# 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 8
Non-nested Models, Encompassing and
Model Selection

8.1
Problems in Choosing Between Models

In the earlier chapters we have suggested various methods of deriving an econometric model which, for one reason or another, may be regarded as 'good' practice. For instance, use of the general to specific methodology (Chapter 4) can result in a single equation model derived from an autoregressive distributed lag model in a systematic way, in that it survives a series of Lagrange Multiplier tests for various linear and/or nonlinear restrictions. On the other hand, one may construct a model using, say, the Engle-Granger approach (Chapter 5). In the multi-equation case, a model may be formulated from a Cowles Commission type structural model, a vector autoregressive model (Chapter 6), or a system of equations based on the principle of exogeneity modelling (Chapter 7). If it is not clear which is the best modelling approach on a priori grounds and various methodologies are applied to derive an empirical model, it is unlikely that one would finish up with identical models. An obvious question which arises in this context is: how can one select the best model?

The answer to the model selection problem is not necessarily obvious even if there is no question as to the modelling methodology believed to be appropriate. Suppose, for instance, that one starts from a simple autoregressive distributed lag model of order one which is regarded as a general model (see Chapter 4):

 yt = α1yt-1 + β0xt + β1xt-1 + ε t (8.1).

Imagine that one model derived from (8.1) through applying the general to specific methodology turns out to be a first order autoregressive process:

 yt = α1yt-1 + ε t (8.2).

It was said in Chapter 4 that the general model (8.1) becomes the specific model (8.2), if it satisfies the restrictions:

 β0 = β1 = 0.

Altematively, from the same general ADL model (8.1) and using the same methodology, one may develop another specific form, for instance a finite distributed lag model:

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