Instrumental variables estimation of heteroskedastic linear models using all lags of instruments

estimation;linear models

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

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,

Testing Conditional Uncorrelatedness

We propose a nonparametric test for conditional uncorrelatedness in multiple-equation models such as seemingly unrelated regressions (SURs), multivariate volatility models, and vector autoregressions (VARs). Under the null hypothesis of conditional uncorrelatedness, the test statistic converges to the standard normal distribution asymptotically. We also study the local power property of the test. Simulation shows that the test behaves quite well in finite samples.