1. Tests on alpha Long-run weak exogeneity (a zero row in alpha) Estimation in partial system A known vector in alpha

2. Long-run weak exogeneity (no long-run feed-back) Or:

3. Deriving a test procedure: or

4. The idea is to decompose the full VAR system into the equations with nonzero alphas and the equations with zero alphas using the design matrices H. Example:

5. Repetition:

6. The conditional and marginal VAR model

7. The concentrated model:

9. Tests of weak exogenity

10. Joint test of weak exogeneity

11. Weak exogeneity and partial models

12. 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?

13. The VAR model with bond rate as weakly exogneous variable

16. Why partial models can be useful:

18. Illustration: the rank test with exogenous variables

19. Testing a known vector in alpha

20. A decomposition of the system:

21. Formulate the conditional and the marginal models

22. Illustration