Title: Spatial lag model with time-lagged effects and spatial weight matrix estimation
Authors: Clifford Lam - London School of Economics and Political Science (United Kingdom)
Cheng Qian - London School of Economics and Political Science (United Kingdom) [presenting]
Abstract: A spatial lag model is considered which has different spatial weight matrices for different time-lagged spatial effects, while allows both the sample size $T$ and the panel dimension $N$ to grow to infinity together. To overcome potential misspecifications of these spatial weight matrices, we estimate each one by a linear combination of a set of $M$ specified spatial weight matrices, with $M$ being finite. Moveover, by penalizing on the coefficients of these linear combinations, oracle properties for these penalized coefficient estimators are proved, including their asymptotic normality and sign consistency. Other parameters of the model are estimated by profile-least square type of estimators after introducing covariates which serve similar functions as instrumental variables. Asymptotic normality for our estimators are developed under a framework of functional dependence, which is a measure of time series dependence. The proposed methods are illustrated using both simulated and real financial data.