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Moran's I 2-Stage Lasso: for Models with Spatial Correlation and Endogenous Variables

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  • Sylvain Barde
  • Rowan Cherodian
  • Guy Tchuente

Abstract

We propose a novel estimation procedure for models with endogenous variables in the presence of spatial correlation based on Eigenvector Spatial Filtering. The procedure, called Moran's $I$ 2-Stage Lasso (Mi-2SL), uses a two-stage Lasso estimator where the Standardised Moran's I is used to set the Lasso tuning parameter. Unlike existing spatial econometric methods, this has the key benefit of not requiring the researcher to explicitly model the spatial correlation process, which is of interest in cases where they are only interested in removing the resulting bias when estimating the direct effect of covariates. We show the conditions necessary for consistent and asymptotically normal parameter estimation assuming the support (relevant) set of eigenvectors is known. Our Monte Carlo simulation results also show that Mi-2SL performs well against common alternatives in the presence of spatial correlation. Our empirical application replicates Cadena and Kovak (2016) instrumental variables estimates using Mi-2SL and shows that in that case, Mi-2SL can boost the performance of the first stage.

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  • Sylvain Barde & Rowan Cherodian & Guy Tchuente, 2024. "Moran's I 2-Stage Lasso: for Models with Spatial Correlation and Endogenous Variables," Papers 2404.02584, arXiv.org.
    • Handle: RePEc:arx:papers:2404.02584
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    4. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    5. Xiaodong Liu & Lung-Fei Lee, 2013. "Two-Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 734-753, August.
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