We propose a remedy for the discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. Methodologists and statisticians agree that "multiple imputation" is a superior approach to the problem of missing data scattered through one's explanatory and dependent variables than the methods currently used in applied data analysis. The reason for this discrepancy lies with the fact that the computational algorithms used to apply the best multiple imputation models have been slow, difficult to implement, impossible to run with existing commercial statistical packages, and demanding of considerable expertise. In this paper, we adapt an existing algorithm, and use it to implement a generalpurpose, multiple imputation model for missing data. This algorithm is considerably faster and easier to use than the leading method recommended in the statistics literature. We also quantify the risks of current missing data practices, ...

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 is possible to 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

Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: the standard practice of interpreting the parameters of log-linearized models estimated by ordinary least squares as elasticities can be highly misleading in the presence of heteroskedasticity. This paper explains why this problem arises and proposes an appropriate estimator. Our criticism to conventional practices and the solution we propose extends to a broad range of economic applications where the equation under study is log-linearized. We develop the argument using one particular illustration, the gravity equation for trade, and apply the proposed technique to provide new estimates of this equation. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method. These discrepancies persist even when the gravity equation takes into account multilateral resistance terms or fixed effects

Seemingly unrelated regression (SUR) models traditionally appear in econometrics but recently also emerged in likelihood factorizations of Gaussian graphical models. The literature on maximum likelihood estimation in SUR seems not to mention the possibility of a multimodal likelihood.

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate

This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regressors and standard “valid” and “relevant” instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interest.

This chapter explains the logic of structural econometric models and compares them to other types of econometric models. We provide a framework researchers can use to develop and evaluate structural econometric models. This framework pays particular attention to describing different sources of unobservables in structural models. We use our framework to evaluate several literatures in industrial organization economics, including the literatures dealing with market power, product differentiation, auctions, regulation and entry.

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.

We attempt to clarify, and suggest how to avoid, several serious misunderstandings about and fal-lacies of causal inference in experimental and observational research. These issues concern some of the most basic advantages and disadvantages of each basic research design. Problems include improper use of hypothesis tests for covariate balance between the treated and control groups, and the consequences of using randomization, blocking before randomization, and matching after treatment assignment to achieve covariate balance. Applied researchers in a wide range of scien-tific disciplines seem to fall prey to one or more of these fallacies, and as a result make suboptimal design or analysis choices. To clarify these points, we derive a new four-part decomposition of the

We thank Art Goldberger for helpful pointers to the literature. Estimating the Returns to College Quality with Multiple