Optimal Instrumental Variables Generators Based on Improved Hausman Regression, with an Application to Hedge Funds Returns

This paper proposes new Hausman-based estimators lying on cumulants optimal instruments. Using these new generated strong instruments in a GMM setting, we obtain new GMM estimators which we call GMM-C and its homologue, the GMM-hm. This procedure improves the method of moments for identifying the parameters of a model. Also, our study gives way to a new indicator signalling the presence of specification errors in financial models. We apply our battery of tests and estimators to a sample of 22 HFR hedge fund indices observed monthly over the period 1990-2005. Our tests reveal that specification errors corrupt parameters estimation of financial models of returns. Therefore, it is not surprising that the ranking of hedge funds is very sensitive to the choice of estimators. Our new indicator of specification errors reveals itself very powerful to detect those errors.