Anatolyev, Stanislav (2003) "The form of the optimal nonlinear instrument for multiperiod conditional moment restrictions", Econometric Theory, Vol. 19, No. 4, pp. 602–609
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.
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Indiana University, USA
Pennsylvania State University, USA
Rutgers University–New Brunswick, USA
University of British Columbia, Canada
University of Virginia, USA
University of Wisconsin–Madison, USA
Bruce E. Hansen and Kenneth D. West (2005) "Generalized Method of Moments and Macroeconomics", Journal of Business and Economic Statistics, Vol. 20, pp. 460-469.