Polynomial regression with normal covariate measurement error
نویسنده
چکیده
This paper derives the exact functional form of an error contaminated regression function when the error free regression is a polynomial function of error free covariates (discrete or continuous) which are contaminated by normally distributed measurement error, with coe¢cients which may be arbitrary functions of error free covariates. The form of higher order central moment error contaminated regressions is examined and by way of example the form of normal measurement error induced heteroskedasticity when the error free regression is linear and homoskedastic is derived. The results of this paper may provide at least a partial explanation of mild non-linearity and heteroskedasticity found in applied econometric work with survey data when error contamination, e.g. of income and expenditure data, is likely. The error contaminated regression function is completely determined by the coe¢cients in the error free regression, the measurement error variance and the density of the observed covariates. This density can be estimated, opening the way to estimation of error free regression functions using only data on the response and the error contaminated covariate, to investigation of the potential impact of measurement error on structural error free regressions and to the development of speci...cation tests sensitive to unmodelled measurement error.
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