## 2.1 Theory

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---

### Role and motivation
- Recent academic and policy debate has reconsidered controls on cross-border capital flows as potential stabilization devices, especially for inflows; the IMF’s Institutional View (IV) endorses use of inflow CFMs during inflow surges and, more recently, prudential use even absent surges when stock vulnerabilities exist.
- Controls on capital outflows (CCOs) have been largely neglected in theory and policy discussions, with a widespread belief that CCOs are expropriatory or the product of corrupt/opportunistic governments (Bartolini and Drazen (1997) referenced).
- Paper’s question: whether CCOs can be socially useful to forestall financial panic; analyzes CCOs from empirical and theoretical perspectives.

### Empirical stylized fact motivating theory
- New panel evidence assembled for the largest set of countries available indicates:
  - Episodes of strong CCO tightening coincide with macroeconomic and financial stress.
  - Stress characterized by a steep fall in GDP growth and rising indicators of banking and currency crises that begin to rise before CCO episodes.
  - Other concurrent symptoms include falling capital flows, current account reversals, and large depreciations of the currency.
- Empirical result summarized as: CCOs are usually deployed in response to crises and declining growth.

### Theoretical rationale: coordination failures and multiple equilibria
- Model environment:
  - Small open economy with foreign investor coordination failures that can produce financial panics and capital flight episodes (multiple equilibria).
  - CCOs can act as coordination devices that eliminate undesired equilibria (capital flight equilibria) and ensure a no-capital-flight equilibrium aligned with fundamentals.
  - Anticipation of contingent CCO application can improve ex ante expected returns and attract more foreign investment.
- Modeling foundations: builds on and adapts elements from Diamond and Dybvig (1983), Holmström and Tirole (2001), and related international finance models (e.g., Bocola and Lorenzoni (2020); Schmitt-Grohé and Uribe (2021)).

### Costs, trade-offs, and normative implications
- Model allows for deadweight losses associated with implementing CCOs, intended to capture:
  - Adverse effects on investor confidence.
  - Broader distortions such as “promoting rent-seeking behavior and corruption, facilitating repression of the financial sector, impeding financial development and distorting the allocation of capital” (IMF 2012a).
- Key normative findings:
  - CCOs can be welfare-improving if the probability of a financial crisis would be large in their absence.
  - Large enough deadweight losses render CCOs unadvisable; the analysis characterizes precisely what “large enough” means in model terms.
  - Even when CCOs can prevent self-fulfilling crises, it is not always optimal to implement them because of associated costs.

### Time inconsistency and commitment issues
- Optimal CCO policy under commitment can be time inconsistent:
  - Contingent CCO policies enhance ex ante returns and investment, but ex post incentives for a government to impose CCOs (or not) can change once initial investments are sunk.
  - Time inconsistency implies welfare-enhancing properties of CCOs may be available only if the government has sufficient credibility.
- Connects to literature on time consistency (Kydland and Prescott (1977); Calvo (1978)); novel application to CCO policy.

### Political opportunism and reputation effects
- Setup: honest, benevolent government may be indistinguishable ex ante from opportunistic government that always imposes capital controls.
- Main results:
  - Benefits from CCO policy increase in the government’s reputation (investors’ prior belief the government is benevolent).
  - Implementation of CCOs may have adverse effects on the honest government’s reputation; in dynamic settings, an honest government may refrain from imposing CCOs when they would be socially desirable to preserve reputation.
  - Differentiates from prior signaling models (e.g., Bartolini and Drazen (1997)) by assuming CCOs can be socially beneficial; reputation deterioration arises from misuse, not from use per se.

### Contribution relative to existing literature
- Adds a coordination-failure rationale for CCOs to literature emphasizing pecuniary and aggregate demand externalities as justifications for capital controls.
- Extends prior work by explicitly modeling practical implementation challenges: deadweight losses, imperfect credibility, and lack of commitment.
- Documents novel results:
  - CCOs can eliminate bad equilibria but need not be optimal.
  - CCO policies can be time inconsistent.
  - Reputation-building concerns can prevent socially beneficial use of CCOs.

*Source: wpiea2024164-print-pdf (section 2.1 Theory) from the provided IMF Working Paper content.*

### 2.1 Theory .............................................................................................................

### 2.1 Theory

### Role and motivation
- Recent academic and policy debate has reconsidered controls on cross-border capital flows as potential stabilization devices, especially for inflows; the IMF’s Institutional View (IV) endorses use of inflow CFMs during inflow surges and, more recently, prudential use even absent surges when stock vulnerabilities exist.
- Controls on capital outflows (CCOs) have been largely neglected in theory and policy discussions, with a widespread belief that CCOs are expropriatory or the product of corrupt/opportunistic governments (Bartolini and Drazen (1997) referenced).
- The paper asks whether CCOs can be socially useful to forestall financial panic and proposes to analyze CCOs from both empirical and theoretical perspectives.

### Empirical stylized fact motivating theory
- New panel evidence assembled for the largest set of countries available indicates:
  - Episodes of strong CCO tightening coincide with macroeconomic and financial stress.
  - Stress is characterized by a steep fall in GDP growth and rising indicators of banking and currency crises that begin to rise before CCO episodes.
  - Other concurrent symptoms include falling capital flows, current account reversals, and large depreciations of the currency.
- Empirical result summarized as: CCOs are usually deployed in response to crises and declining growth.

### Theoretical rationale: coordination failures and multiple equilibria
- The paper develops a model of a small open economy where:
  - Foreign investor coordination failures can produce financial panics and capital flight episodes (multiple equilibria).
  - CCOs can act as coordination devices that eliminate undesired equilibria (capital flight equilibria) and ensure a no-capital-flight equilibrium aligned with fundamentals.
  - Anticipation of contingent CCO application can improve ex ante expected returns and attract more foreign investment.
- The modeling approach builds on and adapts elements from Diamond and Dybvig (1983), Holmström and Tirole (2001), and related international finance models (e.g., Bocola and Lorenzoni (2020); Schmitt-Grohé and Uribe (2021)).

### Costs, trade-offs, and normative implications
- The model allows for deadweight losses associated with implementing CCOs, intended to capture:
  - Adverse effects on investor confidence.
  - Broader distortions such as “promoting rent-seeking behavior and corruption, facilitating repression of the financial sector, impeding financial development and distorting the allocation of capital” (IMF 2012a).
- Key normative findings:
  - CCOs can be welfare-improving if the probability of a financial crisis would be large in their absence.
  - Large enough deadweight losses render CCOs unadvisable; the analysis characterizes precisely what “large enough” means in model terms.
  - Even when CCOs can prevent self-fulfilling crises, it is not always optimal to implement them because of associated costs.

### Time inconsistency and commitment issues
- Optimal CCO policy under commitment can be time inconsistent:
  - While contingent CCO policies enhance ex ante returns and investment, ex post incentives for a government to impose CCOs (or not) can change once initial investments are sunk.
  - Time inconsistency implies welfare-enhancing properties of CCOs may be available only if the government has sufficient credibility.
- This time-inconsistency finding connects to the broader literature on time consistency (Kydland and Prescott (1977); Calvo (1978)) and is novel in the context of CCO policy.

### Political opportunism and reputation effects
- The paper analyzes an honest, benevolent government when investors may believe the government could be opportunistic and always impose capital controls. Main results:
  - Benefits from CCO policy are increasing in the government’s reputation (investors’ prior belief the government is benevolent).
  - Implementation of CCOs may have adverse effects on the honest government’s reputation; in dynamic settings, an honest government may refrain from imposing CCOs when they would be socially desirable to preserve reputation.
  - The analysis differs from prior signaling models (e.g., Bartolini and Drazen (1997)) by assuming CCOs can be socially beneficial; deterioration of reputation arises from misuse, not from use per se.
- Related evidence and models cited: Clayton et al. (2022), Acosta-Henao et al. (2020), Ghosh et al. (2020), Schmitt-Grohé and Uribe (2021), Fornaro (2022).

### Contribution relative to existing literature
- Adds coordination-failure rationale for CCOs to the growing literature that emphasizes pecuniary and aggregate demand externalities as justifications for capital controls.
- Extends prior work by explicitly modeling practical implementation challenges: deadweight losses, imperfect credibility, and lack of commitment.
- Documents novel results: CCOs can eliminate bad equilibria but need not be optimal; CCO policies can be time inconsistent; reputation-building concerns can prevent socially beneficial use of CCOs.

_Italic line: Source: wpiea2024164-print-pdf (section 2.1 Theory) from the provided IMF Working Paper content._

### 2.2 Empirics

### 2.2 Empirics

### Contribution to the empirical literature on capital controls
- Builds on earlier measures of capital controls including Quinn (1997), Quinn and Toyoda (2008), Chinn and Ito (2002, 2006), Schindler (2009), Klein (2012), Fernández et al. (2015, 2016), Binici and Das (2021), and Acosta-Henao et al. (2020).
- Highlights limitations of broad de jure indices (Quinn; Chinn-Ito) for studying outflow restrictions because they do not disaggregate by direction of flows.
- Leverages granular, direction-specific datasets (Schindler 2009; Fernandez et al. 2016; Binici and Das 2021; Acosta-Henao et al. 2020) to systematically characterize the use of outflow controls and document the persistence of CCOs.
- Positions the paper’s model as a framework that can rationalize mixed empirical findings by jointly considering benefits and costs of capital outflow controls (CCOs), incorporating credibility, commitment, and investors’ coordination failures.

### Prior empirical findings on effectiveness of outflow controls (literature synthesis)
- Empirical evidence on outflow controls is sparse and mixed (surveys: Erten et al. (2021); Rebucci and Ma (2020)).
- Examples and contrasting assessments:
  - Malaysia 1998–99: cited as a prominent case argued effective by some (Krugman 1999) but criticized by others (Dornbusch 2001; Johnson and Mitton 2003).
  - Forbes and Klein (2015): across episodes in 1997–2001 and 2007–11, conclude controls did not yield significant improvements in growth, unemployment, and inflation; may have caused significant decline in GDP growth.
  - Magud et al. (2018): mixed results; some episodes (Malaysia, Spain, Thailand) reduced outflow volumes and aided monetary policy independence; less systematic evidence for switching flows to longer maturities.
  - Binici et al. (2010): debt and equity controls can substantially reduce outflows; only high-income countries appear able to impose debt outflow controls.
  - Ben Zeev (2017): outflow controls have no significant shock-absorbing capacity after large external shocks, unlike inflow controls.
  - Saborowski et al. (2014): tightening outflow restrictions effective only with strong macro fundamentals or good institutions, or when restrictions are already comprehensive; otherwise can provoke sizable decline in gross inflows driven by foreign investors.
  - Bhargava et al. (2023): blunt tools (bans, limits) imposed during crises but no systemic evidence they curbed resident or non-resident outflows; may have triggered further sovereign rating downgrades.

### Data sources and measurement strategy used in this paper
- Uses three complementary sources to identify forceful CCO episodes:
  - IMF study on managing capital outflows (IMF 2012b) identifying "significant tightening of outflow controls" between 1998 to 2009.
  - Fernandez et al. (2016) dataset: covers 100 countries from 1995 to 2019; codes AREAER capital account regulation over 10 asset categories, distinguishing direction of flow and residency.
  - Binici and Das (2021): uses IMF’s Taxonomy of Capital Flow Management Measures to capture monthly changes in CFMs since 2012.
- Identification criterion for forceful CCO episodes:
  - A positive change in the index of CCOs (i.e., a tightening) that is greater than or equal to two and a half standard deviations, computed over the entire distribution of positive changes across countries and time.
- Rationale:
  - Combination of sources captures all publicly available measures of CCOs that have been officially identified by the IMF as macro-critical tightenings, while Fernandez et al. (2016) provides broader asset-level granularity.

### Sample, episode statistics, and classification
- Total identified CCO episodes: 31 separate CCO episodes over 26 countries.
- Temporal spread: somewhat uniformly spread between 1998 and 2020.
- Income-level composition of episodes:
  - 8 from high income countries
  - 9 from upper-middle income countries
  - 9 from lower-middle income countries
  - 5 from low income countries
- Exchange rate regime distribution (Ilzetzki et al. (2021) classification):
  - no legal tender: 11 episodes
  - pegs: 8 episodes
  - crawling pegs: 6 episodes
- Detailed episode lists and distributions are reported in the Empirical Appendix (Table A.1; Figs. A.5–A.7).

### Empirical approach and variables analyzed
- Event study plots averaging across episodes and regression analysis to document comovement of CCO episodes with macro variables.
- Main focus: systematic relationship between CCO episodes, real GDP, and macro-financial crises indicators.
- Real GDP: sourced from WEO (IMF 2022); country-specific trends isolated by calculating average growth for each country and de-meaning the series.
- Banking and currency crises indices: from Laeven and Valencia (2018).
- Additional macro variables examined (results in Empirical Appendix): aggregate consumption and investment; capital flows; current account balance; exchange rates; inflation. Sources: WEO and WDI.

### Main empirical stylized fact (preview for modeling)
- Primary finding: CCO tightening episodes are associated with macroeconomic and financial stress — they coincide with a steep fall in GDP growth and the occurrence of banking and currency crises.
- Role for the model: this stylized fact is incorporated as a key building block of the theoretical model developed in later sections to jointly consider benefits and costs of CCOs and to guide empirical analysis of effectiveness, including elements of credibility, commitment, and investors’ coordination failures.

*Source: wpiea2024164-print-pdf - 2.2 Empirics*

### 3.2 Stylized Facts

### 3.2 Stylized Facts

### Macro dynamics around CCO tightenings (Figure 1)
- Episodes: 31 episodes of forceful CCO tightening identified (t = 0 is the year of the episode).
- GDP growth dynamics (demeaned, ten years around episodes):
  - Episodes of CCO tightening coincide with steep falls in GDP growth of about 4 percentage points on average (3 percent in medians).
  - In the year preceding a CCO episode, average (median) GDP growth is above trend growth by about (slightly below) 1 percentage.
  - Growth falls steeply to -3 percent on average (-2 percent in medians) in the year of a CCO episode.
  - Recovery is protracted: average (median) growth rises above trend only two years after the CCO episode.
- Additional co-movements documented in the Empirical Appendix (Figs. A.8-A.9):
  - Falling net and gross capital inflows, particularly in FDI.
  - Gross outflows slow down, particularly in portfolio and FDI.
  - Large reversals in the current account balance.
  - Stagnant consumption and investment.
  - Depreciating currencies and inflation spikes.
- Interpretation: Large CCO tightenings are coincident with periods of macro-financial stress.

### Crisis indicators and timing (Figure 2)
- Sample: 30 episodes for which Laeven and Valencia (2018) crisis indicators exist (one of the 31 episodes lacks this data).
- Crisis indicator spikes coincident with CCO episodes:
  - Banking crisis indicator spikes at 30%.
  - Currency crisis indicator peaks at 25%.
- Both crisis indicators start increasing one year before the CCO episode materializes (i.e., begin rising at t = -1).
- Overall implication: CCOs are implemented when crises have already begun unfolding.

### Regression analysis linking GDP growth and CCO episodes (Table 1)
- Regression specification: Y_{i,t} = β GDP gr_{i,t} + α X_{i,t−1} + ε_{it}, where Y_{i,t} = 1 if country i experienced a CCO episode in year t; GDP gr_{i,t} is demeaned real growth rate; X_{i,t−1} includes lagged macro controls, country fixed effects, time trends, exchange rate regime, inflation, CA balance, gross and net capital flows, consumption and investment growth. In one specification, Laeven and Valencia (2018) crisis indicators are added (not lagged).
- Estimated β-coefficients for GDP growth across five specifications:
  - Column (1): -0.000621***
  - Column (2): -0.000636***
  - Column (3): -0.000690***
  - Column (4): -0.00223***
  - Column (5): -0.00172***
- Crisis indicator coefficients (column 5):
  - Banking Crisis: 0.140***
  - Currency Crisis: 0.120***
- Additional table details (as reported):
  - Country F.E: columns 2–5 included (indicated as 7 in table layout for columns 3–5)
  - Trend (linear and Quad.): included in columns 3–5
  - Macro Controls (lagged): included in columns 4–5
  - Observations: 50, 145, 0, 1450, 1428, 772, 494 (table layout shows Observations row as "50145014501428772494" — preserve numeric string as presented in source table)
  - Countries: 193 193 193 143 143
  - Episodes: 31 31 31 22 22
  - Years: 1995-2021    1995-2021    1995-2021   1995-2020   1995-2017
  - Adjusted R2: 0.002 0.008 0.008 0.020 0.097
- Key takeaways:
  - GDP growth systematically correlates negatively with CCO episodes; the negative β is statistically significant at 1% across specifications.
  - Adding macro controls increases the absolute value of the estimated β.
  - The negative link between growth and CCO episodes remains after controlling for banking and currency crises; those crisis indicators are positively correlated with CCO episodes.

### Probit marginal effects and economic magnitude
- Estimated marginal effects (probit, Empirical Appendix Table A.3):
  - A 1% decrease in GDP growth coincides with an increase in the probability of having a CCO episode by 1.1%.
  - Unconditional probability of a CCO episode is 6.7%.
  - The 1.1% increase implies an increase of around 16.4% (1.1/6.7).

### Causality exploration and counterfactuals
- Timing from Figures 1 and 2 suggests: crisis indicators worsen first, followed by declines in GDP growth and then CCO tightenings as a response.
- Alternative hypothesis (CCOs cause growth/currency/banking crises) examined via a counterfactual 2-stage procedure in the Appendix:
  - Stage 1: Recover CCO shocks by removing the systematic component in CCO indices associated with lagged macroeconomic activity.
  - Stage 2: Use CCO shocks as regressors of contemporary GDP growth; obtain fitted GDP growth assuming only CCO shocks are turned on.
  - Result: Simulated GDP growth barely moves in CCO episodes, indicating CCO shocks have negligible impact on the deep fall in GDP growth documented in Figure 1.

### Robustness checks and additional empirical observations
- Alternative thresholds for identifying CCO episodes:
  - Thresholds of 2 and 1.5 standard deviations deliver similar results regarding the fall in GDP coincident with such episodes (see Figure A.20).
- Persistence:
  - Dynamics of CCO indices in identified episodes show strong persistence in the use of these tools in periods after tightening episodes materialize (Figure A.21).
- Robustness to specification choices:
  - Results robust to using time fixed effects, controlling for the level of development, and adding Driscoll and Kraay standard errors (Tables A.4, A.5, A.7–A.9).
- Residency disaggregation (subset analysis):
  - Analysis on subset of 21 CCO episodes where an index from Fernandez et al. (2016) exists (allows disaggregation by residency):
    - 12 of the 21 cases: CCOs are characterized by tightening of outflows from non-residents.
    - In 16 episodes: CCO episodes involve a tightening in CCO to residents.
- Overall interpretation: Evidence suggests crises trigger both a fall in economic activity and the deployment of CCOs; these empirical facts are used as building blocks in the subsequent theoretical framework.

*Source: wpiea2024164-print-pdf - 3.2 Stylized Facts*

### 4.3 Equilibrium Under Laissez Faire

### 4.3 Equilibrium Under Laissez Faire

### Equilibrium concept and main result
- Equilibria are strategies for individual investors and an aggregate outcome such that, given the aggregate outcome, strategies are optimal for each investor and the aggregate outcome is induced by those strategies together with maintained assumptions.
- p denotes the exogenous probability of a capital flight during a fragile state at t = 1.
- Proposition 1 (Equilibrium under Laissez Faire): Assume ω < 1. Then, under laissez faire, for any given p such that 0≤p≤1 there is an equilibrium in which capital flight occurs with probability pq.
- The condition f(1) > ω is sufficient for an equilibrium with both continuation outcomes to exist; the paper shows this condition holds in equilibrium for any pq provided ω < 1.

### Continuation at t = 1: fragile vs normal states
- At t = 1 the project size I_0 and individual investor contribution i = I_0 − A are taken as given.
- If state is normal: no further changes, at t = 2 project size is I_0 and each foreign investor is paid R I_0.
- If state is fragile: two possible continuation equilibria
  - If all investors believe others will exit (λ = 0), individual payoff from staying is f(0) i = 0 which is less than ω i since ω > 0. Equilibrium: all investors exit.
  - If all investors stay, individual payoff from staying is f(1) i; an investor stays if R I_0 i is greater than ω (i.e., if f(1) > ω). Equilibrium: all investors stay when f(1) > ω.
- A threshold λ̄ is defined by f(λ̄) = ω; for λ < λ̄ investors optimally liquidate, for λ ≥ λ̄ investors optimally stay.

### Treatment of multiplicity and role of p
- When both continuation equilibria exist in the fragile state, the analysis assumes the “run” continuation occurs with probability p (treated as exogenous), acknowledging p may depend on history, institutions, or other unmodeled aspects.

### Determination of initial investment under laissez faire
- From t = 0, expected payoff to an investor in laissez-faire (LF) is
  - Π_LF = pq ω i + (1 − pq) R I_0
- Interpretation:
  - At t = 1 the state is fragile with probability q, and in such a state all investors will exit with probability p; hence probability pq that investment ends with exit and payoff ω i.
  - With probability 1 − pq the project completes and each investor receives R I_0.
- Investors join initially only if Π_LF ≥ i; in equilibrium Π_LF = i (country chooses project size as large as possible).
- Using i = I_0 − A yields the equilibrium condition pq ω (I_0 − A) + (1 − pq) R I_0 = I_0 − A, i.e. I_0 = L A, where the leverage coefficient L is
  - L = [1 − pq ω] / [1 − pq ω − (1 − pq) R]
- Notes on L:
  - L > 1 provided pq is sufficiently small (assumed).
  - L < 1/(1 − R), so initial investment is smaller than in the first-best subsection.
  - The leverage ratio L falls with pq (probability of capital flight): the possibility of capital flight reduces pledgeable income and hence initial borrowing and project size.

### Country payoff under laissez faire
- Final size I_2 = 0 if there is capital flight, and I_2 = I_0 otherwise.
- Expected payoff to the country:
  - E(B I_2) = B (1 − pq) I_0 = B (1 − pq) L A
- Capital flight reduces welfare by: (i) lowering initial project size via reduced pledgeable income; and (ii) with probability pq wiping out the project.

### Existence of equilibrium with capital flight (Proposition 1 restated)
- Provided ω < 1, f(1) > ω holds in equilibrium for any pq because f(1) = (1 − qp ω)/(1 − qp) in equilibrium, a fraction strictly greater than one when ω < 1. Hence an equilibrium with capital flight exists as described.

*Source: wpiea2024164-print-pdf - 4.3 Equilibrium Under Laissez Faire*

### 6.1 Optimal Policy with Commitment

### 6.1 Optimal Policy with Commitment

### Key condition for preferring capital controls
- Capital controls eliminate capital flight and are superior to laissez faire if
  (1−qφ) [ 1 1−(1−qφ)R ] > (1−pq) 1−pqω 1−pqω−(1−pq)R
  (equation (5))
- We assume capital controls satisfy Propositions 2 and 3, so they eliminate capital flight.

### Comparative statics and intuition
- The optimal committed strategy depends on the pair {φ, p}:
  - For combinations of {φ, p} to the left of the blue locus in Figure 5 (φ relatively large or p relatively small), a committed government prefers laissez faire.
  - For combinations to the right (φ relatively small or p relatively large), a committed government imposes capital controls (CCOs) in the fragile state.
- Intuition:
  - Benefit of CCOs: eliminate the capital flight equilibrium; more valuable the higher p, the probability of capital flight in the fragile state.
  - Cost of CCOs: deadweight loss φ; if φ is large, better to risk capital flight than incur φ.

### Illustrative cases (Figure 6)
- φ = 0:
  - Capital controls are costless and imposed for all p; economy reaches first best.
- φ > 0:
  - There exists a threshold ̄p(φ) such that:
    - If p < ̄p(φ): government prefers laissez faire; the country’s expected payoff falls with p (higher exit risk).
    - If p > ̄p(φ): government imposes capital controls; risk of capital flight is eliminated and expected payoff is independent of p.

*If the government can commit at t = 0, it chooses CCOs when p is relatively large and φ is relatively small.*

---

### 6.2 Discretionary CCO policy

### Time consistency question
- Investors’ initial investment I0 and expected benefits BE(I2) depend on expectations at t = 0 about whether capital controls will be imposed if the fragile state occurs.
- If the government can reconsider at t = 1 (when fragile state occurs), the optimality of CCOs may change because I0 is sunk.

### Definition of discretionary equilibrium
- Government chooses π ∈ {L (laissez faire), CCO (capital controls eliminating flight)}.
- A discretionary equilibrium requires policy π to be optimal for the government at t = 1 in the fragile state, given investor strategies and aggregate outcome.

### Proposition 4 (CCO Policy in a Discretionary Equilibrium)
- A discretionary government chooses π = CCO in equilibrium only when
  p > φ
  (equation (6))

### Interpretation
- At t = 1:
  - No CCOs: capital flight occurs with probability p → expected final project size EI2 = (1−p)I0.
  - With CCOs: capital flight eliminated, final project size I2 = (1−φ)I0.
  - Implement CCOs if p > φ.
- Comparison with commitment condition (equation (5)) shows governments generally have an incentive to deviate at t = 1 from the committed optimal policy.

### Consequences
- Corollary: The optimal commitment policy can be time inconsistent.
- Figure 7 illustrates that including time-consistent (discretionary) policies expands the set of {φ, p} combinations where CCOs are actually imposed:
  - For fixed φ, if φ < p < ̄p (between the red and blue lines), a government may announce at t = 0 that it will not impose CCOs but renege at t = 1 if the fragile state occurs.
- Anticipation of reneging reduces initial project size I0 and therefore can lower expected payoff under discretion relative to commitment (Figure 8, right panel).

---

### 6.3 Discussion (Time inconsistency and policy credibility)

### Main insights
- Time inconsistency often arises in models of optimal CCO policy because anticipated CCO policy affects ex ante expected returns, while ex post incentives differ once investments are sunk.
- Policymakers (even benevolent ones) may be tempted to break initial promises when ex post benefits differ from ex ante incentives — a Kydland and Prescott (1977) / Calvo (1978)–type problem.

### Implications for arguments in the CCO debate
- Claims that CCOs are beneficial provided “the rules of the game are clear and known ahead of time” are valid only if pre-announced policies are time consistent.
- Ways to address time inconsistency (sketch):
  - Establish rules or institutions that remove discretion from policymakers (e.g., aspects of international agreements or the IMF’s IV could act as credibility-enhancing “rules”).
  - Specify circumstances under which CCOs should not be used; preventing unjustified use may be the most important element of a rule.
  - Note: temptation to renege can arise even without bad motives (government modeled as benevolent).

---

### 7 Capital Controls and Political Opportunism

### Modeling opportunism
- Government can be honest or opportunist; opportunist government always imposes capital controls.
- In one interpretation, φI0 is expropriation appropriated by opportunist policymaker rather than a deadweight loss; opportunist always uses CCOs.

### Equilibrium notion (politico economic equilibrium)
- Consists of government policy π, investor strategies, and aggregate outcome such that:
  - Investors’ strategies are optimal given outcome, policy, and prior belief β.
  - Aggregate outcome is induced by investor strategies and policy.
  - Policy is optimal for the honest government at t = 1 in the fragile state.

### Proposition 5 (Optimality of CCOs under political opportunism)
- A politico economic equilibrium with π = CCO and no capital flight exists if both conditions hold:
  - p > φ
  - ω < 1 (1−β)(1−φ) +β(1−qφ)
- Intuition:
  - At t = 0 investors believe government honest with probability β and opportunist with probability 1−β.
  - Expected payoff from participating when CCOs may occur is ΠCC = [q(1−φ) + (1−q)]RI0.
  - Market-clearing implies
    I0 − A = βΠCC + (1−β)R(1−φ)I0
    which simplifies to
    I0 = 1 1−[1−(βq+ (1−β))]φ]R A
- Key comparative statics:
  - Initial project size I0 is smaller than in the absence of opportunism; the shortfall increases as β falls.
  - Probability that capital controls occur is βq + (1−β) = q + (1−β)(1−q) > q, so opportunism raises expected incidence of CCOs and reduces pledgeable income.
  - β enters I0 and thus affects investors’ rate of return f(λ) of staying at t = 1.

---

### 8 Capital Controls, Credibility, and Reputation Building

### Reputation channel
- I0 and country payoff increase with β, investors’ prior probability that the government is honest.
- An honest government can try to raise β through actions that signal honesty; reputation building links to capital controls choices.

### Observability and updating
- If investors do not observe government type or state at t = 1 but do observe whether CCOs were imposed:
  - If no CCOs observed at t = 1, investors infer government is honest for sure (opportunist always imposes controls).
  - If CCOs observed, posterior probability government is honest equals
    β q q+ (1−β)(1−q)
    which is strictly less than β.
- Honest government suffers reputation loss when imposing CCOs; this may make it more reluctant to impose CCOs even when justified ex post, if it cares about future interactions.

### Dynamic extension (two-stage model)
- To study reputation effects formally, consider a two-stage repeated economy where first-stage outcomes affect second-stage investor beliefs (β) — each stage follows the static model described earlier.

---

*Italic: Source — wpiea2024164-print-pdf - 6.1 Optimal Policy with Commitment (canonical PDF).*

### 8.1 Repetition and Reputation Building

### 8.1 Repetition and Reputation Building

### Model setup and key assumptions
- The model of the previous sections is repeated twice; each repetition is called a "stage". Each stage has three periods indexed by t = 0,1,2; stages are denoted with a "(s)" superscript for s = 1,2. Example: I(2)0 denotes the project size at the beginning of the second stage (i.e. at t = 0 of s = 2).
- Concreteness assumptions:
  - The government has no commitment power.
  - Lack of commitment has no adverse implications in the stage model (the imposition of capital controls in the fragile state is both optimal and time consistent), which requires, in particular, that p > φ.
  - The government’s total (two-stage) payoff is the sum of payoffs in the two stages (no discounting between stages).

### Second-stage outcomes (dependence on reputation)
- The second stage is identical to the static model analyzed earlier; outcomes depend on the government's reputation at the start of the second stage, β(2).
- Initial project size at start of second stage:
  - I(2)0 = L(β(2))A
  - Leverage ratio: L(β(2)) = 1 / [1 − [1 − (β(2) q + (1 − β(2))) φ] R]
- Comparative statics:
  - dI(2)0 / dβ(2) = (L(2))^2 (1−q) φ R A > 0
- Benevolent government’s expected payoff in second stage:
  - Π(2)(β(2)) = B(1−qφ) I(2)0 = B(1−qφ) L(β(2)) A
- Summary: leverage, investment, and expected welfare in the second stage increase with β(2), the investors’ belief that the government is benevolent.

### First-stage decision in fragile state and reputational trade-off
- In the first stage, when the state is fragile at t = 1:
  - Imposing capital controls rules out the capital flight equilibrium but imposes a deadweight loss of φ, yielding first stage payoff B(1−φ) I(1)0.
  - Because p > φ, capital controls yield a higher first stage payoff than laissez faire.
- Reputation channel: imposing capital controls in the first stage affects β(2) and thus second-stage outcomes and payoffs.
- Notation:
  - Let β(2)CC denote the posterior belief about β at the end of the first stage if capital controls are observed.
- Benevolent government's total (two-stage) payoff from imposing capital controls in first stage (fragile state):
  - B(1−φ) I(1)0 + Π(2)(β(2)CC)
- If government does not impose controls in fragile state of first stage:
  - With probability p there is a run, yielding first-stage payoff B(1−p) I(1)0.
  - Investors infer the government is honest (β = 1) with probability one, so continuation payoff is Π(2)(1).
- The honest government imposes capital controls in the fragile state of the first stage iff
  - p − φ > (1 / (B I(1)0)) [Π(2)(1) − Π(2)(β(2)CC)] (Equation (7))
- Interpretation: Imposing controls yields a short-term gain (first stage) but a long-term cost (reputation loss reducing Π(2)). The honest government chooses controls in stage 1 if short-term gain exceeds long-term reputational cost.

### Need for full equilibrium characterization
- Condition (7) depends on I(1)0 and β(2)CC, each of which depends on expectations and policy choices; hence equilibrium must be fully characterized.

### Dynamic equilibria: characterization and formulas
Equilibrium described in terms of I(1)0, β(2)CC, and policy choice π(1) for honest government in fragile state of first stage. Equilibrium conditions:
  - (i) Given π(1), I(1)0 is optimal for investors at t = 0 in first stage.
  - (ii) Given I(1)0, β(2)CC, capital controls are imposed in fragile state of first stage iff (7) holds; otherwise not.
  - (iii) Given the capital controls decision, β(2)CC is derived using Bayes Rule.

Two equilibrium types (depending on parameters):

1. Partially Revealing Equilibrium
- In fragile state of first stage, benevolent government imposes capital controls; observing controls does not reveal government type for sure.
- Bayes' Rule after observing controls:
  - β(2)CC = β(1) q / [q + (1 − β(1)) (1 − q)] (Equation (8)), where β(1) is investors’ belief at start of first stage.
- Initial project size in first stage:
  - I(1)0 = 1 / [1 − [β(1) (1 − φ q) + (1 − β(1)) (1 − φ)] R ] A (Equation (9))
- For equilibrium, (7) must hold with I(1)0 and β(2)CC as above. If controls observed at end of first stage, β(2) = β(2)CC; if not observed, β(2) = 1.
- Implication: honest government imposes controls in first stage fragile state but loses reputation (β(2)CC < β(1)), reducing second-stage investment and payoffs.

2. Fully Revealing Equilibrium
- In fragile state of first stage, benevolent government does not impose capital controls; if controls are observed, investors conclude government is opportunistic (β(2)CC = 0).
- Initial project size in first stage:
  - I(1)0 = 1 / [1 − [β(1) (1 − p q) + (1 − β(1)) (1 − φ)] R ] A (Equation (10))
- For equilibrium, inequality in (7) must be reversed with I(1)0 and β(2)CC = 0.
- Implication: government refrains from controls in first stage to build reputation, increasing second-stage payoffs by more than the first-stage loss.

### Existence and multiplicity of equilibria (conditions)
- Define ICC and βCC as I(1)0 and β(2) in a partially revealing equilibrium (RHS of (9) and (8)). Define ILF as I(1)0 in fully revealing equilibrium (RHS of (10)). Note: because p > φ, ICC > ILF.
- Existence result:
  - A partially revealing equilibrium exists if (7) is satisfied with I(1)0 = ICC and β(2) = βCC.
  - If no partially revealing equilibrium exists, (7) must fail at those values. Then one shows that (7) fails at I(1)0 = ICC implies it fails at I(1)0 = ILF with β(2)CC = 0, meaning a fully revealing equilibrium exists.
  - Conclusion: at least one equilibrium exists.
- Multiplicity condition:
  - Equilibria of both kinds coexist if
    - (1 / (B I LF)) [Π(2)(1) − Π(2)(0)] > p − φ > (1 / (B I CC)) [Π(2)(1) − Π(2)(β CC)] (Equation (11))
  - Claim: (1 / (B I LF)) [Π(2)(1) − Π(2)(0)] > (1 / (B I CC)) [Π(2)(1) − Π(2)(β CC)] (proved via decomposition using I CC > I LF and Π(2) increasing in β(2)).
  - Hence (11) can hold for appropriate p − φ, and both equilibrium types can coexist.
- Intuition for multiplicity:
  - If investors expect honest government to impose controls only in fragile state, they raise initial I(1)0 (because cost of controls < loss from a run), increasing first-stage payoff importance and making controls more attractive — favoring partially revealing equilibrium.
  - If investors expect honest government not to impose controls, they reduce I(1)0, strengthening reputational incentives against controls — favoring fully revealing equilibrium.
- Alternative expression fixing φ:
  - Condition (11) can be rewritten as
    - θ [1 − R ((1 − β(1)) (1 − φ) + β(1))] + φ / (1 − q R β(1)) θ > p > φ + (1 / (B I CC)) [Π(2)(1) − Π(2)(β CC)] (Equation (12))
    - where θ = [Π(2)(1) − Π(2)(0)] / (A B).
  - Condition (12) gives bounds on p for existence of both equilibrium types; Figure 9 (in source) illustrates equilibrium regions for combinations of β and p > φ.
- Role of p and φ:
  - Larger p − φ makes partially revealing equilibria more likely and fully revealing equilibria less likely (because it raises gains from capital controls without altering reputational costs).
  - Lower initial reputation β(1) makes partially revealing equilibria less likely and fully revealing equilibria more likely (since reputation-building gains are larger when β(1) is lower).

*Source: wpiea2024164-print-pdf - 8.1 Repetition and Reputation Building.*

### References

### References and Empirical Appendix

### References
- Bibliographic compilation of literature cited in the chapter, covering theory, empirical analysis, datasets, and policy discussions on capital controls, macroprudential policy, financial crises, and related topics. Key thematic areas and representative entries include:
  - Capital controls and capital flow management: Acosta-Henao et al. (2020); Ahmed and Zlate (2014); Aizenman and Pasricha (2013); Eichengreen and Rose (2014); Erten, Korinek, and Ocampo (2021); Ghosh, Kim, and Qureshi (2020); Magud, Reinhart, and Rogoff (2018); Pasricha (2012); Fernandez et al. (2016); Binici and Das (2021); Bhargava et al. (2023).
  - Integrated policy framework and IMF work: Adrian et al. (2021) IMF Working Paper (2021/292); Basu et al. (2020) IMF Working Paper (2020/121); IMF institutional and policy papers (IMF (2012a), IMF (2012b), IMF (2015), IMF (2021), IMF (2022) PolicyPaper 2022/008:97, World Economic Outlook Database October, 2022).
  - Macroprudential policy, liquidity, and crises: Benigno et al. (2013); Bianchi (2011); Bianchi and Coulibaly (2022); Bianchi and Lorenzoni (2022); Bianchi and Mendoza (2018); Farhi and Werning (2014, 2016); Korinek (2010); Jeanne and Korinek (2010); Laeven and Valencia (2018) IMF Working Paper 18/206.
  - Country-specific episodes and capital control case studies: Calvo (1978); Dornbusch (2001); Hood (2001); Johnson and Mitton (2003); Forbes (2007); Cipriani et al. (2014); Li et al. (2023); Saborowski et al. (2014).
- The reference list preserves original technical terminology, exact bibliographic details (years, working paper numbers, journal volumes, pages), and cross-references to datasets and evaluation reports (IEO-IMF (2020); Ostry (2022)) as presented in the source content.

### Empirical Appendix — organization and key elements
- General structure:
  - Table A.1 lists the 31 episodes of CCO tightening compiled from three sources and records crisis indicators from Laeven and Valencia (2018).
  - Figures A.1–A.4 expand Figure 2 from the main text, documenting three crisis indicators and robustness across the three sources (A.1: crises indicators; A.2–A.4: source-specific robustness).
  - Figures A.5–A.7 document the 31 CCO episodes across time, exchange rate regime, and income level.
  - Figures A.8–A.19 document dynamics around CCO episodes for control macro variables: Gross Capital Inflows, Gross Capital Outflows, Gross Portfolio Inflows, Gross Portfolio Outflows, Gross FDI Inflows, Gross FDI Outflows, Net Capital Inflows, Current Account Balance, Consumption growth, Investment growth, Exchange Rate appreciation rate, and Inflation.
  - Figure A.20 presents robustness results when the threshold used to identify CCO episodes is relaxed.
  - Figure A.21 documents persistence of CCO indices around identified episodes.
  - Tables A.2 and A.3 report the full set of OLS regression results from the main text (1) and the companion Probit regression (marginal effects).
  - Tables A.4 and A.5 report robustness results controlling for the level of GDP per capita.
  - Table A.6 reports CCO episodes where residency can be identified.
  - Table A.7 reports OLS results correcting cross-sectional dependence through Driscoll and Kraay (1998) standard errors.
  - Tables A.8 and A.9 use year fixed effects in regressions instead of a time trend.
  - Figure A.22 describes methodology and results of the counterfactual analysis where CCO shocks are used to account for growth dynamics in identified episodes.

- Table A.1 (CCO Episodes and Macro-Financial Crises):
  - Reports the 31 CCO episodes and associated crisis indicators (banking crisis, currency crisis, sov. debt crisis) drawn from Laeven and Valencia (2018).
  - Symbol mapping in the table note (preserve exact characters as in source):
    - 4 are those coming from IMF (2012b)
    - ? those from the IMF’s Taxonomy (Binici and Das 2021)
    - ∓ those from Fernandez et al. (2016) index
  - Exact trailing text captured: "Total975" (as presented in the source table).

- Figures — sample descriptions and exact counts preserved:
  - Figure A.1: "The figure depicts the average dynamics of GDP growth (demeaned) in the ten years around the 30 episodes of forceful CCO tightening identified for which crisis indicators of banking, currency and sov. debt crises exist in Laeven and Valencia (2018). t= 0 is the year of the episode. Averages of the dummy variables for these three crises indicators are plotted on the right scale. Out of the 31 episodes in CCO identified, only one does not have data from Laeven and Valencia (2018). GDP Growth and GDP Growth at available episodes are shown for comparison."
  - Figure A.2: Average GDP growth dynamics around the 9 episodes identified in IMF (2012b); crisis indicators plotted; t= 0 is year of episode.
  - Figure A.3: Average GDP growth dynamics around the 9 episodes identified in the Taxonomy (Binici and Das 2021); note that out of the 9 episodes, only one lacks Laeven and Valencia (2018) data.
  - Figure A.4: Average GDP growth dynamics around the 16 episodes identified using Fernandez et al. (2016) index.
  - Figure A.5: Number of episodes by year (1995–2015 axis shown) and right scale showing number of episodes over number of observations by year.
  - Figure A.6: Episodes of CCOs by exchange rate regime (Ilzetzki et al. (2021)); right scale shows number of observations by regime; "30 episodes can be matched with exchange rate regime data."
  - Figure A.7: Episodes of CCOs by income level; right scale shows number of episodes over number of observations by year.
  - Figures A.8–A.13: Average and median dynamics of Gross Total Capital Inflows, Gross Total Capital Outflows, Gross Portfolio Inflows, Gross Portfolio Outflows, Gross FDI Inflows, Gross FDI Outflows in the ten years around forceful CCO tightening episodes; each figure specifies the number of episodes with available data (examples preserved exactly as in source):
    - Gross Total Capital Inflows: around 30 episodes (one episode missing data).
    - Gross Total Capital Outflows: around 28 episodes (three episodes missing data).
    - Gross Portfolio Inflows: around 22 episodes (nine episodes missing data).
    - Gross Portfolio Outflows: around 23 episodes (eight episodes missing data).
    - Gross FDI Inflows: around 28 episodes (three episodes missing data).
    - Gross FDI Outflows: around 22 episodes (nine episodes missing data).
  - Figure A.14: Net Total Capital Inflows (as % of GDP) around 30 episodes (one episode missing data).
  - Figure A.15: Current Account Balance (as % of GDP) around 30 episodes (one episode missing data).
  - Figure A.16: Consumption growth around 28 episodes (three episodes missing data).
  - Figure A.17: Investment growth around 28 episodes (three episodes missing data).
  - Figure A.18: Exchange Rate appreciation rate around 31 episodes (t= 0 is year of episode).
  - Figure A.19: Inflation dynamics around 31 episodes (t= 0 is year of episode).
  - Figures A.20–A.21: Robustness to threshold relaxation (A.20) and persistence of CCO indices (A.21).
  - Figures at the end illustrate robustness to alternative episode thresholds:
    - GDP growth (de-meaned) at Episodes (2.0 sd threshold): "Average at Episodes (43) / Median at Episodes (43)"
    - GDP growth (de-meaned) at Episodes (1.5 sd threshold): "Average at Episodes (67) / Median at Episodes (67)"
  - Final table/figure labels in source note episode classification counts: "No. Episodes IV Taxonomy FKRSU Repeated Total" (table layout preserved as provided).

*Source: wpiea2024164-print-pdf - References (IMF).*

### 2.5 sd threshold9916331

### 2.5 sd threshold9916331

### Robustness: GDP Growth Around Episodes of CCO Tightening
- Both panels depict the average (median) dynamics of GDP growth (demeaned) in the ten years around the episodes of forceful CCO tightening identified using two different thresholds: 2.0 sd and 1.5 sd. t = 0 is the year of the episode.
- The bottom table lists the number of episodes identified from each of the three complementary sources: IV (significant tightening of outflow controls in IMF (2012b)), Taxonomy (IMF’s Taxonomy of CFM, in Binici and Das (2021)) and FKRSU (index by Fernandez et al. (2016)).

### Persistence of Capital Controls (Figure A.21)
- The figure depicts the persistence of Fernandez et al. (2016) KAO index (0-1 index, where 1 is a fully restricted capital account) the following 5 years after the episodes are identified.
- The solid line shows the average for the full list of episodes, except two of them (Zimbabwe 2016 and Fiji 2020) that do not have data on KAO index.
- The dashed line shows the average only for the episodes identified using Fernandez et al. (2016) KAO index.
- Average at Full Episodes (29) versus Average only at FKRSU Episodes (16) are shown; axis range plotted from -1 to 5 (years around event).

### Regression Analysis: CCO Episodes and the Macroeconomy (OLS)
- Table A.2: OLS results — regression of the occurrence of CCO episodes on GDP growth. Macro controls (all lagged): degree of exchange rate flexibility from Ilzetzki et al. (2021); nominal exchange rate growth; inflation; CA balance; Capital Flows (net and gross); consumption and investment growth.
- Selected coefficients and statistics (specifications 1–5):
  - GDP (% gr) coefficients: -0.000621***, -0.000636***, -0.000690***, -0.00223***, -0.00172***.
  - L.Consumption (% gr): 0.00102***, 0.00118***.
  - Banking Crisis: 0.140***.
  - Currency Crisis: 0.120***.
  - Observations by spec: 50145, 01450, 14501, 42877, 2494 (as presented).
  - Countries: 193/195 (specs 1–3), 143/195 (specs 4–5).
  - Episodes: 31/31 (specs 1–3), 22/31 (specs 4–5).
  - Years coverage: 1995-2021 (specs 1–3), 1995-2020 (spec 4), 1995-2017 (spec 5).
  - Adjusted R2: 0.002, 0.008, 0.008, 0.020, 0.097.
- Significance notation: *p <0.10, **p <0.05, ***p <0.01.

### Regression Analysis: CCO Episodes and the Macroeconomy (Probit)
- Table A.3: Probit results — regression of occurrence of CCO episodes on GDP growth (marginal effects interpretation provided).
- Selected coefficients and statistics (specifications 1–5):
  - GDP (% gr) coefficients: -0.0342***, -0.0657***, -0.0754***, -0.162***, -0.150***.
  - t coefficients presented (t, t2) and other covariates: L.ER (app. rate): -0.0594***, -0.0837***; L.Inflation (%): -0.0578**, -0.0737**.
  - L.Consumption (% gr): 0.163***, 0.214***.
  - Banking Crisis: 2.514***.
  - Currency Crisis: 1.714**.
  - Observations by spec: 50146, 92692, 37233, 329 (as presented).
  - Countries in some specs: 26/195 and 17/195 (subsamples).
  - Episodes: 31/31, 22/31.
  - Years coverage: 1995-2021, 1995-2020, 1995-2017.
- Marginal-effect statement: “The marginal effect at the most comprehensive specification implies that if GDP growth would fall a further 1% then the probability of having a CCO episode increases by 1.1%, relative to an unconditional probability of 6.7%, i.e. an increase around 16.4% (1.1/6.7).”

### Robustness: GDP per capita (OLS and Probit)
- Table A.4 (OLS, GDP per capita): Selected coefficients:
  - GDP (% gr): -0.000668***, -0.000682***, -0.000746***, -0.00225***, -0.00172***.
  - GDP per capita (thousand US$): 0.00000117, -0.0000371, 0.000241, 0.000623, -0.0000232.
  - L.Consumption (% gr): 0.00101***, 0.00118***.
  - Banking Crisis: 0.140***.
  - Observations and panel composition mirror Table A.2.
  - Adjusted R2: 0.002, 0.008, 0.008, 0.020, 0.097.
- Table A.5 (Probit, GDP per capita): Selected coefficients:
  - GDP (% gr): -0.0369***, -0.0658***, -0.0776***, -0.168***, -0.145**.
  - GDP per capita (thousand US$): 0.000791, 0.00383, 0.0542, 0.0562, -0.0401.
  - L.Consumption (% gr): 0.160***, 0.218***.
  - Banking Crisis: 2.565***.
  - Currency Crisis: 1.771**.
- Marginal-effect statement: “The marginal effect at the most comprehensive specification implies that if GDP growth would fall a further 1% then the probability of having a CCO episode increases by 4.9%, relative to an unconditional probability of 6.7%, i.e. an increase around 73.1% (4.9/6.7).”

### Residency Components of ∆KAO (Table A.6)
- The table desegregates the ∆KAO (0-1 index, from Fernandez et al. (2016), where 1 is a fully restricted capital account) among three components: ∆KAO NonResident, ∆KAO Resident, and ∆KAO Undet.
- Selected country examples (absolute ∆KAO, shares):
  - Greece 2015: ∆KAO 0.70; ∆KAO NonResident 0.25; ∆KAO Resident 0.15; ∆KAO Undet. 0.30; shares: 36% / 21% / 43%.
  - Ecuador 2008: ∆KAO 0.70; NonResident 0.30; Resident 0.30; Undet. 0.10; shares: 43% / 43% / 14%.
  - Vietnam 1997: ∆KAO 0.51; NonResident 0.29; Resident 0.29; Undet. -0.06; shares: 56% / 56% / -11%.
  - China 2016: ∆KAO 0.10; NonResident 0.00; Resident 0.00; Undet. 0.10; shares: 0% / 0% / 100%.
  - Russia 1998: ∆KAO 0.05; NonResident 0.05; Resident 0.00; Undet. 0.00; shares: 100% / 0% / 0%.
- Summary statistics (bottom rows):
  - Mean ∆KAO: 0.36; Mean ∆KAO NonResident: 0.10; Mean ∆KAO Resident: 0.16; Mean ∆KAO Undet.: 0.10.
  - Median ∆KAO: 0.40; Median NonResident: 0.05; Median Resident: 0.20; Median Undet.: 0.10.
  - Mean % shares: -25% / 48% / 27%.
  - Median % shares: -20% / 50% / 22%.
- Note: Only episodes with positive ∆KAO are analyzed.

### Robustness: OLS with Driscoll-Kraay Standard Errors (Table A.7)
- Table A.7: OLS with cross-sectional dependence adjusted standard errors (Driscoll and Kraay 1998).
- Selected coefficients:
  - GDP (% gr): -0.000621***, -0.000636***, -0.000690***, -0.00223**, -0.00172*.
  - L.CA Balance (%GDP): -0.000591*** (specification 1).
  - L.Consumption (% gr): 0.00102**, 0.00118**.
  - Banking Crisis: 0.140***.
  - Observations and panel composition as in prior OLS tables.
- Adjusted R2: 0.002, 0.008, 0.008, 0.020, 0.097.

### Robustness: OLS with Year Fixed Effects (Table A.8)
- Table A.8: OLS with year fixed-effects.
- Selected coefficients:
  - GDP (% gr): -0.000719***, -0.000739***, -0.000739***, -0.00295***, -0.00215***.
  - L.Consumption (% gr): 0.000955**, 0.00113***.
  - Banking Crisis: 0.137***.
  - Currency Crisis: 0.121***.
  - Year F.E. and Country F.E. included in specifications.
- Adjusted R2: 0.006, 0.012, 0.012, 0.028, 0.097.

### Robustness: Probit with Year Fixed Effects (Table A.9)
- Table A.9: Probit with year fixed-effects.
- Selected coefficients:
  - GDP (% gr): -0.0479***, -0.130***, -0.130***, -0.397***, -0.368***.
  - L.ER (app. rate): -0.0673*, -0.101**.
  - L.Gross Inflows (% gr): 0.00225, 0.00331*.
  - L.Consumption (% gr): 0.286***, 0.325***.
  - Banking Crisis: 2.190**.
  - Currency Crisis: 2.447**.
- Observations: 296, 341, 0410, 176, 176 (as presented).
- Marginal-effect statement: “The marginal effect at the most comprehensive specification implies that if GDP growth would fall a further 1% then the probability of having a CCO episode increases by 2.7%, relative to an unconditional probability of 12.5%, i.e. an increase around 21.6% (2.7/12.5).”

### Counterfactual Analysis and Simulation (Figure A.22)
- Two-stage counterfactual approach:
  1. First-stage regression: Fernandez et al. (2016) CCO index CCO_{i,t} as dependent variable:
     - CCO_{i,t} = β1 CCO_{i,t−1} + β2 GDP gr_{i,t−1} + α1 X_{i,t−1} + ε_{i,t}
     - X_{i,t−1} are lagged covariates (ER regime, ER appreciation rate, inflation, CA Balance, Capital Flows and Banking and Currency crises) and also country F.E. and time trends.
     - CCO shocks:  ̃CCO_{i,t} = CCO_{i,t} − ̂CCO_{i,t}.
  2. Second-stage regression: use CCO shocks to explain GDP growth in episodes neighborhood (between t-5 and t+5):
     - GDP gr_{i,t} = γ ̃CCO_{i,t} + ε_{i,t}.
     - Fitted series: ̂GDP gr_{i,t} = ̂γ ̃CCO_{i,t}.
- Estimator of γ is not significant, with a magnitude of -0.165.
- Figure A.22 shows fitted versus actual GDP growth for the 31 episodes; axis plotted from -3.5 to 1.5 percent for GDP growth.

### Theoretical Appendix — Model Assumptions and Formulation (B.1, B.2)
- Basic assumptions on project size under capital controls π = (τ, φ) (with φ = 0 if τ = 0):
  - If policy applied at t = 1, project size shrinks to I1 = (1−φ) I0.
  - λ is fraction of investors that stay if state is fragile at t = 1; I2 = g(λ) I1 = (1−φ) g(λ) I0.
  - Final payoff RI2 = R(1−φ) g(λ) I0.
  - Rate of return at t = 2 in fragile state: (1−φ) f(λ) where f(λ) ≡ g(λ) R I0 / λ (f(0) is assumed 0).
- Diamond and Dybvig leading example: there exists L, 0 < L < 1, with g(λ) = 0 for λ ≤ L.
- Game-theoretic presentation:
  - Players: government (G) and a continuum of (foreign) investors.
  - Timing: t = 0 policy π and initial contribution i proposed; t = 1 state normal (probability q) or fragile (probability 1−q); fragile node has sunspots with probability p.
  - Investor strategy χ = (χ_s, χ_ns) where χ_s = 1 if investor leaves if sunspots; χ_ns analogous for no sunspots.
  - Aggregate outcomes λ = (λ_s, λ_ns) with λ_s, λ_ns ∈ {0,1} assumed w.l.o.g.
  - Project size dynamics: I0 = A + i; I2 in sunspots I2s = g(λ_s)(1−φ) I0; in no sunspots I2ns = g(λ_ns)(1−φ) I0.
  - Government expected payoff: B E(I2). Investor expected payoff given in text.

### Equilibrium Definition and Key Propositions (B.2)
- Equilibrium (anonymous, symmetric, sequentially perfect): triple (i, χ, λ) satisfies consistency, investor zero expected payoff, and investor optimality.
- Proposition (existence of equilibrium with capital flight) — condition:
  - Assuming (1−τ)ω < (1−φ)/(1−qφ) there is an equilibrium with capital flight characterized by:
    - χ_s = 1, λ_s = 0
    - χ_ns = 0, λ_ns = 1
    - I2s = 0, I2ns = (1−φ) I0
    - I0 = A + i = L A where leverage coefficient L =
      1−qp(1−τ)ω
      -----------------------------------------
      (1−qp(1−τ)ω) − [q(1−p)(1−φ) + (1−q)] R
- Remarks: capital flight occurs at t = 1 with probability pq. Laissez faire leverage coefficient formula also provided:
  - I0 = (1−pqω) / [1−pqω−(1−pq)R] A
- Corollary (no equilibrium with capital flight):
  - If (1−τ)ω < (1−φ) f(0) there cannot be an equilibrium with capital flight.
- Proposition (existence of equilibrium without capital flight) — assuming same condition as earlier:
  - χ_s = 0, λ_s = 1
  - χ_ns = 0, λ_ns = 1
  - I2s = I2ns = (1−φ) I0
  - I0 = A + i = 1 / [1−(1−qφ)R] A

### Optimal Policy With Commitment (B.3)
- Government chooses policy π = (τ, φ) at t = 0 together with i. An optimal policy with commitment maximizes E(I2) over choices (i, π) given equilibrium outcomes.
- Restrict attention to laissez faire π = LF = (0,0) and binding CCOs π = CCO with τ = 1 and φ > 0 (eliminating capital flight).
- Condition for capital controls to be optimal:
  - (1−qφ) [1 / (1−(1−qφ)R)] > (1−pq) [1−pqω] / [1−pqω−(1−pq)R]
- Opposite inequality implies laissez faire is optimal.

### Discretionary Case (B.4)
- If government chooses policy π = (τ, φ) at t = 1 when state is fragile but before sunspot realization, investors’ strategies and aggregate run outcome can depend on π.
- Notation adjusted: χ = (χ^π_s, χ^π_ns), λ = (λ^π_s, λ^π_ns).
- A project size i, policy π, investor strategy χ, and aggregate run outcome λ form a discretionary equilibrium if they satisfy the modified consistency, zero-investor-payoff, and individual optimality conditions under the discretionary timing.

*Source: wpiea2024164-print-pdf - 2.5 sd threshold9916331 — https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024164-print-pdf.pdf*

### 1. The aggregate run outcome is consistent with the strategy pair

### 1. The aggregate run outcome is consistent with the strategy pair

### Core definitions and equilibrium requirements
- Equilibrium requires:
  - The aggregate run outcome λ is consistent with the strategy pair χ and π.
  - The initial proposal i is greater than zero and gives investors a zero expected payoff, given the aggregate outcome λ and policy π.
  - The policy π is optimal for the government at t = 1, given I0 = A + i and the aggregate run outcome λ.
  - The strategy χ is optimal for the typical individual investor, given the aggregate run outcome λ and policy π.

### Discretionary equilibrium (single-stage basic result)
- Proposition:
  - There is a discretionary equilibrium with π = CCO if p > φ.
  - If the inequality is the opposite, there is a discretionary equilibrium with π = LF.
- Proof sketch:
  - Proof involves checking conditions 1–4 above; condition 3 follows subsection 6.2 in the text.

### Political Opportunism (Single Stage) — model structure
- Players:
  - Government G and a continuum of investors.
- Timing and information:
  - At t = 0, "nature" chooses government type: honest or opportunistic. Investors have initial belief β ∈ [0,1] that the government is honest.
  - At t = 1:
    - If G is opportunistic, the state is fragile; opportunistic G imposes π = CCO and I1 = (1−φ) I0.
    - If G is honest:
      - State is normal with probability 1−q → π = LF and I0 = I1 = I2.
      - State is fragile with probability q → honest G chooses π ∈ {LF, CCO} (only nontrivial t = 1 decision for honest G).
  - In fragile state, investors decide to stay or leave after observing π and sunspots.
  - Project size adjusts by state, policy π, and aggregate investment decision. Payoffs depend on I2 as in the basic model.
- Strategies and beliefs:
  - At t = 0 both types propose initial project size I0 and contribution i = I0 − A, chosen to leave investors indifferent.
  - Investors’ strategy χ = (χπs, χπns) specifies stay/leave in fragile state conditional on observed π and sunspots.
  - Aggregate run outcome λ = (λπs, λπns) is the fraction staying under policy π with/without sunspots.
- Equilibrium definition:
  - An equilibrium is (i, I0 = A + i, χ, π, λ) such that:
    1. λ is consistent with χ.
    2. i gives investors an expected zero payoff, given π, λ, and β.
    3. χ is optimal for the individual investor at t = 1, given I0, π, and λ.
    4. π is optimal for the honest G if the state is fragile at t = 1, given I0 and λ.

### Political Opportunism (Single Stage) — equilibrium proposition
- Proposition:
  - There is an equilibrium with:
    - π = CCO,
    - (λCCOs, λCCOns) = (1,1),
    - (λLFs, λLFns) = (0,1),
    - χ = 1 − λ,
    - i = I0 − A with
      I0 = 1 / [1 − [β(1 − φq) + (1 − β)(1 − φ)] R] A
    - provided that
      ω < 1 / [(1 − β)(1 − φ) + β(1 − qφ)]
      and
      p > φ
- Proof highlights:
  - Condition 2 (zero expected payoff) yields
    (1 − β)(1 − φ) R I0 + β[(1 − q) R I0 + q(1 − φ) R I0] = i = I0 − A
    which determines I0.
  - At t = 1:
    - If π = CCO is observed, investors stay because CCOs bind.
    - If π = LF (out-of-equilibrium fragile state), continuation (λLFs, λLFns) = (0,1) implies investors flee with probability p and stay with probability 1 − p; individually optimal if 0 < ω i < R I0, which holds because i > 0 and ω < R(I0/(I0 − A)) under the proposition’s conditions.
  - Condition 4 is satisfied if p > φ.

### Two Stages — model structure (first stage focus)
- Extensions relative to single-stage:
  - Reputation evolution matters: the honest government cares about two-stage payoffs; second-stage payoff Π(β(2)) is determined by reputation β(2).
- Timing and information:
  - At t = 0, "nature" chooses government type; investors have initial belief β(1).
  - At t = 1:
    - If G is opportunistic → fragile state, π = CCO, I1 = (1 − φ) I0.
    - If G is honest → normal with probability 1 − q (π = LF, I0 = I1 = I2), fragile with probability q (honest G chooses π ∈ {LF, CCO}).
  - In fragile state, investors choose stay/leave after observing π and sunspots. First stage ends at t = 2.
  - Second-stage government payoff is Π(β(2)), where β(2) depends on first-stage outcomes:
    - Let βCCO denote posterior belief that G is honest if π = CCO observed.
    - If π = LF observed → β(2) = 1; if fragile and π = CCO observed → β(2) = βCCO.
- Strategies, aggregate outcomes:
  - Initial proposal i and I0 = A + i leave investors indifferent.
  - Honest G’s strategy is π ∈ {LF, CCO}.
  - Investor strategy χ = (χπs, χπns).
  - Aggregate run outcome λ = (λπs, λπns).
- Dynamic equilibrium:
  - A dynamic equilibrium is (i, I0 = A + i, χ, π, λ, βCCO) such that:
    1. λ consistent with χ.
    2. i gives investors expected zero payoff given π, λ, and β(1).
    3. χ optimal for investors at t = 1 given I0, π, λ.
    4. π optimal for honest G in fragile state at t = 1 given I0, βCCO, λ (honest G maximizes two-stage payoff).
    5. βCCO is derived from π using Bayes’ Rule.

### Two Stages — equilibrium propositions
- Proposition (Partially Revealing Equilibrium):
  - There is an equilibrium with:
    - π = CCO,
    - (λCCOs, λCCOns) = (1,1),
    - (λLFs, λLFns) = (0,1),
    - χ = 1 − λ,
    - i = I0 − A with
      I0 = 1 / [1 − [β(1)(1 − φq) + (1 − β(1))(1 − φ)] R] A
    - and
      βCCO = β(1) q / [q + (1 − β(1))(1 − q)]
    - provided that
      ω < R(I0/(I0 − A)))
      and
      p − φ > 1 / (B I0) [Π(2)(1) − Π(2)(βCCO)]
  - Proof highlights:
    - Zero expected payoff condition (no capital flight equilibrium) gives
      i = R I0 [1 − φ(β(1) q + (1 − β(1)))]
      and with I0 = A + i yields the equilibrium I0.
    - If CCOs imposed they bind so (λCCOs, λCCOns) = (1,1).
    - Out-of-equilibrium fragile LF would have (λLFs, λLFns) = (0,1) with individual optimality ensured by ω < R(I0/(I0 − A)).
    - Conditions 4 and 5 follow by the same arguments as in the main text.
- Proposition (Fully Revealing Equilibrium):
  - There is an equilibrium with:
    - π = LF,
    - (λCCOs, λCCOns) = (1,1),
    - (λLFs, λLFns) = (0,1),
    - χ = 1 − λ,
    - i = I0 − A with
      I0 = 1 / [1 − [β(1)(1 − p q) + (1 − β(1))(1 − φ)] R] A
    - and
      βCCO = 0
    - provided that
      ω < R(I0/(I0 − A)))
      and
      0 < p − φ < 1 / (B I0) [Π(2)(1) − Π(2)(0)]
  - Proof:
    - A simple adaptation of prior arguments and the text discussion.

*Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024164-print-pdf.pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024164-print-pdf.pdf_