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.
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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.
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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.
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