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Econometrics 2015, 3(1), 128-155; doi:10.3390/econometrics3010128

Two-Step Lasso Estimation of the Spatial Weights Matrix

Spatial Economics and Econometrics Centre (SEEC), Heriot-Watt University, Edinburgh, Scotland EH14 4AS, UK
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Academic Editor: Kerry Patterson
Received: 31 October 2014 / Accepted: 11 February 2015 / Published: 9 March 2015
(This article belongs to the Special Issue Spatial Econometrics)
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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. View Full-Text
Keywords: lasso; endogeneity; unkown W; spatial weights matrix lasso; endogeneity; unkown W; spatial weights matrix
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ahrens, A.; Bhattacharjee, A. Two-Step Lasso Estimation of the Spatial Weights Matrix. Econometrics 2015, 3, 128-155.

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