Chapter 7

expenditures to switch from home goods toward foreign goods. Domestic output might then be expected to fall in response. Although the domestic traded-goods sector is hurt, consumers evidently beneÞt. On the other hand, a real depreciation may be beneÞcial to the tradedgoods sector and harmful to consumers. The foreign debt of many developing countries, is denominated in US dollars, however, so a real depreciation reßects a real increase in debt servicing costs. These expenditure switching e ects are absent in the ßexible price theories that we have covered thus far.

So what leads you to conclude that PPP does not hold in the long run. Would this make any sense? What theory predicts that PPP does not hold? The Balassa [6]—Samuelson [124] model, which is developed in this chapter provides one such theory. The Balassa—Samuelson model predicts that the long-run real exchange rate depends on relative productivity trends between the home and foreign countries. If relative productivity is governed by a stochastic trend, the real exchange rate will similarly be driven and will not exhibit any mean-reverting behavior.

The research on real exchange rate behavior raises many questions, but as we will see, o ers few concrete answers.

7.1Some Preliminary Issues

The Þrst issue that you confront in real exchange rate research is that data on price levels are generally not available. Instead, you typically have access to a price index PtI, which is the ratio of the price level Pt in the measurement year to the price level in a base year P0. Letting stars denote foreign country variables and lower case letters to denote variables in logarithms, the empirical log real exchange rate uses price indices and amounts to

st +pt −pt is the relative price of the foreign commodity basket in terms of the domestic basket. This term is 0 if PPP holds instantaneously, and is mean-reverting about 0 if PPP is violated in the short run but holds in the long run. Tests of whether PPP holds in the long run

typically ask whether qt is stationary about a Þxed mean because even if PPP holds, measured qt will be (p0 −p0) which need not be 0 due to the base year normalization of the price indices.

An older literature made the distinction between absolute PPP (st+ pt − pt = 0) and relative PPP (∆st + ∆pt − ∆pt = 0). By taking Þrst di erences of the observations, the arbitrary base-year price levels drop out under relative PPP. In this chapter, when we talk about PPP, we mean absolute PPP.

A second issue that you confront in this line of research is that there are as many empirical real exchange rates as there are price indices. As discussed in chapter 3.1, you might use the CPI if your main interest is to investigate the Casellian view of PPP because the CPI includes prices of a broad range of both traded and nontraded Þnal goods. The PPI has a higher traded-goods component than the CPI and is viewed by some as a crude measure of traded-goods prices. If a story about aggregate production forms the basis of your investigation, the gross domestic product deßator may make better sense.

7.2Deviations from the Law-Of-One Price

The root cause of deviations from PPP must be violations of the law-of- one price. Such violations are easy to Þnd. Just check out the price of unleaded regular gasoline at two gas stations located at di erent corners of the same intersection. More puzzling, however, is that international violations of the law-of-one price are several orders of magnitude larger than intranational violations. There is a large empirical literature that studies international violations of the law-of-one price. We will consider two of the many contributions that have attracted attention of international macroeconomists.

Isard’s Study of the Law-Of-One Price

Isard [79] collected unit export and unit import transactions prices for the US, Germany, and Japan from 1970 to 1975 at 4 and 5 digit standard international trade classiÞcation (SITC) levels for machined items. Isard deÞnes the relative export price to be the ratio of the US

dollar price of German exports of these items to the dollar price of US exports of the same items. Between 1970 and 1975, the dollar fell by 55.2 percent while at the same time the relative export price of internal combustion engines, o ce calculating machinery, and forklift trucks increased by 48.1 percent, 47.7 percent, and 39.1 percent, respectively in spite of the fact that German and US prices are both measured in dollars. Evidently, nominal exchange rate changes over this Þve-year period had a big e ect on the real exchange rate.

In a separate regression analysis, he obtains 7-digit export commodities which he matches to 7-digit import unit values in which the imports are distinguished by country of origin. The dependent variable is the US import unit value from Canada, Japan, and Germany, respectively, divided by the unit values of US exports to the rest of the world, both measured in dollars. If the law-of-one price held, this ratio would be 1. Instead, when the ratio is regressed on the DM price of the dollar, the slope coe cient is positive but is signiÞcantly di erent from 1 for Germany and Japan. The slope coe cients and implied standard errors for Germany and Japan are reproduced in Table 7.1.1 The estimates for Germany indicate that import and export prices exhibit insu cient dependence on the exchange rate to be consistent with the law-of-one price, whereas the estimates for Japan suggest that there is too much dependence.

While Isard’s study provides evidence of striking violations of the law-of-one price, it is important to bear in mind that these results were drawn from a very short time-series sample taken from the 1970s. This was a time period of substantial international macroeconomic uncertainty and one in which people may have been relatively unfamiliar with the workings of the ßexible exchange rate system.

1A potential econometric problem in Isard’s analysis is that he runs the regression Rt = a0 + a1St + a2Dt + et + ρet−1 where Rt is the ratio of import to export prices, St is the DM price of the dollar, and Dt is a dummy variable that splits up the sample. The problem is that the regression is run by Cochrane—Orcutt to control for serial correlation in the error term, et, which is inconsistent if the regressors are not strictly (econometrically) exogenous.

Table 7.1: Slope coe cients in Isard’s regression of the US import to export price ratio on nominal exchange rate

centage change in the price of 14 categories of consumer prices sampled in various US and Canadian cities from Sept. 1978 through Dec. 1994.2 Let pijt be the price of good i in city j at time t, measured in US dollars. Let σijk be the volatility of the percentage change in the relative price of good i in cities j and k. That is, σijk is the time-series sample standard deviation of ∆ ln(pijt/pikt). In addition, deÞne Djk as the logarithm of the distance between cities j and k. The idea of the distance variable is to capture potential e ects of transportation costs that may cause violations of the law-of-one price between two locations. Let Bjk be a dummy variable that is 1 if cities j and k are separated by the US-Canadian border and 0 otherwise, and let Xi0 be a vector of control variables, such as a separate dummy variable for each good i and/or for each city in the sample. Engel and Rogers run restricted cross-section regressions

the border adds 11.9 × 10−3 to the average volatility (standard deviation) of prices between two pairs of cities. Based on the estimate of

2The cities are Baltimore, Boston, Chicago, Dallas, Detroit, Houston, Los Angeles, Miami, New York, Philadelphia, Pittsburgh, San Francisco, St. Louis, Washington D.C., Calgary, Edmonton, Montreal, Ottawa, Quebec, Regina, Toronto, Vancouver, and Winnipeg.

α, this is equivalent to an additional 75,000 miles of distance between two cities in the same country. In addition, the border was found to account for 32.4 percent of the variation in the σijk, while log distance was found to explain 20.3 percent.

The striking di erences between within country violations of the law-of-one price and across country violations raise but do not answer the question, “Why is the border is so important?” This is still an open question but possible explanations include,

1.Barriers to international trade, such as tari s, quotas, and nontari barriers such as bureaucratic red tape imposed on foreign businesses. The Engel-Rogers sample spans periods of preand post-trade liberalization between the US and Canada. In subsample analysis, they reject the trade barrier hypothesis.

2.Labor markets are more integrated and homogeneous within countries than they are across countries. This might explain why there would be less volatility in per unit costs of production across cities within the same country and more per unit cost volatility across countries.

3.Nominal price stickiness. Goods prices seem to respond to macroeconomic shocks and news with a lag and behave more sluggishly than asset prices and nominal exchange rates. Engel and Rogers Þnd that this hypothesis does not explain all of the relative price volatility.3

4.Pricing to market. This is a term used to describe how Þrms with monopoly power engage in price discrimination between segmented domestic and foreign markets characterized by di erent elasticities of demand.

3The experiment they run here is as follows. Instead of measuring the relative

intercity price as pijt/(Stpikt) where S is the nominal exchange rate, p is the US dollar price and p is the Canadian dollar price, replace it with (pijt/Pt)/(Pt /pikt) where P and P are the overall price levels in the US and Canada respectively. If the

border e ect is entirely due to sticky prices, the border should be insigniÞcant when the alternative price measure is used. But in fact, the border remains signiÞcant so sticky nominal prices can provide only a partial explanation.

7.3. LONG-RUN DETERMINANTS OF THE REAL EXCHANGE RATE213

What About the Long-Run?

Since the international law-of-one price and purchasing-power parity has Þrmly been shown to break down in the short run, the next step might be to ask whether purchasing-power parity holds in the long run. Recent work on this issue proceeds by testing for a unit root in the log real exchange rate. The null hypothesis in popular unit-root tests is that the series being examined contains a unit root. But before we jump in we should ask whether these tests are interesting from an economic perspective. In order for unit-root tests on the real exchange rate to be interesting, the null hypothesis (that the real exchange rate has a unit root) should have a Þrm theoretical foundation. Otherwise, if we do not reject the unit root, we learn only that the test has insu cient power to reject a null hypothesis that we know to be false, and if we do reject the unit root, we have only conÞrmed what we believed to be true in the Þrst place.

The next section covers the Balassa-Samuelson model which provides a theoretical justiÞcation for PPP to be violated even in the long run.

7.3Long-Run Determinants of the Real Exchange Rate

We study a two-sector small open economy. The sectors are a tradablegoods sector and a nontradable-goods sector. The terms of trade (the relative price of exports in terms of imports) are given by world conditions and are assumed to be Þxed. Before formally developing the model, it will be useful to consider the following sectoral decomposition of the real exchange rate.

Sectoral Real Exchange Rate Decomposition

Let PT be the price of the tradable-good and PN be the price of the (129) nontradable-good, and let the general price level be given by the CobbDouglas form