EMEC022S6 BSc Financial Economics with Accounting

Numbers in parentheses are the standard errors of estimated coefficients, R 2 is thecoefficient of determination, SSR is the sum of squared residuals, BG is the Breusch– Godfrey chi-squared statistic for first-order serial correlation, WH is the White chi-squared statistic for heteroskedasticity, and numbers in square brackets are the p-values of BG and WH.

(a) For the regression based on the full sample, compute: (i) the standard error of the regression; (ii) Theil’s adjusted R

Comment on the goodness of fit of the model. [15%]

(b) Test the statistical significance of the coefficient on X1t in the first regression

(the critical value for the test is 1.98). State clearly what the distribution of your test statistic is under the null hypothesis. [10%]

(c) Test the null hypothesis that the coefficient on X2t in the first regression is equal to 0.4 against the alternative that it is smaller than 0.4 (the critical value for the test is −1.66). State clearly what the distribution of your test statistic is under the null hypothesis. [10%]

(d) Test the null hypothesis that the coefficients on X1t and X2t in the first regression are jointly equal to zero (the critical value for the test is 3.09). State clearly what the distribution of your test statistic is under the null hypothesis.

Test the null hypothesis that the regression coefficients are constant over the sample (the critical value for the test is 2.70). State clearly what the distribution of your test statistic is under the null hypothesis. [20%]

(f) Explain how the model might be modified using dummy variables to allow for a change in all regression coefficients at observation t = 45. [20%]

(g) What assumptions do the tests in (b), (c), (d) and (e) rely on? Are they likely to be satisfied in this model? Explain. [15%]

(a) Suppose that E(Xtut) = 0 for all t, E(utus) = 0 for all t 6= s, and E(u

Where is an unknown constant and Zt > 0 is an observable nonstochastic variable. Explain how to estimate β = (β0, β1) efficiently when:

Include in your answer a careful explanation of why your proposed estimation method would produce an efficient estimate of β in each case. [30%]

(b) Suppose that ut = φut−2 + εt , where φ is a known parameter and εt are unobservable random variables such that E(εt) = 0, E(ε for all t 6= s, and E(Xtεs) = 0 for all t and s. Explain how to estimate β efficiently. Include in your answer a careful explanation of why your proposed estimation method would produce an efficient estimate of β. [20%]

(c) Suppose that E(u 2 t ) = σ 2 u > 0, E(utus) = 0 for all t 6= s, and E(Xtut) 6= 0. Assume that two instruments W1t and W2t are available.

(i) Explain how to compute the generalized instrumental variables estimate

(GIVE) of β by using a two-step procedure based on ordinary least squares

(OLS). What are the advantages of GIVE over OLS in this model? [25%]

(ii) Explain how to test for the validity of the instruments W1t and W2t

How would you test for the validity of instruments in the case where only the instrument W1t is used to compute the GIVE of β? [25%]