Inference on higher-order spatial autoregressive models with increasingly many parameters

This paper develops consistency and asymptotic normality of parameter estimates for a higher-order spatial autoregressive model whose order, and number of regressors, are allowed to approach infinity slowly with sample size. Both least squares and instrumental variables estimates are examined, and the permissible rate of growth of the dimension of the parameter space relative to sample size is studied. Besides allowing the number of parameters to increase with the data, this has the advantage of accommodating some asymptotic regimes that are suggested by certain spatial settings, several of which are discussed. A small empirical example is also included, and a Monte Carlo study analyses various implications of the theory in finite samples.