## 1. Self-fulfilling Currency Crises

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### I. Introduction — purpose and context
- Paper: theoretical study of the impact of weak institutions on currency crises from a public finance perspective.
- Motivation:
  - Empirical literature: weak institutions and corruption hinder economic performance (Mauro, 1995; Wei, 2000a; Acemoglu et al., 2001).
  - Mixed empirical evidence on corruption and currency crises (Johnson et al., 2000; Wei, 2000b; Radelet and Sachs, 1998).
- Approach:
  - Model weak institutions as inefficiency/leakage in tax collection (following Huang and Wei, 2006).
  - Embed leakage into an extended Obstfeld (1996) framework to analyze self-fulfilling currency crises and devaluation magnitudes.
- High-level preview:
  - Weak institutions generally increase likelihood of a self-fulfilling crisis equilibrium and lead to larger currency devaluations when crises occur.
  - Relationship can reverse when institutional weakness is very severe.

### II. Model framework and key mechanisms
- Government objective (loss function):
  - L = β(ε)² + γ(g - g*)² + (y - y*)² + C(ε)
- Supply side and labor technology:
  - Production Y = A N^γ, 0 < γ < 1.
  - Expectations-augmented Phillips curve (notation preserved): y = α u + ε - τ - ε^e.
- Institutional quality specification:
  - Government budget constraint: (1-φ) τ + τε = g, where 0 < φ < 1 and φ denotes degree of institutional weakness (higher φ = lower quality).
  - Interpretation: φ is a fiscal capacity index; weak institutions raise shadow price of formal tax revenue relative to inflation/seigniorage.
- Policy instruments and regimes:
  - Government chooses τ and ε after observing output shock u.
  - Fixed cost of abandoning peg denoted C(ε); without C(ε) floating would dominate.
  - Optimal policies and welfare losses derived for floating and fixed regimes (paper equations referenced).

### III. How institutional weakness affects expected depreciation and policy triggers
- Expected depreciation under floating (paper's expression, eq. (13) summarized qualitatively).
- Comparative statics condition (paper's eq. (15)):
  - Expected depreciation is larger with weaker institutions when γ(1 − φ)(3 − φ) − α² > 0.
- Interpretation and drivers making dEε_Float / dφ > 0 more likely:
  - desired public goods provision g* is high,
  - aversion to exchange rate change β is low,
  - weight on public goods provision γ is high,
  - slope of supply curve α is small.
- Reversal under extreme institutional weakness:
  - As φ → 1 required depreciation can become so large that social loss from inflation outweighs financing gains.
- Numerical example:
  - For α = γ = 1, condition holds only when φ < 0.59 (i.e., revenue leakage < 59%).
- Trigger points for realignment:
  - Cutoffs ū (for devaluation) and u̲ (for revaluation) are derived (paper's eqs. (17) and (18)).
  - Higher ε^e lowers ū, increasing probability that u > ū and devaluation occurs.
  - Key drivers lowering ū: lower realignment cost c̄, higher g*, lower β, higher γ.

### IV. Multiple equilibria and self-fulfilling crises
- Circularity: Eε depends on expectations ε^e and trigger points ū, u̲ (paper's eq. (19)).
- Equilibrium structure:
  - Up to three equilibria possible: ε1, ε2, ε3.
  - Equilibrium 3 is a purely self-fulfilling devaluation: once ε^e is high enough so that ū ≤ −μ (minimum shock), any realized shock yields devaluation; ε3 equals expected depreciation under floating (eq. (13)).
- Sufficient condition for existence of self-fulfilling equilibrium 3 (paper's eq. (20’)):
  - Inequality involves c̄, g*, γ, β, α, φ (see source for full algebra).
- Qualitative factors increasing likelihood of equilibrium 3:
  - low devaluation cost c̄,
  - high desired public goods provision g*,
  - high weight on public goods provision γ,
  - low devaluation aversion β.

### V. Institutional quality and probability of self-fulfilling crises — comparative results and simulations
- Analytical result:
  - d ū_3 / dφ derived in paper; negative slope implies weaker institutions increase probability of self-fulfilling equilibrium. Sign depends on parameters.
- Simulation parameterizations and outcomes (paper figures summarized):
  - Baseline (following Obstfeld practice):
    - α = 1, g* = 0.35, c̄ = 0.0008, β = 1, γ = 1.
    - Finding: -ū_3 is always smaller under weaker institutions → self-fulfilling crisis more likely for reasonable shock ranges.
  - Robustness check:
    - α = 0.25, other parameters same.
    - Finding: ū_3 again smaller with weaker institutions; self-fulfilling equilibrium likely when institutions weak enough.
  - Alternative calibration:
    - α = 0.25, c̄ = 0.003, γ = 0.15, other parameters as in previous case.
    - Finding: ū_3 is smaller for moderate institutional weakness but becomes larger when institutions are very weak; self-fulfilling crisis less likely when institutional problems are very severe.
- Devaluation magnitudes:
  - If equilibrium 3 occurs, mean devaluation rate will be larger for countries with weaker institutions provided condition γ(1 − φ)(3 − φ) − α² > 0 holds.

### VI. Main findings and policy-relevant insights
- Core theoretical findings:
  - Modeling weak institutions as tax revenue leakage (φ) increases incentive to rely on seigniorage (devaluation), raising probability of abandoning exchange peg.
  - Weak institutions generally increase likelihood of a self-fulfilling currency crisis equilibrium.
  - When a self-fulfilling crisis materializes, weaker institutions tend to be associated with larger devaluations, subject to condition γ(1 − φ)(3 − φ) − α² > 0.
  - Very severe institutional weakness can reverse these relationships because extremely large required devaluations increase social loss from inflation, reducing optimal depreciation and making self-fulfilling equilibrium less likely.
- Parameter sensitivities emphasized:
  - Key parameters: α (supply slope), γ (weight on public goods), β (devaluation aversion), g* (public goods target), c̄ (fixed realignment cost), φ (institutional weakness).
  - Numerical threshold example: φ < 0.59 for α = γ = 1 to ensure expected depreciation rises with weaker institutions.
- Policy-relevant implications (from model logic):
  - Improving fiscal capacity (reducing φ) reduces fiscal reliance on seigniorage and lowers the probability of self-fulfilling crises.
  - Reducing fixed costs of realignment and addressing parameters that raise government's incentive to devalue (large g*, high γ, low β) can materially affect crisis probabilities and magnitudes.

*Source: _wp0805 - 1. Self-fulfilling Currency Crises......................................................................................*

### 1. Self-fulfilling Currency Crises......................................................................................

### 1. Self-fulfilling Currency Crises

### Major sections
- 1. Self-fulfilling Currency Crises .............................................................................................10
- 2a. Simulation I ........................................................................................................................14
- 2b. Simulation II ......................................................................................................................14
- 2c. Simulation III .....................................................................................................................14

*Source: _wp0805 - 1. Self-fulfilling Currency Crises......................................................................................*

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

### _wp0805 - References..............................................................................................................

### I. Introduction — purpose and context
- Paper: theoretical study of the impact of weak institutions on currency crises from a public finance perspective.
- Motivation:
  - Empirical literature: weak institutions and corruption hinder economic performance (Mauro, 1995; Wei, 2000a; Acemoglu et al., 2001).
  - Mixed empirical evidence on corruption and currency crises (Johnson et al., 2000; Wei, 2000b; Radelet and Sachs, 1998).
- Approach: model weak institutions as inefficiency/leakage in tax collection (following Huang and Wei, 2006) and embed this in an extended Obstfeld (1996) framework to analyze self-fulfilling currency crises and devaluation magnitudes.
- High-level result preview:
  - Weak institutions generally increase likelihood of a self-fulfilling crisis equilibrium and lead to larger currency devaluations when crises occur.
  - Relationship can reverse when institutional weakness is very severe.

### II. Model framework and key mechanisms
- Objective: government minimizes loss function
  - L = β(ε)² + γ(g - g*)² + (y - y*)² + C(ε)  (represented in paper as eq. (1) with notation preserved in source).
- Supply side:
  - Production Y = A N^γ, 0 < γ < 1.
  - Expectations-augmented Phillips curve derived (eq. (4)/(6) in paper): y = α u + ε - τ - ε^e (notation preserved in source).
- Institutional quality:
  - Modeled as leakage of tax revenue; government budget constraint (eq. (7)): (1-φ) τ + τε = g, where 0 < φ < 1 and φ denotes degree of institutional weakness (higher φ = lower quality).
  - Interpretation: φ is a fiscal capacity index; weak institutions raise shadow price of formal tax revenue relative to inflation/seigniorage.
- Policy instruments and regimes:
  - Government chooses τ and ε after observing output shock u.
  - Fixed cost of abandoning peg denoted C(ε); without C(ε) floating would dominate.
  - Derived optimal policies and welfare losses under floating and fixed regimes (eqs. (8)–(12) and subsequent expressions).

### III. How institutional weakness affects expected depreciation and policy triggers
- Expected depreciation under floating (eq. (13)):
  - Eε_Float = [αγ (1 - φ)] / [βαγ φ + αγ φ - ...]  (full algebra in source; qualitative determinants summarized below).
- Comparative statics and condition for expected depreciation to increase with institutional weakness:
  - dEε_Float / dφ sign determined by condition (paper's eq. (15)):
    - γ(1 − φ)(3 − φ) − α² > 0
  - Interpretation:
    - Expected depreciation is larger with weaker institutions when γ(1 − φ)(3 − φ) − α² > 0.
    - More likely when:
      - desired public goods provision g* is high,
      - aversion to exchange rate change β is low,
      - weight on public goods provision γ is high,
      - slope of supply curve α is small.
    - Extreme institutional weakness (φ → 1) can reverse the effect because required depreciation becomes so large that social loss from inflation outweighs gain from financing public goods.
  - Numerical example: for α = γ = 1, condition holds only when φ < 0.59 (i.e., revenue leakage < 59%).

- Trigger points for realignment:
  - Cutoffs ū (for devaluation) and u̲ (for revaluation) are derived (eqs. (17) and (18)); both depend on expectation ε^e and institutional weakness φ.
  - Higher ε^e lowers ū, increasing likelihood that u > ū and devaluation occurs.
  - Key drivers lowering ū: lower realignment cost c̄, higher g*, lower β, higher γ.

### IV. Multiple equilibria and self-fulfilling crises
- Agent expectations and government reaction create circularity: Eε depends on expectations ε^e and trigger points ū, u̲ (eq. (19)).
- Equilibrium structure (figure 1 in source):
  - Up to three equilibria possible: ε1, ε2, ε3.
  - Equilibrium 3 is a purely self-fulfilling devaluation: once ε^e is high enough so that ū ≤ −μ (minimum shock), any realized shock yields devaluation; ε3 equals expected depreciation under floating (eq. (13)).
- Sufficient condition for existence of self-fulfilling equilibrium 3 (eq. (20’) in source):
  - Derived inequality involving c̄, g*, γ, β, α, φ (see source for full algebra).
  - Qualitative drivers that make existence of equilibrium 3 more likely:
    - low devaluation cost c̄,
    - high desired public goods provision g*,
    - high weight on public goods provision γ,
    - low devaluation aversion β.

### V. Institutional quality and probability of self-fulfilling crises — comparative results and simulations
- Analytical derivative:
  - d ū_3 / dφ computed in the paper (long expression). A negative slope implies weaker institutions increase probability of self-fulfilling equilibrium.
  - Sign depends on parameters; but generally weaker institutions make existence of self-fulfilling equilibrium more likely under many parameterizations.
- Parameter choices and simulation outcomes (as in paper):
  - Baseline follow Obstfeld practice:
    - α = 1, g* = 0.35, c̄ = 0.0008, β = 1, γ = 1.
    - Simulation (Figure 2a): -ū_3 is always smaller under weaker institutions → self-fulfilling crisis more likely for reasonable shock ranges.
  - Robustness check (Figure 2b):
    - α = 0.25, other parameters same → ū_3 again smaller with weaker institutions; self-fulfilling equilibrium likely when institutions weak enough.
  - Alternative calibration (Figure 2c):
    - α = 0.25, c̄ = 0.003, γ = 0.15, other parameters as in Figure 2b → ū_3 is smaller for moderate institutional weakness but becomes larger when institutions are very weak; existence of self-fulfilling crisis less likely when institutional problems are very severe.
- Implications for devaluation magnitudes:
  - If equilibrium 3 occurs, mean devaluation rate will be larger for countries with weaker institutions provided condition γ(1 − φ)(3 − φ) − α² > 0 holds.

### VI. Main findings and policy-relevant insights
- Primary theoretical findings:
  - Weak institutions modeled as tax revenue leakage (φ) increase incentive to rely on seigniorage (devaluation), raising probability of abandoning exchange peg.
  - Weak institutions generally increase likelihood of a self-fulfilling currency crisis equilibrium.
  - When a self-fulfilling crisis materializes, weaker institutions tend to be associated with larger devaluations, subject to condition γ(1 − φ)(3 − φ) − α² > 0.
  - Very severe institutional weakness can reverse these relationships because extremely large required devaluations increase social loss from inflation, reducing optimal depreciation and making self-fulfilling equilibrium less likely.
- Parameter sensitivities emphasized:
  - Key parameters: α (supply slope), γ (weight on public goods), β (devaluation aversion), g* (public goods target), c̄ (fixed realignment cost), φ (institutional weakness).
  - Numerical thresholds: example φ < 0.59 for α = γ = 1 to ensure expected depreciation rises with weaker institutions.
- Conceptual policy implications (drawn from model logic in source):
  - Improving fiscal capacity (reducing φ) reduces fiscal reliance on seigniorage and lowers the probability of self-fulfilling crises.
  - Reducing fixed costs of realignment and addressing parameters that raise government's incentive to devalue (large g*, high γ, low β) can materially affect crisis probabilities and magnitudes.

*Source: _wp0805 - References (text of paper provided in source PDF).*

### References

### _wp0805 - References

### Monetary and Fiscal Policy; Rules and Theory
- Alesina, Alberto and Tabellini, Guido, 1987, "Rules and Discretion with Noncoordinated Monetary and Fiscal Policies." Economic Inquiry, August, 25(4), pp.619–30.
- Barro, Robert J., and David B. Gordon, 1983, "A positive theory of monetary policy in a natural rate model." Journal of Political Economy 91, 589–610.
- Huang, Haizhou, and Shang-Jin Wei, 2006, "Monetary Policy for Developing Countries: The Role of Institutional Quality." Journal of International Economics 79: 239–252.

### Currency Crises and Exchange-rate Models
- Krugman, Paul, 1979, "A Model of Balance of Payment Crises." Journal of Money, Credit and Banking (11): 311–325.
- Obstfeld, Maurice, 1994, "The Logic of Currency Crises." Cahiers Ecolnomiques et Monetarires (Banque de France) 43: 189–213.
- Obstfeld, Maurice, 1996, "Models of Currency Crises with Self-fulfilling Features." European Economic Review, Vol. 40, 1037–1047.
- Obstfeld, Maurice, 1997, "Destabilizing Effects of Exchange-rate Escape Clauses." Journal of International Economics (43): 61–77.

### Corruption, Governance, and Investment
- Mauro, Paolo, 1995, "Corruption and Growth." Quarterly Journal of Economics, 110: 681–712.
- Wei, Shang-Jin, 2000a, "How Taxing is Corruption on International Investors?" Review of Economics and Statistics, February, 82(1): 1–11.
- Wei, Shang-Jin, 2000b, "Local Corruption and Global Capital Flows," Brookings Papers on Economic Activity, 2000(2).

### Corporate Governance and the Asian Financial Crisis
- Johnson, Simon, Peter Boone, Alasdair Breach, and Eric Friedman (2000), "Corporate Governance in the Asian Financial Crisis." Journal of International Economics (58)1–2: 141–186.
- Radelet, Steven, and Jeffrey D. Sachs, "The East Asian Financial Crisis: Diagnosis, Remedies, Prospects." Brookings Papers on Economic Activity, 1998 (1), pp.1–90.

*Source: _wp0805 - References*

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