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8. PARAMETER ESTIMATION OF SINGLE-EQUATION MODEL WITH MISSPECIFICATION ERRORS USING FREQUENTIST AND BAYESIAN APPROACHES by A.A. Adepoju and T. P. Ogundunmade Volume 50 (March, 2019 Issue)
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PARAMETER ESTIMATION OF SINGLE-EQUATION MODEL WITH MISSPECIFICATION ERRORS USING FREQUENTIST AND BAYESIAN APPROACHES

A.A. Adepoju and T. P. Ogundunmade

Department of Statistics, University of Ibadan, Ibadan, Nigeria

Abstract

A major assumption underlying the ordinary least squares method and most estimation techniques in general is correct specification of the model, a violation of which leads to some of the inferential methods providing invalid inference. Unfortunately in practice, most economic relationships are often wrongly specified. These errors arise from one or more sources which can take many forms such as misspecification of the error distribution, inclusion of non-influential variables, measurement errors etc. When the specification is incorrect, inconsistent parameter estimates result and subsequent inferences are suspect. Thus, this study considered the estimation of linear model in the presence of measurement errors (or errors-in-variables) and misspecification of the error term using classical and Bayesian approaches. The RESET test for misspecification was used. The OLS, LTS, and GMM methods were compared with the Bayesian estimator. Sample sizes of 20, 30, 50 and 100 were considered to examine the asymptotic properties of these estimators. The results showed that Least Trimmed Squares (LTS) method outperformed the other classical methods while the Bayesian estimator produced better estimates than the classical methods. All the estimators showed consistent asymptotic behaviour with their MSE decreasing as sample size increased. Finally, misspecification of the error term was a more serious and costly error in a linear regression model than misspecification due to errors-in-variables.

Keywords: Misspecification error, Measurement error, Bayesian estimator, GeneralisedMethod of Moment, Trimmed least squares.

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