Exchange Rates and Interest Rate Parity: A Comprehensive Guide

Posted on Aug 15, 2024 in Economy

Exchange Rate: The exchange rate is the price of one currency expressed in another currency. Exchange rates play a central role in international trade because they allow us to compare the prices of goods and services produced in different countries.

Changes in exchange rates are described as depreciations or appreciations.

All else equal, an appreciation of a country’s currency makes its goods more expensive for foreigners.

Today’s exchange rate between two currencies is affected by expectations about future values of assets in those currencies. Exchange rates react to information on expected future values of the exchange rates. Those are affected by:

  • Inflation
  • Business cycle
  • Current account
  • Changes in interest rates

The Foreign Exchange Market:

Is the market in which international currency trades take place. Foreign currencies are bought and sold by banks, other financial institutions, firms, persons, and central banks. Exchange rates are determined by demand and supply.

Demand for assets in foreign currency is determined by expected returns, risk, and liquidity of the assets:

  • Expected return: percentage difference between the expected value of the asset in the future and the price today.
  • Risk: the variability it contributes to savers’ wealth.
  • Liquidity: the ease with which the asset can be sold or exchanged for goods.

To compare returns on different deposits, market participants need two pieces of information:

  • First: they need to know how the money values of the deposits will change. This is determined by the currency’s interest rate, the amount of that currency an individual can earn by lending a unit of the currency for a year.
  • Second: they need to know how exchange rates will change so that they can translate rates of return measured in different currencies into comparable terms. This is determined by the expected change in the exchange rate over the year.

A simple rule shortens this calculation. First, define the rate of depreciation of the dollar against the euro as the percentage increase in the dollar/euro exchange rate over a year. Once you have calculated the rate of depreciation of the dollar against the euro, our rule is this: The dollar rate of return on euro deposits is approximately the euro interest rate plus the rate of depreciation of the dollar against the euro.

R$;Euro =  REuro + ( Ee$/Euro –  E$/Euro)/E$/Euro

Interest Rate Parity:

The foreign exchange market is in equilibrium when deposits of all currencies offer the same expected rate of return. The condition that the expected return of deposits of any two currencies are equal, when measured in the same currency, is called the interest rate parity.

The equilibrium exchange rate is the exchange rate that ensures that no participant in the market wants to switch to a deposit in another currency. R$;Euro =  REuro + ( Ee$/Euro –  E$/Euro)/E$/Euro

The foreign exchange market is in equilibrium when no type of deposit is in excess demand or excess supply. We can therefore say that the foreign exchange market is in equilibrium when, and only when, the interest parity condition holds.

Suppose the exchange rate is at E2$/Euro:

  • Return on Euro deposits is lower than on Dollar deposits.
  • Owners of Euro deposits want to switch to Dollar deposits.
  • Excess demand for Dollar, excess supply of Euro.
  • Euro becomes cheaper, Dollar more expensive.
  • Exchange rate falls.

Suppose the exchange rate is at E3$/Euro:

  • Return on Euro deposits is higher than on Dollar deposits.
  • Owners of Dollar deposits want to switch to Euro deposits.
  • Excess demand for Euro, excess supply of Dollar.
  • Euro becomes more expensive, Dollar cheaper.
  • Exchange rate rises.

Exchange rate react to changes in exchange rate Expectation and in the interest rate:

  • All else equal, an increase in the interest rate paid on deposits of a currency causes that currency to appreciate against foreign currencies. And on the other way round, if it decreases it causes a depreciation of the dollar.
  • All else equal, a rise in the expected future exchange rate causes a rise in the current exchange rate. Similarly, a fall in the expected future exchange rate causes a fall in the current exchange rate.

The Law of One Price: In competitive markets without transaction costs, identical goods sold in different markets must be sold at the same price when their prices are expressed in the same currency. In other words, if I buy the same product in two different countries, when we talk in the same currency the price of the product has to be the same.

PUSi = E$/€ * PE i à E$/€ = PUSi / PEi

The Purchasing Power Parity (PPP): states that the exchange rate between two countries’ currencies equals the ratio of the countries’ price levels. The PPP theory therefore predicts that a fall in a currency’s domestic purchasing power will be associated with a proportional currency depreciation in the foreign exchange market. Symmetrically, that an increase in the currency’s domestic purchasing power will be associated with a proportional currency appreciation.

  • The absolute PPP: The statement that exchange rates equal relative price levels is sometimes referred to as absolute PPP.
  • The relative PPP: states that the percentage change in the exchange rate between two currencies over any period equals the difference between the percentage changes in national price levels.

(E$/€, t – E$/€, t-1 )/E$/€, t-1 = πUS, t – πE, t

            π: inflation rate.

It makes logical sense to compare percentage exchange rate changes to inflation differences, even when countries base their price level estimates on product baskets that differ in coverage and composition.

Empirical evidence points to strong deviations from PPP in the short run because:

  • Short run price stickiness.
  • Changes in the exchange rate might affect relative prices of close substitutes strongly.
  • Price adjustments caused by excess demand or supply in contrast are slower.
  • In the meantime: sometimes huge deviations.

But in the long run PPP is not fully given, it also has deviations that can be explained by the Balassa-Samuelson Effect. Reasons:

  • Transport costs and trade restrictions let producer prices deviate from consumer prices, which are higher in the foreign country than at home.
  • Monopolistic and oligopolistic market structures allow firms to set different prices in different markets.
  • Inflation rates reported by the countries are based on different goods baskets; changes in the exchange rate however should match actual not official inflation rate differences.

PART 2

Money Market:

Individual money demands of all households and firms can be summed up to an aggregated money demand of the economy. Aggregated money demand is determined by three factors:

  • Interest rate: negative effect on money demand – increase in interest rates decreases money demand.
  • Price level: positive effect on money demand – with higher price level more money needed to keep liquidity at the same level.
  • Real Gross National Income (GNI): positive effect – Liquidity demand increases with average value of transactions.

Md =  P * L( Y ,  R) à Md/ P =  L( R,  Y)

L( Y , R): aggregated real money demand. Positively affected by GNI  Y , negatively by interest rate  R.

Nominal money supply Ms is a policy variable:                 Q =  Ms/ P

  • Exogenous, not determined in an equilibrium process.
  • Determined by the central bank.
  • Not affected by the interest rate R.
  • Vertical line in Q-R-diagram.

The money market is in equilibrium when the money supply set by the central bank equals aggregate money demand.                          Ms =  Md à Ms/ P =  L( R,  Y).

At given price levels P  and GNI Y  , interest rates are determined by aggregated money demand equals aggregated money supply.

Changes:

  • Increasing the money supply: Real money supply increases to M2/P à New equilibrium at lower interest rate à Higher real liquidity holdings of individuals.
  • Increase in the level of output given the money supply and the price level: an increase in output causes the entire aggregate real money demand schedule to shift to the right, moving the equilibrium away from point 1 à There is an excess demand for money equal to Q2 –  Q1 (point 1’) à interest rate is bid up until it reaches the new equilibrium level (point 2). A fall in output has opposite effects. We conclude that an increase in real output raises the interest rate, while a fall in real output lowers the interest rate, given the price level and the money supply.

The Money Supply and the Exchange Rate in the Short Run:

  • Foreign exchange market: Supply of and demand for foreign exchange depending on the Dollar/Euro exchange rate and the Dollar interest rate.
  • Money market: Demand for liquidity depending on the interest rate and an exogenous money supply.
  • Point 1’ satisfies the interest rate parity: Expected Dollar return on deposits in Dollar and Euro are the same.
  • Money market equilibrium in 1 Real money supply in the USA M$/US=PUS equals real money Demand.

An increase in a country’s money supply causes its currency to depreciate in the foreign exchange market, while a reduction in the money supply causes its currency to appreciate à Initially the U.S. money market is in equilibrium at point 1 and the foreign exchange market is in equilibrium at point 1’ with an exchange rate E$/€1. An increase in Europe’s money supply lowers R€ and therefore shifts to the left the schedule linking the expected return on euro deposits to the exchange rate. Foreign exchange market equilibrium is restored at point 2’ with an exchange rate of E$/€2. We see that the increase in European money causes the euro to depreciate against the dollar (that is, causes a fall in the dollar price of euros).

Summary

On the currency market the exchange rate is determined by: the interest rate (differential between any two assets determined in different currencies) and the expected rate of depreciation of the (home) currency.

Interest rates are prices of money determined endogenously on the money market:

  • Interest rates equalize money supply and demand.
  • Money supply is affected by income and interest rates.
  • Money supply is affected by the Central Bank.

Activities of both countries’ Central Banks and their overall economic performance affect the exchange rate.

Exchange Rate Expectation:

To endogenize exchange rate expectations we need a long run model of exchange rate à PPP

Assumptions to the monetary approach to exchange rate determination:

  • Purchasing power parity à E$/Euro = PUS/ PEU
  • Perfectly flexible prices à PUS = MsUS/ L( R$,YUS) and PEU = MsEU /L( R€,YEU)
  • Interest rates and income/output affect the exchange rate only through money demand.

The exchange rate, which is the relative price of American and European money, is fully determined in the long run by the relative supply of those monies and the relative demand for them.

Inflation, interest rate parity, and PPP:

Monetary theory postulates: A permanent increase in the money supply causes a proportional increase in the price level’s long run value. In particular, if the economy is initially at full employment, a permanent increase in the money supply eventually will be followed by a proportional increase in the price level.

Interest rate parity requires:          R$  = REuro  + (Ee$/Euro – E$/Euro )/E$/Euro

Relative PPP states:                   (E$/Euro;t – E$=Euro;t-1 )/E$/Euro;t-1  = π US;t – π EU;t

When we combine them:                                    R$ – R€ = πUSe – πE e

If, as PPP predicts, currency depreciation is expected to offset the international inflation difference (so that the expected dollar depreciation rate is πUSe – πE e), the interest rate difference must equal the expected inflation difference.

The Fisher effect:

All else equal, a rise in a country’s expected inflation rate will eventually cause an equal rise in the interest rate that deposits of this currency offer. Similarly, a fall in the expected inflation rate will eventually cause an equal fall in the interest rate.

The Fisher effect is behind the seemingly paradoxical monetary approach prediction that a currency depreciates in the foreign exchange market when its interest rate rises relative to foreign currency interest rates.

Real interest rate is unchanged à Pure monetary changes do not have long run effects on real variables.

Consequences of different assumptions on price adjustments:

With sticky prices:

  • Decreasing money supply requires increase in interest rate for money market equilibrium.
  • Price level fix, but downward pressure.
  • Increase in interest rate comes with lower inflation expectations and expectation of a long run exchange rate appreciation à Expectation of an appreciation yields an immediate appreciation.

With flexible prices:

  • Accelerated increase in money supply yields an increase in interest rates.
  • Increase in interest rate comes with higher inflation expectations and expectation of a long run exchange rate depreciation à Immediate depreciation follows.

The Real Exchange Rate:

The real exchange rate between two countries’ currencies is a broad summary measure of the prices of one country’s goods and services relative to the other country’s.

Q$/Euro =  E$/Euro* (PEU/ PUS)

The price levels must not be defined over the same basket, in other words, Basket in the USA includes goods and services, which are consumed and produced there, whereas basket in Europe includes goods and services that are consumed and produced here.

Real Depreciation of the Dollar against the Euro: A rise in the real dollar/euro exchange rate (which we call a real depreciation of the dollar against the euro) produces a fall in the purchasing power of a dollar within Europe’s borders relative to its purchasing power within the United States. This change in relative purchasing power occurs because the dollar prices of European goods (E$/€ * PE) rise relative to those of U.S. goods (PUS ). à Hypothetical purchasing power of American goods falls relative to European goods.

Real Appreciation of the dollar against the Euro: is a fall in q$/€. This fall indicates a decrease in the relative price of products purchased in Europe, or a rise in the dollar’s European purchasing power compared with that in the United States.

In the EMU there is no nominal exchange rate à The real exchange rate between any two EMU countries simplifies to                                          qL-Euro/Oe-Euro  = Poe/PL

Demand, supply and the long run real exchange rate:

Long run real exchange rate is a relative price, which is determined by the price ratios of two baskets:

  • Every price index is determined by good’s market demand and supply.
  • The real exchange rate is therefore determined by demand and supply in both countries.

We focus instead on two specific cases for explaining why the long-run values of real exchange rates can change:

  • A change in world relative demand for American products. Imagine that total world spending on American goods and services rises relative to total world spending on European goods and services. à An increase in world relative demand for U.S. output causes a long-run real appreciation of the dollar against the euro (a fall in ). Similarly, a decrease in world relative demand for U.S. output causes a long-run real depreciation of the dollar against the euro (a rise in q$/€).
  • A change in relative output supply. Suppose that the productive efficiency of U.S. labour and capital rises à A relative expansion of U.S. output causes a long-run real depreciation of the dollar against the euro (q$/€ rises).  A relative expansion of European output causes a long-run real appreciation of the dollar against the euro (q$/€ falls).

Nominal and real exchange rates in equilibrium:

Nominal changes in exchange rates can be split in a monetary and a real component:

  • Changes in money supply and demand in a country yield in the long run to the proportional change in the exchange rate that is predicted by the relative PPP.
  • Shifts in (goods) supply and demand, in contrast, yield changes in the nominal exchange rate that oppose the PPP.

E$/Euro =  q$/Euro * ( PUS/ PE )

At a given Dollar/Euro exchange rate, changes in money supply and demand in the US or in Europe have the same effects as predicted by the monetary theory. Changes in the real exchange rate do also affect the long run exchange rate.

Determinants of changes in the long run nominal exchange rate.

  1. A change in relative money supply level
  • Ex: one-time permanent increase in US money supply level.
  • No effect on relative price and output à no effect on the real exchange rate.
  • Proportional increase of PUS with MUS according to PEU = MsEU /L( R€,YEU).
  • Change in the nominal exchange rate according to E$/Euro =  q$/Euro * ( PUS/ PE ).
  • All explained by the monetary approach and PPP.
An increase in the growth rate of relative money supply
  • Raises long run inflation rate and through the Fisher-effect the Dollar interest rate relative to the Euro interest rate.
  • Real money demand in the USA falls à according to PEU = MsEU /L( R€,YEU) Price level PUS  increases.
  • No change in the real exchange rate.
A change in relative demand for goods
  • No dealt with in the monetary approach.
  • Changes in the nominal exchange rate only driven by the real exchange rate.
  • Increase in relative demand for US goods yield Dollar appreciation.
A change in the relative supply of goods
  • Relative expansion of US-output yields real depreciation.
  • Increase in output raises demand for liquidity (shift of the L-curve).
  • According to PEU = MsEU /L( R€,YEU), US price level falls.
  • q$=Euro  up, PUS  down à ambiguous effect on E$=Euro.

Determinants of changes in the long run nominal exchange rate: Summary

  • If deviations from the equilibrium have exclusively monetary sources, long run nominal exchange rate follows the relative PPP.
  • Monetary changes affect purchasing power of the currency for domestic and foreign goods alike.
  • If deviations from the equilibrium result from deviations on goods and service markets, the exchange rate is unlikely to obey the PPP even in the long run.
  • This exchange rate model is integrated in a broader framework with endogenous output/income in the next part.