Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments

Abstract

We propose and evaluate a technique for instrumental variables estimation of linear models with conditional heteroskedasticity. The technique uses approximating parametric models for the projection of right hand side variables onto the instrument space, and for conditional heteroskedasticity and serial correlation of the disturbance. Use of parametric models allows one to exploit information in all lags of instruments, unconstrained by degrees of freedom limitations. Analytical calculations and simulations indicate that there sometimes are large asymptotic and finite sample efficiency gains relative to conventional estimators (Hansen (1982)), and modest gains or losses depending on data generating process and sample size relative to quasi-maximum likelihood. These results are robust to minor misspecification of the parametric models used by our estimator.

Econometricians Have Their Moments: GMM at 32

“…for known observed variables w but unknown d (Á), Newey (1990) shows that the optimal instrument can be constructed via nonparametric estimation of d(w) using nearest neighbour and series approximation methods. In time series settings, the form of the optimal instrument depends additionally on the dynamic structure of the data (see also Hayashi and Sims (1983); Hansen et al, 1988;Heaton & Ogaki, 1991;Anatolyev, 2003;West et al, 2009). While attractive in principle, economic models often do not specify the aspects of the data generation process needed to construct the optimal instrument.…”

“…case in whichfor known observed variables w but unknown d (·), Newey () shows that the optimal instrument can be constructed via nonparametric estimation of d ( w ) using nearest neighbour and series approximation methods. In time series settings, the form of the optimal instrument depends additionally on the dynamic structure of the data (see also Hayashi and Sims (); Hansen et al ., ; Heaton & Ogaki, ; Anatolyev, ; West et al ., ).…”