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Semiparametric Estimation in Time Series of Simultaneous Equations

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Abstract

A system of vector semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are strictly exogenous and represent trends. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary time series. This framework allows for the nonparametric treatment of stochastic trends and subsumes many practical cases. Semiparametric least squares (SLS) estimation is considered and its asymptotic properties are derived. Due to endogeneity in the parametric regressors, SLS is generally inconsistent for the parametric component and a semiparametric instrumental variable least squares (SIVLS) method is proposed instead. Under certain regularity conditions, the SIVLS estimator of the parametric component is shown to be consistent with a limiting normal distribution that is amenable to inference. The rate of convergence in the parametric component is the usual /n rate and is explained by the fact that the common (nonlinear) trend in the system is eliminated nonparametrically by stochastic detrending.

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1769.

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Length: 50 pages
Date of creation: Sep 2010
Date of revision:
Publication status: Published in Journal of Econometrics (September 2013), 176(1): 59–79
Handle: RePEc:cwl:cwldpp:1769

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Simultaneous equation; Stochastic detrending; Vector semiparametric regression;

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  1. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
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