Exchange rates and expectations In this chapter, we emphasized that expectations have an important effect on the exchange rate. In this problem, we use data to get a sense of how large a role expectations play. Using the results in Appendix 2 at the end of this chapter,

you can show that the uncovered interest parity condition, equation (20.4), can be rewritten as \[
\frac{\left(E_{t}-E_{t-1}ight)}{E_{t-1}} \approx\left(i_{t}-i_{t}^{*}ight)-\left(i_{t-1}-i_{t-1}^{*}ight)+\frac{\left(E_{t}^{e}-E_{t-1}^{e}ight)}{E_{t-1}^{e}}
\]
In words, the percentage change in the exchange rate (the appreciation of the domestic currency) is approximately equal to the change in the interest rate differential (between domestic and foreign interest rates) plus the percentage change in exchange rate expectations (the appreciation of the expected domestic currency value). We shall call the interest rate differential the spread.

a. Go to the Web site of the Bank of Canada (www.bankbanque-canada.ca) and obtain data on the monthly 1 -year Treasury bill rate in Canada for the past 10 years. Download the data into a spreadsheet. Now go to the Web site of the Federal Reserve Bank of St. Louis (research.stlouisfed. org/fred2) and download data on the monthly U.S. oneyear Treasury bill rate for the same time period. (You may need to look under "Constant Maturity" Treasury securities rather than "Treasury Bills.") For each month, subtract the Canadian interest rate from the U.S. interest rate to calculate the spread. Then, for each month, calculate the change in the spread from the preceding month. (Make sure to convert the interest rate data into the proper decimal form.)

b. At the Web site of the St. Louis Fed, obtain data on the monthly exchange rate between the U.S. dollar and the Canadian dollar for the same period as your data from part (a). Again, download the data into a spreadsheet. Calculate the percentage appreciation of the U.S. dollar for each month. Using the standard deviation function in your software, calculate the standard deviation of the monthly appreciation of the U.S. dollar. The standard deviation is a measure of the variability of a data series.

c. For each month, subtract the change in the spread (part a) from the percentage appreciation of the dollar (part b). Call this difference the change in expectations. Calculate the standard deviation of the change in expectations. How does it compare to the standard deviation of the monthly appreciation of the dollar?
This exercise is too simple. Still, the gist of this analysis survives in more sophisticated work. In the short run, movements in short-term interest rates do not account for much of the change in the exchange rate. Most of the changes in the exchange rate must be attributed to changing expectations.