Estimation of semiparametric varying-coefficient spatial autoregressive models with missing in the dependent variable

This paper investigates estimation of semiparametric varying-coefficient spatial autoregressive models in which the dependent variable is missing at random. An inverse propensity score weighted sieve two-stage least squares (S-2SLS) estimation with imputation is proposed. The proposed estimators are shown to be consistent, no matter the initial value is taken as the naive S-2SLS estimate or the naive nonlinear least squares estimate, and the asymptotic distribution of the latter is also derived. Simulation studies are carried out to investigate the performance of the proposed estimator. The method is finally exemplified with one real data set on Boston housing prices.