Omitted variables,variability of estimated parameters and the appearance of autocorrelated disturbances

This paper shows that in a standard regression model with omitted variables, the OLS formula for the estimated variance matrix of the regression coefficients is more likely to underestimate the appropriate criterion of estimator reliability which is the Mean Square Errors matrix. Using examples of two and three regressor models, we show that overestimation, though possible, occurs in rather special cases. Throughout, our analysis is contrasted with that of Chaudhuri (1977) and clarifies some ambiguities of that paper. Finally, we disagree with Chaudhuri who distinguishes between the corresponding coefficients in the correct and the misspecified models. This distinction is inappropriate and leads to a misplaced criticism of some GLS variants when errors are serially correlated. A first-order Markov process is an inexact representation of serial correlation which is due to omitted regressors.