Automatic Structure Identification of Semiparametric Spatial Autoregressive Model Based on Smooth-Threshold Estimating Equation

Abstract

Issues concerning spatial dependence among cross-sectional units in econometrics have received more and more attention, while in statistical modeling, rarely can the analysts have a priori knowledge of the dependency relationship of the response variable with respect to independent variables. This paper proposes an automatic structure identification and variable selection procedure for semiparametric spatial autoregressive model, based on the generalized method of moments and the smooth-threshold estimating equations. The novel method is easily implemented without solving any convex optimization problems. Model identification consistency is theoretically established in the sense that the proposed method can automatically separate the linear and zero components from the varying ones with probability approaching to one. Detailed issues on computation and turning parameter selection are discussed. Some Monte Carlo simulations are conducted to demonstrate the finite sample performance of the proposed procedure. Two empirical applications on Boston housing price data and New York leukemia data are further considered.

Keywords

Semiparametric spatial autoregressive model / Generalized method of moments / Automatic structure recovery / Smooth-threshold estimating equation / Consistency