Instrumental variables (IV) and Generalized Method of Moments (GMM) estimators are widely used in applied economics to estimate causal or structural effects. The precision of estimates from these estimators is frequently a concern. Often many instruments are used in an effort to improve precision, leading to bias or poor distributional approximations. Therefore improving the precision of these estimators will vastly improve inference in economics and therefore improve the conduct of applied econometrics and the policy conclusions that derive from such studies. The proposed research will develop better estimators and better measures of precision for IV and GMM estimators. The proposed research consists of two projects: (i) instrumental variables with heteroskedasticity and (ii) GMM in time series. This research will combine forward and reverse versions of jackknife instrumental variable estimators and develop an IV estimator, with many instruments, that is robust to heteroskedasticity. The research will also develop new time series GMM estimator that is based on bias correcting the GMM objective function.
The result of this research will lead to quantum improvements in inferences of causal and structural effects. Estimating such effects is the most common goal of economic empirical work. Consequently this work should have a wide impact on empirical work in economics and the policy conclusions that are derived from such empirical work. For example, the use of heteroskedasticity consistent standard errors is very common in applied work. This project will provide such for instrumental variable estimators with many instruments. Also GMM estimators with many instruments (formed from lags) are often used in time series. This work will provide more accurate methods for these applications. The wider impact of the proposed activity would be its effect on instrumental variables estimation in other disciplines, including biostatistics and political science. In biostatistics these estimators are used to determine experimental effects of treatments of various kinds when subjects can self select out of treatment. The proposed research could improve causal inferences in this very important work.
