Near Unit Root in the Spatial Autoregressive Model

<title>Abstract</title> This paper studies the spatial autoregressive (SAR) model for cross-sectional data when the coefficient of the spatial lag of the dependent variable is near unity. We decompose the data generating process into an unstable component and a stable one, and establish asymptotic properties of QMLE, 2SLSE and linearized QMLE of the parameters. The estimator for the spatial effect has a higher rate of convergence, and the estimators for other parameters have the regular <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="rsea_a_760134_o_ilm0001.gif"/> </inline-formula> rate. The higher rate of convergence reflects how fast the spatial root converges to unity. In contrast to near unit root in time series, the estimators are all asymptotically normal. Similarly to the regular SAR model, QMLE and linearized QMLE are more efficient than 2SLSE.