Three Essays in Econometric Methods

In this document I present three essays that comprise my doctoral dissertation. These essays are positioned in the area of inference with instrumental variables setups and model and moment selection. In the first essay the problem of empirical inference in instrumental variables (iv) setups where the instruments do that do not perfectly satisfy the exclusion restriction is studied. The fractionally resampled Anderson-Rubin Berkowitz et al (2012) [Journal of Econometrics, Vol. 166, pp. 255--266 (2012)] is applied under different scenarios of correlation between the instruments and the structural variables and used to find empirical bounds to the subsampling blocks that allows to perform valid inference over the structural parameters. In the second paper the relative performance of several moment selection criteria currently used in the literature is compared in terms of (1) how accurate is the moment selection and (2) how good is the post-estimation performance in term of bias and root mean square errors. The analysis is performed under different correlation structures in the presence of fixed and diverging number of moments. In the third paper an alternative estimator to the one in Lee et al (2014) [ Journal of the Royal Statistical Society: Series B, forthcoming] is proposed. This estimator can find the variables that switch the regimes consistently in a linear setup. The paper starts by showing that the linfinity bound can be represented as a multiple of the lasso tuning parameter and then this bound is used in a thresholded lasso-type estimator. This estimator achieves a better performance that the estimator in Lee et al (2014) in finding the correct model.