## _wp06179 - 1. Cross-Correlations

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### I. INTRODUCTION
- Focus: determinants of non-life insurance penetration (NLP) across a sample of 70 countries.
- Dependent variable: non-life insurance penetration measured as gross non-life insurance premiums paid as a percentage of GDP (NLP).
- Hypothesis: institutional quality is a deeper determinant of insurability because it reflects transparency and Knightian uncertainty (ambiguity).
- Key conceptual links:
  - Higher institutional quality → greater transparency → lower Knightian uncertainty → higher insurability.
  - Income level (per capita income, PCI) is correlated with institutional quality; institutional quality may underlie PCI’s explanatory power for NLP.
- Scope: excludes life insurance penetration to focus on factors specific to non-life insurance.

### II. INSTITUTIONAL QUALITY AND KNIGHTIAN UNCERTAINTY: AN INTERPRETATION
- WBIs (World Bank governance indexes) are treated as indicators of the degree of Knightian uncertainty because they reflect subjective evaluations of governance that affect ranges of possible events and outcomes.
- Institutional features highlighted:
  - Voice and accountability
  - Political stability
  - Government effectiveness
  - Regulatory quality
  - Rule of law
  - Control of corruption
- Mechanisms:
  - Weak governance (e.g., unreliable reports, corruption, weak courts) increases ambiguity about claims settlement and policy implementation, raising uncertainty for insurers and consumers and lowering insurability.
  - Even with actuarial assessments (e.g., fire risk), weak institutional enforcement and unreliable information add layers of unquantifiable uncertainty.

### III. METHODOLOGY
- Model specification: NLP = f(X1, X2, X3, ...), where Xi include PCI, financial depth (M2/GDP), country risk (CORISK), cost of insurance (C/P), and WBIs.
- Normalization: all variables including NLP normalized as vij = (xij − μi)/σi, producing standardized vectors Xi = {vi1, vi2, ..., vi70}.
- Exploratory approach:
  - Compute Pearson Product Moment Correlation Matrix and test null hypothesis ρ = 0 using t test: t = r * sqrt((n-2)/(1−r^2)).
  - Run multiple regressions: NLPi = β0 + Σk βk Xki + ui.
- Strategy to assess deeper determinants:
  - Examine cross-correlations showing PCI and CORISK are very significantly correlated with WBIs and with each other.
  - Sequential regressions: (a) include all variables; (b) drop PCI; (c) drop PCI and CORISK; (d) exclude WBIs to compare explanatory power of PCI and CORISK.

### IV. CROSS-CORRELATIONS (SELECTED t values from Table 1)
- Per capita income (PCI): 5.6
- M2/GDP: 2.0, 2.9
- Composite risk (CORISK): 5.4, 10.2, 3.9
- Non-life claims/premiums (C/P): 4.5, 4.6, 1.0, 4.4
- Overall index: 6.9, 9.5, 3.4, 19.7, 4.9
- Voice and accountability: 8.5, 6.3, 1.4, 8.4, 3.9
- Political stability: 5.4, 8.6, 2.9, 17.0, 3.7
- Government effectiveness: 5.6, 8.6, 4.2, 17.3, 4.9
- Regulatory quality: 5.9, 6.9, 2.9, 10.8, 3.9
- Rule of law: 5.3, 9.1, 3.9, 16.3, 5.1
- Control of corruption: 5.7, 9.1, 3.7, 16.1, 5.0

### V. REGRESSION RESULTS (summary of Tables 2–4)
- General findings:
  - Most WBIs—particularly the overall index, voice and accountability, and regulatory quality—outperform PCI and CORISK in explaining NLP variation across countries.
  - WBI coefficients are positive: higher institutional quality indicates higher insurability.
  - Non-life claims/premiums (C/P) has high explanatory power and a positive coefficient.
  - Financial depth (M2/GDP) is generally insignificant.
- Specific patterns across specifications:
  - With all variables included (Table 2): WBI indices (overall and voice and accountability) show strong statistical significance.
    - Example: Overall index coefficient 0.8, t = 3.2.
    - Example: Voice and accountability coefficient 0.6, t = 4.1 in one specification.
  - When PCI is dropped (Table 3): explanatory power of WBIs increases; PCI remains statistically insignificant when WBIs are excluded in some specifications.
  - When both PCI and CORISK are dropped (Table 4): WBI significance rises and all WBIs become individually statistically significant in certain specifications.
  - When including PCI but excluding CORISK and WBIs (Table 4, regression 9): PCI becomes statistically significant but remains less significant than most WBIs.
  - When including CORISK but excluding PCI and WBIs (Table 4, regression 10): most WBIs outperform CORISK.
- Notable numeric regression indicators (selected):
  - C/P: coefficient ≈ 0.2 with t-values frequently around 2.0 (e.g., 0.2, t = 2.0; 0.3, t = 2.6).
  - PCI: coefficients around 0.2–0.3 with t-values often below conventional significance thresholds (e.g., 0.2, t = 1.5; 0.3, t = 1.7); in some regressions PCI reaches t = 3.5 when WBIs excluded.
  - Overall index: coefficient 0.8, t = 3.2 (Table 2); coefficient 0.8, t = 3.3 (Table 3).
  - Voice and accountability: coefficient 0.6, t = 4.1; 0.7, t = 5.5 in alternate specifications.
  - Adjusted R2 values reported: 0.5, 0.4, 0.6, 0.3, 0.4 across specifications.
  - Multiple R2 values reported: 0.8, 0.7, 0.8, 0.6, 0.6 across specifications.

### VI. INTERPRETATION OF THE C/P RESULT
- Positive C/P coefficient implies NLP is negatively correlated with P/C (the inverse), meaning NLP rises as the price of insurance (proxied by P/C) declines.
- Possible explanations:
  - Higher C/P in more developed countries may reflect higher quality of insurance or higher claim payment rates.
  - In countries with better governance, lower uncertainty may lead to lower insurance prices for consumers.

### VII. CONCLUSIONS AND POLICY IMPLICATIONS
- Main conclusions:
  - WBIs (institutional quality) are dominant determinants of non-life insurability across the sample and outperform PCI and CORISK in explaining NLP.
  - PCI appears to act as a catch-all variable that captures institutional quality and uncertainty effects among others.
  - Weak governance increases unquantifiable risks (Knightian uncertainty) and lowers insurability.
- Policy implications:
  - Insurance market development should be a priority within broader financial sector development policies.
  - Higher insurability (lower uncertainty) is likely to stimulate higher domestic and foreign investment.
- Suggested further research:
  - Examination of correlations between investment flows, Knightian uncertainty, and the level of insurance coverage across countries.

### VIII. APPENDIX — DATA DESCRIPTION AND SOURCES (selected)
- NLP: Yearly gross non-life insurance premiums in percent of GDP, 1994–2003 average. Source: Swiss Re SIGMA Insurance Research.
- WBIs: six components—voice and accountability; political stability; government effectiveness; regulatory quality; rule of law; control of corruption. Simple average of country ranks (0–100) in 1996, 1998, 2000, and 2002. Overall index constructed as simple average of 1996–2002 indexes. Source: Kaufman, Kraay, and Mastruzzi (2004, revised version).
- CORISK: Composite risk ratings by the International Country Risk Guide. Average of 1992–2002 yearly ratings. Note: CORISK assigns a low value to a high-risk country.
- C/P: Ratio of gross claims to gross premiums. Average of yearly data for 1996–2003 as available. Source: Insurance Information Statistics (ISIS) database. Note: C/P calculated from samples of reporting insurance companies and may not reflect country-wide ratio; inverse (P/C) interpreted as proxy for price of insurance to consumers.
- M2/GDP and PCI: M2/GDP ratio used as proxy for financial depth. Averages of 1994–2003 yearly data for M2/GDP; averages of 1994–2001 yearly data for real per capita income (PCI) in 1995 U.S. dollars. Source: IMF International Financial Statistics.

*Source: Authors' estimates, as presented in _wp06179 - 1. Cross-Correlations (IMF PDF).*

### 1. Cross-Correlations ..................................................................................................

### _wp06179 - 1. Cross-Correlations ..................................................................................................

### I. INTRODUCTION
- Focus: determinants of non-life insurance penetration (NLP) across a sample of 70 countries.
- Dependent variable: non-life insurance penetration measured as gross non-life insurance premiums paid as a percentage of GDP (NLP).
- Hypothesis: institutional quality is a deeper determinant of insurability because it reflects transparency and Knightian uncertainty (ambiguity).
- Key conceptual links:
  - Higher institutional quality → greater transparency → lower Knightian uncertainty → higher insurability.
  - Income level (per capita income, PCI) is correlated with institutional quality; institutional quality may underlie PCI’s explanatory power for NLP.
- Scope: excludes life insurance penetration to focus on factors specific to non-life insurance.

### II. INSTITUTIONAL QUALITY AND KNIGHTIAN UNCERTAINTY: AN INTERPRETATION
- World Bank governance indexes (WBIs) are treated as indicators of the degree of Knightian uncertainty because they reflect subjective evaluations of governance that affect ranges of possible events and outcomes.
- Institutional features affecting perceived uncertainty include:
  - Voice and accountability
  - Political stability
  - Government effectiveness
  - Regulatory quality
  - Rule of law
  - Control of corruption
- Mechanisms described:
  - Weak governance (e.g., unreliable reports, corruption, weak courts) increases ambiguity about claims settlement and policy implementation, raising uncertainty for both insurers and consumers and lowering insurability.
  - Even with actuarial assessments (e.g., fire risk), weak institutional enforcement and unreliable information add layers of unquantifiable uncertainty.

### III. METHODOLOGY
- General model: NLP = f(X1, X2, X3, ...), where Xi include PCI, financial depth (M2/GDP), country risk (CORISK), cost of insurance (C/P), and WBIs.
- Normalization: all variables including NLP normalized as vij = (xij – μi)/σi, producing standardized vectors Xi = {vi1, vi2, ..., vi70}.
- Exploratory approach:
  - Compute Pearson Product Moment Correlation Matrix and test null hypothesis ρ = 0 using t test: t = r * sqrt((n-2)/(1−r^2)).
  - Run multiple regressions: NLPi = β0 + Σk βk Xki + ui.
- Strategy to assess deeper determinants:
  - Examine cross-correlations showing PCI and CORISK are very significantly correlated with WBIs and with each other.
  - Sequential regressions: (a) include all variables; (b) drop PCI; (c) drop PCI and CORISK; (d) exclude WBIs to compare explanatory power of PCI and CORISK.

### IV. CROSS-CORRELATIONS (SELECTED t values from Table 1)
- Per capita income (PCI): 5.6
- M2/GDP: 2.0, 2.9 (two entries shown)
- Composite risk (CORISK): 5.4, 10.2, 3.9 (multiple entries)
- Non-life claims/premiums (C/P): 4.5, 4.6, 1.0, 4.4
- Overall index: 6.9, 9.5, 3.4, 19.7, 4.9
- Voice and accountability: 8.5, 6.3, 1.4, 8.4, 3.9
- Political stability: 5.4, 8.6, 2.9, 17.0, 3.7
- Government effectiveness: 5.6, 8.6, 4.2, 17.3, 4.9
- Regulatory quality: 5.9, 6.9, 2.9, 10.8, 3.9
- Rule of law: 5.3, 9.1, 3.9, 16.3, 5.1
- Control of corruption: 5.7, 9.1, 3.7, 16.1, 5.0

### V. REGRESSION RESULTS (summary of Tables 2–4)
- General findings:
  - Most WBIs—particularly the overall index, voice and accountability, and regulatory quality—outperform PCI and CORISK in explaining NLP variation across countries.
  - WBI coefficients are positive: higher institutional quality indicates higher insurability.
  - Non-life claims/premiums (C/P) has high explanatory power and a positive coefficient (puzzling from supply-side perspective).
  - Financial depth (M2/GDP) is generally insignificant.
- Specific patterns across model specifications:
  - With all variables included (Table 2): WBI indices (overall and voice and accountability) show strong statistical significance (e.g., Overall index coefficient 0.8, t = 3.2; Voice and accountability coefficient 0.6, t = 4.1 in one specification).
  - When PCI is dropped (Table 3): explanatory power of WBIs increases; PCI remains statistically insignificant when WBIs are excluded in some specifications.
  - When both PCI and CORISK are dropped (Table 4): WBI significance rises and all WBIs become individually statistically significant in certain specifications.
  - When including PCI but excluding CORISK and WBIs in one regression (Table 4, regression 9): PCI becomes statistically significant but remains less significant than most WBIs.
  - When including CORISK but excluding PCI and WBIs (Table 4, regression 10): most WBIs outperform CORISK.
- Notable numeric regression indicators (selected):
  - C/P: coefficient ≈ 0.2 with t-values frequently around 2.0 (e.g., 0.2, t = 2.0; 0.3, t = 2.6).
  - PCI: coefficients around 0.2–0.3 with t-values often below conventional significance thresholds (e.g., 0.2, t = 1.5; 0.3, t = 1.7); in some regressions PCI reaches t = 3.5 when WBIs excluded.
  - Overall index: coefficient 0.8, t = 3.2 (Table 2); coefficient 0.8, t = 3.3 (Table 3).
  - Voice and accountability: coefficient 0.6, t = 4.1; 0.7, t = 5.5 in alternate specifications.
  - Adjusted R2 values reported in various regressions: 0.5, 0.4, 0.6, 0.3, and 0.4 across specifications.
  - Multiple R2 values reported: 0.8, 0.7, 0.8, 0.6, 0.6 across specifications.

### VI. INTERPRETATION OF THE C/P RESULT
- Positive C/P coefficient implies NLP is negatively correlated with P/C (the inverse), meaning NLP rises as the price of insurance (proxied by P/C) declines.
- Possible explanations:
  - Higher C/P in more developed countries may reflect higher quality of insurance or higher claim payment rates.
  - In countries with better governance, lower uncertainty may lead to lower insurance prices for consumers.

### VII. CONCLUSIONS AND POLICY IMPLICATIONS
- Main conclusions:
  - WBIs (institutional quality) are dominant determinants of non-life insurability across the sample and outperform PCI and CORISK in explaining NLP.
  - PCI appears to act as a catch-all variable that captures institutional quality and uncertainty effects among others.
  - Weak governance increases unquantifiable risks (Knightian uncertainty) and lowers insurability.
- Policy implications:
  - Insurance market development should be a priority within broader financial sector development policies.
  - Higher insurability (lower uncertainty) is likely to stimulate higher domestic and foreign investment.
- Suggested further research:
  - Examination of correlations between investment flows, Knightian uncertainty, and the level of insurance coverage across countries.

### VIII. APPENDIX — DATA DESCRIPTION AND SOURCES (selected)
- Non-life insurance penetration (NLP): Yearly gross non-life insurance premiums in percent of GDP, 1994–2003 average. Source: Swiss Re SIGMA Insurance Research.
- Institutional Quality Indexes (WBIs): six components—voice and accountability; political stability; government effectiveness; regulatory quality; rule of law; control of corruption. Simple average of country ranks (0–100) in 1996, 1998, 2000, and 2002. Overall index constructed as simple average of 1996–2002 indexes. Source: Kaufman, Kraay, and Mastruzzi (2004, revised version).
- Country risk (CORISK): Composite risk ratings by the International Country Risk Guide. Average of 1992–2002 yearly ratings. Note: CORISK assigns a low value to a high-risk country.
- Cost (price) of insurance (C/P): Ratio of gross claims to gross premiums. Average of yearly data for 1996–2003 as available. Source: Insurance Information Statistics (ISIS) database. Note: C/P calculated from samples of reporting insurance companies and may not reflect country-wide ratio; inverse (P/C) interpreted as proxy for price of insurance to consumers.
- M2/GDP and PCI: M2/GDP ratio used as proxy for financial depth. Averages of 1994–2003 yearly data for M2/GDP; averages of 1994–2001 yearly data for real per capita income (PCI) in 1995 U.S. dollars. Source: IMF International Financial Statistics.

*Source: Authors' estimates, as presented in _wp06179 - 1. Cross-Correlations (IMF PDF).*

### REFERENCES

### _wp06179 - REFERENCES

### Natural disasters and catastrophe risk
- Dacy, Douglas, and Howard Kunreuther, 1969, 
  The Economics of Natural Disasters, The Implications for Federal Policy (New York: Free Press).
- Froot, Kenneth, 1999, 
  Financing Catastrophe Risk (Chicago: University of Chicago Press).
- Swiss Re, SIGMA Insurance Research.

### Insurance markets and economic development
- Outreville, François, 1990, “The Economic Significance of Insurance Markets in Developing Countries,” Journal of Risk and Insurance, Vol. 57, No. 3, pp. 487–98.
- Outreville, François, 1996, “Life Insurance Markets in Developing Countries,” Journal of Risk and Insurance, Vol. 63, No.2, pp. 263-78.
- Ward, Damian, and Ralf Zurbruegg, 2000, “Does Insurance Promote Economic Growth? Evidence from OECD Countries,” Journal of Risk and Insurance, Vol. 67, No. 4, pp. 489–506.
- Insurance Information and Statistics (ISIS), Bureau van Dijk, Brussels, Belgium brussels@bvdep.com.

### Ambiguity, risk, and decision processes
- Knight, Frank, 2002 (originally published in 1921), Risk, Uncertainty and Profit (Washington: Beard Books).
- Kunreuther, Howard, Jacqueline Meszaros, Robin Hogarth, and Marc Spranca, 1995, “Ambiguity and Underwriter Decision Processes,” Journal of Economic Behavior and Organization, Vol. 26, pp. 337–52.
- Hogarth, Robin, and Howard Kunreuther, 1992, “Pricing Insurance and Warranties: Ambiguity and Correlated Risks,” The Geneva Papers on Risk and Insurance Theory, Vol. 17, No. 1, pp. 35–60.
- Erbaş, S. Nuri, 2004, “Ambiguity, Transparency, and Institutional Strength,” IMF Working Paper WP/04/115 (Washington: International Monetary Fund).

### Institutions, governance, and economic performance
- North, Douglas, 1991, “Institutions,” Journal of Economic Perspectives, Vol. 5, No. 1, pp. 97–112.
- North, Douglas, and Barry Weingast, 1989, “Constitutions and Commitment: The Evolution of Institutions Governing Public Choice in Seventeenth Century England,” Journal of Economic History, Vol. 49, No. 4, pp. 803–32.
- Kaufman, Daniel, Aart Kraay, and Massimo Masfruzzi, 2004 (revised version, April 5), “Governance Matters III: Governance Indicators for 1996–2002,” Policy Research Working Paper (Washington: World Bank Development Research Group and World Bank Institute, Governance, Regulation and Finance Division). www.worldbank.org/wbi/governance/govdata2002.html and http://www.worldbank.org/wbi/governance/govdata2002/index.html.
- 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: International Monetary Fund).
- Das, Udbair S., Nigel Davies, and Richard Podpiera, 2003, “Insurance and Issues in Financial Soundness,” IMF Working Paper WP/03/138 (Washington: International Monetary Fund).

### Research outlets and web resources
- Heritage Foundation. (http://www.heritage.org).
- International Country Risk Guide. http://www.icrgonline.com

*REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06179.pdf_