Long term exchange rates and inflation Purchasing power parity and the Balassa-Samuelson effect

Last Thursday Fed increased its main rate (well expected): raised by 0.25 the target range for the federal funds rate to 0.75 per cent to 1 per cent Market expectations for at least four Federal Reserve rate increases this year dipped to less than one-in-five

Motivation and roadmap What are the determinants of exchange rates in the long term? 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) Pi € = E. Pi $ : long term arbitrage mechanism 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 $

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

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€)] MS€ ↑⇒ P € ↑ ⇒ € depreciation (how much depends on velocity of money, here =1) Y€ ↑⇒ money demand ↑ ⇒ P € ↓ ⇒ € appreciation - r€ ↑ ⇒ money demand ↓⇒ P € ↑ ⇒ € depreciation

The Fisher effect (1) 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 €

The Fisher effect (2) So: r€ - r$ = (Ee – E)/ E = π e€ - πe $ If expected inflation in euro zone is lower than in the US, the nominal interest rate r€ will also be lower In LT, a higher nominal interest rate reflects expectations of higher inflation: this explains the association of high interest rate and depreciation in LT in the data see today 10 year interest rates US = 2.6% (2% 2 years ago); Germany: +0.45% (0.33% 2 years ago) The ST and LT links between interest rates and exchange rate changes are opposite!

Empirical validity of the LOP LOP fails: not puzzling for non traded goods (haircuts) More puzzling for traded goods

The usual suspects behind the empirical failure of the LOP Transport costs, trade barriers (tariffs and regulations): make arbitrage more difficult On purpose: lobbies to regulate markets differently to weaken competition Imperfect competition: firms want to segment markets (to have high prices where price elasticity of demand is low) : “pricing to market” Many goods considered to be highly traded contain nontraded components. Retail and wholesale costs (distribution costs) account for around 50% of final consumer price

Price differences for a selection of best-selling cars (% of prices in euro before tax, comparing the most expensive with the cheapest euro zone market)

Berka, Devereux, Engel, 2014, Real Exchange Rates and Sectoral Productivity in the Eurozone; NBER Working Paper No. 20510

Price dispersion across and within Eurozone countries

Empirical validity of PPP Studies overwhelmingly reject PPP as a short-run relationship, better as long term The failure of short-run PPP can be attributed mostly to the stickiness in nominal prices (short run) In long term (after 4-5 years) evidence that exchange rates converge to PPP levels

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

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 € (can also be computed inside € zone) 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

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?

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…) Productivity differences between rich and poor countries much larger for tradables than for non tradables: very large in manufacturing (around 10 between average industrialized and debelopping country), but much smaller in services (haircuts: technology not so different across countries)

2 countries: Poor country, rich country ( 2 countries: Poor country, rich country (*) Price index (CPI) depends on tradables (T) and non tradables 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 Identical countries except in productivity

Labor is mobile between sectors in LT: 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: 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 →w / AT = w*/A*T so w/w* = AT / A*T First result: wages in poorer countries are lower because of lower productivity in tradables Wages in non tradables also lower in poorer countries: 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

P/P* = = (P*T)a x (P*N)1-a (P*N)1-a 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 PT = P*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 much larger in T (AT << A*T) than in N (AN < A*N) No effect on relative prices P/P* if international productivity gap equal in both sectors

Balassa Samuelson effect Poorer countries have lower wages in tradables because of lower productivity in tradables; these translate in lower wages in non tradables and lower non tradables prices (productivity gap not as large in NT)  lower prices in poorer countries As a country gets richer, AT increases (more than AN ); wages in the T sector ↑ and therefore in the N sector too. Its price index increases relative to other countries China? How does its RER compare to what is predicted by Balassa Samuelson? ln(RER) = constant + a ln (GDP/capita)

China’s real effective exchange rate: q = EP*/P Where E, P* are weighted exchange rate and foreign prices (weighted by trade share with China) q decreases means real apppreciation Source: BIS, 2010=100

China real exchange rate expected to appreciate Real effective appreciation of around 20% since 2010 (mostly through nominal appreciation): expected from fast growing country (Balassa Samuelson) China is still a relatively poor country (GDP/cap): lower prices than in OECD countries (PPP should not hold for CPIs: Yuan may not be so undervalued) But as converges to GDP/cap of OECD will appreciate (nominal appreciation or inflation)

In 2000 , 36% undervalued (with respect to Balassa Samuelson prediction). Careful here up is appreciation (just to confuse you…) The Balassa-Samuelson Relationship and the Renminbi, Jeffrey Frankel, december 2006