Economics Letters 6 (I 980) 119- 123 North-Holland Publishing Company 119 zyxwvutsrqpo ESTIMATING THE COVARIANCE MATRIX FOR REGRESSION MODELS WITH AR(l) ERRORS AND LAGGED DEPENDENT VARIABLES * Russell DAVIDSON and James G. MacKINNON Queen’s Utuoersity, Kingston, Ont., Cunada K7L 3N6 Received 29 December 1980 We propose a simple procedure, based on an artificial linear regression, for consistently estimating the covariance matrix of the parameter estimates for linear regression models with serially correlated errors and lagged dependent variables. 1. Introduction Consider a linear regression model with errors which follow a first- order autoregressive process: Yr = X,P+ u,, u, =PUt-l +c,, Et - N(O,c?). (1) Here y, denotes an observation on a dependent variable at time t, (t = 1. . . n), X, denotes a vector of observations on independent variables, and p and p denote respectively a scalar and a (k - 1)-vector of unknown parameters. Most of the procedures to estimate this model which are incorporated into present-day regression packages estimate b conditional on fi by OLS regression, and provide as an estimate of the variance- covariance matrix of j!? the OLS estimate conditional on 6. Such an estimate is asymptotically valid if X, does not contain lagged values of y,, because in that case the information matrix is block diagonal between /I and 6. But as Cooper (1972) has shown, conditional estimates of the * We would like to thank David Backus, Gordon Fisher, Allan Gregory and Michael McAleer for comments on an earlier draft. This research was supported, in part, by the Social Sciences and Humanities Research Council of Canada. 0165-1765/81/0000-0000/$02.50 0 North-Holland