Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T18:28:47.886Z Has data issue: false hasContentIssue false
  • English
  • Français

THE FORM OF THE OPTIMAL NONLINEAR INSTRUMENT FOR MULTIPERIOD CONDITIONAL MOMENT RESTRICTIONS

Published online by Cambridge University Press:  06 June 2003

Stanislav Anatolyev
Stanislav Anatolyev
Affiliation:
New Economic School
Get access Rights & Permissions [Opens in a new window]

Abstract

We present the form of the optimal instrument in a system of multiperiod conditional moment restrictions in the presence of conditional heteroskedasticity. Using Hansen's (1985, Journal of Econometrics 30, 203–228) and Hansen, Heaton, and Ogaki's (1988, Journal of the American Statistical Association 83, 863–871) work on efficiency bounds for generalized method of moments estimators, we show that this form is an autoregressive recurrence parametrized by a few auxiliary processes that are defined through a system of nonlinear stochastic restrictions, with a stability condition among them. In general, the system does not allow inversion and obtaining an explicit solution for the auxiliary parameters.This is a part of my Ph.D. dissertation (Anatolyev, 2000). I am grateful to Kenneth West for introducing me to the subject and providing advice and encouragement. I also thank Bruce Hansen, Yuichi Kitamura, seminar participants at Indiana University, Pennsylvania State University, Rutgers University, University of British Columbia, University of Virginia, and University of Wisconsin, the co-editor Richard Smith, and two referees for helpful comments and suggestions. Research for this paper was supported in part by a fellowship from the Economics Education and Research Consortium, with funds provided by the government of Sweden through the Eurasia Foundation. The opinions expressed in this paper are those of the author and do not necessarily reflect the views of the government of Sweden, the Eurasia Foundation, or any other member of the Economics Education and Research Consortium.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 4 , August 2003 , pp. 602 - 609
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anatolyev, S. (2000) Optimal Instrumental Variables Estimation in Stationary Time Series. Ph.D. dissertation, University of Wisconsin-Madison.
Bougerol, P. & N. Picard (1992) Strict stationarity of generalized autoregressive processes. Annals of Probability 20, 1714–1730.Google Scholar
Brandt, A. (1986) The stochastic equation Yn+1 = AnYn + Bn with stationary coefficients. Advances in Applied Probability 18, 211–220.Google Scholar
Chamberlain, G. (1987) Asymptotic efficiency in estimation with conditional moment restrictions. Journal of Econometrics 34, 305–334.Google Scholar
Eichenbaum, M.S., L.P. Hansen, & K.J. Singleton (1988) A time series analysis of representative agent models of consumption and leisure choice under uncertainty. Quarterly Journal of Economics 103, 51–78.Google Scholar
Gordin, M.I. (1969) The central limit theorem for stationary processes. Soviet Mathematics Doklady 10, 1174–1176.Google Scholar
Hall, R.E. (1988) Intertemporal substitution in consumption. Journal of Political Economy 96, 339–357.Google Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.Google Scholar
Hansen, L.P. (1985) A method for calculating bounds on the asymptotic variance-covariance matrices of generalized method of moments estimators. Journal of Econometrics 30, 203–228.Google Scholar
Hansen, L.P., J.C. Heaton, & M. Ogaki (1988) Efficiency bounds implied by multiperiod conditional moment restrictions. Journal of the American Statistical Association 83, 863–871.Google Scholar
Hansen, L.P & R.J. Hodrick (1980) Forward exchange rates as optimal predictors of future spot rates: An econometric analysis. Journal of Political Economy 88, 829–853.Google Scholar
Hansen, L.P. & K.J. Singleton (1996) Efficient estimation of linear asset pricing models with moving-average errors. Journal of Business and Economic Statistics 14, 53–68.Google Scholar
Hayashi, F. & C. Sims (1983) Nearly efficient estimation of time series models with predetermined, but not exogenous, instruments. Econometrica 51, 783–798.Google Scholar
Heaton, J.C. & M. Ogaki (1991) Efficiency bounds calculations for a time series model, with conditional heteroskedasticity. Economics Letters 35, 167–171.Google Scholar
West, K.D. & D.W. Wilcox (1996) A comparison of alternative instrumental variables estimators of a dynamic linear model. Journal of Business and Economic Statistics 14, 281–293.Google Scholar