although the SSA has performed these forecasts since 1942, no systematic and comprehensive evaluation of their accuracy has ever been published by SSA or anyone else. The absence of a systematic evaluation of forecasts is a concern because the SSA relies on informal procedures that are potentially subject to inadvertent biases and does not share with the public, the scientific community, or other parts of SSA sufficient data or information necessary to replicate or improve its forecasts. These issues result in SSA holding a monopoly position in policy debates as the sole supplier of fully independent forecasts and evaluations of proposals to change Social Security. To assist with the forecasting evaluation problem, we collect all SSA forecasts for years that have passed and discover error patterns that could have been—and could now be—used to improve future forecasts. Specifically, we find that after 2000, SSA forecasting errors grew considerably larger and most of these errors made the Social Security Trust Funds look more financially secure than they actually were. In addition, SSA’s reported uncertainty intervals are overconfident and increasingly so after 2000. We discuss the implications of these systematic forecasting biases for public policy.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/28122.

The financial viability of Social Security, the single largest U.S. Government program, depends on accurate forecasts of the solvency of its intergenerational trust fund. We begin by detailing information necessary for replicating the Social Security Administration’s (SSA’s) forecasting procedures, which until now has been unavailable in the public domain. We then offer a way to improve the quality of these procedures due to age-and sex-specific mortality forecasts. The most recent SSA mortality forecasts were based on the best available technology at the time, which was a combination of linear extrapolation and qualitative judgments. Unfortunately, linear extrapolation excludes known risk factors and is inconsistent with long-standing demographic patterns such as the smoothness of age profiles. Modern statistical methods typically outperform even the best qualitative judgments in these contexts. We show how to use such methods here, enabling researchers to forecast using far more information, such as the known risk factors of smoking and obesity and known demographic patterns. Including this extra information makes a sub¬stantial difference: For example, by only improving mortality forecasting methods, we predict three fewer years of net surplus, $730 billion less in Social Security trust funds, and program costs that are 0.66% greater of projected taxable payroll compared to SSA projections by 2031. More important than specific numerical estimates are the advantages of transparency, replicability, reduction of uncertainty, and what may be the resulting lower vulnerability to the politicization of program forecasts. In addition, by offering with this paper software and detailed replication information, we hope to marshal the efforts of the research community to include ever more informative inputs and to continue to reduce the uncertainties in Social Security forecasts.

This work builds on our article that provides forecasts of US Mortality rates (see King and Soneji, The Future of Death in America), a book developing improved methods for forecasting mortality (Girosi and King, Demographic Forecasting), all data we used (King and Soneji, replication data sets), and open source software that implements the methods (Girosi and King, YourCast). Also available is a New York Times Op-Ed based on this work (King and Soneji, Social Security: It’s Worse Than You Think), and a replication data set for the Op-Ed (King and Soneji, replication data set).

Population mortality forecasts are widely used for allocating public health expenditures, setting research priorities, and evaluating the viability of public pensions, private pensions, and health care financing systems. In part because existing methods seem to forecast worse when based on more information, most forecasts are still based on simple linear extrapolations that ignore known biological risk factors and other prior information. We adapt a Bayesian hierarchical forecasting model capable of including more known health and demographic information than has previously been possible. This leads to the first age- and sex-specific forecasts of American mortality that simultaneously incorporate, in a formal statistical model, the effects of the recent rapid increase in obesity, the steady decline in tobacco consumption, and the well known patterns of smooth mortality age profiles and time trends. Formally including new information in forecasts can matter a great deal. For example, we estimate an increase in male life expectancy at birth from 76.2 years in 2010 to 79.9 years in 2030, which is 1.8 years greater than the U.S. Social Security Administration projection and 1.5 years more than U.S. Census projection. For females, we estimate more modest gains in life expectancy at birth over the next twenty years from 80.5 years to 81.9 years, which is virtually identical to the Social Security Administration projection and 2.0 years less than U.S. Census projections. We show that these patterns are also likely to greatly affect the aging American population structure. We offer an easy-to-use approach so that researchers can include other sources of information and potentially improve on our forecasts too.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/IEANXM.

Katz and King (1999) develop a model for predicting or explaining aggregate electoral results in multiparty democracies. This model is, in principle, analogous to what least squares regression provides American politics researchers in that two-party system. Katz and King applied this model to three-party elections in England and revealed a variety of new features of incumbency advantage and where each party pulls support from. Although the mathematics of their statistical model covers any number of political parties, it is computationally very demanding, and hence slow and numerically imprecise, with more than three. The original goal of our work was to produce an approximate method that works quicker in practice with many parties without making too many theoretical compromises. As it turns out, the method we offer here improves on Katz and King’s (in bias, variance, numerical stability, and computational speed) even when the latter is computationally feasible. We also offer easy-to-use software that implements our suggestions.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/F06OSQ.

We propose a comprehensive statistical model for analyzing multiparty, district-level elections. This model, which provides a tool for comparative politics research analagous to that which regression analysis provides in the American two-party context, can be used to explain or predict how geographic distributions of electoral results depend upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or aggregate areas. We also provide new graphical representations for data exploration, model evaluation, and substantive interpretation. We illustrate the use of this model by attempting to resolve a controversy over the size of and trend in electoral advantage of incumbency in Britain. Contrary to previous analyses, all based on measures now known to be biased, we demonstrate that the advantage is small but meaningful, varies substantially across the parties, and is not growing. Finally, we show how to estimate the party from which each party’s advantage is predominantly drawn. Winner of the Pi Sigma Alpha Awardfor the best paper at the previous year’s meetings of the Midwest Political Science Association, 1998.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/NDS9AT.

An essential component of democracy is the ability to hold legislators accountable via the threat of electoral defeat, a concept that has rarely been quantified directly. Well known massive changes over time in indirect measures — such as incumbency advantage, electoral margins, partisan bias, partisan advantage, split ticket voting, and others — all seem to imply wide swings in electoral accountability. In contrast, we show that the (precisely calibrated) probability of defeating incumbent US House members has been surprisingly constant and remarkably high for two-thirds of a century. We resolve this paradox with a generative statistical model, validated with extensive out-of-sample tests, that uses the full vote distribution to avoid biases induced by the common practice of studying only central tendencies. We show that different states of the partisan battlefield lead in interestingly different ways to the same high probability of incumbent defeat. Many challenges to American democracy remain, but this core feature remains durable.

Based on joint work with Danny Ebanks and Jonathan N. Katz. For more information, see GaryKing.org.

This Note addresses the long-standing discrepancy between scholarly support for the effect of constituency service on incumbency advantage and a large body of contradictory empirical evidence. I show first that many of the methodological problems noticed in past research reduce to a single methodological problem that is readily resolved. The core of this Note then provides among the first systematic empirical evidence for the constituency service hypothesis. Specifically, an extra $10,000 added to the budget of the average state legislator gives this incumbent an additional 1.54 percentage points in the next election (with a 95% confidence interval of 1.14 to 1.94 percentage points).

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/NKCJK6.

In this report, I evaluate evidence described and conclusions drawn in several Exhibits in this case offered by the Plaintiffs. I conclude that the evidence is insufficient to support conclusions about election fraud. Throughout, the authors break the chain of evidence repeatedly – from the 2020 election, to the data analyzed, to the quantitative results presented, to the conclusions drawn – and as such cannot be relied on. In addition, the Exhibits make many crucial assumptions without justification, discussion, or even recognition – each of which can lead to substantial bias, and which was unrecognized and uncorrected. The data analytic and statistical procedures used in the Exhibits for data providence, data analysis, replication information, and statistical analysis all violate professional standards and should be disregarded. [Thanks to Soubhik Barari for research assistance.]

Update: Findings and conclusions of the expert witness report were confirmed in the Court’s ruling in this case: “Not only have Plaintiffs failed to provide the Court with factual support for their extraordinary claims, but they have wholly failed to establish that they have standing for the Court to consider them. Allegations that find favor in the public sphere of gossip and innuendo cannot be a substitute for earnest pleadings and procedure in federal court. They most certainly cannot be the basis for upending Arizona’s 2020 General Election. The Court is left with no alternative but to dismiss this matter in its entirety.”

We demonstrate that exposure to the news media causes Americans to take public stands on specific issues, join national policy conversations, and express themselves publicly—all key components of democratic politics—more often than they would otherwise. After recruiting 48 mostly small media outlets, we chose groups of these outlets to write and publish articles on subjects we approved, on dates we randomly assigned. We estimated the causal effect on proximal measures, such as website pageviews and Twitter discussion of the articles’ specific subjects, and distal ones, such as national Twitter conversation in broad policy areas. Our intervention increased discussion in each broad policy area by approximately 62.7% (relative to a day’s volume), accounting for 13,166 additional posts over the treatment week, with similar effects across population subgroups.

On the Science website: Abstract, Reprint, Full text, and a comment (by Matthew Gentzkow) “Small media, big impact”.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/1EMHTK.

This paper describes, explains, and predicts the practice of party switching among members of the U.S. House of Representatives.

The data for this study is available in my dataverse.

The enormous Nazi voting literature rarely builds on modern statistical or economic research. By adding these approaches, we find that the most widely accepted existing theories of this era cannot distinguish the Weimar elections from almost any others in any country. Via a retrospective voting account, we show that voters most hurt by the depression, and most likely to oppose the government, fall into separate groups with divergent interests. This explains why some turned to the Nazis and others turned away. The consequences of Hitler’s election were extraordinary, but the voting behavior that led to it was not.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/OMYW0P.

The directional and proximity models offer dramatically different theories for how voters make decisions and fundamentally divergent views of the supposed microfoundations on which vast bodies of literature in theoretical rational choice and empirical political behavior have been built. We demonstrate here that the empirical tests in the large and growing body of literature on this subject amount to theoretical debates about which statistical assumption is right. The key statistical assumptions have not been empirically tested and, indeed, turn out to be effectively untestable with exiting methods and data. Unfortunately, these assumptions are also crucial since changing them leads to different conclusions about voter processes.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/TS0UJQ.

Researchers sometimes argue that statisticians have little to contribute when few realizations of the process being estimated are observed. We show that this argument is incorrect even in the extreme situation of estimating the probabilities of events so rare that they have never occurred. We show how statistical forecasting models allow us to use empirical data to improve inferences about the probabilities of these events. Our application is estimating the probability that your vote will be decisive in a U.S. presidential election, a problem that has been studied by political scientists for more than two decades. The exact value of this probability is of only minor interest, but the number has important implications for understanding the optimal allocation of campaign resources, whether states and voter groups receive their fair share of attention from prospective presidents, and how formal “rational choice” models of voter behavior might be able to explain why people vote at all. We show how the probability of a decisive vote can be estimated empirically from state-level forecasts of the presidential election and illustrate with the example of 1992. Based on generalizations of standard political science forecasting models, we estimate the (prospective) probability of a single vote being decisive as about 1 in 10 million for close national elections such as 1992, varying by about a factor of 10 among states. Our results support the argument that subjective probabilities of many types are best obtained through empirically based statistical prediction models rather than solely through mathematical reasoning. We discuss the implications of our findings for the types of decision analyses used in public choice studies.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/0FT6ZL.

In their 1990 Review article, Ian Budge and Richard Hofferbert analyzed the relationship between party platform emphases, control of the White House, and national government spending priorities, reporting strong evidence of a “party mandate” connection between them. Gary King and Michael Laver successfully replicate the original analysis, critique the interpretation of the causal effects, and present a reanalysis showing that platforms have small or nonexistent effects on spending. In response, Budge, Hofferbert, and Michael McDonald agree that their language was somewhat inconsistent on both interactions and causality but defend their conceptualization of “mandates” as involving only an association, not necessarily a causal connection, between party commitments and government policy. Hence, while the causes of government policy are of interest, noncausal associations are sufficient as evidence of party mandates in American politics.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/KGMQBX.

As most political scientists know, the outcome of the U.S. Presidential election can be predicted within a few percentage points (in the popular vote), based on information available months before the election. Thus, the general election campaign for president seems irrelevant to the outcome (except in very close elections), despite all the media coverage of campaign strategy. However, it is also well known that the pre-election opinion polls can vary wildly over the campaign, and this variation is generally attributed to events in the campaign. How can campaign events affect people’s opinions on whom they plan to vote for, and yet not affect the outcome of the election? For that matter, why do voters consistently increase their support for a candidate during his nominating convention, even though the conventions are almost entirely predictable events whose effects can be rationally forecast? In this exploratory study, we consider several intuitively appealing, but ultimately wrong, resolutions to this puzzle, and discuss our current understanding of what causes opinion polls to fluctuate and yet reach a predictable outcome. Our evidence is based on graphical presentation and analysis of over 67,000 individual-level responses from forty-nine commercial polls during the 1988 campaign and many other aggregate poll results from the 1952–1992 campaigns. We show that responses to pollsters during the campaign are not generally informed or even, in a sense we describe, “rational.” In contrast, voters decide which candidate to eventually support based on their enlightened preferences, as formed by the information they have learned during the campaign, as well as basic political cues such as ideology and party identification. We cannot prove this conclusion, but we do show that it is consistent with the aggregate forecasts and individual-level opinion poll responses. Based on the enlightened preferences hypothesis, we conclude that the news media have an important effect on the outcome of Presidential elections–-not due to misleading advertisements, sound bites, or spin doctors, but rather by conveying candidates’ positions on important issues. Winner of the Pi Sigma Alpha Awardfor the best paper at the previous year’s meetings of the Midwest Political Science Association.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/I7GIKD.

A few years ago, explaining what you did for a living to Dad, Aunt Rose, or your friend from high school was pretty complicated. Answering that you develop statistical estimators, work on numerical optimization, or, even better, are working on a great new Markov Chain Monte Carlo implementation of a Bayesian model with heteroskedastic errors for automated text analysis is pretty much the definition of conversation stopper.

Then the media noticed the revolution we’re all apart of, and they glued a label to it. Now “Big Data” is what you and I do. As trivial as this change sounds, we should be grateful for it, as the name seems to resonate with the public and so it helps convey the importance of our field to others better than we had managed to do ourselves. Yet, now that we have everyone’s attention, we need to start clarifying for others – and ourselves – what the revolution means. This is much of what this book is about.

Throughout, we need to remember that for the most part, Big Data is not about the data….

We clarify the theoretical foundations of partisan fairness standards for district-based democratic electoral systems, including essential assumptions and definitions that have not been recognized, formalized, or in some cases even discussed. We also offer extensive empirical evidence for assumptions with observable implications. Throughout, we follow a fundamental principle of statistical inference too often ignored in this literature – defining the quantity of interest separately so its measures can be proven wrong, evaluated, or improved. This enables us to prove which of the many newly proposed fairness measures are statistically appropriate and which are biased, limited, or not measures of the theoretical quantity they seek to estimate at all. Because real world redistricting and gerrymandering involves complicated politics with numerous participants and conflicting goals, measures biased for partisan fairness sometimes still provide useful descriptions of other aspects of electoral systems.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/FTYHPJ.

The origin, meaning, estimation, and application of the concept of partisan symmetry in legislative redistricting, and the justiciability of partisan gerrymandering. An edited transcript of a talk at the “Redistricting and Representation Forum,” American Academy of Arts & Sciences, Cambridge, MA 11/8/2017.

Here also is a video of the original talk.

Katz, King, and Rosenblatt (2020) introduces a theoretical framework for understanding redistricting and electoral systems, built on basic statistical and social science principles of inference. DeFord et al. (Forthcoming, 2021) instead focuses solely on descriptive measures, which lead to the problems identified in our arti- cle. In this paper, we illustrate the essential role of these basic principles and then offer statistical, mathematical, and substantive corrections required to apply DeFord et al.’s calculations to social science questions of interest, while also showing how to easily resolve all claimed paradoxes and problems. We are grateful to the authors for their interest in our work and for this opportunity to clarify these principles and our theoretical framework.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/AFTR6W.

SUMMARY OF ARGUMENT Plaintiffs ask this Court to do what it has done many times before. For generations, it has resolved cases involving elections and cases on which elections ride. It has adjudicated controversies that divide the American people and those, like this one, where Americans are largely in agreement. In doing so, the Court has sensibly adhered to its long-standing and circumspect approach: it has announced a workable principle, one that lends itself to a manageable test, while allowing the lower courts to work out the precise contours of that test with time and experience.

Partisan symmetry, the principle put forward by the plaintiffs, is just such a workable principle. The standard is highly intuitive, deeply rooted in history, and accepted by virtually all social scientists. Tests for partisan symmetry are reliable, transparent, and easy to calculate without undue reliance on experts or unnecessary judicial intrusion on state redistricting judgments. Under any of these tests, Wisconsin’s districts cannot withstand constitutional scrutiny.

We derive a unified statistical method with which one can produce substantially improved definitions and estimates of almost any feature of two-party electoral systems that can be defined based on district vote shares. Our single method enables one to calculate more efficient estimates, with more trustworthy assessments of their uncertainty, than each of the separate multifarious existing measures of partisan bias, electoral responsiveness, seats-votes curves, expected or predicted vote in each district in a legislature, the probability that a given party will win the seat in each district, the proportion of incumbents or others who will lose their seats, the proportion of women or minority candidates to be elected, the incumbency advantage and other causal effects, the likely effects on the electoral system and district votes of proposed electoral reforms, such as term limitations, campaign spending limits, and drawing majority-minority districts, and numerous others. To illustrate, we estimate the partisan bias and electoral responsiveness of the U.S. House of Representatives since 1900 and evaluate the fairness of competing redistricting plans for the 1992 Ohio state legislature.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/MEJOPN.

In this paper, we formalize existing normative criteria used to judge presidential selection contests by modeling the translation of citizen votes in primaries and caucuses into delegates to the national party conventions. We use a statistical model that enables us to separate the form of electoral responsiveness in presidential selection systems, as well as the degree of bias toward each of the candidates. We find that (1) the Republican nomination system is more responsive to changes in citizen votes than the Democratic system and (2) non-PR primaries are always more responsive than PR primaries and (3) surprisingly, caucuses are more proportional than even primaries held under PR rules and (4) significant bias in favor of a candidate was a good prediction of the winner of the nomination contest. We also (5) evaluate the claims of Ronald Reagan in 1976 and Jesse Jackson in 1988 that the selection systems were substantially biased against their candidates. We find no evidence to support Reagan’s claim, but substantial evidence that Jackson was correct.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/AJL7ZZ.

Background. Estimates of maternal mortality are important for informing policy and resource allocation, both globally and for individual countries, and to track progress towards Sustainable Development Goals. The Global Maternal Health (GMatH) model was developed for policy analysis and produces global and country-level estimates of maternal mortality. Estimates are also produced by models from the United Nations (UN) and Global Burden of Disease (GBD).

Methods. We compared country-level estimates for 2020 of maternal deaths and the maternal mortality ratio (MMR) across the UN (v2023), GBD (v2021), and GMatH (v2023) models. We summarized the differences, assessed model convergence, and characterized the available empirical mortality data for countries with large differences to shed light on potential reasons for these differences.

Findings. On average, the GMatH estimates of country-level maternal deaths in 2020 were 272 larger (43% higher) than the UN estimates, and 728 larger (49% higher) than the GBD estimates. Country-level MMRs were on average 22.3 higher (19% higher) than the UN estimates and 48.1 higher (22% higher) than the GBD estimates. Overall, 87.9% of the UN country-level MMR estimates were convergent with the GMatH model, and 82.8% of the GBD MMR estimates were convergent, but large differences were found for some countries. Among countries with the largest differences across models, survey-based estimates of the pregnancy mortality ratio were usually the only empirical mortality data available.

Interpretation. Although estimates of maternal mortality are similar across the GMatH, UN, and GBD models for most countries, there are also large differences. Our structural modelling approach leverages multiple types of data across the reproductive life course, including pregnancy mortality ratios, allowing for more robust estimation of maternal health indicators. Comparing results across models helps to build confidence in estimates where they are similar and sheds light on potential reasons for differences where they diverge to help refine estimates and guide policies to reduce maternal mortality.

Background

Maternal mortality remains a challenge in global health, with well-known disparities across countries. However, less is known about disparities in maternal health by subgroups within countries. The aim of this study is to estimate maternal health indicators for subgroups of women within each country.

Methods

In this simulation-based analysis, we used the empirically calibrated Global Maternal Health (GMatH) microsimulation model to estimate a range of maternal health indicators by subgroup (urban/rural location and level of education) for 200 countries/territories from 1990 to 2050. Education levels were defined as low (less than primary), middle (less than secondary), and high (completed secondary or higher). The model simulates the reproductive lifecycle of each woman, accounting for individual-level factors such as family planning preferences, biological factors (e.g., anemia), and history of maternal complications, and how these factors vary by subgroup. We also estimated the impact of scaling up women’s education on projected maternal health outcomes compared to clinical and health system-focused interventions.

Findings

We find large subgroup differences in maternal health outcomes, with an estimated global maternal mortality ratio (MMR) in 2022 of 292 (95% UI 250–341) for rural women and 100 (95% UI 84–116) for urban women, and 536 (95% UI 450–594), 143 (95% UI 117–174), and 85 (95% UI 67–108) for low, middle, and high education levels, respectively. Ensuring all women complete secondary school is associated with a large impact on the projected global MMR in 2030 (97 [95% UI 76–120]) compared to current trends (167 [95% UI 142–188]), with especially large improvements in countries such as Afghanistan, Chad, Madagascar, Niger, and Yemen.

Interpretation

Substantial subgroup disparities present a challenge for global maternal health and health equity. Outcomes are especially poor for rural women with low education, highlighting the need to ensure that policy interventions adequately address barriers to care in rural areas, and the importance of investing in social determinants of health, such as women’s education, in addition to health system interventions to improve maternal health for all women.

Purpose: The COVID-19 death-rate in Italy continues to climb, surpassing that in every other country. We implement one of the first nationally representative surveys about this unprecedented public health crisis and use it to evaluate the Italian government’ public health efforts and citizen responses. Findings: (1) Public health messaging is being heard. Except for slightly lower compliance among young adults, all subgroups we studied understand how to keep themselves and others safe from the SARS-Cov-2 virus. Remarkably, even those who do not trust the government, or think the government has been untruthful about the crisis believe the messaging and claim to be acting in accordance. (2) The quarantine is beginning to have serious negative effects on the population’s mental health. Policy Recommendations: Communications focus should move from explaining to citizens that they should stay at home to what they can do there. We need interventions that make staying at home and following public health protocols more desirable. These interventions could include virtual social interactions, such as online social reading activities, classes, exercise routines, etc. — all designed to reduce the boredom of long term social isolation and to increase the attractiveness of following public health recommendations. Interventions like these will grow in importance as the crisis wears on around the world, and staying inside wears on people.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/1SBQCX.

The financial viability of Social Security, the single largest U.S. Government program, depends on accurate forecasts of the solvency of its intergenerational trust fund. We begin by detailing information necessary for replicating the Social Security Administration’s (SSA’s) forecasting procedures, which until now has been unavailable in the public domain. We then offer a way to improve the quality of these procedures due to age-and sex-specific mortality forecasts. The most recent SSA mortality forecasts were based on the best available technology at the time, which was a combination of linear extrapolation and qualitative judgments. Unfortunately, linear extrapolation excludes known risk factors and is inconsistent with long-standing demographic patterns such as the smoothness of age profiles. Modern statistical methods typically outperform even the best qualitative judgments in these contexts. We show how to use such methods here, enabling researchers to forecast using far more information, such as the known risk factors of smoking and obesity and known demographic patterns. Including this extra information makes a sub¬stantial difference: For example, by only improving mortality forecasting methods, we predict three fewer years of net surplus, $730 billion less in Social Security trust funds, and program costs that are 0.66% greater of projected taxable payroll compared to SSA projections by 2031. More important than specific numerical estimates are the advantages of transparency, replicability, reduction of uncertainty, and what may be the resulting lower vulnerability to the politicization of program forecasts. In addition, by offering with this paper software and detailed replication information, we hope to marshal the efforts of the research community to include ever more informative inputs and to continue to reduce the uncertainties in Social Security forecasts.

This work builds on our article that provides forecasts of US Mortality rates (see King and Soneji, The Future of Death in America), a book developing improved methods for forecasting mortality (Girosi and King, Demographic Forecasting), all data we used (King and Soneji, replication data sets), and open source software that implements the methods (Girosi and King, YourCast). Also available is a New York Times Op-Ed based on this work (King and Soneji, Social Security: It’s Worse Than You Think), and a replication data set for the Op-Ed (King and Soneji, replication data set).

Population mortality forecasts are widely used for allocating public health expenditures, setting research priorities, and evaluating the viability of public pensions, private pensions, and health care financing systems. In part because existing methods seem to forecast worse when based on more information, most forecasts are still based on simple linear extrapolations that ignore known biological risk factors and other prior information. We adapt a Bayesian hierarchical forecasting model capable of including more known health and demographic information than has previously been possible. This leads to the first age- and sex-specific forecasts of American mortality that simultaneously incorporate, in a formal statistical model, the effects of the recent rapid increase in obesity, the steady decline in tobacco consumption, and the well known patterns of smooth mortality age profiles and time trends. Formally including new information in forecasts can matter a great deal. For example, we estimate an increase in male life expectancy at birth from 76.2 years in 2010 to 79.9 years in 2030, which is 1.8 years greater than the U.S. Social Security Administration projection and 1.5 years more than U.S. Census projection. For females, we estimate more modest gains in life expectancy at birth over the next twenty years from 80.5 years to 81.9 years, which is virtually identical to the Social Security Administration projection and 2.0 years less than U.S. Census projections. We show that these patterns are also likely to greatly affect the aging American population structure. We offer an easy-to-use approach so that researchers can include other sources of information and potentially improve on our forecasts too.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/IEANXM.

Background

Maternal mortality remains a challenge in global health, with well-known disparities across countries. However, less is known about disparities in maternal health by subgroups within countries. The aim of this study is to estimate maternal health indicators for subgroups of women within each country.

Methods

In this simulation-based analysis, we used the empirically calibrated Global Maternal Health (GMatH) microsimulation model to estimate a range of maternal health indicators by subgroup (urban/rural location and level of education) for 200 countries/territories from 1990 to 2050. Education levels were defined as low (less than primary), middle (less than secondary), and high (completed secondary or higher). The model simulates the reproductive lifecycle of each woman, accounting for individual-level factors such as family planning preferences, biological factors (e.g., anemia), and history of maternal complications, and how these factors vary by subgroup. We also estimated the impact of scaling up women’s education on projected maternal health outcomes compared to clinical and health system-focused interventions.

Findings

We find large subgroup differences in maternal health outcomes, with an estimated global maternal mortality ratio (MMR) in 2022 of 292 (95% UI 250–341) for rural women and 100 (95% UI 84–116) for urban women, and 536 (95% UI 450–594), 143 (95% UI 117–174), and 85 (95% UI 67–108) for low, middle, and high education levels, respectively. Ensuring all women complete secondary school is associated with a large impact on the projected global MMR in 2030 (97 [95% UI 76–120]) compared to current trends (167 [95% UI 142–188]), with especially large improvements in countries such as Afghanistan, Chad, Madagascar, Niger, and Yemen.

Interpretation

Substantial subgroup disparities present a challenge for global maternal health and health equity. Outcomes are especially poor for rural women with low education, highlighting the need to ensure that policy interventions adequately address barriers to care in rural areas, and the importance of investing in social determinants of health, such as women’s education, in addition to health system interventions to improve maternal health for all women.

The financial stability of four of the five largest U.S. federal entitlement programs, strategic decision making in several industries, and many academic publications all depend on the accuracy of demographic and financial forecasts made by the Social Security Administration (SSA). Although the SSA has performed these forecasts since 1942, no systematic and comprehensive evaluation of their accuracy has ever been published by SSA or anyone else. The absence of a systematic evaluation of forecasts is a concern because the SSA relies on informal procedures that are potentially subject to inadvertent biases and does not share with the public, the scientific community, or other parts of SSA sufficient data or information necessary to replicate or improve its forecasts. These issues result in SSA holding a monopoly position in policy debates as the sole supplier of fully independent forecasts and evaluations of proposals to change Social Security. To assist with the forecasting evaluation problem, we collect all SSA forecasts for years that have passed and discover error patterns that could have been—and could now be—used to improve future forecasts. Specifically, we find that after 2000, SSA forecasting errors grew considerably larger and most of these errors made the Social Security Trust Funds look more financially secure than they actually were. In addition, SSA’s reported uncertainty intervals are overconfident and increasingly so after 2000. We discuss the implications of these systematic forecasting biases for public policy.

Replication data at the Harvard Dataverse: https://doi.org/10.7910/DVN/28122.

The financial viability of Social Security, the single largest U.S. Government program, depends on accurate forecasts of the solvency of its intergenerational trust fund. We begin by detailing information necessary for replicating the Social Security Administration’s (SSA’s) forecasting procedures, which until now has been unavailable in the public domain. We then offer a way to improve the quality of these procedures due to age-and sex-specific mortality forecasts. The most recent SSA mortality forecasts were based on the best available technology at the time, which was a combination of linear extrapolation and qualitative judgments. Unfortunately, linear extrapolation excludes known risk factors and is inconsistent with long-standing demographic patterns such as the smoothness of age profiles. Modern statistical methods typically outperform even the best qualitative judgments in these contexts. We show how to use such methods here, enabling researchers to forecast using far more information, such as the known risk factors of smoking and obesity and known demographic patterns. Including this extra information makes a sub¬stantial difference: For example, by only improving mortality forecasting methods, we predict three fewer years of net surplus, $730 billion less in Social Security trust funds, and program costs that are 0.66% greater of projected taxable payroll compared to SSA projections by 2031. More important than specific numerical estimates are the advantages of transparency, replicability, reduction of uncertainty, and what may be the resulting lower vulnerability to the politicization of program forecasts. In addition, by offering with this paper software and detailed replication information, we hope to marshal the efforts of the research community to include ever more informative inputs and to continue to reduce the uncertainties in Social Security forecasts.

This work builds on our article that provides forecasts of US Mortality rates (see King and Soneji, The Future of Death in America), a book developing improved methods for forecasting mortality (Girosi and King, Demographic Forecasting), all data we used (King and Soneji, replication data sets), and open source software that implements the methods (Girosi and King, YourCast). Also available is a New York Times Op-Ed based on this work (King and Soneji, Social Security: It’s Worse Than You Think), and a replication data set for the Op-Ed (King and Soneji, replication data set).

Few would disagree that health policies and programmes ought to be based on valid, timely and relevant information, focused on those aspects of health development that are in greatest need of improvement. For example, vaccination programmes rely heavily on information on cases and deaths to document needs and to monitor progress on childhood illness and mortality. The same strong information basis is necessary for policies on health inequality. The reduction of health inequality is widely accepted as a key goal for societies, but any policy needs reliable research on the extent and causes of health inequality. Given that child deaths still constitute 19% of all deaths globally and 24% of all deaths in developing countries (1), reducing inequalities in child survival is a good beginning.

The between-group component of total health inequality has been studied extensively by numerous scholars. They have expertly analysed the causes of differences in health status and mortality across population subgroups, defined by income, education, race/ethnicity, country, region, social class, and other group identifiers (2–9).