This material was originally created for Starting Point: Teaching Economics
and is replicated here as part of the SERC Pedagogic Service.

#### Summary

In this case, students learn how, over a long period of time, the nominal value of a currency is related to the ratio of prices at home and abroad. They will search for a nominal exchange rate (e.g. the Japanese yen / U.S. dollar exchange rate), the consumer price levels in the domestic (the U.S. in this example) and in the foreign country (Japan in this example) and compute the ratio between the price levels. Students will plot this ratio as an approximation of the purchasing power parity (PPP) and identify periods when it does, and does not, inform the evolution of nominal exchange rates.

Through peer instruction, students will address each of the following issues:
1. Why does the purchasing power parity (PPP) increase or decrease over time?
2. When does the purchasing power parity (PPP) inform the value of a currency better: in the short run or in the long run?
3. What factors, besides price levels, influence the value of a currency?

## Learning Goals

After the completion of this module students will be able to:
1. Use FRED graphs to perform data manipulations.
2. Use FRED graphs to perform a visual data comparison
3. Test how the purchasing power parity theory fits the actual data.
4. Understand the difference between the short-run and the long-run.

## Context for Use

Ideally this module should be directed to an international or financial economics class; if the course syllabus has room for it, the data plotting can be used in an economics principles course as well. It can be used as an applied exercise included in a large lecture or student groups can be assigned to replicate it outside of class as a basis for a short assignment. Between the presentation of the data and the ensuing discussion, instructors should allocate 20-30 minutes of classroom time. The discussion could focus on the underlying assumptions of the purchasing power parity principle and on what factors may undermine it.

Note that a more advanced treatment of this topic may compute the purchasing power parity both in absolute and in relative terms, experiment by changing the base period for the price indexes, and explore different data frequencies (e.g. quarterly, semiannual, or annual). These exercises may be used to illustrate how the choices made regarding data can either support or undermine a theoretical construct.

Prerequisite skills: Graph literacy
Prerequisite concepts: Nominal exchange rates; Law of One Price; Consumer price index

## Description and Teaching Materials

Within a lecture discussing long-term determinants of exchange rates, an instructor will use this module to help students understand the computation of the purchasing power parity and to guide a discussion of its applicability.

(Step 1)
The instructor will first present a graph of a nominal exchange rate (Category: Money, Banking & Finance > Exchange Rates > By Country > [Select one]) For example, Japan (DEXJPUS).

The instructor should point out that foreign exchange is traded on a daily (five business days a week) basis and that exchange rates can be plotted with a high level of frequency. This fact will become relevant when introducing the price indexes.

The instructor can ask students to identify periods when the exchange rate is increasing or decreasing in order to practice the concept of currency appreciation and depreciation. Questions of volatility can also be brought up by pointing out sudden and large changes in the value of the exchange rate.

(Step 2)
Starting from scratch, the instructor should then present the graphs for the price levels at home and abroad. Both consumer and producer price indexes are available for many countries. In this example we will use the consumer price index (Category: International Data > Indicators > Prices > Consumer Price Index). Make sure to first select the U.S. (CPIAUCSL) and then Add Data Series to New Line in the graph the series for the Japanese consumer price index (JPNCPIALLMINMEI).

The instructor should point out that the price indexes are computed once a month, much less frequently than the foreign exchange rate.

Notes:
- The instructor should Copy to All Lines the shortest data range (usually for the foreign country) to facilitate the interpretation of the graph.
- The base period should be the same for both countries: Units > Index (Scale equal to 100 for chosen period) > (the international series use 2005 as the base year)

Students will find that the cost of living at home and abroad is different both in levels and in rates of growth. Recalling the concept of the Law of One Price the instructor could check the student understanding of this concept by asking for the expected direction of change of the exchange rate.

(Step 3)
The instructor will combine the exchange rate and price information in one graph.
First, we compute the purchasing power parity between the two currencies. Starting with the graph of the price levels described above, the instructor will Remove Line 2 (the price level abroad) and then Add Data Series to Line 1 (the price level abroad) in order to Create Your Own Data Transformation: b/a (price level abroad / price level in the U.S.)

Note:
The definition of the exchange rate determines how the purchasing power parity is computed. The FRED database reports exchange rates as the number of units of foreign currency per US dollar. Thus, the purchasing power parity must be computed as price level abroad over the price level in the U.S. A class discussion question could be how to compute the purchasing power parity when the exchange rate is reported as the number of U.S. dollars per unit of foreign currency.

(Step 4)
Finally, the instructor will add to the graph above the plot of the exchange rate series: Add Data Series to New Line, selecting Scale > Right.

The following is a list of questions that could be asked:
Are the purchasing power parity and the nominal interest rate ever/frequently identical? Should we expect them to be identical?
Which series is more volatile, the purchasing power parity or the nominal interest rate? What could explain the difference in volatility?
Are there years when the purchasing power parity theory points to a currency appreciation (depreciation) while the actual nominal interest rate moves in the opposite direction? What could explain this divergence?
When does the purchasing power parity theory work best at explaining the evolution of the nominal exchange rate: in the short run or in the long run?

Further sophistication:
Use the producer price index instead of the consumer price index for the computation of the purchasing power parity and compare the plots.
Change the frequency of the nominal exchange rate data from daily to monthly, quarterly, semiannual... and compare the plots.

## Teaching Notes and Tips

Be sure to present the argument about how the Law of One Price should make the nominal exchange rate equal to the ratio of prices at home and abroad. A commonly referenced example on this topic is the Big Mac Index. The Economist computes this index annually and has created an interactive web page: http://www.economist.com/content/big-mac-index

An instructor may want to explore the fact that the computation of the purchasing power parity is influenced by the choice of prices, or price indexes, one employs. Furthermore, even when employing identically named price indexes across countries the composition of the basket of goods and services changes from country to country. The Division of International Labor Comparisons of the Bureau of Labor Statistics publishes a report on international indexes of consumer prices:
http://www.bls.gov/fls/intl_consumer_prices.pdf

From this activity to the computation of the real exchange rate only a small step is needed. The following resource should help the instructor make that connection. It would be advisable not to try and discuss the purchasing power parity theory and real exchange rates during the same class period. The Back to Basics series by the International Monetary Fund has an issue entitled "Why Real Exchange Rates":
http://www.imf.org/external/pubs/ft/fandd/2007/09/pdf/basics.pdf

## Assessment

The recommended method for assessment for an international or financial economics class would be to have students write up a short memo where they test the applicability of the purchasing power parity theory to the actual data. This should be a take-home assignment.

## References and Resources

1. The Big Mac Index as an example of the Law of One Price:
http://www.economist.com/content/big-mac-index

2. International comparison of price indexes:
http://www.bls.gov/fls/intl_consumer_prices.pdf

3. The International Monetary Fund basic introduction to the real exchange rate
http://www.imf.org/external/pubs/ft/fandd/2007/09/pdf/basics.pdf

4. NBER paper: "A Century of Purchasing-Power Parity" by Alan Taylor (2000):
http://www.nber.org/papers/w8012.pdf