Methods for Observational Data
Evaluating Model Dependence
This program is designed to improve causal inference via a method of matching that is widely applicable in observational data and easy to understand and use (if you understand how to draw a histogram, you will understand this method). The program implements the coarsened exact matching (CEM) algorithm, described below. CEM may be used alone or in combination with any existing matching method. This algorithm, and its statistical properties, are described in Iacus, King, and Porro (2008).
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.
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 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.
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.
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.
We propose a simplified approach to matching for causal inference that simultaneously optimizes balance (similarity between the treated and control groups) and matched sample size. Existing approaches either fix the matched sample size and maximize balance or fix balance and maximize sample size, leaving analysts to settle for suboptimal solutions or attempt manual optimization by iteratively tweaking their matching method and rechecking balance. To jointly maximize balance and sample size, we introduce the matching frontier, the set of matching solutions with maximum possible balance for each sample size. Rather than iterating, researchers can choose matching solutions from the frontier for analysis in one step. We derive fast algorithms that calculate the matching frontier for several commonly used balance metrics. We demonstrate with analyses of the effect of sex on judging and job training programs that show how the methods we introduce can extract new knowledge from existing data sets.
Easy to use, open source, software is available here to implement all methods in the paper.
We show that propensity score matching (PSM), an enormously popular method of preprocessing data for causal inference, often accomplishes the opposite of its intended goal -- increasing imbalance, inefficiency, model dependence, and bias. PSM supposedly makes it easier to find matches by projecting a large number of covariates to a scalar propensity score and applying a single model to produce an unbiased estimate. However, in observational analysis the data generation process is rarely known and so users typically try many models before choosing one to present. The weakness of PSM comes from its attempts to approximate a completely randomized experiment, rather than, as with other matching methods, a more efficient fully blocked randomized experiment. PSM is thus uniquely blind to the often large portion of imbalance that can be eliminated by approximating full blocking with other matching methods. Moreover, in data balanced enough to approximate complete randomization, either to begin with or after pruning some observations, PSM approximates random matching which, we show, increases imbalance even relative to the original data. 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.
Researchers who generate data often optimize efficiency and robustness by choosing stratified over simple random sampling designs. Yet, all theories of inference proposed to justify matching methods are based on simple random sampling. This is all the more troubling because, although these theories require exact matching, most matching applications resort to some form of ex post stratification (on a propensity score, distance metric, or the covariates) to find approximate matches, thus nullifying the statistical properties these theories are designed to ensure. Fortunately, the type of sampling used in a theory of inference is an axiom, rather than an assumption vulnerable to being proven wrong, and so we can replace simple with stratified sampling, so long as we can show, as we do here, that the implications of the theory are coherent and remain true. Properties of estimators based on this theory are much easier to understand and can be satisfied without the unattractive properties of existing theories, such as assumptions hidden in data analyses rather than stated up front, asymptotics, unfamiliar estimators, and complex variance calculations. Our theory of inference makes it possible for researchers to treat matching as a simple form of preprocessing to reduce model dependence, after which all the familiar inferential techniques and uncertainty calculations can be applied. This theory also allows binary, multicategory, and continuous treatment variables from the outset and straightforward extensions for imperfect treatment assignment and different versions of treatments.
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 \(\approx 62.7\%\) (relative to a day’s volume), accounting for 13,166 additional posts over the treatment week, with similar effects across population subgroups.
A vast literature demonstrates that voters around the world who benefit from their governments' discretionary spending cast more ballots for the incumbent party than those who do not benefit. But contrary to most theories of political accountability, some suggest that voters also reward incumbent parties for implementing "programmatic" spending legislation, over which incumbents have no discretion, and even when passed with support from all major parties. Why voters would attribute responsibility when none exists is unclear, as is why minority party legislators would approve of legislation that would cost them votes. We study the electoral effects of two large prominent programmatic policies that fit the ideal type especially well, with unusually large scale experiments that bring more evidence to bear on this question than has previously been possible. For the first policy, we design and implement ourselves one of the largest randomized social experiments ever. For the second policy, we reanalyze studies that used a large scale randomized experiment and a natural experiment to study the same question but came to opposite conclusions. Using corrected data and improved statistical methods, we show that the evidence from all analyses of both policies is consistent: programmatic policies have no effect on voter support for incumbents. We conclude by discussing how the many other studies in the literature may be interpreted in light of our results.
This is a poster presentation describing (1) the largest ever experimental study of media effects, with more than 50 cooperating traditional media sites, normally unavailable web site analytics, the text of hundreds of thousands of news articles, and tens of millions of social media posts, and (2) a design we used in preparation that attempts to anticipate experimental outcomes
We highlight common problems in the application of random treatment assignment in large scale program evaluation. Random assignment is the defining feature of modern experimental design. Yet, errors in design, implementation, and analysis often result in real world applications not benefiting from the advantages of randomization. The errors we highlight cover the control of variability, levels of randomization, size of treatment arms, and power to detect causal effects, as well as the many problems that commonly lead to post-treatment bias. We illustrate with an application to the Medicare Health Support evaluation, including recommendations for improving the design and analysis of this and other large scale randomized experiments.
We attempt to clarify, and suggest how to avoid, several serious misunderstandings about and fallacies 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 scientific 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 key estimation errors in making causal inferences. We then show how this decomposition can help scholars from different experimental and observational research traditions better understand each other’s inferential problems and attempted solutions.
This article describes WhatIf: Software for Evaluating Counterfactuals, an R package that implements the methods for evaluating counterfactuals introduced in King and Zeng (2006a) and King and Zeng (2006b). It offers easy-to-use techniques for assessing a counterfactual’s model dependence without having to conduct sensitivity testing over specified classes of models. These same methods can be used to approximate the common support of the treatment and control groups in causal inference.
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 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 implements the methods in this paper:
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.