## _wp0949 - 9. Estimated Real Exchange Rate Misalignment

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---

### I. Introduction
- Armenia’s real effective exchange rate (REER) appreciated rapidly in recent years due to large foreign exchange inflows (notably remittances and FDI) and high export prices (notably copper and molybdenum).
- During 2005–2007, real appreciation was accompanied by nominal appreciation. In 2008 the Central Bank of Armenia (CBA) changed from a managed float without a predetermined path to a soft peg and kept the nominal rate vis-à-vis the U.S. dollar within a very tight band until the dram devaluation in early March 2009.
- Main cross-method finding:
  - All three approaches used—PPP, BEER, and ES—suggest the dram was overvalued by about 20–30 percent as of end-2008.
  - While most approaches suggest the dram was close to equilibrium (i.e., within a 10-percent band) most of the time during the 2000–07 period, 2008 is the only year for which all approaches suggest a significant deviation from equilibrium.

### II. Purchasing Power Parity (PPP) Approach
- Methodology:
  - Define PPP exchange rate as the nominal exchange rate E at which Armenian price level P equals foreign price level P* (PE = P*). Under PPP the real exchange rate equals one.
  - Use Balassa-Samuelson hypothesis to estimate an “equilibrium distance to PPP” by regressing relative price levels on relative GDP per capita (PPP GDP per capita) as a proxy for relative productivity.
- Key empirical relationship:
  - Estimated log-linear relationship from sample of 180 countries:
    - Log (real exchange rate) = -1.83 + 0.39*Log (PPP GDP per capita).
  - Interpretation: every 1 percent increase in PPP GDP per capita is associated with a real appreciation of 0.39 percent.
  - Historical comparisons: slope 0.39 is close to Rogoff (1996) 0.37, De Broeck and Slok (2001) 0.41, and Frankel (2005) 0.38.
- Armenian price level indicators:
  - Armenian prices in U.S. dollar terms increased from about one third to almost two thirds of U.S. prices; specifically, the Armenian price level was 63 percent in 2008.
  - In 1993 the Armenian price level was about 10 percent of the U.S. price level.
- PPP-based misalignment estimate:
  - The PPP approach suggests the dram was overvalued by as much as 30 percent in 2008.
  - Evolution described: highly undervalued in early 1990s, slightly overvalued during 1995–2000, back to equilibrium by 2001, slightly undervalued post-2001, then appreciation of actual REER relative to equilibrium since 2003 leading to ~30 percent overvaluation in 2008.
- Caveats:
  - PPP approach only examines the relationship between real exchange rate and productivity and omits other determinants.
  - Estimated equilibrium relationship is based on a large cross-section that may not be representative of Armenia.
  - The estimated relationship is a historical average assuming exchange rates are on average in equilibrium.
  - GDP per capita is a rough proxy for the relative productivity differential.

### III. Behavioral Equilibrium Exchange Rate (BEER) Approach
- Methodology:
  - Estimate the long-run statistical relationship (cointegrating relationship) between REER and fundamentals using time-series data for Armenia.
  - Fundamentals included: relative productivity differential, terms of trade, net international reserves (NIR), and remittances.
  - Productivity measures: use both “relative productivity” and the “relative productivity differential” (difference between Armenia’s relative productivity and that of trade partners). EU used as comparator for trade-partner productivity (EU accounts for 34 percent of Armenia’s external trade).
  - Sectoral choices: agriculture excluded; construction treated as tradable for Armenia based on external demand, labor mobility, and observed productivity growth.
- Expected signs and economic intuition:
  - Terms of trade: improvement expected to cause real appreciation.
  - NIR: theoretically ambiguous; empirically generally positive relationship with REER (positive sign interpreted as reflecting net BOP inflows and REER).
  - Remittances: expected to cause real appreciation; Atoyan and Oomes (2006) find a one percentage point of GDP increase in total remittance leads to a one percentage point increase in dram appreciation.
- Empirical evidence and tests:
  - A co-integrating vector exists between REER, terms of trade, remittances, NIR, and the relative productivity differential (cointegrating vector estimated for data up to end-2007; 2008 used for projection).
  - Augmented Dickey-Fuller (ADF) unit root test results (Sample: 1998Q1:2007Q4; all variables in logs):
    - Real effective exchange rate: Level t-Statistic 0.28 Prob. 0.97; First Difference t-Statistic -5.16 Prob. 0.00
    - Terms of Trade (Exports deflator divided by imports deflator): Level t-Statistic -2.34 Prob. 0.40; First Difference t-Statistic -3.57 Prob. 0.05
    - Net International Reserves (in US dollars): Level t-Statistic -2.71 Prob. 0.24; First Difference t-Statistic -4.35 Prob. 0.01
    - Remittances including other transfers: Level t-Statistic -3.09 Prob. 0.12; First Difference t-Statistic -7.14 Prob. 0.00
    - Relative productivity differential: Level t-Statistic -1.17 Prob. 0.68; First Difference t-Statistic -2.99 Prob. 0.05
  - Estimated cointegrating vector (dependent variable: real effective exchange rate; sample 1998Q1:2007Q4; number of lags 4; Log likelihood 447.6; Akaike information criterion -20.1; Schwarz criterion -14.8; Serial correlation LM (prob.) 0.71):
    - Terms of Trade coefficient: 0.09 (t-statistics 9.17)
    - Remittances coefficient: 0.20 (t-statistics 20.25)
    - Net International Reserves coefficient: 0.42 (t-statistics 49.82)
    - Relative Productivity Differential coefficient: 0.07 (t-statistics 3.44)
    - Trend: -0.05 (t-statistics -78.30)
    - Constant: 1.86
- BEER misalignment estimate:
  - The BEER approach suggests the dram was overvalued by about 20 percent at end-2008 (the error correction term was 21 percent at end-2008).
- Additional findings and caveats:
  - Evidence of Balassa-Samuelson effect in Armenia appears conditional on developments in the construction sector; excluding construction or treating it as nontradable removes long-term relationship evidence.
  - Short sample length limits robustness checks; no unique cointegrating vector found; cointegration techniques assume misalignment is zero on average (residual zero by construction), which is problematic in short samples.

### IV. External Sustainability (ES) Approach
- Purpose and method:
  - Focuses on the relation between sustainability of foreign asset position, the current account, and the real exchange rate.
  - Consists of a calibration exercise requiring assumptions about potential growth rate, inflation rate, and rates of return on external assets and liabilities.
- External sustainability framework and NFA stabilization:
  - Objective: determine the trade or current account balance (as ratios to GDP) that stabilize the net foreign asset (NFA) position at a given benchmark level.
  - Intertemporal budget constraint requirement: the present value of future trade surpluses must be sufficient to pay back outstanding external liabilities.
  - Stabilization target: a stable ratio between NFA and GDP is analogous to stabilizing public debt-to-GDP at a benchmark level.
- Key equations and definitions:
  - NFA accumulation equation (levels): NFAt = NFAt-1 + CAt + KGt + KTt + Et
    - where CA is the current account balance, KG are capital gains from valuation changes, KT are capital transfers, and E are errors and omissions.
  - Ratios to GDP (lower-case letters) and transformed accumulation equation:
    - (1) nt = (1/(1+gt+πt)) [ nt-1 + cat + kgt + ktt + et ]  (ratio-form accumulation)
    - Stabilization condition for NFA-to-GDP at benchmark s_nfa implies:
      - (2) s_ca = (1+gs+π_s) s_nfa − (s_kg + s_kt + s_e)  (equation (2) determines CA ratio that stabilizes NFA)
  - Notation highlights:
    - gt = growth rate of real GDP
    - πt = inflation rate of net foreign assets
    - s_nfa = benchmark NFA-to-GDP ratio
    - s_ca = current account balance as ratio to GDP that stabilizes NFA
- Calibration choices and scenarios:
  - Benchmark NFA-to-GDP ratio used: end-2006 position of -24.2 percent.
  - Assumed inflation rate of NFA: 2.5 percent.
  - Armenia long-term GDP growth central calibration: 3 percent.
  - Alternative growth scenarios:
    - low growth: 2 percent
    - high growth: 4 percent
  - Treatment of capital transfers:
    - Typical literature assumption: s_kt = 0
    - This paper calibrates equation (2) first assuming s_kt = 0, and then assumes a value for s_kt consistent with medium-term forecasts for capital transfers.
- Real effective exchange rate (RER) adjustment methodology:
  - Compute elasticity of current account (CA) to real exchange rate (RER):
    - CAε = Xε + (X/GDP)ε − (M/GDP)ε  (source expresses CAε in terms of export and import elasticities and export/import ratios to GDP)
    - More explicitly preserved from source: CAε = Xε * (X/GDP) - Mε * (M/GDP)
    - Xε = elasticity of exports to the real exchange rate
    - Mε = elasticity of imports to the real exchange rate
    - X/GDP and M/GDP = ratios of exports and imports to GDP, respectively
  - Required RER adjustment derived from CA elasticity:
    - ΔRER = ΔCA / CAε  (source formula: 1/CAε * ΔCA ⇒ ΔRER)
- Elasticity calibration and data used:
  - Trade elasticities used:
    - Xε = -0.71
    - Mε = 0.92
  - Export and import ratios to GDP calibrated with both end-2006 and end-2007 figures (figures referenced in source).
- Quantitative ES findings on RER misalignment (as of end-2008, relative to NFA-stabilizing CA):
  - Assuming g = 3 percent (central): overvalued by about 20 percent.
  - Assuming g = 2 percent (low): overvalued by 24 percent.
  - Assuming g = 4 percent (high): overvalued by 16 percent.
- Historical pattern implied by ES approach:
  - RER close to equilibrium during 2004–06.
  - Some overvaluation in 2007.
  - Significant overvaluation by end-2008.
  - ES approach differs from BEER and PPP on 2003 (ES suggests overvaluation in 2003 while others suggest undervaluation).
- Robustness and limitations:
  - Results are somewhat sensitive to parameter choices, notably the NFA-to-GDP benchmark and the potential growth rate.
  - Despite parameter sensitivity, the trend of increasing overvaluation culminating in significant overvaluation at end-2008 is robust and broadly consistent with PPP and BEER approaches and with BEER estimates by the Central Bank of Armenia.
  - Caution: exact misalignment magnitudes could be questioned on calibration grounds, but directional conclusions are reinforced by multiple approaches.

### V. Conclusion (paper’s main finding)
- Main finding: the Armenian real exchange rate was overvalued by an estimated 20–30 percent prior to the devaluation of the dram in March 2009.
- Confirmation: this finding is supported by three approaches—PPP, BEER, and ES—and by BEER estimates from the Central Bank of Armenia.
- Cross-approach agreement:
  - All approaches suggest RER close to equilibrium (within a 10-percent band) in 2001, 2002, 2004, 2005, and 2006.
  - 2008 is the only year from 2000 for which all approaches indicate a significant deviation from equilibrium.

*Source: _wp0949 - 9. Estimated Real Exchange Rate Misalignment (excerpts from the provided PDF chapter).*

### References..............................................................................................................

### _wp0949 - References

### References
- References................................................................................................................................19

### Tables
- 1. BEER Approach: Augmented Dickey-Fuller Test Results..................................................13
- 2. BEER Approach: Estimated Cointegrating Vector..............................................................13

### Figures
- 1. Estimated Real Exchange Rate Misalignment .......................................................................3
- 2. Armenian Price Level Relative to U.S. Price Level ..............................................................4
- 3. Relative Price Levels and Relative Incomes..........................................................................6
- 4. PPP Approach Equilibrium and Atual Real Exchanges ........................................................7
- 5. PPP Approach: Real Exchange Rate Misalignment ..............................................................8
- 6. BEER Approach: Equilibrium and Actual REER ...............................................................14
- 7. BEER Approach: Real Exchange Rate Misalignment.........................................................14
- 8. ES Approach: Real Exchange Rate Misalignment ..............................................................17

*Source: _wp0949 - References..............................................................................................................*

### 9. Estimated Real Exchange Rate Misalignment .....................................................................18

### _wp0949 - 9. Estimated Real Exchange Rate Misalignment

### I. INTRODUCTION
- Armenia’s real effective exchange rate (REER) appreciated rapidly in recent years due to large foreign exchange inflows (notably remittances and FDI) and high export prices (notably copper and molybdenum).
- During 2005–2007, real appreciation was accompanied by nominal appreciation. In 2008 the Central Bank of Armenia (CBA) changed from a managed float without a predetermined path to a soft peg and kept the nominal rate vis-à-vis the U.S. dollar within a very tight band until the dram devaluation in early March 2009.
- All three approaches used in this paper—the purchasing power parity (PPP) approach, the behavioral equilibrium exchange rate (BEER) approach, and the external sustainability (ES) approach—suggest the dram was overvalued by about 20–30 percent as of end-2008.
- While most approaches suggest the dram was close to equilibrium (i.e., within a 10-percent band) most of the time during the 2000–07 period, 2008 is the only year for which all approaches suggest a significant deviation from equilibrium.

### II. PURCHASING POWER PARITY (PPP) APPROACH
- Methodology:
  - Define PPP exchange rate as the nominal exchange rate E at which Armenian price level P equals foreign price level P* (PE = P*). Under PPP the real exchange rate equals one.
  - Use Balassa-Samuelson hypothesis to estimate an “equilibrium distance to PPP” by regressing relative price levels on relative GDP per capita (PPP GDP per capita) as a proxy for relative productivity.
- Key empirical relationships and estimates:
  - Estimated log-linear relationship from sample of 180 countries:
    - Log (real exchange rate) = -1.83 + 0.39*Log (PPP GDP per capita).
  - Interpretation: every 1 percent increase in PPP GDP per capita is associated with a real appreciation of 0.39 percent.
  - Historical comparisons: slope 0.39 is close to Rogoff (1996) 0.37, De Broeck and Slok (2001) 0.41, and Frankel (2005) 0.38.
- Armenian price level and PPP indicators:
  - Armenian prices in U.S. dollar terms increased from about one third to almost two thirds of U.S. prices; specifically, the Armenian price level was 63 percent in 2008.
  - In 1993 the Armenian price level was about 10 percent of the U.S. price level.
- PPP-based misalignment estimate:
  - The PPP approach suggests the dram was overvalued by as much as 30 percent in 2008.
  - Evolution: highly undervalued in early 1990s, slightly overvalued during 1995–2000, back to equilibrium by 2001, slightly undervalued post-2001, then appreciation of actual REER relative to equilibrium since 2003 leading to ~30 percent overvaluation in 2008.
- Caveats and shortcomings:
  - PPP approach only examines the relationship between real exchange rate and productivity and omits other determinants.
  - Estimated equilibrium relationship is based on a large cross-section that may not be representative of Armenia.
  - The estimated relationship is a historical average assuming exchange rates are on average in equilibrium.
  - GDP per capita is a rough proxy for the relative productivity differential.

### III. BEHAVIORAL EQUILIBRIUM REAL EXCHANGE RATE (BEER) APPROACH
- Methodology:
  - Estimate the long-run statistical relationship (cointegrating relationship) between REER and fundamentals using time-series data for Armenia.
  - Fundamentals included: relative productivity differential, terms of trade, net international reserves (NIR), and remittances.
  - Productivity measures: use both “relative productivity” and the “relative productivity differential” (difference between Armenia’s relative productivity and that of trade partners). EU used as comparator for trade-partner productivity (EU accounts for 34 percent of Armenia’s external trade).
  - Sectoral choices: agriculture excluded; construction treated as tradable for Armenia based on external demand, labor mobility, and observed productivity growth.
- Expected signs and economic intuition:
  - Terms of trade: improvement expected to cause real appreciation.
  - NIR: theoretically ambiguous; empirically generally positive relationship with REER (positive sign interpreted as reflecting net BOP inflows and REER).
  - Remittances: expected to cause real appreciation; Atoyan and Oomes (2006) find a one percentage point of GDP increase in total remittance leads to a one percentage point increase in dram appreciation.
- Empirical results:
  - A co-integrating vector exists between REER, terms of trade, remittances, NIR, and the relative productivity differential (cointegrating vector estimated for data up to end-2007; 2008 used for projection).
  - Augmented Dickey-Fuller (ADF) unit root tests (Sample: 1998Q1:2007Q4; all variables in logs) show nonstationarity in levels and stationarity in first differences, supporting cointegration testing.
    - ADF test results (Level / First Difference) and associated t-statistics and probabilities:
      - Real effective exchange rate: t-Statistic 0.28 Prob. 0.97 / t-Statistic -5.16 Prob. 0.00
      - Terms of Trade (Exports deflator divided by imports deflator): t-Statistic -2.34 Prob. 0.40 / t-Statistic -3.57 Prob. 0.05
      - Net International Reserves (in US dollars): t-Statistic -2.71 Prob. 0.24 / t-Statistic -4.35 Prob. 0.01
      - Remittances including other transfers: t-Statistic -3.09 Prob. 0.12 / t-Statistic -7.14 Prob. 0.00
      - Relative productivity differential: t-Statistic -1.17 Prob. 0.68 / t-Statistic -2.99 Prob. 0.05
  - Estimated cointegrating vector (dependent variable: real effective exchange rate; sample 1998Q1:2007Q4; number of lags 4; Log likelihood 447.6; Akaike information criterion -20.1; Schwarz criterion -14.8; Serial correlation LM (prob.) 0.71):
    - Terms of Trade coefficient: 0.09 (t-statistics 9.17)
    - Remittances coefficient: 0.20 (t-statistics 20.25)
    - Net International Reserves coefficient: 0.42 (t-statistics 49.82)
    - Relative Productivity Differential coefficient: 0.07 (t-statistics 3.44)
    - Trend: -0.05 (t-statistics -78.30)
    - Constant: 1.86
  - BEER misalignment estimate:
    - The BEER approach suggests the dram was overvalued by about 20 percent at end-2008 (the error correction term was 21 percent at end-2008).
- Additional findings and caveats:
  - Evidence of Balassa-Samuelson effect in Armenia appears conditional on developments in the construction sector; excluding construction or treating it as nontradable removes long-term relationship evidence.
  - Short sample length limits robustness checks; no unique cointegrating vector found; cointegration techniques assume misalignment is zero on average (residual zero by construction), which is problematic in short samples.

### IV. EXTERNAL SUSTAINABILITY (ES) APPROACH
- Purpose and method:
  - Focuses on the relation between sustainability of foreign asset position, the current account, and the real exchange rate.
  - Consists of a calibration exercise requiring assumptions about potential growth rate, inflation rate, and rates of return on external assets and liabilities.
- Implementation:
  - The ES approach consists of three steps (detailed steps not included in the supplied content).

*Source: _wp0949 - 9. Estimated Real Exchange Rate Misalignment (excerpts from the provided PDF chapter).*

### 1.      Determine the trade or current account balance as ratios to GDP that stabilize the net

### _wp0949 - 1.      Determine the trade or current account balance as ratios to GDP that stabilize the net

### External sustainability framework and NFA stabilization
- Objective: determine the trade or current account balance (as ratios to GDP) that stabilize the net foreign asset (NFA) position at a given benchmark level.
- Intertemporal budget constraint requirement: the present value of future trade surpluses must be sufficient to pay back outstanding external liabilities.
- Stabilization target: a stable ratio between NFA and GDP is analogous to stabilizing public debt-to-GDP at a benchmark level.

### Key equations and definitions
- NFA accumulation equation (levels): NFAt = NFAt-1 + CAt + KGt + KTt + Et
  - where CA is the current account balance, KG are capital gains from valuation changes, KT are capital transfers, and E are errors and omissions.
- Ratios to GDP (lower-case letters) and transformed accumulation equation:
  - (1) nt = (1/(1+gt+πt)) [ nt-1 + cat + kgt + ktt + et ]  (presented in source as the ratio-form accumulation; symbol structure preserved from source)
  - Stabilization condition for NFA-to-GDP at benchmark s_nfa implies:
    - (2) s_ca = (1+gs+π_s) s_nfa − (s_kg + s_kt + s_e)  (equation (2) as described in source; determines CA ratio that stabilizes NFA)
- Notation highlights:
  - gt = growth rate of real GDP
  - πt = inflation rate of net foreign assets
  - s_nfa = benchmark NFA-to-GDP ratio
  - s_ca = current account balance as ratio to GDP that stabilizes NFA

### Calibration choices and scenarios
- Benchmark NFA-to-GDP ratio used: end-2006 position of -24.2 percent.
- Assumed inflation rate of NFA: 2.5 percent.
- Armenia long-term GDP growth central calibration: 3 percent.
- Alternative growth scenarios:
  - low growth: 2 percent
  - high growth: 4 percent
- Treatment of capital transfers:
  - Typical literature assumption: s_kt = 0
  - This paper calibrates equation (2) first assuming s_kt = 0, and then assumes a value for s_kt consistent with medium-term forecasts for capital transfers.

### Comparative statics and implications from equation (2)
- Growth effect:
  - Faster real GDP growth (higher gt) allows a larger current account deficit while keeping the NFA-to-GDP ratio stable.
  - This is highlighted as especially relevant for Armenia, which had double-digit growth in recent years and thus could sustain larger current account deficits without compromising external sustainability.
- Capital transfers effect:
  - Larger capital transfers (s_kt > 0) permit further current account deficits with a stable NFA-to-GDP ratio.
  - Though capital transfers are often assumed to converge to zero, convergence can be slow, making nonzero s_kt realistic over the medium term.
- Sensitivities:
  - Results are sensitive to the choice of NFA-to-GDP benchmark and the potential growth rate.

### Real effective exchange rate (RER) adjustment methodology
- Compute elasticity of current account (CA) to real exchange rate (RER):
  - CAε = Xε + (X/GDP)ε − (M/GDP)ε  (source expresses CAε in terms of export and import elasticities and export/import ratios to GDP)
  - More explicitly: CAε = Xε * (X/GDP) - Mε * (M/GDP)  (structure preserved from source formulation)
  - Xε = elasticity of exports to the real exchange rate
  - Mε = elasticity of imports to the real exchange rate
  - X/GDP and M/GDP = ratios of exports and imports to GDP, respectively
- Required RER adjustment derived from CA elasticity:
  - ΔRER = ΔCA / CAε  (source formula: 1/CAε * ΔCA ⇒ ΔRER; preserved relation showing RER change needed to close CA gap)

### Elasticity calibration and data used
- Trade elasticities used:
  - Xε = -0.71
  - Mε = 0.92
  - These follow values used by the IMF’s Consultative Group on Exchange Rate Issues (CGER).
- Export and import ratios to GDP calibrated with both end-2006 and end-2007 figures (figures referenced in source).

### Quantitative findings on RER misalignment (ES approach)
- ES approach RER overvaluation estimates as of end-2008 (relative to NFA-stabilizing CA):
  - Assuming g = 3 percent (central): overvalued by about 20 percent.
  - Assuming g = 2 percent (low): overvalued by 24 percent.
  - Assuming g = 4 percent (high): overvalued by 16 percent.
- Historical pattern implied by ES approach (consistent trend across calibrations):
  - RER close to equilibrium during 2004–06.
  - Some overvaluation in 2007.
  - Significant overvaluation by end-2008.
  - ES approach differs from BEER and PPP on 2003 (ES suggests overvaluation in 2003 while others suggest undervaluation).

### Robustness and limitations
- Sensitivity:
  - Results are somewhat sensitive to parameter choices, notably the NFA-to-GDP benchmark and the potential growth rate.
- Consistency:
  - Despite parameter sensitivity, the trend of increasing overvaluation culminating in significant overvaluation at end-2008 is robust and broadly consistent with PPP and BEER approaches and with BEER estimates by the Central Bank of Armenia.
- Caution:
  - Exact misalignment magnitudes could be questioned on calibration grounds, but directional conclusions are reinforced by multiple approaches.

### Conclusion (summary of paper’s main finding)
- Main finding: the Armenian real exchange rate was overvalued by an estimated 20–30 percent prior to the devaluation of the dram in March 2009.
- Confirmation: this finding is supported by three approaches—PPP, BEER, and ES—and by BEER estimates from the Central Bank of Armenia.
- Cross-approach agreement:
  - All approaches suggest RER close to equilibrium (within a 10-percent band) in 2001, 2002, 2004, 2005, and 2006.
  - 2008 is the only year from 2000 for which all approaches indicate a significant deviation from equilibrium.

*Source: IMF working paper content unit _wp0949 - 1. Determine the trade or current account balance as ratios to GDP that stabilize the net*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0949.pdf_