## _wp07230

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---

### I. Introduction — purpose, context, and contributions
- Defines the equity premium puzzle (EPP) as "the differential between return to equity and return to safe assets in excess of the premium that can be explained on the basis of a reasonable degree of risk aversion."
- Notes traditional fundamentals (consumption smoothing, liquidity constraints, financial sector development, age composition of investors, tax differences) explain part of the equity-safe return differential but observed premia may remain large and imply empirically unsupported extreme risk aversion.
- Emphasizes Knightian uncertainty (ambiguity) as pervasive in financial markets; ambiguity implies probabilities and payoffs are not known with precision and decision makers exhibit ambiguity aversion.
- Paper’s two main contributions:
  - Proposes ambiguity aversion as a possible explanation for EPP: if equity returns are perceived as more ambiguous than safe-asset returns, an ambiguity premium on equity can increase the observed equity premium.
  - Documents EPP across a large cross-country sample (53 countries: 29 emerging, 24 mature) over 1996–05 and examines the role of institutional quality and other indexes as proxies for uncertainty.
- Empirical approach: correlation tests and regressions showing statistically significant correlations between equity premium and some uncertainty proxies; suggests ambiguity aversion can explain a significant portion of large equity premia where institutional quality reflects uncertainty.

### II. Equity premium is a global phenomenon — data, measurement, and main observations
- Sample and measurement:
  - 53 countries: 29 emerging markets and 24 mature markets.
  - Period: 1996–05.
  - Real stock market return = yearly percentage change in nominal stock market index divided by CPI.
  - Real safe asset return = nominal return minus CPI inflation.
  - Real equity premium = real stock market return minus real safe asset return (dividend yield excluded).
- Key period-average statistics (as reported for Table 1; percent and sample/period σ preserved exactly):
  - All sample countries, 1996-2000:
    - Equity premium: 6.21
    - σs (sample): 16.3
    - σp (period): 17.7
    - Stock market return: 10.7
    - σs (sample): 15.9
    - σp (period): 12.5
    - Safe asset return: 4.3
    - σs (sample): 3.7
    - σp (period): 0.4
  - Emerging markets, 1996-2000:
    - Equity premium: 0.02
    - σs (sample): 16.6
    - σp (period): 22.5
    - Stock market return: 5.6
    - σs (sample): 16.7
    - σp (period): 22.3
    - Safe asset return: 5.1
    - σs (sample): 4.4
    - σp (period): 0.8
  - Mature markets, 1996-2000:
    - Equity premium: 13.6
    - σs (sample): 12.2
    - σp (period): 14.3
    - Stock market return: 16.9
    - σs (sample): 12.4
    - σp (period): 14.5
    - Safe asset return: 3.3
    - σs (sample): 2.3
    - σp (period): 0.3
  - All sample countries, 2001-2005:
    - Equity premium: 11.9
    - σs (sample): 17.2
    - σp (period): 19.5
    - Stock market return: 14.3
    - σs (sample): 16.9
    - σp (period): 18.7
    - Safe asset return: 2.4
    - σs (sample): 2.5
    - σp (period): 0.9
  - Emerging markets, 2001-2005:
    - Equity premium: 20.5
    - σs (sample): 18.6
    - σp (period): 19.2
    - Stock market return: 23.1
    - σs (sample): 17.7
    - σp (period): 18.0
    - Safe asset return: 2.6
    - σs (sample): 3.3
    - σp (period): 1.4
  - Mature markets, 2001-2005:
    - Equity premium: 1.5
    - σs (sample): 6.4
    - σp (period): 20.4
    - Stock market return: 3.7
    - σs (sample): 6.6
    - σp (period): 20.1
    - Safe asset return: 2.2
    - σs (sample): 0.9
    - σp (period): 0.3
  - All sample countries, 1996-2005:
    - Equity premium: 9.1
    - σs (sample): 8.2
    - σp (period): 18.8
    - Stock market return: 12.5
    - σs (sample): 8.4
    - σp (period): 18.3
    - Safe asset return: 3.4
    - σs (sample): 2.8
    - σp (period): 1.2
- Main empirical observations and patterns:
  - EPP observed globally: during 1996–05 average equity premium ranges from 7.5 to 10.5 percent across subsamples and is comparable to or exceeds premia in earlier literature.
  - Equity premium higher in emerging markets: during 1996–05 equity premium is 3 percent higher in emerging markets than in mature markets.
  - Subperiod dynamics:
    - 1996–00: equity premium in emerging markets is (nearly) zero while it is close to 14 percent in mature markets.
    - 2001–05: equity premium in emerging markets jumps to 20.5 percent while it declines to 1.5 percent in mature markets — a 19 percent difference between emerging and mature markets in 2001–05.
    - The 2001–05 surge in emerging market equity premium is largely due to a fourfold jump in equity return while safe asset return is about half of its 1996–00 level.
  - Volatility:
    - Stock return shows greater variation (σs) than safe asset return across the sample.
    - Variation in both stock and safe asset returns is substantially greater in emerging markets than in mature markets.
- Correlations and simple regressions (1996–2005 country averages; Table 3 examples):
  - Stock return regressed on safe asset return:
    - All sample countries: coefficient 0.8; P-value 0.06
    - Emerging markets: coefficient 0.6; P-value 0.30
    - Mature markets: coefficient 1.3; P-value 0.07
  - Equity premium regressed on stock market return:
    - All sample countries: coefficient 0.9; P-value 0.00
    - Emerging markets: coefficient 0.9; P-value 0.00
    - Mature markets: coefficient 0.9; P-value 0.00
  - Equity premium regressed on safe asset return:
    - All sample countries: coefficient -0.2; P-value 0.56
    - Emerging markets: coefficient -0.4; P-value 0.41
    - Mature markets: coefficient 0.3; P-value 0.63
- Time-series correlations over 1996–05 (Table 4 examples):
  - Stock return regressed on safe asset return:
    - All sample countries: coefficient -5.8; P-value 0.29
    - Emerging markets: coefficient -8.0; P-value 0.05
    - Mature markets: coefficient 6.9; P-value 0.52
  - Equity premium regressed on stock market return:
    - All sample countries: coefficient 1.0; P-value 0.00
    - Emerging markets: coefficient 1.0; P-value 0.00
    - Mature markets: coefficient 1.0; P-value 0.00
  - Equity premium regressed on safe asset return:
    - All sample countries: coefficient -6.8; P-value 0.22
    - Emerging markets: coefficient -9.0; P-value 0.03
    - Mature markets: coefficient 5.9; P-value 0.58
- Interpretation:
  - Main determinant of equity premium in both emerging and mature markets is stock (equity) return.
  - In emerging markets, evidence of significant negative correlation between stock return and safe asset return over time and negative correlation between equity premium and safe asset return.

### III. Ambiguity and equity premium — conceptual example and theoretical framing
- Framework and CPT decomposition:
  - Uses cumulative prospect theory (CPT) to illustrate how ambiguity and subjective probabilities affect asset choices and required premia.
  - Safe prospect: invest $Y and receive $C (rate of return = C/Y).
  - Risky prospect: invest $Y and receive $R with probability p; investor’s subjective probability assessment denoted w(p).
  - Utility U(.) with U' > 0, U'' < 0, and U(0) = 0.
  - Expected utility from risky payoff expressed as w(p)U(R).
  - Observed equity return differential (A-C)/Y decomposed into:
    - risk premium: (R-C)/Y
    - ambiguity premium in excess of the risk premium: (A-R)/Y
  - Key relations: Certainty-equivalent condition under CPT leads to R (Equation (1)); ambiguous compound-lottery assessment leads to A (Equation (2)); (A-C)/Y = (A-R)/Y + (R-C)/Y (Equation (3)).
- Conceptual implication: CPT subjective probability weighting w(.) can make w(p)U(R) ≤ w(q)w(z)U(A); ambiguity aversion can raise observed equity premium beyond EUT prediction.

### Simulations and numerical examples
- Simulations show ambiguity premium can significantly augment the equity premium; small changes in behavioral parameters can generate high equity premiums.
- Parameter examples and settings reported explicitly:
  - Probability values: p = 0.70, q = 0.85, z = 0.82 (with p = qz).
  - Risk aversion parameter, θ = 0.50.
  - Subjective probability weighting parameter, α = 0.65.
- Authors’ caution: "The impact of CPT subjective probability weighting and ambiguity on equity premium remains to be tested in a formal asset pricing model."
- Probability weighting and ambiguity under CPT (example values):
  - 0.017 is w(0.017) = 0.065 and w(0.983) = 0.905 (earlier numerical illustration).
  - If α = 0.55, then w(0.017) = 0.10 and w(0.983) = 0.837.
  - Implication: subjective valuation of low-probability disaster states is substantially higher under CPT; anticipations of recessions (not necessarily disasters) may suffice to generate relatively high equity premia.
- Simulated sample probabilities for gains and losses in real per capita income (Table 3; percent):
  - Gains (G1 < G2 < G3): 0-5, 5-10, >10
    - All (gains): 69.5, 14.8, 0.6
    - Emerging (gains): 57.6, 23.1, 0.7
    - Mature (gains): 84.0, 4.8, 0.4
  - Losses (L1 < L2 < L3): 0-5, 5-10, >10
    - All (losses): 46.1, 19.3, 3.3, 14.3, 3.5, 4.5
    - Emerging (losses): 36.7, 24.8, 3.7, 14.6, 4.7, 5.7
    - Mature (losses): 61.1, 9.8, 2.7, 14.5, 1.4, 2.7
  - Note: Percent increase or decrease in per capita GDP measured in 2000 U.S. dollars. w(p) parameter α = 0.65.
- Loss aversion and myopic evaluation:
  - Myopic loss aversion (Benartzi and Thaler, 1995) with CPT weighting can account for equity premium.
  - If portfolio evaluation horizon were longer (20 years), simulations suggest risk premium may decline from 6.5 to 1.4 percent in that framework.
  - Extension: combining loss aversion with ambiguity aversion may account for even higher equity premium (left for future research).

### Cross-country patterns, institutional channels, and regression evidence
- Selected sample averages (Table 6; 1996–00, 2001–05, 1996–05):
  - Real equity premium: 6.21, 1.99, 9.10
  - Real stock market return: 10.7, 14.3, 12.5
  - Real safe asset return: 4.3, 2.4, 3.4
  - Real growth rate: 3.6, 3.5, 3.6
  - Equity market capitalization (in percent of GDP): 70, 74, 73
  - Bond market capitalization (in percent of GDP): 68, 82, 75
  - Credit to private sector (in percent of GDP): 69, 77, 73
  - Overall World Bank index: 68, 67, 68
- Empirical observations:
  - Equity premium mainly determined by stock return; stock return and equity premium positively correlated with real growth.
  - Equity market capitalization and bond market capitalization averages in mature markets are two or more times higher than in emerging markets.
  - Credit to private sector shows negative correlation with equity premium and stock return.
  - Unanticipated inflation declined in emerging markets and is negatively correlated with equity premium, stock return, and safe asset return.
- Cross-correlation and regression findings (selected reported coefficient/p-value entries preserved exactly):
  - Recurrent negative and significant coefficients for Credit to private sector across multiple tables and periods (examples summarized):
    - Table 1 (1996–00, All): Credit to private sector "-0.3 0.06", "-0.4 0.02", "-0.4 0.05".
    - Table 3 (1996–05, All): Credit to private sector "-0.4 0.03", "-0.5 0.01", "-0.4 0.04".
    - Table 6 (1996–05, All incl. uncertainty proxies): Credit to private sector "-0.6 0.00", "-0.7 0.00", "-0.4 0.08".
  - Age composition often positive and significant:
    - Table 1 (1996–00, All): Age composition "0.5 0.00", "0.4 0.02".
    - Table 6 (1996–05, Emerging): Age composition "1.0 0.01", "0.9 0.01".
  - Tax ratio (CIT/PIT) heterogeneous; several significant entries across tables (mixed signs).
  - Unanticipated inflation negative and sometimes significant in emerging market panels.
  - Inclusion of World Bank indexes and other uncertainty proxies alters coefficients and significance:
    - Voice and accountability (All): -0.6, -0.6, -0.5 in selected entries.
    - Political stability (Emerging): -1.0, -1.1, -0.8, -1.1 in some specifications.
    - Government effectiveness (All): -1.4, -1.3, -1.1; Emerging -1.4, -1.4, -1.0.
    - Rule of law (All): 1.5, 1.2; Emerging 1.3, 1.3, 0.9.
    - Control of corruption (Emerging): 1.3.
  - Other uncertainty proxies (Table 10 examples):
    - Heritage indexes — Government intervention: All 0.4, 0.4; Emerging 0.5, 0.5; Mature overall index -1.0.
    - World Bank Enterprise Surveys — Infrastructure: All 0.7, 0.7.
    - Tax burden: All 1.0, 1.0.
    - World Values Survey Confidence Index: Average categories 1-7 All 0.4, categories 2-7 All 0.3.
- R Square and model fit examples:
  - R Square varies by specification; examples reported:
    - Table 1 All sample countries: "0.5 0.4 0.3".
    - Table 4 Emerging markets (incl. uncertainty proxies): "0.7 0.7 0.5".
    - Table 6 Emerging markets (incl. uncertainty proxies): "0.8 0.8 0.6".
- Interpretation:
  - Institutional quality matters as much as fundamentals in explaining equity premium.
  - Equity premium and stock return have significant negative correlations with World Bank indexes for voice and accountability, political stability, and government effectiveness — consistent with hypothesis that higher institutional quality reduces ambiguity and thus ambiguity premium.
  - For some institutional measures (rule of law, control of corruption) and the World Values Survey confidence index, positive correlations with stock return/equity premium observed — possibly reflecting incentive effects stimulating higher-return, longer-term investments.
  - Institutional quality indexes significant in emerging markets regressions but less so in mature markets; emerging markets display greater variation in institutional quality (e.g., voice and accountability SD: emerging 22.1 vs mature 13.6).

### Policy-relevant implications and research recommendations
- Policy implications:
  - Institutional-strengthening measures can reduce ambiguity and thereby lower ambiguity premia in asset returns; relevant elements include:
    - voice and accountability; political stability; government effectiveness; regulatory quality; rule of law; control of corruption.
  - Financial-market policy measures that increase transparency, strengthen investor protection, and improve credibility of macroeconomic policy (e.g., credible inflation targeting, central bank independence, accurate data dissemination) can reduce unquantifiable uncertainty and lower required returns on both equity and safe assets.
- Research directions proposed:
  - Develop formal asset pricing models embedding CPT subjective probability weighting and ambiguity to quantify impact on equity premium.
  - Undertake time-series analyses of the impact of ambiguity on asset returns across countries to assess dynamics of risk vs. ambiguity aversion and implications for financial-market behavior and crises.
  - Test CPT subjective probability weighting and ambiguity effects in formal asset pricing frameworks (authors note this remains to be tested).

*Source: _wp07230 (authors' estimates; Appendix I, Tables 1,2; Appendix II–III simulations, regressions, and references).*

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

### _wp07230 - References..............................................................................................................

### I. Introduction — purpose, context, and contributions
- Defines the equity premium puzzle (EPP) as "the differential between return to equity and return to safe assets in excess of the premium that can be explained on the basis of a reasonable degree of risk aversion."
- Notes that traditional fundamentals (consumption smoothing, liquidity constraints, financial sector development, age composition of investors, tax differences) can explain part of the equity-safe return differential but observed premia may remain large and imply empirically unsupported extreme risk aversion.
- Emphasizes Knightian uncertainty (ambiguity) as pervasive in financial markets; ambiguity implies probabilities and payoffs are not known with precision and decision makers exhibit ambiguity aversion.
- Paper’s two main contributions:
  - Proposes ambiguity aversion as a possible explanation for EPP: if equity returns are perceived as more ambiguous than safe-asset returns, an ambiguity premium on equity can increase the observed equity premium.
  - Documents EPP across a large cross-country sample (53 countries: 29 emerging, 24 mature) and examines the role of institutional quality and other indexes as proxies for uncertainty.
- Empirical approach highlights correlation tests and regressions showing statistically significant correlations between equity premium and some uncertainty proxies; suggests ambiguity aversion can explain a significant portion of large equity premia where institutional quality reflects uncertainty.

### II. Equity premium is a global phenomenon — data, measurement, and main observations
- Sample and period:
  - 53 countries total: 29 emerging markets and 24 mature markets.
  - Overall period under consideration: 1996–05.
  - Real stock market return = yearly percentage change in nominal stock market index divided by CPI.
  - Real safe asset return = nominal return minus CPI inflation.
  - Real equity premium = real stock market return minus real safe asset return (dividend yield excluded).
- Key statistical findings (period averages presented in Table 1; percent and standard deviations preserved as reported):
  - All sample countries, 1996-2000:
    - Equity premium: 6.21
    - σs (sample): 16.3
    - σp (period): 17.7
    - Stock market return: 10.7
    - σs (sample): 15.9
    - σp (period): 12.5
    - Safe asset return: 4.3
    - σs (sample): 3.7
    - σp (period): 0.4
  - Emerging markets, 1996-2000:
    - Equity premium: 0.02
    - σs (sample): 16.6
    - σp (period): 22.5
    - Stock market return: 5.6
    - σs (sample): 16.7
    - σp (period): 22.3
    - Safe asset return: 5.1
    - σs (sample): 4.4
    - σp (period): 0.8
  - Mature markets, 1996-2000:
    - Equity premium: 13.6
    - σs (sample): 12.2
    - σp (period): 14.3
    - Stock market return: 16.9
    - σs (sample): 12.4
    - σp (period): 14.5
    - Safe asset return: 3.3
    - σs (sample): 2.3
    - σp (period): 0.3
  - All sample countries, 2001-2005:
    - Equity premium: 11.9
    - σs (sample): 17.2
    - σp (period): 19.5
    - Stock market return: 14.3
    - σs (sample): 16.9
    - σp (period): 18.7
    - Safe asset return: 2.4
    - σs (sample): 2.5
    - σp (period): 0.9
  - Emerging markets, 2001-2005:
    - Equity premium: 20.5
    - σs (sample): 18.6
    - σp (period): 19.2
    - Stock market return: 23.1
    - σs (sample): 17.7
    - σp (period): 18.0
    - Safe asset return: 2.6
    - σs (sample): 3.3
    - σp (period): 1.4
  - Mature markets, 2001-2005:
    - Equity premium: 1.5
    - σs (sample): 6.4
    - σp (period): 20.4
    - Stock market return: 3.7
    - σs (sample): 6.6
    - σp (period): 20.1
    - Safe asset return: 2.2
    - σs (sample): 0.9
    - σp (period): 0.3
  - All sample countries, 1996-2005:
    - Equity premium: 9.1
    - σs (sample): 8.2
    - σp (period): 18.8
    - Stock market return: 12.5
    - σs (sample): 8.4
    - σp (period): 18.3
    - Safe asset return: 3.4
    - σs (sample): 2.8
    - σp (period): 1.2
- Main empirical observations and patterns:
  - EPP is observed globally: during 1996–05 average equity premium ranges from 7.5 to 10.5 percent across subsamples and is comparable to or exceeds premia reported in earlier literature.
  - Equity premium is higher in emerging markets: during 1996–05 equity premium is 3 percent higher in emerging markets than in mature markets.
  - Subperiod dynamics:
    - 1996–00: equity premium in emerging markets is (nearly) zero while it is close to 14 percent in mature markets.
    - 2001–05: equity premium in emerging markets jumps to 20.5 percent while it declines to 1.5 percent in mature markets — a 19 percent difference between emerging and mature markets in 2001–05.
    - The 2001–05 surge in emerging market equity premium is largely due to a fourfold jump in equity return while safe asset return is about half of its 1996–00 level.
  - Volatility:
    - Stock return shows greater variation (σs) than safe asset return across the sample, justifying a risk premium on equity.
    - Variation in both stock and safe asset returns is substantially greater in emerging markets than in mature markets.
  - Correlations and determinants (from simple regressions based on 1996–2005 country averages; Table 3):
    - Stock return regressed on safe asset return:
      - All sample countries: coefficient 0.8; P-value 0.06
      - Emerging markets: coefficient 0.6; P-value 0.30
      - Mature markets: coefficient 1.3; P-value 0.07
    - Equity premium regressed on stock market return:
      - All sample countries: coefficient 0.9; P-value 0.00
      - Emerging markets: coefficient 0.9; P-value 0.00
      - Mature markets: coefficient 0.9; P-value 0.00
    - Equity premium regressed on safe asset return:
      - All sample countries: coefficient -0.2; P-value 0.56
      - Emerging markets: coefficient -0.4; P-value 0.41
      - Mature markets: coefficient 0.3; P-value 0.63
  - Time-series correlations over 1996–05 (Table 4):
    - Stock return regressed on safe asset return:
      - All sample countries: coefficient -5.8; P-value 0.29
      - Emerging markets: coefficient -8.0; P-value 0.05
      - Mature markets: coefficient 6.9; P-value 0.52
    - Equity premium regressed on stock market return:
      - All sample countries: coefficient 1.0; P-value 0.00
      - Emerging markets: coefficient 1.0; P-value 0.00
      - Mature markets: coefficient 1.0; P-value 0.00
    - Equity premium regressed on safe asset return:
      - All sample countries: coefficient -6.8; P-value 0.22
      - Emerging markets: coefficient -9.0; P-value 0.03
      - Mature markets: coefficient 5.9; P-value 0.58
  - Interpretation:
    - The main determinant of equity premium in both emerging and mature markets is stock (equity) return.
    - In emerging markets, there is evidence of a significant negative correlation between stock return and safe asset return over time and a significant negative correlation between equity premium and safe asset return, consistent with the above.

### III. Ambiguity and equity premium — conceptual example and theoretical framing
- The paper uses cumulative prospect theory (CPT) to illustrate how ambiguity and subjective probabilities can affect asset choices and required premia.
- Basic setup of the illustrative example:
  - Safe prospect: invest $Y and receive $C (rate of return = C/Y).
  - Risky prospect: invest $Y and receive $R with probability p; investor’s subjective probability assessment denoted w(p).
  - Utility function U(.) with U' > 0, U'' < 0, and U(0) = 0.
  - Expected utility from risky payoff expressed as w(p)U(R).
- Purpose of the example:
  - To show how ambiguity aversion (through subjective weighting of probabilities w(p)) can raise the required compensation for holding equities relative to safe assets, producing an ambiguity premium that adds to the risk premium and helps explain observed large equity premia.
- Appendix II noted for further discussion of CPT application to these results and relation to other models (e.g., Rietz-Barro hypotheses and prior literature).

*Source: _wp07230 - References (authors' estimates; Appendix I, Tables 1,2).*

### appendix also provides numerical examples and simulations, and a discussion on the Rietz-Barro hypothesis on

### _wp07230 - appendix also provides numerical examples and simulations, and a discussion on the Rietz-Barro hypothesis on

### CPT framework and decomposition of equity premium
- Under cumulative prospect theory (CPT) the observed equity return differential (A-C)/Y can be decomposed into:
  - risk premium: (R-C)/Y
  - ambiguity premium in excess of the risk premium: (A-R)/Y
- Key expressions (as presented):
  - Certainty-equivalent condition under CPT: U(C) ≤ w(p)U(R) with inverse-utility manipulation leading to R given by Equation (1).
  - Ambiguous compound-lottery assessment under CPT: w(q)w(z)U(A); with w(p) = w(qz) ≥ w(q)w(z) and indifference condition leading to A given by Equation (2).
  - Relationship across levels: (A-C)/Y = (A-R)/Y + (R-C)/Y (Equation (3)).
- Conceptual implication: Because CPT subjective probability weighting w(.) can make w(p)U(R) ≤ w(q)w(z)U(A), ambiguity aversion can raise the observed equity premium beyond what expected utility theory (EUT) predicts.

### Simulations and numerical examples
- Simple simulations (Table 5) based on Equations (1)–(3) and a CPT probability weighting function indicate:
  - Ambiguity premium can significantly augment the magnitude of the equity premium.
  - For relatively small changes in behavioral parameter values (probability weighting parameter, α, and risk aversion parameter, θ), it is possible to generate high equity premiums.
- Parameter examples and simulation settings explicitly reported:
  - Probability values: p = 0.70, q = 0.85, z = 0.82 (with p = qz).
  - Risk aversion parameter, θ = 0.50.
  - Subjective probability weighting parameter, α = 0.65.
- Authors’ caution: "The impact of CPT subjective probability weighting and ambiguity on equity premium remains to be tested in a formal asset pricing model."

### Cross-country patterns and institutional channels (data summary)
- Selected sample averages (Table 6; values correspond to 1996–00, 2001–05, 1996–05 respectively):
  - Real equity premium: 6.21, 1.99, 9.10
  - Real stock market return: 10.7, 14.3, 12.5
  - Real safe asset return: 4.3, 2.4, 3.4
  - Real growth rate: 3.6, 3.5, 3.6
  - Equity market capitalization (in percent of GDP): 70, 74, 73
  - Bond market capitalization (in percent of GDP): 68, 82, 75
  - Credit to private sector (in percent of GDP): 69, 77, 73
  - Overall World Bank index (1996-2000; 2002-2005; 1996-2005 averages): 68, 67, 68
- Empirical observations:
  - Equity premium is mainly determined by stock return; correlation between stock return and safe asset return is generally not significant at the 5 percent level.
  - Equity premium and stock return are positively correlated with real growth.
  - Equity market capitalization and bond market capitalization averages in mature markets are two or more times higher than in emerging markets.
  - Credit to private sector shows a negative correlation with equity premium and stock return (consistent with greater liquidity lowering returns).
  - Unanticipated inflation declined in emerging markets and is negatively correlated with equity premium, stock return, and safe asset return.

### Cross-correlation and regression findings
- Cross-correlation highlights (Table 7; significance indicated via t statistics in source):
  - Stock return (STR) correlations: All sample t-values 25.4, 48.9, 18.6 (as presented in table header context).
  - Safe asset return (SAFE) marginal significance indicated at (1.9) for All and Mature during 2001–05.
- Regression methodology:
  - Dependent variables: equity premium, stock returns, safe asset returns.
  - Variables normalized as vij = (xij – μi)/σi; regressions run as Yi = c0 + Σ ck Xki + ui (Equation (4)).
- Main regression results excluding World Bank indexes (Table 8; statistically significant coefficient signs and magnitudes summarized):
  - Equity premium positively correlated with real growth (All: 0.3).
  - Equity premium negatively correlated with credit to private sector (All: -0.3 to -0.5 depending on period/sample).
  - Equity premium negatively correlated with unanticipated inflation (All: -0.4).
  - Equity premium positively correlated with tax ratio (CIT/PIT) (All: 0.3).
  - Age composition: All 0.5; Mature 0.8, 0.7 in specified periods.
- Regression results including World Bank indexes (Table 9; selected coefficient values reported exactly as shown):
  - Real growth rate: All 0.3; Emerging 0.4, 0.4 in some period specifications.
  - Equity market capitalization: Mature 0.8, 0.8 and -1.0, -1.0 in different period columns.
  - Credit to private sector: All -0.4, -0.5, -0.6, -0.7, -0.4 (various period/sample entries).
  - Tax ratio (CIT/PIT): All 0.3, 0.3, -0.4, -0.4 (various entries); Emerging 0.5, 0.5, -0.4 in some entries.
  - Age composition: All 0.8, 0.7, -0.5, 0.6; Emerging 1.0, 0.9; Mature 0.9, 0.9.
  - World Bank indexes (selected coefficients as reported):
    - Voice and accountability (All): -0.6, -0.6, -0.5; Emerging -0.7, -0.5, -0.8, -0.7.
    - Political stability (Emerging): -1.0, -1.1, -0.8, -1.1.
    - Government effectiveness (All): -1.4, -1.3, -1.1; Emerging -1.4, -1.4, -1.0.
    - Rule of law (All): 1.5, 1.2; Emerging 1.3, 1.3, 0.9.
    - Control of corruption (Emerging): 1.3.
- Results for other uncertainty proxies (Table 10; coefficient values):
  - Heritage indexes — Government intervention: All 0.4, 0.4; Emerging 0.5, 0.5; Mature overall index -1.0.
  - World Bank Enterprise Surveys — Infrastructure: All 0.7, 0.7.
  - Tax burden: All 1.0, 1.0.
  - World Values Survey Confidence Index: Average of categories 1-7 All 0.4, 0.4; Average of categories 2-7 All 0.3.

### Interpretation and substantive findings
- Institutional quality matters as much as fundamentals in explaining equity premium:
  - Equity premium and stock return have significant negative correlations with World Bank indexes for voice and accountability, political stability, and government effectiveness — consistent with the hypothesis that higher institutional quality reduces ambiguity and therefore reduces ambiguity premium.
  - For some institutional measures (rule of law, control of corruption) and the World Values Survey confidence index, positive correlations with stock return and equity premium are observed — plausibly reflecting incentive effects (better rule of law and control of corruption may stimulate higher-return, longer-term investments).
- Differences between emerging and mature markets:
  - Institutional quality indexes are significant in emerging markets regressions but less so in mature markets.
  - Emerging markets display greater variation in institutional quality (sample standard deviations reported in text; e.g., voice and accountability SD in emerging markets 22.1 vs mature markets 13.6).
  - When stock market activity picked up in emerging markets during 2001–05, markets appears to have added a significant ambiguity premium to stock returns.
- Ambiguity aversion as a component of EPP:
  - Authors argue ambiguity aversion (modeled via CPT) can be instrumental in explaining a large part of the equity premium puzzle (EPP): ambiguity premium augments the risk premium that EUT would attribute to observed returns.
  - Safe assets show less ambiguity than equity across countries in the institutional quality spectrum, aligning with lower ambiguity premium for safe assets.

### Policy-relevant implications and research recommendations
- Institutional-strengthening measures can reduce ambiguity and thereby lower ambiguity premia in asset returns; relevant institutional elements include:
  - voice and accountability; political stability; government effectiveness; regulatory quality; rule of law; control of corruption.
- Financial-market policy implications:
  - Policies that increase transparency, strengthen investor protection, and improve the credibility of macroeconomic policy (e.g., credible inflation targeting, central bank independence, accurate data dissemination) can reduce unquantifiable uncertainty and lower required returns on both equity and safe assets.
- Research directions proposed by authors:
  - Develop formal asset pricing models that embed CPT subjective probability weighting and ambiguity to quantify the impact on equity premium.
  - Undertake time-series analyses of the impact of ambiguity on asset returns across countries to assess dynamics of risk vs. ambiguity aversion and implications for financial-market behavior and crises.

*Source: _wp07230 - appendix also provides numerical examples and simulations, and a discussion on the Rietz-Barro hypothesis on (authors’ simulations and empirical analysis as presented in the supplied content).*

### Appendix I.

### Appendix I.

### Table 1. Data Sources for Stock Market Indexes
- 1 Argentina S&PIFC
- 2 Australia AS51 Index
- 3 Austria WBI Index
- 4 Bahrain S&PIFC
- 5 Belgium BEL20 Index
- 6 Brazil IBOV Index
- 7 Canada SPTSX Index
- 8 Chile IPSA Index
- 9 China SHCOMP Index
- 10 Colombia IGBC Index
- 11 Czech Republic PX Index
- 12 Denmark KFX Index
- 13 Egypt S&PIFC
- 14 Finland HEX Index
- 15 France CAC Index
- 16 Germany DAX Index
- 17 Greece ASE Index
- 18 Hong Kong HSI Index
- 19 Hungary BUX Index
- 20 India SENSEX Index
- 21 Indonesia JCI Index
- 22 Ireland ISEQ Index
- 23 Israel WFOE
- 24 Italy SPMIB Index
- 25 Japan NKY Index
- 26 Jordan S&PIFC
- 27 Korea KOSPI Index
- 28 Kuwait KGGIGEN Index
- 29 Malaysia KLCI Index
- 30 Mexico MEXBOL Index
- 31 Morocco S&PIFC
- 32 Netherlands AEX Index
- 33 New Zealand NZSE Index
- 34 Nigeria S&PIFC
- 35 Norway Oslo SE Total Index
- 36 Pakistan S&PIFC
- 37 Peru S&PIFC
- 38 Philippines S&PIFC
- 39 Poland WIG20 Index
- 40 Portugal BVLX Index
- 41 Russia RTSI$ Index
- 42 Saudi Arabia S&PIFC
- 43 Singapore STI Index
- 44 Slovakia SKSM Index
- 45 South Africa JALSH Index
- 46 Spain IBEX Index
- 47 Sweden SBX Index
- 48 Switzerland Swiss Exchange
- 49 Thailand SET Index
- 50 Tunisia S&PIFC
- 51 Turkey XU100 Index
- 52 UK UKX Index
- 53 US SPX Index

Memorandum item:
- Equity market capitalization data sources are Datastream; S&PIFC Emerging Markets Database; and World Federation of Exchanges.

### Table 2. Selected Safe Asset Returns and Data Sources (items 1–25)
- 1 Argentina Deposit rate IFS
- 2 Australia 15-year treasury bond rate IFS
- 3 Austria 10-year government bond yield Central Bank of Denmark
- 4 Bahrain Treasury bill rate Central Bank of Bahrain
- 5 Belgium 10-year government bond yield Central Bank of Denmark
- 6 Brazil Domestic currency treasury bill rate IFS
- 7 Canada 3-5 year government bond yield IFS
- 8 Chile Interest rate on 10-year indexed promissory notes Central Bank of Chile
- 9 China 12-month institutional investor deposits IFS
- 10 Colombia 360-day certificate of deposit rate Bank of Colombia
- 11 Czech Republic Treasury bill rate IFS
- 12 Denmark 10-year government bond yield Central Bank of Denmark
- 13 Egypt 3-month deposit rate IFS
- 14 Finland 10-year government bond yield Central Bank of Denmark
- 15 France 10-year government bond yield Central Bank of Denmark
- 16 Germany 10-year government bond yield Central Bank of Denmark
- 17 Greece 12-month treasury bill yield up to 1998; government bond yield for 1998-2005 IFS
- 18 Hong Kong Treasury bill rate IFS
- 19 Hungary Treasury bill rate IFS
- 20 India Government bond yield IFS
- 21 Indonesia JIBOR 12-month rupiah rate Bloomberg
- 22 Ireland 10-year government bond yield Central Bank of Denmark
- 23 Israel Treasury bill rate IFS
- 24 Italy 10-year government bond yield Central Bank of Denmark
- 25 Japan 11-year government bond yield Central Bank of Denmark

### Table 2. Selected Safe Asset Returns and Data Sources (items 26–53)
- 26 Jordan Deposit rate IFS
- 27 Korea Time deposit at deposit money banks, one year or more IFS
- 28 Kuwait Saving deposits rate IFS
- 29 Malaysia 5-year government bond rate IFS
- 30 Mexico Treasury bill rate IFS
- 31 Morocco 3-month time deposits rate IFS
- 32 Netherlands 10-year government bond yield Central Bank of Denmark
- 33 New Zealand Government bond yield IFS
- 34 Nigeria Treasury bill rate IFS
- 35 Norway 10-year government bond yield Central Bank of Denmark
- 36 Pakistan Call rate for 1998-99; treasury bill rate otherwise IFS
- 37 Peru Deposit rate IFS
- 38 Philippines Government bond yield IFS
- 39 Poland Money market rate, 1996-2000; treasury bill rate 2001-2006 IFS
- 40 Portugal 10-year government bond yield Central Bank of Denmark
- 41 Russia Weighted average GKOs yield Central Bank of Russia
- 42 Saudi Arabia 52-week Saudi Riyal treasury bill rate IFS
- 43 Singapore Treasury bill rate IFS
- 44 Slovakia Government bond yield Central Bank of Slovakia
- 45 South Africa Treasury bill rate IFS
- 46 Spain 10-year government bond yield Central Bank of Denmark
- 47 Sweden 10-year government bond yield Central Bank of Denmark
- 48 Switzerland 5-7 year government bond index yield Swiss Bond Index
- 49 Thailand Government bond yield IFS
- 50 Tunisia Money market rate IFS
- 51 Turkey 12-month deposit rate Central Bank of Turkey
- 52 UK 10-year government bond yield Central Bank of Denmark
- 53 US 10-year government bond yield Central Bank of Denmark

Memorandum item:
- Bond market capitalization data sources are BIS Quarterly Review (December 2006), International Bonds and Notes (all issuers, by residence of issuer, in US$ billion), amounts outstanding (Table 14 B), plus, Domestic Debt Securities (by sector and residence of issuer, in US$ billion), amounts outstanding (Table 16A).

*Source: _wp07230 - Appendix I.*

### 0.017 is w(0.017) = 0.065 and of w(p) = w(0.983) = 0.905. As before, the implication is that

### _wp07230 - 0.017 is w(0.017) = 0.065 and of w(p) = w(0.983) = 0.905. As before, the implication is that

### Probability weighting and ambiguity under CPT
- The subjective valuation of the probability of a disaster state, w(1-p), is significantly higher under CPT, while the subjective probability of a “normal” state, w(p), is lower.
- Experimental results indicate decision makers are risk averse for low probability losses and this choice pattern is more pronounced in ambiguity (Tversky and Fox, 1995).
- If the probability weighting function is more subadditive in ambiguity (i.e., the value of α is lower), example with α = 0.55 yields:
  - w(0.017) = 0.10
  - w(0.983) = 0.837
- Consequence: in ambiguity, subjective probabilities assigned to low probability events can be quite high, so associated losses need not be as high as a 15 percent drop in consumption to generate relatively high equity premia. Anticipations of recessions, not necessarily disasters, may suffice to generate relatively high equity premia.

### Simulations and probability calculations (CPT context)
- The simulations in Table 3 identify three ranges of percentage gains (G1 < G2 < G3) and losses (L1 < L2 < L3) in real per capita income and calculate associated probabilities (upper panel of Table 4).
- Let probability pi be associated with Gi or Li. CPT probabilities for gains and losses (lower panel) calculated as:
  - U(G1) or U(L1): [w(p1+p2+p3)-w(p2+p3)]
  - U(G2) or U(L2): [w(p2+p3)-w(p3)]
  - U(G3) or U(L3): w(p3)

- Table 3. Estimated and Simulated Sample Probabilities for Gains and Losses in Real Per Capita Income (in percent)
  - Gains (G1 < G2 < G3): 0-5 5-10 >10
  - Losses (L1 < L2 < L3): 0-5 5-10 >10
  - All (gains): 69.5 14.8 0.6
  - Emerging (gains): 57.6 23.1 0.7
  - Mature (gains): 84.0 4.8 0.4
  - All (losses): 46.1 19.3 3.3 14.3 3.5 4.5
  - Emerging (losses): 36.7 24.8 3.7 14.6 4.7 5.7
  - Mature (losses): 61.1 9.8 2.7 14.5 1.4 2.7
- Note: Percent increase or decrease in per capita GDP measured in 2000 U.S. dollars.
- w(p) probability weighting parameter, α = 0.65.
- Sample probability (p) shown in Table 3 (as listed above).

### Loss aversion, myopic evaluation, and implications for equity premium
- Mixed prospects involve loss aversion.
- Benartzi and Thaler (1995) show myopic loss aversion, along with CPT probability weighting, may account for equity premium.
  - Myopic loss aversion refers to frequent or short-term (12–month) evaluation of losses and gains, as opposed to longer-term evaluation.
  - If the time horizon for portfolio evaluation were longer (20 years), stocks may become more attractive relative to safe assets and risk premium may decline to a negligible level (from 6.5 to 1.4 percent, according to those authors simulations).
- Barberis and others (2001) provide a formal model of the impact of loss aversion on asset prices, explaining high mean and variance of equity prices and low correlation with consumption growth.
- If ambiguity is extended to mixed prospects involving both losses and gains, loss aversion combined with ambiguity aversion may account for an even higher equity premium.
  - The example in Table 4 does not represent an extension of ambiguity to mixed prospects; this is left for future research.

### Robustness check: regressions with real per capita income growth
- Regressions shown in text Tables 8 and 9 were re-run for the period 1996–05 after substituting real per capita income growth rate for real growth rate.
- In terms of significance of the independent variables, the results were the same (available from the authors).

*Source: Authors' simulations and exposition in the provided content unit.*

### Appendix III.

### _wp07230 - Appendix III

### Overview
- Appendix III reports regression results across multiple specifications and subsamples (All sample countries, Emerging markets, Mature markets) for different periods: 1996–00, 2001–05, 1996–05.
- Dependent variables reported in tables are: Equity Premium; Stock Return; Safe Asset Return.
- Regressors include macro and financial variables (Real growth rate; Equity market capitalization; Bond market capitalization; Credit to private sector; Lagged consumption; Unanticipated inflation; Tax ratio (CIT/PIT); Age composition) and, in some specifications, uncertainty proxies (World Bank Indexes and other indexes summarized later).
- Each reported cell contains a coefficient and an associated p value (presented as "Coef.p value" pairs).

### Key statistically notable findings across specifications
- Credit to private sector frequently exhibits negative coefficients with low p values in multiple tables and subsamples:
  - Table 1 (1996–00, All sample countries): Credit to private sector "-0.3 0.06", "-0.4 0.02", "-0.4 0.05".
  - Table 3 (1996–05, All sample countries): Credit to private sector "-0.4 0.03", "-0.5 0.01", "-0.4 0.04".
  - Table 6 (1996–05, All sample countries, including uncertainty proxies): Credit to private sector "-0.6 0.00", "-0.7 0.00", "-0.4 0.08".
  - Table 8 (Summary of Other Uncertainty Proxies, 1995–05): Heritage indexes, All: "Credit to private sector -0.4 0.02", Emerging/Mature entries show "-0.6 0.00" and "-0.4 0.04".
  - Table 9 (Statistically Significant Results Excluding Real Growth and Including Uncertainty Proxies): Credit to private sector entries show "All -0.6 -0.6 -0.6 -0.7", Emerging "-0.5 -0.4", Mature "-0.5 -0.6 -0.6 -0.5".

- Age composition often shows positive and statistically significant coefficients in several specifications:
  - Table 1 (1996–00, All sample countries): Age composition "0.5 0.00", "0.4 0.02".
  - Table 4 (including uncertainty proxies, 1996–00, All sample countries): Age composition "0.8 0.00", "0.7 0.01".
  - Table 6 (including uncertainty proxies, 1996–05, Emerging markets): Age composition "1.0 0.01", "0.9 0.01".
  - Table 9: Age composition entries: "All 0.7 0.6 -0.4 0.5", Emerging "-1.2 -0.4 0.9 0.8", Mature "0.8 0.8".

- Tax ratio (CIT/PIT) shows mixed effects; several negative and statistically significant coefficients in some specifications:
  - Table 2 (2001–05, All sample countries): Tax ratio "0.3 0.01", "0.3 0.03", "-0.4 0.00" (note differing signs across dependent variables).
  - Table 3 (1996–05, All sample countries): Tax ratio "0.2 0.24", "0.0 0.98", "-0.5 0.00".
  - Table 8 (Summary, 1995–05): Heritage indexes All: "Tax ratio (CIT/PIT) -0.5 0.00"; World Bank Enterprise Surveys All: "Tax ratio (CIT/PIT) -0.8 0.03"; World Values Survey Confidence All: "Tax ratio (CIT/PIT) -0.6 0.00".
  - Table 9: Tax ratio entries include "All -0.3 0.3 0.3 -0.4 -0.4", Emerging "0.5 -0.5".

- Unanticipated inflation shows negative and sometimes significant coefficients in emerging markets and in pooled samples:
  - Table 1 (1996–00, Emerging markets): Unanticipated inflation "-0.7 0.02", "-0.7 0.01".
  - Table 2 (2001–05, All sample countries): Unanticipated inflation "0.1 0.45", "0.0 0.77", "-0.4 0.00" (negative and significant for one dependent variable).
  - Table 8 summary: World Bank Enterprise Surveys All: "Unanticipated inflation -0.4 0.04", Emerging "-0.4 0.03".
  - Table 9: Unanticipated inflation listed as "All -0.4 -0.3 -0.3", Emerging "-0.4", Mature "1.1 0.9 0.8 -1.3" (varied signs across subsamples/dependent variables).

- Equity market capitalization and Bond market capitalization coefficients vary by subsample and period; some notable significant coefficients:
  - Table 4 (1996–00, Mature markets, Equity Premium): Equity market capitalization "0.8 0.06", "0.8 0.08" for Stock Return; Bond market capitalization "-0.5 0.08", "-0.5 0.14".
  - Table 5 (2001–05, Emerging markets, Credit to private sector): "0.2 0.70", "0.2 0.67", "0.0 0.90" (Credit positive/non-significant here).
  - Table 8 summary: World Bank Enterprise Surveys All: "Bond market capitalization 1.3 0.06 1.3 0.07"; Bond market capitalization also appears in other cells.

- Lagged consumption has occasional negative and statistically significant coefficients:
  - Table 2 (2001–05, All sample countries): Lagged consumption "-0.2 0.05", "-0.3 0.02", "-0.2 0.04".
  - Table 9: Lagged consumption "All -0.2", Emerging entries shown but p values not provided in that condensed presentation.

### Role of World Bank Indexes and other uncertainty proxies (selected significant entries)
- Inclusion of World Bank Indexes (Voice and accountability; Political stability; Government effectiveness; Regulatory quality; Rule of law; Control of corruption) in regressions affects coefficients and R Squares:
  - Table 4 (1996–00, All sample countries): Voice and accountability "-0.6 0.02", "-0.6 0.03"; other indexes show mostly non-significant p values in that panel.
  - Table 4 (1996–00, Emerging markets): Voice and accountability "-0.7 0.03", "-0.5 0.08", "0.6 0.14" across dependent variables; Political stability "-0.6 0.19" etc.
  - Table 6 (1996–05, All sample countries): Rule of law "1.5 0.03", "1.2 0.07" for some dependent variables; Control of corruption "0.3 0.62", "0.7 0.29" etc.
  - Table 5 (2001–05, All sample countries): Government effectiveness "-1.4 0.02", "-1.3 0.02" (noted as significant negative coefficients for some dependent variables).
  - Table 8 (Summary of Other Uncertainty Proxies, 1995–05): Heritage indexes, World Bank Enterprise Surveys, World Values Survey Confidence Index entries summarized with statistically significant findings: e.g., Heritage indexes All: "Government intervention 0.4 0.01"; World Values Survey Confidence All: "Age 0.5 0.04", "Average of categories 1-7 0.4 0.02".

- R Square values vary across specifications and subsamples, indicating differing explanatory power:
  - Examples: Table 1 R Square All sample countries "0.5 0.4 0.3"; Emerging markets "0.5 0.6 0.3"; Mature markets "0.7 0.7 0.3".
  - Table 4 R Square All sample countries "0.6 0.5 0.3"; Emerging markets "0.7 0.7 0.5"; Mature markets "0.8 0.8 0.6".
  - Table 6 R Square All sample countries "0.6 0.6 0.4"; Emerging markets "0.8 0.8 0.6"; Mature markets "0.6 0.6 0.6".

### Consolidated notable coefficient/p-value examples (selection from tables)
- Table 1 (1996–00, All sample countries):
  - Real growth rate: "0.3 0.01", "0.3 0.04", "-0.2 0.26".
  - Equity market capitalization: "0.2 0.33", "0.2 0.26", "0.1 0.44".
  - Credit to private sector: "-0.3 0.06", "-0.4 0.02", "-0.4 0.05".
  - Age composition: "0.5 0.00", "0.4 0.02", "-0.3 0.10".
  - R Square: "0.5 0.4 0.3".

- Table 2 (2001–05, All sample countries):
  - Real growth rate: "-0.1 0.55", "-0.2 0.26", "-0.5 0.00".
  - Lagged consumption: "-0.2 0.05", "-0.3 0.02", "-0.2 0.04".
  - Tax ratio (CIT/PIT): "0.3 0.01", "0.3 0.03", "-0.4 0.00".
  - R Square: "0.5 0.5 0.6".

- Table 3 (1996–05, All sample countries):
  - Credit to private sector: "-0.4 0.03", "-0.5 0.01", "-0.4 0.04".
  - Tax ratio (CIT/PIT): "0.2 0.24", "0.0 0.98", "-0.5 0.00".
  - R Square: "0.3 0.3 0.4".

- Table 4 (Including uncertainty proxies, 1996–00, All sample countries):
  - Credit to private sector: "-0.4 0.02", "-0.5 0.01", "-0.3 0.26".
  - Age composition: "0.8 0.00", "0.7 0.01", "-0.5 0.14".
  - World Bank Indexes, Voice and accountability: "-0.6 0.02", "-0.6 0.03", "0.3 0.32".
  - R Square: "0.6 0.5 0.3".

- Table 6 (Including uncertainty proxies, 1996–05, All sample countries):
  - Credit to private sector: "-0.6 0.00", "-0.7 0.00", "-0.4 0.08".
  - Age composition: "0.6 0.03", "0.4 0.14", "-0.5 0.13".
  - Rule of law: "1.5 0.03", "1.2 0.07", "-0.6 0.43".
  - R Square: "0.6 0.6 0.4".

- Table 8 (Summary of Other Uncertainty Proxies, 1995–05; only statistically significant results shown):
  - Heritage indexes, All: "Credit to private sector -0.4 0.02"; "Government intervention 0.4 0.01".
  - World Bank Enterprise Surveys, All: "Unanticipated inflation -0.4 0.04"; "Tax ratio (CIT/PIT) -0.8 0.03"; "Infrastructure 0.7 0.00".
  - World Values Survey Confidence, All: "Credit to private sector -0.4 0.06"; "Tax ratio (CIT/PIT) -0.6 0.00"; "Age 0.5 0.04"; "Average of categories 1-7 0.4 0.02".

- Table 9 (Statistically Significant Results Excluding Real Growth and Including Uncertainty Proxies):
  - Equity market capitalization: Mature "0.9 0.9 -1.0 -1.0" (coefficient entries shown).
  - Bond market capitalization: Emerging "0.5"; Mature "-0.6 -0.5".
  - Credit to private sector: All "-0.6 -0.6 -0.6 -0.7"; Emerging "-0.5 -0.4"; Mature "-0.5 -0.6 -0.6 -0.5".
  - Unanticipated inflation: All "-0.4 -0.3 -0.3"; Emerging "-0.4"; Mature "1.1 0.9 0.8 -1.3".
  - World Bank indexes: multiple coefficient entries including Voice and accountability All "-1.0 -0.9 0.5 -0.5", Emerging "-1.1 -0.9 1.2 -0.8 -0.7"; Government effectiveness All "-1.4 -1.4 -1.0", Emerging "-1.3 -1.3 -0.9"; Rule of law All "1.5 1.2", Emerging "-1.4 1.1 1.1 1.0 0.8"; Control of corruption Emerging "1.3 1.2", Mature "1.2".

### Interpretation highlights (as presented in tables)
- Credit to private sector is a recurrent negative correlate of equity premia/returns/safe asset returns in many samples and specifications (numerous negative coefficients with low p values).
- Age composition often enters with positive coefficients in pooled and some subsample regressions, indicating demographic composition is associated with asset return measures in these regressions.
- Inclusion of uncertainty proxies and governance indexes alters coefficient magnitudes and significance, with several World Bank Index components (Voice and accountability; Government effectiveness; Rule of law; Control of corruption) appearing with statistically significant coefficients in the consolidated summary (Table 9).
- Tax ratio (CIT/PIT) shows heterogeneous effects across dependent variables and subsamples; several specifications report statistically significant negative coefficients.
- Unanticipated inflation shows negative and sometimes significant coefficients, particularly in emerging market panels.

### R Square and model fit
- R Square values reported across tables indicate modest explanatory power varying by dependent variable and subsample; examples include:
  - Table 1 All sample countries: "0.5 0.4 0.3".
  - Table 4 Emerging markets (including uncertainty proxies): "0.7 0.7 0.5".
  - Table 6 Emerging markets (including uncertainty proxies): "0.8 0.8 0.6".
  - Table 9 notes that only coefficients statistically significant at least at the 10 percent level are presented.

*Source: Authors' estimates.*

### REFERENCES

### _wp07230 - REFERENCES

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- Mehra, R., 2003, “The Equity Premium: Why is This Puzzle?” Financial Analysts Journal, 54–69.
- North, Douglass C., 1994, “Economic Performance Through Time,” American Economic Review 84(3), 359–368.
- ____, 1991, “Institutions,” Journal of Economic Perspectives 5(1), 97–112.
- Rietz, T.A., 1988, “The Equity Premium Puzzle: A Solution,” Journal of Monetary Economics 22(1), 117–131.
- Rodrik, Dani, Arvind Subramanian, and Francesco Trebbi, 2002, “Institutions Rule: The Primacy of Institutions Over Integration and Geography in Economic Development,” IMF Working Paper WP/02/189 (Washington DC: International Monetary Fund).
- Schiller, Robert J., 1993, “Stock Prices and Social Dynamics,” Chapter 7 in Richard H. Thaler (ed.), 167–217.
- Segal, Uzi, 1987, “The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach,” International Economic Review 28(1), 175–202.
- Starmer, Chris and Robert Sugden, 1993, “Testing for Juxtaposition and Event-Splitting Effects, Journal of Risk and Uncertainty 6, 235–254.
- Stulz, René M., 2005, “The Limits of Financial Globalization,” Journal of Finance 60(4), 1595–1638.
- Summers, Lawrence H., 1993, “Does the Stock Market Rationally Reflect Fundamental Values?” Chapter 6 in Richard H. Thaler (ed.), 153–166.
- Thaler, Richard H. (ed.), 1993, Advances in Behavioral Finance, The Russel Sage Foundation, New York.
- Tversky, Amos and Daniel Kahneman, 1992, “Advance in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty 5, 297–323.
- ____, and Peter Wakker, 1995, “Risk Attitudes and Decision Weights,” Econometrica 63(6), 1225–1280.
- ____, and Craig R. Fox, 1995, “Weighing Risk and Uncertainty,” Psychological Review 102 (2), 269–283.
- Weil, Phillipe, 1989, “The Equity Premium Puzzle and the Risk-Free Rate Puzzle,” Journal of Monetary Economics 1989(24), 401–421.
- Zeckhauser, Richard, 2006, “Investing in the Unknown and Unknowable,” Capitalism and Society 1(2), Article 5, 1–39.

### References to Data Sources (available on the internet)
- Bureau of International Statistics (BIS).
- Datastream.
- Global Competitiveness Index.
- Heritage Foundation, Index of Economic Freedom.
- International Country Risk Guide.
- International Financial Statistics, IMF.
- S&P IFC Emerging Markets Database.
- Transparency International.
- United States Census Bureau, International Database.
- World Bank, Governance Indicators (Institutional Quality Indexes).
- ____, Enterprise Surveys.
- ____, Doing Business.
- World Federations of Exchanges.
- World Values Survey.
- Sources shown in Appendix I, Tables 1 and 2.

*Source: _wp07230 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07230.pdf_