Econometricians have long found it productive to study identification and statistical inference sequentially. One first analyzes identification of a population distribution and then considers induction from finite samples to the population, assuming that the finite sample properties are the same as that of the population. The PI has developed a major research program on partial identification of probability distributions. The research described here will extend this research program in two important directions.
Policy makers make treatment choices based on a finite sample of data, knowing that different individuals should receive different treatments because of different responses to treatment. The first direction of extension is to use statistical decision theory to integrate the study of identification and statistical inference in the analysis of treatment response. The traditional way to cope with sampling processes that partially identify population parameters has been to combine the available data with strong assumptions to yield point identification. Such assumptions often are not well motivated, and empirical researchers often debate their validity. The approach proposed here allows researchers to learn from the available data without imposing untenable assumptions. Providing a framework for statistical treatment rules for treatment choices and parametric prediction with missing data, this research will help solve one of the major problems in econometrics and statistical inference.
The second direction of extension is the computation of estimates of identification regions for parametric best predictors when data are missing. Many persistent public policy controversies reflect divergent beliefs about the effects of government policy on society. Such divergent beliefs are often manifested in competing policy studies that use different analytical approaches or data sources to reach different policy conclusions. However, there may be no way to determine which study (if either) makes realistic conjectures and which (if either) draws empirically correct conclusions. The research outlined here provides an innovative approach to empirical inference that enables the public to better evaluate the credibility of existing policy studies and can enhance the credibility of future policy research.
The results of this research may not only have a strong impact on economic science, it is likely to have a strong impact on public policy formulation and evaluation.
