Econometric Models
Long-run short cuts

Most economic theories are formulated in terms of long-run relationships, and their testable implications usually involve either the long-run multipliers or other aspects of the model's behaviour in a long-run, steady-state equilibrium. Econometric analyses of time-series data, on the other hand, devote considerable effort to the correct specification of short-run behaviour. It would be very convenient if it were possible to obtain good estimates of a model's long-run properties without first having to undertake an extensive analysis of its short-run dynamics. In Discussion Paper No. 154, Trevor Breusch and Research Fellow Mike Wickens show how this can be achieved and propose a new strategy for constructing dynamic models.

Breusch and Wickens note that the variables in an econometric model can be combined in a variety of ways to yield a reformulation of the original model. The reformulated model contains a new set of variables and parameters which are combinations of those in the original model. Some of these reformulations may provide direct estimates, for example, of the original model's long-run multipliers. The authors argue, however, that some commonly used dynamic models, such as the error correction model (ECM), possess unnecessarily restrictive properties, and that certain reformulations of general dynamic models possess the advantages of the ECM without its disadvantages.

These reformulations are one example of a more general model transformation, in which both the dependent and explanatory variables of the original model are replaced by linear combinations of all these variables; the equation is then 'renormalized' on a new dependent variable. Breusch and Wickens show that for linear models the coefficients of such a reformulated model, when estimated using instrumental variables, are identical to those obtained by estimating the original model and then substituting these estimates in expressions for the coefficients of the reformulated model. The long-run coefficients of a model can, therefore, be obtained directly by estimating a transformed model using instrumental variables.

Breusch and Wickens also show that it may be unnecessary to specify correctly a model's short-run dynamics in order to estimate its long-run parameters satisfactorily, provided that the variables entering the long-run solution are 'trend- stationary'. Such variables can be represented as the sum of a time trend and a (stationary) random variable. The relationship between trending variables is dominated by their trends: even though these variables deviate from their trends, these deviations make no contribution to the model's long-run behaviour, at least for large sample sizes. Breusch and Wickens do not recommend omitting short-run dynamics in practice, however, since this may result in less satisfactory estimates in small samples.

The authors conclude by proposing a general method of constructing dynamic models. A reformulated version of the general dynamic model should be estimated initially, to establish whether the long-run properties of the model are consistent with economic theory. Only if this test is passed and if the unrestricted model also satisfies the usual diagnostic tests is it worth seeking a simpler model with fewer parameters. This procedure should, the authors argue, avoid much wasted effort, since the long-run properties of the final model should be virtually the same as those of the original model.


Dynamic Specification, the Long Run, and the Estimation of Transformed Regression Models
Trevor Breusch and Mike Wickens

Discussion Paper No. 154, February 1987 (ATE)