Simple many-instruments robust standard errors through concentrated instrumental variables

- Concentrated Instrumental Variables (CIV) are proposed as an alternative to LIML.
- Reformulating LIML through CIV leads to simple many-instruments robust standard errors.
- A two-step, 2SLS-based estimator is proposed that is almost as good as LIML.

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.