Cointegration, Seasonality, Encompassing, and the Demand for Money in the United Kingdom

Abstract

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 cointegration, error correction, general-to-specific modeling, 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.

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