Economics 712 Fall 2006 Steven N. Durlauf Final Examination You have 90 minutes to complete the exam. Closed note, closed book, no calculators, etc. Section 1. (90 points) For each of the following propositions, explain whether it is true, false, uncertain and explain your answer. Credit will be entirely determined by the explanation. 1. If money does not Granger cause output, then a change in the money supply rule will have no effect on the variance of output. 2. If money does Granger cause output, then a change in the money supply rule will affect the variance of output. 3. If a strictly indeterministic process is stationary in levels, then the trend component of its Beveridge Nelson decomposition is identically equal to zero. 4. In the Cagan hyperinflation model, money and prices are cointegrated. 5. In the dividend stock price model, with risk neutral agents and a constant discount rate, the variance of stock prices is bounded from above by the variance of dividends. 6. For strictly indeterministic, second-order stationary process, the zero frequency of the spectral density must equal zero. 1 7. The spectral density of a second-order stationary process is finite at all frequencies. 8. The variance of xt xt t k , the k period ahead forecast error for the WienerKolmogorov projection of xt onto its history, is strictly increasing in k . 9. If xt L t if t is an uncorrelated process, then it represents the fundamental innovations to the process. 10. Model averaging methods require that one assume that each candidate model has an equal ex ante probability. Section 2. (120 points) Let yt denote output and mt denote the money supply. Suppose that output obeys the structural relationship yt yt 1 mt 1 t , t white noise Suppose that the policymaker does not know the value of ; the parameter, with probability p, equals and with probability 1 p equals , 0 1 . Consider feedback rules of the form. mt 1 fyt 1 , where f can either equal f or f , 0 f f 1. A. (60 points) Describe the minimax and Bayesian approaches to the choice of the policy parameter, assuming the policymaker’s loss function equals the variance of output. 2 B. (20 points) Describe the optimal parameter choice under each decision criterion if f and f ? Describe the optimal parameter choice for these parameter assumptions if the loss function of the policymaker is the zero frequency of the spectral density. Explain the difference. C. (20 points) Describe the optimal parameter choice under each decision criterion when the restrictions on various parameters are changed so that .3 , .8 , f 0 , and f .8 . Repeat when the restrictions on various parameters are changed so that .3 , .4 , f 0 , and f .4 . Explain the difference. Section 3. (90 points) Describe an econometric strategy for determining whether the effects of foreign aid on economic growth depend on the quality of a country’s government. Assume that measures of relevant variables exist and be explicit about the econometric strategy you would employ. 3