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This paper studies nonparametric identification of nonseparable models when true endogenous variables are unobservable because of information frictions. We consider identification of various structural parameters such as the average structural function and quantile structural effects, based on the instrumental variables and control variables approaches, and show how the identification results can be extended to the case of the unobservable true endogenous variables. The identification results are further extended to the nonseparable models where both the true endogenous variables and instrumental variables are unobservable because of information frictions, which have been neglected despite their theoretical and empirical importance. Our identification strategy is constructive in the sense that it produces explicit forms of the identified parameters and suggests corresponding nonparametric estimation strategies from these closed-form expressions. Uniform convergence rates of the proposed estimators are provided.
We apply the results to analyze nonseparable consumer demand system using the PSID data. The estimated outcomes underscore the importance of addressing both the endogeneity and information frictions in the form of measurement errors on the family expenditure.
Contact Person: Gray Calhoun