## 1. Tests of Order of Integration, January 1995–June 2004

## Source details

**Canonical URL:** [1. Tests of Order of Integration, January 1995–June 2004](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05135.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05135.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05135.pdf.json)

---

### Background and motivation
- The simple purchasing power parity (PPP) hypothesis is a weak model of the long-run real exchange rate.
- Time-varying models relating fundamentals to real exchange rate behavior have produced mixed results.
- Prior findings informing this study:
  - Cashin, Céspedes, and Sahay (2002): for commodity-exporting countries, real commodity export prices and real exchange rates move together in the long run.
  - Choudhri and Khan (2004): Balassa-Samuelson effects and terms of trade influence the real exchange rate in developing countries.

### Context for Algeria
- This paper applies the Cashin et al. (2002) framework to Algeria.
- Since 1995 authorities aimed to maintain a stable real effective exchange rate (REER) against a basket weighted by trade shares.
- Despite that objective, the REER varied continuously over the last decade; in 2002–03 the REER of the Algerian dinar depreciated by 17½ percent.
- Research questions:
  - Was the 2002–03 evolution of the dinar consistent with the equilibrium REER?
  - Can fundamentals explain the exchange rate path over the last decade?

### Main empirical findings
- Existence of a time-varying equilibrium REER in Algeria is supported.
- Long-run drivers:
  - Balassa-Samuelson effect (relative productivity, proxied by LRGDPC) and real oil prices (LROIL) explain the long-run equilibrium REER.
- Estimated long-run REER equation (annual VECM, 1970–2003):
  - LREER = 4.64 + 1.88 LRGDPC + 0.24 LROIL
    - Standard errors (as reported): (0.11) for the constant; (0.08) for coefficients (as reported).
    - t-statistics (as reported): [16.42] for LRGDPC; [2.66] for LROIL.
  - Interpretations:
    - A 1 percent increase in real GDP per capita relative to trading partners is associated with an appreciation of the REER of almost 2 percent.
    - A 1 percent increase in real oil prices is associated with an appreciation of the REER of about 0.2 percent.
- Cointegration:
  - At most one cointegrating vector among LREER, LRGDPC, and LROIL at the 5 percent level (Engle-Granger and Johansen).
  - Cointegration coefficients are plausible, significant, and of the correct sign.
- Adjustment and half-life estimates:
  - AR(1) OLS regression coefficient α = 0.984; HLS = abs(log(1/2)/log(α)) = 42 months (about 42 months or three and a half years).
  - From the VECM cointegration parameter of 0.6, the half-life speed (HLS) of dissipation of a unit impulse is 0.75 years (nine months): 50 percent of such a gap would be eliminated within nine months.
  - The model’s VECM adjustment speed (nine months) is comparable to Cashin et al. (2002) finding of eight months and much shorter than Rogoff’s (1996) estimate of three to five years.
- Misalignment assessment:
  - No signs of notable misalignment in 2002–03; actual REER was close to estimated equilibrium.
  - The gap between actual and smoothed equilibrium REER declined from +9 percent in 2001 to +2 percent in 2002 and to -6 percent on average in the period described.

### Developments in the Algerian exchange rate regime and institutional features
- Historical regime and major adjustments:
  - From January 1974 the dinar was pegged to a basket with a large U.S. dollar weight.
  - U.S. dollar appreciation during 1980–85 raised the real value of the dinar by about 50 percent in 1980–85.
  - 1986–1988: dinar depreciated against the basket by 31 percent.
  - Late 1980s: parallel market premium reached about 400 percent under restrictions.
  - 1989–1991: dinar depreciated by more than 200 percent nominally.
  - 1991: dinar depreciated by more than 100 percent to DA 22 per U.S. dollar.
  - 1991–94: nominal depreciation averaged 4 percent annually, to about DA 24 per U.S. dollar on the official market.
  - 1994: two-step devaluation totaling 70 percent between April and September 1994.
  - Since 1995: policy aimed at a stable real exchange rate against a basket; managed float implemented in 1995; interbank market established in 1996.
  - 1995–1998: REER appreciated by more than 20 percent; 1998–2001: REER depreciated by 13 percent.
  - June–December 2003: dinar appreciated against the U.S. dollar by 11½ percent and the REER appreciated by 7½ percent.
- Institutional features:
  - Hydrocarbon exports account for more than 95 percent of total exports.
  - By law, foreign exchange receipts from hydrocarbon exports must be converted into dinars directly at the central bank.
  - Capital account transactions are subject to strict controls.
  - Bank of Algeria strongly influences the official nominal exchange rate and periodically adjusts it to achieve its REER target.
  - With external convertibility for current transactions in 1997 the parallel market reportedly shrank; spread between interbank and parallel market rates was about 25 percent at end-2003.

### PPP testing and stationarity results
- Monthly REER stationarity tests (1995:01–2004:06, INS monthly REER, log):
  - ADF and Phillips-Perron statistics indicate the REER is non-stationary.
  - Conclusion: PPP does not hold in Algeria; equilibrium REER may vary over time.
  - Half-life from AR(1) indicates 50 percent of a unit impulse dissipates in about 42 months (three and a half years), rejecting short-lived deviations from PPP.
- Annual dataset tests (1970–2003):
  - ADF tests indicate LREER, LRGDPC, and LROIL are I(1) (nonstationary in levels, stationary in first differences).
  - Reported ADF(2) statistics:
    - LREER: Level t-ADF = -0.089; First difference t-ADF = -4.03 **
    - LRGDPC: Level t-ADF = -0.849; First difference t-ADF = -4.36 **
    - LROIL: Level t-ADF = -2.679; First difference t-ADF = -6.52 **
  - * and ** denote rejection at 5 percent and 1 percent critical values.

### Equilibrium REER model, VECM specification, and diagnostics
- Model framework:
  - Cashin et al. (2002) commodity-price- and relative-productivity-augmented PPP model employed.
  - Definitions:
    - LREER = real effective exchange rate (INS data, 2001=100), log.
    - LRGDPC = Real GDP per capita relative to trading partners, normalized to 1 in 2001, log.
    - LROIL = real price of oil (U.K. Brent spot price deflated by manufactured exports unit price index for developed countries, 2001=100), log.
- VECM details:
  - Annual data 1970–2003; variables I(1).
  - Engle-Granger and Johansen indicate at most one cointegrating vector at the 5 percent level.
  - VECM with four lags for changes in each variable (lag structure supported by tests); addition of a fifth lag yields joint insignificance.
  - Exclusion tests: none of the variables can be excluded from the long-run relationship.
  - Normality test for residuals rejected due to excess kurtosis.
- Selected numeric outputs used in interpretation:
  - Cointegration relation coefficients:
    - Constant: 4.64 (standard error reported as (0.11) in text)
    - LRGDPC coefficient: 1.88, t-statistic [16.42]
    - LROIL coefficient: 0.24, t-statistic [2.66]
  - Cointegration vector parameter: 0.6.
  - VECM-derived half-life HLS = 0.75 years (nine months).

### Model structure, theoretical implications, and technical notes
- Theoretical setup:
  - Small open economy with a nontradable good and an exportable primary commodity; labor is the only factor and mobile across domestic sectors.
  - Primary commodity production: Y_x = a_x . L_x
  - Nontradable production: Y_n = a_n . L_n
  - Domestic prices: P_x = w/a_x  and  P_n = w/a_n
  - Relative price: P_n = a_x / a_n . P_x
  - Preferences and consumer price: C = κ . C_n^γ . C_t^(1-γ) with κ = 1/[γ^γ (1-γ)^(1-γ)] and P = (P_n)^γ . (P_t)^(1-γ)
  - Law of one price for imports: P_t = P*_t / E
  - Foreign sector structure and price aggregators specified in the model.
  - Derived real exchange rate relation: E P / P* = (a_x / a*_i . a*_n / a_n . P*_x / P*_i)^γ
- Modeling assumptions and notes:
  - Primary commodity price assumed exogenous and completely exported (not consumed domestically).
  - Nontradable relative price determined by technological factors, independent of demand.
  - Labor mobility within domestic and foreign regions, not across regions.
  - Hodrick-Prescott filter (smoothing factor 100) used to derive a smoothed equilibrium REER to neutralize temporary fluctuations; end-point HP assessments can be inaccurate.

### Interpretation, recent assessment, and policy implications
- Drivers of REER movements:
  - Low productivity growth in the nonhydrocarbon sector is the main factor behind depreciation of the equilibrium REER over the last twenty years.
  - Movements in the REER largely reflect developments in relative productivity and, to a lesser extent, real oil prices.
- Recent history and alignment:
  - The 2003 depreciation "was a little more than what was required by the fundamentals."
  - Authorities' correction in the second half of 2003 (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."
  - The smoothed equilibrium REER in Figure 3 is derived with a Hodrick-Prescott filter with smoothing factor 100.
  - Small end-2003 gap between equilibrium and actual REER could reflect temporary shocks not captured by the long-run model and HP end-point inaccuracy.
- Policy recommendations:
  - Continue with a managed float.
  - Do not target a constant REER over a prolonged period because such 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.
- Adjustment dynamics implication:
  - Given the VECM half-life of nine months, temporary shocks to the REER are expected to dissipate fairly quickly absent further shocks.
  - Model-derived estimates replicate recognized historical periods of overvaluation; the 2002–03 depreciation and subsequent 2003 appreciation were consistent with fundamentals.

*Source: _wp05135 (PDF chapter/section).*

### 1. Tests of Order of Integration, January 1995–June 2004.............................................7

### 1. Tests of Order of Integration, January 1995–June 2004

### Background and motivation
- The simple purchasing power parity (PPP) hypothesis has proven to be a weak model of the long-run real exchange rate.
- Time-varying models relating economic fundamentals to real exchange rate behavior have produced mixed and often controversial results.
- Cashin, Céspedes, and Sahay (2002) developed a long-run equilibrium exchange rate model for commodity-exporting countries; they found that in many commodity-dependent low-income countries real commodity export prices and real exchange rates move together in the long run.
- Choudhri and Khan (2004) found that Balassa-Samuelson effects are relevant for developing countries and that the terms of trade also influence the real exchange rate.

### Context for Algeria
- The paper applies the Cashin et al. (2002) model to Algeria.
- Since 1995, the authorities have aimed at maintaining a stable real effective exchange rate (REER) against a basket of currencies weighted on the basis of the trade shares of Algeria’s main trading partners.
- Despite this policy objective, the REER has varied continuously over the last decade (Figure 1).
- In 2002–03, the REER of the Algerian dinar depreciated by 17½ percent.

### Research questions posed
- To what extent was the evolution of the Algerian dinar in 2002–03 consistent with the equilibrium real exchange rate?
- Can economic fundamentals explain the exchange rate path in Algeria over the last decade?

### Key findings
- The study finds evidence for the existence of a time-varying equilibrium real exchange rate in Algeria.
- The Balassa-Samuelson effect together with real oil prices (i.e., the terms of trade) explain the long-run equilibrium REER.
- These results indicate that Choudhri and Khan’s (2004) conclusions about the relevance of Balassa-Samuelson effects and terms of trade extend to the Algerian case when analyzed with the Cashin et al. (2002) framework.

*Source: 1. Tests of Order of Integration, January 1995–June 2004 (IMF working paper section).*

### conclusions are also applicable for the case of Algeria. The convergence speed towards

### _wp05135 - conclusions are also applicable for the case of Algeria. The convergence speed towards

### Key findings
- Equilibrium REER convergence:
  - The estimated coefficient α of the AR(1) OLS regression is equal to 0.984, thus the HLS=abs(log(1/2)/log(α))=42 months (about 42 months or three and a half years).
  - From the VECM cointegration parameter of 0.6, the half-life speed (HLS) of dissipation of a unit impulse is 0.75 years. In other words, 50 percent of such a gap would be eliminated within nine months.
  - The model’s adjustment speed (nine months) is comparable to Cashin et al. (2002) finding of eight months and is much shorter than Rogoff’s (1996) estimate of three to five years.
- Long-run cointegration:
  - There is at most one cointegrating vector among LREER, LRGDPC, and LROIL at the 5 percent confidence level (Engle-Granger and Johansen procedures).
  - The coefficients of the cointegration vector are plausible, significant, and of the correct sign.
- Estimated long-run REER equation:
  - LREER = 4.64 + 1.88 LRGDPC + 0.24 LROIL
    - Standard errors: (0.11) for the constant; (0.08) for coefficients (as reported).
    - t-statistics reported: [16.42] for LRGDPC; [2.66] for LROIL.
  - Interpretations:
    - 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.
- Misalignment assessment:
  - Figures 3 and 4 (as described) show no current signs of misalignment of the Algerian dinar; the actual REER was close to its estimated equilibrium in 2002–03.
  - The gap between actual and smoothed equilibrium REER declined from +9 percent in 2001 to +2 percent in 2002 and to -6 percent on average in the period described.

### Developments in the Algerian exchange rate regime
- Historical regime and major adjustments:
  - From January 1974, the Algerian dinar was pegged to a basket of currencies with a relatively large U.S. dollar weight.
  - The U.S. dollar appreciation during 1980–85 led to a rise in the real value of the dinar of about 50 percent during 1980–85.
  - Between 1986 and 1988, the dinar depreciated against the basket by 31 percent.
  - Parallel market premium reached about 400 percent in the late 1980s under restrictions.
  - Between 1989 and 1991 the dinar depreciated by more than 200 percent in nominal terms.
  - In 1991 the dinar depreciated by more than 100 percent to DA 22 per U.S. dollar.
  - During 1991–94 the rate of nominal depreciation averaged 4 percent annually, bringing the value to about DA 24 per U.S. dollar on the official market.
  - In 1994 a two-step devaluation of the dinar totaling 70 percent took place between April and September 1994.
  - Since 1995 the policy aimed at maintaining a stable real exchange rate against a basket weighted by trading partners and competitors; a managed float regime was implemented in 1995, interbank market established in 1996.
  - Between 1995 and 1998 the REER appreciated by more than 20 percent; between 1998 and 2001 it depreciated by 13 percent.
  - Between June and December 2003 the Algerian dinar appreciated against the U.S. dollar by 11½ percent and the REER appreciated by 7½ percent.
- Institutional features:
  - Hydrocarbon exports account for more than 95 percent of total exports.
  - By law, foreign exchange receipts from hydrocarbon exports must be converted into dinars directly at the central bank.
  - Capital account transactions are subject to strict controls.
  - The Bank of Algeria strongly influences the nominal exchange rate on the official market and periodically adjusts it to achieve its real exchange rate target.
  - With external convertibility for current transactions in 1997, the parallel market reportedly shrank; the spread between interbank and parallel market rates was about 25 percent at end-2003.

### Literature review and methodological context
- PPP and stationarity:
  - PPP implies the real exchange rate will revert to its mean; if REER is stationary and convergence is fast, PPP can be considered to hold.
  - PPP has proven a weak model for long-run REER; many studies fail to find cointegrating relationships consistent with PPP.
  - The equilibrium real exchange rate is time-varying and influenced by fundamentals (Balassa-Samuelson effect, government spending, cumulated current account imbalances, real interest rate differentials, etc.).
- Commodity exports and REER:
  - Chen and Rogoff (2002) and Cashin et al. (2002) found strong influence of commodity export prices on real exchange rates for commodity-dependent countries.
  - Choudhri and Khan (2004) found evidence of Balassa-Samuelson effects in developing countries.
- Prior empirical challenges:
  - Meese and Rogoff (1983) showed many linear structural exchange rate models did not outperform a random walk.
  - Edison and Melick (1999) did not find cointegration between real exchange rates and real interest rate differentials; Rogoff (1996) found mixed evidence on Balassa-Samuelson.

### PPP testing for Algeria (empirical results)
- REER stationarity tests (1995:01–2004:06, INS monthly REER, log):
  - ADF and Phillips-Perron statistics indicate the REER is non-stationary (Table 1).
  - Result: PPP does not hold in Algeria; equilibrium REER may vary over time.
  - Half-life from AR(1) indicates 50 percent of a unit impulse dissipates in about 42 months or three and a half years (rejecting short-lived deviations from PPP).
- Annual dataset tests (1970–2003):
  - ADF tests indicate LREER, LRGDPC, and LROIL are nonstationary in levels but stationary in first differences (integrated of order one, I(1)).
  - Reported ADF(2) statistics:
    - LREER: Level t-ADF = -0.089; First difference t-ADF = -4.03 **
    - LRGDPC: Level t-ADF = -0.849; First difference t-ADF = -4.36 **
    - LROIL: Level t-ADF = -2.679; First difference t-ADF = -6.52 **
  - * and ** denote rejection at 5 percent and 1 percent critical values.

### Equilibrium REER model and cointegration results
- Model framework:
  - Cashin et al. (2002) commodity price- and relative productivity-augmented PPP model employed:
    - EP/P* = f(ax/a*i, a*n*/an, P*x/P*i)
    - Definitions used:
      - LREER = real effective exchange rate (INS data, 2001=100), log.
      - LRGDPC = Real GDP per capita relative to trading partners, normalized to 1 in 2001, log (proxy for productivity differentials/Balassa-Samuelson).
      - LROIL = real price of oil (U.K. Brent spot price deflated by manufactured exports unit price index for developed countries, 2001=100), log (proxy for commodity terms of trade).
- Cointegration and VECM:
  - Annual data from 1970 to 2003 used; ADF indicates variables are I(1).
  - Engle-Granger and Johansen procedures indicate at most one cointegrating vector at the 5 percent level.
  - VECM used with four lags for changes in each variable (lag structure supported by tests).
  - Exclusion tests suggest none of the variables can be excluded from the long-run relationship.
  - Normality test for residuals rejected due to excess kurtosis.
  - Lag structure appears correct; adding a fifth lag yields joint insignificance for that lag.
- Selected VECM numeric outputs:
  - Cointegration relation coefficients and t-statistics (as reported):
    - Constant: 4.64 (standard error reported as (0.11) in text)
    - LRGDPC coefficient: 1.88, t-statistic [16.42]
    - LROIL coefficient: 0.24, t-statistic [2.66]
  - Cointegration vector parameter: 0.6 (used to compute adjustment speed).
  - Speed of adjustment of the real exchange rate: half lifetime HLS = 0.75 years (nine months).

### Implications and interpretation
- Main drivers:
  - Low productivity growth in the nonhydrocarbon sector has been the main factor behind the depreciation of the equilibrium real exchange rate over the last twenty years.
  - Movements in the REER largely reflect developments in Algeria’s productivity relative to trading partners and, to a lesser extent, changes in real oil prices.
- Policy-relevant observations:
  - The central bank’s active management of the nominal exchange rate, combined with hydrocarbon export concentration (more than 95 percent of exports) and legal conversion requirements, results in the central bank holding the counterpart of most foreign exchange market transactions.
  - Given the estimated relatively rapid adjustment of the REER toward equilibrium (half-life of nine months in the VECM), temporary shocks to the REER are expected to dissipate fairly quickly in the absence of further shocks.
- Current alignment:
  - The analysis shows the REER was close to its equilibrium level in 2002–03.

*Source: _wp05135 (PDF chapter/section) — content provided in the supplied excerpt.*

### 2003. This depreciation was a little

### _wp05135 - 2003. This depreciation was a little

### Main findings on REER dynamics and recent history
- The 2003 depreciation "was a little more than what was required by the fundamentals."
- The authorities' correction 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."
- The 1986–88 depreciation responded to the reverse oil shock and "brought the 1985 overvalued exchange rate back to its equilibrium."
- Deviations of the real exchange rate from its equilibrium level are adjusted fairly rapidly: HLS = 9 months.
- The smoothed equilibrium REER in Figure 3 is derived with a Hodrick-Prescott filter with a smoothing factor of 100.
- The small gap between equilibrium and actual REER at end-2003 "could be due to temporary shocks not captured by the long-run equilibrium model" and "the assessment of the equilibrium level using the Hodrick-Prescott filter is not very accurate for end-point data."
- The implied half-life computation described: the time (T) required to dissipate x percent (in this case, 50 percent) of a shock is determined according to (1-Θ)^T = (1-x), where Θ is the coefficient of the error-correction term and T is the required number of periods (years).

### Conclusions and policy implications
- "The main conclusion is that 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 in line with Cashin et al. (2002).
- "Balassa-Samuelson- and commodity-price-augmented PPP determines the real exchange rate in Algeria."
- "Furthermore, the analysis shows that the REER was not misaligned in 2002–03."
- Model-derived estimates replicate recognized periods of currency overvaluation in Algeria; the 2002-03 depreciation and subsequent 2003 appreciation "were consistent with developments in its fundamental determinants."
- Policy recommendation: continue with a managed float, but do not target a constant REER over a prolonged period because 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."

### Theoretical framework: model structure and key equations
- Economy: small open economy producing a nontradable good and an exportable primary commodity; labor is the only factor and is mobile across domestic sectors.
- Primary commodity sector production function: Y_x = a_x . L_x
- Nontradable sector production function: Y_n = a_n . L_n
- Price equations (domestic): P_x = w/a_x  and  P_n = w/a_n
- Relative price result: P_n = a_x / a_n . P_x
- Preferences and aggregate consumption: C = κ . C_n^γ . C_t^(1-γ)  where κ = 1/[γ^γ (1-γ)^(1-γ)]
- Minimum cost (consumer price): P = (P_n)^γ . (P_t)^(1-γ)
- Law of one price for imports: P_t = P*_t / E  (E = nominal exchange rate, foreign currency per local currency)
- Foreign sector: three sectors (nontradable, intermediate, final); foreign nontradable production: Y*_n = a*_n . L*_n; foreign intermediate production: Y*_i = a*_i . L*_i
- Foreign nontradable price: P*_n = a*_i / a*_n . P*_i
- Final (tradable) good production technology in foreign economy: Y*_t = v . (Y*_i)^β . (Y*_x)^(1-β)
- Cost of tradable in foreign currency: P*_t = (P*_i)^β . (P*_x)^(1-β)
- Foreign consumer price index: P* = (P*_n)^γ . (P*_t)^(1-γ)
- Real exchange rate relation derived: E P / P* = (a_x / a*_i . a*_n / a_n . P*_x / P*_i)^γ

### Model implications and technical notes
- Primary commodity price assumed exogenous.
- Nontradable relative price is "completely determined by technological factors and is independent of demand conditions."
- Primary commodity is assumed not consumed domestically and is completely exported.
- Labor mobility is assumed within domestic and within foreign regions but not across regions.
- Hodrick-Prescott filtering used to derive smoothed equilibrium REER to neutralize temporary fluctuations in explanatory variables and provide a proxy for long-run equilibrium values.

*Source: _wp05135 - 2003. This depreciation was a little*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp05135.pdf_