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Nonparametric Estimation and Hypothesis Testing in Econometric Models

By A. Ullah ~

Abstract: In this paper we systematically review and develop nonparametric estimation and testing techniques in the context of econometric models. The results are discussed under the settings of regression model and kernel estimation, although as indicated in the paper these results can go through for other econometric models and for the nearest neighbor estimation. A nontechnical survey of the asymptotic properties of kernel regression estimation is also presented. The technique described in the paper are useful for the empirical analysis of the economic relations whose true functional forms are usually unknown.

1 Introduction

Consider an economic model

y =R(x)+u where y is a dependent variable, x is a vector o f regressors, u is the disturbance and

R(x) = E ( y l x ) . Often, in practice, the estimation o f the derivatives o f R(x)are o f interest. For example, the first derivative indicates the response coefficient (regression coefficient) o f y with respect to x, and the second derivauve indicates the curvature o f

R(x). In the parametric econometrics the estimation o f these derivatives and testing

1 Aman Ullah, Department of Economics, University of Western Ontario, London, Ontario, N6A 5C2, Canada. I thank L Ahmad, A. Bera, A. Pagan, C. Robinson, A. Zellner, and the participants of the workshops at the Universities of Chicago, Northern Illinois, Stanford, Riverside and Santa Barbara, for their comments on the subject matter of this paper. The work on this paper was done when the author was a vising scholar at the Stanford University. The SSHRC research grant and research facilities at the Stanford University are gratefully acknowledged.

0377-7332/88/3-4/223-249 $2.50 9 1988 Physica-Verlag, Heidelberg

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