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Tests on alpha
• Long-run weak exogeneity (a zero row in alpha)
• Estimation in partial system
• A known vector in alpha
Long-run weak exogeneity (no long-run feed-back)
Or:
Deriving a test procedure:
or
or
The idea is to decompose the full VAR system intothe equations with nonzero alphas and the equationswith zero alphas using the design matrices H.
Example:
Repetition:
The conditional and marginal VAR model
The concentrated model:
Tests of weak exogenity
Joint test of weak exogeneity
Weak exogeneity and partial models
Under which conditions on the VAR model is it possible to estimate the long-run money demand relation in a singel equation error correction model without loss of information?
The VAR model with bond rate as weakly exogneous variable
Why partial models can be useful:
Illustration: the rank test with exogenous variables
Testing a known vector in alpha
A decomposition of the system:
Formulate the conditional and the marginal models
Illustration