International Finance Master in International Economic Policy Long term exchange rate and inflation Lectures 5 Nicolas Coeurdacier nicolas.coeurdacier@sciences-po.fr
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 P i = E. P i $ If P i > E. P i $ : 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: E PPP = P / P $
The PPP exchange rate: E PPP ( /$) = P / P $ P / P $ $ undervalued, overvalued $ overvalued, undervalued 45 Nominal Exchange rate ( /$)
Relative PPP The variation of the exchange rate is equal to the difference in the variation in prices, the difference in inflation rates (approximation) E t = P t / P $t (E t E t-1 )/E t-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 = M S / 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 $ = (M S / MS $ ) x [L (r $, Y $ )/L (r, Y )] Hence under money neutrality in LT, E%Changes = %Change in M S - %Change in MS $
The Fisher effect In LT, interest parity condition is also verified: r = r $ + (E e E)/ E In LT: relative PPP (E t E t-1 )/E t-1 = π t - π $t implies that expected depreciation equals expected inflation differential: (E e E)/ E = π e - πe $ Where π e = (Pe P )/ P
The Fisher effect 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)
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 European Prices in USD Source: J Haskeland H Wolf, The Law of One Price: a case study, NBER WP 8112
Price differentials in Europe for identical car models (exc. taxes); 2009 France Germany UK Lowest VW Passat 115% 124% 82% UK Renault Clio 3 NISSAN Micra FIAT Panda 130% 131% 98% Hungary 93% 113% 110% 77% Poland 71% 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? E Big Mac = P US /P i 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: (E t E t-1 )/E t-1 = π t -π $t (q t q t-1 )/q t-1 = (E t E t-1 )/E t-1 -π t + π $t = 0
Long Run PPP: $/ real exchange rate (in logs) 0.5 The mean reversion of real exchange rates 0.4 0.3 0.2 overvalued relative to PPP 0.1 0-0.1-0.2-0.3-0.4 undervalued relative to PPP -0.5 1791 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)
Long Run PPP: $/ real exchange rate (in levels) 3 The mean reversion of real exchange rates 2,8 2,6 2,4 2,2 2 1,8 1,6 1,4 Mean RER value 1,2 1 2004 2002 2000 1998 1996 1994 1992 1990 1988 1986 1984 1982 1980 1978 1976 1974 1972 1970 1968 1966 1964 1962 1960 Spot Exchange Rate $/ Real Exchange Rate (US/UK) (2000=Spot=1,5) Note: Higher values means a dollar depreciation (or a appreciation)
The Yen/$ 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: i / us i us S 2001 P 2001 P 2001 log log log + / = α + β ε i us i us t + S 1960 P 1960 P 1960 1 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 5 years to eliminate half of the gap)
Relative PPP prevails in the very long-run but fails in the short-run %Depreciation 6 0 1 Year Window 4 3 2 7 1 0-7 -23 %Depreciation 30 23 17-40 -4 0-2 0 In fla ti o n d i ffe re n ti a l 0 2 0 4 0 6 0 %Depreciation 12 9 6 3 0-3 -6 Infla tion Diffe re ntia l -10-5 0 5 10 15 10 3-3 -10-20 -10 0 10 20 30 20 Year Window Inflation Differential Remember relative PPP: (E t E t-1 )/E t-1 = π t - π $t 5 Year Window
The Balassa-Samuelson effect Why are prices higher in rich countries? Same question as: why E x P rich > P poor? Why does the real exchange rate of countries that grow relative to rest of world appreciate? q = E x P world / P Examples: Japan, South Korea, Ireland, today China?
The Balassa-Samuelson model Key distinction: Tradable goods (manufactured goods) and non tradable (services) Around 75% of the consumption basket in industrialized countries is non tradable (health, education, most services ) even if definition of a tradable good/service becomes blurred (internet) Productivity differences between rich and poor countries is much larger for tradables than for non tradables: it is very large for example in manufacturing (of an order of 10), but much smaller in services (think of haircuts: technology is not hugely different across countries)
The Balassa-Samuelson model: a simple example Workers can be hairdressers (non-traded) or work in the textile industry (traded). Workers can produce haircuts or T-shirts. T-shirts sold 1$ 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 2 countries: Poor country, rich country (*) Price index depends on tradables (T) and nontradables (N) : P = (P T ) a x (P N ) 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
Labor is mobile between sectors: Arbitrage w = w T = w N ; 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 = P T A T A T : marginal productivity of labor (nb of units of goods produced with one more unit of labor) real wage = marginal productivity of labor : w / P T = A T ; w/ P N = A N 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): P T = P* T and P T = w / A T so w/w* = A T / A* T P* T = w* / 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 P N / P* N = (w /A N )/ (w* /A* N ) = (A T / A* T )/(A N / A *N ) as P N = w /A N, P* N = w/ A* N and w/w* = A T / 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 (A T < A* T ), poor country has lower non-tradable prices like in the simple example
Relative Price index between countries (use PPP on tradables): (P T ) a x (P N ) 1-a (P N ) 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: (A T / A* T ) 1-a P/P* = < 1 if A T / A* T < A N / A *N (A N / A *N ) 1-a The productivity differential between poor and rich countries is much larger in T (A T << A* T ) than in N (A N < 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, A T increases (more than A N ); 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.