long term exchange rate and...
TRANSCRIPT
Long term exchange rate
and inflation
Lectures 5Nicolas Coeurdacier
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.