Identification Problems in the Social Sciences

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Econometricians have long found it useful to separate inferential problems into statistical and identification components. Studies of identification seek to characterize the conclusions that could be drawn if the researcher had available a sample of unlimited size. Studies of statistical inference seek to characterize the generally weaker conclusions that can be drawn given a sample of positive but finite size. Statistical and identification problems limit in distinct ways the conclusions that may be drawn in empirical research. Statistical problems are most severe when the available sample is small. Identification problems are most severe when the researcher knows little about the population under study and the sampling process yields only weak data on the population.The proposed research will continue the investigator's program of work on identification problems in the social sciences. This program is deliberately conservative in the assumptions that it brings to bear. The investigator believes that it is not sufficient for empirical researchers to know the inferences that can be made if assumptions strong enough to yield identification are imposed. It is also important to characterize the inferences that can be made without imposing such assumptions, which often lack credibility. Conservative analysis allows the establishment of a domain of consensus among researchers who may hold disparate beliefs about what assumptions are appropriate.The investigator will study how empirical analysis of treatment response informs the normative problem of treatment choice in heterogeneous populations. Recent work by the investigator has shown how identification problems generate ambiguity about the identity of optimal treatment rules. The planned research will analyze the complementary statistical problem of induction from finite samples to populations, which generates further ambiguity. The long-run objective is a coherent integrated analysis of identification and statistical inference.The investigator will also study problems of incomplete identification of regressions that arise under empirically relevant sampling processes. One problem to be examined is inference on long regressions using data on short regressions. This research has immediate application to the longstanding ecological inference problem. Another problem to be analyzed is inference on regressions when only interval measures of covariates are available.