1. COMPULSORY Provide brief answers to all the following: (a) A sample of 20 observations corresponding to the model: Y = + X + u, gave the P P P following data: (X X)2 = 215:4, (Y Y )2 = 86:9, and (X X)(Y Y ) = 106:04. Estimate . (5 marks) (b) Prove that r2 = byx bxy , where byx is the least-squares (LS) slope in the regression of Y on X , bxy is the LS slope in the regression of X on Y , and r is the coe¢ cient of correlation between X and Y . (5 marks) (c) Present four alternative in‡ ation/unemployment regressions. (5 marks) (d) Give one reason for autocorrelated disturbances. (5 marks) (e) Explain how we might use the Breusch-Godfrey statistic to test estimated residuals for serial correlation. (5 marks) (f) The following regression equation is estimated as a production function for Q: lnQ = 1:37 + 0:632 lnK + 0:452 lnL, cov(bk ; bl ) = 0:055;
where the standard errors are given in parentheses. Test the hypothesis that capital (K ) and labor (L) elasticities of output are identical. (5 marks) Continued (Turn over)
ANSWER TWO QUESTIONS FROM THE FOLLOWING: 2. (a) Economic theory supplies the economic interpretation for the predicted relationships between nominal (in‡ ation) uncertainty, real (output growth) uncertainty, output growth, and in‡ ation. Discuss …ve testable hypotheses regarding bidirectional causality among these four variables. (25 marks) + yt
(b) An investigator estimates a linear relation for German output growth (yt ): yt = 1 + ut , t = 1850; : : : ; 1999. The values of …ve test statistics are shown in Table 1: Discuss the results. Is the above equation correctly speci…ed? (10 marks)
3. (a) i) Show how various examples of typical hypotheses …t into...