Identification and estimation of counterfactual outcomes
As counterfactual outcomes are important objects of inference, one may be interested in the identification and estimation of counterfactual outcomes. The possible identification of counterfactual outcomes follows from model structures and observed decisions and outcomes (Heckman, 1990; Lee, 1995). Observed outcomes and choice probabilities provide sample information. Latent variable models provide prior structural restrictions.
Professor C. Manski in a series of articles put aside the latent-variable model perspective to go back to probabilistic basics. His results are summarized in Manski (1994). The main findings provide informative bounds on some counterfactual outcomes. Without latent variable modeling, if one is not satisfied with just bounds, the identification and evaluation of a counterfactual outcome would require extra prior restrictions on some other counterfactual outcomes. Statisticians approach the selected sample as a mixture problem. A widely-used method of evaluation in statistics is the method of matching (Rubin, 1987). Heckman, Ichimura, and Todd (1998) show that the fundamental identification condition (or assumption) for the matching method is a condition imposed on a specific counterfactual outcome. Corresponding to the two-sector model in (18.2)-(18.3), this identification condition requires that o2e = 0 (Heckman et al., 1998, pp. 268-9). Professor J. Heckman and his associates in a series of forthcoming papers contrast the econometrics and statistical approaches on program evaluation. Some preliminary review can be found in M. J. Lee (1997).
* The author acknowledges research support from the Research Grants Council of Hong Kong under grant HKUST595/96H for his research.
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