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Title: Two stage lasso-based least square estimation of spatial autoregressive model with many instrument variables Authors:  Pu Wang - The University of Hong Kong (China) [presenting]
Abstract: A lasso and post-lasso based two stage least square estimation of spatial autoregressive models are studied when some or all regressors are endogenous in the presence of many instruments. In order to handle the bias-variance trade off caused by many instruments, we use Lasso and post Lasso methods in the first-stage to find the most informative instruments and obtain prediction of conditional expectations of endogenous variables given instruments. We show that if the conditional expectation is approximate sparse, i.e., only a small set of instruments can explain the most portion of conditional expectation, our Lasso based estimation is root n consistent and asymptotically normal. The method will be valid even when the number of instruments increases at the same rate or faster than the sample size.