  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.
