Nonparametric Regression with Common Shocks

Eduardo A. Souza-Rodrigues
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Eduardo A. Souza-Rodrigues: Department of Economics, University of Toronto, Max Gluskin House, 150 St. George Street, 324, Toronto, ON M5S 3G7, Canada

Econometrics, 2016, vol. 4, issue 3, 1-17

Abstract: This paper considers a nonparametric regression model for cross-sectional data in the presence of common shocks. Common shocks are allowed to be very general in nature; they do not need to be finite dimensional with a known (small) number of factors. I investigate the properties of the Nadaraya-Watson kernel estimator and determine how general the common shocks can be while still obtaining meaningful kernel estimates. Restrictions on the common shocks are necessary because kernel estimators typically manipulate conditional densities, and conditional densities do not necessarily exist in the present case. By appealing to disintegration theory, I provide sufficient conditions for the existence of such conditional densities and show that the estimator converges in probability to the Kolmogorov conditional expectation given the sigma-field generated by the common shocks. I also establish the rate of convergence and the asymptotic distribution of the kernel estimator.

Keywords: nonparametric regression; common shocks; cross-sectional dependence; disintegration theory (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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