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Higher Order Approximation of IV Estimators with Invalid Instruments

Research output: Working paper

Published
Publication date12/2018
Place of PublicationLancaster
PublisherLancaster University, Department of Economics
Original languageEnglish

Publication series

NameEconomics Working Papers Series

Abstract

This paper considers the instrument selection problem in instrumental
variable (IV) regression model when there is a large set of instruments with potential invalidity. I derive higher-order mean square error (MSE) approximation of two-stage least squares (2SLS), limited information maximum likelihood (LIML), Fuller (FULL) and bias-adjusted 2SLS (B2SLS) estimators with allowing for local violation of the instrument-exogeneity conditions. Based on the approximation to the higher-order MSE, I propose instrument selection criteria that are robust to potential invalidity of instruments. Furthermore, I also show the optimality results of instrument selection criteria in Donald and Newey (2001, Econometrica) under faster than N^(-1/2) locally invalid instruments specication.