Abstract:
Estimation of the parameters in a system of regression equations are usually being calculated by ordinary least squares, generalized least squares or maximum likelihood estimation. Ordinary least squares estimation is used on the equations separately and produces best, linear and unbiased estimates only if the regression equations are not correlated via the disturbance terms or if the disturbances are not generated by an autoregressive moving average process. <br><br> Generalized least squares and maximum likelihood estimation are applied to the regression equations together and provide best, linear and unbiased estimates. If, however, the covariance matrix of the disturbances is unknown, these two estimation procedures result in numerical optimization procedures. <br><br> In this study it is shown that the Kalman filter, in addition to the state .space approach to a system of equations, is a superior estimation method when correlation among the disturbances of different equations exists.
