III. The Equilibrium Real Exchange Rate in a Commodity Exporting Country: Algeria’s Experience49
The real effective exchange rate (REER) varied significantly during the last decade. Moreover, in 2002-03, it depreciated by 17½ percent. By estimating an equilibrium path for Algeria’s REER over the period from 1970 to 2003, this chapter assesses the existence of any current real exchange rate misalignment. It finds that the Balassa-Samuelson effect together with real oil prices explain the long-run evolution of the equilibrium REER and that the current REER is in line with equilibrium.
1. The rapid increase in hydrocarbon exports since 2000 raises questions on the evolution of the Algerian dinar’s real exchange rate and its effect on private sector development. Algeria’s main challenge is to manage its volatile external inflows from hydrocarbon exports to strengthen the outlook for private sector-driven economic growth and employment. While fiscal and monetary policies have an important role in maintaining macroeconomic stability, management of the exchange rate is essential in order not to harm the competitiveness of the nonhydrocarbon tradable sector (Dutch disease). A prolonged departure from the equilibrium real exchange rate could generate major problems for the economy.
2. The real effective exchange rate (REER) varied significantly during the lastdecade. Algeria s exchange rate regime is a managed float with no pre-announced path for the exchange rate. Since 1995, the authorities aimed at maintaining a stable REER against a basket of currencies weighted on the basis of the trade shares of the country’s main trading partners.50 However, the REER has varied continuously over the last decade (Figure 1).51 Moreover, in 2002–03, the REER of the Algerian dinar depreciated by 17½ percent.
Figure 1.Real Effective Exchange Rate (1990=100) January 1995-September 2004
3. The literature emphasizes that equilibrium real exchange rates are determined by fundamental determinants. A well-known problem with the purchasing power parity approach (constant real exchange rate rule) is that it fails to take into account that the equilibrium real exchange rate, defined as the price of tradable goods relative to nontradable goods that is consistent with both internal and external balance, is itself an endogenous variable that is likely to change through time in response to a variety of disturbances.52 The literature shows that exogenous time-varying factors determine exchange rate dynamics and the equilibrium path of the exchange rate.
4. The significant depreciation of the REER in 2002-03 raises questions as to what extent the evolution of the Algerian dinar was consistent with the equilibrium real exchange rate over the last decade, in particular in 2002–03, and whether fundamentals can explain the exchange rate path in Algeria.
5. This study addresses these questions by estimating an equilibrium path for Algeria’s REER over the period from 1970 to 2003. It examines the fundamental determinants of the Algerian dinar in real terms, and, based on these results, assesses the existence of any current real exchange rate misalignment.
6. The main findings of the study are:
- There are no signs of a current misalignment in the real exchange rate. Both the long-run equilibrium model and the behavior of macroeconomic variables show that the REER was close to its equilibrium level in 2002–03.
- Algeria’s equilibrium real exchange rate varies over time. The Balassa-Samuelson effect together with real oil prices explain the long-run evolution of the equilibrium REER. The convergence speed towards equilibrium is 9 months, similar to the findings in other commodity-exporting countries. The poor productivity of the nonhydrocarbon sector has been the main factor behind the depreciation of the equilibrium real exchange rate over the last twenty years.
7. The remainder of the study is organized as follows. After briefly describing the evolution of the Algerian exchange rate regime in Section B, Section C reviews the existing literature on the equilibrium real exchange rate. Section D uses different tools to determine the long-run equilibrium real exchange rate. First, it tests the purchasing power parity (PPP) theory for the market-determined REER. Then, it investigates the presence of a long-run cointegrating relationship between the real exchange rate and certain explanatory variables, estimates the speed at which the real exchange rate converges toward its equilibrium level, and assesses the gap between the actual and the equilibrium real exchange rate levels. Section E discusses the equilibrium REER from a forward-looking perspective, and Section F concludes.
B. Developments in the Algerian Exchange Regime
8. From January 1974, the exchange rate of the Algerian dinar was pegged to a basket of currencies—in which the US dollar was assigned a relatively large weight due to its importance in oil export receipts and debt-service payments—with adjustments taking place from time to time. The substantial appreciation of the US dollar during the first half of the 1980s led to a strong rise in the real value of the Algerian dinar (of about 50 percent during 1980–85), thus undermining the competitiveness of nonhydrocarbon exports and stimulating imports.
9. In 1986, Algeria’s economy experienced the reverse oil shock, and the government responded to the dramatic erosion of export revenue by borrowing abroad and intensifying import restrictions. In parallel, the Bank of Algeria adopted an active exchange rate policy, and the Algerian dinar depreciated against the basket by 31 percent between 1986 and 1988. However, the restrictions imposed on the allocation of foreign exchange increased demand for foreign exchange in the informal market, driving the premium in the parallel market rate to about 500 percent. This rigid system was replaced in 1988 by a system of foreign exchange allocation to the five public commercial banks within a framework of credit ceilings, which were consistent with balance of payments targets. The public banks in turn would allocate foreign exchange to their client public enterprises. Between 1989 and 1991, the Algerian dinar was allowed to depreciate (more than 200 percent in nominal terms) to counteract the terms of trade losses during this period.
10. From 1991, the Council on Money and Credit was made responsible for setting foreign exchange and external debt policy, and for approving foreign investments and joint ventures. The supplementary budget of August 1990 granted businesses and individuals the right to hold foreign currency accounts. In 1991, as part of an attempt to realign domestic relative prices and increase openness, the Algerian dinar was devalued by more than 100 percent to DA 22 per US dollar. During 1991-94, the rate of nominal depreciation averaged 4 percent annually, bringing the value of the Algerian dinar to about DA 24 per US dollar on the official market. This relative stability of the nominal rate did not correspond to economic fundamentals: adverse terms of trade shocks and expansionary fiscal and monetary policies led to inflation being persistently higher than in Algeria’s trading partners. The Algerian dinar, therefore, appreciated by 50 percent in real terms between October 1991 and end 1993.
11. In 1994, the authorities put in place an adjustment program with the objective of correcting the previous real appreciation of the Algerian dinar. A two-step devaluation of the Algerian dinar (in total 70 percent) took place between April and September 1994. The spread between the parallel market and the official exchange rates fell to about 200 percent during this time.
12. Since 1995, Algeria’s foreign exchange policy has aimed at maintaining a stable real exchange rate against a basket of currencies weighted according to the country’s main trading partners and competitors. In 1995, the managed float regime was implemented through fixing sessions between the Bank of Algeria and commercial banks. An interbank foreign exchange market was established in 1996 to allow a free determination of the exchange rate. Between 1995 and 1998 the REER appreciated by more than 20 percent, followed by a depreciation of 13 percent between 1998 and 2001. Following 16 months of real depreciation since early 2002, due to the appreciation of the euro against the US dollar, the authorities intervened in the foreign exchange market in the second half of 2003 to realign the REER to its end-2002 level instead of its end-1995 level. Between June and November 2003, the Algerian dinar appreciated against the US dollar by 24½ percent and the REER increased by 11 percent.
13. The central bank strongly influences the nominal exchange rate on the official market. Through its intervention, the Bank of Algeria adjusts periodically the nominal exchange rate so as to achieve its real exchange rate target. In practice, the central bank holds the counterpart of the majority of the transactions on the foreign exchange market, as a result of the combination of three factors: (a) hydrocarbon exports account for more than 95 percent of total exports; (b) by law, the foreign exchange receipts from hydrocarbon exports have to be converted into dinars directly at the central bank outside the interbank market; and (c) capital account transactions are subject to strict controls.
14. With the advent of the external convertibility of the dinar for current account transactions in 1997, the authorities have indicated that the parallel market has shrunk. The exchange rate spread between the interbank market and the parallel market is currently about 25 percent.
C. Review of the Literature
15. Purchasing power parity (PPP) implies that the real exchange rate will revert to its mean, although it may deviate from its mean for several years at a time.53 The concept of PPP is often the first port of call for economists and market analysts who wish to estimate exchange rate equilibrium. The most widely used methodology to confirm or reject the PPP is based on the analysis of the time series properties of the REER, which is assumed to measure changes in price level differences between a country and its trading partners (Rogoff 1996). If the REER series is stationary and the speed of convergence of the REER towards its mean is fast enough, then the PPP can be considered to hold. Slow convergence is inconsistent with the PPP, which only allows for short-term deviations from equilibrium.
16. PPP has proven to be a weak model of the long-run real exchange rate. Most studies have failed to find cointegrating relationships that are consistent with PPP (or, equivalently, consistent with a stationary real exchange rate). Meese and Rogoff (1983) demonstrated that a variety of linear structural exchange rate models failed to forecast more accurately than a random walk model for both real and nominal exchange rates. Recent work has therefore emphasized the time-varying nature of the long-run real exchange rate. The equilibrium real exchange rate is not a single rate, but a path of real exchange rates over time that is affected by the current and expected values of variables that affect internal and external equilibrium. These variables are known as fundamentals. The multitude of potential fundamentals offered by researchers in their attempts to resolve the PPP puzzle include the Balassa-Samuelson effect,54 government spending, cumulated current account imbalances, and real interest rate differentials as important drivers of long-run deviations from purchasing power parity (see Froot and Rogoff (1995) and Rogoff (1996)). Clark and MacDonald (2000) extended the approach to better differentiate between permanent and transitory components of the real exchange rate.
17. Several models have been developed to determine the equilibrium real exchange rate in developing countries. Edwards (1989, 1994) made a seminal attempt to build an equilibrium real exchange rate model specifically tailored to developing countries by exploring the long-run co-movements of the real exchange rate with variables such as the terms of trade, productivity, net foreign assets, the fiscal balance and measures of openness of the trade and exchange system. Khan and Ostry (1991) provided panel data estimates of the elasticity of the equilibrium real exchange rate with respect to terms of trade shocks and commercial policies in a static model.
18. The connection between economic fundamentals and exchange rate behavior has also been controversial. Many studies have failed to find a statistical link between real exchange rates and fundamentals. Edison and Melick (1999) failed to find cointegration between real exchange rates and real interest rate differentials, and Rogoff (1996) found a mixed empirical track record of the Balassa-Samuelson effect on real exchange rates. Recent efforts to confront these challenges have explored new approaches on both theoretical and empirical fronts, including incorporating non-linearity in modeling exchange rate dynamics.55 Alternatively, it has also been recognized that if one could find a source of real shocks that is sufficiently volatile, one could potentially go a long way towards resolving these major empirical exchange rate puzzles. In this respect, Chen and Rogoff (2002) found for four commodity-exporting developed countries that the dollar price of commodity exports exhibits a strong influence on real exchange rates. Similarly, Cashin, Cespedes, and Sahay (2002) show that in many commodity-dependent low-income countries, the real price of commodity exports and real exchange rates move together in the long run.
D. Determination of the Equilibrium Real Exchange Rate in Algeria
Purchasing power parity
19. PPP does not hold in Algeria, suggesting that the equilibrium real exchange rate may vary over time.Figure 1 shows that the REER did not converge towards its mean between January 1995 and June 2004. Furthermore the augmented Dickey-Fuller and Phillips-Perron test statistics show that the REER is non-stationary (Table 1).56 Finally, similarly to others’ findings, 50 percent of a unit impulse (half-life speed (HLS)) dissipates in about 42 months or three and a half years, thus rejecting the hypothesis that deviations from PPP are short-lived.57 This result suggests that the equilibrium real exchange rate of the Algerian dinar may depend on fundamental variables.
|LREER 1/||12||-1.60||12||-2.93 *|
|LREER 1/||6||-1.18||6||-9.01 **|
LREER is the real effective exchange rate expressed in log.
LREER is the real effective exchange rate expressed in log.
The Equilibrium Real Exchange Rate and Fundamentals
20. Given that Algeria is a commodity exporting country, the model used is that developed by Cashin et al. (2002) for commodity-dependent countries (see Appendix). It is a commodity-price- and relative productivity-augmented PPP model. The REER is defined as a function of relative productivities between tradables and nontradables sectors, as well as the terms of trade:
- EP/P* = the real exchange rate defined as the domestic price of the domestic basket of consumption goods relative to the price of the foreign basket of consumption goods expressed in foreign currency.
- ax/a*i = productivity differential between exports and import (foreign) sectors; or between domestic and foreign tradables sectors.
- a*n/an = productivity differential between the foreign and domestic nontradables sectors; and
- P*x/P*i = commodity terms of trade (or the price of the primary commodity with respect to the intermediate foreign good) measured in foreign prices.
21. The first two terms in equation (1) capture the Balassa-Samuelson effect _a productivity improvement in the commodity sector will tend to raise wages throughout the economy_ which translates into a price increase in the non-tradables sector, which, in turn, leads to an appreciation of the real exchange rate. The third term reflects the impact of the terms of trade. An increase in export prices leads to higher wages, and translates into an increase in non-tradable goods prices as well.
22. The variables used in Algeria’s model are the following:
- LREER = the real effective exchange rate using INS data (2001=100); in logarithmic terms.
- LRGDPC = Real GDP per capita relative to trading partners. Normalized for each country to 1 in 2001; in logarithmic terms. Given the absence of data on unit labor costs, and as often done in estimation of equilibrium exchange rates, this variable is used as a proxy for the productivity differentials (Balassa-Samuelson effect).
- LROIL= real price of oil calculated, as in Cashin et al. (2002), by deflating the UK Brent spot price index by the manufactured exports unit price index for developed countries (2001=100); in logarithmic terms. This is a proxy for the commodity terms of trade (P*x/P*i).
23. The visual observation of the movements in the three variables in Figure 2 suggests that movements in the REER largely reflect developments in Algeria’s productivity relative to its trading partners (a deterioration over almost the entire period), and, to a lesser extent, changes in real oil prices.
Figure 2.Determinants of the Real Effective Exchange Rate, 1970-2003
24. The dataset consists of annual data from 1970 to 2003. The ADF test indicates that the nonstationarity hypothesis cannot be rejected at the 5 percent confidence level in all three variables. However, for the first difference of the same variables, the hypothesis of nonstationarity is rejected at 5 and 1 percent confidence, suggesting that these variables are integrated of order one, I(1) (Table 2).
25. The econometric analysis confirms the existence of a cointegration relationship between REER, real oil prices, and Algeria’s productivity differential relative to its trading partners. Table 3 shows the estimation of the vector error-correction model (VECM) using four lags for the changes in each variable (the lag structure is supported by appropriate tests). The Engle-Granger (1987) and Johansen (1995) maximum likelihood procedures are used to determine the number of cointegrating vectors among the variables.58 Both procedures indicate that there is at most one co-integrating vector (at the 5 percent confidence level). The coefficients of the cointegration vector are plausible, significant, and of the correct sign. The cointegration analysis is appropriate (all variables are non stationary) and meaningful (not driven by the stationarity of one variable). Furthermore, the exclusion test suggests that none of the variables can be excluded from the long-run relationship (Table 4). The hypothesis that the residuals have a normal distribution is rejected due to excess kurtosis. The lag structure appears to be correct: if a fifth lag is introduced, the tests accept the hypothesis that the additional lag is jointly insignificant across equations.
|Number of cointegrating vectors|
|Trace statistic||Max Eigenvalue statistic|
|5% 1%||5% 1%|
|1 1||1 1|
|Estimates of the cointegrating relationship with the real exchange rate|
|Speed of adjustment of the real exchange rate|
|Half lifetime of the deviation from equilibrium exchange rate|
|in years||0.75||in months||9|
|Exclusion test 1/|
|VEC Lag Exclusion Wald Tests 2/|
|(Chi-squared test statistics)|
|DLag 1||DLag 2||DLag 3||DLag 4||df|
|[ 0.00]||[ 0.00]||[ 0.00]||[ 0.00]|
Significance level at 5%. Ho: Variable can be excluded.
Numbers in [ ] are probability values
Significance level at 5%. Ho: Variable can be excluded.
Numbers in [ ] are probability values
26. The estimated long-run real exchange rate equilibrium equation takes the following form:
|LREER = 4.64 + 1.88 LRGDPC + 0.24 LROIL|
- An increase in real GDP per capita relative to trading partner countries of 1 percent is associated with an appreciation of the REER of almost 2 percent.
- An increase in real oil prices of 1 percent is associated with an appreciation of the REER of about 0.2 percent.
27. Whenever the real exchange rate deviates from its equilibrium level due to a specific shock, it reverts to its equilibrium level fairly quickly in the absence of further shocks. Depending on the cause of the gap, the adjustment requires that the real exchange rate either moves progressively toward a new equilibrium level, or returns from its temporary deviation to the initial equilibrium value. The parameter of the cointegration vector of 0.6 implies that the half life speed (HLS) of dissipation of a unit impulse is 0.75 years.59 In other words, the model estimates that 50 percent of such a gap would be eliminated within 9 months. This adjustment speed is comparable to the 8 months found by Cashin et al. (2002), and much shorter than Rogoffs (1996) estimate of three to five years.
28. Figure 3 and 4 show that there are no current signs of misalignment of the Algerian dinar.60 The actual REER appears to have been close to its estimated equilibrium in 2002-03. Following the appreciation of the euro against the U dollar in 2002-03, the gap between th actual and the smoothed equilibrium REER declined from +9 percent in 2001 to +2 percent in 2002 and to -6 percent on average in 2003. This depreciation was a little more than what was required by the fundamentals. However, the correction made by the authorities in the second half of 2003 (by appreciating the nominal exchange rate) brought the REER back to close to its equilibrium level. By year-end, the REER was 3 percent higher than its annual average level. 61Figure 4 also shows the 1986-88 depreciation in response to the reverse oil shock, which brought the 1985 overvalued exchange rate back to its equilibrium. However, the 1994–95 perceived overvaluation is barely illustrated by the model.
Figure 3.Actual and Equilibrium REER Figure 4.Gap: Actual Minus Equilibrium REER
29. The behavior of other macroeconomic variables also supports the assessment that the REER was not misaligned in 2003. The high import growth in 2002–04 together with the decline in nonhydrocarbon exports in 2003 are not consistent with a real undervaluation. Furthermore, the low inflation in 2002–03 also does not fit well with the existence of a misalignment in the REER. If the exchange rate was significantly below its equilibrium value, inflationary pressures would have materialized.
E. Forward-Looking Perspective
30. The future path of the equilibrium real exchange rate beyond the short term is uncertain. The authorities’ prospective policies include two new aspects that will have an important impact on the equilibrium REER: further trade liberalization and fiscal consolidation. While the projected increase in real oil prices in 2005 will be associated with an appreciation of the equilibrium real exchange rate, the impact of these policies on the equilibrium real exchange rate is not straightforward.62 In addition, whereas the impact of trade liberalization on the long-run equilibrium would be captured by movements in Algeria’s real productivity relative to its trading partners, the relation between fiscal consolidation and fundamentals is ambiguous.
Further trade liberalization
31. External trade liberalization is associated with a tendency for the equilibrium real exchange rate to depreciate. Trade liberalization would have an impact on the equilibrium real exchange rate through both substitution and income effects: (i) a reduction in tariffs would increase demand for tradables relative to nontradables. This substitution effect would, in turn, tend to reduce the price of home goods, and hence favor a real depreciation; (ii) trade liberalization would also raise real income in the economy, which in turn would affect aggregate demand for all goods, including nontradables and hence the response of the equilibrium real exchange rate. However, the income effect is expected to be smaller than the substitution effect. Therefore, if trade liberalization is not accompanied by structural reforms, the equilibrium real exchange rate would tend to depreciate.
32. However, if trade liberalization is accompanied by reform-driven productivity gains, this would limit the depreciation of the equilibrium REER. Structural reforms would tend to increase productivity, leading to an appreciation of the equilibrium real exchange rate, thus offsetting the initial tendency for depreciation. Close monitoring of Algeria’s real productivity relative to its trading partners would help to determine the likely path of the equilibrium real exchange rate.
33. Fiscal policy is the main transmission channel of oil price fluctuations into the Algerian economy. This occurs because the majority of hydrocarbon receipts go to the government, and, thus far, there has been a strong correlation between government spending and hydrocarbon revenue. Therefore, the real oil price has been an important factor in determining the equilibrium real exchange rate. However, if the authorities delink government spending from hydrocarbon revenue, it is not clear if real oil prices alone would provide enough information on the equilibrium real exchange rate path. Thus, even in an environment of increasing oil prices, if government spending declines in oil price equivalent terms, it will be important to closely monitor the impact of future fiscal policy on the economy together with the already identified fundamentals.
34. The authorities’ planned fiscal consolidation for 2005 and beyond would have an ambiguous effect on the real exchange rate. An improvement in the fiscal balance induced by a control of spending will tend to increase total savings and reduce aggregate demand.63 As part of the decline in spending falls on nontradables, this would bring about a depreciation of the real exchange rate. However, the improvement in the external position generated by fiscal consolidation would be associated with a real appreciation.
35. Drawing on the existing literature, this study estimates the long-run equilibrium real exchange rate path for Algeria. The main conclusions are:
- REER movements in Algeria can be explained by fundamental variables. The long-run real exchange rate of Algeria is time-varying, and dependent on movements in relative productivity and real oil prices. Deviations of the real exchange rate from its equilibrium value are adjusted fairly rapidly (HLS=9 months), confirming that Balassa-Samuelson- and commodity-price-augmented PPP determines the real exchange rate in Algeria.
- The REER was not misaligned in 2002-03. Model-derived estimates of the long-run equilibrium real exchange rate replicate most recognized periods of currency overvaluation in Algeria. The estimates support the conclusion that the 2002-03 depreciation of the REER followed by an appreciation in the second half of 2003 were consistent with developments in its fundamental determinants.
36. The results of this study have important implications for Algeria’s exchange rate policy. Although Algeria should continue with a managed float, targeting a constant REER is not warranted as such a policy does not accommodate real shocks by allowing the nominal exchange rate and/or relative prices to move. Exchange rate policy should be directed to align the real exchange rate with its fundamental determinants, namely relative productivity and real oil prices. However, since the impact of the planned fiscal consolidation is not captured by current fundamentals, exchange rate management in the period ahead faces the challenge of taking into account the impact of such consolidation on aggregate demand.
The model is based on a small open economy that produces two different types of goods: a nontradable good and an exportable good. The production of this exportable good is associated with the production of a primary commodity. Factors are mobile and both goods are produced domestically.
A. Domestic production
There are two different sectors in the domestic economy: one sector produces an exportable called “primary commodity”; the other sector consists of a continuum of firms producing a nontradable good. For simplicity, it is assumed that the production of these two different types of goods requires labor as the only factor. The production functions are:
Where x represents the primary commodity sector, n the nontradable good sector, L the amount of the labor input demanded by each sector, and a, the productivity of labor in each sector. The model assumes that labor can move freely across sectors in such a way that the labor wage w must be the same across sectors. The price equations are as follows:
In equilibrium, the marginal productivity of labor must equal the real wage in each sector. It is assumed that the price of the primary commodity is exogenous, and that there is perfect competition in the nontradables sector. These assumptions yield:
Thus, the relative price of the nontradable good Pn with respect to the primary commodity Px is completely determined by technological factors and is independent of demand conditions.
B. Domestic Consumers
The economy is inhabited by a continuum of identical individuals that supply labor inelastically (with L = Lx+ Ln) and consume a nontradable good and a tradable good. This tradable good is imported from the rest of the world and is not produced domestically. The assumptions on preferences imply that the primary commodity is also not consumed domestically. Each individual chooses the consumption of the nontradable and tradable good to maximize utility, which is assumed to be increasing in the level of aggregate consumption given by:
where Cn represents purchases of the nontradable good, Ct purchases of the imported good and k= 1/[γγ(1-γ)(1-γ)] is a constant. The minimum cost of one unit of consumption C 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. Now, the law of one price is assumed to hold for the imported good:
Where E is the nominal exchange rate, defined as the amount of foreign currency per local currency, and P*t is the price of the tradable (imported) good in terms of foreign currency.
C. Foreign Production and Consumption
So far it was 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.65 The foreign region consists of three different sectors: a nontradable sector; an intermediate sector; and a final goods sector. The nontradable 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:
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:
Labor mobility across (foreign) sectors ensures that the foreign wage is equated across sectors.66 The price of the foreign nontradable good as a function of relative productivities and the price of the foreign intermediate good is:
The production of the final good involves two intermediate inputs. The first is the primary commodity (produced by several countries, among them the domestic economy). The second is an intermediate good produced in the rest of the world. Producers of this final good, also called the tradable good, produce it by assembling the foreign intermediate input Yt* and the foreign primary commodity Yx* through the following technology:
Now, it is straightforward to show that the cost of one unit of the tradable good in terms of the foreign currency is given by:
Foreign consumers are assumed to consume the foreign nontradable good and this final good in the same fashion as the domestic consumers. They also supply labor inelastically to the different sectors. Therefore, the consumer price index for the foreign economy can be represented by:
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