# State one advantage of using a Vector Auto regression (VAR) model. [1]

A. Answer all questions. (15 marks, 1 mark each)

1. Violating which of the classical linear regression model assumption will lead to a biased OLS estimator? [1]

2. In a system of equations given below, Y’s are endogenous while X’s are exogenous. Which of the equation is just identified? Explain. [2]

3. State one advantage of using a Vector Auto regression (VAR) model. [1]

4. In the following VAR model, write down the null hypothesis for the Granger causality test of ݕଶdoes not Granger cause ݕଵ? [1]

5. In a VAR model, name the method of analysing the proportion of the movements in the dependent variables that are due to their “own” shocks, versus shocks to the other variables. [1] Section B. Answer ALL questions (35 marks) Question B1 (20 marks)

(a)State the overreaction hypothesis and how can one use regression (B1-1) to test for the overreaction hypothesis? [2]

(b) Suppose the loser stocks are generally more risky, explain the drawback of using regression (B1-1) when testing the overreaction hypothesis. How would you correct for it? [2]

Using the data employed by Clare and Thomas (1995), suppose you are interested in analyzing whether there are quarterly return differences between the loser and winner portfolios. You estimated the following regression by OLS:
2020 Nov ECON339 Spring Session/T3 Wollongong/PSB Academy Page 3 of 3 where R denotes monthly excess return over the stock market, iQ is a dummy variable for i=1, 2 and 3 such that 1iQif return is in the i-th quarter and 0 otherwise. The result is 680.0RSS,03.0ˆ,005.0ˆ,01.0ˆ,02.0ˆ321

(c) What is the difference in the mean return between the first and second quarter? [1]

(d) Now define a fourth quarter dummy as tQ,41 if return is in the fourth quarter and 0 otherwise. Suppose you drop the first quarter dummy from regression (B1-2) and include the fourth quarter dummy instead such that tttttDeQQQR,33,22,44. (B1-3) What will the estimated value of 324,,,now be? [4]

(e) Can one run the following regression titiitDuQR41,, (B1-5) to analyse whether there are quarterly return differences between the loser and winner portfolio? Explain. [2] Question B2 (10 marks) In the paper by Terence C. Mills and Alessandra G. Mills (1991) on “The International Transmission of Bond Market Movements”, they investigate the relationships between the government bond yield of four countries, namely the US, the UK, West Germany (WG) and Japan. Mills and Mills (1991) performed unit root tests on each of the four countries bond yield and found the yield to be an I(1) process. They also performed a cointegration test on all four countries bond yield but failed to find any cointegrating relationships amongst them. They then estimated a Vector (VAR) of lag order 8. To generate variance decompositions from their model, they considered two Cholesky orderings: the first ordering (I) is (US, UK, WG, Japan) and the second ordering (II) is (Japan, UK, WG, US).

(a) What is the pre-requisite of the variables for a cointegration relationship to exist between them?

[1] (b) Suppose you believe that the US and UK bond prices possess a long-run relationship. Explain how you can undertake a formal test on this conjecture.

[2] (d) What is the rationale of using the second ordering when presenting the impulse responses results?

[5] (c) Write out the system of four regressions involving the four countries bond yield. For purpose of exposition and simplicity of notation, use only one 1 lag and let ri denote the yield for country i= US, UK, WG and JP.