Purchasing power parity (PPP) is built on the notion of arbitrage across goods markets and the Law of One Price. The Law of One Price is the principle that in a PCM setting, homogeneous goods will sell for the same price in two markets, taking into account the exchange rate. Focus on PPP

PPP conditions do not imply anything about causal linkages between prices and exchange rates or vice versa. Both prices and exchange rates are jointly determined by other variables in the economy. PPP is an equilibrium condition that must be satisfied when the economy is at its long-term equilibrium.

In reality, seemingly “homogeneous” goods may differ in a number of important respects which undermine tests of the Law of One Price. One test of the Law of One Price is the Big Mac index, which has been published annually in The Economist since –It was devised as a light-hearted guide to whether currencies are at their “correct” level, based on PPP. PPP in practice

Is there McParity? Cross-country comparison of Big Mac prices: –prices of Big Macs in 41 countries (published in the Economist (1986- )) advantages: homogeneous good, quality control over inputs disadvantages:imperfect competition (strategic pricing), are inputs the same? (nontradables?), government regulations may affect product pricing

Empirical Evidence on Prices and Exchange Rates Source: The Economist, April 29, 2000 Switzerland Britain South Korea France Argentina Euro Area Taiwan Italy Canada Indonesia Brazil Thailand Hong Kong Russia Hungary Malaysia Ratio of Big Mac Prices in US$ Relative to U.S. Price U.S. Price is $2.51/Big Mac

Researchers have investigated whether current deviations for Big Mac Parity help forecast future changes in exchange rates. Answer: Yes, sort of. The Economist claims that the Big Mac method predicted the depreciation in the Euro following its introduction in 1999.

Persistent deviations from PPP A manager may really only care about the duration of deviations from PPP…do they last several months? Years? Forever? Key question: Is there mean reversion in the real exchange rate; does it tend to go back to q=1? Let’s look at a graph of the real exchange rate, which also clearly indicates the deviation from PPP

Mean reversion: RER tends to return to q=1

Empirical Evidence on Prices and Exchange Rates A parity condition can be viewed as a 45° line passing through the origin with the Left Hand Side (LHS) and Right Hand Side (RHS) variables plotted on the x and y axes. Thus, parity conditions can be tested by running the simple linear regression: LHS t =  +  RHS t +  t Parity holds when the data cannot reject a null hypothesis where  = 0,  = 1, and the error terms have classical properties.

Regression test of relative PPP If relative PPP true, s $/peso = p US – p mex This is expressed in % changes Run regression of the form: s $/peso,t =  +  ( p US,t – p mex,t ) +  t Regression test of relative PPP means testing the “null hypothesis”  =0,  =1. Remember: we may reject or fail to reject the null hypothesis. We are not allowed to say we accept it!

Test for US-Germany: Quarterly data, Estimates, with standard errors in parentheses:  = (se=0.010)  = 0.50 (se=1.05) R2 = Null hypothesis: PPP true:  =0,  =1. Construct t-statistic; if absolute value of t < 2, cannot reject null hypothesis. t = (estimate-true value under null)/se Test  =0: t = (.005 – 0)/0.01 = 0.50 cannot reject Test  =1: t = (0.50-1)/1.05 = cannot reject Conclusion: These data do not reject relative PPP for US- Germany over this period. But…we will see that the data can’t reject the alternative hypothesis that  =0,  =0 either!

Alternative hypothesis: exchange rate changes are completely unrelated to inflation differentials:  =0,  =0 Construct the t-statistics:  =0: t = (.005 – 0)/0.01 = 0.50 cannot reject  =0: t = (0.50-0)/1.05 = cannot reject The 95% confidence interval for  is the estimate plus/minus two standard errors: 0.50 – 2(1.05) <  < (1.05) <  These data are very uninformative about 

Quarterly Deviations from Relative PPP CPI: Germany and the United States, (US-German) Inflation Spot Rate Changes  =  = 0.15 R 2 = N = 107 (0.007) (0.83) D–W = 1.83 % Deviations Average Inflation Difference

More Empirical Evidence on PPP During a hyperinflation period, even the demanding regression-style test tends to support PPP. This means: fails to reject PPP, while not failing to reject  =0,  =0. –But, this is mainly due to the fact that monetary influences on prices completely dominate “real” influences on product prices.

More Empirical Evidence on PPP Long-run data indicated that the real exchange rate did not evolve as a random walk, but demonstrated a clear tendency to revert back to its central value. This long-run tendency is called mean reversion. Definition: A variable follows a random walk if upward and downward movements are always equally likely; if the future path of the variable is completely unpredictable from past information.

Empirical Evidence on Prices and Exchange Rates Note that the real exchange rate itself may not be constant. –It may change on a permanent basis if a real shock affected one country but not its trading partners. –The Balassa-Samuelson hypothesis states that countries that have experienced high productivity gains, higher real income growth and higher real incomes should have appreciating real exchange rates.

Empirical Evidence on Prices and Exchange Rates Empirical tests confirm that... –PPP is a poor descriptor of exchange rate behavior in the short run, where the rates are quite volatile and domestic prices are somewhat sticky. –But in longer-run analysis, it appears that PPP offers a reasonably good guide.

Policy Matters - Private Enterprises If managers can identify the deviations from parity that are growing larger or likely to persist, then profit-maximizing decisions can be made. Knowing that deviations from parity occur, managers may adopt strategies that reduce their exposure to the risks of such deviations.

Policy Matters - Public Policymakers Deviations from PPP, by definition, measure changes in a country’s international competitiveness, and reveal whether a currency is overvalued or undervalued relative to a simple standard. However, there are limitations on the usefulness of PPP in policy decisions, as real macroeconomic disturbances call for a change in the real exchange rate.

The covered interest parity diagram r $ -r &  A  B  C  E  E

International Financial and Exchange Rate Adjustments D&D& London money market & $ Forward market & E $/&,fwd D &,fwd S &,fwd Spot market & E $/& D&D& S&S& e0e0 Interest rate S&S& iLiL New York money market Interest rate D$D$ S$S$ i NY e 0, fwd

The interdependence of the parity conditions ( U n c o v e r e d ) i n t e r e s t p a r i t y (Expected) PPP F i s h e r - o p e n

Interest parity in the presence of transaction costs r $ -r & Unprofitable arbitrage Incentive to borrow in pounds and invest in dollars Incentive to borrow in dollars and invest in pounds

Round-trip covered interest arbitrage $ borrowing ----& investment $0$0 $n$n &0&0 &n&n &0&0 &n&n $0$0 $n$n

One-way covered interest arbitrage Spot dollars to future pounds $0$0 $n$n &0&0 &n&n Future pounds to spot dollars &0&0 &n&n $0$0 $n$n