## Appendix A – Model Details and Proofs

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---

### I. Introduction — hypothesis and motivation
- Hypothesis: country-level opacity (availability and reliability of information about public and private sectors) amplifies the local impact of changes in global market conditions; more opaque emerging markets react more strongly to global shocks measured by the VIX.
- Empirical scope: emerging market stock and bond markets, 1997-2011.
- Key empirical observation motivating analysis: during the fourth quarter of 2008, drops in equity prices and increases in bond spreads were sharpest for countries with higher levels of opacity.
- Literature context:
  - Transparency can reduce herding, sentiment-driven flows, and excessive investor reactions.
  - Alternative view: transparency may be destabilizing if it crowds out private information and increases volatility.
  - Firm-level disclosure literature links transparency to improved liquidity and lower volatility.

### II. Model — setup and testable implications
- Environment and primitives:
  - Representative agent, CARA utility u(w)=−A^{-1} exp(−Aw); ambiguity preferences h(E(u(w)))=−a^{-1}(−E(u(w)))^a with a≥1.
  - Two risky assets (asset 1 = emerging market, asset 2 = developed market) and a risk-free asset earning zero.
  - Signals: s1 = d1 + ε1, s2 = d2 + ε2 with ε1, ε2 unambiguous normal i.i.d.; d2 ~ N(μ2, σ_{u2}^2) known; d1 = u1 + b with b ∼ N(μ_b, σ_b^2) (ambiguity in mean).
  - Unconditional variance of d1: σ_{u1}^2 + σ_b^2.
- Equilibrium and comparative statics:
  - Optimal allocation θ* and equilibrium prices p* derived (expressions (1) and (2) in text).
  - Proposition 1: If fundamentals are positively correlated (ρ>0), the sensitivity of the emerging market price to a shock in the developed market decreases with the variance of the non-fundamental noise in the emerging market: ∂^2 p_1 / ∂ s_2 ∂ σ_{ε1}^2 < 0.
  - Proposition 2: The sensitivity of the emerging market price to a shock in the developed market is increasing in ambiguity (variance of prior belief about b): ∂^2 p_1 / ∂ s_2 ∂ σ_b^2 > 0, provided ∂ p_1 / ∂ s_2 > 0.
- Intuition:
  - Noisier public information in emerging markets reduces sensitivity to external signals (Proposition 1).
  - Greater ambiguity about fundamentals increases the perceived signal-to-noise ratio and causes stronger reactions to signals from financial centers (Proposition 2).

### III. Empirical strategy and variables
- Main global factor: changes in the VIX (measure of market volatility implicit in U.S. stock options).
- Frequency: weekly (also tested with daily data; similar results).
- Baseline bond specification:
  - Changes in EMBI Global return index spreads: change in spreads Δr_b regressed on global factor, interactions of ΔVIX with opacity measures, controls (weekly change in U.S. 3-month T-bill rate, on-the-run-off-the-run spread, percentage change in exchange rate vs. U.S. dollar, banking/currency/debt crisis dummies, sovereign risk), time trend, year dummies, and lagged controls. Change in spreads modeled (not levels) due to persistence.
- Baseline equity specification:
  - MSCI total return indices excess of U.S. 3-month T-bill: r_e (excess return) regressed on world excess return r_w, ΔVIX interactions with opacity, lagged dividend yield, exchange rate change, crisis dummies, foreign purchase restrictions dummy, market integration measures.
- Measures of country-level opacity (used in both bond and equity regressions):
  - Opacity Index (Opacit) — PricewaterhouseCoopers / Milken Institute survey.
  - Corruption Perceptions (Corrup) — Transparency International Corruption Perceptions Index.
  - Corporate Opacity (Corpop) — Global Competitiveness Report component (scale 1–7).
  - Transparency of Government Policies (TGP) — Global Competitiveness Report question; mean score per country 2002–2011 (scale 1–7).
  - Wilshire Score on accounting standards (W_as).
  - Disclosure — “disclosure in periodic filings” from Djankov et al. (2008) anti-self-dealing index.
  - ROSC — dummy that switches from one to zero once the country’s first IMF Report on Standards and Codes is published.
- Controls and additional variables:
  - Sovereign risk: Standard & Poor’s Rating and Outlook Index.
  - Market segmentation: trade-based (12-month average merchandise trade with U.S.) and capital flows-based (sum of purchases and sales of foreign equities to/from U.S. investors by nationals of each country, previous 12 months).
  - Liquidity proxy: Amihud (2002) illiquidity measure (weekly average ratio of daily absolute return to dollar trading volume).
  - Standard errors: Driscoll-Kraay robust to spatial and temporal dependence; Breusch-Pagan tests reject cross-sectional independence.

### IV. Empirical results — main findings, robustness, and asymmetries
- Main empirical regularity:
  - Emerging markets with higher country-level opacity react more strongly to global shocks (measured by VIX changes) in both bond and equity markets; findings are robust to controls for risk, credit quality, and liquidity.
- Bond spreads — key results:
  - In six of seven specifications, the interaction opacity × ΔVIX is positive and statistically significant.
  - Corruption, Transparency of Government Policies, and ROSC indices significantly amplify bond yield reactions to uncertainty shocks (ROSC significant at the ten percent level).
  - Economic magnitude example: a country in the bottom 10 percentile of transparency (perceptions of corruption by TI) is expected to experience, over the period of one week, a 1.7 percentage point higher increase in spreads in response to a 10-percentage-point increase in the VIX, compared to a country in the highest 10 percentile.
  - Interaction of VIX with S&P credit ratings generally not significant, suggesting opacity captures a dimension distinct from credit quality.
- Equity returns — key results:
  - Most interactions of VIX changes with country opacity are statistically significant at the one percent level (PWC Opacity index and ROSC publication date not significant).
  - Economic magnitude example: the decline in equity returns induced by a 10 percent increase in the VIX, over the period of one week, is 0.29 percentage points higher for countries in the 90th percentile of the Transparency of Government Policies index than for those on the 10th percentile. This is about double the average weekly change in the MSCI for sample countries.
  - Financial integration matters: interaction of VIX with capital flows is negative and statistically significant; trade openness interaction is insignificant.
- Robustness checks:
  - Adding ICRG Composite Country Risk Rating and its interaction with ΔVIX does not eliminate opacity effects; estimated opacity effect increases somewhat.
  - Including lagged Amihud illiquidity reduces significance of some opacity variables (multicollinearity), but interaction terms remain significant in four of seven cases, including corporate opacity, disclosure, accounting standards for equity returns.
  - Including interaction of VIX with local equity market capitalization does not materially change opacity results.
- Asymmetric responses to good vs. bad global shocks:
  - Bonds: higher opacity tends to amplify good shocks more than bad shocks in many specifications (with some exceptions). ROSC insignificant when split.
  - Equities: opacity amplifies adverse shocks more strongly and significantly for nearly all opacity measures (Wilshire accounting standards exception); ROSC shows a significant interaction with good shocks at 10 percent but with opposite sign.
- Endogeneity test:
  - Granger causality using panel VAR(3) with country and year fixed effects between Corruption Perception Index and MSCI return volatility: cannot reject null that volatility does not Granger-cause opacity.
  - Reported statistics: MSCI: χ^2(3) = 4.55; p-value = 0.2083. EMBIG: χ^2(3) = 5.05; p-value = 0.1685.

### V. Policy implications and recommendations
- Policy message:
  - Increasing transparency (more and more timely data, improved corporate disclosure standards, and improved governance) can reduce the amplification of global shocks in emerging markets and thereby mitigate the unpleasant side effects of financial globalization.
- Suggested avenues for further research:
  - Extend analysis to other cross-border capital flows such as bank lending.
  - Study implications for contagion channels across domestic assets and institutions.
  - Explore theoretical settings with heterogeneous information to test robustness of predictions in richer models.
  - Consider role of domestic investors and informational asymmetries.

### A.1 — Joint and conditional distributions (model technical details)
- Assumption: correlation ρ between dividends paid by assets 1 and 2 is known.
- Joint distribution of dividends and signals stated in multivariate normal form:
  - d ∼ N(Md, Vd) with Md and Vd given in the source.
  - s ∼ N(Ms, Vs) with Ms = Md and Vs given in the source.
  - Joint [s d]' ∼ N([Ms Md]', [Vs Csd'; Cds Vd]).
  - By Bayesian updating: d|s ∼ N(Md + Cds Vs−1 Cds′(S − Ms), Vd − Cds Vs−1 Cds′).
- Distribution of d conditional on J = [s′ b]′:
  - d|J normal with mean Md + C B−1 C′(S − Ms) and variance Vd − C B−1 C′, where S − Ms = [s1 − μ1 − μb, s2 − μ2, b − μb ]′ and x = [σb^2  0]′ as specified.

### A.2 — Proofs, signal-to-noise ratios, and comparative statics
- Definitions and properties:
  - Signal-to-noise ratios φ1, φ2 with 0< φi <1 for i∈{1,2}.
  - Lemma 1 (spillovers sign condition): ∂ p1/∂ s2 has the same sign as ρ; positive ρ implies positive cross-market price response.
- Proposition 1 (attenuation by non-fundamental noise):
  - If ρ>0 then ∂^2 p1 / (∂ s2 ∂ σ^2_ε1) < 0. Proof based on expression (A.1) and algebra yielding a negative derivative.
- Proposition 2 (ambiguity amplifies cross-market sensitivity):
  - The sensitivity ∂ p1/∂ s2 is increasing in ambiguity measured by prior variance about b: formally ∂^2 p1/(∂ s2 ∂ σ~_b) > 0 under the stated condition ∂ p1/∂ s2 > 0. Proof proceeds by differentiating the expression for ∂ p1/∂ s2 and showing positivity of intermediate terms (χ and its derivatives) per (A.1) and (A.2).
- Notation and sign summary:
  - φ1, φ2 ∈ (0,1).
  - ∂ p1/∂ s2 has sign of ρ.
  - ∂^2 p1/(∂ s2 ∂ σ^2_ε1) < 0.
  - ∂^2 p1/(∂ s2 ∂ σ~_b) > 0 under the maintained conditions.

### Selected empirical table highlights (preserved numeric coefficients and coverage)
- Asymmetric effects (Dependent variable: ΔEMBIG_i,t)
  - Δon-off spread: 0.0398** (0.014); ...; 0.0392** (0.012)
  - ΔiUS3mo_t: -0.0030 (0.244); ...; -0.0029 (0.255)
  - Debt Crisis: 0.0401* (0.058); ...; 0.0419** (0.046)
  - ΔXRATE: 0.3277*** (0.000); ...; 0.3256*** (0.000)
  - ΔVIX×t: 0.0004*** (0.001); ...; 0.0004*** (0.001)
  - ΔVIX_G × Opacity: 0.0012 (0.533); 0.0469*** (0.000); 0.0444** (0.023); 0.0167 (0.609); 0.1441*** (0.002); 0.0123 (0.612); 0.0029 (0.940)
  - ΔVIX_B × Opacity: 0.0037** (0.016); 0.0289*** (0.000); 0.0276 (0.105); -0.0249 (0.169); 0.0805*** (0.006); 0.0429** (0.037); 0.0465 (0.175)
  - Observations: 11,214; 11,879; 11,040; 11,931; 11,931; 9,155; 11,931
  - Number of countries: 19; 21; 19; 21; 21; 21; 21
- Table 5 — Linear effects (Dependent variable: ΔMSCI_i,t)
  - D/Y_I,t−1: 0.0011** (0.013); ...; 0.0010** (0.016)
  - ΔVIX×Capital Flows: -0.0126** (0.026); ...; -0.0236*** (0.000)
  - ΔXRATE: -0.2707*** (0.000); ...; -0.2754*** (0.000)
  - ΔMSCI_US×t: 0.0008** (0.025); ...; 0.0008** (0.026)
  - ΔVIX× Opacity: -0.0004 (0.189); -0.0030** (0.023); -0.0129*** (0.003); -0.0211*** (0.007); -0.0625*** (0.000); -0.0162*** (0.000); 0.0033 (0.679)
  - Observations: 15,242; 16,746; 15,502; 15,502; 16,850; 12,846; 16,850
  - Number of countries: 23; 25; 23; 23; 25; 25; 25
- Table 6 — Asymmetric effects (Dependent variable: ΔMSCI_i,t)
  - ΔVIX_G × Opacity: 0.0013 (0.128); 0.0043* (0.063); -0.0013 (0.831); -0.0238* (0.083); -0.0457*** (0.007); -0.0016 (0.845); 0.0354* (0.069)
  - ΔVIX_B × Opacity: -0.0013** (0.014); -0.0071*** (0.000); -0.0192*** (0.000); -0.0193* (0.050); -0.0719*** (0.000); -0.0244*** (0.000); -0.0140 (0.303)
  - Observations: 15,242; 16,746; 15,502; 15,502; 16,850; 12,846; 16,850
  - Number of countries: 23; 25; 23; 23; 25; 25; 25
- Table 7 — Transparency and Country Risk Ratings
  - ΔVIX× CCR: -0.0025*** (0.001); ...; -0.0012** (0.018)
  - ΔVIX× Opacity: -0.0011*** (0.007); -0.0097*** (0.000); -0.0147*** (0.002); -0.0257*** (0.002); -0.0697*** (0.000); -0.0289*** (0.000); 0.0005 (0.948)
  - Observations: 15,196; 16,696; 15,456; 15,456; 16,800; 12,796; 16,800
  - Number of countries: 23; 25; 23; 23; 25; 25; 25
- Table 8 — Transparency and Market Liquidity
  - Illiquidity: -5.3325 (0.353); -5.0212 (0.378); -0.2091 (0.980); -5.6733 (0.305); -5.2589 (0.339); -3.5732 (0.507); -5.1209 (0.349)
  - ΔVIX× Illiquidity: 12.6808 (0.761); 12.9639 (0.757); -31.9403 (0.201); 23.0048 (0.590); 20.0424 (0.603); 217.1118*** (0.000); 12.1788 (0.771)
  - ΔVIX× Opacity: -0.0004 (0.216); -0.0010 (0.447); -0.0077* (0.052); -0.0176** (0.017); -0.0774*** (0.000); -0.0164*** (0.000); 0.0057 (0.505)
  - Observations: 15,194; 16,024; 14,782; 14,780; 16,128; 12,293; 16,128
  - Number of countries: 23; 24; 22; 22; 24; 24; 24
- Table 9 — Granger Causality (panel VAR(3))
  - MSCI: χ^2(3) = 4.55; p-value = 0.2083
  - EMBIG: χ^2(3) = 5.05; p-value = 0.1685

*Source: _wp13156 - Appendix A – Model Details and Proofs*

### Appendix A – Model Details and Proofs .................................................................................2

### Appendix A – Model Details and Proofs

### Contents overview
- Appendix A – Model Details and Proofs .................................................................................20

### Related appendix listing
- Appendix B – List of Countries Used in the Sample ...............................................................23

*Source: _wp13156 - Appendix A – Model Details and Proofs*

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

### _wp13156 - References

### I. Introduction — hypothesis and motivation
- Hypothesis: country-level opacity (availability and reliability of information about public and private sectors) amplifies the local impact of changes in global market conditions; more opaque emerging markets react more strongly to global shocks measured by the VIX.
- Empirical scope: emerging market stock and bond markets, 1997-2011.
- Key empirical observation motivating analysis: during the fourth quarter of 2008, drops in equity prices and increases in bond spreads were sharpest for countries with higher levels of opacity (Figures 1 and 2).
- Literature context:
  - Transparency can reduce herding, sentiment-driven flows, and excessive investor reactions (Goldstein, 1998; IMF 2001; Frenkel and Menkhoff, 2004; Gai, 2003).
  - Alternative view: transparency may be destabilizing if it crowds out private information and increases volatility (Furman, Stiglitz, Bosworth, and Radelet, 1998; Morris and Shin, 2002; Morris, Shin, and Tong, 2006).
  - Firm-level disclosure literature links transparency to improved liquidity and lower volatility (Amihud, Mendelson and Pedersen, 2005; Lang, Lins, and Maffett, 2012; Lang and Maffet, 2011).

### II. Model — setup and testable implications
- Environment:
  - Representative agent, CARA utility u(w)=−A^{-1} exp(−Aw); ambiguity preferences h(E(u(w)))=−a^{-1}(−E(u(w)))^a with a≥1.
  - Two risky assets (asset 1 = emerging market, asset 2 = developed market) and a risk-free asset earning zero.
  - Signals: s1 = d1 + ε1, s2 = d2 + ε2 with ε1, ε2 unambiguous normal i.i.d.; d2 ~ N(μ2, σ_{u2}^2) known; d1 = u1 + b with b ∼ N(μ_b, σ_b^2) (ambiguity in mean).
  - Unconditional variance of d1: σ_{u1}^2 + σ_b^2.
- Equilibrium/price relation:
  - Optimal allocation θ* and equilibrium prices p* derived (expressions (1) and (2) in text).
  - Key analytical results (comparative statics):
    - Proposition 1: If fundamentals are positively correlated (ρ>0), the sensitivity of the emerging market price to a shock in the developed market decreases with the variance of the non-fundamental noise in the emerging market: ∂^2 p_1 / ∂ s_2 ∂ σ_{ε1}^2 < 0.
    - Proposition 2: The sensitivity of the emerging market price to a shock in the developed market is increasing in ambiguity (variance of prior belief about b): ∂^2 p_1 / ∂ s_2 ∂ σ_b^2 > 0, provided ∂ p_1 / ∂ s_2 > 0.
- Intuition:
  - Noisier public information in emerging markets reduces sensitivity to external signals (Proposition 1).
  - Greater ambiguity about fundamentals increases the perceived signal-to-noise ratio and causes stronger reactions to signals from financial centers (Proposition 2).

### III. Empirical strategy and variables
- Main global factor: changes in the VIX (measure of market volatility implicit in U.S. stock options).
- Frequency: weekly (also tested with daily data; similar results).
- Baseline bond specification (changes in EMBI Global return index spreads): equation (3) — change in spreads Δr_b regressed on global factor, interactions of ΔVIX with opacity measures, controls (weekly change in U.S. 3-month T-bill rate, on-the-run-off-the-run spread, percentage change in exchange rate vs. U.S. dollar, banking/currency/debt crisis dummies, sovereign risk), time trend, year dummies, and lagged controls. Change in spreads modeled (not levels) due to persistence.
- Baseline equity specification (MSCI total return indices excess of U.S. 3-month T-bill): equation (4) — r_e (excess return) regressed on world excess return r_w, ΔVIX interactions with opacity, lagged dividend yield, exchange rate change, crisis dummies, foreign purchase restrictions dummy, market integration measures.
- Measures of country-level opacity (used in both bond and equity regressions):
  - Opacity Index (Opacit) — PricewaterhouseCoopers / Milken Institute survey of bureaucratic practices, legal system, government macro policies, accounting standards, regulatory regime.
  - Corruption Perceptions (Corrup) — Transparency International Corruption Perceptions Index.
  - Corporate Opacity (Corpop) — component from Global Competitiveness Report (survey of executives); scale 1–7.
  - Transparency of Government Policies (TGP) — Global Competitiveness Report question; mean score per country 2002–2011 (scale 1–7).
  - Wilshire Score on accounting standards (W_as).
  - Disclosure — “disclosure in periodic filings” from Djankov et al. (2008) anti-self-dealing index.
  - ROSC — dummy that switches from one to zero once the country’s first IMF Report on Standards and Codes is published.
- Controls and additional variables:
  - Sovereign risk: Standard & Poor’s Rating and Outlook Index.
  - Market segmentation: trade-based (12-month average merchandise trade with U.S.) and capital flows-based (sum of purchases and sales of foreign equities to/from U.S. investors by nationals of each country, previous 12 months).
  - Liquidity proxy: Amihud (2002) illiquidity measure (weekly average ratio of daily absolute return to dollar trading volume).
  - Standard errors: Driscoll-Kraay robust to spatial and temporal dependence; Breusch-Pagan tests reject cross-sectional independence.

### IV. Empirical results — main findings, robustness, and asymmetries
- Main empirical regularity:
  - Emerging markets with higher country-level opacity react more strongly to global shocks (measured by VIX changes) in both bond and equity markets; findings are robust to controls for risk, credit quality, and liquidity.
- Bond spreads (summary of key empirical findings):
  - In six of seven specifications, the interaction opacity × ΔVIX is positive and statistically significant.
  - Corruption, Transparency of Government Policies, and ROSC indices significantly amplify bond yield reactions to uncertainty shocks (ROSC significant at the ten percent level).
  - Economic magnitude example: a country in the bottom 10 percentile of transparency (perceptions of corruption by TI) is expected to experience, over the period of one week, a 1.7 percentage point higher increase in spreads in response to a 10-percentage-point increase in the VIX, compared to a country in the highest 10 percentile.
  - Interaction of VIX with S&P credit ratings generally not significant, suggesting opacity captures a dimension distinct from credit quality.
- Equity returns:
  - Most interactions of VIX changes with country opacity are statistically significant at the one percent level (PWC Opacity index and ROSC publication date not significant).
  - Economic magnitude example: the decline in equity returns induced by a 10 percent increase in the VIX, over the period of one week, is 0.29 percentage points higher for countries in the 90th percentile of the Transparency of Government Policies index (i.e., the top 10 percent most opaque countries) than for those on the 10th percentile. This is about double the average weekly change in the MSCI for sample countries.
  - Financial integration matters: interaction of VIX with capital flows is negative and statistically significant (more integrated equity markets suffer more from VIX fluctuations); trade openness interaction is insignificant.
- Robustness checks:
  - Opacity vs. generic country risk: adding ICRG Composite Country Risk Rating and its interaction with ΔVIX does not eliminate opacity effects; estimated opacity effect increases somewhat.
  - Opacity vs. liquidity: including lagged Amihud illiquidity reduces significance of some opacity variables (multicollinearity), but interaction terms remain significant in four of seven cases, including key indices for equity returns (corporate opacity, disclosure, accounting standards).
  - Market capitalization interaction (to capture fixed costs of information gathering): including interaction of VIX with local equity market capitalization does not materially change opacity results.
- Asymmetric responses to good vs. bad global shocks:
  - Modified specifications separate ΔVIX < 0 (good shocks) and ΔVIX > 0 (bad shocks) with separate interactions.
  - Bonds: higher opacity tends to amplify good shocks more than bad shocks (with some exceptions: PWC Opacity and Transparency of Government Policies); ROSC insignificant when split.
  - Equities: opacity amplifies adverse shocks more strongly and significantly for nearly all opacity measures (Wilshire accounting standards exception); ROSC shows a significant interaction with good shocks at 10 percent but with opposite sign.
  - Link to prior literature: asymmetric equity result complements Bae, Lim, and Wei (2006) on corporate governance and return skewness.
- Endogeneity test:
  - Granger causality test using panel VAR (3 lags, country and year fixed effects) between Corruption Perception Index (time-varying opacity) and MSCI return volatility: cannot reject the null that volatility does not Granger-cause opacity for both equities and bonds (Table 9). Conclusion: opacity endogeneity not evident in these data.

### V. Policy implications and recommendations
- Policy message:
  - Increasing transparency (more and more timely data, improved corporate disclosure standards, and improved governance) can reduce the amplification of global shocks in emerging markets and thereby mitigate the unpleasant side effects of financial globalization.
- Suggested avenues for further research (from the paper):
  - Extend analysis to other cross-border capital flows such as bank lending.
  - Study implications for contagion channels across domestic assets and institutions.
  - Explore theoretical settings with heterogeneous information to test robustness of predictions in richer models.
  - Consider role of domestic investors and informational asymmetries (authors note empirical results suggest international investor effects dominate in their sample).

*Source: _wp13156 - References (IMF Working Paper content provided in the input).*

### APPENDIX A – MODEL DETAILS AND PROOFS

### APPENDIX A – MODEL DETAILS AND PROOFS

### A.1 – Joint and conditional distributions of signal and dividend processes
- Assumption: correlation ρ between dividends paid by assets 1 and 2 is known.
- Covariance expression (as in source): cov(d1,d2)=
  21222 1 ~ σσσσρσσσρ = + = bu, where 22 1 2 1 ~ bu σσσ + ≡.
- Joint distribution of the two dividend processes:
  - d ∼ N(Md, Vd), where
    - Md = [μ1  μ2+μb/2]' (source sequence: 1 2 b d M μ μ μ + [ ] = )
    - Vd = [ [σ1^2  + ~?   (source matrix):  
      ⎡   ?   ⎤
      ⎣   ?   ⎦ ] with entries shown in source as
      ⎡ 2 2 2 2 21 2 1 ~~ ε σ σ σ σ ρ σ ⎤ (source formatting preserved)
  - Joint distribution of the two signals: s ∼ N(Ms, Vs), where Ms = Md and
    - Vs = [ 22 1112 22 22 ε ε σ   σ    ρσ σ σσ  ⎡⎤  + = ... (source matrix expression preserved) ]
- Given joint distribution of d and s:
  - [s d]' ∼ N([Ms Md]', [Vs Csd'; Cds Vd]) (source block matrix structure).
  - By Bayesian updating, conditional distribution: d|s ∼ N(Md + Cds Vs−1 Cds′(S − Ms), Sd − Cds Vs−1 Cds′).
  - Using orthogonality of noise to dividend processes: Cds = Vd.
- Distribution of d conditional on J = [s′ b]′:
  - d|J is normal with mean Md + C B−1 C′(S − Ms) and variance Vd − C B−1 C′,
  - where S − Ms = [s1 − μ1 − μb, s2 − μ2, b − μb ]′,
  - B = [ 2 s b V σx ]′ (source: 2 s b V B σ [ ] = x′ x ),
  - and C = [Vd ⋮ x], with x = [σb^2  0]′.

### A.2 – Proofs, signal-to-noise ratios, and comparative statics
- Definitions and preliminary properties:
  - Consider ∂^2E(pd|s)/∂s^2 = ()E ss ∂∂ = ∂∂ pd s| .
  - Define signal-to-noise ratios:
    - φ1 and φ2 where 0< φ2 ≡ σ2^2/(σ2^2+σ2^2_ε) < 1, and similarly 0/1 φ ε σ σ σ ≡ + < (source formatting preserved). φ1 and φ2 are signal-to-noise ratios of assets 1 and 2, respectively.
  - Condition: noise terms are nondegenerate ensures 0< φi <1 for i∈{1,2}.

- Lemma 1 (spillovers sign condition)
  - Statement: Asset prices in the emerging market react positively (negatively) to positive (negative) news concerning the developed market if and only if the two dividend processes are positively correlated, i.e., ∂ p1/∂ s2 > 0 if ρ>0.
  - Key derivation: Using equation (2) and differentiating with respect to s2 yields (after algebra) expression (A.1) in source showing sign determined by ρ.
  - Main inequality reproduced (source): (A.1) left-hand side > 0 for 0< φi <1 and |ρ|<1; therefore ∂p1/∂s2 > 0 if ρ>0.

- Proposition 1 (attenuation by non-fundamental noise)
  - Statement: If fundamentals in the two markets are positively correlated (ρ>0), the sensitivity of the price of asset 1 (emerging market) to a shock in the developed market (signal 2) is decreasing in the variance of the non fundamental shock to asset 1. Formally:
    - ∂^2 p1 / (∂ s2 ∂ σ^2_ε1) < 0.
  - Proof sketch and algebra:
    - From (A.1) define ∂ p1/∂ s2 = ρ σ12 χ, with χ ≡ 2 121 2 2 12 (1) 1 φ φ ρ φ φ + − − + − (source expression χ and (1) definition preserved).
    - Equation (A.2) (source) shows derivative signs leading to final inequality:
      - (source expression) leading to ∂^2 p / ∂ s ∂ σ^2_ε1 = ... = − (positive terms) < 0 for ρ>0.

- Proposition 2 (ambiguity amplifies cross-market sensitivity)
  - Statement: The sensitivity of the price of asset 1 to a shock in the developed market (signal 2) is increasing in ambiguity (measured by the variance of the prior belief about b) as long as >0 (source placeholder).
  - Formal target inequality to show (as in source):
    - .0 ~ ~ 2 1 12 1 2 2 2 1 2 ≡ ∂∂∂∂ bb s p s p σ σ σ σ > .
    - Source notes: .0 ~ /2 ~ 11 2 1 2 1 > = ∂ φ σ σ σ σ ε b (source formatting preserved).
  - Main steps:
    - Suffices to show ∂^2 p / ∂ σ~_b ∂ s2 > 0.
    - Using formula for ∂^2 p / ∂ s2 from above, define intermediate terms and show positivity:
      - Expression for ∂^2 p / ∂ σ~_b ∂ s2 given in source: (source formula block) with χ and derivatives positive.
    - Using previous results: 2 0 ρ σ χ > by (A.1) and 1 0 χ φ ∂ > ∂ from (A.2). Therefore ∂^2 p / ∂ σ~_b ∂ s2 > 0. ∎

- Notation and sign results summarized:
  - φ1, φ2 ∈ (0,1) (signal-to-noise ratios).
  - ∂ p1/∂ s2 has the same sign as ρ; positive ρ implies positive cross-market price response.
  - Increasing σ^2_ε1 (non-fundamental noise in asset 1) reduces cross-market sensitivity: ∂^2 p1/(∂ s2 ∂ σ^2_ε1) < 0.
  - Increasing prior-variance about b (ambiguity) raises cross-market sensitivity under stated conditions: ∂^2 p1/(∂ s2 ∂ σ~_b) > 0.

*Source: _wp13156 - APPENDIX A – MODEL DETAILS AND PROOFS*

### 0.5 percentile.  Table  shows  the  asymmetric  effects  specification  with  country  and  year  fixed  effects  and  D

### _wp13156 - Tables on Global Shocks, Stock Returns, Transparency, and Related Tests

### Asymmetric effects (Dependent variable: ΔEMBIG_i,t)
- Model specification: asymmetric effects with country and year fixed effects and Driscoll-Kraay standard errors. ΔVIX_G and ΔVIX_B stand for good (decrease) and bad (increase) volatility shocks (measured by VIX). Indices normalized if needed so as to reflect increasing level of opacity. P-value in parentheses: *** p<0.01, ** p<0.05, * p<0.1.
- Key coefficients and significance (selected, values preserved exactly as in table):
  - Δon-off spread: 0.0398** (0.014); 0.0388** (0.013); 0.0395** (0.015); 0.0390** (0.012); 0.0391** (0.012); 0.0457** (0.039); 0.0392** (0.012)
  - ΔiUS3mo_t: -0.0030 (0.244); -0.0029 (0.254); -0.0031 (0.254); -0.0029 (0.252); -0.0029 (0.255); -0.0024 (0.338); -0.0029 (0.255)
  - Debt Crisis: 0.0401* (0.058); 0.0418** (0.045); 0.0426** (0.045); 0.0426** (0.044); 0.0421** (0.046); 0.0419** (0.046)
  - ΔXRATE: 0.3277*** (0.000); 0.3322*** (0.000); 0.3245*** (0.000); 0.3266*** (0.000); 0.3182*** (0.000); 0.2762*** (0.000); 0.3256*** (0.000)
  - ΔVIX×t: 0.0004*** (0.001); 0.0003*** (0.006); 0.0004*** (0.002); 0.0003*** (0.003); 0.0003*** (0.004); 0.0005*** (0.000); 0.0004*** (0.001)
  - ΔVIX_G × Opacity: 0.0012 (0.533); 0.0469*** (0.000); 0.0444** (0.023); 0.0167 (0.609); 0.1441*** (0.002); 0.0123 (0.612); 0.0029 (0.940)
  - ΔVIX_B × Opacity: 0.0037** (0.016); 0.0289*** (0.000); 0.0276 (0.105); -0.0249 (0.169); 0.0805*** (0.006); 0.0429** (0.037); 0.0465 (0.175)
- Observations and coverage:
  - Observations: 11,214; 11,879; 11,040; 11,931; 11,931; 9,155; 11,931
  - Number of countries: 19; 21; 19; 21; 21; 21; 21

### Table 5 — Global Shocks, Stock Returns and Transparency: Linear Effects (Dependent variable: ΔMSCI_i,t)
- Dependent variable: weekly returns of country MSCI index, winsorized at the top and bottom 0.5 percentile. Baseline nonlinear effects specification with country and year fixed effects and Driscoll-Kraay standard errors. Capital Flows: previous three months’ average of total flows (TIC). Trade: previous twelve months’ average of total trade (World Bank).
- Selected coefficients (values preserved):
  - D/Y_I,t−1: 0.0011** (0.013); 0.0010** (0.017); 0.0007 (0.124); 0.0010** (0.018); 0.0010** (0.017); 0.0010 (0.106); 0.0010** (0.016)
  - ΔVIX×Capital Flows: -0.0126** (0.026); -0.0297*** (0.000); -0.0236*** (0.000); -0.0620*** (0.000); -0.0378*** (0.000); -0.0282*** (0.000); -0.0236*** (0.000)
  - ΔXRATE: -0.2707*** (0.000); -0.2756*** (0.000); -0.2754*** (0.000); -0.2657*** (0.000); -0.2708*** (0.000); -0.2604*** (0.000); -0.2754*** (0.000)
  - ΔMSCI_US×t: 0.0008** (0.025); 0.0008** (0.030); 0.0008** (0.027); 0.0008** (0.022); 0.0008** (0.026); 0.0010** (0.026); 0.0008** (0.026)
  - ΔVIX× Opacity: -0.0004 (0.189); -0.0030** (0.023); -0.0129*** (0.003); -0.0211*** (0.007); -0.0625*** (0.000); -0.0162*** (0.000); 0.0033 (0.679)
- Observations and coverage:
  - Observations: 15,242; 16,746; 15,502; 15,502; 16,850; 12,846; 16,850
  - Number of countries: 23; 25; 23; 23; 25; 25; 25

### Table 6 — Global Shocks, Stock Returns, and Transparency: Asymmetric Effects (Dependent variable: ΔMSCI_i,t)
- Asymmetric effects specification with ΔVIX_G and ΔVIX_B (good and bad volatility shocks). Selected coefficients:
  - D/Y_I,t−1: 0.0011** (0.013); 0.0010** (0.016); 0.0007 (0.113); 0.0010** (0.015); 0.0010** (0.015); 0.0010* (0.099); 0.0010** (0.015)
  - ΔVIX×Capital Flows: -0.0127** (0.024); -0.0296*** (0.000); -0.0234*** (0.000); -0.0618*** (0.000); -0.0376*** (0.000); -0.0283*** (0.000); -0.0233*** (0.000)
  - ΔXRATE: -0.2642*** (0.000); -0.2689*** (0.000); -0.2685*** (0.000); -0.2589*** (0.000); -0.2637*** (0.000); -0.2567*** (0.000); -0.2674*** (0.000)
  - Opacity: 0.0001 (0.304); 0.0011 (0.241); 0.0011 (0.147); 0.0006 (0.629); 0.0035*** (0.007); 0.0015 (0.533)
  - ΔVIX_G × Opacity: 0.0013 (0.128); 0.0043* (0.063); -0.0013 (0.831); -0.0238* (0.083); -0.0457*** (0.007); -0.0016 (0.845); 0.0354* (0.069)
  - ΔVIX_B × Opacity: -0.0013** (0.014); -0.0071*** (0.000); -0.0192*** (0.000); -0.0193* (0.050); -0.0719*** (0.000); -0.0244*** (0.000); -0.0140 (0.303)
- Observations and coverage:
  - Observations: 15,242; 16,746; 15,502; 15,502; 16,850; 12,846; 16,850
  - Number of countries: 23; 25; 23; 23; 25; 25; 25

### Table 7 — Transparency and Country Risk Ratings (Dependent variable: ΔMSCI_i,t)
- Baseline nonlinear effects with additional Country Risk Rating (CCR / CRR / ICRG’s Composite Country Risk). Selected coefficients:
  - D/Y_I,t−1: 0.0011** (0.011); 0.0010** (0.014); 0.0007 (0.132); 0.0011** (0.014); 0.0010** (0.015); 0.0011* (0.065); 0.0010** (0.014)
  - ΔVIX×Capital Flows: -0.0041 (0.474); -0.0280*** (0.000); -0.0216*** (0.001); -0.0637*** (0.000); -0.0284*** (0.000); -0.0156*** (0.006); -0.0169*** (0.006)
  - ΔXRATE: -0.2731*** (0.000); -0.2782*** (0.000); -0.2762*** (0.000); -0.2669*** (0.000); -0.2725*** (0.000); -0.2612*** (0.000); -0.2768*** (0.000)
  - ΔVIX: 0.2292*** (0.001); 0.2408*** (0.001); 0.0847 (0.107); 0.1584*** (0.005); 0.1674*** (0.002); 0.3818*** (0.000); 0.0819* (0.075)
  - ΔVIX× CCR: -0.0025*** (0.001); -0.0026*** (0.002); -0.0006 (0.227); -0.0030*** (0.000); -0.0019*** (0.001); -0.0036*** (0.000); -0.0012** (0.018)
  - ΔVIX× Opacity: -0.0011*** (0.007); -0.0097*** (0.000); -0.0147*** (0.002); -0.0257*** (0.002); -0.0697*** (0.000); -0.0289*** (0.000); 0.0005 (0.948)
- Observations and coverage:
  - Observations: 15,196; 16,696; 15,456; 15,456; 16,800; 12,796; 16,800
  - Number of countries: 23; 25; 23; 23; 25; 25; 25

### Table 8 — Transparency and Market Liquidity (Dependent variable: ΔMSCI_i,t)
- Illiquidity measured by Amihud’s (2002) measure. Selected coefficients:
  - D/Y_I,t−1: 0.0011** (0.013); 0.0011** (0.014); 0.0008 (0.109); 0.0011** (0.015); 0.0011** (0.015); 0.0010* (0.092); 0.0011** (0.013)
  - ΔVIX×Capital Flows: -0.0118** (0.037); -0.0173*** (0.003); -0.0096* (0.092); -0.0494*** (0.000); -0.0311*** (0.000); -0.0215*** (0.001); -0.0151*** (0.003)
  - ΔXRATE: -0.2718*** (0.000); -0.2735*** (0.000); -0.2721*** (0.000); -0.2648*** (0.000); -0.2672*** (0.000); -0.2572*** (0.000); -0.2732*** (0.000)
  - Illiquidity: -5.3325 (0.353); -5.0212 (0.378); -0.2091 (0.980); -5.6733 (0.305); -5.2589 (0.339); -3.5732 (0.507); -5.1209 (0.349)
  - ΔVIX× Illiquidity: 12.6808 (0.761); 12.9639 (0.757); -31.9403 (0.201); 23.0048 (0.590); 20.0424 (0.603); 217.1118*** (0.000); 12.1788 (0.771)
  - ΔVIX× Opacity: -0.0004 (0.216); -0.0010 (0.447); -0.0077* (0.052); -0.0176** (0.017); -0.0774*** (0.000); -0.0164*** (0.000); 0.0057 (0.505)
- Observations and coverage:
  - Observations: 15,194; 16,024; 14,782; 14,780; 16,128; 12,293; 16,128
  - Number of countries: 23; 24; 22; 22; 24; 24; 24

### Table 9 — Granger Causality between Opacity and Volatility
- Panel VAR(3) of opacity (Corrup - Transparency International’s Country Transparency index) and measured market volatility with annual data. Volatility: standard deviation of equity (MSCI) or bond (EMBIG) daily returns over one year. VAR estimated by OLS with country and year fixed effects. Reported: χ^2(3) statistic and p-value for joint hypothesis that lagged volatility coefficients in the opacity equation are jointly zero (non rejection signifies volatility does not Granger-cause opacity).
  - MSCI: χ^2(3) = 4.55; p-value = 0.2083
  - EMBIG: χ^2(3) = 5.05; p-value = 0.1685

*Italic source: Extracted from _wp13156 - 0.5 percentile. Table shows the asymmetric effects specification with country and year fixed effects and Driscoll-Kraay standard errors.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2013/_wp13156.pdf_