Optimality of the quasi-score estimator in a mean–variance model with applications to measurement error models

We consider a regression of y$y$ on x$x$ given by a pair of mean and variance functions with a parameter vector θ$\theta$ to be estimated that also appears in the distribution of the regressor variable x$x$. The estimation of θ$\theta$ is based on an extended quasi-score (QS) function. We show that the QS estimator is optimal within a wide class of estimators based on linear-in-y$y$ unbiased estimating functions. Of special interest is the case where the distribution of x$x$ depends only on a subvector α$\alpha$ of θ$\theta$, which may be considered a nuisance parameter. In general, α$\alpha$ must be estimated simultaneously together with the rest of θ$\theta$, but there are cases where α$\alpha$ can be pre-estimated. A major application of this model is the classical measurement error model, where the corrected score (CS) estimator is an alternative to the QS estimator. We derive conditions under which the QS estimator is strictly more efficient than the CS estimator.     

GEE estimation of the covariance structure of a bivariate panel data model with an application to wage dynamics and the incidence of profit-sharing in West Germany

We propose a generalized estimating equations (GEE) approach to the estimation of the mean and covariance structure of bivariate time series processes of panel data. The one-step approach allows for mixed continuous and discrete dependent variables. A Monte Carlo Study is presented to compare our particular GEE estimator with more standard GEE-estimators. In the empirical illustration, we apply our estimator to the analysis of individual wage dynamics and the incidence of profit-sharing in West Germany. Our findings show that time-invariant unobserved individual ability jointly influences individual wages and participation in profit sharing schemes.