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Finite Population Causal Standard Errors -- by Alberto Abadie, Susan Athey, Guido W. Imbens, Jeffrey M. WooldridgeWhen a researcher estimates the parameters of a regression function using information on all 50 states in the United States, or information on all visits to a website, what is the interpretation of the standard errors? Researchers typically report standard errors that are designed to capture sampling variation, based on viewing the data as a random sample drawn from a large population of interest, even in applications where it is difficult to articulate what that population of interest is and how it differs from the sample. In this paper we explore alternative interpretations for the uncertainty associated with regression estimates. As a leading example we focus on the case where some parameters of the regression function are intended to capture causal effects. We derive standard errors for causal effects using a generalization of randomization inference. Intuitively, these standard errors capture the fact that even if we observe outcomes for all units in the population of interest, there are for each unit missing potential outcomes for the treatment levels the unit was not exposed to. We show that our randomization-based standard errors in general are smaller than the conventional robust standard errors, and provide conditions under which they agree with them. More generally, correct statistical inference requires precise characterizations of the population of interest, the parameters that we aim to estimate within such population, and the sampling process. Estimation of causal parameters is one example where appropriate inferential methods may differ from conventional practice, but there are others.
http://papers.nber.org/papers/w20325#fromrss
http://papers.nber.org/papers/w20325#fromrssShould Student Employment Be Subsidized? Conditional Counterfactuals and the Outcomes of Work-Study Participation -- by Judith Scott-Clayton, Veronica MinayaStudent employment subsidies are one of the largest types of federal employment subsidies, and one of the oldest forms of student aid. Yet it is unclear whether they help or harm students' long term outcomes. We present a framework that decomposes overall effects into a weighted average of effects for marginal and inframarginal workers. We then develop an application of propensity scores, which we call conditional-counterfactual matching, in which we estimate the overall impact, and the impact under two distinct counterfactuals: working at an unsubsidized job, or not working at all. Finally, we estimate the effects of the largest student employment subsidy program--Federal Work-Study (FWS)--for a broad range of participants and outcomes. Our results suggest that about half of FWS participants are inframarginal workers, for whom FWS reduces hours worked and improves academic outcomes, but has little impact on future employment. For students who would not have worked otherwise, the pattern of effects reverses. With the exception of first-year GPA, we find scant evidence of negative effects of FWS for any outcome or subgroup. However, positive effects are largest for lower-income and lower-SAT subgroups, suggesting there may be gains to improved targeting of funds.
http://papers.nber.org/papers/w20329#fromrss
http://papers.nber.org/papers/w20329#fromrssAn Empirical Model of Network Formation: Detecting Homophily When Agents Are Heterogenous -- by Bryan S. GrahamI formalize a widely-used empirical model of network formation. The model allows for assortative matching on observables (homophily) as well as unobserved agent level heterogeneity in link surplus (degree heterogeneity). The joint distribution of observed and unobserved agent-level characteristics is left unrestricted. Inferences about homophily do not depend upon untestable assumptions about this distribution. The model is non-standard since the dimension of the heterogeneity parameter grows with the number of agents, and hence network size. Nevertheless, under certain conditions, a joint maximum likelihood (ML) procedure, which simultaneously estimates the common and agent-level parameters governing link formation, is consistent. Although the asymptotic sampling distribution of the common parameter is Normal, it (i) contains a bias term and (ii) its variance does not coincide with the inverse of Fisher's information matrix. Standard ML asymptotic inference procedures are invalid. Forming confidence intervals with a bias-corrected maximum likelihood estimate, and appropriate standard error estimates, results in correct coverage. I assess the value of these results for understanding finite sample behavior via a set of Monte Carlo experiments and through an empirical analysis of risk-sharing links in a rural Tanzanian village (cf., De Weerdt, 2004).
http://papers.nber.org/papers/w20341#fromrss
http://papers.nber.org/papers/w20341#fromrssBroken or Fixed Effects? -- by Charles E. Gibbons, Juan Carlos Suarez Serrato, Michael B. UrbancicThis paper provides empirical evidence of an established theoretical result: in the presence of heterogeneous treatment effects, OLS is generally not a consistent estimator of the sample-weighted average treatment effect (SWE). We propose two alternative estimators that do recover the SWE in the presence of group-specific heterogeneity. We derive tests to detect the presence of heterogeneous treatment effects and to distinguish between the OLS and SWE. We document that heterogeneous treatment effects are common and the SWE is often statistically and economically different from the OLS estimate by extending eight influential papers. In all but one paper, there is statistically significant treatment effect heterogeneity; in five, the SWE is statistically different from the OLS estimator; and in five, the SWE and OLS estimators are economically different.
http://papers.nber.org/papers/w20342#fromrss
http://papers.nber.org/papers/w20342#fromrss