In a weak and many instruments setting, 2SLS can be severely biased towards OLS and the standard errors can be way too small. LIML is an attractive alternative, especially when the many-instruments robust (MIR) standard errors are used as proposed by Bekker (1994).
In this note we present an alternative approach to LIML through concentrated instrumental variables (CIV). This is a class of instrumental variables indexed by a single parameter. When this parameter belongs to a certain set, 2SLS estimators using CIV instruments, are many-instruments consistent. We refer to them as CIV estimators. Moreover, the usual expression for the asymptotic variance of IV estimators is many instruments consistent. One particular choice of CIV parameter, within this set, yields LIML. We thus get an alternative to the many-instruments robust (MIR) standard errors of Bekker (1994) that is of the usual simple IV form.
As a byproduct, we present a new estimator, which we call the CIVE. This is a two-step estimator where the CIV parameter is based on 2SLS in the first step. It avoids LIML but is equally good to a very high degree. This suggests a simple MIR estimation strategy in an weak and many instruments setting: do 2SLS to obtain the CIV parameter, and then obtain the CIVE by another 2SLS step. (C) 2016 Elsevier B.V. All rights reserved.
- Weak instruments
- Concentrated instruments