## _wp09219

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---

### I. Introduction — purpose and stylized facts
- Research question: Why do some financial crises generate contagion across countries while others remain local?
- Proposed mechanism: the "uncertainty channel of contagion" — surprise crises increase investor uncertainty about the precision of information-gathering technologies, raising aggregate uncertainty about fundamentals in other countries and increasing their crisis probability.
- Empirical scope and data:
  - Sample of 38 countries with monthly data from December 1993 to September 2005.
  - Crisis episodes included: Mexico (1994-95), Thailand (1997), Russia (1998), Brazil (1999), Turkey (2001), Argentina (2001-02).
  - Crisis measure: sharp falls in stock market returns consistent with firms abandoning projects and collapse of market value.
- Stylized facts illustrated:
  - Thailand (1997): severe Baht devaluation and stock-market drop increased forecast dispersion for neighboring countries; Korea later experienced November 1997 currency and stock market crisis.
  - Argentina (2001): default announcement in December 2001 left uncertainty regarding neighboring economies' fundamentals barely changed and, conditional on other variables, actually decreased.
- Two key empirical findings previewed:
  - Surprise crises (Mexico, Thailand, Russia) → increase uncertainty in other countries, stronger intra-regionally.
  - Anticipated crises (Brazil, Turkey, Argentina) → decrease uncertainty in other countries, stronger intra-regionally.
  - Higher uncertainty → higher probability of crisis in another economy; effect significant after controlling for other channels.

### II. Model — structure, assumptions, and testable predictions
- Environment and timing:
  - Two-country, two-period model (countries A and B; events in A occur in period 1, in B in period 2).
  - Fundamentals: single parameter θ_c; firm project return R(θ) with R' > 0, R'' > 0 and R(0) = 0.
  - Private liquidity shock S_c ~ N(0, 1).
  - Investors have CARA utility U(W) = -e^{-γW}; risk-free rate normalized to zero.
- Information and behavior:
  - Two investor types: informed (pay cost c to acquire technology) and uninformed; share informed is λ.
  - Signals: x_{I,i} = θ_c + ε_{I,i} with precision α_I = 1/σ^2_I; x_{U,i} = θ_c + ε_{U,i} with α_U = 1; assume α_I > α_U.
  - Investors uncertain about actual precision; common prior α̂_I. Posterior beliefs update after observing crises in country A:
    - If an anticipated crisis materializes posterior is G_I α̂_I > α̂_I.
    - If an anticipated crisis does not occur, or if a surprise crisis occurs, posterior is B_I α̂ where α_U < B_I α̂ < α̂_I.
  - Belief updates affect equilibrium λ endogenously.
- Firm decision and crisis threshold:
  - Firm abandons project iff θ_c < 0 (given assumptions).
  - Existence of cutoff θ*_c(γ, S_c, α̂_I) > 0 defined by S_c P_c(θ*_c, S_c) = S_c θ*_c. Firm discontinues if θ_c < θ*_c.
  - Comparative statics for θ*_c:
    - 0 < ∂θ*_c / ∂γ.
    - 0 < ∂θ*_c / ∂S_c.
    - 0̂ < ∂θ*_c / ∂α̂_I (threshold lower for higher beliefs on precision).
    - 0 < ∂θ*_c / ∂λ (threshold lower for higher proportion of informed investors).
- Endogenous informed share λ (Proposition 2):
  - λ = 0 if c > b; λ = 1 if c < a; λ ∈ (0,1) if c ∈ [a,b], where a and b depend on γ and α̂_I (exact functional forms preserved in source).
  - Corollary: for interior λ, ∂λ/∂α̂_I > 0 for beliefs α̂_I not too large; caveat that if α̂_I is very large further increases can reduce λ (Grossman–Stiglitz/Diamond–Verrecchia paradox).
- Intuition and testable predictions:
  - Surprise crisis → investors lower belief in precision → λ falls → forecast variance rises → crisis probability abroad rises.
  - Prediction 1: Surprise crises increase variance of forecasts in other countries; anticipated crises decrease it.
  - Prediction 2: Increases (decreases) in variance of forecasts raise (lower) probability of crisis in another economy.

### III. Empirical approach — data, variables, and estimation strategy
- Data:
  - Monthly panel of 38 countries (15 developed and 23 emerging) from December 1993 to September 2005.
  - Uncertainty proxy: standard deviation of Consensus Economics GDP growth forecasts (weighted average of current and following year in main analysis; robustness checks with only current- or only following-year forecasts).
  - Crisis dummy: month where IFC investable US dollar total return index undershoots its sample mean by more than two standard deviations; subsequent months counted until returns revert to one standard deviation band. Supplemented with MSCI or national sources when needed.
- Controls:
  - Domestic: mean of growth forecasts, stock market volatility, ICRG financial/economic/political risk indices.
  - External: 10-year US government bond yield.
  - Contagion channels: common creditors (consolidated BIS-based index of dependence), bilateral trade shares (exports to crisis country as share of total exports), common overexposed fund investors (Broner, Gelos and Reinhart index for emerging sample).
- Two-step estimation:
  - Step 1 (fixed-effects panel): UNC_{B,t} = α_0 + ∑ α_j CR_{j,t-1} + α_8 Z_{B,t-1} + α_9 INT_{t-1} + δ_B + ε_{B,t} where CR_{j,t-1} are crisis dummies for the six initial-crisis countries, Z_{B,t-1} domestic controls, INT US interest rate, δ_B country fixed effects.
  - Step 2 (discrete-choice for crisis probability): pooled probit/logit and linear probability models
    - Interaction specification: Pr{CR_B,t = 1 | X} = G{... ∑ β*(CR_{A,t-1} × CTG_{A,B,t-1}) + β_2 (UNC_{B,t-1} × CR_{A,t-1}) + ... + δ_B + η_{B,t} }
    - Separate-entry specification: Pr(CR_B = 1 | X) = G{β_0 + ∑ β_j CR_{j,t-1} + β_7 UNC_{B,t-1} + β_8 Z_{B,t-1} + δ_B + η_{B,t}}.
  - Robustness: probit, logit, and linear probability; regional and emerging-market subsamples; inclusion of overexposed fund investors index when available.

### IV. Empirical findings — Step 1 (effect of crisis on uncertainty)
- Main patterns:
  - Surprise crises (Mexico, Russia, Thailand) significantly increase uncertainty regarding fundamentals in other countries.
  - Anticipated crises (Brazil, Turkey, Argentina) decrease uncertainty in potentially-affected countries; Brazilian crisis effects sometimes insignificant.
- Heterogeneity:
  - Surprise-crisis effects stronger in emerging markets than in full sample.
  - Surprise crises show strong positive within-region effects; Thai crisis had the strongest impact among the three surprise crises.
  - Anticipated-crisis decreases stronger in emerging markets for Argentina and Turkey.
- Control variable results (signs and reported significance):
  - US bond yield: positive and strongly significant effect on uncertainty globally; stronger in emerging markets.
  - Lagged mean growth expectations: negative effect on uncertainty.
  - Lagged crises in potentially-affected countries: positive and significant effect on uncertainty.
  - Past stock market volatility: strong positive and significant effect on uncertainty.
  - ICRG risk indices: mostly not significant.

### V. Empirical findings — Step 2 (effect of uncertainty on crisis probability)
- Core results:
  - UNC variable has a positive and strongly significant effect on probability of a crisis in pooled probit specifications.
  - Effect is stronger in emerging economies.
  - Logit: positive effect; in full sample not significant in one specification, but positive and significant for emerging markets.
  - Linear probability: effect remains strongly significant though magnitude smaller.
  - Results hold when restricting attention to surprise crises (Mexican, Russian, Thai).
- Alternative contagion channels:
  - Without controlling for overexposed common fund investors, common creditors and trade shares have high explanatory power.
  - Once controlling for overexposed common fund investors (emerging market subsample), common creditors and trade-share channels become insignificant (Table 8).
- Domestic controls and external rates:
  - Mean growth expectations and stock market volatility often have correct sign but are frequently insignificant.
  - US long-term interest rate: strong and positive relationship with probability of a stock market crisis.
- Separate-entry specification:
  - UNC retains distinctly positive and significant effect on crisis probability when entered alongside initial-crisis dummies.
- Magnitude (marginal effects reported):
  - A 1 percent increase in the measure of uncertainty is associated with a 1.8 percent increase in the probability of a stock market crisis in that country (conditioning on incidence of crises in initial-crisis countries, US long-term interest rate, and domestic variables).
  - Unconditional stock market crisis probability: 4.5 percent in the entire sample and 6.8 percent in the emerging market sample.
  - Interpretation: the effect size is non-negligible relative to unconditional probabilities.

### VI. Integrated interpretation, robustness, and validation
- Empirical evidence supports model hypotheses:
  - Surprise crises → increases in uncertainty abroad → higher crisis probability abroad (uncertainty channel of contagion).
  - Anticipated crises → decreases in uncertainty abroad → reduced crisis probability abroad.
- Robustness checks:
  - Results robust to controlling for trade links, common creditors, and overexposed fund investors (where data available).
  - Regional and emerging-market subsample analyses corroborate main findings.
- Methodological note:
  - Exploiting cross-sectional variation with panel fixed effects across multiple crisis episodes enables quantification of the uncertainty channel beyond single-episode time-series studies.

### VII. Policy implications and recommendations
- Surveillance and transparency:
  - Immediate policy implication: surveillance activities should be an important element of efforts to promote international financial stability.
  - Closer monitoring of country fundamentals and public reporting can help lower the risk that a surprise crisis in one country causes harmful spillovers to others.
- Rationale:
  - Better information and transparency reduce the likelihood investors are surprised by crises, thereby reducing endogenous increases in uncertainty that propagate crises.

### VIII. Appendix highlights (theoretical proofs and empirical tables)
- Theoretical appendix provides derivation of equilibrium price function and proofs:
  - Proposition 1: existence of cutoff θ*_c(γ, S_c, I^α) > 0 with firm discontinuation if θ_c < θ*_c.
  - Corollary 1: comparative statics for θ*_c (∂θ*_c/∂γ > 0; ∂θ*_c/∂S_c > 0; 0̂ < ∂θ*_c/∂I^α; 0 < ∂θ*_c/∂λ).
  - Proposition 2 and Corollary 2: characterization of equilibrium λ and its response to beliefs on precision α̂_I (interior λ increases in α̂_I for values not too large).
- Empirical appendix tables referenced:
  - Table 5: Sample of Countries.
  - Table 6: List of Variables (variable construction, including uncertainty proxy and crisis dummy).
  - Table 7: Step 2 results restricting attention to Mexican, Russian and Thai crises.
  - Table 8: Step 2 results including overexposed common fund investor control (emerging market sample).

*Source: _wp09219 (IMF working paper PDF chapter/section).*

### References .................................................................................................. 39

### _wp09219 - References .................................................................................................. 39

### I. INTRODUCTION — summary of purpose and stylized facts
- Research question: Why do some financial crises generate contagion across countries while others remain local?
- Proposed mechanism: the "uncertainty channel of contagion" — surprise crises increase investor uncertainty about the precision of information-gathering technologies, raising aggregate uncertainty about fundamentals in other countries and increasing their crisis probability.
- Stylized facts illustrated:
  - Figures referenced:
    - Figure 1: "Uncertainty Around the Period of the Thai Crisis" — after the severe devaluation of the Baht in early July 1997 and a substantial drop in stock market returns one month later, uncertainty (dispersion of GDP forecast-based analyst forecasts) increased substantially for several neighboring countries; Korea later experienced a currency and stock market crisis in November 1997.
    - Figure 2: "Uncertainty Around the Period of the Argentinean Crisis" — following Argentina's default announcement in December 2001, uncertainty regarding neighboring economies' fundamentals barely changed and, conditional on other variables, actually decreased.
- Main empirical sample and scope:
  - Sample: 38 countries with monthly data from December 1993 to September 2005.
  - Included crisis episodes: Mexico (1994-95), Thailand (1997), Russia (1998), Brazil (1999), Turkey (2001), Argentina (2001-02).
  - Crisis measure: sharp falls in stock market returns consistent with firms abandoning projects and collapse of market value.
- Two key empirical findings:
  - Surprise crises (Mexico, Thailand, Russia) increase uncertainty regarding fundamentals in other countries, stronger within the same region.
  - Anticipated crises (Brazil, Turkey, Argentina) decrease uncertainty in other countries, stronger within the same region.
  - Higher uncertainty is associated with a higher probability of a crisis in another economy, significant even after controlling for other channels (common creditors, trade links, size effect of initial stock market, overexposed common fund investors).
  - The marginal analysis indicates the effect is not negligible in size.
- Empirical strategy:
  - Two-step approach:
    1. Fixed-effects panel estimations to relate initial-country crisis to uncertainty regarding fundamentals in other countries.
    2. Quantify effect of increased uncertainty on the probability of a crisis in another economy.

### II. RELATED LITERATURE — contextual positioning
- Channels and prior mechanisms explored in literature:
  - Trade linkages and macroeconomic similarities (e.g., Gerlach and Smets (1996), Glick and Rose (1999), Goldstein (1998)).
  - Common investors: banks (Van Rijckeghem and Weder, 2001; Kaminsky and Reinhart, 2000; Caramazza, Ricci and Salgado, 2004) and mutual funds (Broner, Gelos and Reinhart, 2006; Borensztein and Gelos 2000).
  - Theoretical models: herding due to fixed information costs (Calvo and Mendoza, 2000), differentially-informed investors (Kodres and Pritsker, 2002), wealth effects (Goldstein and Pauzner, 2004).
- Contribution of current work:
  - Introduces a new mechanism where contagion operates through endogenous shifts in the share of informed investors (λ), driven by changes in investor beliefs about information precision following observed crises.
  - Links the surprise vs. anticipated nature of initial crises to differential contagion outcomes — a feature not present in some prior models (e.g., Kodres and Pritsker (2002)).
  - First attempt, to the authors' knowledge, to quantify the role of uncertainty in contagion using panel methods across multiple crisis episodes.
- Relation to empirical studies on uncertainty:
  - Prior studies examined dispersion of GDP forecasts and crises in individual episodes (Prati and Sbracia (2002), Bannier (2006), Tillman (2004)); current paper differs by exploiting cross-sectional variation via panel estimations, longer time horizon, and focus on sharp stock-market falls beyond just currency crises.

### III. MODEL — structure, assumptions, and predictions
- Objectives: Illustrate mechanism behind the uncertainty channel of contagion; focus on sharp drops in stock prices as crisis indicators.
- Environment (two-country setup):
  - Countries: A and B.
  - Agents: a representative firm in each country and foreign investors.
  - Two investor groups: continuum measure one investing exclusively in A and in B respectively.
  - Time: discrete, t = 1, 2. Events for country A occur in period 1; country B in period 2.
  - Fundamentals: single parameter θ_c where c ∈ {A, B}; unconditional distribution of θ is the improper uniform over the real line (following Angeletos and Werning (2006)).
  - Firm project returns: rate of return R(θ) ∈ C_2 with R' > 0, R'' > 0 and R(0) = 0.
  - Private liquidity shock: S_c ~ N(0, 1) for c ∈ {A, B}.
  - Securities: residual value per share equals θ; securities issued at beginning and payoffs delivered at end of period.
  - Risk-free rate normalized to zero.
  - Investor preferences: constant absolute risk aversion utility U(W) = -e^{-γW}.
- Information structure:
  - Investors do not observe fundamentals perfectly; receive signals and may pay cost c to acquire an information-gathering technology.
  - Informed investors (subscript I) vs. uninformed investors (subscript U); measure of informed investors is λ; uninformed measure is (1 - λ).
  - Signal structures:
    - Informed signal: x_{I,i} = θ_c + ε_{I,i}, with ε_{I,i} ~ N(0, σ^2_I).
    - Uninformed signal: x_{U,i} = θ_c + ε_{U,i}, with ε_{U,i} ~ N(0, σ^2_U).
    - Signal precisions: α_I = 1/σ^2_I and α_U = 1/σ^2_U; assume α_I > α_U and set α_U = 1 for simplicity.
    - Stochastic variables ε_{I,i}, ε_{U,i}, and S_c are independent.
  - Behavioral element: investors are unsure about actual precision of the technology; they hold common prior α̂_I > α_U.
    - If an anticipated crisis materializes, posterior belief is G_I α̂_I > α̂_I.
    - If an anticipated crisis does not occur, or if a surprise crisis occurs, posterior belief is B_I α̂ where α_U < B_I α̂ < α̂_I.
    - Investors update beliefs about the technology's precision by observing crises in other countries; these posterior belief shifts affect λ endogenously.
- Timing:
  - All events concerning country A occur in period 1 (initial-crisis country); country B events occur in period 2 (potential contagion target).
- Theoretical predictions (testable):
  - Prediction 1: Surprise crises increase uncertainty (measured by dispersion of fundamentals beliefs) in other countries; anticipated crises decrease uncertainty.
  - Prediction 2: An increase in uncertainty is associated with a higher probability of a financial crisis in another economy.

### IV. EMPIRICAL APPROACH — data and estimation strategy (as described)
- Data:
  - Panel of 38 countries, monthly frequency, December 1993 to September 2005.
  - Crisis episodes covered: Mexico (1994-95), Thailand (1997), Russia (1998), Brazil (1999), Turkey (2001), Argentina (2001-02).
- Estimation:
  - Step 1: Fixed-effects panel estimations linking initial-country crisis to uncertainty regarding fundamentals in other countries.
  - Step 2: Quantify effect of increased uncertainty on probability of crisis in another economy (probability estimations), controlling for other contagion channels.
- Controls and robustness:
  - Controls for other contagion mechanisms mentioned in the literature: common creditors, trade links, initial stock market size, overexposed common fund investors.
  - Robustness checks include restricting attention to individual crisis episodes (e.g., Mexican, Russian, Thai crises) and additional controls for common overexposed fund investors (tables and figures referenced in the source list, e.g., Tables 1–8 and Figures 1–2).

### V. CENTRAL empirical findings and implications
- Empirical findings:
  - Mexico, Thailand, Russia (surprise crises) → increased uncertainty about fundamentals in other countries, stronger intra-regionally.
  - Brazil, Turkey, Argentina (anticipated crises) → decreased uncertainty in other countries, stronger intra-regionally.
  - Higher uncertainty → higher probability of crisis in other economies; effect remains significant after controlling for alternative contagion channels.
  - Marginal effects: the impact of uncertainty on crisis probability is quantitatively non-negligible (detailed marginal results presented in the paper's tables).
- Implication for contagion theory:
  - The surprise vs. anticipated distinction matters because investor updates to beliefs about information precision change the endogenous share of informed investors λ, thereby affecting aggregate uncertainty and crisis risk abroad.
- Methodological implication:
  - Exploiting cross-sectional variation with panel fixed effects and a multi-crisis sample enables quantification of the uncertainty channel beyond single-episode time-series analyses.

*Source: _wp09219 - References .................................................................................................. 39*

### 1. Investors decide whether or not to invest in the information-gathering technology.

### _wp09219 - 1. Investors decide whether or not to invest in the information-gathering technology.

### Model structure and timing
- Two-period model. In period 1:
  - Investors decide whether or not to acquire the information-gathering technology.
  - Investors receive their individual signals on θ_A and purchase (or short) the securities issued by the firm.
  - Based on realized fundamentals and their liquidity shock, the firm decides whether to continue its project or not.
- Period 2 follows the same ordering, except investors update their priors on the reliability of the information-gathering technology after events in Country A.

### D. Investor's problem
- Individual investor maximization problem:
  - max E[W_i^γ e^{-γW_i()}()]  (notation as in source)
  - subject to W_{i,c} = W_{0,i} - cI_{j} + k_{j,i} P_c - k_{j,i} θ_c = 0, where j ∈ {I, U} and I_j = 1 if investor is informed and pays cost c to obtain the technology. (Equation (2) in source.)
- Linear price functions are assumed. Price serves as a noisy signal because supply is uncertain and unobserved; conditional on fundamentals the price realization is normally distributed.
- Equilibrium price function (see Appendix in source for derivation):
  - P̂_c = θ_c − λ_c α̂_I (S_c) − (1−λ_c) ... (Equation (3) in source; presented in source as)
  - () c I cc SP λαλ γ θ −+ − = 1 ˆ
  - Interpretation from source: Equation (3) is the price of the security issued by the firm in country c, with fundamentals θ_c and liquidity shock S_c. (θ_c − P_c) is the discount relative to fundamental value. Expected discount is zero; realized discount positive if security is in positive supply.
- Key comparative statics (textual):
  - Higher γ (absolute risk aversion) and lower beliefs on precision increase the discount and the firm's cost of funds.
  - If perfect information (α̂_I → ∞), equilibrium price equals payout θ_c.
  - If liquidity shock were public, prices would be fully informative and the informed/uninformed decision would be irrelevant.

### E. Firm's problem and crisis threshold
- Firm yields R(θ) per unit invested. Firm abandons project if R(θ) < 0, equivalent under assumptions to θ < 0.
- With a liquidity shock the firm raises P_c(θ_c, S_c) per share. Firm continues project if:
  - P_c S_c > θ_c S_c  (Equation (4) in source)
  - Or equivalently S_c P_c(θ_c,S_c) > S_c θ_c
- Proposition 1 (existence of cutoff):
  - For a positive liquidity shock, there exists θ*_c(γ, S_c, α̂_I) > 0 implicitly defined by
    - S_c P_c(θ*_c, S_c) = S_c θ*_c  (Equation (5) in source)
  - Firm discontinues project if θ_c < θ*_c(γ, S_c, α̂_I).
- Corollary 1 (comparative statics on θ*_c):
  - (i) θ*_c increases if investors are more risk-averse: 0 < ∂θ*_c / ∂γ.
  - (ii) θ*_c is higher for higher realizations of the liquidity shock: 0 < ∂θ*_c / ∂S_c.
  - (iii) θ*_c is lower for higher beliefs on the precision of information-gathering technology: 0̂ < ∂θ*_c / ∂α̂_I  (presented in source as 0̂* < ∂/∂I α̂ θ_c ? — preserved as in source: 0ˆ* < ∂/∂_I c α θ).
  - (iv) θ*_c is lower for a higher proportion of informed investors: 0 < ∂θ*_c / ∂λ_c.
- Interpretation from source:
  - Higher θ*_c implies higher likelihood investors assign to project discontinuation (a "crisis").
  - Discontinuation is interpreted as a crisis episode (sharp loss of firm value → drop in stock market index for the country).
- Anticipated vs surprise crisis definition (source):
  - Market expectation summarized by E[θ_A | P_A].
  - Crisis is anticipated if either E[θ_A | P_A] < 0 or E[P_A R(θ_A) - θ_A | P_A, S_A > 0] < 0.
  - All investors share a common posterior belief on signal precision based on whether an anticipated crisis materializes or not.

### F. Endogenizing the share of informed investors
- Observed variance of forecasts (conditional on θ), given uncorrelated noise terms for informed and uninformed signals:
  - V_forecast|θ = σ_U^2 λ + σ_I^2 (1−λ)  (source expression preserved as)
  - ()() 2 2 22 1| UI forecastV σ λ σ λ θ −+ =  (Equation (6) in source)
- Timing: decision to acquire technology is made prior to the period and realization of random variables. All agents ex-ante identical.
  - All acquire if EU_I > EU_U; none acquire if EU_I < EU_U; interior λ ∈ (0,1) when EU_I = EU_U.
- Proposition 2: Equilibrium share λ of informed investors:
  - λ = 0 if c > b
  - λ = 1 if c < a
  - λ ∈ (0,1) if c ∈ [a,b]
  - where
    - a = ( (2 + ... ) ln(2) / 1 ... ) (preserved from source as)
    - () ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + + = 22 2 ˆ ˆˆ ln 2 1 I II a αγ αγα γ
    - b = (I α̂ ln 2 1 / γ) (presented in source as) () I b α γ ˆ ln 2 1 = .
- Interpretation:
  - Share of informed investors depends on cost c. Too large or too small c → λ = 0 or λ = 1. Intermediate c → interior λ.
  - Boundary values depend on γ and α̂_I. Low γ and high α̂_I widen interval for interior solutions.
- Corollary 2:
  - For interior λ, fraction of informed investors increases for higher beliefs of precision α̂_I, i.e., 0̂ > ∂λ / ∂α̂_I, for beliefs α̂_I that are not too large.
  - Caveat (Grossman–Stiglitz/Diamond–Verrecchia paradox): more informative prices reduce incentives to acquire information; if α̂_I is too large, further increases can reduce λ.

### G. Summary of model implications and testable hypotheses
- Surprise crisis → investors lower belief in precision → smaller share of informed investors (Corollary 2) → higher variance of forecasts → endogenous increase in crisis probability (Corollary 1 (iii) and (iv)).
- Intuition: noisier signals → investors act less aggressively → demand less for deviations → prices become noisier aggregators → higher wedge between price and payout → higher cost of funds → termination more likely.
- Testable hypotheses (from source):
  - Hypothesis 1: An anticipated (surprise) crisis in Country A results in an decrease (increase) in the variance of forecasts regarding the fundamentals in Country B.
  - Hypothesis 2: An increase (decrease) in the variance of forecasts results in a higher (lower) probability of a crisis in Country B.

### IV. Empirical analysis — methodology (two-step strategy)
- Goal: verify effect of initial crisis in Country A on uncertainty in Country B (step 1), and effect of uncertainty in B on probability of crisis there controlling for other contagion channels (step 2).
- Step 1 — estimate effect of crisis in A on uncertainty in B using fixed effects panel regressions:
  - UNC_{B,t} = α_0 + α_1 CR_{Arg,t-1} + ... + α_6 CR_{Tur,t-1} + α_7 CR_{B,t-1} + α_8 Z_{B,t-1} + α_9 INT_{t-1} + δ_B + ε_{B,t}  (Equation (7) in source)
  - UNC_{B,t}: level of uncertainty in country B at time t.
  - CR_{A,t-1}: crisis dummies for initial crisis countries: Argentina, Brazil, Mexico, Russia, Thailand, and Turkey. These six countries excluded from the group of B countries.
  - Z_{B,t-1}: other domestic drivers of uncertainty (mean of growth expectations, stock market volatility, proxies for economic, financial and political risks).
  - INT_t: interest rate in advanced economies.
  - δ_B: country fixed effects.
- Step 2 — estimate effect of uncertainty on probability of a crisis in B using discrete-dependent variable regressions (probit/logit and linear probability specifications):
  - Interaction specification (Equation (8) in source; notation preserved):
    - Pr{CR_B,t = 1 | X} = G{ ... ∑∑_{A ∈ {Arg,...,Tur}} β * (CR_{A,t-1} × CTG_{A,B,t-1}) + β_2 (UNC_{B,t-1} × CR_{A,t-1}) + ... + β_?? Z_{B,t-1} + δ_B + η_{B,t} }  (source presents detailed indexed form; see Equation (8))
  - G(.) denotes standard normal (probit) or logistic (logit) CDF.
  - CTG_{A,B,t-1}: control variables for alternative contagion channels (common creditors, trade links, dependence on common overexposed fund investors, market size of crisis country), interacted with crisis dummy for initial-crisis countries.
  - Coefficient of interest β_2 captures effect of uncertainty on crisis probability.
  - To ensure β_2 does not simply capture direct effect of crises in A, estimate separate specification with UNC and initial-crisis variables entered separately:
    - Pr(CR_B = 1 | Xβ) = G{β_0 + β_1 CR_{Arg,t-1} + ... + β_6 CR_{Tur,t-1} + β_7 UNC_{B,t-1} + β_8 Z_{B,t-1} + δ_B + η_{B,t}}  (Equation (9) in source)
  - Robustness: run probit and logit, and linear probability model to mitigate incidental-parameter problem.

### IV. Empirical analysis — data (as provided)
- Data: rich monthly panel comprising observations from December 1993 to September (text in source ends with "September" at the point provided).

_Italic: Source — _wp09219 - 1. Investors decide whether or not to invest in the information-gathering technology. (PDF chapter/section)_

### 2005. The sample comprises 38 countries—15 developed and 23 emerging—where the

### _wp09219 - 2005. The sample comprises 38 countries—15 developed and 23 emerging—where the

### Data and key variables
- Sample: 38 countries—15 developed and 23 emerging (set of countries listed in Table 5 in the Appendix).
- Measure of uncertainty regarding fundamentals:
  - Defined as the variance of private signals around the true value of fundamentals that affect the rate of return on investments.
  - Proxy used: standard deviation of GDP growth forecasts from Consensus Economics (weighted average of current and following year forecasts in main analysis; robustness checks using only current year forecasts and only following-year forecasts produced qualitatively the same and quantitatively similar results).
- Crisis definition:
  - Monthly stock market returns from the International Finance Corporation (IFC) investable US dollar total return index (nominal US dollar returns).
  - A month is a crisis month if total return undershoots its sample mean by more than two standard deviations; subsequent months are crisis months until returns revert to the one standard deviation band around the sample mean.
  - When needed, returns complemented with data from MSCI or national sources.
- Domestic control variables:
  - Mean of growth forecasts (Consensus Economics) to control for state of the economy.
  - Volatility of stock market returns to disentangle uncertainty regarding fundamentals from general market variability.
  - Indices of financial, economic, and political risk from the International Country Risk Guide (ICRG).
- External controls and contagion-channel controls:
  - Interest rate on 10-year US government bonds to control for advanced-economy interest rates.
  - Common creditor channel: consolidated BIS banking statistics used to construct an index reflecting dependence on common creditors (index construction differs from Van Rijckeghem and Weder (2001) — reflects dependence rather than competition for funds).
  - Trade linkages: bilateral export data from IMF Direction of Trade Statistics; measure used is share of exports to Country A relative to Country B’s total exports (contrast with Glick and Rose (1999) choice).
  - Common overexposed fund investments: index developed by Broner, Gelos and Reinhart (2006) (available for emerging market sample excluding Ukraine).

### Estimation approach
- Step 1: Fixed-effects panel regressions (equation (7)) to estimate effect of an initial crisis in “Country A” on uncertainty in “Country B”.
- Step 2: Pooled probit regression (equation (8)) and robustness checks with logit and linear probability models to estimate effect of uncertainty on the probability of a crisis.
- Controls included for country effects, US long-term interest rate in financial centers, alternative contagion channels, and domestic variables.
- Robustness: analyses run on regional and emerging-market sub-samples; separate regressions including index of overexposed common fund investors for emerging markets.

### Effect of a crisis on uncertainty in other countries (Step 1)
- Main empirical pattern:
  - Surprise crises (Mexican, Russian, Thai) significantly increase uncertainty regarding fundamentals in other countries.
  - Anticipated crises (Brazilian, Turkish, Argentine) decrease uncertainty in potentially-affected countries; effect of Brazilian crisis is less clear/insignificant in some regressions.
- Subsample and heterogeneity findings:
  - Surprise crises prompt stronger effects on uncertainty in emerging markets than in the full sample of all countries.
  - Surprise crises show strong positive effects within their own region; among the three surprise crises the Thai crisis had the strongest impact on uncertainty in other countries.
  - Anticipated crises show a similar pattern with stronger impacts in emerging markets for Argentine and Turkish crises; Brazilian crisis coefficients are insignificant.
- Coefficients on control variables (signs and significance as reported):
  - US bond yield: positive and strongly significant effect on uncertainty globally, stronger effect in emerging markets.
  - Lag of mean growth expectations: negative effect on uncertainty.
  - Lag of crises in potentially-affected countries: positive and significant effect on uncertainty.
  - Past stock market volatility: strong positive and significant effect on uncertainty.
  - ICRG financial, economic, and political risk indices: coefficients mostly not significant.

### Effect of increased uncertainty on the probability of a crisis (Step 2)
- Main findings:
  - Uncertainty variable has a positive and strongly significant effect on probability of a crisis in pooled probit specifications (Table 2, columns (1) and (2)).
  - Effect is stronger in emerging economies (Column (2)).
  - Logit results: positive effect; in all countries not significant at conventional levels in one specification (column (3)), but positive and significant for emerging markets (column (4)).
  - Linear probability model: magnitude smaller but effect remains strongly significant and not negligible (columns (5) and (6)).
  - Results hold when restricting attention to surprise crises (Mexican, Russian, Thai).
- Alternative contagion channels:
  - If overexposed common fund investors not controlled for, common creditors and trade shares have high explanatory power for occurrence of crises.
  - Once controlling for overexposed common fund investors (available only for emerging market sample), common creditors and trade share channels become insignificant (see Table 8 in Appendix).
  - Implication: common creditors and trade-share channels are not entirely robust when overexposure channel is included (at least in emerging market sample).
- Domestic control variables:
  - Mean growth expectations and stock market volatility have correct sign but often insignificant.
- US long-term interest rates:
  - Strong and positive relationship with probability of a stock market crisis.
- Separate entry test:
  - When uncertainty and initial-crisis variables enter separately (no interaction), uncertainty still has a distinctly positive and significant effect on a crisis event in the same economy (Table 3).
- Magnitude (marginal effects; Table 4):
  - A 1 percent increase in the measure of uncertainty is associated with a 1.8 percent increase in the probability of a stock market crisis in that country (conditioning on incidence of crises in initial-crisis countries, US long-term interest rate, and domestic variables).
  - Unconditional stock market crisis probability: 4.5 percent in the entire sample and 6.8 percent in the emerging market sample.
  - Interpretation: effect size is non-negligible relative to unconditional probabilities.

### Integrated interpretation and validation of the theoretical model
- Empirical results support the theoretical model’s hypotheses:
  - Surprise crises increase uncertainty in other countries, which in turn raises those countries’ probability of crisis (the “uncertainty channel of contagion”).
  - Anticipated crises decrease uncertainty in other countries, thereby reducing their crisis probability.
- Robustness: effects of uncertainty remain significant after controlling for trade links, overexposed fund investors, and common creditors.

### Policy implications and recommendations
- Surveillance and monitoring:
  - Immediate policy implication: surveillance activities should be an important element of efforts to promote international financial stability.
  - Closer monitoring of country fundamentals and public reporting can help lower the risk that a surprise crisis in one country causes harmful spillovers to others.
- Rationale:
  - Better information and transparency can reduce the likelihood that investors are surprised by crises and thus reduce the endogenous increase in uncertainty that can propagate crises across countries.

### Appendix highlights (theoretical results and additional tables)
- Theoretical appendix derives equilibrium price function and presents proofs for propositions:
  - Proposition 1: Existence of threshold θ*_c(γ, S_c, I^α) > 0 such that firm discontinues project if θ_c < θ*_c(γ, S_c, I^α).
  - Corollary 1: Comparative statics for θ*_c:
    - 0 <∂θ*_c/∂γ (threshold increases with investor risk aversion).
    - 0 <∂θ*_c/∂S_c (threshold higher for higher liquidity shock realizations).
    - 0̂ >∂θ*_c/∂I^α (threshold lower for higher beliefs on precision of information-gathering technology).
    - 0 <∂θ*_c/∂λ (threshold lower for higher proportion of informed investors).
  - Proposition 2 and Corollary 2: Characterization of equilibrium share of informed investors λ (λ = 0 if c > b; λ = 1 if c < a; λ in (0,1) if c in [a,b]) and comparative static that interior λ increases with higher beliefs on precision of information-gathering technology for I^α not too large.
- Additional empirical tables noted in Appendix:
  - Table 5: Sample of Countries.
  - Table 6: List of Variables (construction details, including variable construction for uncertainty proxy and crisis dummy).
  - Table 7: Step 2 – Effect of Uncertainty on the Probability of a Crisis, restricting attention to the Mexican, Russian and Thai crises.
  - Table 8: Step 2 – Effect of Uncertainty on the Probability of a Crisis, additional control for common overexposed fund investors.

*Source: _wp09219 - 2005. The sample comprises 38 countries—15 developed and 23 emerging—where the (IMF working paper PDF content provided).*

### References

### References

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*Source: _wp09219 - References*

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