Stochastic Restricted Biased Estimators in misspecified regression model with incomplete prior information

In this article, the analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted Principal Component Regression Estimator (SRPCR), Stochastic Restricted r-k class estimator (SRrk) and Stochastic Restricted r-d class estimator (SRrd) were examined in the misspecified regression model due to missing relevant explanatory variables when incomplete prior information of the regression coefficients is available. Further, the superiority conditions between estimators and their respective predictors were obtained in the mean square error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo simulation study were used to illustrate the theoretical findings.Comment: 35 Pages, 6 Figure

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution

Imposing Observation-Varying Equality Constraints Using Generalised Restricted Least Squares

Linear equality restrictions derived from economic theory are frequently observation-varying. Except in special cases, Restricted Least Squares (RLS) cannot be used to impose such restrictions without either underconstraining or overconstraining the parameter space. We solve the problem by developing a new estimator that collapses to RLS in cases where the restrictions are observation-invariant. We derive some theoretical properties of our so-called Generalised Restricted Least Squares (GRLS) estimator, and conduct a simulation experiment involving the estimation of a constant returns to scale production function. We find that GRLS significantly outperforms RLS in both small and large samples.

Asymptotic optimality of the quasi-score estimator in a class of linear score estimators

We prove that the quasi-score estimator in a mean-variance model is optimal in the class of (unbiased) linear score estimators, in the sense that the difference of the asymptotic covariance matrices of the linear score and quasi-score estimator is positive semi-definite. We also give conditions under which this difference is zero or under which it is positive definite. This result can be applied to measurement error models where it implies that the quasi-score estimator is asymptotically more efficient than the corrected score estimator