## _wp11122 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

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---

### I. Introduction — purpose and mechanism
- Purpose:
  - Develop a world general equilibrium model with heterogeneity across countries in GDP volatility to assess how differences in GDP volatility influence the dispersion of net foreign assets (NFA) and current account (CA) imbalances.
- Key mechanism:
  - Countries receive a stochastic GDP endowment each period (Can be consumed or lent internationally).
  - International borrowing allowed up to an exogenous limit (borrowing constraint).
  - Impatience condition: Rβ/G^γ < 1 implies a finite optimal NFA in the presence of uncertainty because impatience (borrowing desire) is counterbalanced by precautionary savings due to income volatility.
  - Optimal NFA a* defined as the level of foreign assets that is expected to be stable (if a_{t−1}=a* and Z_t = 1 then a_t = a*).

### II. Optimal NFA in partial equilibrium — calibration and sensitivity
- Benchmark parameter calibration:
  - world interest rate (risk free): 3%
  - deterministic annual growth rate: 1%
  - borrowing constraint: 100% of GDP
  - risk aversion coefficient γ: 2
  - income process estimated from HP-filtered real per capita US GDP 1980–2008: ρ = 0.73, σ = 1.2%
  - discount factor β set to 0.99 (to sustain a 3% world interest rate in general equilibrium)
- Partial equilibrium numerical result:
  - predicted optimal NFA a* = −46% of GDP under benchmark calibration.
- Sensitivity findings (partial equilibrium):
  - a* is extremely sensitive to the world interest rate R, especially as R approaches the impatience limit G^γ/β.
  - a* increases with tighter borrowing constraint, greater persistency ρ, and higher volatility σ.
  - If the impatience condition is comfortably satisfied (R well below G^γ/β), sensitivity of a* to R is weaker, and sensitivity to other parameters is reduced.

### III. World general equilibrium — setup and calibration
- Approach:
  - Solve a world general equilibrium with six regions to endogenously pin down the world interest rate that clears the international bond market.
  - To avoid stochastic world rate complications, solve as a replicated world (infinite replicas of six regions) so idiosyncratic uncertainty washes out at aggregate level.
- Regions considered: US, Euro Area, Japan, China, oil exporting countries, rest of the world.
- Region-specific GDP volatility estimates and 2008 GDP (Table 1 reproduced values):
  - US: ρ = 0.73, σ = 0.01, GDP (USD billions) = 14,400
  - Euro Area: ρ = 0.78, σ = 0.01, GDP (USD billions) = 13,600
  - Japan: ρ = 0.90, σ = 0.009, GDP (USD billions) = 4,890
  - China: ρ = 0.75, σ = 0.016, GDP (USD billions) = 4,530
  - Oil exporters: ρ = 0.77, σ = 0.03, GDP (USD billions) = 4,470
  - Rest of the world: ρ = 0.73, σ = 0.02, GDP (USD billions) = 18,500
- Common assumptions across regions in calibration:
  - borrowing constraint = 100% of GDP
  - deterministic growth rate G = 1%
  - risk aversion γ = 2, discount factor β = 0.99 (to generate a 3% equilibrium world interest rate)

### IV. Stationary equilibrium — equilibrium interest rate and predicted NFA
- Market-clearing world interest rate: 3% (value that clears aggregated net bond supply using 2008 GDP weights).
- Predicted equilibrium NFA positions at 3%:
  - Oil exporting countries: accumulate almost three times GDP (≈ 3.0 × GDP).
  - US, Euro Area, Japan: borrow more than 30% of GDP (borrower positions > 30% of GDP).
  - If using GDP deflated by CPI (alternative calibration), oil exporters’ σ rises to 7.2% and their predicted optimal NFA approaches 5 times GDP (≈ 5.0 × GDP).
- Comparison to actual 2007 NFA:
  - Model-predicted dispersion of NFA is considerably larger than 2007 observed values (Lane and Milesi-Ferretti (2007) data): current holdings of oil exporters and US debt position are small relative to model predictions; predictions for Japan and China differ in sign from observed positions.

### V. Transition dynamics — speed of convergence and CA implications
- Convergence speed: extremely slow.
  - Example: oil exporters accumulate after 150 years less than one third of their optimal asset holdings.
- Current account implications from starting at 2007 NFA positions (no GDP shocks):
  - Oil exporters run CA surplus of only 0.1% of GDP.
  - Developed economies run deficits of around 0.03% of GDP.
  - Therefore, heterogeneity in GDP volatility can yield large cross-country NFA dispersion but only small CA imbalances because equilibrium world interest rate is close to the rate that keeps 2007 NFA stable for many countries.

### VI. Sensitivity analysis (two-region aggregation and parameter variations)
- Two-region aggregation (for numerical speed):
  - Region A (US-EURO-Japan): weighted means ρ = 0.78, σ = 0.011, GDP 2008 = 32,890 (USD billions)
  - Region B (China-OIL-ROW): weighted means ρ = 0.74, σ = 0.021, GDP 2008 = 27,500 (USD billions)
- Robustness:
  - NFA targets and CA dynamics are fairly robust to common-parameter variations in β, G, and borrowing constraint a.
  - Proportional ±50% changes in σ across all countries moderately affect NFA and CA.
  - Country-specific parameter changes can have large effects for that country and on world interest rate if country is large (parameters β and G directly affect impatience condition).
- Market-clearing observation reiterated: a value for world interest rate fairly close to G^γ/β is needed for regions to hold positive international assets.

### VII. When precautionary savings matter for current accounts — two key instances
- A. Proximity to borrowing constraints
  - Precautionary motive strengthens exponentially as country approaches borrowing limit because negative shocks cannot be offset by further borrowing.
  - Example dynamics (world interest rate held at 3%, volatility parameters of rest of world):
    - Initial NFA a0 closer to constraint a = −1 generates larger optimal CA surpluses.
    - A country with initial NFA at the constraint a0 = −1 should run a CA surplus of more than 1% of GDP to move rapidly away from the constraint.
  - Risk of constraint tightening magnifies CA surpluses:
    - Example: constraint could tighten to −80% of GDP with 0.1 probability; this risk can greatly magnify the optimal surplus as country seeks to bring NFA above −80% of GDP quickly to avoid abrupt consumption drops.
- B. High idiosyncratic or aggregate volatility
  - Multiplying regional σ by μ_σ = 5 (higher uncertainty) increases CA imbalances substantially:
    - Example: “China-Oil-ROW” region CA surplus increases from 0.03% of GDP (benchmark μ_σ = 1) to 1.5% of GDP when μ_σ = 5.
  - Explanation: higher volatilities make regions’ optimal NFA elastic to interest rate at values well below G^γ/β, producing larger differences between the equilibrium world interest rate and rates that would keep NFA constant → larger drift in Euler equation → larger CA imbalances.
  - Justification for considering higher volatilities: idiosyncratic within-country income volatility (not captured by aggregate GDP measures) is much larger and limited domestic risk-sharing implies stronger precautionary motives (Mendoza, Quadrini and Ríos-Rull (2009); Sandri (2010)).

### VIII. Key quantitative highlights (preserved numeric values)
- Benchmark parameters:
  - R = 3%
  - G = 1%
  - borrowing constraint = 100% of GDP
  - γ = 2
  - β = 0.99
  - US estimated ρ = 0.73 and σ = 1.2% (from US 1980–2008 HP-filtered data)
- Partial equilibrium optimal NFA example: a* = −46% of GDP (benchmark).
- Region-specific estimates (Table 1 exact values):
  - US: ρ = 0.73; σ = 0.01; GDP = 14,400 (USD billions)
  - Euro Area: ρ = 0.78; σ = 0.01; GDP = 13,600 (USD billions)
  - Japan: ρ = 0.90; σ = 0.009; GDP = 4,890 (USD billions)
  - China: ρ = 0.75; σ = 0.016; GDP = 4,530 (USD billions)
  - Oil exporters: ρ = 0.77; σ = 0.03; GDP = 4,470 (USD billions)
  - Rest of the world: ρ = 0.73; σ = 0.02; GDP = 18,500 (USD billions)
- Equilibrium outcomes:
  - world interest rate that clears market: 3%
  - oil exporters predicted NFA ≈ 3 × GDP (near three times GDP); alternative CPI-deflated calibration → predicted NFA ≈ 5 × GDP
  - US, Euro Area, Japan predicted borrower positions > 30% of GDP
  - Convergence example: after 150 years oil exporters accumulate < one third of optimal holdings
  - CA magnitudes from 2007 starting positions: oil exporters CA surplus ≈ 0.1% of GDP; advanced economies deficits ≈ 0.03% of GDP
  - Two-region aggregation parameters: region A GDP 32,890 (USD billions), region B GDP 27,500 (USD billions); region A ρ = 0.78, σ = 0.011; region B ρ = 0.74, σ = 0.021
  - Constraint-tightening risk example: alternate constraint to −0.8 with probability 0.1
  - High-volatility example: μ_σ = 5 raises “China-Oil-ROW” CA surplus from 0.03% to 1.5% of GDP

### IX. Policy-relevant conclusions and research directions
- Main conclusions:
  - Heterogeneity in GDP volatility can explain a large dispersion in equilibrium NFA positions across countries, with volatile regions (oil exporters) predicted to accumulate large positive NFA and stable developed economies to be net debtors.
  - The convergence process to those targets is extremely slow, implying that heterogeneity in volatility alone cannot account for large observed current account imbalances.
  - Precautionary savings matter significantly for current accounts when countries are close to borrowing constraints or face risk of constraint tightening, and when idiosyncratic (within-country) volatility is high.
- Policy implications:
  - Interpreting large CA surpluses solely as precautionary accumulation against aggregate GDP risk is likely to be misleading unless countries are near borrowing constraints or face high idiosyncratic income risk.
  - Countries near borrowing constraints may need policies that reduce constraint risk or enhance domestic risk-sharing to avoid sharp precautionary-driven CA surpluses.
- Suggested research directions:
  - Relax the single-homogeneous-good assumption to differentiate tradable vs. non-tradable and domestic vs. foreign goods, and study how substitutability interacts with volatility heterogeneity to affect NFA and CA predictions.
  - Develop better cross-country comparable data on household income volatility and the effectiveness of domestic financial markets and fiscal policies for risk-sharing to assess idiosyncratic-risk driven precautionary motives.
  - Apply the model framework to within-Europe imbalances given good data coverage.

*Source: _wp11122 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .*

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

### _wp11122 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### I. Introduction — purpose and mechanism
- Purpose: develop a world general equilibrium model with heterogeneity across countries in GDP volatility to assess how differences in GDP volatility influence the dispersion of net foreign assets (NFA) and current account (CA) imbalances.
- Key mechanism:
  - Countries receive a stochastic GDP endowment each period (Can be consumed or lent internationally).
  - International borrowing allowed up to an exogenous limit (borrowing constraint).
  - Impatience condition: Rβ/G^γ < 1 implies a finite optimal NFA in the presence of uncertainty because impatience (borrowing desire) is counterbalanced by precautionary savings due to income volatility.
  - Optimal NFA a* defined as the level of foreign assets that is expected to be stable (if a_{t−1}=a* and Z_t = 1 then a_t = a*).

### II. Optimal NFA in partial equilibrium — calibration and sensitivity
- Benchmark parameter calibration:
  - world interest rate (risk free): 3%
  - deterministic annual growth rate: 1%
  - borrowing constraint: 100% of GDP
  - risk aversion coefficient γ: 2
  - income process estimated from HP-filtered real per capita US GDP 1980–2008: ρ = 0.73, σ = 1.2%
  - discount factor β set to 0.99 (to sustain a 3% world interest rate in general equilibrium)
- Partial equilibrium numerical result:
  - predicted optimal NFA a* = −46% of GDP under benchmark calibration.
- Sensitivity findings (partial equilibrium):
  - a* is extremely sensitive to the world interest rate R, especially as R approaches the impatience limit G^γ/β.
  - a* increases with tighter borrowing constraint, greater persistency ρ, and higher volatility σ.
  - If the impatience condition is comfortably satisfied (R well below G^γ/β), sensitivity of a* to R is weaker, and sensitivity to other parameters is reduced.

### III. World general equilibrium — setup and calibration
- Approach:
  - Solve a world general equilibrium with six regions to endogenously pin down the world interest rate that clears the international bond market.
  - To avoid stochastic world rate complications, solve as a replicated world (infinite replicas of six regions) so idiosyncratic uncertainty washes out at aggregate level.
- Regions considered: US, Euro Area, Japan, China, oil exporting countries, rest of the world.
- Region-specific GDP volatility estimates and 2008 GDP (Table 1 reproduced values):
  - US: ρ = 0.73, σ = 0.01, GDP (USD billions) = 14,400
  - Euro Area: ρ = 0.78, σ = 0.01, GDP (USD billions) = 13,600
  - Japan: ρ = 0.90, σ = 0.009, GDP (USD billions) = 4,890
  - China: ρ = 0.75, σ = 0.016, GDP (USD billions) = 4,530
  - Oil exporters: ρ = 0.77, σ = 0.03, GDP (USD billions) = 4,470
  - Rest of the world: ρ = 0.73, σ = 0.02, GDP (USD billions) = 18,500
- Common assumptions across regions in calibration:
  - borrowing constraint = 100% of GDP
  - deterministic growth rate G = 1%
  - risk aversion γ = 2, discount factor β = 0.99 (to generate a 3% equilibrium world interest rate)

### IV. Stationary equilibrium — equilibrium interest rate and predicted NFA
- Market-clearing world interest rate: 3% (value that clears aggregated net bond supply using 2008 GDP weights).
- Predicted equilibrium NFA positions at 3%:
  - Oil exporting countries: accumulate almost three times GDP (≈ 3.0 × GDP).
  - US, Euro Area, Japan: borrow more than 30% of GDP (borrower positions > 30% of GDP).
  - If using GDP deflated by CPI (alternative calibration), oil exporters’ σ rises to 7.2% and their predicted optimal NFA approaches 5 times GDP (≈ 5.0 × GDP).
- Comparison to actual 2007 NFA:
  - Model-predicted dispersion of NFA is considerably larger than 2007 observed values (Lane and Milesi-Ferretti (2007) data): current holdings of oil exporters and US debt position are small relative to model predictions; predictions for Japan and China differ in sign from observed positions.

### V. Transition dynamics — speed of convergence and CA implications
- Convergence speed: extremely slow.
  - Example: oil exporters accumulate after 150 years less than one third of their optimal asset holdings.
- Current account implications from starting at 2007 NFA positions (no GDP shocks):
  - Oil exporters run CA surplus of only 0.1% of GDP.
  - Developed economies run deficits of around 0.03% of GDP.
  - Therefore, heterogeneity in GDP volatility can yield large cross-country NFA dispersion but only small CA imbalances because equilibrium world interest rate is close to the rate that keeps 2007 NFA stable for many countries.

### VI. Sensitivity analysis (two-region aggregation and parameter variations)
- Two-region aggregation (for numerical speed):
  - Region A (US-EURO-Japan): weighted means ρ = 0.78, σ = 0.011, GDP 2008 = 32,890 (USD billions)
  - Region B (China-OIL-ROW): weighted means ρ = 0.74, σ = 0.021, GDP 2008 = 27,500 (USD billions)
- Robustness:
  - NFA targets and CA dynamics are fairly robust to common-parameter variations in β, G, and borrowing constraint a.
  - Proportional ±50% changes in σ across all countries moderately affect NFA and CA.
  - Country-specific parameter changes can have large effects for that country and on world interest rate if country is large (parameters β and G directly affect impatience condition).
- Market-clearing observation reiterated: a value for world interest rate fairly close to G^γ/β is needed for regions to hold positive international assets.

### VII. When precautionary savings matter for current accounts — two key instances
- A. Proximity to borrowing constraints
  - Precautionary motive strengthens exponentially as country approaches borrowing limit because negative shocks cannot be offset by further borrowing.
  - Example dynamics (world interest rate held at 3%, volatility parameters of rest of world):
    - Initial NFA a0 closer to constraint a = −1 generates larger optimal CA surpluses.
    - A country with initial NFA at the constraint a0 = −1 should run a CA surplus of more than 1% of GDP to move rapidly away from the constraint.
  - Risk of constraint tightening magnifies CA surpluses:
    - Example: constraint could tighten to −80% of GDP with 0.1 probability; this risk can greatly magnify the optimal surplus as country seeks to bring NFA above −80% of GDP quickly to avoid abrupt consumption drops.
- B. High idiosyncratic or aggregate volatility
  - Multiplying regional σ by μ_σ = 5 (higher uncertainty) increases CA imbalances substantially:
    - Example: “China-Oil-ROW” region CA surplus increases from 0.03% of GDP (benchmark μ_σ = 1) to 1.5% of GDP when μ_σ = 5.
  - Explanation: higher volatilities make regions’ optimal NFA elastic to interest rate at values well below G^γ/β, producing larger differences between the equilibrium world interest rate and rates that would keep NFA constant → larger drift in Euler equation → larger CA imbalances.
  - Justification for considering higher volatilities: idiosyncratic within-country income volatility (not captured by aggregate GDP measures) is much larger and limited domestic risk-sharing implies stronger precautionary motives (Mendoza, Quadrini and Ríos-Rull (2009); Sandri (2010)).

### VIII. Key quantitative highlights (preserved numeric values)
- Benchmark parameters:
  - R = 3%
  - G = 1%
  - borrowing constraint = 100% of GDP
  - γ = 2
  - β = 0.99
  - US estimated ρ = 0.73 and σ = 1.2% (from US 1980–2008 HP-filtered data)
- Partial equilibrium optimal NFA example: a* = −46% of GDP (benchmark).
- Region-specific estimates (Table 1 exact values):
  - US: ρ = 0.73; σ = 0.01; GDP = 14,400 (USD billions)
  - Euro Area: ρ = 0.78; σ = 0.01; GDP = 13,600 (USD billions)
  - Japan: ρ = 0.90; σ = 0.009; GDP = 4,890 (USD billions)
  - China: ρ = 0.75; σ = 0.016; GDP = 4,530 (USD billions)
  - Oil exporters: ρ = 0.77; σ = 0.03; GDP = 4,470 (USD billions)
  - Rest of the world: ρ = 0.73; σ = 0.02; GDP = 18,500 (USD billions)
- Equilibrium outcomes:
  - world interest rate that clears market: 3%
  - oil exporters predicted NFA ≈ 3 × GDP (near three times GDP); alternative CPI-deflated calibration → predicted NFA ≈ 5 × GDP
  - US, Euro Area, Japan predicted borrower positions > 30% of GDP
  - Convergence example: after 150 years oil exporters accumulate < one third of optimal holdings
  - CA magnitudes from 2007 starting positions: oil exporters CA surplus ≈ 0.1% of GDP; advanced economies deficits ≈ 0.03% of GDP
  - Two-region aggregation parameters: region A GDP 32,890 (USD billions), region B GDP 27,500 (USD billions); region A ρ = 0.78, σ = 0.011; region B ρ = 0.74, σ = 0.021
  - Constraint-tightening risk example: alternate constraint to −0.8 with probability 0.1
  - High-volatility example: μ_σ = 5 raises “China-Oil-ROW” CA surplus from 0.03% to 1.5% of GDP

### IX. Policy-relevant conclusions and research directions
- Main conclusions:
  - Heterogeneity in GDP volatility can explain a large dispersion in equilibrium NFA positions across countries, with volatile regions (oil exporters) predicted to accumulate large positive NFA and stable developed economies to be net debtors.
  - The convergence process to those targets is extremely slow, implying that heterogeneity in volatility alone cannot account for large observed current account imbalances.
  - Precautionary savings matter significantly for current accounts when countries are close to borrowing constraints or face risk of constraint tightening, and when idiosyncratic (within-country) volatility is high.
- Policy implications:
  - Interpreting large CA surpluses solely as precautionary accumulation against aggregate GDP risk is likely to be misleading unless countries are near borrowing constraints or face high idiosyncratic income risk.
  - Countries near borrowing constraints may need policies that reduce constraint risk or enhance domestic risk-sharing to avoid sharp precautionary-driven CA surpluses.
- Suggested research directions:
  - Relax the single-homogeneous-good assumption to differentiate tradable vs. non-tradable and domestic vs. foreign goods, and study how substitutability interacts with volatility heterogeneity to affect NFA and CA predictions.
  - Develop better cross-country comparable data on household income volatility and the effectiveness of domestic financial markets and fiscal policies for risk-sharing to assess idiosyncratic-risk driven precautionary motives.
  - Apply the model framework to within-Europe imbalances given good data coverage.

*Source: _wp11122 - References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .*

### REFERENCES

### _wp11122 - REFERENCES

### International real/business cycle literature and small open economy models
- Backus, David K., Patrick J. Kehoe, and Finn E. Kydland, 1992, “International Real Business Cycles,”Journal of Political Economy, Vol. 100, No. 4, pp. 745-775.
- Lucas, Robert E., Jr., 1987,Models of Business Cycles(Basil Blackwell, New York).
- Mendoza, Enrique G., 1991, “Real Business Cycles in a Small Open Economy,”American Economic Review, Vol. 81, No. 4, pp. 797-818.
- Clarida, Richard H., 1990, “International Lending and Borrowing in a Stochastic Stationary Equilibrium,”International Economic Review, Vol. 31, No. 3, pp. 543-558.
- Baxter, Marianne, and Mario J. Crucini, 1995, “Business Cycles and the Asset Structure of Foreign Trade,”International Economic Review, Vol. 36, No. 4, pp. 821-854.

### External imbalances, external wealth, and global imbalances
- Lane, Philip R., and Gian Maria Milesi-Ferretti, 2007, “The External Wealth of Nations Mark II: Revised and Extended Estimates of Foreign Assets and Liabilities,”Journal of International Economics, Vol. 73, No. 2, pp. 223-250.
- Fogli, Alessandra, and Fabrizio Perri, 2006, “The Great Moderation and the U.S. External Imbalance,”Monetary and Economic Studies, Vol. 24, No. S-1, pp. 209-234.
- Fogli, Alessandra, and Fabrizio Perri, 2010, “Macroeconomic Volatility and External Imbalances,”Working Paper.
- , Vincenzo Quadrini, and Jos ́e-V ́ıctor R ́ıos-Rull, 2009, “Financial Integration, Financial Development, and Global Imbalances,”Journal of Political Economy, Vol. 117, No. 3.

### Precautionary savings, uncertainty, and current account dynamics
- Ghosh, Atish R., and Jonathan D. Ostry, 1997, “Macroeconomic Uncertainty, Precautionary Saving and the Current Account,”Journal of Monetary Economics, Vol. 40, No. 1, pp. 121-139.
- Durdu, Ceyhun Bora, Enrique G. Mendoza, and Marco E. Terrones, 2009, “Precautionary Demand for Foreign Assets in Sudden Stop Economies: an Assessment of the New Merchantilism,”Journal of Development Economics, Vol. 89, pp. 194 - 209.
- Bems, Rudolfs, and Irineu de Carvalho Filho, 2009, “Current Account and Precautionary Savings for Exporters of Exhaustible Resources,”IMF Working Paper No.09/33.
- Jeanne, Olivier, and Damiano Sandri, 2010, “Precautionary Savings in the Open Economy: Exact Solution and Approximate Rules,”Working Paper.

### Risk, volatility, and financial/entrepreneurial channels
- Fern ́andez-Villaverde, Jes ́us, Pablo A. Guerr ́on-Quintana, Juan Rubio-Ram ́ırez, and Mart ́ın Uribe, 2009, “Risk Matters: the Real Effects of Volatility Shocks,”NBER Working Paper No. 14875.
- Sandri, Damiano, 2010, “Growth and Capital Flows with Risky Entrepreneuship,”IMF Working Paper No.10/37.
- Song, Zheng M., Kjetil Storesletten, and Fabrizio Zilibotti, 2009, “Growing like China,”CEPR Discussion Paper No. 7149.
- Carroll, Christopher D., 2009, “Theoretical Foundation of Buffer Stock Saving,”Unpublished Manuscript, Johns Hopkins University.

### Foundational macroeconomic texts
- Blanchard, Olivier J., and Stanley Fisher, 1989,Lectures on Macroeconomics(Cambridge, Massachusetts, London, England: The MIT Press).

*Source: _wp11122 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2011/_wp11122.pdf_