1. Show how the following two equation structural system for yt and zt can be transformed into an equivalent reduced form VAR representation. You need to derive the two reduced form equations and show that he reduced form parameters are composite values of the parameters given in the original system. Using the reduced form equations, you have derived to show how the contemporaneous values of each of the variables appearing on the right-hand side of this system are correlated with the disturbance terms in the original system and explain what problems, if any, this causes for OLS estimation of the original system:

Original System:

y_t = α₁₀ +β₁₂ z_t + γ₁₁ y_(t-1) + γ₁₂ z_(t-1) + x₁₁ y_(t-2) + x₁₂ z_(t-2) + u_1t

z_t = α₂₀ + β₂₁ y_t + γ₂₁ y_(t-1) + γ₂₂ z_(t-1) + x₂₁ y_(t-2) + x₂₂ z_(t-2) + u_2t

2. This question requires you to use the Eviews data Causality1.wf1 provided on Blackboard.

The data set consists of two-time series on the variables x and y over the period 1950Q1 to 2013Q4.

(a) Use Eviews to determine the appropriate lag to use in the VAR representation of these data. Report and interpret the table provided by Eviews for this test.

(b) On the basis of the lag length chosen in part (a) undertake a multivariate LM test for serial correlation. Report and interpret the table provided by Eviews for this test.

(c) On the basis of the VAR used in parts (a) and (b) report Chi-squared and F-tests for Granger Causality. Report and interpret the tables provided by Eviews for both these tests and compare the results.

(d) Report (multiple stacked) graphs of the time series for x and y. Comment on what you find.

3. Explain what is meant by predicted causality and compare the tests suggested by Granger and Sims.

Attachment:- Assignment.rar