The Limiting Behavior of the Estimated Parameters in a Misspecified Random Field Regression Model

CREATES Research Paper No. 2008-45

43 Pages Posted: 2 Sep 2008

See all articles by Christian M. Dahl

Christian M. Dahl

Department of Business and Economics

Qin Yu

Ohio State University (OSU) - Fisher College of Business

Date Written: September 2, 2008

Abstract

This paper examines the limiting properties of the estimated parameters in the random field regression model recently proposed by Hamilton (Econometrica, 2001). Though the model is parametric, it enjoys the flexibility of the nonparametric approach since it can approximate a large collection of nonlinear functions and it has the added advantage that there is no curse of dimensionality. Contrary to existing literature on the asymptotic properties of the estimated parameters in random field models our results do not require that the explanatory variables are sampled on a grid. However, as a consequence the random field model specification introduces non-stationarity and non-ergodicity in the misspecified model and it becomes non-trivial, relative to the existing literature, to establish the limiting behavior of the estimated parameters. The asymptotic results are obtained by applying some convenient new uniform convergence results that we propose. This theory may have applications beyond those presented here. Our results indicate that classical statistical inference techniques, in general, works very well for random field regression models in finite samples and that these models succesfully can fit and uncover many types of nonlinear structures in data.

Keywords: Random fields regressions, Estimation, Inference, Asymptotics

JEL Classification: C12, C13, C14, C45

Suggested Citation

Dahl, Christian M. and Yu, Qin, The Limiting Behavior of the Estimated Parameters in a Misspecified Random Field Regression Model (September 2, 2008). CREATES Research Paper No. 2008-45. Available at SSRN: https://ssrn.com/abstract=1262227 or http://dx.doi.org/10.2139/ssrn.1262227

Christian M. Dahl (Contact Author)

Department of Business and Economics ( email )

Campusvej 55
DK-5230 Odense M
Denmark
29125486 (Phone)

Qin Yu

Ohio State University (OSU) - Fisher College of Business ( email )

2100 Neil Avenue
Columbus, OH 43210-1144
United States

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