Chapter

1 Commodity Currencies and the Real Exchange Rate

Author(s):
Charalambos Tsangarides, Carlo Cottarelli, Gian Milesi-Ferretti, and Atish Ghosh
Published Date:
September 2008
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The neglect to allow for the effect of changes in the terms of trade is, perhaps, the most unsatisfactory characteristic of Prof. Cassel’s “Purchasing Power Parity Theory of the Foreign Exchanges.” For this not only upsets the validity of his conclusions over the long period, but renders them even more deceptive over the short period.

John Maynard Keynes, A Treatise on Money

Attempts by economists to model long-run movements in real (price-level-adjusted) exchange rates have typically proven to be rather unsuccessful. Meese and Rogoff (1983) demonstrated that a variety of linear structural exchange rate models failed to forecast more accurately than a naïve random walk model for both real and nominal exchange rates, and their key finding has not been overturned in the succeeding three decades. If the real exchange rate follows a random walk, then innovations to the real exchange rate persist and the time series can fluctuate without bound. This result is contrary to the theory of purchasing power parity, which states that there is a constant equilibrium level to which exchange rates converge, such that foreign currencies should possess the same purchasing power. Accordingly, purchasing power parity has proven to be a weak model of the long-run real exchange rate, and recent work has emphasized the time-varying nature of that rate.

There is a large empirical literature on the determinants of the long-run real exchange rate, which has emphasized sectoral productivity differentials, government spending, cumulated current account imbalances, and interest rate differentials as important drivers of long-run deviations from purchasing power parity (see Froot and Rogoff, 1995, and Rogoff, 1996, for recent surveys). This literature has mainly concentrated on understanding the sources of real exchange rate fluctuations in developed countries, and the fruits of the associated research have been mixed, with many studies failing to find a statistical link between real exchange rates and the foregoing explanators.

In contrast to the preponderance of developed country studies of the behavior of real exchange rates, evidence on the behavior of developing country real exchange rates has been scarce. Those studies that have examined the determinants of developing country real exchange rates have largely focused on Latin America, and have emphasized the role of movements in the terms of trade in driving real exchange rate movements (see Diaz-Alejandro, 1982, and Edwards, 1989). There is also an extensive literature for some developed countries that links exogenous movements in the terms of trade and changes in their real exchange rates, particularly for commodity exporters Canada and Australia (see, among others, Amano and Van Norden, 1995, and Gruen and Wilkinson, 1994).

Rogoff (1996) summarizes the multitude of potential explanators offered by researchers in their attempts to resolve the purchasing power parity puzzle, which refers to the finding of many researchers that the speed of mean reversion of real exchange rates is too slow to be consistent with purchasing power parity. Chief among these explanators has been the recognition that real factors have a role in the determination of real exchange rates, through such channels as the Balassa-Samuelson effect, real interest rate differentials, and portfolio balance models (in which higher net foreign assets drive an appreciation of the exchange rate). In the context of commodity-exporting countries, almost all of which are also developing countries, the real factor of primary interest in the determination of the real exchange rate is the terms of trade.

Indeed, because primary commodities dominate the exports of developing countries, fluctuations in world commodity prices have the potential to explain a large share of movements in their terms of trade. Whereas terms-of-trade fluctuations have been considered a key determinant of real exchange rates (De Gregorio and Wolf, 1994; Chinn and Johnston, 1996; Montiel, 1997), it is surprising that there has been no comprehensive empirical work done to assess the mechanisms through which changes in real commodity prices affect the real exchange rate.1 This chapter takes Keynes (1930) seriously and examines whether price movements within the tradables sector, in particular, changes in the price of commodity exports relative to that of imports, are a major determinant of movements in real exchange rates of commodity-dependent countries. In doing so, we are not claiming that real commodity prices have a unique role in the determination of the real exchange rate, but commodity prices are likely to be the most important source of persistent changes in the real exchange rate of commodity-dependent countries.

Importantly, Obstfeld and Rogoff (2000) point out that in the presence of sticky producer prices and perfect pass-throughs, standard measures of the terms of trade will move one-to-one mechanically with the real exchange rate, making it extremely difficult to identify causality between the real exchange rate and terms of trade. More generally, if the extent of exchange rate pass-through is less for exports than for imports, a depreciation of the local currency will raise the local currency price of exports relatively less than it will raise the local currency price of imports—this will yield a decline in the terms of trade. Deaton and Miller (1996) use a measure of the terms of trade expressed in world prices to ameliorate this potential endogeneity problem. We follow Deaton and Miller and construct, for each commodity-dependent economy, an index of real commodity prices that is defined as the world (nominal) price of its commodity exports relative to the world price of manufactured goods exports. Our measure of the world price of commodity exports aggregates changes in world commodity prices using actual national export shares of the commodity exports. For large commodity-exporting countries, world relative commodity prices are likely to be better at capturing the exogenous component of terms-of-trade shocks than standard terms-of-trade measures (Chen and Rogoff, 2003).2

The key objective of this chapter is to determine how many commodity-exporting countries have “commodity currencies,” in that movements in real commodity prices can explain fluctuations in their real exchange rates. The chapter does so in several ways. First, a new monthly data set of country-specific export price indices is constructed for 58 countries over the period January 1980 to March 2002. Each country’s export price index is a geometrically weighted average of world commodity prices, using country-specific export shares as weights. Second, using empirical techniques that allow for structural shifts in the long-run relationship between time series, we find strong evidence of a long-run relationship between the real exchange rate and real commodity prices for about one-third of the commodity-exporting countries in our sample. For these commodity currencies, movements in real commodity prices are an important determinant of long-run deviations of real exchange rates from purchasing power parity. Accordingly, the long-run real exchange rate of countries with commodity currencies is not constant (as would be implied by purchasing power parity–based models) but is time-varying, being dependent on movements in real commodity prices. Third, weak-exogeneity tests carried out within an error correction framework indicate that for most countries with commodity currencies, causality runs from real commodity prices to the real exchange rate. When deviations from the long-run equilibrium relationship occur in economies with commodity currencies, it is usually the real exchange rate that adjusts to restore long-run equilibrium. For countries with commodity currencies, the average half-life of adjustment of the real exchange rate to its equilibrium with real commodity prices is about ten months, which is much shorter-lived than Rogoff’s (1996) consensus estimate of the half-life of real exchange rate deviations from purchasing power parity of between three and five years.

The chapter is organized as follows. The second section briefly sets out the theoretical relationship between real commodity prices and the real exchange rate. The third section explains the sources and construction of the national real exchange rate and real commodity export price data used in this study. The fourth section applies cointegration and error correction methodology to examine both the long-run and short-run determinants of the real exchange rate in commodity-dependent countries, especially the relationship between the real exchange rate and real commodity prices. It then draws inferences regarding causality between the two series and examines the speed of reversion of real exchange rates in countries with commodity currencies to their time-varying (commodity-price-dependent) long-run equilibrium. The fifth section concludes.

Theoretical Framework

In describing the theoretical link between the real exchange rate and real commodity prices, we consider a small open economy that produces two different types of goods: a nontradable good and an exportable good (see Appendix 1.1 for additional details). For the purpose of our work, we associate the production of this exportable good with the production of a primary commodity (agricultural or mineral product). Nevertheless, our analysis is in line with the literature that stresses the role of the terms of trade in determining the real exchange rate, which includes (among others) work by De Gregorio and Wolf (1994) and Obstfeld and Rogoff (1996).

The domestic economy is composed of two different sectors: one producing an exportable good, referred to as the “primary commodity,” and the other producing a nontraded good. Firms in both the export and nontraded sectors use only labor in order to produce these goods. In particular, we assume that production is carried out by competitive firms that have access to a constant returns to scale technology. Labor is free to move across sectors, thereby ensuring that wages are equated across sectors and that only supply side factors are relevant. Accordingly, we abstract from demand side considerations and concentrate on a representation of long-run relative price determination.

Domestic consumers supply labor inelastically and consume both a nontraded and a final tradable good. This tradable good is imported from the rest of the world and is not produced domestically. Foreign firms use the primary commodity jointly with an intermediate good, produced only abroad, as inputs in the production process of the final tradable good. Additionally, foreign households consume the final tradable good and a nontraded good (produced abroad).

For the purpose of the empirical analysis, we define the real exchange rate as the foreign price of the domestic basket of consumption (EP) relative to the foreign price of the foreign basket of consumption (P*). After some algebra, provided in Appendix 1.1, we can show that the determination of the real exchange rate may be summarized by the following relation:

where the term PX*/PI* corresponds to the commodity terms of trade (or the price of the primary commodity with respect to that of the intermediate foreign good) measured in foreign prices, aX/aI* reflects the productivity differentials between the export and import (foreign) sectors, and aN*/aN accounts for the productivity differentials between the local and foreign nontraded sectors. These last two terms embody the Balassa-Samuelson effect—an increase in productivity in the commodity sector will tend to increase wages, which translates into an increase in the price of the nontraded good. As the relative price of the primary commodity is exogenously determined, the final effect will be an appreciation of the real exchange rate.

In the empirical analysis of this chapter, we center our work on explaining the evolution of the real exchange rate of commodity-dependent economies, that is, economies in which one of the major sources driving movements in the real exchange rate is fluctuations in the commodity terms of trade. How do fluctuations in the relative commodity price translate into movements in the real exchange rate? In our simple model, an increase in the international price of the economy’s primary commodity will increase wages in the commodity sector. As wages are equal across sectors, the increase in wages will raise the relative price of the nontraded good and therefore appreciate the real exchange rate.

Data

The data used to examine whether there is a relationship between the real exchange rate of individual countries and the real price of their commodity exports are monthly time series, obtained from the International Monetary Fund’s International Financial Statistics (IFS) and Information Notice System (INS) databases over the period January 1980 to March 2002, which gives a total of 267 observations.

Real Exchange Rates and Real Commodity Prices

The definition of the real exchange rate is the real effective exchange rate (REER) based on consumer prices. As such, we examine the behavior of REER based on (1) the nominal effective exchange rate, which is the trade-weighted average of bilateral exchange rates vis-à-vis trading partners’ currencies, adjusted for (2) differentials between the domestic price level (which is the consumer price index) and the foreign price level (which is the trade-weighted average of trading partners’ consumer price indices). We analyze effective rather than bilateral real exchange rates, as the effective rate measures the international competitiveness of a country against all its trade partners and helps in avoiding potential biases associated with the choice of base country in bilateral real exchange rate analyses.

The REER indices measure how nominal effective exchange rates, adjusted for price differentials between the home country and its trading partners, have moved over a period of time. The CPI-based REER indicator is calculated as a weighted geometric average of the level of consumer prices in the home country relative to that in its trading partners, expressed in a common currency. The International Monetary Fund’s seasonally adjusted, CPI-based REER indicator for country i is defined as

where j is an index that runs (from 1 to n) over country i’s trade partner (or competitor) countries; Wij is the trade weight attached by country i to country j, which is based on 1988–90 average data on the composition of trade in manufacturing, non-oil primary commodities, and tourism services; Pi and Pj are the seasonally adjusted consumer price indices in countries i and j; and Ri and Rj are the nominal exchange rates of countries i and j’s currencies in U.S. dollars. A decline (depreciation) in a country’s REER index indicates a rise in its international competitiveness (defined as the price of domestic tradable goods relative to that of foreign tradables). The national REER series are expressed in logarithmic form (see Appendix 1.2 for additional details).

The real price of commodity exports (RCOMP) is defined as the nominal price of commodity exports (NCOMP) deflated by the International Monetary Fund’s index of (the unit value of) manufactured exports (MUV).3 This chapter follows Deaton and Miller (1996) and constructs NCOMP as a geometrically weighted index of the nominal prices of 44 individual commodity exports, where for each country:

Where

Pk is the index of the dollar world price of commodity k (taken from the IFS); Wk is the weighting item, which is the value of exports of commodity k in the total value of all K commodity exports, for the constant base period j; and Q is the quantity of exports of commodity k (taken from UN Commodity Trade Statistics [Comtrade] data).4 Importantly, each country’s NCOMP will be unique, because Wk is country specific.5 The national RCOMP series are expressed in logarithmic form (see Appendix 1.3 for details).

Most previous studies of the macroeconomic effects of commodity price movements in developing countries have used either the prices of individual primary commodities (Cuddington and Urzua, 1989), terms-of-trade indices (Montiel, 1997), or aggregate (non-country-specific) indices of commodity price movements (Grilli and Yang, 1988). The exceptions have been the country-specific indices of prices of commodity exports constructed by Deaton and Miller (1996) and Dehn (2000).6 Few exporters of nonfuel commodities are so specialized that the export prices of a single commodity can well approximate movements in an index of commodity export prices based on the export baskets of individual commodity-exporting countries. In addition, terms-of-trade indices are also typically calculated using export and unit values, which are affected by the composition of exports and so by the composition of GDP (Deaton and Miller, 1996). Finally, movements in aggregate commodity price indices are likely to represent poorly movements in country-specific commodity export price indices, as prices of individual commodities do not tend to move together on world commodity markets (Cashin, McDermott, and Scott, 2002).7

Potential Commodity Currency Countries

In selecting commodity-dependent developing countries to be included in our sample, we followed the classification of developing countries used in the International Monetary Fund’s World Economic Outlook for the years 1988–92, the midpoint of our sample (IMF, 1996). The International Monetary Fund classifies developing countries by the composition of their export earnings and other income from abroad, and its classification system has five categories: fuel (Standard International Trade Classification [SITC] 3); manufactures (SITC 5 to 8, with the exception of 68); nonfuel primary products (SITC 0, 1, 2, 4, and 68); services, income, and private transfers (exporters of services and recipients of income from abroad, including workers’ remittances); and diversified export earnings. Countries whose 1988–92 export earnings in any of the first four categories accounted for more than half of total export earnings are assigned to that group, and countries whose export earnings were not dominated by any of the first four categories are defined as countries with diversified export earnings (see IMF, 1996).

Those developing countries in the IMF’s category of nonfuel primary products are included in our sample, as are those in the category diversified export earnings, as many of these countries derive a large (yet not dominant) share of their export earnings from the export of nonfuel primary products. On this basis, the number of countries with potential commodity currencies is 73. Of these 73 countries, 12 are excluded from our analysis because a consistent time series of data on their real effective exchange rate is unavailable. Of the remaining 61 countries, 8 are excluded because of the unavailability of UN Comtrade data on their commodity exports, leaving 53 developing countries in our sample. In addition, five commodity-dependent industrial countries (Australia, Canada, Iceland, New Zealand, and Norway) are included in our sample, to enable us to compare and contrast their results with those of the commodity-dependent developing countries.

As expected, the export of commodities is a major source of export income for the 58 countries in our sample of commodity-exporting countries. In Table 1.1 we report the export share of the three most important commodity exports and the share in total exports of the 44 individual commodities used to construct the indices of the nominal world price of national export baskets. During the 1990s, the cross-country mean share of total export receipts derived from primary commodity exports was about 48 percent. Among sub-Saharan African countries, commodity exports typically exceeded 50 percent of total exports, especially in Burundi (97 percent), Malawi (90 percent), and Zambia (88 percent). Even among developed countries, the share of primary commodity exports in total exports was quite high (for example, Australia, 54 percent; Iceland, 56 percent; Norway, 63 percent). In addition, many countries remained overwhelmingly dependent on export receipts from their dominant commodity exportable. Cases in which the dominant exportable exceeded 90 percent of the country’s commodity export receipts include Niger (uranium), Dominica (bananas), Ethiopia (coffee), Zambia (copper), and Mauritius (sugar) (see Table 1.1).

Table 1.1.Principal Commodity Exports and Percentage Share of Primary Commodities in Total Exports, 1991–99
CountryPrincipal ExportsShare of Exports
12312344
ArgentinaSoy mealWheatMaize18131141
AustraliaCoalGoldAluminum22141254
BangladeshShrimpTeaFish761588
BoliviaZincTinGold27181356
BrazillronCoffeeAluminum21151035
BurundiCoffeeGoldTea5935297
CameroonCocoaHardwood logsAluminum23221453
CanadaSoftwood sawnAluminumWheat28141216
Central African RepublicCottonCoffeeSoftwood logs829543
ChileCopperFishFishmeal709658
ColombiaCoffeeCoalBananas48191840
Costa RicaBananasCoffeeFish4333531
Côte d’lvoireCocoaCoffeeCotton6514665
DominicaBananasTobacco98132
EcuadorBananasShrimpCoffee4530849
EthiopiaCoffeeHidesCotton915271
GhanaCocoaGoldAluminum6124772
GuatemalaCoffeeSugarBananas47241449
HondurasCoffeeBananasShrimp4730667
IcelandFishAluminumShrimp7320756
IndiaRiceShrimpSoy meal18151231
IndonesiaCrude petroleumNatural gasNatural rubber3423743
KenyaTeaCoffeeFish5330545
MadagascarCoffeeShrimpSugar4240639
MalawiTobaccoTeaSugar788790
MalaysiaPalm oilNatural rubberHardwood logs44151513
MaliCottonGold881285
MauritaniaIronFishGold6534164
MauritiusSugarWheat97127
MexicoCrude petroleumCopperCoffee725515
MoroccoPhosphate rockFishLead5514714
MozambiqueCottonSugarMaize3319926
MyanmarHardwood logsRiceShrimp6018752
New ZealandLambBeefWool20171436
NicaraguaCoffeeBeefShrimp32151469
NigerUraniumTobacco96368
NorwayCrude petroleumNatural gasFish6713863
PakistanRiceCottonSugar46281312
Papua NewCopperGoldPalm oil23232059
Guinea
ParaguaySoybeansCottonSoy meal4426979
PhilippinesCoconut oilCopperBananas29211210
PeruCopperFishmealGold28191569
St. Vincent andBananasWheatRice60231772
the Grenadines
SenegalPhosphate rockGroundnut oilFish29291626
South AfricaGoldCoalIron4620539
Sri LankaTeaNatural rubberTobacco789620
SudanCottonGoldSugar45121244
SurinameAluminumRiceNickel808586
Syrian ArabCrude petroleumCottonWheat888274
Republic
TanzaniaCoffeeTobaccoCotton27181759
ThailandRiceNatural rubberShrimp26242316
TogoPhosphate rockCottonCoffee4440984
TunisiaTobaccoPhosphate rockShrimp2321208
TurkeyTobaccoWheatSugar3416148
UgandaCoffeeFishGold718484
UruguayBeefRiceFish36271332
ZambiaCopperSugar97288
ZimbabweTobaccoCottonNickel588854
Sources: United Nations (Comtrade); International Monetary Fund, commodity price indices.Note: Columns 1–3 present the three largest commodity exports of each country and their share of that country’s total commodity exports. The column labeled “44” presents, for each country, the share in its total exports accounted for by the 44 commodities that the IMF tracks (which were used in the construction of the nominal national commodity price series). All data are averages of annual data for the period 1991–99. See Appendix 1.3 for additional details.
Sources: United Nations (Comtrade); International Monetary Fund, commodity price indices.Note: Columns 1–3 present the three largest commodity exports of each country and their share of that country’s total commodity exports. The column labeled “44” presents, for each country, the share in its total exports accounted for by the 44 commodities that the IMF tracks (which were used in the construction of the nominal national commodity price series). All data are averages of annual data for the period 1991–99. See Appendix 1.3 for additional details.

The REER data (base 1990 = 100) for four selected countries—Australia and Burundi (which have flexible nominal exchange rates) and Mali and Togo (which have fixed nominal exchange rates)—are depicted graphically in Figure 1.1. An increase in the REER series indicates a real appreciation of the country’s currency. Several features of the data stand out. First, a cursory inspection of the REER series indicates that the countries have real exchange rates that appear to exhibit symptoms of drift or nonstationarity. There appear to be substantial and sustained deviations from purchasing power parity (that is, nonstationarity in REER). Typically, the evolution of REER appears to be a highly persistent, slow-moving process; REER does not appear to cycle about any particular equilibrium value. Second, sharp movements in REER during the 1980s and 1990s are a relatively frequent occurrence, especially for countries experiencing rapid nominal devaluations, such as the countries of the CFA franc zone (which includes Mali and Togo). Figure 1.1 also displays the RCOMP indices (base 1990 = 100) for the four selected countries. It is readily apparent through visual examination of the data that the real commodity prices and real exchange rates of many countries (such as Australia and Burundi in the figure) display a close relationship, and those of other countries (like Mali and Togo in the figure) appear to display a close relationship once a onetime shift in the mean real exchange rate is accounted for. In the following section we examine these relationships in some detail.

Figure 1.1.Real Exchange Rate and Real Commodity Price, Selected Commodity-Exporting Countries, 1980–2002

(Indices, 1990 = 100)

Empirical Analysis of Comovement

We use the Engle and Granger (1987) cointegration approach to assess whether there is a long-run relationship between real exchange rates and real commodity prices, which implies that deviations from any long-run relationship are self-correcting. This approach allows us to examine the usefulness of specifying the real exchange rate simply as a function of real commodity prices. For those countries where cointegration between real exchange rates and real commodity prices can be established, we then ascertain the direction of causality between the two series using the error correction methodology of Engle and Granger (1987). Finally, we measure the speed with which the real exchange rate of countries with commodity currencies reverts to both their constant equilibrium level (as implied by purchasing power parity) and their time-varying equilibrium with real commodity prices.

Is There a Long-Run Relationship Between Real Exchange Rates and Real Commodity Prices?

Economic theory has established that the long-run (equilibrium) real exchange rate is determined by the long-run value of certain “fundamentals,” such as the terms of trade, real interest rate differentials, and productivity differentials. Deviations of the actual real exchange rate from the equilibrium real exchange rate dictated by these fundamentals should be short-lived. If the real exchange rate is an integrated process, then the fundamental determinants of the real exchange rate should themselves be integrated processes. In addition, the nonstationarity of the real exchange rate means that cointegration methods should be used to examine whether there is a long-run relationship between the fundamentals and the real exchange rate.

As set out in the “Theoretical Framework” section, the fundamental determinant of the real exchange rate in commodity-dependent countries is real commodity prices. In conducting our analysis we test, for each country, several hypotheses. First, that its real exchange rate and real commodity price series are nonstationary. Second, whether for each country there is a long-run (cointegrating) relationship between its real exchange rate and the real price of its commodity exports. Third, given that we establish cointegration, we test for parameter instability in the cointegrated model.

Order of Integration of the Series

We use the Phillips-Perron (1988) and Kwiatkowski and others (1992) unit root tests to assess the time-series properties of our data. While the Phillips-Perron test maintains the null hypothesis of nonstationarity of the time series, the Kwiatkowski test uses a null hypothesis of stationarity. For both tests we include a constant term and trend in the fitted regression, and we employ the Bartlett kernel with Andrews’ (1991) automatic bandwidth selector and the prewhitened kernel estimator of Andrews and Monahan (1992). The results for both tests give very little evidence for stationarity—they indicate that for all countries both series (REER and RCOMP) are typically nonstationary in levels and stationary in first-difference form.8 The results of these tests for the stationarity of the real exchange rate are consistent with those of earlier work (see Boyd and Smith, 1999). Similarly, shocks to world commodity prices have been found to be highly persistent (Cashin, Liang, and McDermott, 2000).

One possible reason for the inability to reject the null hypothesis of nonstationarity of the real exchange rate is that there may be macroeconomic disturbances, such as shocks to real commodity prices, which induce persistent deviations of real exchange rates from purchasing power parity. If the observed deviation from parity of each country’s real exchange rate is caused by real commodity prices, then real exchange rates can be expected to be cointegrated with real commodity prices. Accordingly, in subsequent sections we treat real exchange rates and real commodity prices as I(1) variables and go on to examine (for each country) whether there is a long-run relationship between these series for the period 1980–2002. An examination for the existence of cointegration is an important check on the adequacy of our model. If the long-run real exchange rate is determined by factors other than real commodity prices, then their omission from the cointegrating regression should prevent us from finding evidence of cointegration. However, a finding of cointegration would imply that real commodity prices adequately capture all the permanent innovations in the real exchange rate over the sample period (Amano and Van Norden, 1995).

Examining for Cointegration: Allowing for Structural Change

When data drawn from time periods characterized by changing institutional developments are examined, the failure to find a long-run (cointegrating) relationship between a group of variables could in fact reflect the existence of a cointegrating relationship that has experienced a structural change. Gregory and Hansen (1996a) demonstrate that the power of standard tests for cointegration falls when no allowance is made for structural shifts in the relationship between nonstationary series. Accordingly, the first step in the estimation procedure is to allow for the possibility that the cointegrated (long-run) relationship between the real effective exchange rate and real commodity prices has shifted at an unknown point in the sample. The possibility of a structural shift is allowed for because the period 1980–2002 was marked by some significant changes in the policy framework of many countries, such as sharp nominal exchange rate adjustments and changes in nominal exchange rate regimes, and by rapid fluctuations in the world prices of many primary commodities. This period provides a very severe test of the commodity currency model of real exchange rate movements and suggests that there is a possibility of a regime shift in behavior as economic agents adapt to any new economic environment. Moreover, the timing of any such regime shift is likely to be unknown, because there is not necessarily a one-to-one correspondence between potential causes of a regime shift and its occurrence in the data. Use of the Gregory-Hansen (1996a) test for cointegration is therefore helpful in this instance, since it allows the timing of any regime shift to be unknown a priori.

Gregory and Hansen (1996a) commence with the standard model for cointegration in the presence of no structural change, namely:

where REER and RCOMP are I(1) variables, and the residual £t is I(0). In the context of the data considered here, there is an apparent level shift in the long-run relationship between the real exchange rate and real commodity price series, which typically occurs as a level shift in the real (and nominal) exchange rate. Accordingly, as an alternative to Equation (1.2), Gregory and Hansen propose a model in which structural change occurs with a shift in the intercept term:

where β0 denotes the cointegrating intercept coefficients before the shift, β2 denotes the change in the intercept coefficients, and RCOMP and εt are as described previously. Importantly, structural change is modeled using the following dummy variable:

where the unknown parameter π∈ (0,1) denotes the timing of the change point in terms of a fraction of the sample and [ ] denotes integer part. Given that the timing of shifts () in the relationship between macroeconomic series is unlikely to be known a priori, the Gregory-Hansen test for shifts in cointegrated models is useful, as it does not require information on the timing of such events.

A test of the null hypothesis of no cointegration is conducted, against the alternative hypothesis given by Equation (1.3). The Phillips-Perron Z(t) cointegration test statistic is computed for each possible shift π ∈Π;, using the residuals from the cointegrating regression of Equation (1.3). The set Π can be any compact subset of (0,1), but following Gregory and Hansen (1996a), Π is here taken to be the compact subset Π = [0.15T, 0.85T]. π is chosen so that Z(t) takes on the smallest value (largest negative value) across all possible break points, since the smallest Z(t) gives the least-favorable result for the null hypothesis (that is, the greater chance of rejecting the null of no cointegration). We denote the smallest of these Z(t) statistics as Z(t)*.

Although the Gregory-Hansen (1996a) test was designed to investigate whether there is a cointegrating relation after a structural shift is allowed for, the test also has the ability to detect cointegration when there is no structural shift. Consequently, a rejection of the null hypothesis of no cointegration may not be indicative of changes in the cointegrating vector, as the existence of a stable cointegrating relationship could also induce such a rejection. Accordingly, Gregory and Hansen (1996b) recommend testing for cointegration using standard statistics that assume a stable cointegrating relation.

The Phillips-Ouliaris (1990)) cointegration statistics test the null hypothesis of no cointegration between REER and RCOMP against the alternative hypothesis of a stable cointegration relationship. The null of the Gregory-Hansen (1996a) model is also no cointegration between REER and RCOMP, whereas the alternative hypothesis is cointegration with a one-time structural shift of unknown timing in the cointegrating relationship (change in cointegrating intercept coefficients). Note that if a conventional cointegration test (such as the Phillips-Ouliaris Z(t) and Z(α;) tests) does not reject the null of no cointegration but the Gregory-Hansen Z(t)* test does, then there is evidence of a structural shift in the cointegrating relationship (Gregory and Hansen, 1996a).

The results of the Gregory-Hansen (1996a) cointegration test are set out in Appendix 1.4. For 19 countries, the Gregory-Hansen statistics are consistent with a long-run cointegrating relationship between REER and RCOMP (allowing for a structural shift), as conventional cointegration tests cannot reject the null of no cointegration but the Gregory-Hansen test does. Importantly, significant values of the test statistic appear to coincide broadly with periods of nominal exchange rate revaluation, such as the 1994 devaluation of the nominal exchange rate of the CFA franc zone countries (Reinhart and Rogoff, 2002).9 In addition, we find that for all but 10 of the 58 countries, the Phillips-Ouliaris Z(t) and Z(α) statistics are too small to reject the null of no cointegration, so there is a long-run cointegrating relationship between REER and RCOMP (see Appendix 1.4). Our finding of cointegration indicates that real commodity prices capture the permanent innovations in the real exchange rates of these commodity currencies.

Importantly, if both conventional cointegration tests and the Gregory-Hansen test reject the null hypothesis of no cointegration (as occurs for Bolivia, Costa Rica, and Kenya), then although it is clear that there is strong evidence in favor of a long-run relationship, it is unclear whether a structural shift has occurred because (as noted earlier) the Gregory-Hansen test is powerful against conventional cointegration. In this case, further investigation is necessary to enable a distinction to be drawn between cointegration with stable parameters and cointegration with a structural shift, as the null hypothesis of no cointegration is rejected in comparison with either alternative hypothesis. Gregory and Hansen (1996b) suggest using Hansen’s (1992) parameter instability tests (which are based on the residuals of a fully modified least-squares regression), in which the null hypothesis is cointegration with stable parameters, to determine whether there has been a shift in the cointegration relationship. For all three Hansen (1992) tests, the null hypothesis is that the cointe-grating parameters are constant, whereas the alternative hypothesis is no cointegration due to a change in the parameters at some unknown point in the sample. In particular, under the alternative hypothesis of parameter instability, the SupF test is focused on any abrupt shift in the cointegrating vector; the MeanF and Lc tests detect any gradual changes in the regression coefficients.10 Using the Hansen (1992) tests, we find no evidence of an unstable relationship between REER and RCOMP for any of the three countries for which both conventional cointegration tests and the Gregory-Hansen test reject the null hypothesis of no cointegration, and so we conclude that there is cointegration with stable parameters.

Cointegration Results and Long-Run Elasticity Estimates

For those 19 countries for which the null hypothesis of no cointegration can be rejected using the Z(t)* test, the cointegrating relationship between each country’s REER and RCOMP (as set out in Equation (1.3)) was estimated using Phillips and Hansen’s (1990) fully modified (FM) method. FM estimation is a semiparametric procedure that modifies a least-squares regression to account for potential endogeneity of the regressors and serial correlation caused by cointegrating relationships.11 The FM method yields an asymptotically correct variance-covariance estimator when cointegrating vectors in the presence of serial correlation and endogeneity are estimated. The results are set out in the lower panel of Table 1.2.12 Estimates of the commodity price elasticity of the real exchange rate are found to be statistically significant, while there is typically a downward shift in the constant term in the cointegrating regression. All cointegrating regressions have excellent explanatory ability, with coefficients of determination ranging between about 0.7 and 0.95. This is consistent with real commodity prices having a strong influence on movements in real exchange rates for those countries with commodity currencies.

Table 1.2.Cointegration and Stability Tests, Real Exchange Rate and Real Commodity Prices, 1980–2002
Cointegrating

Parameters
Hansen Tests
CountryRCOMPDUMR2Lc (4)MeanFSupF
(1)(2a)(2b)(3)(5)(6)
Countries rejecting the null hypothesis of no cointegration in favor of cointegration
Australia0.506 (0.122)0.7290.0360.4561.644
Bangladesh0.327 (0.087)0.3710.0760.4571.373
Bolivia1.164 (0.174)0.5190.2392.3868.732
Burundi0.559 (0.088)0.7180.1190.6811.568
Ecuador2.028 (0.339)0.3490.2192.0707.020
Iceland0.162 (0.053)0.4090.1232.3145.197
Kenya0.359 (0.107)0.5890.2111.3893.105
Paraguay0.989 (0.169)0.6340.1141.0224.015
Countries rejecting the null hypothesis of no cointegration in favor of cointegration with a structural shift
Central African Republic0.230 (0.058)–0.506 (0.034)0.909
Ghana1.270 (0.256)–1.451 (0.260)0.861
lndonesia1.169 (0.125)–0.581 (0.086)0.869
Malawi0.391 (0.135)–0.306 (0.055)0.699
Mali0.287 (0.058)–0.494 (0.036)0.904
Mauritania1.049 (0.064)–0.257 (0.038)0.947
Morocco0.709 (0.065)0.189 (0.029)0.854
Niger0.419 (0.026)–0.460 (0.027)0.957
Papua New Guinea0.366 (0.074)–0.231 (0.037)0.869
Togo0.297 (0.059)–0.308 (0.030)0.868
Tunisia0.164 (0.061)–0.291 (0.024)0.964
Note: The data (described in Appendices 1.2 and 1.3) for all countries are monthly and are expressed in logarithmic form. The estimated cointegrating parameters are from the fully modified cointegrating regression (Phillips and Hansen, 1990): REER = β0 + β1RCOMP + β2DUM + ε, where REER is the country’s real effective exchange rate, RCOMP is the national real commodity price, and DUM is the dummy for the shift in the cointegrating relationship. They are reported in columns (2a) (for RCOMP) and (2b) (for DUM); the asymptotically correct standard errors of these estimates are in parentheses. All cointegrating regressions have been conducted using the Bartlett kernel, the Andrews (1991) automatic bandwidth selector, and the prewhitened kernel estimator of Andrews and Monahan (1992). Column (3) presents values for R2, which is the regression’s adjusted coefficient of determination. In columns (4)–(6), the 5 (10) percent critical values for the Hansen (1992) tests of parameter stability (Lc, MeanF, and SupF) are 0.623, 6.22, and 15.2 (0.497, 5.20, and 13.4), respectively. Gregory-Hansen (1996a) tests for the presence of a regime shift in the cointegrating vector (reported in Appendix 1.4) reveal that the null hypothesis of no cointegration can be rejected, indicating a significant level shift in the cointegrating relation, for the CFA franc zone countries of Cameroon, the Central African Republic, Côte d’lvoire, Mali, Niger, Senegal, and Togo (all in 1993:12); Bolivia (in 1986:01); Costa Rica (in 1998:12); Ghana (in 1983:09); Indonesia (in 1997:10); Kenya (in 1995:05); Madagascar (in 1986:04); Malawi (in 1994:08); Mauritania (in 1998:03); Mauritius (in 1986:03); Morocco (in 1992:12); Papua New Guinea (in 1995:03); Peru (in 1988:12); the Syrian Arab Republic (in 1988:05); and Tunisia (in 1986:06). Accordingly, level shift dummy variables (DUM) have been included in the estimation of the cointegrating regressions for these countries (see lower panel).
Note: The data (described in Appendices 1.2 and 1.3) for all countries are monthly and are expressed in logarithmic form. The estimated cointegrating parameters are from the fully modified cointegrating regression (Phillips and Hansen, 1990): REER = β0 + β1RCOMP + β2DUM + ε, where REER is the country’s real effective exchange rate, RCOMP is the national real commodity price, and DUM is the dummy for the shift in the cointegrating relationship. They are reported in columns (2a) (for RCOMP) and (2b) (for DUM); the asymptotically correct standard errors of these estimates are in parentheses. All cointegrating regressions have been conducted using the Bartlett kernel, the Andrews (1991) automatic bandwidth selector, and the prewhitened kernel estimator of Andrews and Monahan (1992). Column (3) presents values for R2, which is the regression’s adjusted coefficient of determination. In columns (4)–(6), the 5 (10) percent critical values for the Hansen (1992) tests of parameter stability (Lc, MeanF, and SupF) are 0.623, 6.22, and 15.2 (0.497, 5.20, and 13.4), respectively. Gregory-Hansen (1996a) tests for the presence of a regime shift in the cointegrating vector (reported in Appendix 1.4) reveal that the null hypothesis of no cointegration can be rejected, indicating a significant level shift in the cointegrating relation, for the CFA franc zone countries of Cameroon, the Central African Republic, Côte d’lvoire, Mali, Niger, Senegal, and Togo (all in 1993:12); Bolivia (in 1986:01); Costa Rica (in 1998:12); Ghana (in 1983:09); Indonesia (in 1997:10); Kenya (in 1995:05); Madagascar (in 1986:04); Malawi (in 1994:08); Mauritania (in 1998:03); Mauritius (in 1986:03); Morocco (in 1992:12); Papua New Guinea (in 1995:03); Peru (in 1988:12); the Syrian Arab Republic (in 1988:05); and Tunisia (in 1986:06). Accordingly, level shift dummy variables (DUM) have been included in the estimation of the cointegrating regressions for these countries (see lower panel).

For the 10 countries for which the null hypothesis of no cointegration could be rejected using the Phillips-Ouliaris Z(t) or Z(α) tests, the cointegrating relationship between each country’s REER and RCOMP (as set out in Equation (1.2)) was again estimated using Phillips and Hansen’s (1990) FM method; the results are set out in the upper panel of Table 1.2.13 All estimates of the commodity price elasticity of the real exchange rate are positive, and all cointegrating regressions have good explanatory ability, with coefficients of determination ranging between about 0.35 and 0.7.

One potential problem with time-series regression models is that the estimated parameters may be unstable. In particular, the many exogenous shocks and policy changes that significantly affect small economies may cause the parameter estimates in the cointegrating relationship between each country’s REER and RCOMP to change over time. Accordingly, when the relationship between these variables is interpreted, it is important that the long-run parameter estimates be structurally stable. To examine the hypothesis of parameter instability in the context of FM estimation of a cointegrated regression model, we again use the tests suggested by Hansen (1992). The results show no evidence of instability in the relationship (at the 5 percent level of significance), for any of the eight countries found to have a cointegrating relationship, between the country’s REER and RCOMP, as the null of parameter stability is not rejected by any of the tests (see columns (4)–(6) of the upper panel of Table 1.2). Accordingly, evidence of a stable cointegrating relation between the two series is found for these eight countries.

For those commodity currency countries for which a long-run relationship is indicated between their REER and RCOMP (the 8 countries exhibiting cointegration with stable parameters and the 11 countries exhibiting coin-tegration with a structural shift), the value of the elasticity of each country’s REER with respect to RCOMP is of particular interest. Estimates of this elasticity range from about 0.162 (for Iceland) to 2.03 (for Ecuador). Across all countries with commodity currencies, the median value of this elasticity is 0.42, indicating that a 10 percent rise in real commodity prices is typically associated with a 4.2 percent appreciation of the real exchange rate.

How completely can real commodity prices explain movements in the real exchange rate of countries with commodity currencies? On average across these 19 countries, more than 85 percent of the variation in the real exchange rate can be accounted for by real commodity prices (and the structural shift dummy, where appropriate), which is a remarkably strong result. Clearly, movements in real commodity prices are an important driver of real exchange rates in such commodity-dependent countries.14

In summary, standard cointegration tests provide evidence of long-run relationships between the real exchange rate and real commodity prices. The evidence for a cointegrating relationship between these variables, allowing for a structural shift (of unknown timing), is also conclusive. In general, the timing of a shift in the long-run relationship between real exchange rates and real commodity prices coincides with periods of sharp revaluation of real exchange rates, typically arising from nominal exchange rate devaluation.15 For one-third (19 of 58) of the commodity-exporting countries in our sample, the general inference to be drawn from our findings is that movements in national real exchange rates are dependent on the evolution of world real commodity prices.

Causality and Exogeneity Tests

Evidence of cointegration rules out the possibility of the estimated relationship’s being a “spurious regression.” As noted in the subsection “Is There a Long-Run Relationship Between Real Exchange Rates and Real Commodity Prices?” for about one-third of the countries in our sample, a long-run relationship between the real exchange rate and real commodity prices was found in the data. Given that cointegration has been established, then the nonstationary variable RCOMP can be thought of as encompassing the long-run component of REER, and the residual in the cointegrat-ing regression captures the short-run movements of REER. It is well known that when two or more variables are cointegrated, there necessarily exists causality (in the Granger sense) in at least one direction, and the direction of causality can be ascertained using the error correction methodology suggested by Engle and Granger (1987). In the presence of cointegration, there is an error correction representation of the relationship that implies that changes in the dependent variable are a function of the magnitude of disequilibrium in the cointegrating relationship (captured by the error correction term) and of changes in other explanatory variables. Prior to estimating the error correction model, we follow Engle (1984) and Engle, Hendry, and Richard (1983) and apply a Lagrange multiplier test statistic to test for weak exogeneity of real commodity prices in the real exchange rate error correction equation. In addition, a likelihood ratio test statistic is applied to the joint significance of the sum of the lags of each explanatory variable to test for strict or “short-term” Granger noncausality.16

Weak exogeneity and Granger noncausality tests are conducted using the error correction procedure, only for those countries for which a cointe-grating relationship between the real commodity price and real exchange rate has been established. In error correction form the model becomes

where η and η′ are constant terms, e and e′ are disturbance terms, and the lagged error correction term (REER—kRCOMP)t–1 is the lagged residual from the cointegrating regression (of Equations (1.2) and (1.3)) between REERt and RCOMPt, and measures the deviation from purchasing power parity in the previous period.17 In Equation (1.5), REERt is influenced by RCOMPt, either through the lagged dynamic terms of RCOMPt if all the β, are not equal to zero (“short-run” Granger causality), or through the lagged error correction term if Θ is nonzero (“long-run” Granger causality). The speed-of-adjustment parameters (Θ and Ω in Equations (1.5) and (1.6)) indicate how quickly the system returns to its long-run equilibrium after a temporary departure from it.

The null hypothesis of Engle’s (1984) weak-exogeneity test is Ω = α12 = 0, where !12 = corr(et, e′t).18 Nonrejection of the null of weak exogeneity of real commodity prices implies that real commodity prices are exogenous to the system and do not respond to any deviation from the long-run equilibrium, and accordingly that all of the adjustment to deviations from the long-run equilibrium (through the error correction component) correspond to adjustments in the real exchange rate. That is, nonrejection of the weak-exogeneity null implies that Equation (1.6) is redundant.

For those countries with commodity currencies, the results of the causality and exogeneity analysis using the error correction procedure are provided in Table 1.3. The weak-exogeneity test results support the hypothesis that real commodity prices are statistically exogenous for 10 of the 19 commodity currency countries (at the 1 percent level of significance). The resulting TR2 is small for these 10 commodity currency countries, indicating that the data provide no evidence against the hypothesis of weak exogeneity of real commodity prices, and that the disequilibrium error from the cointegrating relationship significantly influences changes in the real exchange rate. This result implies that for these countries, the real exchange ratereal commodity price relationship can be modeled in a single-equation error correction framework.19 For the 10 countries satisfying Engle’s (1984) test of weak exogeneity of real commodity prices, with Θ less than zero (which ensures error correction) and statistically significant, a positive (negative) disequilibrium term (REER–kRCOMP)t–1 will ensure that REER declines (rises) toward its long-run equilibrium path.20 These results imply that RCOMP was the initial receptor of exogenous shocks to the long-term relationship and REER had to adjust to reestablish the long-run equilibrium. Accordingly, we find that for the majority of countries with commodity currencies, it is solely the real exchange rate that adjusts to preserve the long-run equilibrium with commodity prices, and there is evidence in support of the notion that rising real commodity prices lead to increasing (appreciating) real exchange rates.21

Table 1.3.Real Exchange Rate and Real Commodity Prices: Exogeneity and Causality, 1980–2002
CountryHalf-Life

of Real

Exchange

Rate

Deviations

from PPP

(months)
Half-Life

of Real

Exchange Rate

Deviations

from

Commodity

Price

Equilibrium

(months)
LagEngle Test

of Weak

Exogeneity:

X2 statistic
βj = 0:

X2 statistic

(p-value)
Θ

(t-statistic)
(1)(2)(3)(4)(5)(6)(7)
Bangladesh20.6612.2511.9715.49–0.055
(0.00)(–1.78)
Bolivia5.732.3811.030.71–0.253
(0.70)(–5.96)
Burundi76.6711.6014.973.12–0.058
(0.21)(–3.31)
Central African86.3011.8114.8315.05–0.057
Republic(0.00)(–3.91)
Ghana66.959.9916.823.46–0.067
(0.17)(–3.33)
Iceland97.288.1014.154.37–0.082
(0.11)(–3.55)
Kenya20.667.4415.5428.06–0.089
(0.00)(–3.86)
Mali76.679.4111.0424.24–0.071
(0.00)(–4.13)
Papua New Guinea20.5313.2422.312.14–0.051
(0.34)(–1.91)
Togo27.2710.1516.0928.11–0.066
(0.00)(–4.04)
Median39.7210.07–0.067
Standard deviation0.060
Note: See the error correction model of Equation (1.5). The cointegrating vectors employed are obtained using ordinary least-squares estimation and include a level shift dummy variable (parameter value not reported) where the Gregory-Hansen test indicated it was appropriate. In column (2), the half-life is the length of time it takes for a unit impulse to dissipate by half. The least-squares estimate of the half-life is calculated using the formula presented in note 22 of the text. In column (3), the implied half-life of real exchange rate deviations from commodity price equilibrium is calculated as follows. The time (T) required to dissipate xpercent (in this case, 50 percent) of the deviation is determined according to (1–Θ)T= (1–x), where Θ is the coefficient of the error correction term (given in column (7)) and Tis the required number of periods (months). Lagrange multiplier tests for serial correlation (with the order of serial correlation tested being one more than the optimal lag length of the error correction model) indicate that there is little evidence of residual serial correlation. In column (4), lag is the number of lagged first-difference terms in the error correction model of Equation (1.5) and is determined by minimizing the Akaike information criterion. In column (5), the critical value of Engle’s (1984) Lagrange multiplier test of weak exogeneity is distributed as x2 (2); the value is 5.99 (9.21) at the 5 (1) percent level of significance. Test statistics less than the critical value indicate that the null hypothesis of weak exogeneity of RCOMPin the REERerror correction model of Equation (1.5) cannot be rejected. Column (6) presents the value of the likelihood ratio test statistic of the null hypothesis that all the βj= 0 in the error correction model of Equation (1.5), with associated p-values in parentheses. Column (7) provides the value of the parameter on the error correction term (Θ) in Equation (1.5), with associated t-statistic in parentheses.
Note: See the error correction model of Equation (1.5). The cointegrating vectors employed are obtained using ordinary least-squares estimation and include a level shift dummy variable (parameter value not reported) where the Gregory-Hansen test indicated it was appropriate. In column (2), the half-life is the length of time it takes for a unit impulse to dissipate by half. The least-squares estimate of the half-life is calculated using the formula presented in note 22 of the text. In column (3), the implied half-life of real exchange rate deviations from commodity price equilibrium is calculated as follows. The time (T) required to dissipate xpercent (in this case, 50 percent) of the deviation is determined according to (1–Θ)T= (1–x), where Θ is the coefficient of the error correction term (given in column (7)) and Tis the required number of periods (months). Lagrange multiplier tests for serial correlation (with the order of serial correlation tested being one more than the optimal lag length of the error correction model) indicate that there is little evidence of residual serial correlation. In column (4), lag is the number of lagged first-difference terms in the error correction model of Equation (1.5) and is determined by minimizing the Akaike information criterion. In column (5), the critical value of Engle’s (1984) Lagrange multiplier test of weak exogeneity is distributed as x2 (2); the value is 5.99 (9.21) at the 5 (1) percent level of significance. Test statistics less than the critical value indicate that the null hypothesis of weak exogeneity of RCOMPin the REERerror correction model of Equation (1.5) cannot be rejected. Column (6) presents the value of the likelihood ratio test statistic of the null hypothesis that all the βj= 0 in the error correction model of Equation (1.5), with associated p-values in parentheses. Column (7) provides the value of the parameter on the error correction term (Θ) in Equation (1.5), with associated t-statistic in parentheses.

Commodity Currencies and the Purchasing Power Parity Puzzle

Although the central issue discussed in this chapter is the role real commodity prices play in driving movements in the real exchange rate, our econometric results also appear to offer a potential resolution of the well-known “purchasing power parity puzzle” (Rogoff, 1996). This puzzle concerns the finding by many researchers that the speed of mean reversion of real exchange rates is too slow to be consistent with purchasing power parity, which is the proposition that exchange rates are determined by movements in relative prices. In summarizing the results from studies using long-horizon data, Froot and Rogoff (1995)) and Rogoff (1996) report the consensus in the literature that the half-life of a shock (the time it takes for the shock to dissipate by 50 percent) to the real exchange rate is about three to five years, implying a slow speed of reversion to (constant) parity of between 13 and 20 percent per year. Such a slow speed of reversion to purchasing power parity is difficult to reconcile with nominal rigidities (where one would expect substantial parity reversion over one to two years) and is also difficult to reconcile with the observed high short-term volatility of real exchange rates.

A potential solution to Rogoff’s (1996) purchasing power parity puzzle may lie in identifying a (real) shock that is both sufficiently volatile and persistent to rehabilitate the purchasing power parity approach to real exchange rate determination (Chen and Rogoff, 2003). Previous work indicates that fluctuations in world commodity prices would certainly fit the bill as a source of real shocks that are both highly persistent and rather volatile (Cashin, Liang, and McDermott, 2000; Cashin, McDermott, and Scott, 2002; Cashin and McDermott, 2002). Accordingly, in this section we examine whether real commodity prices are an important variable in accounting for medium- to long-term deviations of commodity currency real exchange rates from purchasing power parity. We do so after controlling for real shocks, by incorporating real commodity prices as a determinant of the equilibrium real exchange rate of commodity currencies. We then examine the persistence of shocks to real exchange rates in reverting to their commodity-price-dependent equilibria.

To examine the extent of persistence in commodity currency real exchange rates, we begin by estimating a standard first-order autoregres-sive model (or Dickey-Fuller regression), without controlling for commodity prices, and focus on the magnitude of the least-squares estimates of the autoregressive parameter. Across all countries, the median half-life of parity reversion is 36 months for our sample of 58 commodity-dependent countries, whereas for the 19 countries with commodity currencies, the median half-life of parity reversion is somewhat longer at 49 months.22 These results are consistent with Rogoff’s (1996) consensus of half-lives of parity reversion of between 36 and 60 months.

Next we turn to the results from our error correction model, which provides information on the speed at which real exchange rates adjust to reestablish their long-run equilibrium relationship with real commodity prices (see column (3) of Table 1.3). The magnitude of Θ (the coefficient on the error correction term in Equation (1.5)) indicates that for some countries (such as Bangladesh and Papua New Guinea) only about 5 percent of the deviation of REER from long-run equilibrium is eliminated in one month (implying a half-life for parity deviation of about 13 months), whereas for other countries (such as Kenya and Iceland) about 8 percent of the deviation is eliminated in one month (implying a half-life for parity deviation of about 8 months), a very rapid speed of adjustment. For each of the 10 commodity currency countries with weakly exogenous commodity prices, the half-life of the reversion of the real exchange rate to its (constant) long-run average level (reported in column (2) of Table 1.3) is much longer than the half-life of the reversion of the real exchange rate to its (time-varying) long-run equilibrium with real commodity prices (reported in column (3) of the table).23

Averaging across these 10 commodity currency countries, the median speed of error correction of real exchange rates is about 6½ percent per month (Table 1.3). The elimination of 6½ percent of the deviation of the real exchange rate from its equilibrium level per month is the equivalent of a median half-life of parity deviation of about 10 months, which is much smaller than the typical half-life (of about three to five years) reported in the simple purchasing power parity–based regressions analyzed earlier (Rogoff, 1996). That is, although the real exchange rate of these 10 countries has a slow reversion to its average level (the median half-life of parity deviations is 39 months), it has a much faster speed of adjustment toward its long-run equilibrium (the median half-life of deviations is about 10 months), where that equilibrium depends on the evolution of real commodity prices as a fundamental determinant of the real exchange rate (see columns (2) and (3) of Table 1.3). These results indicate that, particularly for commodity-dependent developing countries, controlling for the influence of real commodity prices on the real exchange rate is an important channel by which to reduce the measured persistence of real exchange rate shocks.

Conclusions

In this chapter we have examined the evidence for a real commodity price explanation of movements in the real exchange rates of 58 commodity-dependent countries over the period 1980–2002. For about one-third of these commodity-exporting countries, we find robust evidence in support of the long-run comovement of national real exchange rate and real commodity export price series. While the real exchange rate and real commodity prices of these countries with commodity currencies will be subject to transitory deviations from their long-run equilibrium, these two series move together over time such that they revert to an equilibrium relationship. In addition, weak-exogeneity tests indicate that, for the majority of countries with commodity currencies, it is the real exchange rate that adjusts to restore the long-run equilibrium with real commodity prices. The half-lives for adjustment of real exchange rates to equilibrium in this group of commodity currency countries are found to be extremely short: about 10 months. These estimates cast doubt on the universality of Rogoff’s (1996) consensus estimate of the half-life of the reversion of real exchange rates to purchasing power parity of about three to five years. As presciently conjectured by Keynes (1930), purchasing power parity is a weak model of the long-run real exchange rate in countries with commodity currencies, as these countries typically experience large and long-lived real shocks. The long-run real exchange rate of commodity currencies is not constant (as would be implied by parity-based models) but is time-varying, being dependent on movements in real commodity prices.

Appendix 1.1 Details of the Theoretical Framework

In this appendix we present in detail the theoretical framework presented in the chapter’s second section. We study a small open economy that produces two types of goods, a nontraded good and an exportable good, which is associated with the production of a primary commodity. The details of the model are as follows.

Domestic Production

There are two different sectors in the domestic economy: one sector produces an exportable referred to as the primary commodity; the other sector consists of a continuum of firms producing a nontradable good. For simplicity, we assume that the production of these two different types of goods requires labor as the only factor. In particular, the production function for the primary commodity is given by yX = aXLX, where LX is the amount of labor input demanded by the commodity sector and aX measures how productive labor is in this sector. In a similar fashion, the nontraded good is produced through the production function yN = aNLN, where aN captures the productivity of labor in the production of this good and LN is the employment of labor in the nontradables sector. Crucially, we assume that labor can move freely across sectors in such a way that labor wages (w) must be the same across sectors. Profit maximization in both sectors yields the familiar conditions: PX = w/aX and PN = w/aN, where PN is the price of the nontraded good and PX the price of the primary commodity.

In equilibrium, the marginal productivity of labor must equal the real wage in each sector. We assume that the price of the primary commodity is exogenous for (competitive) firms in the commodity sector and that there is perfect competition in the nontraded sector. Therefore, we can rewrite the price of the nontraded good in order to express it as a function of the price of the exportable and the relative productivities between the export and nontradables sectors. We obtain

Thus, the relative price of the nontraded good (PN) with respect to the primary commodity (PX) is completely determined by technological factors and is independent of demand conditions. Note that an increase in the price of the primary commodity will increase the wage in that sector. Given our freely mobile labor assumption, wages and prices will also rise in the nontraded sector.

Domestic Consumers

The economy is inhabited by a continuum of identical individuals who supply labor inelastically (with L = LX + LN) and consume a nontraded good and a tradable good. This tradable good is imported from the rest of the world and is not produced domestically. Our assumptions on preferences imply that the primary commodity is also not consumed domestically. Each individual chooses the consumption of the nontraded and tradable good to maximize utility, which is assumed to be increasing in the level of aggregate consumption given by C=κCNγCT1γ where CN represents purchases of the nontraded good and CT purchases of the imported good and κ = 1/[γγ(1–γ)(1–γ)] is an irrelevant constant. The minimum cost of one unit of consumption is given by

where PT is the price in local currency of one unit of the tradable good. As usual, P is defined as the consumer price index. The law of one price is assumed to hold for the imported good, so that PT=PT*/E, where E is the nominal exchange rate (defined as the amount of foreign currency per local currency), and PT* is the price of the tradable (imported) good in terms of foreign currency. We now specify in more detail the rest of the world.

Foreign Production and Consumption

So far we have assumed that the primary commodity is not consumed by domestic agents and is therefore completely exported. In addition, the domestic economy also imports a good that is produced only by foreign firms.24 The foreign region consists of three different sectors: a nontraded sector, an intermediate sector, and a final goods sector. The nontraded sector produces a good that is consumed only by foreigners using labor as the only factor. The technology available for the production of this good is given by YN*=aN*LN*. The foreign economy also produces an intermediate good that is used in the production of the final good. This intermediate good is produced using labor as the only factor. In particular, the production function available to firms in this sector is represented by YI*=aI*LI*. Labor mobility across (foreign) sectors ensures that the (foreign) wage is equated across sectors.25 Again, we can express the price of the foreign nontraded good as a function of relative productivities and the price of the foreign intermediate good:

The production of the final good involves two intermediate inputs. The first is the primary commodity (produced by several countries, among them our domestic economy). The second is an intermediate good produced in the rest of the world. Producers of this final good, also referred to as the tradable good, produce it by assembling the foreign intermediate input (YI) and the foreign primary commodity (YX) through the following technology: YT*=v(YI*)β(YX*)1β. It is straightforward to show that the cost of one unit of the tradable good in terms of the foreign currency is given by PT*=(PI*)β(YX*)1β. Foreign consumers are assumed to consume the foreign nontraded good and this final good in the same fashion as domestic consumers. Foreigners also supply labor inelastically to the different sectors. Therefore, the consumer price index for the foreign economy can be represented by

Real Exchange Rate Determination

It is now straightforward to show how the real exchange rate is determined in the domestic economy. First, we define the real exchange rate as the foreign price of the domestic basket of consumption relative to the foreign price of a foreign basket of consumption (EP/P*). Using 5/2/2010Equations (1.A.1), (1.A.2), (1.A.3), and (1.A.4), we can show that

which is Equation (1.1) as set out in the chapter’s “Theoretical Framework” section.

Appendix 1.2 Description of the Data

The data are of monthly frequency, for the period 1980:01–2002:03. The 58 potential commodity currency countries in our sample are listed in Appendix 1.4. The primary data sources are the IMF’s International Financial Statistics (IFS) and Information Notice System (INS) databases. A description of the series follows.

REER: Trade-weighted measure of the seasonally adjusted, CPI-based real effective exchange rate (base 1990 = 100); obtained from the INS.

NCOMP: The nominal commodity export price index for each country (base 1990 = 100, seasonally adjusted), calculated using UN Comtrade data on the (1991–99 average) share of each commodity in total primary commodity exports and the IMF’s (U.S.-dollar-based) data on world commodity prices (taken from the IFS). The derivation of this index is described in detail in Appendix 1.3.

RCOMP: The real commodity export price index, calculated by deflating each country’s NCOMP by the IMF’s index of the unit value of developed country manufactured exports (MUV).

MUV: Unit value index (in U.S. dollars) of manufactures exported by 20 developed countries, with country weights based on the countries’ total 1995 exports of manufactures (base 1995 = 100); obtained from the IFS.

Appendix 1.3 Construction of the Country-Specific Nominal Price Indices of Commodity Exports

The country-specific nominal export price indices (NCOMP) for the period 1980:01–2002:03 were constructed as set out in the following.

For each country, we calculated the 1991–99 average total value of primary commodity exports; the 44 individual nonfuel commodity weights were calculated by dividing the 1991–99 average value of each individual commodity export by the 1991–99 average total value of primary commodity exports. All commodity weights used were gross export weights as found in the World Bank’s World Integrated Trade Solution (WITS), which supplies UN Comtrade data provided by the UN Statistical Department. Once the country-specific commodity export weights were established, these weights were held fixed over time and used to weight the individual (U.S.-dollar-based) price indices of the same commodities—taken from the IFS—to form, for each country, a geometric weighted-average index of (U.S.-dollar-based) nominal commodity export prices (base 1990 = 100). The national index of nominal commodity export prices were then seasonally adjusted using the X11.2 variant of the Census Method 11 procedure.

Nominal Commodity Prices

The prices (taken from the IFS) of the following 44 nonfuel commodities were used in the calculation of the national commodity price indices: aluminum, bananas, beef, coal, cocoa, coconut oil, coffee, copper, cotton, fish, fish meal, gold, groundnut oil, groundnuts, hardwood logs, hides, iron, lamb, lead, maize, natural rubber, nickel, palm oil, palm kernel oil, phosphate rock, platinum, potash, rice, shrimp, silver, softwood logs, softwood sawn, soy meal, soy oil, soybeans, sugar (three types), sun-/safflower oil, tea, tin, tobacco, wheat, wool, uranium, and zinc. A brief description of the individual commodity prices is available in a longer working paper version of this chapter (see Cashin, Céspedes, and Sahay, 2002).

Appendix 1.4 Cointegration Tests: Real Exchange Rate and Real Commodity Prices, Commodity-Exporting Countries, 1980–2002
Table 1.4.
CountryZ(t)Z(a)Z(t)*Shift Date
(1)(2)(3)(4)(5)
Argentina–2.05–8.82–3.84
Australia–3.63*–24.76*–3.53
Bangladesh–3.45*–23.17*–3.84
Bolivia–6.07*–64.24*–6.21*[1986:01]
Brazil–2.61–13.86–3.29
Burundi–3.53*–20.89*–3.48
Cameroon–1.69–5.99–5.20*[1993:12]
Canada–1.07–2.63–3.41
Central African Republic–1.93–7.29–5.87*[1993:12]
Chile–1.48–4.32–3.95
Colombia–1.60–5.99–3.16
Costa Rica–4.03*–27.52*–5.01*[1998:12]
Cote d’lvoire–2.13–8.56–4.89*[1993:12]
Dominica–2.98–14.64–3.15
Ecuador–3.82*–26.99*–3.70
Ethiopia–1.28–4.02–4.65*[1993:03]
Ghana–2.44–11.52–4.87*[1983:09]
Guatemala–1.87–8.26–3.05
Honduras–2.12–9.08–3.32
Iceland–3.66*–25.98*–4.22
India–2.07–8.02–3.51
Indonesia–2.59–14.13–4.88*[1997:10]
Kenya–3.73*–28.85*–5.19*[1995:05]
Madagascar–2.64–14.66–5.29*[1986:04]
Malawi–3.01–17.69–4.66*[1994:08]
Malaysia–2.05–8.16–2.96
Mali–2.07–8.47–5.61*[1993:12]
Mauritania–2.47–12.65–5.21*[1998:03]
Mauritius–2.11–8.81–5.12*[1986:07]
Mexico–2.28–11.75–3.10
Morocco–2.07–6.77–4.63*[1992:12]
Mozambique–1.93–7.23–3.35
Myanmar–3.291.48–3.32
New Zealand–2.47–12.46–2.70
Nicaragua–2.91–16.50–3.22
Niger–2.19–9.13–6.49*[1993:12]
Norway–3.03–15.70–4.51
Pakistan–2.19–9.31–3.88
Papua New Guinea–2.47–12.38–4.76*[1995:03]
Paraguay–3.65*–25.64*–4.32
Philippines–2.94–16.84–3.17
Peru–3.17–19.39–6.28*[1988:12]
St. Vincent and the Grenadines–2.47–11.25–3.32
Senegal–1.59–5.35–5.65*[1993:12]
South Africa–1.68–9.27–2.78
Sri Lanka–2.51–13.54–4.19
Sudan–2.38–11.00–3.51
Suriname–2.68–13.91–3.56
Syrian Arab Republic–1.51–4.32–4.80*[1988:05]
Tanzania–2.18–9.75–3.67
Thailand–3.25–19.34–3.85
Togo–2.50–12.14–5.32*[1993:12]
Tunisia–2.92–16.69–6.36*[1986:06]
Turkey–3.10–17.32–3.94
Uganda–3.25–18.17–3.92
Uruguay–1.77–6.14–3.55
Zambia–3.42*–22.39*–3.67
Zimbabwe–1.20–6.24–1.60
Note: The data (described in Appendices 1.1 and 1.2) for all countries are monthly and are expressed in logarithmic form. The estimated regression from which the residuals are derived is REER = βo + β1RCOMP + ε, where REER is the country’s real effective exchange rate; RCOMP is the national real commodity price; and ε is the residual. In column (2), the 5 (10) percent critical value (for T = 267) for the Phillips-Ouliaris (1990) residual-based Z(t) test (with a constant) is–3.36 (–3.06), based on MacKinnon (1991). In column (3), the 5 (10) percent critical value (for T = 250) for the Phillips-Ouliaris (1990) residual-based Z(α) test (with a constant) is–20.05 (–16.65), taken from Haug (1992). In column (4), the 5 (10) percent critical value for the Gregory-Hansen (1996a)Z(t)* test for the presence of a level shift in the cointegrating vector is–4.61 (–4.34); the year and month in which the structural change is estimated to have occurred is given in square brackets (column (5)).

statistically significant at the 5 percent level, indicating that the null hypothesis of no cointegration can be rejected.

Note: The data (described in Appendices 1.1 and 1.2) for all countries are monthly and are expressed in logarithmic form. The estimated regression from which the residuals are derived is REER = βo + β1RCOMP + ε, where REER is the country’s real effective exchange rate; RCOMP is the national real commodity price; and ε is the residual. In column (2), the 5 (10) percent critical value (for T = 267) for the Phillips-Ouliaris (1990) residual-based Z(t) test (with a constant) is–3.36 (–3.06), based on MacKinnon (1991). In column (3), the 5 (10) percent critical value (for T = 250) for the Phillips-Ouliaris (1990) residual-based Z(α) test (with a constant) is–20.05 (–16.65), taken from Haug (1992). In column (4), the 5 (10) percent critical value for the Gregory-Hansen (1996a)Z(t)* test for the presence of a level shift in the cointegrating vector is–4.61 (–4.34); the year and month in which the structural change is estimated to have occurred is given in square brackets (column (5)).

statistically significant at the 5 percent level, indicating that the null hypothesis of no cointegration can be rejected.

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This chapter is a modified version of an article published in Journal of Development Economics 75 (2004), 239–68, and is included here with the permission of the journal’s publisher, Elsevier. The authors are grateful to John McDermott, Paul Nicholson, Sam Ouliaris, Paolo Pesenti, Carmen Reinhart, Ken Rogoff, Miguel Savastano, seminar participants at the Third Annual IMF Research Conference, and especially a coeditor and an anonymous reviewer for comments and suggestions on earlier drafts.

1

Two earlier country-specific analyses are Edwards (1985), which examines the relationship between real coffee prices and Colombia’s real exchange rate, and Chen and Rogoff (2003), which finds that commodity price movements influence the real exchange rates of developed country commodity exporters Australia, New Zealand, and Canada.

2

Deaton and Laroque (1992) find that as the terms of trade is an aggregate price index, it is a poor measure of the short-lived booms and long-lived troughs frequently observed in the prices of major exports of commodity-dependent countries. Bidarkota and Crucini (2000) and Baxter and Kouparitsas (2000) find that, for developing countries, real commodity prices (the prices of nonfuel commodities relative to those of manufactured goods) are much more volatile than the terms of trade.

3

This real price is also described in the literature as the commodity terms of trade. MUV is a unit value index of exports from 20 industrial countries, and use of MUV as a deflator is common to most studies in the commodity price literature (see Grilli and Yang, 1988; Deaton and Miller, 1996; and Cashin, Liang, and McDermott, 2000).

4

In this chapter, “commodity exports” are defined as nonfuel primary products (agricultural and mineral primary products) exports—see Appendices 1.1 and 1.2 for additional details.

5

Baxter and Kouparitsas (2000) show that, for exporters of nonfuel commodities, the terms of trade are essentially the relative prices of their commodity exports and manufactured imports. Across both developing and developed countries, there is little variation in the import share devoted to manufactured goods (averaging about 65 percent of the import basket), nonfuel goods (20 percent), and fuels (15 percent). Accordingly, Baxter and Kouparitsas find that cross-country differences in movements in the terms of trade largely emerge on the export price side.

6

Our national commodity price indices differ from those of Deaton and Miller (1996) and Dehn (2000) as they are based on monthly, rather than quarterly or annual, data and cover an expanded range of individual commodities.

7

Following Deaton and Miller (1996), the commodity export weights used in the construction of our national commodity price indices are held fixed over time as we are interested in constructing a potentially exogenous variable, and so exclude volume effects of changes in commodity export prices.

8

We also applied the Zivot-Andrews (1992) unit root test, which allows for an exogenous change in the level of the series. With a few exceptions, all test statistics for the two series are again not statistically significant, indicating nonrejection of the unit root null. Accordingly, we conclude that the REER and RCOMP series of most countries exhibit behavior consistent with unit root nonstationarity in levels. Although not consistent with every test result (using these unit root tests, there is some conflicting evidence as to whether the REER series of Mauritania and Togo and the RCOMP series of Chile are nonstationary in levels), these conclusions seem reasonable. The detailed results of the unit root tests are available from the authors.

9

This concept of a long-run relationship that is subject to structural change formalizes the idea of Dornbusch and Vogelsang (1991) of purchasing power parity holding once allowance is made for a shift in the mean level of the real exchange rate. Work by Flynn and Boucher (1993) and Hegwood and Papell (1998) also allows for a structural break in cointegration analyses of the determinants of the real exchange rate. Flynn and Boucher (1993) find that cointegration analyses are biased against finding stationarity of the residuals from the long-run regression if allowance is not made for structural breaks (typically caused by government interventions affecting the level of the nominal [and real] exchange rate).

10

The MeanF and SupF tests require truncation of the sample of size T to avoid the test statistics’ diverging to infinity: we follow Hansen (1992) and use the subset [0.15T, 0.85T]. Hansen’s (1992) parameter stability tests are based on the residuals of a fully modified least-squares regression (Phillips and Hansen, 1990).

11

For the Phillips-Hansen (1990) FM estimation we employ the Bartlett kernel, Andrews’ (1991) automatic bandwidth selector, and the prewhitened kernel estimator of Andrews and Monahan (1992). The regression was conducted without a trend term, which was found to be not statistically significantly different from zero in the cointegrating regressions. This absence of a significant time trend in the cointegrating regressions indicates that, with real commodity prices controlled for, there is little support for sectoral productivity differentials (the Balassa-Samuelson effect) driving commodity currency real exchange rates.

12

Ordinary least-squares estimation could be used to yield consistent estimates of the cointegrating parameters. However, least-squares estimation is inefficient and yields nonstandard distributions of the estimators, making standard inference tests problematic in the least-squares framework, whereas these difficulties are overcome in the FM method (Phillips and Hansen, 1990). Importantly, FM-based estimates are robust to any potential endogeneity of real commodity prices.

Although the null hypothesis of no cointegration could be rejected in favor of the alternative hypothesis of cointegration (allowing for a structural shift) for Cameroon, Cote d’lvoire, Ethiopia, Madagascar, Mauritius, Peru, the Syrian Arab Republic and Senegal, for these countries the coefficient on RCOMP in the cointegrating regression was found to be either negative or positive (yet not significantly different from zero), and so these countries were deemed not to be commodity currency countries. Accordingly, they are not listed either in the lower part of Table 1.2 or in Table 1.3.

13

Although the null hypothesis of no cointegration could be rejected in favor of the alternative hypothesis of cointegration for Costa Rica and Zambia, for these countries the coefficient on RCOMP in the cointegrating regression was found not to be significantly different from zero, and so these countries were deemed not to be commodity currency countries. Accordingly, they are not listed in either the upper part of Table 1.2 or in Table 1.3.

14

Cointegration of two or more variables implies that these variables move together over time such that they revert to a long-run equilibrium relationship. Given that real commodity prices and the real exchange rate are cointegrated (as was found for the 19 countries with commodity currencies), then the econometric problems typically associated with exogeneity issues (such as simultaneity bias, consistency, and identification) are asymptotically negligible in such static cointegrating regressions (see McDermott and Wong, 1990). Indeed, if a set of nonstationary variables is cointegrated (as defined by Engle and Granger, 1987), then the concept of exogeneity is not useful, as a particular attraction of cointegrat-ing regressions is that all of the variables may be treated as jointly endogenous.

15

In many countries (especially those with pegged nominal exchange rates), real exchange rate movements occur chiefly through large and rapid nominal devaluation, rather than through cumulative inflation differentials (Goldfajn and Valdes, 1999). In addition, if the speed of adjustment of the real exchange rate to its equilibrium is very slow, the estimation may be picking up a long period of exchange rate misalignment that is abruptly corrected by a devaluation as a change in the constant term of the cointegrating regression.

In the case of commodity currencies, the real exchange rate has a time-varying long-run relationship with real commodity prices, after the structural shift in the cointegrat-ing relationship induced by a level shift in the real exchange rate is taken into account. Moreover, just as univariate unit root tests for purchasing power parity—based equilibrium real exchange rates will be biased toward nonrejection of the unit root null if potential structural breaks (intercept changes) are not accounted for (Perron and Vogelsang, 1992; Papell, 2002), cointegration tests of whether the real exchange rate has a time-varying equilibrium relationship with its real fundamentals will also be biased toward nonrejection of the no-cointegration null if potential structural breaks are not accounted for (Gregory and Hansen, 1996a). Indeed, the failure of empirical models of exchange rate determination to account for structural breaks in the long-run relationship between the real exchange rate and its fundamentals could account for a sizeable share of the poor empirical performance of such models.

16

Real commodity prices are weakly exogenous with respect to the real exchange rate if inference can be conducted conditional on the sample values of real commodity prices with no loss of relevant sample information (see Engle, Hendry, and Richard, 1983). Rejection of the null hypothesis of Granger noncausality implies that one variable can be predicted using past values of another variable; that is, real commodity prices Granger-cause the real exchange rate if the real exchange rate can be predicted from past values of real commodity prices. In an error correction model, one or more of the differenced variables must be Granger-caused by the lagged error correction term.

17

The cointegrating vectors used are obtained using ordinary least-squares estimation and include a level shift dummy variable (φt, parameter value not reported) where the Gregory-Hansen test of the subsection “Examining for Cointegration: Allowing for Structural Change” indicated that Equation (1.3) was the appropriate cointegrating regression.

18

We are grateful to an anonymous reviewer for suggesting further analysis of weak exogeneity issues. The appropriate test for the weak exogeneity of RCOMP is done by testing ũ1 and u˜1and[(REERκRCOMP)t1Θ^u˜2], as omitted from Equation (1.6), where Θ^ is the estimated parameter on the error correction term in Equation (1.5), ũ1 are the residuals from Equation (1.5), and ũ2 are the residuals from the regression of ∆RCOMP on η′, ∆∑REER, and ∆∑RCOMP. The test of weak exogeneity of real commodity prices is computed as TR2 (T = 265) of the regression of ũ2 on η, ũ1, ∆∑REER, and ∆∑RCOMP. This statistic is asymptotically distributed as X2(2) under the null; the 5 (1) percent critical value is 5.99 (9.21). The weak-exogeneity test is biased toward rejecting the null hypothesis of weak exogeneity if there exists any form of misspecification in the model. For additional details on the Lagrange multiplier test of weak exogeneity, see Engle (1984) and McDermott and Wong (1990).

19

In addition, for five countries (for example, Bangladesh and Togo), the likelihood ratio test provides evidence that short-run movement in RCOMP helps predict (Granger-causes) part of the short-run movement in REER.

20

This finding that the coefficient on the error correction term is appropriately negative and significantly different from zero also means that econometric specifications based on first differences of the variables alone probably ignore useful information about the parity-reverting properties of the real exchange rate.

21

For nine countries, the null hypothesis of weak exogeneity of real commodity prices was rejected. In all cases (except Australia), the null was rejected not because the error terms in Equations (1.5) and (1.6) were correlated (that is, not because corr(et, e′t) ≠ 0 in Engle’s (1984) exogeneity test), but because of the endogeneity of RCOMP (that is, RCOMP is adjusting to restore the long-run equilibrium relationship with REER [Ω ≠ 0 in Equation (1.6)]). This finding is some comfort, as correlation of the error terms in Equations (1.5) and (1.6) would imply that the error correction models were misspecified. Importantly, in all nine countries for which weak exogeneity of real commodity prices was rejected, the estimated Θ in Equation (1.5) was negative (which ensures error correction) and statistically significant. Accordingly, for these nine countries both the real exchange rate and real commodity prices adjust to close any given deviation from long-run equilibrium, so that the speed of reversion of REER in response to deviations from long-run equilibrium cannot be calculated for these commodity currencies.

22

The half-life is the length of time it takes for a unit impulse to dissipate by half. The least-squares estimate of the half-life is calculated using the formula HL = ABS(log(1/2)/log(α)), where α is the autoregressive parameter derived from the Dickey-Fuller (or AR(1)) least-squares regression. These half-life results are comparable to those obtained by Cheung and Lai (2000) using least-squares estimation on monthly bilateral (post-Bretton Woods) dollar real exchange rates for developed countries, which yielded an average half-life of 3.3 years.

23

In comparison with the relatively slow adjustment speed of real exchange rates to parity typically found for developed countries, nominal rigidities appear to be less important for countries with commodity currencies (which are predominantly developing countries). This relatively fast adjustment of wages and nontraded goods prices for commodity currency countries is consistent with the relatively small formal sector of developing countries in comparison with that of developed countries, and with developed countries’ relatively larger share of nontraded goods prices in domestic prices (see Baffes, Elbadawi, and O’Connell, 1999).

24

When we refer to the foreign economy, we do not mean the rest of the world. The rest of the world also includes other countries producing the primary commodity.

25

We assume that labor can move freely across sectors within each region (domestic and foreign) but cannot move across regions.

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