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