Estimation and inference in spatial models with dominant units

Estimation and inference in the spatial econometrics literature are carried out assuming that the matrix of spatial or network connections has uniformly bounded absolute column sums in the number of cross-section units, n. In this paper, we consider spatial models where this restriction is relaxed. The linear-quadratic central limit theorem of Kelejian and Prucha (2001) is generalized and then used to establish the asymptotic properties of the GMM estimator due to Lee (2007) in the presence of dominant units. A new Bias-Corrected Method of Moments estimator is also proposed that avoids the problem of weak instruments by self-instrumenting the spatially lagged dependent variable. Both estimators are shown to be consistent and asymptotically normal, depending on the rate at which the maximum column sum of the weights matrix rises with n. The small sample properties of the estimators are investigated by Monte Carlo experiments and shown to be satisfactory. An empirical application to sectoral price changes in the US over the pre- and post-2008 financial crisis is also provided. It is shown that the share of capital can be estimated reasonably well from the degree of sectoral interdependence using the input-output tables, despite the evidence of dominant sectors being present in the US economy.