ECON 425
Topics in Monetary Economics:
The International Monetary System
from the Gold Standard to War in Ukraine
Final Exam
December 9, 2024
Instructions:
You have six hours to work on this exam. It is worth 100 points, contributing to your overall score for the course as described in the Syllabus. You may consult all course materials and standard Internet resources while working on the exam, but your work must be original and you may not solicitor obtain assistance from or provide assistance to other people for any part of the exam (this includes obtaining help from artificial intelligence). Activities considered cheating include copying or closely paraphrasing content from websites, discussing exam questions with other students, and/or using ChatGPT or similar tools. All exams will be checked for originality and copied content, and anyone found cheating will be assigned a zero score for the exam. Read carefully each part of each question before you jump into working on it and do not panic if you cannot complete everything. The exam is also intended to stretch your knowledge by forcing you to use the tools and information you have acquired. I want to see how you think about issues based on what you learned. If there is a question you cannot answer, do not get bogged down and move on to the next question. Write legibly.
Problem 1: International Monetary Policy Cooperation after a Crisis (50 Points)
We can use a slightly modified version of the model you analyzed in Homework 4 to study interna- tional monetary policy cooperation in response to a Önancial crisis.
Suppose we modify the money demand equations for the Home and Foreign countries in the model by introducing money velocities v and v* as follows:
m + v = p + y; (1)
m* + v* = p* + y* : (2)
Velocity is the rate at which agents in each country dispose of money for transactions. For given money supply, higher velocity translates into higher prices and/or output.
The introduction of velocities v and v* is the only change we make to the Homework 4 model. Hence, refer to Homework 4, pages 1 and 2, for the description of the rest of the model.
Assume that velocity in each country is an independently and identically distributed exogenous shock with average value of zero, like the exogenous productivity shock x in the production function (as for other variables, v and v* measure the percent deviations of Home and Foreign money velocity from the zero-shock equilibrium). We take velocity as the indicator of the situation of credit markets: A credit market collapse results in a drop in velocity (negative realizations of both v and v* in aglobal credit crisis) as agents have an incentive to hold on to liquidity and the number of transactions in the economy drops.
As in Homework 4, assume that Home wage setters chose wat time -1 to minimize E-1 (n2 )=2, and similarly in Foreign. Also continue to assume that the central bank in each country wants to stabilize CPI and employment at their zero-shock levels, and it minimizes the same loss function as in Homework 4 (bottom of page 3).
● Show that the following results hold in our extended model with velocity shocks (it is enough to show this for one country, say, Home):
w = E-1 (m + v) = 0;
w* = E-1 (m* + v* ) = 0;
n = m + v;
n* = m* + v* ;
y = (1 - α) (m + v) - x;
y* = (1 - α) (m* + v* ) - x
p = α (m + v) + x;
p* = α (m* + v* ) + x:
Note that there are two ways to show this: one is by using ''brute force'' and doing the algebra, the other is by being smart, thinking carefully about the one change we made relative to the Homework 4 model, and what it should imply for these equations and those in the next bullet relative to results in Homework 4. Feel free to use the smart strategy if you figure it out, but explain it clearly.
Note: A credit crisis (a drop in velocity) puts downward pressure on employment, output, and prices.
● Show (by doing the algebra or by being smart) that the nominal exchange rate and the terms of trade are determined by:
and Home and Foreign CPIs are:
● Assume equal country size (a = 1=2) and show that the Örst-order condition for the
optimal choice of money supply by the Home central bank under non-cooperation is:
and that it can be rewritten as:
Define the following coefficients:
Then, we can rewrite equation (3) as:
or:
● Explain the signs of the Home central bankís responses to Foreign money supply, Foreign money velocity, Home money velocity, and the productivity shock. Note: Explain does not mean ìstate in words.î It means explain why the sign is what it is.
● Show (by brute force or by being smart, but explaining it) that the foreign central bankís behavior is determined by the reaction function:
● Show that the Nash equilibrium level of Home money supply is:
If you use the expressions for H1(N) and H2(N), you can verify that:
Take this for granted. I am not asking you to prove it.
Taking the expression for H3(N) into account, it follows that:
● Show (by brute force or by being smart, but explain it) that the Nash equilibrium level of Foreign money supply is:
● What is the intuition for how the central banks respond to velocity shocks in the Nash equilibrium?
● If x = 0, what are the Nash equilibrium values of the central banksíloss functions LCB and LCB* ?
● What is the intuition for these values?
● Show that the first-order condition for the optimal choice of m when the two central banks coordinate their policies (i.e., jointly minimize a combination of the loss functions with weights equal to 1/2) is:
Proceeding as in the non-cooperative case, we can rewrite equation (8) as:
where we define:
This implies the cooperative setting of m according to:
● Show (by using brute force or by being smart, but explaining it) that the Örst- order condition for the cooperative choice of m* yields:
● Show (by using brute force or by being smart, but explaining it) that the solution for Home money supply under cooperation (mC ) is:
Using the expressions for H1(C) and H2(C) shows that H1(C) - H2(C) = 1 - √ (1 - α2 ). Hence, taking
H3(C) = √ α into account, we have:
● Show (by using brute force or by being smart, but explaining it) that the solution for Foreign money supply under cooperation (m*C) is::
● Why do the central banks respond to velocity shocks in the same way as they did in the Nash equilibrium?
● If x = 0, is there anything to be gained from international monetary cooperation in response to the velocity shocks U and U* ? Why?
However, the responses to the productivity shock x differ between Nash and cooperative equi- libria. In particular, we can verify that the cooperative responses are less aggressive than the non-cooperative ones (I am not asking you to verify it).
● What explains the reduction in policy aggressiveness when central banks coop- erate in responding to x?
Now remember what we learned from Ben Bernankeís article on the Great Depression: Credit market crises have negative supply-side e§ects as asymmetric information issues make access to credit harder and prevent Örms from operating e¢ ciently. In our model, we can capture this by positing that the shock x, instead of being purely independent from U and U* , depends on these variables: x = x (U, U*).
In particular, suppose that, when U and U* become negative (a global credit crisis), 儿 becomes positive (a productivity loss). Suppose that parameter values are such that the overall response of monetary policy to the combination of velocity and productivity shocks in each country is expansionary in both the Nash equilibrium and the cooperative one.
● How does the response to the combined shocks in the cooperative equilibrium di§er from that in the Nash equilibrium (is it more or less expansionary)?
● Why?
Bottom line: Using a small extension to the Homework 4 problem and remembering what we learned from Ben Bernanke o§ers a possible explanation for why central banks may find it desirable to coordinate their responses to global credit crises.
Problem 2: A Simple Theory of Exchange Rate Random Walks (30 points)
Richard Meese and Kenneth Rogo§ argued in a 1983 Journal of International Economics paper that the exchange rate models written in the 1970s (like Rudiger Dornbuschísovershooting model) could not predict the future exchange rate better than a random walk, i.e., better than just taking the current exchange rate as our best forecast of the future exchange rate. This result was a major stumbling bloc for exchange rate theories for decades because it was viewed as inconsistent with theory. This problem asks you to explore a simple theoretical model that generates random walk behavior of the exchange rate.
Consider two countries, Home and Foreign, and suppose uncovered interest rate parity (UIP) holds, so that:
it - it(*) = Et("t+1) - "t ;
where it and it(*) are the Home and Foreign nominal interest rates, "t is the exchange rate (units of
Home currency per unity of Foreign), and Et is the expectation operator conditional on information available at time t.
Assume that the Home and Foreign central banks set their interest rates in response to CPI ináation according to the policy rules:
it = Tπt + ξt
and:
it(*) = Tπt(*) + ξt(*) ;
with T > 1, where πt and πt(*) are the Home and Foreign CPI ináation rates, and ξt and ξt(*) are iden-
tically and independently distributed random shocks such that Et(ξt+1) = Et(ξt(*)+1) = 0. Ináation
rates are deÖned by πt 三 pt -pt-1 and πt(*) 三 pt(*) -pt(*)-1 , where pt and pt(*) are the Home and Foreign
CPIs.
Assume also that purchasing power parity (PPP) holds, so that:
pt - pt(*) = "t:
● Use the policy rules of the central banks, the definitions of ináation rates, and PPP to show that policy behavior by the central banks implies:
it — it(*) = T("t — "t-1 ) + ξt — ξt(*):
● Combine this equation with the UIP condition to show that the exchange rate satisÖes the equation:
Et("t+1) — "t = T("t — "t-1 ) + ξt — ξt(*): (11)
Trust me on the following statement: Given the assumption T > 1, this equation has a unique solution for the exchange rate in every period t that has the form.
"t = "t-1 + η (ξt — ξt(*)) ; (12)
where η is a parameter (to be determined) that measures the responsiveness of the exchange rate to the di§erence between exogenous Home and Foreign interest rate shocks.
● What do this form of the solution for the exchange rate and the assumptions we made above imply for Et("t+1)?
For (12) to be the solution for "t, we must find the value of η such that, if we substitute (12) into (11) for "t, we obtain 0 = 0.
● Substitute (12) into (11) for "t, use the result you obtained in the previous bullet, and show that it must be:
This result implies that the solution for the exchange rate in the model of this problem is:
● Is this solution consistent with your intuition for what should happen to the exchange rate if a central bank imparted a contractionary shock to monetary policy? Brie'y explain your answer.
● Is the solution for the exchange rate consistent with Meese and Rogoff's finding mentioned at the beginning of this problem?
Essay Question: The Case for Flexible Exchange Rates and the Role of Nominal Rigidity and Currency of Price Setting (20 Points)
Using a maximum of two letter-size pages, explain Friedman's case for flexible exchange rates, and why price stickiness and currency of price setting matter. If you type your essay, use double spacing and a 12-point font.