Abstract
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.
Highlights
Correlation in cross-sectional data poses considerable challenges, complicating both modelling and statistical inference
In this paper we allow the spatial lag order p in (1.1) and the number of regressors k to increase slowly with n, as opposed to being fixed. This scheme reflects the practical reality that the richness of a parametric model often deepens with sample size, and has been explored previously in various settings
Because of endogeneity of the Winyn, i = 1, . . . , pn, IV estimation has been employed for estimation of Spatial autoregressive (SAR) models, and we introduce instruments for the endogenous component Hn
Summary
Correlation in cross-sectional data poses considerable challenges, complicating both modelling and statistical inference. In this paper we allow the spatial lag order p in (1.1) and the number of regressors k to increase slowly with n, as opposed to being fixed This scheme reflects the practical reality that the richness of a parametric model often deepens with sample size, and has been explored previously in various settings. P obtain Win from Vn by replacing each Vjn, j= i, by a matrix of zeros This structure can be thought of as extending a choice of Wn in (1.2) suggested by Case (1991, 1992), where each of p districts contains m farmers, so n = mp, and there is interdistrict independence, implying a block diagonal Wn, and homogeneous within-district reactions, so.
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