A critique of the Granger representation theorem
The Granger representation theorem states that if a set of nonstationary variables are cointegrated then they can be characterized as generated by an error correction mechanism. This paper uses the continuous time equivalent representation for two variables to demonstrate the relatively large number of restrictions required to represent a cointegrating relationship as an error correction mechanism. It is shown that the restrictions result from placing too much importance on the long run, which excludes interesting and possibly important short run dynamics. This is surprising because these restrictions are at odds with the a-theoretical vector autoregressive approach, which criticises the ad-hoc specification and identification of the Cowles foundation style structural models. The second criticism relates to the justification of using cointegration because economic theories are mostly about long run relationships with little to contribute to modeling short run economic behaviour. It is argued in this paper that cointegration places too much importance on the long run and excludes interesting short run dynamics. After the formal presentation of the conditions for stability of an economic model, an exchange rate and endogenous growth examples are provided. They highlight the importance of short run dynamics in modeling economic behaviour and providing policy prescriptions. It is then shown that applying the cointegrating restrictions eliminates these short run dynamics. It is also possible that many researchers are not aware of the restrictions that this procedure forces on the parameters which are to be estimated. This paper demonstrates these restrictions on the coefficients of economic relationships.
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