Inference in Econometric Models with Asymptotic Discontinuities

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This proposal deals with the problem of inference based on statistics whose asymptotic distributions are discontinuous functions of the true distribution that generates the observations. Numerous problems in econometrics and other areas of statistics exhibit this feature. The proposal involves a combination of (i) the development of new and improved general methods for inference based on statistics with asymptotic discontinuities and (ii) further analysis of particular models where asymptotic discontinuities arise. General methods that are not based on subsampling or the m out of n bootstrap are developed. The motivation for this is that there are reasons to believe that subsampling and m out of n bootstrap-based tests do not provide as high power as is possible in models with asymptotic discontinuities. In addition, the latter methods are well known to exhibit relatively large errors in asymptotic size.Considerable effort will be devoted to moment inequality models. For such models, this project investigates a new class of generalized moment selection procedures and recursive size-correction procedures. The project introduces new procedures for conditional moment inequality models. It analyzes existing and develops new confidence sets and tests in nonlinear regression, ARMA(1, 1), threshold AR, and stochastic dominance models, all of which exhibit asymptotic discontinuities. Finally, this project undertakes research on the asymptotic risk of estimators and measures of uncertainly in the context of asymptotic discontinuities.On a different topic, this project studies a new method of heteroskedasticity and autocorrelation (HAC) inference based on combining ideas in Ibragimov and Müller (2006) and Andrews (2004). Finally, the project continues research initiated in Andrews, Moreira, and Stock (2006) on optimal inference with weak instruments. This research focuses on inference in the presence of heteroskedasticity.The broader impact of the proposed research includes the following. (i) The proposed research will benefit society through improved empirical methods that lead to more accurate empirical research and, consequently, better informed policy analysis.(ii) The research will promote teaching and training through the use of graduate students as research assistants and collaborative researchers and through the development of lecture notes related to the sponsored research. (iii) The research will involve groups that are under-represented in economics and econometrics, in particular women. Four of the graduate students that the PI will work with, viz., Xu Cheng, Yaxin Duan, Sun-Young Park, and Xiaoxia Shi, are women. (iv) The research will enhance infrastructure by making new computer software available for use by the profession. (v) The results of the research will be disseminated broadly via presentation at international conferences