The modelling strategy applied follows recent developments in the econometric literature, in particular the work of Clements and Mizon (1991), Hendry and Mizon (1993) and Johansen (1988), and we label it structural econometric modelling (SEM)¹⁶. Via a series of testable restrictions and reductions, this modelling strategy transforms an initial VAR in levels into a set of linear structural equations that incorporate both long and short-run dynamics¹⁷. Starting from an unrestricted vector autoregressive model (VAR), the hypothesis of cointegration is formulated as a hypothesis of reduced rank of the longrun impact matrix Π. The VAR is generated by the vector zt, which defines the potential endogenous variables of the model. Taking first differences the VAR can be transformed into

(4)

where the estimates of

describe the short-run dynamics to changes in zt and

captures the long-run adjustments, and D contains deterministic terms. This modelling strategy involves the transformation of the initial VAR into a constrained VAR (CVAR) by placing restrictions on the cointegration space. Secondly, the CVAR is then made more parsimonious (PVAR) by successively removing insignificant short-term variables, based on F-tests, until all remaining variables are significant at the 5% level. This PVAR is then transformed into a simultaneous equation model (SEM) by determining the short-term causality amongst the system variables.

In order to reduce the dimensionality of the system further, by increasing robustness to changes, the individual equations are then finally estimated with Full Information Maximum Likelihood estimation (FIML). Considering the datadriven nature of the identification procedure, an important test statistic is the ability of the SEM to parsimoniously encompass the PVAR (see Clements and Mizon (1991)). A specific set of equations represents an acceptable parameterisation of the original VAR, if it contains roughly the same information as the PVAR from which it was derived given the restrictions imposed.

 

16 A recent application of this modelling technique in the field of exchange rate economics is MacDonald and Marsh (1996).

17 While Clement and Mizon (1991) and Hendry and Mizon (1993) do not suggest a particular stratgey to identify the short-run dynamics, Johansen and Juselius (1994) identify the short-run independently from the long-run following an exploartive identification processs. Hsiao (1997) stresses, however, the necessity of identifying the long and short-run structure simultaneously. Since no consensus about the identification problem of the short and long run dynamics has been reached as yet, we decided to follow the first two approaches.

Prof. Ronald MacDonald, Prof. Norbert Fiess

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Summary: Index