Inflation and Exchange Rates

Recall two kinds of inflation that we distinguish in this class

Money inflation: an increase in the money supply Price inflation: an increase in the price level Money inflation is the primary cause of price

inflation Law of one price

The idea that the same goods should sell for the same price

Inflation and Exchange Rates

Arbitrage: buying and selling to take advantage of price discrepancies.

Buy where prices are low, sell where high Transportation & other transaction costs may

prevent arbitrage Arbitrage tends to reduce price discrepancies as

supply is shifted from low-price areas to high-price areas

International arbitrage

The law of one price when applied to international markets suggests that identical goods should cost the same in different countries after exchange rates have been factored in.

Suppose potatoes are $1.00 per pound and the exchange rate is $1.50/£

We would expect potatoes to sell for £0.67 per pound in UK (or £1.47 per kilo)

The ability to arbitrage divergences from this price depends on transportation costs, quotas and tariffs, different consumer tastes, etc.

Law of One PriceApplied to the Price Level

Given PLUK

, the price level in the UK, the law of one price suggests that the same price level ought to prevail in the US after exchange of currency:

PLUS

= XR($/£) x PLUK

If this condition is satisfied, there is purchasing power

parity (PPP) between these two currencies Absolute PPP rearranges this equation

XR($/£) = PLUS

/ PLUK

Example: if the UK price level (£/basket) is 2/3 of the US price level ($/basket), the XR should be 3/2 = $1.50/£

Law of One PriceApplied to the Price Level

The difference form of the PPP equation is

ΔXR($/£) = ΔPLUS – ΔPLUK

Example: if the UK price level rises 5% in one year and the US price level rises 3% in the same year, the theory predicts the XR would fall by 2%

Problems Difficult to compare “baskets” between countries Price levels are retrospective, XR are prospective Many goods are non-tradable

Problems with PPP

Difficult to choose a “basket” (price index) that can be applied to two countries

A product that is important to one country may be unimportant or non-existent in the other.

Some goods and services are non-tradable or entail high transportation costs

Trade barriers may inhibit arbitrage Markets for some goods may be highly competitive

in one country, monopolized in another Tax policies are different. European VAT taxes are

included in prices, US sales taxes are not

Problems with PPP

Any price data is very approximate Price levels are retrospective, exchange rates are

prospective – they reflect market participants’ estimates of future developments

Exchange Rates and Price Levels

Long the run version of absolute PPP (correlation of XR with price levels) works well (3 years or more, Fig. 16.2)

Short run correlation is not so good Also, the long run relative version of PPP

(correlation of XR changes with price level changes) works well in the long run, not well in the short run

Why? In the long run, capital and labor can be moved so that some nontradeable goods are produced where they were previously underpriced

The Big Mac Index

The Big Mac Index

A semi-serious effort by The Economist magazine to assess the purchasing power of various currencies

Why the Big Mac? McDonald’s has locations in almost every country

US 18,500 England 1,250

Japan 3,598 France 1,200

China 1,500 Australia 780

Brazil 1,413 Mexico 500

Canada 1,400 Spain 435

Germany 1,361 Italy 392

The Big Mac Index

Big Macs are available all around the world and are the same everywhere. Use their prices, converted to US$, to judge other currencies’ purchasing power.

Problems with the Big Mac as a price index Big Macs not tradeable nor are they completely

uniform across countries Purchasers of Big Mac get to sit at a table where

real estate may be very expensive The price may vary widely within a country

And yet, it seems to work about as well as other price indices

Big Mac PPP Calculations

Note US Big Mac price (averaged across the country)

Note the price in some country in its local currency Change the local price to US$ using the current XR Compute the percent difference between the local

price in US$ and the US price. If the local price is lower, the currency is under-

valued If the local price is higher, the currency is over-

valued

Real Interest Rate Parity Theory

We have seen how interest rate differentials affect capital flows. Now we see how real interest rates affect real exchange rates

Real interest rates are interest rates adjusted for anticipated price inflation: r = i – %ΔPL

“i” is the nominal interest rate (% per annum) %ΔPL is the anticipated percent change in the

price level (price inflation) “r” is the real, inflation-adjusted interest rate

Real Interest Rate Parity Theory

Real interest rate theory suggests that a real interest rate differential between two countries should be reflected in the expected change in the real exchange rate of their currencies. Example:

rUK

– rUS

= %ΔRXR

Example: US i=5% nominal, past %ΔPL=3%, real r=2% UK i=7% nominal, past %ΔPL=6%, real r=1%

Expected change in real XR = rUK

-rUS

= -1%

The US$ versus other currencies

The US dollar index shows the US dollar in terms of a basket of foreign currencies consisting of

57.6% Euros 13.6% Yen 11.9% Pound sterling 9.1% Canadian dollar 4.2% Swedish kroner 3.6% Swiss franc

US Dollar Index History