The estimators of random coefficient models

Abstract

This thesis concentrates on the estimators of Random Coefficient models. A Bayesian estimator with non-standard posterior density implementing Griddy Gibbs Sampler technique for Hildreth-Houck type Random Coefficient Model is introduced and it is compared with a range of existing estimators for Random Coefficient models. Monte Carlo experiments are used for comparing this estimator with Swamy and Tinsley (1980), Method of Moments and Zaman (1998) Modified Maximum Likelihood estimators on the basis of biases, Mean Square Errors and efficiencies of parameter estimates. The results show that performances of estimators are affected by sample size, balance of design matrix and variance structure of stochastic regression coefficients. In most of the cases estimates for variance parameter of regression coefficients are seriously biased for all estimators expect the Bayesian Griddy Gibbs estimator. The Bayesian Griddy Gibbs and Method of Moments estimators show better performance compared with others, the best one changes in line with some observable and unobservable criteria. In empirical work, using both methods in estimation and selecting the estimates with minimum out of sample forecast Mean Square Error might be recommended. Asymptotically Maximum likelihood estimator is unbiased and achieves Cramer Rao Lower Bound; therefore it can not be improved upon. The finite sample properties of Modified Maximum Likelihood estimator are studied with a separate Monte Carlo study and it is shown that except very high sample sizes relative to the dimension of the problem there is substantial room for improvement of the Modified Maximum Likelihood estimator in finite samples.