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**Purchasing Power Parity**

Purchasing Power Parity and Exchange Rate Determination PPP Deviations and the Real Exchange Rate Evidence on PPP

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**Purchasing Power Parity in a Perfect Capital Market**

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.

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**Purchasing Power Parity**

Let PUS and PUK represent the weighted average price level for goods in the U.S. and U.K. market baskets respectively. Absolute PPP predicts that these two price measures will be equal after adjusting for the exchange rate: PUS = S$/£ PUK Absolute PPP requires that the consumption baskets are identical across the two countries.

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**Purchasing Power Parity and Exchange Rate Determination**

The exchange rate between two currencies should equal the ratio of the countries’ price levels: S($/£) = P£ P$ For example, if an ounce of gold costs $300 in the U.S. and £150 in the U.K., then the price of one pound in terms of dollars should be: S($/£) = P£ P$ £150 $300 = = $2/£

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**Relative Purchasing Power Parity**

Suppose absolute PPP is violated. Introduce K so that: PUS, t +1 = K S$/£, t +1 PUK, t +1 (a) PUS, t = K S$/£, t PUK, t (b) %ΔpUS = %Δ s + %Δ pUK + %Δ s %Δ pUK For small % changes, or when continuous rates are used, the cross-product term %Δ s %Δ pUK can be ignored. % exchange rate = % U.S.prices – % U.K.prices

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**Relative Purchasing Power Parity**

Note that %Δp = π, the rate of inflation Relative PPP states that the rate of change in the exchange rate is equal to the differences in the rates of inflation: %Δs = (1 + £ ) ($ – £) ≈ $ – £ If U.S. inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 2.78% or around 3%.

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Ex-Ante PPP Ex-Ante PPP says that relative PPP will hold in an expected value sense, i.e. Where E is the expectations operator signifying that E(·) is an expected value.

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**Purchasing Power Parity in a Perfect Capital Market**

An index of the real exchange rate is defined as: Spot (Real, t) = Spot (Nominal, t) . Spot (PPP, t) Example Today’s spot exchange rate is $1.80/£ PPP spot rate is $1.50/£ Real exchange rate index = 1.80/1.50 = 1.20 At 1.20, the £ is “overvalued” on a PPP basis. 1.0 British good can be exchanged for 1.2 U.S. goods. So, sellers of British goods have “lost competitiveness” on international markets.

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**PPP Deviations and the Real Exchange Rate**

The real exchange rate is The real exchange rate is calculated by correcting the nominal exchange rate for the price levels in the two countries. If PPP holds then When PPP holds, the real exchange rate is constant.

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Real Exchange Rates

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**Purchasing Power Parity in a Perfect Capital Market**

Example Base period nominal exchange rate = $1.50/£ Prices of U.S. goods had risen by 8% Prices of U.K. goods had risen by 4% PPP spot rate = $1.50/£ 1.08/1.04 = $1.5577/£ A nominal exchange rate of $1.5577/£ would reestablish PPP in comparison to the base period. Nominal exchange rates greater than $1.5577/£ represent £ “overvaluation” ($ undervaluation), while rates less than $1.5577/£ represent $ “overvaluation” (£ undervaluation).

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**The Big Mac PPP Standard**

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Evidence on PPP PPP probably doesn’t hold precisely in the real world for a variety of reasons. Haircuts cost 10 times as much in the developed world as in the developing world. Film, on the other hand, is a highly standardized commodity that is actively traded across borders. Shipping costs, as well as tariffs and quotas can lead to deviations from PPP. Productivity differences in traded and non-traded goods. PPP-determined exchange rates still provide a valuable benchmark.

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**How Large is China’s Economy**

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**Purchasing Power Parity in a Perfect Capital Market**

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.

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**Relaxing the Perfect Capital Market Assumptions**

Transaction Costs Transport and menu costs lead to a neutral band around the PPP line, within which it is not profitable to execute arbitrage transactions. Taxes Tariffs have an effect similar to transaction costs. Uncertainty Arbitrageurs will seek a greater profit to compensate for risks, thus leading to a wider band around the PPP line before arbitrage becomes profitable.

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**Empirical Evidence on Prices and Exchange Rates**

A parity condition can be viewed as a 45° line passing through the origin with the LHS and RHS variables plotted on the x and y axes. Thus, parity conditions can be tested by running the simple linear regression: yt = 0 + 1 xt + ut Parity holds when the data cannot reject a null hypothesis where 0 = 0, 1 = 1, and the error terms have classical properties.

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**Some Terminology Dependent Variable, or Left-Hand Side Variable, or**

In the simple linear regression model, where yt = b0 + b1xt + ut, we typically refer to y as the Dependent Variable, or Left-Hand Side Variable, or Explained Variable, or Regressand

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Some Terminology, cont. In the simple linear regression of y on x, we typically refer to x as the Independent Variable, or Right-Hand Side Variable, or Explanatory Variable, or Regressor, or Covariate, or Control Variables

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A Simple Assumption The average value of u, the error term, in the population is 0. That is, E(u) = 0 This is not a restrictive assumption, since we can always use b0 to normalize E(u) to 0

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OLS estimated slope is

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**The Intercept Estimate**

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**Summary of OLS slope estimate**

The slope estimate is the sample covariance between x and y divided by the sample variance of x If x and y are positively correlated, the slope will be positive If x and y are negatively correlated, the slope will be negative

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More OLS Intuitively, OLS is fitting a line through the sample points such that the sum of squared residuals is as small as possible, hence the term least squares The residual, û, is an estimate of the error term, u, and is the difference between the fitted line (sample regression function) and the sample point

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**. . . . { Sample regression line, sample data points**

and the associated estimated error terms y . y4 { û4 . y3 } û3 . y2 û2 { . } û1 y1 x1 x2 x3 x4 x

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**Empirical Evidence on Prices and Exchange Rates**

With the rise of e-commerce, investigating the Law of One Price becomes easier and violations more puzzling. A recent Wall Street Journal article highlighted the case of a popular book that sold for $16.20 at Amazon.com (U.S.), for $13.52 at Amazon.co.uk (Britain), and for $27.00 at Amazon.de (Germany).

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**Empirical Evidence on Prices and Exchange Rates**

To examine the relative PPP condition, we can compare the exchange rate change to the contemporaneous inflation differential: Δst = b0 + 1 (Δp$ – ΔpDM)t + ut It seems that PPP is a poor explanation of exchange-rate changes on a period-by-period basis. However, there is a tendency for PPP to reassert itself as time passes (mean reversion).

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**Quarterly Deviations from Relative PPP CPI: Germany and the United States, 1973-1999**

(US-German) Inflation Spot Rate Changes = = R2 = N = 107 (0.007) (0.83) D–W = 1.83 % Deviations Average Difference

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**Empirical Evidence on Prices and Exchange Rates**

During a hyperinflation period, even the demanding regression-style test tends to support PPP. This is due in some degree to dollarization. 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.

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**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.

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**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.

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**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.

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**Policy Matters - Private Enterprises**

In a number of instances, international price differentials in some commodities have been both large and persistent. More interesting perhaps are the international price differentials across “branded goods” like McDonald’s Big Mac and The Economist, whose prices are set by brand managers rather than by market forces.

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**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.

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