Discussiones Mathematicae Probability and Statistics 20(1) (2000) 63-83

Ansgar Steland

*Europeau University Frankfurt (Oder)
D-15207 Frankfurt (Oder) Germany*

Generalized Methods of Moments (GMM) estimators are a popular tool in econometrics since introduced by Hansen (1982), because this approach provides feasible solutions for many problems present in economic data where least squares or maximum likelihood methods fail when naively applied. These problems may arise in errors-in-variable regression, estimation of labor demand curves, and asset pricing in finance, which are discussed here.

In this paper we study a GMM estimator for the rank modelingapproach (RMA), which analyzes the ordinal structure of a response variable. Assuming m-dependent data consistency and asymptotic normality of the proposed estimator are shown including the important case that the instruments depend on lagged regressors.Consistent estimators for the asymptotic covariance matrices are proposed. Further, the construction of minimum variance RMA-GMM estimators is discussed. Finite sample properties are studied by a small simulation study.

**Keywords:** asset pricing, labor demand curves, nonparametric regression; rank
statistics; minimum variance estimation.

**1991 Mathematics Subject Classifications:** 62G05, 62G10.

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Received 26 November 1998

Revised 29 September 1999