# New Directions in Econometric Practice: General to Specific Modelling, Cointegration, and Vector Autoregression

By Wojciech W. Charemza; Derek F. Deadman | Go to book overview

Chapter 4
General to Specific Modelling

4.1
Autoregressive Distributed Lag Modelling

One of the main methodological innovations of the Davidson et al. ( 1978) approach to modelling consumption (see Chapter 3) was that a 'good' empirical econometric model could be developed by starting from a relatively large, general model and by gradually reducing its size and transforming the variables through the testing of various linear and nonlinear restrictions. Let us reconsider equations (3.7) and (3.10) from Chapter 3. We said that equation (3.10) was a general one, without any restrictions on parameters and (3.7) was a specific one. That is, equation (3.7) could be derived from equation (3.10) by imposing various restrictions on the parameters in equation (3.10). After estimation, we compared the results for (3.10) (MODEL 3.6 in Section 3.7) with that for (3.7) (MODEL 3.5) and concluded that because the unrestricted estimates seemed quite close to those implied by the restrictions, the specific model was a valid one, in that it did not contradict the general model.

In this chapter we present a detailed discussion of general to specific modelling. By general to specific modelling we mean the formulation of a fairly unrestricted dynamic model, herewith called a general model, which is subsequently tested, transformed and reduced in size by performing a number of tests for restrictions. A general model in a convenient notation is presented and sets of restrictions on this model which would eventually lead to economically interpretable models are discussed. We also describe how the validity of the restrictions imposed may be tested statistically, as the procedure applied in Chapter 3 (namely judging intuitively whether the restricted and unrestricted coefficients are 'close' or 'remote' from each other) is not statistically rigorous.

The general model is usually described in an autoregressive distributed lag (ADL) form. This means that a dependent variable yt is expressed as a function of its own lagged values, and the current and lagged values of all explanatory variables. A straightforward notation for an ADL model uses the lag operator Lr, defined for a variable xt as:

 Lrxt = xt-r

It is also convenient to use scalar polynomials in L:

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