# 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 7
Exogeneity and Structural Invariance

7.1
Data Generating Processes

In Chapter 6 we outlined the principal assumptions of multi-equation modelling within the Cowles Commission framework, and introduced in greater detail, the 'atheoretical' VAR approach. We stated that the two principal assumptions of structural modelling, namely the endo-exogenous division of the variables and the zero restrictions imposed on a model's parameters, are abandoned in FAR modelling. There are no exogenous variables in the system and, due to the lack of zero restrictions, there is nothing like a 'structural form' of the model.

The VAR approach is quite difficult to apply in the real world. In practice, VAR modelling for more than four variables is rarely feasible. An investigator has to include many lags on many variables in each equation. The number of parameters to be estimated becomes large and even a single equation may become impossible to estimate, due to the shortage of observations. Moreover, the fact that the VAR approach is 'atheoretical' makes the development of an economically sensible model from a VAR system a quite difficult task (although, as shown in Chapter 6, not necessarily impossible).

The method of multi-equation modelling presented in this chapter, which we will call exogeneity modelling, can be thought of as a compromise in some respects between the need to keep the size of the model manageable and consistent with economic theory on the one hand, and the properties of the statistical data used for the modelling on the other. Generally speaking, exogeneity modelling still allows for some a priori zero restrictions to be imposed and therefore for control over the size of the model, but the endoexogenous division between variables is not given a priori any more. This division constitutes a testable hypothesis and because of this it is, to some extent, connected with the former problem of zero restrictions. If a certain variable is not exogenous, it should be modelled within the system and therefore some of the hypothetical zero restrictions may not be valid.

Exogeneity modelling can be envisaged as bringing together elements from both structural and VAR modelling. It bears some resemblance to the concept of recursive systems (for example, see Wold ( 1954)), which were regarded in the 1950s as a criticism of simultaneous equation structural modelling. According to Wold, simultaneity does not exist in the economy as

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