Problem Set 1 - Exchange Rate Economics
Q1. Purchasing power parity.
1. Write out the expression absolute PPP.
2 Explain why one cannot typically test for absolute PPP.
3. For what data series can one test for absolute PPP?
4. Show the steps necessary to obtain relative PPP in growth rates.
5. If relative PPP holds, is this a necessary and/or sufficient condition for absolute PPP to hold?
6. Show why mean reversion in the real exchange rate is consistent with relative PPP holding.
Q2. Covered and uncovered interest parity.
1. Assume that covered interest parity holds, so (1+i) = (F/S)(1+i*). Fill in the following grid (carry your answer out to three decimal places), for (a) and (b).
2. Assume that uncovered interest parity holds, so (1+i) = (Se/S)(1+i*). Fill in the following grid (carry your answer out to three decimal places), for (c) and (d).
|
|
i
|
i*
|
F
|
S
|
|
a.
|
0.05
|
0.07
|
2.40
|
|
|
b.
|
0.05
|
|
2.40
|
2.450
|
|
|
i
|
i*
|
Se
|
S
|
|
c.
|
|
0.06
|
2.40
|
2.450
|
|
d.
|
0.06
|
0.08
|
|
2.450
|
Q3. Using real data to evaluate PPP and UIP.
Consider the tables drawn from the Economist, April 10th, 2004 edition, on the attached pages. Answer these questions using equations.
1. Using the 3 month interest rates, and assuming UIP holds, calculate the expected change in the dollar/euro exchange rate over the next three months. Be sure to state what the rate will be, in annualized terms, and what will be the actual percentage change in the dollar/euro exchange rate.
2. Given the empirical evidence on the relationship between exchange rate changes and interest differentials provided in the table in the handout on CIP and UIP, what do you expect to happen to the dollar/euro rate? Explain.
3. Using 10 year bonds, calculate what the implied change in the dollar/pound exchange rate is, over the next ten years.
4. Given the inflation rates over the past year, what should have been the rate of change in the US dollar/Canadian dollar exchange rate if relative purchasing power parity held?
5. Interpret the Economist poll of expected inflation rate for 2004 as the expected change from December 2003 to December 2004. What is the expected change in the US dollar/Australian dollar? (If you use the March 5-11, 2005 edition of the Economist, answer the question, using the measure of expected inflation for 2005 to answer the question).
4. [Optional] Using real world data to test for uncovered interest parity. Download the data available at: https://www.ssc.wisc.edu/~mchinn/chinn_meredith_UIPdata.xls.
1. If the software you are using can do it, plot the forward premium (assuming covered interest parity holds) and ex post depreciation.
2. Estimate the Fama regression for all the USD/DEM and USD/JPY, and the DEM/JPY, at the three months horizon.
3. What do the residuals from this regression look like?
4. Estimate the Fama regression for all the USD/DEM and USD/JPY, and the DEM/JPY, at the 10 year horizon.