Using many valid instrumental variables has the potential to improve efficiencybut makes the usual inference procedures inaccurate. We give corrected standarderrors, an extension of Bekker (1994) to nonnormal disturbances, that adjust formany instruments. We find that this adujstment is useful in empirical work, simulations,and in the asymptotic theory. Use of the corrected standard errors int-ratios leads to an asymptotic approximation order that is the same when thenumber of instrumental variables grow as when the number of instruments is fixed.We also give a version of the Kleibergen (2002) weak instrument statistic that isrobust to many instruments.
Centre for microdata methods and practice