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Does purchasing power parity (PPP) hold in the long run?

A look at the franc/dollar exchange rate on the Swiss national holiday

Part of the “My favorite FRED graph” guest post series.

“Under the skin of any international economist lies a deep-seated belief in some variant of the PPP theory of the exchange rate.” —Dornbusch and Krugman (1976)

Most models in international macroeconomics assume purchasing power parity (PPP) holds in the long run. But what is PPP and what is the long run?

A good starting point is the law of one price (LOP), which states that the same good in different competitive markets must sell for the same price, when transportation costs and barriers between those markets are not important. Intuitively, LOP holds because, if prices were lower in country A and higher in country B, people would simply buy the lower-priced good in country A and sell it in country B at a higher price.

Purchasing power parity (PPP) is the application of LOP across countries for all goods and services—or for representative groups (“baskets”) of goods and services such as those used to compute the consumer price index. If absolute PPP holds, a typical basket of goods in country A has exactly the same price as it does in country B, when prices are expressed in a common currency.

Consider the case of Switzerland and the United States:

If P(CH) is the level of average prices in Switzerland, P(US) is the level of average prices in the U.S., and E is the Swiss franc/U.S. dollar exchange rate (number of francs per U.S. dollar), then absolute PPP holds if P(CH) = E · P(US).

PPP thus implies that the exchange rate is determined by the ratio of average prices.

If LOP holds for all goods and services, PPP will also hold. But there are good reasons why LOP doesn’t hold for all goods and services. Certain services (think of haircuts or restaurant meals) cannot be traded across countries. Certain goods are costly to transport (think cement). And certain goods have tariffs. For instance, meat is much more expensive in Switzerland than in Italy, France, or Germany, but a person can’t legally import large quantities of meat into Switzerland without paying large import duties.

Moving from the law of one price to purchasing power party is also complicated by the fact that people in different countries consume different goods. This is partly due to local tastes (more wine in Italy and more beer in Germany), but also income levels (in poorer countries, the typical household allocates a larger share of their expenditures to food). Absolute PPP doesn’t hold, as shown by the fact that PPP exchange rates normally deviate from nominal exchange rates.

A less-rigorous version of PPP is relative PPP, which states that the percentage change in the exchange rate is equal to the difference in the percentage changes in average prices—that is, the inflation rate. (Formally: (Et-Et-1)/Et-1= π(CH)t-π(USA)t, where π(x)t is the inflation rate in country x at time t.)

Relative PPP doesn’t hold at any one moment in time because the exchange rate is much more volatile than the average price level. However, standard economic models assume it holds in the long run—that is, when prices have had the time to adjust. There seems to be a consensus in the literature that in the “long-run PPP may hold in the sense that there is significant mean reversion of the real exchange rate, although there may be factors impinging on the equilibrium real exchange rate through time” (Taylor and Taylor, 2004).

The FRED graph above looks at the case of Switzerland versus the United States. The blue line plots the ratio between Swiss and U.S. prices (the ratio is rescaled so that it takes value 100 in 1990). The negative slope shows that Swiss inflation has been substantially lower than U.S. inflation. The ratio between Swiss and U.S. prices has decreased by about 73%. The green line plots the behavior of the exchange rate between the Swiss franc and the U.S. dollar rescaled to take value 100 in 1980. It shows that over 1970-2021 the Swiss franc appreciated by about 75%, which matches the behavior of relative prices. Over this 50-year period, PPP between U.S. and Switzerland seems to hold.

How this graph was created: Search FRED for and select “Switzerland CPI.” From the “Edit Graph” panel, use the “Add Line” tab to search for and select “CPI USA.” Apply formula a/b and at the bottom choose the “Index” as the unit, applying 100 for 1990-01-01. Use the “Add Line” tab to search for “Switzerland USA exchange rate” and apply 100 for 1980-01-01.

Suggested by Ugo Panizza.

The continuity of the discount rate

FRED data provide a window into financial history

When a commercial bank borrows from its District Federal Reserve Bank, it is using the Fed’s discount window. As described by the Board of Governors, this lending program provides commercial banks with short-term liquidity to support the smooth flow of credit to households and businesses. The operation of the discount window has evolved in response to the changing needs of the economy and financial system, and this FRED Blog post looks at its history through the lens of data.

The FRED graph above shows the interest rate that financially sound commercial banks pay when borrowing from the Federal Reserve. It is called the “discount window primary credit rate” because it offers the best credit terms to qualifying depository institutions. The daily data series starts on January 9, 2003, when the primary and secondary discount window program started making liquidity available to more commercial banks under different terms and at different costs. The source of the data is the Board of Governors.

But the discount window has been in operation since 1914, when the Federal Reserve System was established. Do you want to know how this tool of monetary policy operated further back in time? Keep on reading.

Before the primary and secondary credit programs were put in place, the Fed determined access to short-term liquidity for commercial banks through the adjustment and extended credit programs. There was and still is a third, seasonal  credit program not discussed here. The FRED graph above adds a second line (in red) to our initial graph. It shows the monthly average discount rate on loans to member banks and it extends the data back in time to January 1950. Note that the data source is listed as the International Monetary Fund, but the original data are reported by the Board of Governors through the Data Download Program.

Between 1914, when the Federal Reserve System was established, and the first half of 1922, when Federal Reserve District banks started buying large amounts of government securities in the open market, management of the discount window was intended as the principal instrument of central banking operations.

The FRED graph above adds a third line (in green) to our second graph. It shows the values of the basic discount rate that the Federal Reserve Bank of St. Louis charged to its member banks between November 16, 1914, and the launch of the primary and secondary discount window program in 2003. Notice that the data have no consistent frequency, as they were recorded only when the interest rate changed. Subject to approval by the Board of Governors, each of the 12 Reserve Banks in the Federal Reserve System can set its own discount rate. In practice, since the 1930s, the rates of the 12 Reserve Banks have rarely differed, and then only for a day or two. However, before 1933, there were more often differences in the rates across the Banks.

How these graphs were created: To create the first graph, search for and select “Discount Window Primary Credit Rate.” To create the second graph, from the “Edit Graph” panel, use the “Add Line” tab to search for and select “Interest Rates, Discount Rate for United States.” To create the third graph, repeat the last step to add “Federal Reserve Bank of St. Louis Basic Discount Rate (DISCONTINUED)” to the graph.

Suggested by Diego Mendez-Carbajo.

Trying to measure manager vs. non-manager pay

Working with disparate data definitions

How much more do managers earn than the workers they manage? Sometimes the data can answer a question like this directly. But in this case, we must do a little work.

First, our investigation today is motivated by the fact that earnings for non-managers are persistently lower than earnings for the total pool of employees, which includes managers. But we don’t have data for the earnings of managers alone. A few developments during the pandemic make this question even more interesting: Non-manager weekly earnings rose when the pandemic hit, but non-manager hourly earnings (rate of pay) did not rise when the pandemic hit. So, did non-managers work more hours for the same rate of pay? Let’s see.

We compare weekly earnings for (i) the entire pool of workers and (ii) just non-managers so we can try to suss out what managers make. Non-managers earn about $170 per week less than the pool of all workers (which includes managers), and the graph above shows no visible evolution in that difference.

Our second FRED graph compares the same datasets but in terms of percent change from a year ago. We see no systematic difference between the two until the pandemic hits. At that point, non-managers started making significantly greater gains than the average of all workers; and they continue to do so.

Now, “weekly earnings” are a product of hourly pay and weekly hours. So, we focus on hourly pay in the graph above—again, in terms of percent change from a year ago. We see that non-manager pay didn’t immediately increase more once the pandemic hit. The increase only in the latter part of the pandemic seems to imply weekly hours must have increased more in the early stages of the pandemic. Did they?

We cannot see any difference at all in the two lines showing weekly hours. How is that possible? We would have expected the blue line to be significantly higher than the red line early in the pandemic. The problem is that the hours measured in the first graph aren’t the same as those in the last graph. The first uses the concept of average hours, which essentially represent regular work hours for an employee. The last graph considers aggregate hours, which is a total of all hours worked in the economy, and thus multiplies the average hours by employment. And the latter changed quite a bit during the pandemic. So, as it turns out, the decomposition we wanted to perform here doesn’t work. Which is why it’s so important to understand the precise definitions of the data you’re working with.

How these graphs were created: Search FRED for “average weekly earnings” and sele ct the production and non-supervisory workers series. From the “Edit Graph” panel, search for the same seriesbut pick “all employees.” You have the first graph. For the second, set units to “percent change from previous year” and apply to all. For the third and fourth graphs, repeat the operations with “average hourly earning” and “aggregate weekly hours.”

Suggested by Christian Zimmermann.

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