long term exchange rate and...

Long term exchange rate

and inflation

Lectures 5Nicolas Coeurdacier

nicolas.coeurdacier@sciences-po.fr

International Finance

Master in International Economic Policy

Motivation and roadmap

• What are the determinants of exchange rates in the

long term?

• Is the Yuan undervalued?

• Why do poor countries have lower prices?

Roadmap:

• The law of one price, purchasing power parity (PPP):

theory and empirics

• The Balassa Samuelson effect: real exchange rates,

growth and productivity

The law of one price (LOP)

• Long term perspective on exchange rates = when

prices are flexible

• On competitive markets, in absence of transport costs and

tariffs… two identical goods must be sold at the same price

(expressed in the same currency)

• Law of one Price = long term arbitrage mechanism

Pi € = E. Pi $

• If Pi € > E. Pi $ : buy the US produced good, sell it in Europe;

increase demand in US, increase supply in Europe: price

converge

Purchasing power parity (PPP)

• P € = E. P $ where P € and P $ are price indices of US and euro zone

• E = P € / P $ : Absolute version of PPP

• Idea developed by Ricardo (1772–1823 ) then Cassel (1866–

1945 )

• An increase in the general level of prices reduces purchasing

power of domestic currency and leads to a depreciation

• The price levels of different countries are equalized when

measured in the same currency:

P € = E x P $

• PPP exchange rate: EPPP= P € / P $

The PPP exchange rate: E PPP(€/$) = P € / P $

45°°°°

Nominal Exchange rate (€/$)

P € / P $

$ undervalued, €

overvalued

$ overvalued, €

undervalued

Relative PPP

• The variation of the exchange rate is equal to

the difference in the variation in prices, the

difference in inflation rates (approximation)

• Et = P €t / P $t ⇒ (Et – Et-1)/Et-1 = π €t - π $t

π €t and π $t: inflation in € zone and US

• π €t = (P€t – P€t-1)/ P€t-1

Back to the monetary approach to exchange

rates (long term, LT)

• PPP in LT: E = P € / P $

• Prices in LT: P€= MS€ / L (r€ , Y€) ; P$= MS

$ / L (r$,Y$)

where r€ , Y€ are LT values

In LT, E is determined by relative supplies and

demands of money in the two countries:

E = P € / P $ = (MS€ / MS

$ ) x [L (r$ , Y$)/L (r€ , Y€)]

Hence under money neutrality in LT,

E%Changes = %Change in MS€- %Change in MS

$

The Fisher effect

• In LT, interest parity condition is also verified:

r€ = r$ + (Ee – E)/ E

• In LT: relative PPP (Et – Et-1)/Et-1 = π €t - π $t

implies that expected depreciation equals

expected inflation differential:

(Ee – E)/ E = πe€ - πe

$

Where π e€ = (Pe

€ – P €)/ P €

• So:

r€ - r$ = (Ee – E)/ E = π e€ - πe

$

• If inflation in euro zone is higher than in the US, the nominal interest rate r€ will also be higher

• In LT, a high nominal interest rate reflects expectations of high inflation: this explains the association of high interest rate and depreciation in LT

• Where does higher inflation come from? an ↑ in the rate of growth of money supply (not only its level). A change in the level of money supply changes the level of prices. A change in the growth rate of money supply changes the rate of growth of prices (inflation)

The Fisher effect

10 years interest rates: France and Germany: source

ECB

Empirical validity of the LOP

– LOP fails in short run : not puzzling for non traded goods (haircuts); but also for traded goods

– Transport costs, trade barriers (tariffs and regulations): make

arbitrage more difficult

– Imperfect competition: firms segment markets (to have high

prices where price elasticity of demand is low) : “pricing to

market”. “Branding”.

– Many goods considered to be highly traded contain nontraded

components. Retail and wholesale costs (distribution costs)

account for around 50% of final consumer price

Empirical validity of PPP

• Studies overwhelmingly reject PPP as a short-run relationship, better as long term

• The variance of floating nominal exchange rates is an order of magnitude greater than the variance of relative price indices

• The failure of short-run PPP can be attributed partly to the stickiness in nominal prices (short run)

• Works much better in the long term

The IKEA Law of One Price

Source: J Haskeland H Wolf, ‘The Law of One Price: a case study’, NBER WP 8112

European Prices in USD

Price differentials in Europe for identical car

models (exc. taxes); 2009

France Germany UK Lowest

VW Passat 115% 124% 82% UK

Renault Clio 3

130% 131% 98% Hungary 93%

NISSAN Micra

113% 110% 77% Poland 71%

FIAT Panda

116% 126% 94% Hungary 92%

Source: EU commission

What is the exchange

rate of country i

consistent with LOP for

the Big Mac?

Required appreciation or

depreciation to satisfy

LOP?

EBig Mac = PUS/Pi

The Economist - Oct. 2010

Long term real exchange rate

• Real exchange rate (RER) defined as the relative price

index of goods and services between two countries: q

= E x P $ / P €

A real depreciation of € vis a vis the $ (q ) can come

from nominal depreciation (E ), an increase in P $ or a

fall in P €

• Relative PPP ⇒⇒⇒⇒ RER is constant !

PPP: (Et – Et-1)/Et-1 = π €t - π $t

(qt – qt-1)/qt-1 = (Et – Et-1)/Et-1 - π €t + π $t = 0

Long Run PPP: $/£ real exchange rate (in logs)

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.517

91

1803

1815

1827

1839

1851

1863

1875

1887

1899

1911

1923

1935

1947

1959

1971

1983

1995

Note: Higher values means a (real) dollar depreciation (or a £ appreciation)

£ overvalued relative to PPP

£ undervalued relative to PPP

The mean reversion of real exchange rates

Long Run PPP: $/£ real exchange rate (in levels)

1

1,2

1,4

1,6

1,8

2

2,2

2,4

2,6

2,8

3

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Spot Exchange Rate $/£ Real Exchange Rate (US/UK) (2000=Spot=1,5)

Mean RER value

Note: Higher values means a dollar depreciation (or a £ appreciation)

The mean reversion of real exchange rates

The Yen/$ exchange rate and the relative price ratio over the long term

Empirical test of relative PPP in the long-run

Looking across countries over a long time period [1960;2001], run the following regression where (i) is a country:

Relative PPP assumption: β is expect to be = 1 (and α = zero).

Can inflation differentials over 41 years explain exchange rate variations over the same period?

YES! β is fairly close to one for this sample of countries (see graph)

Convergence towards PPP: slow reversion towards PPP (from 3 to 5years to eliminate half of the gap)

11960

2001

1960

2001

1960/

2001/

logloglog ++++++++

−−−−

++++====

tus

us

i

i

usi

usi

PP

PP

SS εεεεββββαααα

Remember relative PPP:

(Et – Et-1)/Et-1 = π €t - π $t

-40

-23

-7

10

27

43

60

-40 -20 0 20 40 60In fla ti o n d i ffe re n ti a l

-10

-3

3

10

17

23

30

-20 -10 0 10 20 30

-6

-3

0

3

6

9

12

-10 -5 0 5 10 15Infla tion Diffe re ntia l

Relative PPP prevails in the very long-run but fails in the short-run

1 Year Window

5 Year Window

Inflation Differential

20 Year Window

%Depreciation

%Depreciation

%Depreciation

The Balassa-Samuelson effect

• Why are prices higher in rich countries?

• Same question as: why E x P rich > P poor?

• Why does the real exchange rate of countries that

grow relative to rest of world appreciate?

q = E x Pworld / P ↓

• Examples: Japan, South Korea, Ireland, today China?

• Key distinction: Tradable goods (manufactured goods) and non

tradable (services)

• Around 75% of the consumption basket in industrialized

countries is non tradable (health, education, most services…)

even if definition of a tradable good/service becomes blurred

(internet)

• Productivity differences between rich and poor countries is

much larger for tradables than for non tradables: it is very large

for example in manufacturing (of an order of 10), but much

smaller in services (think of haircuts: technology is not hugely

different across countries)

The Balassa-Samuelson model

Workers can be hairdressers (non-traded) or work in

the textile industry (traded). Workers can produce

haircuts or T-shirts.

T-shirts sold 1$ in international markets.

US worker produces 50 T-shirts/hour, Indian worker

only 10.

Both US and Indian hairdressers make 5 haircuts/

hour.

Question: what is the price of an haircut in India and in

the US?

The Balassa-Samuelson model: a simple example

• 2 countries: Poor country, rich country (*)

• Price index depends on tradables (T) and non-tradables (N) :

P = (PT)a x (PN)1-a ; P* = (P*T)a x (P*N)1-a

• Share a and 1-a (around 25% and 75%)

• One factor of production: labor

• Mobile between sectors (in long term) but not between countries

• Two countries are identical except in productivity

The Balassa-Samuelson model

• Labor is mobile between sectors:

Arbitrage ⇒ w = wT = wN ; w*= w*T = w*N

Profit max. by firms ⇒ marginal cost of labor = marginal

value of employing one more unit of labor (otherwise

labor demand by firms does not max. profits): for example

in T: w = PT AT

AT: marginal productivity of labor (nb of units of goods

produced with one more unit of labor)

real wage = marginal productivity of labor :

w / PT = AT ; w/ PN = AN

w* / P*T = A*T ; w* / P*N = A*N

• PPP for tradable goods (not for non tradables)

Choose numeraire so that E = 1 (normalization with no

real consequence): PT = P*T

and PT = w / AT P*T = w* / A*T

so w/w* = AT / A*T

First result: wages in poorer countries are lower

because labor productivity in tradables sector is lower

(technology)

Wages in non tradables are also lower in poorer

countries because wages are equalized by arbitrage

across sectors inside each country

Balassa Samuelson effect

PN / P*N = (w /AN)/ (w* /A*N) = (AT / A*T)/(AN / A*N)

as PN = w /AN , P*N = w/ A*N and w/w* = AT / A*T

The relative price of non tradables depends on the

relative productivities in the tradable and non tradable

sectors.

If rich country more productive in tradables (AT < A*T),

poor country has lower non-tradable prices like in the

simple example

Relative Price index between countries (use PPP on

tradables):

(PT)a x (PN)1-a (PN)1-a

P/P* = =

(P*T)a x (P*N)1-a (P*N)1-a

(Use PPP in T)

Balassa Samuelson effect

Relative prices between countries depends on relative

productivities between tradables and non tradables:

(AT / A*T)1-a

P/P* = < 1 if AT / A*T < AN / A*N

(AN / A*N)1-a

The productivity differential between poor and rich countries is much larger in T (AT << A*T) than in N (AN < A*N)

No effect on relative prices P/P* if the gap in productivity is equal in both sectors

Balassa Samuelson effect

Poorer countries have lower wages in tradables

because of lower productivity; these translate in lower

wages in non tradables and lower prices in this sector

as productivity gap is not as large: prices are lower in

poorer countries.

As a country gets richer, AT increases (more than AN );

its wages in the T sector ↑ and therefore in the N

sector too. Its price index increases relative to other

countries

Is China real exchange rate undervalued?

• By Big mac index or PPP (on all goods) yardstick:

around 40 to 50%

• Also, if calculate RER that eliminates the chinese CA

surplus

• But China is still a poor country (GDP/cap): relative to

what Balassa Samuelson predicts, yuan is undervalued

by 12%

• Could come through nominal appreciation or domestic

inflation

Income convergence and exchange rate appreciation (here appreciation is up!)

Source: Reisen , 2009

Brief Summary

• According to Purchasing Power Parity (PPP), exchange rates

and prices should adjust such that goods in different

countries have the same price when expressed in the same

currency.

• In the (very) long run changes in nominal exchange rates

reflect differences in inflation as predicted by relative PPP.

• Failures of PPP in the short-run are due to price rigidities,

barriers to international trade, pricing-to-market…

• Due to the Balassa Samuelson effect, poor countries have

lower prices and face appreciating real exchange rates

when catching-up in terms of productivity.