Chapter 15 B&W - The Real Exchange Rate

Why is the US the global reserve currency/vehicle currency?

• Strong robust economy with persistent growth

• Strong institutions

• Historically it has been the global reserve currency so it’s difficult to change the structure(s) that are based on the US dollar (inertia)

What is triangular arbitrage and how are arbitrage opportunities eliminated?

• When cross rates are not mutually consistent with three currencies so the trader buys and sells the currencies in a specific order to make a profit

• Once the ‘undervalued’ currency is purchased, its value increases as demand increases and the demand falls for the ‘overvalued’ currency leading to cross rates equalising almost instantaneously

Explain the process of CIRP.

• Result of arbitrage between domestic and foreign currency in the absence of risk taking

• American investor has the choice between investing in US bonds or UK bonds

• Gov. bonds are low risk generally but UK bonds are riskier as value of £ may change over investment period

• They can agree to a forward exchange rate so they recieve (1+i*)St/Ft instead of (1+i*)

• Because the forward exchange rate has been agreed to, investment is covered/hedged.

• The benchmark for judging the attractiveness of the British bond is the US bond therefore ROR must equalise

• (1+ i) = (1+i*)St/Ft

Explain the process of UIRP.

• Result of arbitrage between domestic and foreign currency in the presence of risk-taking

• Assume the investors are risk neutral therefore the risk premiums* = 0

• The £ investment is then sold at St+1

• The expected return in $ from one $ invested in pounds is (1+i*)St/Se t+1

• The no-profit condition for a risk-neutral investors implies that both returns must equalise

• 1+i = (1+i*)Se/Se t+1

*even with the addition of a risk premium, UIRP still holds

What happens if i*> i?

• Investors will borrow domestic currency and convert that into the foreign currency and invest into foreign assets

• However, investors will eventually need to convert back to repay loans so this ‘future selling’ will cause that foreign currency to depreciate

• As they convert back into the domestic currency by purchasing, the domestic currency then depreciates

What is the real interest rate parity condition?

• The interest rate differential is equal to the expected exchange rate appreciation of the domestic currency

• Along with PPP which equates the inflation differential to the rate of appreciation of currency in the medium to long-run

• pit+1* - pit+1 = (St+1-St)/St

• If foreign and domestic forecasts of inflation are consistent with PPP then… domestic real interest rates must equal foreign interest rates

• r* = r - International Fisher Equation

What is the difference in behaviour in the exchange rate from the short run to the long run?

In the short run, it behaves more like the price of an asset whereas in the long run it behaves more like the relative price of goods due to sticky prices

What are the implications of the interest rate parity condition?

• Volatility suggests moments are likely driven by market expectations of the future

• Start with the UIRP condition: 1+i = (1+i*)S^e/S^e_t+1

• Current spot exchange rate is determined by i and i* and market’s expectation of the next period’s exchange rate

• Like all asset prices, S is forward looking so any appreciation expected will show up in current exchange rate

• We can keep iterating the UIRP condition forward to show that today’s exchange rate is explained by i and i* and expected exchange rate

• As they try to guess S^e_t+1, they link it with expectations of i_t+1 and i*_t+1 etc.

Iterate the UIRP condition forward.

• 1+ i_t = (1+ i*_t)St/S^e_t+1

• S_t = (1+i_t)(S^e_t+1)/(1+ i*_t)

• S_t+1 = (1+i_t)(S^e_t+2)/(1+ i*_t+1)

• S^e_t+1 = (1+i^e_t+1)(S^e_t+2)/(1+i*^e_t+1)

• S_t =(1+i_t)/(1+i*_t)*(1+i_t+1)/(1+i*_t+1)*S^e_t+2

What is an apparent contradiction?

If i> i*, S should appreciate immediately according to the iterated form of the UIRP condition yet the original UIRP condition states that if i> i*, the currency should depreciate

Explain the process of overshooting.

• Given i*, UIRP links i to expected rate of appreciation

• Thus when i> i*, there’s a jump in adjustment to allow for future depreciation so UIRP holds in both periods

• The exchange rate must appreciate now to be consistent with the expected depreciation in the future following a tightening of monetary policy

What are Mussa’s Stylised Facts?

1. On a daily basis, changes in floating foreign exchange rates are unpredictable

2. On a month-to-month basis, over 90% of exchange rate movements are unexpected, less than 10% are predictable

3. Countries with high inflation rates have depreciating currencies

4. Countries with rapidly expanding money supplies tend to have depreciating exchange rates vis-à-vis countries with slowly expanding money supplies

5. In the longer run, excess of domestic over foreign interest rates is roughly equal to expected rate of appreciation of foreign currency

6. Actual changes in the spot exchange rate will tend to overshoot any smoothly adjusting measure of the equilibrium real exchange rate

7. In the longer run, countries with persistent trade deficits tend to have depreciating currencies and vice versa

What does the intertemporal budget constraint state?

A nation cannot borrow beyond its means and that accumulated assets will eventually be spent

What is the formula for the primary current account?

PCA₁ + PCA₂/1+r = -F₁

What is F₁? What does it mean when it’s positive/negative?

• Net external position of country at beginning of period

• It’s positive when the country was a net lender previously

• It’s negative when a country was a net debtor

What is the formula for PCA₂? What does it imply?

• PCA₂ = -(1+r)(F₁+PCA₁)= -F₂

• By the end of period 2, the country must repay its accumulated debt or spend its assets

What does it mean if F₂ > 0 ? What about F₂ < 0 ?

• A positive asset position: allows country to run a deficit in the second period

• An external indebtedness position: requires a surplus in second period

What is the link between the PCA and RER?

A lower RER leads to an improved PCA ceteris paribus as it creates export demand and reduces import demand

What does the national budget constraint require?

PCA must be consistent with the solvency condition i.e. PCA must be = to -F₂

What is the short run equilibrium RER? What if F₂ > 0? What about F₂ <0?

• The intersection of the PCA and short run -F₂

• Lower level of net foreign assets today implies a lower deficit tomorrow

• Long run equilibrium RER must depreciate to generate surplus

What is non-price competitiveness and its effects on the PCA ?

• The relative attractiveness of goods holding RER constant

• Shifts PCA schedule up to PCA’ leading to higher equilibrium exchange rate

• In long run, surplus is then eliminated by real appreciation

What is the effect of natural resources on the PCA?

• PCA = PCA^non-oil + PCA^oil

• PCA^oil is negative + substantial

• Leads to a large surplus which then leads to a sharp real appreciation

• Other industries become relatively less competitive due to the RER appreciation (dutch disease)

What is the Balassa-Samuelson effect?

Price levels in richer/more productive in terms of traded goods are systemically higher than in poor ones as a result of higher non-traded goods prices

What is the long-run equilibrium nominal exchange rate driven by?

It’s driven by the long-run equilibrium real exchange rate and by the long-run price levels at home and abroad.