2SIV Estimation of A Dynamic Spatial Panel Data Model with Endogenous Spatial Weight Matrices

The spatial panel data model is a standard tool for analyzing data with both spatial correlation and dynamic dependences among economic units. Conventional estimation methods rely on the key assumption that the spatial weight matrix is strictly exogenous, which would likely be violated in some empirical applications where spatial weights are determined by economic factors. This paper studies the estimation method of a dynamic spatial panel model with individual …xed e¤ects when the time dimension is short. The spatial weight matrices are constructed by some economic variables and can be endogenous and time varying. We establish the consistency and asymptotic normality of the two-stage instrumental variable (2SIV) estimator and investigate their …nite sample properties by a Monte Carlo study. This model is applied to study the …scal interactions among the 91 non-oil countries. JEL classi…cation: C31; C51 Keywords: Spatial panel models; Endogenous spatial weight matrices; Fixed e¤ects 1 Introduction Spatial panel data models are standard tools to analyze data with both cross-sectional and dynamic dependences among economic units. They are generalized from a cross-sectional spatial autoregressive (SAR) model proposed by Cli¤ & Ord (1973). Recently, there is much progress in empirical and theoretical works on spatial panel data models. Static spatial panel data models can be applied to agricultural economics (Druska & Horrace, 2004), transportation research (Frazier & Kockelman, 2005), public economics (Egger et al., 2005), consumer demand (Baltagi & Li 2006), to name a few. Dynamic spatial panel data model can be applied to the growth convergence of countries and regions (Ertur & Koch, 2007), regional markets (Keller & Shiue, 2007), labor economics (Foote, 2007), public economics (Revelli, 2001; Tao, 2005; Franzese, 2007; Michela, 2007), and some other …elds. For the estimation and statistical inference, random e¤ects and …xed e¤ects spatial panel models are most commonly used. For the random e¤ects model, Baltagi et al. (2003, 2007a, 2007b), Mutl (2006) and Kapoor et al. (2007) investigate various speci…cations with error