It is not easy to spot clear cases of mean reversion in macroeconomic time-series, even allowing the series to revert to some deterministic trend rather than a fixed mean. At the same time, macroeconomic series do not usually drift apart for too long; they seem to be driven by the same fluctuating trends. Developing methods for time-series analysis suggest that there is potentially much to gain, in a statistical sense, from taking account of these common fluctuating trends. In applications of these time-series methods, the estimated long-run (`cointegration') relations are often interpreted as reflecting equilibrium relations, and what is left over is consequently viewed as indications of temporary disequilibria. Empirical analyses often focus on the long-run relations, while the short-run fluctuations are regarded as being fairly uninteresting and/ or inexplicable.

In Discussion Paper No. 1120, Research Affiliate Paul Söderlind and Anders Vredin use simulations of the model to illustrate that imposing simple economic restrictions can significantly improve the performance of statistical methods, at least for the kind of sample sizes that are available to macroeconomists. They show three things. First, tests of long-run relations have much to gain from imposing the number of common trends. Second, the precision of short-run forecasts is not particularly improved by imposing the correct long-run relations, but this changes as the forecasting horizon becomes longer. Third, identification of shocks to the economy, based on imposing long-run restrictions on estimated systems of equations, seems to face a trade-off: the short-run movements are better captured without imposing further restrictions, while the opposite holds for medium- and long-term movements.

Applied Cointegration Analysis in the Mirror of Macroeconomic Theory
Paul Söderlind and Anders Vredin

Discussion Paper No. 1120, January 1995 (IM)