PREDICTION WITH A LINEAR-REGRESSION MODEL AND ERRORS IN A REGRESSOR

The subject under study is prediction with a simple linear regression model in the presence of errors in variables. The paper focuses on the case of a non-stochastic true regressor (x). For a wide range of true x-values around the mean of x in the estimation period, predictions based on OLS on the observed variables is to be preferred in terms of MSE to a predictor based on consistent estimation of the parameters. This can be so also when x follows a trend and predictions are made for the next observation. When the error variance of the regressor in the prediction period differs from the mean error variance in the estimation period sample, a predictor based on a modified OLS estimator, adjusted for that difference, behaves like the OLS predictor in the case of equal error variances.