Abstract
The vast majority of spatial econometric research relies on the assumption that the spatial network structure is known a priori. This study considers a two-step estimation strategy for estimating the n(n-1) interaction effects in a spatial autoregressive panel model where the spatial dimension is potentially large. The identifying assumption is approximate sparsity of the spatial weights matrix. The proposed estimation methodology exploits the Lasso estimator and mimics two-stage least squares (2SLS) to account for endogeneity of the spatial lag. The developed two-step estimator is of more general interest. It may be used in applications where the number of endogenous regressors and the number of instrumental variables is larger than the number of observations. We derive convergence rates for the two-step Lasso estimator. Our Monte Carlo simulation results show that the two-step estimator is consistent and successfully recovers the spatial network structure for reasonable sample size, T.
Highlights
This study proposes an estimator, based on the Lasso estimator, for an approximately sparse spatial weights matrix in a high-dimensional setting
The vast majority of spatial econometric research relies on the assumption that the spatial weights matrix, Wn, which measures the strength of interactions between units, is known a priori
The choice of spatial weights has been a focus of criticism of spatial econometric methods, since estimation results highly depend on the researcher’s specification of the spatial weights matrix [1,2,3]
Summary
This study proposes an estimator, based on the Lasso estimator, for an approximately sparse spatial weights matrix in a high-dimensional setting. Estimation of the spatial weights matrix in a low-dimensional small n panel, under different structural assumptions on the autocovariances or using moment conditions is discussed in [7,8]. Bailey et al [9] consider sparsity of the spatial weights matrix as an alternative identification assumption based on a large T panel setting and the spatial error model. There are a few previous studies which apply Lasso-type estimators to high-dimensional spatial panel models and assume sparsity..
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