Scandinavian Working Papers in Economics

Oslo University, Department of Economics

No 01/2017: Identification and Method of Moments Estimation in Polynomial Measurement Error Models

Erik Biørn ()
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Erik Biørn: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway

Abstract: Estimation of polynomial regression equations in one error-ridden variable and a number of error-free regressors, as well as an instrument set for the former is considered. Procedures for identification, operating on moments up to a certain order, are elaborated for single- and multi-equation models. Weak distributional assumptions are made for the error and the latent regressor. Simple order-conditions are derived, and procedures involving recursive identification of the moments of the regressor and its measurement errors together with the coefficients of the polynomials are considered. A Generalized Method of Moments (GMM) algorithm involving the instruments and proceeding stepwise from the identification procedures, is presented. An illustration for systems of linear, quadratic and cubic Engel functions, with household consumption and income data is given.

Keywords: Errors in variables; Polynomial regression; Error distribution; Identification; Instrumental variables; Method of Moments; Engel functions

JEL-codes: C21; C23; C31; C33; C51; E21

23 pages, January 30, 2017

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