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PPP and the Law of One Price: Empirical Evidence and

Implication for Theory and Policy

Charles EngelUniversity of Wisconsin

August 19, 2004

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Definition of PPP• Work with 2-country example throughout – U.S.

and Europe.• Let P$ be the dollar price of a basket of U.S.

consumer goods, and P*$ be the dollar price of a basket of European consumer goods

• “Absolute” PPP says P$ = P*$ . (Typically we do not test absolute PPP because the most readily available price data are in the form of indexes. But, for example, the Penn World Table data show that there is a tendency for price levels to be higher in higher-income countries.)

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• “Relative” PPP says P$ =k P*$ , where k is some constant. In log terms, we have p$ =c+ p*$

• As we all know, relative PPP is violated at any point in time for virtually any pair of countries.

• Instead, we ask if limit (as k→∞)

Et(p$,t+k - p*$,t+k)=c• That is, does the real exchange rate converge?

If it does, then c is the unconditional mean of the real exchange rate.

• Typically, we take the alternative to be that the real exchange rate has a unit root. So we test for “long-run” PPP by testing for a unit root in the real exchange rate.

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A short list of early papers that tested for unit root in real exchange rates:

• Frankel (1986) in “How open is the US economy?”, Haver, ed.

• Huizinga (1987) Carnegie-Rochester• Edison (1987) JMCB• Meese and Rogoff (1988) J. Finance• Enders (1988) ReStat

Since real exchange rates are very persistent, standard unit root tests have low power in “short” (i.e., post-Bretton Woods) samples.

Researchers have tried longer samples and panel tests to increase power.

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Some papers that have used longer samples:• Frankel (1986)• Edison (1987)• Abuaf and Jorion (1990) J. Finance• Diebold, Husted, and Rush (1991) JPE• Glen (1992) JIE• Cheung and Lai (1994) Econ. Letters• Lothian and Taylor (1994) JPE

• In short samples among advanced countries, PPP generally is not rejected.

•But in longer samples, it usually is.

•Concerns about mixing different time periods. Has d.g.p. changed? Is there sample selection bias?

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A number of studies increase power by examining PPP across panels of countries:

• Frankel and Rose (1996) JIE• Wu (1996) JMCB• Lothian (1997) JIMF• O’Connell (1998) JIE• Papell (1998) JIE

•Panel studies generally reject PPP

•But they often must impose unrealistic assumptions: common rate of convergence, independent errors, common unconditional mean

•Their power tends to disappear and rejections are less frequent when these problems are addressed.

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• One reason panel studies tend to reject is that they often include high-inflation LDCs. It seems that PPP convergence is much faster for high-inflation countries.

• This is borne out by a number of studies that focus on LDCs:

• Bahmani-Oskooee (1993) World Development• Mahdavi and Zhou (1994) J. Macro.• Zhou (1997) Southern Econ. J.• Boyd and Smith (1999) Manchester School

• Notably, Cheung and Lai (2000) JIE, compare LDCs and advanced countries. Rejection of unit root null is much more likely in LDCs. Average convergence is faster in LDCs. This appears most closely related to high inflation in LDCs.

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But what economic hypothesis lies behind PPP?

Why are we testing for PPP?• It is useful to think about reasons why PPP

might fail. We will focus on three reasons, and will work with a 3-good example:

p$ = α1p$US + α2p$

EU + αNp$N

p$US dollar price of US produced goods in US

p$EU dollar price of European goods in US

p$N dollar price of U.S. non-traded goods

αi weights in price index. α1+α2+αN = 1

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• Likewise:

p*$ = β1p*$US + β 2p*$

EU + β Np*$N

p*$US dollar price of US produced goods in

Europe

p*$EU dollar price of European goods in

Europe

p*$N dollar price of European non-traded

goods

β i weights in price index. β 1+ β 2+ β N = 1

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Let’s assume that there are three types of independent shocks:

• Deviations from the law of one price for traded goods: p$

US- p*$US and p$

EU- p*$EU. Assume the

same economic force drives both so that

p$US- p*$

US = p$EU- p*$

EU ( LOOP)• Terms of trade shocks:

p$US-p$

EU (= p*$US-p*$

EU) ( TOT)• Shocks to relative price of non-traded goods:

p$N-p$

T ( NTUS) and p*$N-p*$

T ( NTEU)where

p$T (α1p$

US + α2p$EU )/(1-αN)

p*$T (β 1p*$

US + β 2p*$EU )/(1-βN)

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With a little bit of algebra, we find:

p$ - p*$ = LOOP +

TOT(w-w*)/[(1+w)(1+w*)] +

αNNTUS – βNNTEU

where

w α1/ α2 w* β 1/ β 2

What might make each of these terms non-zero or non-stationary?

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Deviations from the law of one price:• Transport costs, tariffs, or other barriers to trade• Prices are sticky in local currency, but exchange

rate fluctuates. That is,

p$US- p*$

US = p$US- s$/€ - p*€

US

• Consumer prices of “traded goods” contain a large non-traded component representing marketing and distribution.

• In empirical work, we may not be pricing comparable goods.

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Terms of trade

• Note that terms of trade changes can only influence the real exchange rate if the weights in the price indexes are different.

For example, if there is home bias, w > w*, then an increase in the price of the good produced at home will push up the home CPI relative to the foreign CPI: an improvement in the terms of trade causes a real appreciation.

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Relative price of non-traded goods• This is the traditional alley for looking for real

exchange rate movements. Note it requires αNNTUS to move relative to βNNTEU

• Balassa-Samuelson offers one theory of this term: based on differences in productivity of traded goods. Evidence on this is mixed.

• Kravis-Lipsey-Bhagwati suggest that when FPE does not hold, labor abundant countries will have lower wages. Non-traded goods are labor intensive.

• Preferences are not homothetic. As income increases, demand for non-traded goods rises.

• All these offer explanations for why rich countries have higher price levels.

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How important is each component?

Engel (1999) examines the question for OECD countries relative to the U.S. using various measures of prices.

That paper notes that among OECD countries, expenditure shares on traded goods are not much different, so in the main it leaves out the TOT term and decomposes the real ex. rate as:

p$t - p*$t = LOOPt + NTt

where

NTt αNNTUS – βNNTEU

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The paper examines MSE decompostions of k-differences in the real exchange rate and its components. That is, it looks at:

MSE[Δk(LOOPt)]/ MSE[Δk(p$t - p*$t )] and

MSE[Δk(NTt)]/ MSE[Δk(p$t - p*$t )]

where

Δk k – difference.

Note that there is little co-movement between LOOP and NT , so

MSE[Δk(LOOPt)]+MSE[Δk(NTt)]MSE[Δk(p$t - p*$t )]

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Engel (1999) finds:• For most measures of prices, the LOOP term

accounts for over 95% of the MSE of real US exchange rates at horizons less than one year.

• Surprisingly, even at quite long horizons (20 years or more), this finding holds up for most countries relative to the US (the exception being Canada, where the LOOP share falls to 40%)

• The results are not quite so dramatic when the PPI is used to measure the price of traded goods (though it is more difficult to maintain the “equal weights” hypothesis with PPIs.)

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Betts and Kehoe (2004) find:

• LOOP component accounts for most of MSE among advanced countries

• LOOP’s share is larger when CPIs are used to measure traded goods instead of PPIs

• Its share is smaller when two countries trade a lot

• Results are all consistent with Engel (1999).

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• Engel (1999) and Engel (JMCB, 2001) finds that LOOP accounts for a large MSE under “fixed” exchange rate regimes, though in both studies the time period includes significant devaluations.

• Mendoza (2001) and Naknoi (2004) find that the LOOP share of the MSE is much smaller when nominal exchange rates are fixed.

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Long-run PPP could fail because any of the three terms - LOOP, TOT or NT - have unit roots.If any one of them has a unit root, will a test for PPP reject a unit root?Engel (2000) argues not, at least for advanced countries. We know LOOP is very volatile, but surely converges eventually. But if NT or TOT have a unit root, we would not be able to discover it looking at aggregate price data. The LOOP movements mask the NT and TOT movements.

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• Engel (2000) constructs artificial LOOP and NT series that match some properties of data for US-UK from Engel (1999).

• LOOP term is a persistent AR(1), with high innovation variance.

• NT term is assumed to be a random walk, with small innovation variance.

• By construction, then, LOOP + NT has a unit root. It follows an ARIMA (2,1,1).

• Engel (2000) finds that the true size of unit root tests with nominal size of 5 percent is > 80%. The tests usually reject a unit root even though there is one.

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• What is wrong with the tests?• Technically, it is because they do not handle well

large moving average roots under the null. But in this case, the MA coefficient is close to -1.

• But, in common sense terms, if we are trying to find out whether there is a persistent NT term, we should look at data on NT, rather than data on p$ - p*$ .

• The general lesson is this: PPP is an idea that goes back to the days before macro had micro foundations. Tests of PPP are not that revealing.

• There is much interesting work on LOOP, NT, and TOT.

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Rogoff’s (1996) “PPP puzzle”• Among advanced, low-inflation countries, the

real exchange rate is very volatile and very persistent. The half-life of the real exchange rate is 3-5 years.

• There are plausible theories for why TOT or NT might be very persistent, but they are not volatile enough to be the main drivers of the real exchange rate.

• Models with sticky nominal prices and floating exchange rates can explain the volatility of the real exchange rate through LOOP deviations, but the persistence is inexplicable.

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LOOP Deviations

• Engel and Rogers (1996, AER) look at determinants of volatility of short-run changes in pij – pik among U.S. and Canadian cities. (The price of good i between cities j and k.)

• Distance explains some of these LOOP deviations: more distant city pairs have more volatile pij – pik. This probably reflects better integration of markets in nearby cities, but does not directly capture transportation costs.

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• But Engel and Rogers (1996) find a very large “border” effect: variance of changes in pij – pik is much larger when j and k are in different countries.

• This probably mostly reflects nominal exchange rate volatility between U.S. and Canada, combined with prices that are sticky in local currencies.

• But that does not explain it all. That paper finds a large border effect even when relative prices are measured as (pij –pj) – (pik-pk) so no nominal exchange rate is used in measuring the relative price. There are other “barriers” at the border. Exchange rates explain ½ of border effect.

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• Engel and Rogers (2004, Economic Policy) ask whether the introduction of the euro in 1999 reduced dispersion of prices in Europe.

• They use actual price data of 139 goods in 18 eurozone cities, from the Economist Intelligence Unit.

• In fact, they find little convergence post-1999. In fact, prices have even diverged a bit.

• But there was substantial convergence in the early 1990s, when many real barriers to trade within Europe were lifted.

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• But the findings of Engel and Rogers (1996), and those of Mendoza (2001) and Naknoi (2004) suggest that nominal exchange rate volatility combined with local-currency pricing accounts for much of the failure of LOOP.

• Engel (1999, 2001) also consider the possibility that there is a significant non-traded component in measures of traded goods prices that accounts for failures of LOOP. That paper concludes that such an explanation is unlikely unless the non-traded component were extremely large.

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• But Burstein, Eichenbaum, and Rebelo (2004) ask why, when there are large devaluations, consumer prices in the devaluing country fall so much? Is it really local-currency pricing?

• They find some evidence of a role for non-traded distribution services being important. But their explanation still relies on a local-currency stickiness – the stickiness of prices of non-traded distribution services (or wage stickiness.)

• But they claim the actual violation of the law of one price is not large.

• They also argue that there is some mismeasurement of prices during devaluations.

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• Especially for advanced countries, local-currency pricing (LCP) explains the high volatility in p$

T- s$/€ - p*€

T when prices are measured using consumer prices. That is, p$

T is sticky in dollars and p*€T is

sticky in euros.• But Obstfeld and Rogoff (2000, JIE) argue that

when we look at trade prices, it appears more like prices are set in producer’s currencies (PCP). They find that p$

US - p$EU is very highly (negatively)

correlated with s$/€ . This would happen if p$US is

set in dollars, and

p$EU = s$/€ + p€

EU, where p€EU is set in euros.

• That is, “pass-through” is close to traded goods prices.

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Exchange Rate Pass-Through to Inflation

• Recently a number of economists at central banks have examined how exchange rate changes “pass through” to inflation

• To me, the idea of these studies is unclear. It seems as though they want to see how changes in import prices affect inflation.

• This is analogous to the old fallacy commonly repeated in news reports that “food prices contributed to inflation” or “gas prices raised inflation.”

• Relative price movements do not determine inflation.

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• The correlation of exchange rate changes and inflation would depend on the source of the change in exchange rates.

• For example, a general monetary inflation at home would also lead to a depreciation. Prices and the exchange rate would rise together.

• But a general monetary inflation abroad would lead to an appreciation of the home currency, but no direct effect on local inflation (if monetary policy stabilizes prices.)

• Clearly, the correlation between inflation and depreciation depends primarily on the monetary policy in a country.

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Trying to Make Sense of the Exercise

• We could ask: If nominal prices of locally produced goods are stabilized, how would overall inflation be affected by an import price increase?

• In terms of our example, define

z$ = (α1p$US+αNp$

N)/(1-α2)

Then p$ = α2p$EU + (1-α2) z$

• p$ rises by α2 times the increase in p$EU, holding

z$ constant.

• Or, p$ - z$ = α2(p$EU-z$)

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• The international trade literature has models of how p$

EU-z$ responds to exogenous changes in the real exchange rate.

• The 1st part of the paper I wrote on price-setting that is on the reading list summarizes one strand of that literature.

• It derives an equation that we can write as:

p$EU- z$ = δ(s$/€ + w€ - z$) + u

• δ is the “pass-through” coefficient. It can be greater or less than one, depending on shape of demand curves and cost functions. It is a structural parameter.

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• The trade literature has estimated this equation:

p$EU- z$ = δ(s$/€ + w€ - z$) + u

• It treats estimates of δ as estimates of a structural parameter on the grounds that s$/€ + w€ - z$ is exogenous for a firm or maybe for imports as a whole

• But that is wrong. The question should be is s$/€ + w€ - z$ uncorrelated with u?

• If not, then estimated δ is not structural. Instead it is a “reduced form” coefficient.

• This is of paramount importance for policy makers because of Lucas critique.

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• The previous slide does not consider adjustment. Given the persistence of the terms of trade and real exchange rates, careful modeling of the dynamic process is important.

• With the dynamic equation in hand, one can make unconditional forecasts of p$

EU- z$.

• But we cannot use these forecasts to make conditional forecasts (i.e., if we change our policy, here is how p$

EU- z$) because of Lucas critique.

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• One more important issue: prices of imported goods at the dock are not the same as consumer prices.

• A key question is how changes in prices at the dock get passed through to consumer prices.

• Maybe we should think of all imported goods as intermediate goods. Some clearly are, but even finished goods are still “intermediate” until they have been distributed to consumers.

• Here, data is lacking. Commonly available price statistics do not allow us to examine how import prices at the dock feed into consumer prices.

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Summary on Pass-through and Inflation

• The question must be phrased carefully. It may be that none of the current literature has considered the question carefully enough.

• If parameter estimates are not structural, we cannot use them for policy analysis. They can be uses for unconditional forecasting.

• An equally interesting (or maybe more interesting) question is how prices at the dock are passed through to consumer prices.

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Policy Implications

• Friedman argued in favor of exchange rate flexibility.

• Consider the terms of trade: p$US - s$/€ - p€

EU.• Friedman believed that p$

US and p€EU adjust

slowly to real shocks. Prices are sticky in the producer’s currency (PCP.)

• Relative price changes can occur, however, if s$/€ adjusts freely.

• Friedman believed the market would let s$/€ adjust to real shocks. In the modern version, Obstfeld and Rogoff (2000, JIE) say monetary policy should aim at achieving this adjustment.

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Components of OR Model1. Households maximize expected utility of

consumption and leisure over an infinite horizon.

2. Money balances are held (money in utility.)3. In essence, asset markets are complete –

complete international risk sharing.4. A continuum of goods is produced in each of 2

countries. All producers are monopolists.5. Firm managers maximize the value of the firm.6. Output is produced using labor.7. There may be productivity shocks.

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Price Setting in OR Model

• There is nominal price stickiness• Firms must set prices one period in advance.• Each firm sets one price, in its own currency, for

home and foreign consumers.• The price is set optimally.• This type of price stickiness means that the price

of imported goods varies one for one with the exchange rate.

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Monetary Policy

• OR derive the policy rule that maximizes expected utility for households. (No difference between cooperative and non-cooperative rules.)

• They find that under the optimal rule, the flexible price allocations are achieved.

• The optimal rule can be described as one in which the exchange rate is an intermediate target, and it is adjusted so as to achieve optimal terms of trade adjustment.

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Devereux-Engel (2003, ReStud)

• This paper maintains almost exactly the same model as OR with one major exception: firms set two prices in advance. They set a price in local currency for home consumers, and one in foreign currency for foreign consumers.

• They call this local currency pricing (LCP).• They also examine the optimal monetary rule

(and again, it is the same for cooperative and non-cooperative.)

• Under the optimal rule, exchange rates are fixed.

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Why is the policy so different?

• First, exchange rates cannot achieve any changes in the relative prices of home and foreign goods, since both p$

US and p$EU are fixed

in dollars, and p€US and p€

EU are fixed in euros.• Now there are deviations from the law of one

price. Since, for example, p$US and p€

US are fixed in local currencies, the relative price across locations: p$

US- s$/€ - p*€US changes as the

exchange rate changes.• This is a distortion that is dealt with optimally by

having a monetary policy that fixes exchange rates.

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How do we reconcile these papers?

• Obstfeld-Rogoff rely on producer-currency pricing (PCP), while Devereux-Engel assume local-currency pricing (LCP)

• Who is right?• Neither is exactly right.• But PCP is closer to being right when looking at

import prices (OR, 2000, JIE). • LCP is closer to being right when looking at

consumer prices (Engel, 1993, JME).

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Devereux-Engel (2004)

• All traded goods are intermediate goods. Prices are set in advance in producers’ currencies. (Allows some prices to be set flexibly.)

• Imported intermediates and locally-produced intermediates are combined to produce final goods.

• Final goods are non-traded. Their prices are set in local currencies.

• Otherwise, model shares features of OR (2000) and DE (2003).

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Monetary Policy

• The paper considers the optimal monetary policy rule.

• Under the optimal rule, exchange rates are less volatile than the terms of trade.

• There is a fundamental tradeoff in setting policy. On the one hand, policy should aim to allow the exchange rate to change to achieve optimal terms of trade adjustment.

• On the other hand, exchange rate movements lead to distortions in consumer prices.

• Policy cannot eliminate both distortions, so there is a tradeoff.

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• The importance of each objective can only be assessed by a careful calibration of a general equilibrium model

• DE suggest that the terms of trade goal may not be so important: First, many traded goods prices adjust quickly, so the distortion is self-correcting.

• Second, the damage from the distortion may be small in the short run, because short-run elasticities of substitution are small.

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To whom does this model apply?

• These considerations seem important for Canada. Should the exchange rate be targeted to achieve optimal terms of trade changes? Or should deviations from the law of one price for consumer goods be minimized.

• In general, the models seem most applicable to advanced, low-inflation countries.

• In emerging economies, issues of credibility and financial vulnerability may be important.

• But that is a quantitative matter that deserves study.

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Conclusions

• Studies of exchange rates and prices should be motivated by well-framed questions. Probably best framed in the context of a model.

• Does not necessarily imply estimation of structural g.e. models, which is perilous.

• Well designed empirical studies of exchange rates and prices may provide valuable insights into policy questions.

• PPP is probably too “aggregate” to provide valuable insights.