Cointegration, seasonality, encompassing, and the demand for money in the UK
Neil R. Ericsson, David F. Hendry and Hong-Anh Tran*
Virtually all previous narrow money demand studies for the United Kingdom have used seasonally adjusted data for money, prices and expenditure. This paper develops a constant, data-coherent M1 demand equation for the United Kingdom with seasonally unadjusted data. For that model, we address issues of cointegra-tion, error correction, general-to-specific modelling, dynamic specification, model evaluation and testing, parameter constancy and exogeneity. We also establish theoretical and empirical relationships between seasonally adjusted and unadjusted data, and so between models using those data. Finally, we derive and implement encompassing tests for comparing models using adjusted data with models using unadjusted data. Unlike the 'standard' encompassing framework, variance dominance is not always a necessary condition for encompassing.
Wallis ( 1974) and Sims ( 1974) examine the effects of seasonal adjustment when estimating econometric relationships. Wallis considers the implications of estimation with seasonally adjusted data when the underlying economic relation involves the unadjusted data. Sims investigates the converse situation, in which the____________________