Long lags or seasonal mis-specification? A note on co-integration testing and the consumption function

Abstract

Writing in this journal, Sumner (2004) advocates use of long lag lengths when conducting co-integration tests. Replication of Sumner's consumption model suggests long lag lengths are a mis-specification: the true underlying model is periodic. We test for periodically distributed unit roots – unit roots that differ with the season and vary with past behaviour. Co-integration between income and consumption, based on a periodic error correction model, is rejected. A PADL specification is preferred for modelling the income–consumption relationship, using seasonally unadjusted data.

Acknowledgements

We are indebted to M. Sumner for his seasonally unadjusted data (1963q1 to 1996q4 at 1990 prices) and welcome discussion of these issues. Statistical analysis used Shazam Econometrics Computer Program Version 7, Microfit Version 4.1, Microsoft Excel, Open Office and Lotus 1-2-3.

Notes

¹ A periodically distributed unit root has other applications: on a lighter (or perhaps darker) note, Vampires venture forth regularly throughout the year and presumably their lust for blood is related to the degree of satiation derived from human victims on previous forays (Hartl et al., 1992).

² Adding one extra lag when testing, as per Dolado and Lütkepohl (1996).