Ch. 8: Exchange Rates in the Long Run: The Monetary Approach

Lectures 7 and 8 (Feenstra and Taylor, Chapter 14, numbered Chapter 3 in the slides) explain how exchange rates are determined in the long run. Uncovered interest parity from the previous chapter gives the spot rate as E $/€ = E e $/€ × (1 + i €)/(1 + i $), but it takes the expected future exchange rate as given. To forecast the future exchange rate, investors need a theory of the long run. That theory has two parts: purchasing power parity (PPP), which links the exchange rate to the price levels of two countries, and the monetary theory of the price level, which links price levels to money supply and demand. Combined they form the monetary approach to exchange rates. The chapter has five sections: exchange rates and prices in the long run (PPP); money, prices and exchange rates (simple model); the monetary approach, implications and evidence; money, interest rates and prices (general model); and monetary and exchange rate regimes (nominal anchors).

Introductory example: Canada and the United States, 1970 to 1990

A standard basket of goods in Canada cost C$100 in 1970 and C$392 in 1990 (inflation of 292%). A basket that cost $100 in the United States in 1970 cost $336 in 1990 (inflation of 236%). Did US goods become cheaper, so that Americans bought fewer Canadian goods and Canadians more US goods? No. In 1970 C$1 was almost exactly $1, so both baskets cost the same in a common currency. By 1990 the Canadian dollar had depreciated: $1 cost C$1.16. The US basket of $336 then cost 336 × 1.16 = C$390, almost the same as the Canadian basket of C$392. In the long run prices and exchange rates adjust so that the purchasing power of each currency stays comparable across countries: the higher Canadian inflation was offset by a depreciation of the Canadian dollar.

The law of one price

Arbitrage occurs in goods markets as well as in asset markets: prices of goods in different countries, expressed in a common currency, tend to be equalised. Applied to a single good this is the law of one price; applied to a basket of goods it is purchasing power parity. The theory assumes an idealised world of frictionless trade without transaction costs.

Purchasing power parity and the real exchange rate

PPP is the macroeconomic counterpart of LOOP. For baskets of goods with price levels P US and P EUR:

The nominal exchange rate is a nominal concept (the rate at which currencies are exchanged); the real exchange rate is a real concept (the rate at which baskets of goods are exchanged). Terminology:

• If q US/EUR rises (more US goods are needed for one European basket), Home (the United States) experiences a real depreciation.
• If q US/EUR falls, Home experiences a real appreciation.
• If q is below 1 by x%, foreign goods are x% cheaper than home goods: the dollar is strong, the euro is weak and the euro is undervalued by x%.
• If q is above 1 by x%, foreign goods are x% more expensive: the dollar is weak, the euro strong and overvalued by x%. Example: the European basket costs $550 in dollar terms and the US basket $500; q = 550/500 = 1.10, so the euro is 10% overvalued.

In the building-block diagram of PPP, the price levels are exogenous variables and the exchange rate is the endogenous variable predicted by the model.

Relative PPP, inflation and depreciation

The rate of change of the price level is the inflation rate: if the price level goes from 100 to 103.5 in a year, inflation is 3.5%. If equation 3-1 holds in levels, it also holds in rates of change. The rate of change of E is ΔE $/€,t / E $/€,t = (E t+1 minus E t)/E t; the rate of change of the ratio P US/P EUR equals US inflation minus European inflation.

Important points: relative PPP concerns changes in prices and exchange rates, absolute PPP their levels. Absolute PPP implies relative PPP, but not the other way round. Example: if all goods always cost 20% more in country A than in B, absolute PPP fails; but if the inflation differential (say 5%) always equals the rate of depreciation (5%), relative PPP still holds.

Evidence for PPP in the long run and short run

• Long run: a scatterplot for 82 countries (1975 to 2005) of the average depreciation against the dollar versus the inflation differential against the United States shows a strong correlation close to the 45-degree line predicted by relative PPP.
• Short run: data for the United States and United Kingdom (1975 to 2009) show that the exchange rate and relative price levels do not move together in the short run. Relative price levels change slowly within a small range, while exchange rates move abruptly with large fluctuations. Absolute PPP does not hold in the short run, but the two series drift together over decades, so PPP is a better guide to the long run.

How slow is convergence to PPP? Deviations from PPP are persistent: estimates suggest they die out at about 15% per year (the speed of convergence). About half of a deviation remains after four years: a four-year half-life (0.85 to the power 4 = 0.52).

Example: the home basket costs $100 and the foreign basket $90 in home currency. The real exchange rate is 0.90; the home currency is overvalued (foreign goods are cheaper). The deviation from PPP is minus 0.10. After one year 15% of it (0.015) has disappeared, so the deviation is minus 0.085 and q is forecast at 0.915, a small real depreciation. After four years about half of the deviation is gone (0.1 × 0.52 = 0.052 remains), so q is about 0.95, only about 5% from PPP. (The slide phrases this as 52% erased; with a 15% speed the remaining share after four years is 52%, which gives the same rounded result.)

What explains deviations from PPP?

• Transaction costs: transport, tariffs, duties, shipping delays, the cost of building distribution networks and meeting legal and regulatory requirements abroad. On average more than 20% of the price of internationally traded goods.
• Nontraded goods: some goods and services (haircuts, housing) are inherently nontradable, with infinitely high transaction costs; most goods lie somewhere between tradable and nontradable.
• Imperfect competition and legal obstacles: many goods are differentiated products with brands, copyrights and legal protection; firms with market power can charge different prices across countries (pricing to market).
• Price stickiness: prices do not adjust quickly to changes in market conditions, while exchange rates do.

The Big Mac Index and the Tall Latte Index

Selected rows from the July 2009 Big Mac table (US price $3.57; the caption on the slide mentions $3.22, but the implied rates in the table are computed with $3.57):

Calculation for China: price in dollars = 12.5/6.83 = $1.83; q = 1.83/3.57 = 0.51, so the yuan is about 49% undervalued. The Economist also publishes a Starbucks Tall Latte index, based on the same PPP logic. For most major currencies it tells the same story as the Big Mac index (both show the euro overvalued against the dollar), but results for Asian currencies are mixed, which illustrates that nontraded inputs (rent, local labour), market power and local tastes cause deviations from LOOP.

Money: functions, measurement and supply

In the long run the exchange rate equals the ratio of price levels, but what determines price levels? Monetary theory: in the long run price levels are determined by the supply of and demand for money. Money has three functions:

1. Store of value: it can be used to buy goods and services in the future. If the opportunity cost of holding money is low, people hold it more willingly than other assets.
2. Unit of account: all prices are quoted in it.
3. Medium of exchange: it allows buying and selling without inefficient barter; money is the most liquid asset.

Measurement: monetary aggregates include currency, M0 (currency plus bank reserves, the monetary base), M1 (currency plus demand deposits) and M2 (M1 plus savings and small time deposits). Normally bank reserves are close to zero so M0 and currency are almost equal, but reserves spiked in the 2008 financial crisis, when private banks sold securities to the Fed and held the cash in their Fed reserve accounts as a precautionary hoard. Money supply: the central bank controls it; the model assumes the central bank's tools let it control M1 indirectly but accurately.

Money demand and equilibrium: the simple model (quantity theory)

The need to conduct transactions is assumed proportional to income, so aggregate money demand rises in proportion to nominal income:

Money growth, inflation and depreciation

Define the money growth rate μ US = (M t+1 minus M t)/M t and the real income growth rate g US = (Y t+1 minus Y t)/Y t. With L constant, the growth rate of P = M/(L Y) is money growth minus income growth:

Intuition: a looser US monetary policy in the long run (faster money growth) makes the dollar depreciate faster; faster US economic growth makes the dollar appreciate faster, all else equal.

Forecasting with the simple model

Using the monetary model to forecast answers a hypothetical question: what path would the exchange rate follow if prices were flexible and PPP held? Assume US and European real income growth are zero and the European price level is constant (zero inflation).

Case 1: a one-time 10% increase in the money supply. Real balances M/P stay constant because real income is constant, so P rises 10%; PPP means E rises 10%: the dollar depreciates by 10%.

Case 2: an increase in the rate of money growth. The money supply grows at rate μ; at time T the United States raises the growth rate to μ + Δμ. Real balances remain constant, so P is always a constant multiple of M and, by PPP, E is always a constant multiple of P. Before T, M, P and E all grow at μ; after T they all grow at μ + Δμ. The inflation rate and the rate of depreciation both rise by Δμ. In the simple model there is no jump in the levels, only a kink in their growth paths.

Evidence for the monetary approach

• Inflation rates versus money growth rates, 76 countries, 1975 to 2005: strong correlation close to the 45-degree line predicted by the monetary model.
• Depreciation against the dollar versus the money growth differential relative to the United States, 82 countries, 1975 to 2005: again close to the 45-degree line.

Hyperinflations. A hyperinflation is traditionally defined as a sustained inflation of more than 50% per month. Zimbabwe had the first hyperinflation of the twenty-first century: inflation of 58% in 1999, 132% in 2001, 385% in 2003 and 586% in 2005 turned into hyperinflation, and the currency was eventually replaced by US dollars and South African rand. Currencies that lose value rapidly can become extinct (dollarization, as in Ecuador), or governments redenominate: a new unit equals 10 to the power N old units. Argentina replaced the peso by the peso argentino at 10,000 to 1 (1983), that by the austral at 1,000 to 1 (1985) and that by the convertible peso at 10,000 to 1 (1992), so one convertible peso equalled 10,000,000,000 old pesos. In July 1946 Hungary had about 76 thousand billion billion pengő in circulation. Evidence: across twentieth-century hyperinflations, the cumulative depreciation against the dollar and the cumulative rise in the price level lie very close to the 45-degree line (PPP holds well when inflation is extreme). And real money balances collapse during hyperinflations: people economise by holding less of the rapidly depreciating money, the higher the peak monthly inflation rate, the larger the fall. This shows that money demand is not stable, which motivates the general model.

The general model: money demand depends on the interest rate

The quantity theory assumes a stable money demand, which is implausible. In the general model, money demand also falls when the nominal interest rate (the opportunity cost of holding money instead of interest-bearing assets) rises:

The Fisher effect and real interest parity

Combining relative PPP (expected depreciation = expected inflation differential) with the UIP approximation (expected depreciation = i $ minus i €) gives:

Evidence. For 62 countries (1995 to 2005) the nominal interest rate differential against the United States and the inflation differential lie close to the 45-degree line, supporting the Fisher effect. Real interest rate differentials of the UK, Germany and France against the United States (1970 to 1999) were not zero at every moment but were close to zero on average: real interest parity, like PPP, is a long-run tendency.

The fundamental equation and forecasting in the general model

Forecast: increase in the US money growth rate from μ to μ + Δμ at time T.

1. Before T, M, P and E all grow at rate μ; foreign prices are constant.
2. At T money growth rises by Δμ, so inflation rises by Δμ; by the Fisher effect the nominal interest rate i $ also rises by Δμ.
3. A higher interest rate lowers real money demand L(i) Y, which falls with a discrete jump at T.
4. Since the money supply M moves continuously, real balances M/P can only fall if the price level P jumps up at T.
5. After T, prices grow at the new, higher rate μ + Δμ. With a stable foreign price level, PPP implies that E follows the same path: a one-time jump (depreciation) at T followed by faster depreciation.

So in the general model a rise in money growth leads to a rise in inflation, a one-time drop in real money demand and hence a one-time jump in the price level and the exchange rate, on top of the higher growth rates. This explains why exchange rates can move sharply on news about future monetary policy.

Monetary regimes and nominal anchors

A central aim of economic policy is to keep inflation within bounds. This requires that policy makers be subject to a long-run constraint, a nominal anchor. The combination of long-run nominal anchoring and short-run flexibility is called the monetary regime. With Home (H) and Foreign (F), three nominal anchors follow from the long-run relations:

Table 3-2 (exchange rate regimes and nominal anchors). Countries without their own currency (dollarized or in a currency union) have a "superfixed" exchange rate target. Pegs, bands and crawls also target the exchange rate. Managed floats have no preset path for the exchange rate and may use any of the three anchors. Free floaters pay no serious attention to exchange rate targets and, if they have an anchor, use a money supply target or an inflation target with interest rate policy. Countries with "freely falling" exchange rates have no serious target and high inflation and depreciation. Many countries target implicitly without announcing it, and some mix several targets.

Nominal anchors in practice (Table 3-3, global disinflation).

In the 1970s most of the world struggled with high inflation, which continued in the 1980s. Disinflation began in the advanced economies in the early 1980s; emerging and developing countries had even higher inflation until the 1990s, when many countries introduced effective nominal anchors. Most of these policies became credible, helped by greater central-bank independence.

Key points

1. PPP implies that the exchange rate equals the relative price level and the real exchange rate equals 1.
2. Evidence for PPP is weak in the short run and more favourable in the long run; short-run deviations reflect market frictions, imperfections that limit arbitrage, and price stickiness.
3. The quantity theory explains price levels by money supply and real income; combined with PPP it gives the monetary approach to the exchange rate.
4. With forecasts of money and income, the monetary approach forecasts the exchange rate, but only under flexible prices, so it is a long-run, not a short-run, tool.
5. PPP plus UIP implies the Fisher effect (interest differentials equal inflation differentials) and real interest parity; these are long-run results with somewhat favourable evidence.
6. In the general model money demand falls with the nominal interest rate; a rise in money growth raises inflation and interest rates, lowers real money demand and causes a one-time jump in the price level and exchange rate.
7. Policy makers use nominal anchors (exchange rate, money growth or inflation targets) to keep inflation low; their explicit adoption contributed to worldwide disinflation.