Rates of convergence for estimating regression coefficients in heteroskedastic discrete response models
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In this paper, we consider estimation of discrete response models exhibiting conditional heteroskedasticity of a multiplicative form, where the latent error term is assumed to be the product of an unknown scale function and a homoskedastic error term. It is first shown that for estimation of the slope coefficients in a binary choice model under this type of restriction, the semiparametric information bound is zero, even when the homoskedastic error term is parametrically specified. Hence, it is impossible to attain the parametric convergence rate for the parameters of interest. However, for ordered response models where the response variable can take at least three different values, the parameters of interest can be estimated at the parametric rate under the multiplicative heteroskedasticity assumption. Two estimation procedures are proposed. The first estimator, based on a parametric restriction on the homoskedastic component of the error term, is a two-step maximum likelihood estimators, where the unknown scale function is estimated nonparametrically in the first stage. The second procedure, which does not require the parametric restriction, estimates the parameters by a kernel weighted least-squares procedure. Under regularity conditions which are standard in the literature, both estimators are shown to be √n-consistent and asymptotically normal. © 2003 Elsevier B.V. All rights reserved.
Published Version (Please cite this version)10.1016/S0304-4076(03)00148-9
Publication InfoChen, S; & Khan, S (2003). Rates of convergence for estimating regression coefficients in heteroskedastic discrete response models. Journal of Econometrics, 117(2). pp. 245-278. 10.1016/S0304-4076(03)00148-9. Retrieved from https://hdl.handle.net/10161/1899.
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Professor of Economics
Professor Khan is on leave at Boston College for the 2016-17 academic year.Professor Khan specializes in the fields of mathematical economics, statistics, and applied econometrics. His studies have explored a variety of subjects from covariate dependent censoring and non-stationary panel data, to causal effects of education on wage inequality and the variables affecting infant mortality rates in Brazil. He was awarded funding by National Science Foundation grants for his projects ent