## _wp0907

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---

### Introduction
- Purpose: assess the level of the real effective exchange rate in Australia and New Zealand using panel-based IMF CGER methodology with refinements.
- Methodological modifications tested:
  - Estimate each model as both a standard unrestricted panel regression using ordinary least squares (OLS) and as a restricted panel regression using the generalized method of moments (GMM).
  - Estimate each model using a large sample of economies and a narrower panel of economically similar economies.
  - Conduct exchange rate assessments at two time horizons: the current time (within sample) and the medium-term (out of sample).
- Main lesson: econometric models offer systematic diagnostic guidance but tend to offer conflicting results and are highly uncertain; they must be complemented with standard country surveillance in the context of Article IV.

### Real Exchange Rate Developments (Australia and New Zealand)
- 2001 to mid-2008:
  - The Australian dollar appreciated by more than 30 percent in nominal effective terms.
  - The New Zealand dollar appreciated by about 35 percent in nominal effective terms.
  - In real effective terms, both currencies appreciated by over 30 percent.
- Since mid-2008, both the Australian and New Zealand dollars have depreciated significantly. (2008 data are mostly based on data to October.)
- Drivers:
  - Movements in real effective interest rate differentials; relationship appears stronger at shorter horizons, consistent with carry-trade behavior.
  - Higher terms of trade: Australia—coal, iron ore, other minerals; New Zealand—dairy prices.
  - Deterioration of trade balances and current account balances as exchange rates strengthened; New Zealand’s trade balance moved from a surplus and its current account deficit widened considerably.
- Stationarity comparison:
  - As of October 2008, both countries’ real effective exchange rate is above its long-run historical average (using IMF and central bank measures).
- Assessment context:
  - Most exchange rate assessments focus on medium-term consistency with fundamentals; short-run drivers (e.g., interest rate differentials) differ from medium-run drivers.
  - Elevated market volatility (VIX) in recent months complicates assessments.

### Empirical Models: Data Coverage and Econometric Methodology
- Dataset and coverage:
  - Estimation dataset covers 55 industrial and emerging market economies over the period 1973–2007.
  - Two country groupings: a 55-country sample (wide panel) and a 9-country sample (narrow panel).
  - The narrow panel economies are: Australia, Canada, Chile, Denmark, Finland, New Zealand, Norway, South Africa, and Sweden.
- Econometric approach:
  - Models estimated by OLS and by GMM (using lagged explanatory variables as instruments, where appropriate).
  - For GMM, a general to specific model strategy is used to derive a parsimonious specification.
  - Both estimation techniques correct for cross-section specific unconditional heteroskedasticity and contemporaneous correlation of unknown form.
- Tradeoff:
  - Wide panel exploits cross-country variation but may impose problematic cross-economy equality restrictions on slope coefficients.
  - Narrow panel reduces structural heterogeneity at potential cost to variance properties.

### Macroeconomic Balance (MB) Approach — Framework and Variables
- Three steps:
  1. Estimate the equilibrium current account balance (current account norm).
  2. Determine the cyclically adjusted or underlying current account balance.
  3. Calculate the exchange rate adjustment required to close the gap between the underlying and equilibrium current account balances using estimated current account elasticity to the real effective exchange rate.
- Equilibrium current account regression:
  - ca_it = β_0,i + β' x_it + ε_it, with ε_it ~ N(0, σ^2)
  - ca_it is the ratio of the current account balance to GDP; x_it is a vector of explanatory variables.
- CGER explanatory variables:
  - Ratio of the retirement age population to the working age population (old age dependency ratio).
  - Population growth rate.
  - Logarithm of income per capita expressed in terms of purchasing power.
  - Growth rate of income per capita expressed in terms of purchasing power.
  - Ratio of the oil trade balance to GDP.
  - Ratio of the fiscal balance to GDP.
  - Lagged ratio of the net foreign asset (NFA) position to GDP.

### MB Approach — Key Estimation Findings (GMM and OLS consistency)
- Estimates of the equilibrium current account are broadly similar across econometric techniques and country coverage.
- Estimated coefficients under GMM are statistically significant, have expected signs, and plausible magnitudes:
  - Old age dependency ratio:
    - Coefficient is negative: a higher dependency ratio reduces the current account balance.
    - A 1 percentage point increase in the dependency ratio relative to trading partners would lower the current account norm by about ½ percent of GDP.
  - Population growth:
    - Coefficient is negative; magnitude varies with estimation method.
    - A 1 percentage point increase in population growth relative to trading partners would lead to a worsening of the current account norm by 1 to 4 percent of GDP.
  - Relative income growth:
    - Coefficient is negative.
    - A 1 percentage point increase in relative income growth would reduce the current account norm by 0.4 percent of GDP.
  - Oil trade balance:
    - Coefficient is positive.
    - For Australia and New Zealand (net oil importers), a widening of the oil trade deficit implies a decrease in the current account norm.
  - Relative fiscal balance:
    - Coefficient is positive.
    - (Estimation indicates a one percent increase in the fiscal balance implies an improvement in the current account norm of approximately — text ends.)
  - Initial NFA position:
    - Coefficient is positive and quite small: "An increase in NFA of 10 percent of GDP would increase the current account norm by about 0.01 percent of GDP."
    - "The size of the coefficient is robust to changes in the estimation sample period."

- Selected coefficient estimates from Table 1 (dependent variable: Ratio of current account balance to GDP):
  - Relative old-age dependency: -0.62*** (Narrow OLS), -0.58*** (Narrow GMM), -0.66*** (Wide OLS), -0.74*** (Wide GMM)
  - Relative population growth: -0.79** (Narrow OLS), -4.26** (Narrow GMM), 0.49 (Wide OLS), -1.14 (Wide GMM)
  - Relative income: -0.09*** (Narrow OLS), ... (Narrow GMM), 0.07 (Wide OLS), 0.06 (Wide GMM)
  - Relative income growth: -0.02*** (Narrow OLS), -0.38** (Narrow GMM), 0.38*** (Wide OLS), ... (Wide GMM)
  - Oil trade balance: 0.73*** (Narrow OLS), 0.88*** (Narrow GMM), 1.26*** (Wide OLS), 1.31*** (Wide GMM)
  - Relative fiscal balance: 0.17*** (Narrow OLS), 0.08*** (Narrow GMM), 0.18** (Wide OLS), 0.15** (Wide GMM)
  - Initial net foreign assets: 0.001** (Narrow OLS), 0.001** (Narrow GMM), -0.002 (Wide OLS), 0.001 (Wide GMM)
  - Observations: 735 (Narrow OLS), 714 (Narrow GMM), 174 (Wide OLS), 169 (Wide GMM)
  - R-squared: 0.73 (Narrow OLS), 0.67 (Narrow GMM), 0.76 (Wide OLS), 0.78 (Wide GMM)
- Note: Statistical significance at the 1 percent, 5 percent, and 10 percent levels is indicated by ***, **, and *, respectively. Variables excluded from the final specification are indicated by “...”.
- Point estimates are decomposed into time-varying contributions from each explanatory variable to give country-specific interpretations (Figure 3). Using wide panel GMM results, equilibrium current account deficits have been driven by a set of common factors:
  - High relative population growth contributed to large current account deficits.
  - Relatively low dependency ratios and relatively strong fiscal balances supported current account deficits.
  - Relatively low income growth reduced private investment, reducing equilibrium current account deficits.
  - Oil trade deficits exacerbated equilibrium current account deficits.

### Equilibrium Real Exchange Rate (ERER) Approach — Model, Decomposition, and Estimates
- Model specification:
  - ln Q_it = β_0,i + β' x_it + ε_it, where Q_it is real effective exchange rate; x_it includes log(terms of trade), log(output per worker in PPP terms), ratio of government consumption to GDP, and ratio of NFA position to GDP.
- Empirical sign interpretation:
  - "The coefficients on all three explanatory variables are positive, implying that an increase in any variable would lead to an appreciation."
- Decomposition highlights the role of terms of trade in driving currency strength:
  - Australia: improvement in terms of trade primary source of persistent appreciation of the Australian dollar; high relative productivity and government consumption held equilibrium exchange rate above PPP level but contributions diminished over time.
  - New Zealand: improvement in terms of trade associated, on average, with persistent appreciation of the dollar in real effective terms.
- Selected coefficient estimates from Table 2 (dependent variable: Real effective exchange rate):
  - Terms of trade: 0.33*** (Narrow OLS), 0.41*** (Narrow GMM), 0.34*** (Wide OLS), 0.39*** (Wide GMM)
  - Relative productivity: 0.15 (Narrow OLS), 0.26*** (Narrow GMM), -0.42** (Wide OLS), ... (Wide GMM)
  - Relative government consumption: 0.38*** (Narrow OLS), 1.76*** (Narrow GMM), 3.54 (Wide OLS), ... (Wide GMM)
  - Initial net foreign assets: 0.00** (Narrow OLS), ... (Narrow GMM), -0.03*** (Wide OLS), ... (Wide GMM)
  - Observations: 724 (Narrow OLS), 1006 (Narrow GMM), 165 (Wide OLS), 238 (Wide GMM)
  - R-squared: 0.52 (Narrow OLS), 0.67 (Narrow GMM), 0.48 (Wide OLS), 0.19 (Wide GMM)
- Note on fixed effects: Large fixed effect may reflect index normalization (real effective exchange rate measured as index equals an arbitrary value in a base year), not necessarily omitted time-invariant explanatory variables.

### External Sustainability (ES) Approach — Modeling Benchmark NFA and Findings
- ES approach steps:
  - (i) Estimate ratio of current account to GDP that would stabilize NFA at a benchmark.
  - (ii) Determine medium-term expected current account balance.
  - (iii) Assess REER adjustment needed to close gap between medium-term current account and NFA-stabilizing current account.
- Benchmark NFA level:
  - Can be calibrated to most recently observed NFA or central tendency of recent values, or modeled via panel regression:
    - nfa_it = β_0,i + β' x_it + ε_it
    - x_it includes log(output per worker in PPP terms), ratio of retirement age population to working-age population, ratio of government net asset position to GDP.
- Selected coefficient estimates from Table 3 (dependent variable: Ratio of net foreign assets to GDP):
  - Relative productivity: -0.34*** (Narrow OLS), -0.39*** (Narrow GMM), -0.12 (Wide OLS), ... (Wide GMM)
  - Relative old age dependency: 0.69** (Narrow OLS), ... (Narrow GMM), -0.95 (Wide OLS), ... (Wide GMM)
  - Government net assets: -0.21*** (Narrow OLS), 0.17*** (Narrow GMM), 0.53*** (Wide OLS), 0.58*** (Wide GMM)
  - Observations: 527 (Narrow OLS), 514 (Narrow GMM), 159 (Wide OLS), 198 (Wide GMM)
  - R-squared: 0.90 (Narrow OLS), 0.67 (Narrow GMM), 0.71 (Wide OLS), 0.69 (Wide GMM)
- Interpretation for Australia and New Zealand:
  - Fixed effects account for majority of estimated equilibrium net foreign debt positions (Figure 5).
  - Suggests omission of relevant time-invariant cross-country variables (candidate: real value of stock of natural resources).

### Exchange Rate Assessments — Baseline Results (medium-run horizon: 2013)
- Baseline construction:
  - Medium-run horizon: 2013 ("the level reached after lagged exchange rate effects have worked themselves out and output gaps have closed").
  - Baseline uses GMM model estimates for sample of 55 countries.
  - Medium-term forecast of explanatory variables based on the October 2008 World Economic Outlook (WEO), unless otherwise indicated.
- MB and ES approaches:
  - Assessments based on required REER adjustment to close gap between estimated current account norm and underlying (projected) current account from WEO forecasts.
  - Magnitude of exchange rate adjustment derived by dividing current account gap by semi-elasticity of current account with respect to REER.
- ERER approach:
  - Magnitude of exchange rate adjustment calculated as difference between country’s REER and estimated equilibrium value.
- Baseline numeric results (exact wording preserved):
  - Australia:
    - ERER model indicates the dollar is 18 percent undervalued.
    - ES model suggests the dollar to be overvalued by 17 percent.
    - MB model estimates: 3 percent overvalued.
  - New Zealand:
    - ERER model: 7 percent undervalued.
    - ES model: 11 percent overvalued.
- Baseline table point estimates (percent; results based on five year conditional forecasts):
  - Australia
    - Macroeconomic balance: -4.5; -5.0; 2.8
    - Equilibrium real exchange rate: -17.8
    - External sustainability: -2.4; -5.0; 16.7
  - New Zealand
    - Macroeconomic balance: -5.2; -5.6; 1.6
    - Equilibrium real exchange rate: -7.0
    - External sustainability: -3.3; -5.6; 11.1
- Model inputs:
  - Australia: semi-elasticity of -0.16, NFA to GDP norm of -49.5, medium-run equilibrium nominal GDP growth rate of 5.3 percent.
  - New Zealand: semi-elasticity of -0.21, NFA to GDP norm of -71.2, medium-run equilibrium GDP growth rate of 4.8 percent.
- (Text fragment) "These results are based on the assumption that the underlying current account deficit for Australia is" — text ends.

### Uncertainty and Confidence Intervals
- 90 percent confidence intervals capture model uncertainty and are wide (Figure 6):
  - Australia: range from 30 percent undervalued to 25 percent overvalued (i.e., -30 to +25 percent).
  - New Zealand: range from -22 percent undervalued to 20 percent overvalued.
- Note: confidence intervals may overstate uncertainty because they are inflated by model misspecification and unmodeled cyclical components.

### Robustness Tests — Reference Period Sensitivity
- Large exchange rate moves since mid-2008 make assessments highly sensitive to reference period and WEO forecast vintage.
- Example swings (models estimated for the sample of 55 countries using GMM; assessment date 2013):
  - Australia (MB / ERER / ES)
    - June 2008: 2/ 8.1 8.0 18.4
    - August 2008: 3/ 5.0 3.3 21.4
    - October 2008: 4/ 2.8 -17.8 16.7
  - New Zealand (MB / ERER / ES)
    - June 2008: 2/ 13.9 12.2 19.1
    - August 2008: 3/ 6.7 1.5 19.0
    - October 2008: 4/ 1.6 -7.0 11.1
- Footnotes:
  - 2/ Based on Spring 2008 WEO and reference period for exchange rate is end-December 2007.
  - 3/ Based on Spring 2008 WEO and reference period for exchange rate is end-August 2008.
  - 4/ Based on October 2008 WEO and reference period for exchange rate is end-October 2008.

### Robustness Tests — Auxiliary Parameters
- MB approach: sensitivity to current account (CA) projections and trade elasticity (Table 6)
  - CA/GDP projection scenarios and resulting REER under/overvaluation (percent):
    - Australia (CA/GDP projections: -4.0, -5.0, -6.0)
      - Elasticity -0.11: -5.2; 3.9; 13.0
      - Elasticity -0.16: -3.6; 2.8; 8.9
      - Elasticity -0.21: -2.7; 2.0; 6.8
    - New Zealand (CA/GDP projections: -4.6, -5.6, -6.6)
      - Elasticity -0.16: -4.1; 2.1; 8.4
      - Elasticity -0.21: -3.1; 1.6; 6.4
      - Elasticity -0.26: -2.5; 1.3; 5.2
  - Plausible sensitivity ranges noted:
    - Australia: REER assessment ranges between an undervaluation of 5 percent and an overvaluation of 13 percent.
    - New Zealand: range from an undervaluation of 4 percent to an overvaluation of 8 percent.
  - Caveat: these specific sensitivity results were not derived by statistical methods and have no assignable confidence level.

- ES approach: sensitivity to NFA norms and nominal growth assumption
  - Baseline versus alternative (observed end-2007) NFA norms (Table 7; 2013 projections using GMM applied to 55 countries):
    - Australia
      - Baseline (estimated) NFA norm: -47.4; Alternative (observed end-2007): -61.9
      - Current account norm: -2.4; -3.1
      - Degree of misalignment: 16.7; 12.0
      - Growth rate used: 5.3 percent
    - New Zealand
      - Baseline NFA norm: -71.2; Alternative observed: -87.2
      - Current account norm: -3.3; -4.0
      - Degree of misalignment: 11.1; 7.6
      - Growth rate used: 4.8 percent
  - Growth rate sensitivity (Table 8; 2013 projections using GMM applied to 55 countries):
    - A 1 percentage point change in the growth rate alters the overvaluation estimate by nearly 3 percentage points for both countries.
    - Australia (baseline growth 5.3 percent; low 4.3; high 6.3):
      - Current account norm: -2.0; -2.4; -2.8
      - Degree of misalignment: 19.5; 16.7; 13.9
    - New Zealand (baseline growth 4.8 percent; low 3.8; high 5.8):
      - Current account norm: -2.6; -3.3; -3.9
      - Degree of misalignment: 14.3; 11.1; 8.0

### Robustness Tests — Assessment Horizon
- Assessment horizon matters (GMM estimator applied to 55 countries; results for 2008 vs 2013):
  - Australia (2008 / 2013)
    - Macroeconomic balance: 7.8; 2.8
    - Equilibrium real exchange rate: 0.5; -17.8
    - External sustainability: 24.2; 16.7
  - New Zealand (2008 / 2013)
    - Macroeconomic balance: 16.8; 1.6
    - Equilibrium real exchange rate: 10.7; -7.0
    - External sustainability: 23.4; 11.1
- General pattern:
  - Current-horizon (2008) assessments often suggest larger overvaluations; ES model is less sensitive to horizon and tends to show the largest overvaluation.

### Robustness Tests — Country Coverage and Estimation Method
- Country coverage (2013 projections):
  - Wide sample (55 countries) vs narrow sample (9 countries):
    - Australia
      - Macroeconomic balance: 2.8; 0.0
      - Equilibrium real exchange rate: -17.8; -26.9
      - External sustainability: 16.7; 14.8
    - New Zealand
      - Macroeconomic balance: 1.6; -1.4
      - Equilibrium real exchange rate: -7.0; -8.4
      - External sustainability: 11.1; 12.9
  - Narrow sample tends to produce smaller overvaluation estimates for Australia; mixed results for New Zealand.
- Estimation method (2013 projections):
  - OLS vs GMM results:
    - Australia
      - Macroeconomic balance: 9.0 (OLS); 2.8 (GMM)
      - Equilibrium real exchange rate: -6.2 (OLS); -7.0 (GMM)
      - External sustainability: 16.4 (OLS); 16.7 (GMM)
    - New Zealand
      - Macroeconomic balance: 3.7 (OLS); 1.6 (GMM)
      - Equilibrium real exchange rate: -6.2 (OLS); -7.0 (GMM)
      - External sustainability: 11.0 (OLS); 11.1 (GMM)
  - Estimation choice can materially change point estimates (example: MB for Australia differs by 6.2 percentage points between OLS and GMM).

### Aggregate Result of Robustness Testing
- Small deviations from baseline assumptions can lead to substantial changes in overvaluation estimates (illustrated in Figure 7).
- Across tests:
  - ES model tends to report larger overvaluations.
  - ERER often indicates undervaluation.
  - MB tends to lie between or indicate currencies broadly in line with fundamentals.

### Concluding Remarks
- Three commonly used equilibrium exchange rate models (MB, ERER, ES) were estimated and applied to Australia and New Zealand using October 2008 WEO data and 2013 projections.
- Key takeaways:
  - Baseline: currencies broadly in line with fundamentals but with wide model disagreement.
  - Numerical exchange rate assessments are weak and should be treated as diagnostic tools rather than definitive yardsticks.
  - Sources of uncertainty include model specification, sample heterogeneity, reference period, auxiliary parameter choices (trade elasticities, NFA norms, growth rates), assessment horizon, country coverage, and estimation method.
- Practical implication: exchange rate misalignment estimates are imprecise and highly sensitive to modeling assumptions.

### Appendix I — Dataset and Model Variable Definitions
- Country coverage:
  - Wide panel (55 countries): Algeria, Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, Croatia, the Czech Republic, Denmark, Egypt, Finland, France, Germany, Greece, Hong Kong SAR, Hungary, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Luxembourg, Malaysia, Mexico, Morocco, the Netherlands, New Zealand, Norway, Pakistan, Peru, the Philippines, Poland, Portugal, Russia, Saudi Arabia, Singapore, the Slovak Republic, Slovenia, South Africa, Spain, Sweden, Switzerland, Taiwan POC, Thailand, Tunisia, Turkey, the United Kingdom, the United States, and Venezuela.
  - Narrow panel (9 countries): Australia, Canada, Chile, Denmark, Finland, New Zealand, Norway, South Africa, and Sweden.
- Dataset: annual observations 1973–2007; WEO forecasts 2008–2013 (October 2008 vintage). Panel is unbalanced.
- Model variable definitions:
  - Macroeconomic balance approach
    - Dependent: ratio of the current account balance to GDP.
    - Explanatory: ratio of retirement age population to working age population; growth rate of population; log of income per capita (PPP); growth rate of income per capita (PPP); ratio of oil trade balance to GDP; ratio of fiscal balance to GDP; lagged ratio of NFA to GDP.
  - Equilibrium real exchange rate (ERER) approach
    - Dependent: log of the real effective exchange rate.
    - Explanatory: log of the terms of trade; log of output per worker (PPP); ratio of government consumption to GDP; ratio of NFA to GDP.
  - External sustainability (ES) approach
    - Dependent: ratio of the NFA position to GDP.
    - Explanatory: log of output per worker (PPP); ratio of retirement age population to working age population; ratio of government net asset position to GDP.
- Data sources:
  - October 2008 WEO database (conditional on a constant real effective exchange rate) where possible.
  - Effective exchange rate data: Information Notice System database.
  - NFA position data: International Investment Position database.
  - Population share data: World Development Indicators database.

*Source: IMF staff estimates and analysis based on the October 2008 WEO vintage (document text supplied).*

### 1.     Estimation Results for the Macroeconomic Balance Approach ......................................10

### 1.     Estimation Results for the Macroeconomic Balance Approach

### Introduction
- Purpose: assess the level of the real effective exchange rate in Australia and New Zealand using panel-based IMF CGER methodology with refinements.
- Three methodological modifications tested:
  - Estimate each model as both a standard unrestricted panel regression using ordinary least squares (OLS) and as a restricted panel regression using the generalized method of moments (GMM).
  - Estimate each model using a large sample of economies and a narrower panel of economically similar economies.
  - Conduct exchange rate assessments at two time horizons: the current time (within sample) and the medium-term (out of sample).
- Main lesson: econometric models offer systematic diagnostic guidance but tend to offer conflicting results and are highly uncertain; they must be complemented with standard country surveillance in the context of Article IV.

### Real Exchange Rate Developments (Australia and New Zealand)
- From 2001 to mid-2008:
  - The Australian dollar appreciated by more than 30 percent in nominal effective terms.
  - The New Zealand dollar appreciated by about 35 percent in nominal effective terms.
  - In real effective terms, both currencies appreciated by over 30 percent.
- Since mid-2008, both the Australian and New Zealand dollars have depreciated significantly. (2008 data are mostly based on data to October.)
- Drivers noted:
  - Movements in real effective interest rate differentials; relationship appears stronger at shorter horizons, consistent with carry-trade behavior.
  - Higher terms of trade: Australia—coal, iron ore, other minerals; New Zealand—dairy prices.
  - Deterioration of trade balances and current account balances as exchange rates strengthened; New Zealand’s trade balance moved from a surplus and its current account deficit widened considerably.
- Stationarity comparison:
  - As of October 2008, both countries’ real effective exchange rate is above its long-run historical average (using IMF and central bank measures).
- Assessment context:
  - Most exchange rate assessments focus on medium-term consistency with fundamentals; short-run drivers (e.g., interest rate differentials) differ from medium-run drivers.
  - Elevated market volatility (VIX) in recent months complicates assessments.

### Empirical Models: Data Coverage and Econometric Methodology
- Dataset and coverage:
  - Estimation dataset covers 55 industrial and emerging market economies over the period 1973–2007.
  - Two country groupings: a 55-country sample (wide panel) and a 9-country sample (narrow panel).
  - The narrow panel economies are: Australia, Canada, Chile, Denmark, Finland, New Zealand, Norway, South Africa, and Sweden.
- Econometric approach:
  - Models estimated by OLS and by GMM (using lagged explanatory variables as instruments, where appropriate).
  - For GMM, a general to specific model strategy is used to derive a parsimonious specification.
  - Both estimation techniques correct for cross-section specific unconditional heteroskedasticity and contemporaneous correlation of unknown form.
- Tradeoff noted:
  - Wide panel exploits cross-country variation but may impose problematic cross-economy equality restrictions on slope coefficients.
  - Narrow panel reduces structural heterogeneity at potential cost to variance properties.

### The Macroeconomic Balance (MB) Approach: Framework
- Three steps:
  1. Estimate the equilibrium current account balance (current account norm).
  2. Determine the cyclically adjusted or underlying current account balance.
  3. Calculate the exchange rate adjustment required to close the gap between the underlying and equilibrium current account balances using estimated current account elasticity to the real effective exchange rate.
- Equilibrium current account derived from the panel regression:
  - ca_it = β_0,i + β'x_it + ε_it, with ε_it ~ N(0, σ^2)
  - where ca_it is the ratio of the current account balance to GDP and x_it is a vector of explanatory variables.

### MB Approach: Explanatory Variables
- Variables included (CGER methodology):
  - Ratio of the retirement age population to the working age population (old age dependency ratio).
  - Population growth rate.
  - Logarithm of income per capita expressed in terms of purchasing power.
  - Growth rate of income per capita expressed in terms of purchasing power.
  - Ratio of the oil trade balance to GDP.
  - Ratio of the fiscal balance to GDP.
  - Lagged ratio of the net foreign asset (NFA) position to GDP.

### MB Approach: Key Estimation Findings (GMM and OLS consistency)
- Estimates of the equilibrium current account are broadly similar across econometric techniques and country coverage.
- Estimated coefficients under GMM are statistically significant, have expected signs, and plausible magnitudes:
  - Old age dependency ratio:
    - Coefficient is negative: a higher dependency ratio reduces the current account balance.
    - A 1 percentage point increase in the dependency ratio relative to trading partners would lower the current account norm by about ½ percent of GDP.
  - Population growth:
    - Coefficient is negative; magnitude varies with estimation method.
    - A 1 percentage point increase in population growth relative to trading partners would lead to a worsening of the current account norm by 1 to 4 percent of GDP.
  - Relative income growth:
    - Coefficient is negative.
    - A 1 percentage point increase in relative income growth would reduce the current account norm by 0.4 percent of GDP.
  - Oil trade balance:
    - Coefficient is positive.
    - For Australia and New Zealand (net oil importers), a widening of the oil trade deficit implies a decrease in the current account norm.
  - Relative fiscal balance:
    - Coefficient is positive.
    - (Estimation indicates a one percent increase in the fiscal balance implies an improvement in the current account norm of approximately — text ends.)

*Source: IMF staff estimates, from "Estimation Results for the Macroeconomic Balance Approach" (content unit)._

### 0.1 percent of GDP.

### _wp0907 - 0.1 percent of GDP.

### Macroeconomic Balance (MB) Approach — key findings and estimates
- The coefficient on the initial NFA position is positive and quite small: "An increase in NFA of 10 percent of GDP would increase the current account norm by about 0.01 percent of GDP."
- "The size of the coefficient is robust to changes in the estimation sample period."
- Point estimates are decomposed into time-varying contributions from each explanatory variable to give country-specific interpretations (Figure 3). Using wide panel GMM results, equilibrium current account deficits have been driven by a set of common factors.
- Country-specific contributions noted:
  - High relative population growth contributed to large current account deficits.
  - Relatively low dependency ratios and relatively strong fiscal balances supported current account deficits.
  - Relatively low income growth reduced private investment, reducing equilibrium current account deficits.
  - Oil trade deficits exacerbated equilibrium current account deficits.

- Table 1: Estimation results for the MB approach (dependent variable: Ratio of current account balance to GDP). Key coefficient estimates shown exactly as in source:
  - Relative old-age dependency: -0.62*** (Narrow OLS), -0.58*** (Narrow GMM), -0.66*** (Wide OLS), -0.74*** (Wide GMM)
  - Relative population growth: -0.79** (Narrow OLS), -4.26** (Narrow GMM), 0.49 (Wide OLS), -1.14 (Wide GMM)
  - Relative income: -0.09*** (Narrow OLS), ... (Narrow GMM), 0.07 (Wide OLS), 0.06 (Wide GMM)
  - Relative income growth: -0.02*** (Narrow OLS), -0.38** (Narrow GMM), 0.38*** (Wide OLS), ... (Wide GMM)
  - Oil trade balance: 0.73*** (Narrow OLS), 0.88*** (Narrow GMM), 1.26*** (Wide OLS), 1.31*** (Wide GMM)
  - Relative fiscal balance: 0.17*** (Narrow OLS), 0.08*** (Narrow GMM), 0.18** (Wide OLS), 0.15** (Wide GMM)
  - Initial net foreign assets: 0.001** (Narrow OLS), 0.001** (Narrow GMM), -0.002 (Wide OLS), 0.001 (Wide GMM)
  - Observations: 735 (Narrow OLS), 714 (Narrow GMM), 174 (Wide OLS), 169 (Wide GMM)
  - R-squared: 0.73 (Narrow OLS), 0.67 (Narrow GMM), 0.76 (Wide OLS), 0.78 (Wide GMM)
- Note: Statistical significance at the 1 percent, 5 percent, and 10 percent levels is indicated by ***, **, and *, respectively. Variables excluded from the final specification are indicated by “...”.

### Equilibrium Real Exchange Rate (ERER) Approach — model, decomposition, and estimates
- Model specification: ln Q_it = β_0,i + β' x_it + ε_it, where Q_it is real effective exchange rate, x_it includes log(terms of trade), log(output per worker in PPP terms), ratio of government consumption to GDP, and ratio of NFA position to GDP.
- "The coefficients on all three explanatory variables are positive, implying that an increase in any variable would lead to an appreciation."
- Decomposition highlights role of terms of trade in driving currency strength (Figure 4):
  - For Australia: improvement in terms of trade primary source of persistent appreciation of the Australian dollar; high relative productivity and government consumption held equilibrium exchange rate above PPP level but contributions diminished over time.
  - For New Zealand: improvement in terms of trade associated, on average, with persistent appreciation of the dollar in real effective terms.
- Table 2: Estimation results for the ERER approach (dependent variable: Real effective exchange rate). Key coefficient estimates shown exactly as in source:
  - Terms of trade: 0.33*** (Narrow OLS), 0.41*** (Narrow GMM), 0.34*** (Wide OLS), 0.39*** (Wide GMM)
  - Relative productivity: 0.15 (Narrow OLS), 0.26*** (Narrow GMM), -0.42** (Wide OLS), ... (Wide GMM)
  - Relative government consumption: 0.38*** (Narrow OLS), 1.76*** (Narrow GMM), 3.54 (Wide OLS), ... (Wide GMM)
  - Initial net foreign assets: 0.00** (Narrow OLS), ... (Narrow GMM), -0.03*** (Wide OLS), ... (Wide GMM)
  - Observations: 724 (Narrow OLS), 1006 (Narrow GMM), 165 (Wide OLS), 238 (Wide GMM)
  - R-squared: 0.52 (Narrow OLS), 0.67 (Narrow GMM), 0.48 (Wide OLS), 0.19 (Wide GMM)
- Note on fixed effects: Large fixed effect may reflect index normalization (real effective exchange rate measured as index equals an arbitrary value in a base year), not necessarily omitted time-invariant explanatory variables.

### External Sustainability (ES) Approach — modeling benchmark NFA and findings
- ES approach steps:
  - (i) Estimate ratio of current account to GDP that would stabilize NFA at a benchmark.
  - (ii) Determine medium-term expected current account balance.
  - (iii) Assess real effective exchange rate adjustment needed to close gap between medium-term current account and NFA-stabilizing current account.
- Benchmark NFA level: can be calibrated to most recently observed NFA or central tendency of recent values, or modeled via panel regression:
  - nfa_it = β_0,i + β' x_it + ε_it, where nfa_it is ratio of NFA to GDP; x_it includes log(output per worker in PPP terms), ratio of retirement age population to working-age population, ratio of government net asset position to GDP.
- Table 3: Estimation results for ratio of NFA to GDP (dependent variable: Ratio of net foreign assets to GDP). Key coefficient estimates shown exactly as in source:
  - Relative productivity: -0.34*** (Narrow OLS), -0.39*** (Narrow GMM), -0.12 (Wide OLS), ... (Wide GMM)
  - Relative old age dependency: 0.69** (Narrow OLS), ... (Narrow GMM), -0.95 (Wide OLS), ... (Wide GMM)
  - Government net assets: -0.21*** (Narrow OLS), 0.17*** (Narrow GMM), 0.53*** (Wide OLS), 0.58*** (Wide GMM)
  - Observations: 527 (Narrow OLS), 514 (Narrow GMM), 159 (Wide OLS), 198 (Wide GMM)
  - R-squared: 0.90 (Narrow OLS), 0.67 (Narrow GMM), 0.71 (Wide OLS), 0.69 (Wide GMM)
- Key interpretation for Australia and New Zealand:
  - Fixed effects account for majority of estimated equilibrium net foreign debt positions (Figure 5).
  - Suggests omission of relevant time-invariant cross-country variables (candidate: real value of stock of natural resources).

### Exchange Rate Assessments — Baseline results (medium-run horizon: 2013)
- Baseline construction details:
  - Medium-run horizon: 2013 (the projection is taken to be the underlying current account, "the level reached after lagged exchange rate effects have worked themselves out and output gaps have closed").
  - Baseline uses GMM model estimates for sample of 55 countries.
  - Medium-term forecast of explanatory variables based on the October 2008 World Economic Outlook (WEO), unless otherwise indicated.
- For MB and ES approaches:
  - Assessments based on required real effective exchange rate adjustment to close gap between estimated current account norm and underlying (projected) current account from WEO forecasts.
  - Magnitude of exchange rate adjustment derived by dividing current account gap by semi-elasticity of current account with respect to real effective exchange rate.
- For ERER approach:
  - Magnitude of exchange rate adjustment calculated as difference between country’s real effective exchange rate and estimated equilibrium value.
- Baseline numeric results for exchange rate level assessments (exact wording preserved):
  - For Australia:
    - ERER model indicates the dollar is 18 percent undervalued.
    - ES model suggests the dollar to be overvalued by 17 percent.
    - MB model estimates: 3 percent overvalued.
  - For New Zealand:
    - ERER model: 7 percent undervalued.
    - ES model: 11 percent overvalued.
- Note: "These results are based on the assumption that the underlying current account deficit for Australia is" (text ends at this point in supplied content).

*Source: IMF staff estimates and tables and figures as presented in the supplied content.*

### 5.0 percent of GDP and 5.6 percent of GDP for New Zealand (i.e., the WEO forecast for

### _wp0907 - 5.0 percent of GDP and 5.6 percent of GDP for New Zealand (i.e., the WEO forecast for

### Baseline results (October 2008 data; 2013 projections)
- Baseline conclusion: Australian and New Zealand dollars were broadly in line with fundamentals, but models diverge:
  - ERER model: suggests undervaluation for both currencies.
  - MB model: implies currencies broadly in line with fundamentals.
  - ES model: indicates both currencies are overvalued.
- Table 4 baseline point estimates (percent; results based on five year conditional forecasts):
  - Australia
    - Macroeconomic balance: -4.5; -5.0; 2.8
    - Equilibrium real exchange rate: -17.8
    - External sustainability: -2.4; -5.0; 16.7
  - New Zealand
    - Macroeconomic balance: -5.2; -5.6; 1.6
    - Equilibrium real exchange rate: -7.0
    - External sustainability: -3.3; -5.6; 11.1
- Model inputs noted:
  - Australia estimates use semi-elasticity of -0.16, NFA to GDP norm of -49.5, medium-run equilibrium nominal GDP growth rate of 5.3 percent.
  - New Zealand estimates use semi-elasticity of -0.21, NFA to GDP norm of -71.2, medium-run equilibrium GDP growth rate of 4.8 percent.

### Uncertainty and confidence intervals
- 90 percent confidence intervals capture model uncertainty and are wide (Figure 6):
  - Australia: range from 30 percent undervalued to 25 percent overvalued (i.e., -30 to +25 percent).
  - New Zealand: range from -22 percent undervalued to 20 percent overvalued.
- Note: confidence intervals may overstate uncertainty because they are inflated by model misspecification and unmodeled cyclical components.

### Robustness tests — Reference period sensitivity
- Large exchange rate moves since mid-2008 make assessments highly sensitive to reference period and WEO forecast vintage.
- Example swings (Table 5; results reported based on models estimated for the sample of 55 countries using GMM; assessment date 2013):
  - Australia (MB / ERER / ES)
    - June 2008: 2/ 8.1 8.0 18.4
    - August 2008: 3/ 5.0 3.3 21.4
    - October 2008: 4/ 2.8 -17.8 16.7
  - New Zealand (MB / ERER / ES)
    - June 2008: 2/ 13.9 12.2 19.1
    - August 2008: 3/ 6.7 1.5 19.0
    - October 2008: 4/ 1.6 -7.0 11.1
- Footnotes for Table 5:
  - 2/ Based on Spring 2008 WEO and reference period for exchange rate is end-December 2007.
  - 3/ Based on Spring 2008 WEO and reference period for exchange rate is end-August 2008.
  - 4/ Based on October 2008 WEO and reference period for exchange rate is end-October 2008.

### Robustness tests — Auxiliary parameters

- MB approach: sensitivity to current account (CA) projections and trade elasticity (Table 6)
  - CA/GDP projection scenarios and resulting REER under/overvaluation (percent):
    - Australia (CA/GDP projections: -4.0, -5.0, -6.0)
      - Elasticity -0.11: -5.2; 3.9; 13.0
      - Elasticity -0.16: -3.6; 2.8; 8.9
      - Elasticity -0.21: -2.7; 2.0; 6.8
    - New Zealand (CA/GDP projections: -4.6, -5.6, -6.6)
      - Elasticity -0.16: -4.1; 2.1; 8.4
      - Elasticity -0.21: -3.1; 1.6; 6.4
      - Elasticity -0.26: -2.5; 1.3; 5.2
  - Plausible sensitivity ranges noted:
    - Australia: REER assessment ranges between an undervaluation of 5 percent and an overvaluation of 13 percent.
    - New Zealand: range from an undervaluation of 4 percent to an overvaluation of 8 percent.
  - Caveat: these specific sensitivity results were not derived by statistical methods and have no assignable confidence level.

- ES approach: sensitivity to NFA norms and nominal growth assumption
  - Baseline versus alternative (observed end-2007) NFA norms (Table 7; 2013 projections using GMM applied to 55 countries):
    - Australia
      - Baseline (estimated) NFA norm: -47.4; Alternative (observed end-2007): -61.9
      - Current account norm: -2.4; -3.1
      - Degree of misalignment: 16.7; 12.0
      - Growth rate used: 5.3 percent
    - New Zealand
      - Baseline NFA norm: -71.2; Alternative observed: -87.2
      - Current account norm: -3.3; -4.0
      - Degree of misalignment: 11.1; 7.6
      - Growth rate used: 4.8 percent
  - Growth rate sensitivity (Table 8; 2013 projections using GMM applied to 55 countries):
    - A 1 percentage point change in the growth rate alters the overvaluation estimate by nearly 3 percentage points for both countries.
    - Australia (baseline growth 5.3 percent; low 4.3; high 6.3):
      - Current account norm: -2.0; -2.4; -2.8
      - Degree of misalignment: 19.5; 16.7; 13.9
    - New Zealand (baseline growth 4.8 percent; low 3.8; high 5.8):
      - Current account norm: -2.6; -3.3; -3.9
      - Degree of misalignment: 14.3; 11.1; 8.0

### Robustness tests — Assessment horizon
- Assessment horizon matters (Table 9; GMM estimator applied to 55 countries; results for 2008 vs 2013):
  - Australia (2008 / 2013)
    - Macroeconomic balance: 7.8; 2.8
    - Equilibrium real exchange rate: 0.5; -17.8
    - External sustainability: 24.2; 16.7
  - New Zealand (2008 / 2013)
    - Macroeconomic balance: 16.8; 1.6
    - Equilibrium real exchange rate: 10.7; -7.0
    - External sustainability: 23.4; 11.1
- General pattern:
  - Current-horizon (2008) assessments often suggest larger overvaluations; ES model is less sensitive to horizon and tends to show the largest overvaluation.

### Robustness tests — Country coverage and estimation method
- Country coverage (Table 10; results reported based on 2013 projections):
  - Wide sample (55 countries) vs narrow sample (9 countries):
    - Australia
      - Macroeconomic balance: 2.8; 0.0
      - Equilibrium real exchange rate: -17.8; -26.9
      - External sustainability: 16.7; 14.8
    - New Zealand
      - Macroeconomic balance: 1.6; -1.4
      - Equilibrium real exchange rate: -7.0; -8.4
      - External sustainability: 11.1; 12.9
  - Narrow sample tends to produce smaller overvaluation estimates for Australia; mixed results for New Zealand.
- Estimation method (Table 11; 2013 projections):
  - OLS vs GMM results:
    - Australia
      - Macroeconomic balance: 9.0 (OLS); 2.8 (GMM)
      - Equilibrium real exchange rate: -6.2 (OLS); -7.0 (GMM)
      - External sustainability: 16.4 (OLS); 16.7 (GMM)
    - New Zealand
      - Macroeconomic balance: 3.7 (OLS); 1.6 (GMM)
      - Equilibrium real exchange rate: -6.2 (OLS); -7.0 (GMM)
      - External sustainability: 11.0 (OLS); 11.1 (GMM)
  - Estimation choice can materially change point estimates (example: MB for Australia differs by 6.2 percentage points between OLS and GMM).

### Aggregate result of robustness testing
- Small deviations from baseline assumptions can lead to substantial changes in overvaluation estimates (illustrated in Figure 7).
- Across tests, ES model tends to report larger overvaluations; ERER often indicates undervaluation; MB tends to lie between or indicate currencies broadly in line with fundamentals.

### Concluding remarks
- Three commonly used equilibrium exchange rate models (MB, ERER, ES) were estimated and applied to Australia and New Zealand using October 2008 WEO data and 2013 projections.
- Key takeaways:
  - Baseline: currencies broadly in line with fundamentals but with wide model disagreement.
  - Numerical exchange rate assessments are weak and should be treated as diagnostic tools rather than definitive yardsticks.
  - Sources of uncertainty include model specification, sample heterogeneity, reference period, auxiliary parameter choices (trade elasticities, NFA norms, growth rates), assessment horizon, country coverage, and estimation method.
- Practical implication: exchange rate misalignment estimates are imprecise and highly sensitive to modeling assumptions.

### Appendix I — Dataset and model variable definitions
- Country coverage:
  - Wide panel (55 countries): Algeria, Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, Croatia, the Czech Republic, Denmark, Egypt, Finland, France, Germany, Greece, Hong Kong SAR, Hungary, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Luxembourg, Malaysia, Mexico, Morocco, the Netherlands, New Zealand, Norway, Pakistan, Peru, the Philippines, Poland, Portugal, Russia, Saudi Arabia, Singapore, the Slovak Republic, Slovenia, South Africa, Spain, Sweden, Switzerland, Taiwan POC, Thailand, Tunisia, Turkey, the United Kingdom, the United States, and Venezuela.
  - Narrow panel (9 countries): Australia, Canada, Chile, Denmark, Finland, New Zealand, Norway, South Africa, and Sweden.
- Dataset: annual observations 1973–2007; WEO forecasts 2008–2013 (October 2008 vintage). Panel is unbalanced.
- Model variable definitions:
  - Macroeconomic balance approach
    - Dependent: ratio of the current account balance to GDP.
    - Explanatory: ratio of retirement age population to working age population; growth rate of population; log of income per capita (PPP); growth rate of income per capita (PPP); ratio of oil trade balance to GDP; ratio of fiscal balance to GDP; lagged ratio of NFA to GDP.
  - Equilibrium real exchange rate (ERER) approach
    - Dependent: log of the real effective exchange rate.
    - Explanatory: log of the terms of trade; log of output per worker (PPP); ratio of government consumption to GDP; ratio of NFA to GDP.
  - External sustainability (ES) approach
    - Dependent: ratio of the NFA position to GDP.
    - Explanatory: log of output per worker (PPP); ratio of retirement age population to working age population; ratio of government net asset position to GDP.
- Data sources:
  - October 2008 WEO database (conditional on a constant real effective exchange rate) where possible.
  - Effective exchange rate data: Information Notice System database.
  - NFA position data: International Investment Position database.
  - Population share data: World Development Indicators database.

*Source: IMF staff estimates and analysis based on the October 2008 WEO vintage (document text supplied).*

### Appendix II. The Theoretical Framework

### Appendix II. The Theoretical Framework

### Macroeconomic Balance Approach
- Medium-run equilibrium of the current account balance to GDP ratio is jointly modeled from intertemporal and intratemporal perspectives; the medium-run equilibrium real effective exchange rate (REER) is inferred as the REER value that reconciles these intertemporal and intratemporal current account balance estimates.
- Intertemporal models of the current account:
  - Private saving: modeled via household utility maximization.
  - Private investment: modeled via firm value maximization.
  - Public saving and investment: typically treated as exogenous.
- Overlapping generations models (household utility maximization):
  - Predict temporary but persistent deviations of the private saving rate from its long-run equilibrium in response to demographic change.
  - Household disposable income is typically hump-shaped over the life cycle; consumption smoothing implies a reduction in the private saving rate when the economically inactive share of the population increases.
  - Common empirical proxies: the ratio of the retirement age population to the working age population, and the growth rate of the population — both expected to be negatively associated with the private saving rate and with the ratio of the current account balance to output.
- Neoclassical growth models (firm value maximization):
  - Predict temporary but persistent deviations of the private investment rate from its long-run equilibrium in response to unbalanced growth.
  - Under conditional convergence (Barro and Sala‑i‑Martin (1999)): private capital investment rate is negatively associated with level of income per capita and positively associated with growth rate of income per capita.
  - Implied associations for the current account balance to output: positive with level of income per capita; negative with growth rate of income per capita.
- Fiscal considerations:
  - Under Ricardian equivalence, the current account balance is invariant to the fiscal balance.
  - Departures from Ricardian equivalence typically imply the ratio of the current account balance to output is positively associated with the fiscal balance; such departures are empirically well documented.

### Equilibrium Real Exchange Rate Approach
- Definitions and decomposition:
  - S_it: nominal effective exchange rate (geometric trade-weighted average of nominal bilateral exchange rates S_it, each measuring price of domestic currency in terms of foreign currency).
  - Q_it: real effective exchange rate (geometric trade-weighted average of real bilateral exchange rates Q_it, each measuring the price of a basket of domestic goods and services in terms of a basket of foreign goods and services).
  - P_it: price of domestic basket; P*_it: geometric trade-weighted average of prices of foreign baskets. Relationship (a):
    - ln Q_it = ln S_it + ln P*_it − ln P_it  (label a)
  - Decomposition of P*_it as geometric trade-weighted average of tradables P^T_it and nontradables P^N_it with parameter θ where 0 ≤ θ ≤ 1 (label b):
    - ln P*_it = θ ln P^T_it + (1 − θ) ln P^N_it  (label b)
  - Combination yields decomposition (label c) separating deviations from long-run PPP into:
    - deviations from law of one price for tradables, and
    - deviations of the price of nontradables in terms of tradables from a geometric trade-weighted average across trading partners.
  - If exchange rate pass-through is complete, decomposition can be expressed in terms of terms of trade T_it (label d).
- Empirical evidence:
  - Campa and Goldberg (2002) find exchange rate pass-through is incomplete in the short run but complete in the long run. This suggests a positive association between the REER and the terms of trade. (Footnote 1: derivation assumes GDP-based REER.)
- Balassa–Samuelson mechanism:
  - Small open economy with tradable and nontradable outputs; capital mobile internationally and across sectors domestically; labor mobile across sectors domestically.
  - If productivity growth in tradables exceeds that in nontradables, wage equalization raises the relative price of nontradables in terms of tradables over time; if this rise is faster domestically than among trading partners, REER appreciation follows.
  - Froot and Rogoff (1995) note the mechanism operates even without productivity growth differentials if tradables are relatively capital intensive.
  - Stylized implication: positive association between REER and output per worker, expressed as deviation from a trade-weighted average across trading partners. (Footnote 2: bypasses separate measurement of tradables and nontradables productivity.)
- Demand-side factors:
  - Relaxing strong Balassa–Samuelson assumptions allows REER dependence on demand factors.
  - Common assumption: government consumption is biased toward nontradables ⇒ REER positively associated with ratio of government consumption to output, expressed as deviation from trade-weighted average across trading partners.
- External position and expenditure switching:
  - Intertemporal budget balance implies net creditor economies tend to run trade deficits and net debtor economies tend to run trade surpluses in medium-run equilibrium.
  - To induce expenditure switching, economies running trade deficits will tend to have relatively overvalued REERs; economies running trade surpluses will tend to have relatively undervalued REERs.
  - Suggests a positive association between REER and ratio of the net foreign assets (NFA) position to output.

### External Sustainability Approach
- Net foreign creditor/debtor status depends on accumulated net capital flows.
  - Private net capital flows tend to equalize marginal product of capital across economies.
  - Public net capital flows may arise independently of rate-of-return considerations.
- Neoclassical growth framework implications:
  - Marginal product of capital increases with productivity and decreases with capital abundance.
  - Implied associations for the ratio of the NFA position to output:
    - Negative association with output per worker.
    - Positive association with the ratio of the retirement age population to the working age population.

*Source: _wp0907 - Appendix II. The Theoretical Framework (IMF PDF)*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0907.pdf_