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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

Matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases. The absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data. In this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results. We focus on matching with replacement with a fixed number of matches. First, we show that matching estimators are not N1/2-consistent in general and describe conditions under which matching estimators do attain N1/2-consistency. Second, we show that even in settings where matching estimators are N1/2-consistent, simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound. Third, we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions. Software for implementing these methods is available in Matlab, Stata, and R.

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The difference-in-differences (DID) estimator is one of the most popular tools for applied research in economics to evaluate the effects of public interventions and other treatments of interest on some relevant outcome variables. However, it is well-known that the DID estimator is based on strong identifying assumptions. In particular, the conventional DID estimator requires that, in absence of the treatment, the average outcomes for the treated and control groups would have followed parallel paths over time. This assumption may be implausible if pretreatment characteristics that are thought to be associated with the dynamics of the outcome variable are unbalanced between the treated and the untreated. That would be the case, for example, if selection for treatment is influenced by individual-transitory shocks on past outcomes (Ashenfelter’s Dip). This paper considers the case in which differences in observed characteristics create non-parallel outcome dynamics between treated and controls. It is shown that, in such case, a simple two-step strategy can be used to estimate the average effect of the treatment for the treated. In addition, the estimation framework proposed in this paper allows the use of covariates to describe how the average effect of the treatment varies with changes in observed characteristics.

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We survey 1,050 Chief Financial Officers (CFOs) in the U.S., Europe, and Asia to directly assess whether their firms are credit constrained during the global financial crisis of 2008. We study whether corporate spending plans differ conditional on this survey-based measure of financial constraint. Our evidence indicates that constrained firms planned deeper cuts in tech spending, employment, and capital spending. Constrained firms also burned through more cash, drew more heavily on lines of credit for fear banks would restrict access in the future, and sold more assets to fund their operations. We also find that the inability to borrow externally caused many firms to bypass attractive investment opportunities, with 86 % of constrained U.S. CFOs saying their investment in attractive projects was restricted during the credit crisis of 2008. More than half of the respondents said they canceled or postponed their planned investments. Our results also hold in Europe and Asia, and in many cases are stronger in those economies. Our analysis adds to the portfolio of approaches and knowledge about the impact of credit constraints on real firm behavior.

Between 1991 and 1997 West Germany spent on average about 3.6 bn Euro per year on public sector sponsored training programmes for the unemployed. We base our empirical analysis on a new administrative data base that plausibly allows for selectivity correction by microeconometric matching methods. We identify the effects of different types of training programmes over a horizon of more than seven years. Using bias corrected weighted multiple neighbours matching we find that all programmes have negative effects in the short run and positive effects over a horizon of about four years. However, for substantive training programmes with duration of about two years gains in employment probabilities of more than 10 % points appear to be sustainable, but come at the price of large negative lock-in effects.

Abstract. When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970s, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods—or developing methods related to matching—do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed. Key words and phrases: Observational study, propensity scores, subclassification, weighting.

Causal effect modeling with naturalistic rather than experimental data is challenging. In observational studies participants in different treatment conditions may also differ on pretreatment characteristics that influence outcomes. Propensity score methods can theoretically eliminate these confounds for all observed covariates, but accurate estimation of propensity scores is impeded by large numbers of covariates, uncertain functional forms for their associations with treatment selection, and other problems. This paper demonstrates that boosting, a modern statistical technique, can overcome many of these obstacles. We illustrate this approach with a study of adolescent probationers in substance abuse treatment programs. Propensity score weights estimated using boosting eliminate most pretreatment group differences, and substantially alter the apparent relative effects of adolescent substance abuse treatment. Experimental studies offer the most rigorous evidence with which to establish treatment efficacy, but they are not always practical or feasible. Experimental treatment evaluations can be expensive to field and may be too slow to produce answers to pressing questions. In some cases