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Econometrics 2016, 4(3), 36; doi:10.3390/econometrics4030036

Nonparametric Regression with Common Shocks

1
Department of Economics, University of Toronto, Max Gluskin House, 150 St. George Street, 324, Toronto, ON M5S 3G7, Canada
1
University of Toronto, Toronto, ON, Canada
Academic Editor: Kerry Patterson
Received: 7 April 2016 / Revised: 20 July 2016 / Accepted: 16 August 2016 / Published: 1 September 2016
View Full-Text   |   Download PDF [306 KB, uploaded 1 September 2016]

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. View Full-Text
Keywords: nonparametric regression; common shocks; cross-sectional dependence; disintegration theory nonparametric regression; common shocks; cross-sectional dependence; disintegration theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Souza-Rodrigues, E.A. Nonparametric Regression with Common Shocks. Econometrics 2016, 4, 36.

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