Semiparametric Estimation in Time Series of Simultaneous Equations

Jiti Gao and Peter Phillips

No 1769, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Simultaneous equation; Stochastic detrending; Vector semiparametric regression (search for similar items in EconPapers)
JEL-codes: C23 C25 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2010-09
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Journal of Econometrics (September 2013), 176(1): 59–79

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