Publication:
Essays on Semiparametric Identification and Estimation

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2023-03
Defense date
2023-04-26
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The unifying theme of this dissertation is semiparametric identification and estimation. A parameter is semiparametrically identified if the researcher can recover its value from the available data, even if the data does not completely pin down the whole model. This framework covers several parameters of economic interest: treatment effects, marginal effects or counterfactual parameters. Chapter 1 of the dissertation specifically studies a counterfactual parameter: the Counterfactual Average Structural Function (CASF). The parameter is an average with respect to a counterfactual distribution (which may be induced by a policy). I give conditions on the counterfactual distribution so that the CASF is identified via a Control Function Assumption. I also examine under which conditions is the CASF root-n estimable (that is, regularly identified). The researcher must estimate a Control Function prior to computing the CASF. The Control Function acts then as a regressor in an intermediate step. Estimation of the CASF is thus a problem of generated regressors. Chapter 2 of this dissertation studies estimation of parameters that are (regularly) identified by moment conditions in the presence of generated regressors. It proposes to modify the original moment condition to construct a Locally Robust version. Locally Robust moment conditions are locally insensitive to estimation done in previous steps and, therefore, they allow for regressors to be generated by Machine Learning techniques. Whether the CASF is regularly identified or not depends on a finite variance condition. Chapter 3 of the dissertation formally analyzes the link between finite variance and regular identification. It does so in the general framework of a model generated by a (possibly infinite dimensional) parameter living in a normed space. The chapter studies semiparametric identification and root-n estimability in this setup.
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Modelos econométricos, Métodos de distribución libre y no paramétrica, Modelos causales, Modelos causales, Estadística analítica, Modelos econométricos, Modelos econométricos, Métodos de distribución libre y no paramétrica, Modelos causales, Modelos causales, Estadística analítica
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