An efficient residual-adjusted two-step estimator for a SARAR model

This article proposes an efficient two-step estimator for a spatial autoregressive (SAR) model with SAR disturbances (SARAR). By leveraging the residual-adjusted estimation framework of Hatanaka (1974, 1976) and Dhrymes (1974), our estimator achieves asymptotic efficiency comparable to the quasi-maximum likelihood estimator (QMLE) or the best generalized method of moments estimator (BGMME) in Liu, Lee, and Bollingerm (2010), while significantly reducing computational complexity and execution time. Monte Carlo simulations demonstrate the superior performance of our numerical procedure across both small and relatively large sample sizes. An empirical application to U.S. county-level homicide data reveals significant positive spatial spillover effects, highlighting the critical need for multi-regional collaboration in crime prevention and economic development policies to reduce homicide rates.