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Title: Continuously updated indirect inference in SAR models with unobserved heterogeneity Authors:  Peter CB Phillips - Yale University (United States)
Francesca Rossi - University of Southampton (United Kingdom)
Maria Kyriacou - University of Southampton (United Kingdom) [presenting]
Abstract: Spatial units are often heterogeneous as they vary in many of their observed characteristics such as income and so the assumption homoskedasticity may not hold. In the presence of unobserved heterogeneity the (Q)LE of both the spatial parameter and the exogenous regressors coefficients become, in general, inconsistent. There is an evident lack of estimation methods that account for the presence of hetersokedasticity while allowing for a wider class of heteroskedastic designs and also more realistic weight matrix designs. A Robust Generalized Methods of Moments (RGMM) estimator has been previously proposed which is consistent in heteroskeskadic situations. Also a GMM method robust to heteroskedasticity has been considered. Modifying the QMLE/MLE estimator has been proposed to restore consistency under mild forms of heteroskedasticity. There is yet a method that provides finite sample refinements for moderate sample sizes for general forms of hetersoskedasticy without being restrictive in the design of the exogenously given weights matrix. We propose an indirect inference based method robust to unobserved heterogeneity, the Continuously Updated Indirect Inference (CUII) which is derived using a binding function with continuously updated diagonal variance/covariance matrix. Simulation results reveal that our proposed CUII estimator is effective in reducing both bias and MSE compared to QML/ML and the RGMM estimator.