Working papers / Rutgers University, Department of Economics 2004,21
This paper analyzes the conditions under which consistent estimation can be achieved in instrumental Variables (IV) regression when the available instruments are weak, in the local-to-zero sense of Staiger and Stock (1997) and using the many-instrument framework of Morimune (1983) and Bekker (1994). Our analysis of an extended k-class of estimators that includes Jackknife IV (JIVE) establishes that consistent estimation depends importantly on the relative magnitudes of rn, the growth rate of the concentration parameter, and Kn, the number of instruments: In particular, LIML and JIVE are consistent when (Kn)5 /rn goes to zero, while two-stage least squares is consistent only if (Kn)5 /rn goes to zero, as n goes to infinity. We argue that the use of many instruments may be beneficial for estimation, as the resulting concentration parameter growth may allow consistent estimation, in certain cases.
instrumental variables k-class estimators local to zero framework pathwise asymptotics weak instruments