An Efficient, Three-Step Algorithm for Estimating Error-Correction Models with an Application to the U.S. Macroeconomy

This paper describes a three-step algorithm for estimating a system of error-correction equations that can be easily programmed using least-squares procedures. Nonetheless, the algorithm is both statistically and computationally efficient and when iterated gives maximum likelihood estimates of cointegration effects. Most important, the algorithm can handle different levels of cointegration, over-identified systems, breaks in trend, and complicated specifications for the short-run dynamics. The procedure is demonstrated with some small macroeconometric models, which suggest that breaks in the long-run trends for output and money are both statistically and economically significant in the 1961-94 period