1. Market Power, Risk-Taking and Insolvency in the U. S
Market Power, Risk-Taking and Insolvency in the U.S. Property-Liability Insurance Industry
Vivian Jeng
National ChengChi University
Chia-Ling Ho
Tamkang University
Gene C. Lai
Washington State University

2. Outlines The importance of Risk-taking vs. Market power
The importance of Insolvency vs. Market power

3. 1. The Importance of Market Power and Risk-Taking
The existence of market power implies high price, better profits or a gain of monopolistic rent.
Risk-taking has been critical for investors and stakeholders of banks or insurers. (Ho, Lai and Lee, 2013)
Catastrophes or long-tail liability claims can be huge for property-liability insurers, ex. recent events such as Hurricane Sandy or tsunamis.

4. Two key issues worth mentioning in P-L insurance industry
Adverse selection: policyholders who believe they are overcharged may tend to exit from the market.
The remaining policyholders may be high-risk.
Guarantee fund mechanism in the industry: according to Cummins (1988), it may encourage insurers from taking high-risk because of moral hazard.

5. Market Power-Risk Relationship
The impact of adverse selection on this relationship:
On banking:
Boyd and De Nicolo (2005) in their banking analysis suggest that higher market power results in higher risk
Banks with higher market power  charge higher interest rate to loan customers adverse selection stands a riskier set of borrowers remain.

6. On Insurance industry:
Martinez-Miera and Repullo (2010) further considers the fact that higher interest rates increase the banks’ revenues from loans
We may obtain a U-shaped relationship between market power and the risk of borrowers.
On Insurance industry:
Insurers with higher market power  collude with each other and charge higher premium to policyholders a riskier set of policyholders remain.

7. The impact of guarantee fund on this relationship:
Harrington and Danzon (1994) propose that insurers may price below cost when facing competition because of guarantee funds.
Firms with lower market power tend to be more risky due to moral hazard.

8. In sum:
Relative to other firms, risks for firms with strong market power and firms which are price-takers can be large.
If higher premium increase insurers’ revenues
A U-shaped relationship between market power and risk may be found.
Risk
Market Power

9. 2. Market Power-Insolvency Relationship
Browne and Hoyt (1995) examine the P-L industry characteristics related to insurer insolvencies.
Number of insurers is used to proxy competition in a time-series model using macroeconomic variables, and higher competition results in higher insolvency rate.
We use firm-level data to examine the market power-insolvency relationship.

10. How to measure market power?
Measures of Market power : Lerner Index
Lerner Index= (P-MC)/ P
It identifies the degree of monopoly power and consider the difference between a firm’s price and its marginal cost
=1: market power is high and close to monopolistic
=0: low and close to perfect competitive
(price takers)
0<LI<1: most cases
Maudos and Fernandez de Guevara (2007) apply the Lerner index to estimate the market power

11. Past Literatures in banking industry
Market power-risk relationship in Banking
Keeley (1990, JF)
Franchise value is critical for banks. Competition reduces franchise values of banks and induces the banks to take more risks.
Boyd and De Nicolo (2005, JF)
U-shape relationship: Martinez-Miera and Repullo (2010, RFS):

12. Methodologies
Risk= f (Lerner index, Lerner index2, other exogeneous variables)
Use generalized method of moments (GMM) method for the existence of endogeneity
Does not require distributional assumptions on error terms
Accounts for heteroskedasticity
Will examine White test and Hansen’s J-statistic to ensure the necessity of using GMM

14. Dependent variables Risk: Underwriting risk Investment risk Total risk
Previous arguments mostly lie on the discussion of underwriting functions.
Based on Ho, Lai and Lee (2013), we consider risks from three different aspects
Underwriting risk
Standard deviation of loss ratio
Investment risk
Standard deviation of return on investment (ROI)
Total risk
Standard deviation of ROA

15. Independent variables
Lerner index: (P-MC)/ P
Price: inverse of loss ratio (Tennyson, 1997; Cummins et al, 2001)
Marginal cost:
Calculated from the translog cost function and then derive from total cost:

16. For translog cost function,
Output: total assets (Berg and Kim, 1994; Fernadez de Guevara et al, 2005)
Inputs:
Labor
Business service
Equity capital
Debt capital

17. Control variables Business Herfindahl index
Geographic Herfindahl index
Firm size
Reinsurance ratio
Mutual dummy
Group dummy
Commercial line %

18. Data and Summary Statistics
From , NAIC data
Abnormal data is deleted
Negative premiums, assets or equity
Reinsurance ratio or Herfindahl index >=1
22854 firm-year observations
Variables are winsorized at 1% & 99%

19. Descriptive Statistics of Variables
Mean
Std Dev
Minimum
Maximum
STDlossratio
0.1148
0.1534
0.0069
1.1495
STDROI
0.0147
0.0167
0.0013
0.1173
STDROA
0.0347
0.0318
0.0033
0.1903
Lerner Index
0.8184
0.0947
0.3835
0.9855
Bherfindahl
0.4916
0.3129
0.0997
1.0000
Geoherfindahl
0.6083
0.3827
0.0426
Firmsize
1.9671
Reinsurance_ratio
0.3366
0.2765
0.0000
0.9541
Mutual
0.2437
0.4293
Group
0.6651
0.4720
Com
0.6132
0.3722
Insolvency
0.0035
0.0587 N
22854

20. Key issue average value is discussed: Lerner index: 0.8184
Commercial %: 61.3%
Insolvency rate: 0.35%

21. Summary I: underwriting risk
STDlossratio = ( )LI LI2
A quadratic relationship between market power and firm risk.
Both firms with high market power and relatively low market power (price takers) may have high risks.
The inflection point is 0.77, close to 25th of the Lerner index distribution
¾ of the observations state a high market power-high risk relationship.
Implication: firms with high market power may collude with each other, and due to adverse selection, high-risk policyholders may leave in the underwriting portfolio.

22. Investment risk and Total risk
We do not see market power to affect risk in the investment risk model.
Similar to underwriting risk model, market power also has a quadratic relationship with total risk.
The relationship between market power and total risk mostly comes from underwriting risk.

23. Logistic Regressions of Insolvency on Competition Variables
Estimate
Insolvency
(Chi-Square)
Sig.
Intercept
6.4591 *
(2.88)
Lerner Indext-1
(1.99)
Lerner Index Squaredt-1 **
(4.27)
Bherfindahlt-1
(4.46)
Geoherfindahl t-1
(6.01)
Firmsize t-1
0.1623
(2.07)
Estimate
Insolvency
(Chi-Square)
Sig.
Reinsurance_ratio t-1
(1.82)
Mutual t-1
1.0683 **
(5.97)
Group t-1
0.2148
(0.38)
Com t-1 *
(3.18)
Log-Likelihood
-267.3 N
17218
Note: The values of independent variables are lagged one year prior to the insolvency events (i.e. year t-1 value). The dependent variable is 1 if a firm becomes insolvent and 0 if else. ***, ** and * represent statistical significance at 0.01, 0.05 and 0.1 levels, respectively.

24. Logistic Regression results
Market power also has a quadratic relationship with the probability of firm insolvency.
Insurers with market power at two extremes in the prior year are more likely to become insolvent in the current year.
Vs. Browne and Hoyt (1995): one side, insurers with higher market power are less likely to become insolvent.

25. Further Checks
Consider the interaction term between market power and commercial line ratio:
The higher the commercial %, a stronger relationship between high market power and high risk.
Adverse selection may be more likely to happen in commercial lines than in personal lines…

26. Contributions
We examine the relationship between market power and risk in the U.S. P-L insurance industry.
We show the existence of asymmetric information, including adverse selection of insurers-policyholders and moral hazard problem has effect on the firm risk.
We control endogenity for market power-risk relationship.

27. Regressions of Underwriting Risk Model
STDlossratio
Estimate
(T-value)
Sig.
Intercept
1.1802
***
(3.86)
Lerner Index
(-3.48)
Lerner Index Squared
1.8563
(3.39)
Bherfindahl
0.0623
(7.47)
Geoherfindahl
0.0239
(4.26)
Firmsize **
(-2.33)
Estimate
(T-value)
Sig.
Reinsurance_ratio
0.0421
***
(5.42)
Mutual
(-0.01)
Group
0.0187
(4.29)
Com
0.0324
(5.68)
Adj R-Square
0.0357 N
21082
P-value of
0.3502
Hansen's J-statistic
0.0001
Heterogeneity test

28. Regressions of Investment Risk Model
STDROI
Estimate
(T-value)
Sig.
Intercept
0.0954
(0.89)
Lerner Index
(-0.7)
Lerner Index Squared
0.1274
(0.65)
Bherfindahl
(-0.31)
Geoherfindahl
***
(-2.87)
Firmsize
0.0001
(0.67)
Estimate
(T-value)
Sig.
reinsurance_ratio
0.0004
(0.43)
Mutual *
(-1.88)
Group
(0.84)
Com
(0.23)
Adj R-Square
0.0094 N
21082
P-value of
0.4608
Hansen's J-statistic
0.0001
Heterogeneity test

29. Regressions of Total Risk Model
STDROA
Estimate
(T-value)
Sig.
Intercept
0.4575
***
(6.55)
Lerner Index
(-5.23)
Lerner Index Squared
0.6096
(4.94)
Bherfindahl
0.0037 **
(2.06)
Geoherfindahl
0.0041
(3.48)
Firmsize
(-6.93)
Estimate
(T-value)
Sig.
reinsurance_ratio
(-0.63)
Mutual
***
(-4.19)
Group
0.0006
(0.67)
Com
(-3.93)
Adj R-Square
0.014 N
21082
P-value of
0.3511
Hansen's J-statistic
0.0001
Heterogeneity test

30. Future Directions
What are the determinants of firm market power?

31. Commercial Line Interaction Terms
Total Risk
Estimate
(T-value)
Sig.
Intercept
0.4888
***
(7.16)
Lerner Index
(-5.5)
Lerner Index Squared
0.5913
(4.92)
Bherfindahl
0.0034 *
(1.85)
Geoherfindahl
0.0046
(3.82)
Firmsize
(-7.03)
Wreinsurance_ratio
(-0.1)
Estimate
(T-value)
Sig.
Mutual1
***
(-3.78)
Group
0.001
(1.01)
Com
(-4.93)
Com*Lerner Index
0.0774
(4.73)
Adj R-Square
0.0189 N
21294
P-value of
0.239
Hansen's J-statistic
0.0001
Heterogeneity test

32. Group Interaction Terms
Model 1
Estimate
wstd5_lossratio
(T-value)
Sig.
Intercept
0.9878
***
(3.16)
Lerner Index
(-2.83)
Lerner Index Squared
1.5931
(2.76)
Wherfindahl
0.0652
(7.96)
Wgeoherfindahl
0.0237
(4.36)
Wfirmsize **
(-1.96)
Wreinsurance_ratio
0.0469
(6.07)
Model 1
Estimate
wstd5_lossratio
(T-value)
Sig.
Mutual
0.0000
(-0.01)
Group
0.0966 **
(2.24)
Com
0.0344
***
(5.8)
Group*Lerner Index *
(-1.9)
Adj R-Square
0.0504 N
21011
P-value of
0.4249
Hansen's J-statistic
0.0001
Heterogeneity test