## 1 INTRODUCTION

One of Denis Sargan's lasting contributions to macroeconometric modelling is the idea of separating the long run from the short run when formulating dynamic relationships between economic variables; see Sargan (1964). The error-correction model has since gained widespread popularity which has been further enhanced by the emergence of the theory of cointegrated variables. In the meantime, the basic error-correction model has been extended by introducing the possibility of the error-correction being non-linear (see Escribano, 1985). The current paper consider non-linear error-correction, parameter constancy and long macroeconomic time series. Hendry and Ericsson (1991) developed a non-linear error-correction model with constant parameters for the UK money demand in 1878–1975. Ericsson, Hendry and Prestwich (1998), henceforth EHP, recently successfully extended the model to cover the years 1878–1993. Their model is a single-equation error-correction model in which short-term dynamics are built around a theory-based long-run equilibrium relationship. The model contains a non-linear error-correction mechanism which is specified following Escribano (1985). This type of model involves higher powers of the disequilibrium term; see EHP. It turns out that non-linear error-correction is a prerequisite for parameter constancy. If it is replaced by an ordinary linear error-correction mechanism, other things equal, the hypothesis of parameter constancy, when tested by an appropriate stability test, is rejected. Non-linearity thus plays a key role in the modelling effort of EHP.

Our aim is to reconsider non-linear error-correction in EHP. Teräsvirta (1998a) recently suggested that the Escribano-type error-correction in EHP may be seen as an approximation to an error-correction characterized by smooth transition regression (STR); see, for example, Granger and Teräsvirta (1993) and Teräsvirta (1998b). We shall examine this possibility by generalizing the error-correction mechanism in EHP directly using the STR framework. Sarno (1998) applied a similar idea when modelling Italian money demand using long annual (1861–1991) time series. Alternatively, one may start with a step back and model the non-linearity in the data with an STR model, applying the modelling cycle described in Teräsvirta (1998b). This implies that we begin with a model with linear error-correction and test linearity against STR. If it is rejected, we find the appropriate transition variable by a specification search. It will be seen that this procedure leads to an error-correction mechanism different from that in EHP. The results of the two approaches are compared with each other and with the Escribano-type model in EHP. Encompassing tests, among other things, are applied for this purpose. It appears from the results for the two STR models that the STR-based error-correction is an improvement over the specification in EHP.

The outline of the paper is as follows. Section 2 reviews the economic theory EHP applied and reminds the reader of their dummy variables. Section 3 introduces the statistical model and discusses the actual modelling, and Section 4 presents conclusions.