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 sometimes there 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. [Supplemental materials are available for this article. Go to the publisher's online edition of Econometric Reviews for the following free supplemental resources: two appendices containing additional results from this article.]Efficiency, Efficiency bounds, Instrumental variables, Optimal instrument, Stationary time series,

Estimating Discount Functions with Consumption Choices over the Lifecycle

“…for our baseline estimates. Many authors have found optimally-weighted GMM procedures lead to biased estimates in small samples (e.g., Altonji and Segal, 1996;West et al, 2009). An important advantage of diagonal weighting matrices is that the contribution of each moment to q (θ, χ) can be easily computed.…”