http://www.gmu.edu/departments/economics/bcaplan

Econ 816

Spring, 2000

**HW#2 Answers**

** **

**Part 1: Mathematical Problems**

1. If m_{t}
is constant, then the money supply shocks all disappear. Just set the variance of the money shock
equal to zero! Therefore, using the
results from the notes:

_{} and _{}

Intuitively, getting rid of monetary instability gets rid of the economic shocks associated with monetary uncertainty.

2. _{} AND _{}.

Main intuition: To raise the nominal interest rate
by 1%, you need to *permanently* raise the __expected__ rate
of money growth by 1%. Notice that even
when money has no real effects, the central bank could permanently raise
nominal interest rates in this manner!

Secondary intuition: To actually hit the pegged
rate, you have to adjust the rate of money growth on a period-by-period
basis. But since shocks are transitory,
your expected money supply in any period is independent of __past__ shocks.

3. Romer, problem 9.4.

a. Your
hypothesis is that: i_{t}=r+E_{t}p_{t+1}, with r
constant.

Imposing rational expectations, p_{t+1}=E_{t}p_{t+1}+e_{t+1}.

Regressing i on a constant and p_{t+1}, so i_{t}=a+bp_{t+1}+e_{t}:

_{}

So b, your best estimate for b, is less than 1.

b. p_{t+1}=a+bi_{t}+u_{t};
estimating b:

_{}

c. Inflation
assumed to be white noise process: p_{t}=rp_{t}+e_{t}.

Regressing i_{t} on many lags of inflation:

_{}

With constant real interest rate, nominal rates move
1:1 with *expected*
inflation. However, if inflation is a
white noise process, it does not follow that the betas sum to one. In fact, the white noise assumption implies
E_{t}p_{t}=rp_{t-1,} so:

b_{0}=r, and all of the other betas
=0. Therefore, _{}, which is not necessarily equal to 1.

**Part 2: Analytical Problems**

** **

*I attach sample answers from Eric Crampton for the first two questions,
along with some general and question-specific comments.*

* *

1. When do **deviations** from "rational expectations
in the aggregate" occur? When do
severe instances of the "bias towards zero in aggregate perceptions"
appear? Is there any common pattern
that both deviations from RE share?

*Many people didn't seem to understand
the distinction between:*

* *

*i. rational expectations*

*ii. rational expectations in the aggregate*

*iii. DEVIATIONS from rational expectations in the aggregate*

* *

*Haltiwanger and Waldman explored
(ii). As they explained, (i) is a
special case of (ii). If everyone has
RE, then RE in the aggregate has to hold; but just because RE holds in the
aggregate, it does not follow that everyone has RE.*

* *

*Moreover, the question asked about
(iii), not (ii). Many people summarized
the H&W article, which you were not asked to do. Few if any people mentioned the most obvious connection between
deviations "RE in the aggregate" and "the bias towards
zero": the latter is a special case of the former!*

* *

*Last, many people said that e.g.
"Synergy causes RE in the aggregate." No. RE in the aggregate
(as opposed to regular RE) matters
more when there is synergy, but synergy does not cause RE in the aggregate.*

2. Agree or disagree: Caplan's "rational irrationality" analysis suggests that the rational expectations assumption probably applies in all macroeconomic models so long as they do not have a political component.

*Most people just summarized the main idea of the paper. The good answers usually disagreed, noting
that it is possible to have a macro model without politics with small private
error costs (for example, Akerlof and Yellen's model of second-order small
deviations from rationality).*

3. Pick a specific government policy that you think is inefficient. Which, if any, of Caplan's findings in "Systematically Biased Beliefs About Economics," would explain the existence of this policy? Do Caplan's findings make "special interest"/rent-seeking explanations of your example superfluous?

*Answers here were not too bad.*