Chapter 5 Empirical Results
5.1 Result Analysis
We use the translogarithmic cost function discussed as above to estimate the coefficient, and the results are shown in table 6. The adjusted R square is 0.966, indicating that this model can be highly-explained by the variables. The coefficients of β 、β 、J 、J J& and θ& are -0.025,
0.073, 0.043, 0.024, -0.067 and -0029 respectively, and nearly all of these coefficients are significant in the model. The next step is to apply these values into formula (6) to obtain the marginal cost, and then we further calculate the Lerner index by formula (4).
Table 6. Estimated Coefficient of Translog Cost Function
Variable Estimate T value Variable Estimate T value
lnTA -0.253 -1.43 lnTATrend -0.029*** -3.72
Note: * represents significance level of 10%
** represents significance level of 5%
*** represents significance level of 1%
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Table 7 presents the descriptive statistics of all dependent and independent variables. The mean of Lerner index (LI) is 0.569, implying that on average, the majority of the insurers have a certain level of market power. The insurer with highest market power is MS&AD insurance group after merger in 2010 as mentioned above and insurer with lowest market power is Sony Assurance Company in 2002. The firm with the highest output price (P) and marginal cost (MC) is H.S. in 20107.
The data shows that firm size (FS) is a left-skewed distribution and the mean is 15.028, indicating that large insurers are more than small ones. Insurer with largest firm size is TMN insurance group and the smallest firm size is H.S. insurance in 2010. For the proportion of long-tail business (PLT), the mean is 0.129 and the maximum is only 0.248, from which we observe that Japanese nonlife insurers prefer taking short-tail business more than long-tail business. The mean of business diversification (DVF) is 0.619, indicating that most firms are moderately diversified with their business and nearly 85% of the samples are higher than 0.5.
The mean of reinsurance rate (RR) is 18.8% in Japanese non-life insurance market and this indicates that most insurers choose to retain risk instead of transferring risk to other firms8. In Japanese insurance industry, the market concentration (HHI) grows from 864.15 to 1693.19 year by year from 1986 to 2010. As for organization form (OF), the only two insurers held as mutual
7 H.S. has the lowest total assets in 2010, leading to the highest output price, and in the same year H.S. has the highest ratio of total cost to total asset, causing its highest marginal cost.
8 Unum has reinsurance ratio of 60% in1999 and this is the only observation higher than 0.5.
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company are Kyoei mutual fire & marine insurance company and Dai-Ichi life insurance company.
The descriptive statistics of dependent variables are discussed as below. The mean of total risk (SROA) is 0.011, the firm with the highest total risk is Sony Assurance in 2005 and the firm with the lowest total risk (SROA) is Taiyo in 1997. The mean of underwriting risk (SLR) is 0.035, Meiji Yasuda General Insurance faces the highest underwriting risk in 2007 and JI Accident &
Fire Insurance faces the lowest underwriting risk in 2007. The mean of investment risk (SROI) is 0.041, the highest investment risk occurs to Fuji Fire and Marine Insurance in 1998 and the lowest investment risk occurs to Sonpo 24 Insurance Company Limited in 2004. On average, underwriting risk is higher than investment risk in our data. The range is wide for total risk and especially for underwriting risk, indicating that the loss ratio varies widely with different insurers, and this can be attributed to their ways of operation.
As for financial solvency, we use the natural logarithm of the Z-index as the financial solvency variable in our model. The mean of the natural logarithm of the Z-index (lnZ) is 4.368.
Taiyo Life Insurance Company has the highest solvency in 1997 due to its very low standard deviation of return on asset (0.00002). Besides, owing to its negative return on asset (-0.0471) and relatively low ratio of equity to total asset (0.05031), ACE Insurance Japan has the lowest financial stability in 2002.
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Variable N Mean Std. Minimum Maximum
P 535 0.320 0.143 0.072 1.032
HHI 535 1161.740 317.871 864.150 1693.190
OF 535 0.955 0.207 0.000 1.000
SROA 535 0.011 0.025 0.000 0.232
SLR 535 0.035 0.053 0.000 0.510
SROI 535 0.041 0.030 0.000 0.147
lnZ 535 4.368 1.863 -1.963 8.560
Table 8 presents the Pearson correlation coefficient between the independent variables. It shows none of the correlation coefficient bigger than 0.7 or smaller than -0.7, meaning that no strong relation exists, and therefore implies that no multi-collinearity problem exists. We observe that firm size has a moderate positive relation with percentage of long-tailed business and diversification and the correlation coefficient between percentage of long-tailed business and diversification is 0.633, indicating that firms with larger size may be willing to take on more long-tailed business and therefore they would manage to diversify their revenue sources. HHI also has a moderate negative relation with diversification, and the possible reason is that the increases in market concentration insurers may reduce the motivation of firms with high market share to diversify their premium sources and choose to consolidate their original business revenue
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Table 8. Pearson correlation coefficient
LI FS PLT RR DVF HHI OF
Note: * Statistical significance at 10 % level ** Statistical significance at 5% level *** Statistical significance at 1% level
Table 9 shows the results of the relation between risks and the degree of competition in Japanese property-liability insurance industry. We first show the results of using total risks as our dependent variable in the first column. In the total risk model, the coefficient of Lerner index is negative (-1.277), the coefficient of quadratic term is positive (1.113) and both are significant at 5 percent level. The inflection point for Lerner index in the total risk model is 0.574 and it is approximately 62th percentile of the Lerner index distribution. This implies that nearly 62% of the sample presents higher market power (lower competition) decreasing total risk and indicates that our main data supports the inverse relation between market power and total risk..
We find a similar result for underwriting risk. In the second column, the coefficient of Lerner index is negative (-1.880), the coefficient of quadratic term is positive (1.655) and both
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are significant at 10 percent level. The inflection point for Lerner index here is 0.568, which lies approximately the 60th percentile of the sample. Our main sample shows that market power is negatively associated to underwriting risk, implying higher market power would improve underwriting risk.
An opposite situation happens in investment risk model. In the last column, the coefficient of Lerner index is significantly positive (1.778) at 5 percent level and the quadratic term is significantly negative (-1.536) at 1 percent level. With 63% of our data lying below the inflection point (0.579) of Lerner index, the result presents a positive relation established between market power and investment risk. The higher market power, the higher investment risk might be.
As for other control variables, the percentage of long-tail business (PLT) is negatively related to all of the three kinds of risks, indicating that firms with higher ratio of long-tail business would face lower risks in Japanese general insurance industry. Diversification variable (DVF) is negatively significant to underwriting and investment risks, meaning that higher degree of diversification would decrease underwriting and investment risk. The reinsurance ratio (RR) has a positive relation with total risk and underwriting risk. We reckon that insurers may write policies without carefulness on account of reinsurance arrangement, contributing the positive relation between underwriting risk and reinsurance ratio.
In this result, firm size (FS) is only negatively significant related to investment risk and its squared term is positively significant. With 90% of the data lying above the inflection point (12.5), an inverse relationship is found between frim size and investment risk. The greater size of
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a firm may improve its investment risk.
Table 9. The effect of market power on risks.
Variable
Total Risk Underwriting Risk Investment Risk
Estimate T value Estimate T value Estimate T value
Intercept 0.000 -0.18 0.000 0.15 0.002 0.46
White Test 246*** <.0001 80.48*** 0.007 328.9*** <.0001
Hansen’s J 1.29 0.525 1.67 0.434 4.66 0.198
Adjusted tf 0.36 0.004 0.06
N 535 535 535
Note: The rejection of White test implies the inexistence of heteroscedasticity .
The rejection of Hansen’s J test implies the invalidity of instrument variables used.
* Statistical significance at 10 % level ** Statistical significance at 5% level *** Statistical significance at 1% level
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Table 10. The effect of market power on risks for separated periods.
Note: * Statistical significance at 10 % level ** Statistical significance at 5% level *** Statistical significance at 1% level
The rejection of White test implies the inexistence of heteroscedasticity . The rejection of Hansen’s J test implies the invalidity of instrument variables used.
1986 - 1996 1997 - 2010
Total Risk Underwriting Risk Investment Risk Total Risk Underwriting Risk Investment Risk Variable Estimate T value Estimate T value Estimate T value Estimate T value Estimate T value Estimate T value Intercept -0.014*** -3.37 0.038 1.37 0.285*** 6.07 0.001 0.16 0.022 1.27 -0.002 -0.44 Lerner Index -1.980** -2.28 7.040 1.06 -17.715 -1.56 -1.229** -2.10 -8.244** -2.05 0.830* 1.72 urqnrq vnsrwf 1.621** 2.27 -5.665 -1.05 14.267 1.53 1.080** 2.19 6.899** 2.08 -0.733* -1.84 FS -0.019*** -3.41 -0.069 -1.61 -0.010 -0.24 -0.012 -1.33 0.184*** 2.21 -0.021** -2.14 FSS 0.001*** 3.37 0.002 1.51 0.000 0.28 0.000 1.18 -0.006*** -2.24 0.001** 2.17 PLT -0.069*** -2.94 -0.093 -0.25 -0.055 -0.28 -0.081** -2.29 -0.594** -2.03 -0.114*** -2.89 RR 0.015* 1.79 -0.006 -0.12 0.071 0.78 0.010* 1.88 0.076** 2.14 0.004 0.9 DVF -0.018*** -3.18 -0.035 -0.56 -0.059 -1.43 -0.023 -1.14 0.101 0.27 0.005 0.44 HHI 0.000*** -2.85 0.000* 1.70 0.001*** 6.22 0.000*** 3.07 0.000*** 4.33 0.000*** -4.67 OF -0.001 -1.01 -0.150*** -2.08 0.023 1.41 -0.001 -0.27 -0.022 -1.45 -0.002 -0.33 White Test 163.6*** <.0001 95.83*** <.0001 79.54*** 0.005 142.5*** <.0001 103.9*** <.0001 125.4*** <.0001 Hansen’s J
0.31 0.857 7.64* 0.054 3.97 0.265 1.41 0.495 0.16 0.983 7.44* 0.059
Adjusted tf 0.282 0.537 0.180 0.289 0.081 0.102
N 213 322
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negatively significant (-1.980) at 10% level and the quadratic term is positively significant (1.621) at 10% level. With 93% of the data lying below the inflection point (0.611) of the accumulated Lerner distribution, this presents an inverse relation between market power and total risk. For 1986-1996, firms with higher market power tend to face lower total risk.As of the effect in the period of 1997-2010, for total risk, the Lerner index is negatively significant (-1.229) at 5% level and its square term is positively significant at 5% level. The inflection point is 0.569 and it represents approximately 45th percentile of the distribution, implying the relation found between market power and total risk is nearly U-shaped. The firm with higher market power would decrease total risk, but when threshold obtained, higher market power might increase total risk. But for underwriting risk, our main sample suggests a negative effect of market power upon underwriting risk10 during 1997-2010. For investment risk, because this model failed to pass the Hansen’s J test, the result doesn’t show support of the relation between market power and investment risk if the period is separated.
As for other control variables, practically all the variables except for organization form (OF) have impact on total risk in the period from 1986-1996 but firm size (FS), diversification (DVF) and are not significant in the next period. In the period of 1997-2010, most of the variables have
9 We also try to introduce time variable and its interaction term with other variables to test the relation. The result is showed in appendix II.
10 The coefficient of Lerner index is negatively significant (-8.244) at 5 percent level and its quadratic term is positively significant (6.899) at 5 percent level. Its inflection point (0.597) lies the 59th percentile of the distribution.
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effect on underwriting risk except for diversification (DVF) and organization form (OF), and the same situation is also presented for investment risk but reinsurance ratio (RR) is not significant.
The directions of effect in the regression are consistent with our discussion above.
To sum up, firms with higher market power may decrease total risk before 1996 but afterwards the relation changes into U-shaped. For underwriting risk, an inverse relation appears in the period from 1996 to 2010 in our research. There is no evidence indicating that marker power is associated with investment risk if the period is separated. From these results, we infer that the series of changes in Japanese financial regulations starting in 1996 have transformed the pattern of market power’s impact on risks, which is consistent with our initial anticipation11.
Lastly, we follow Turk-Ariss et al. (2010) to adopt z-index as a proxy for financial solvency in the GMM model to examine the relationship between competition and solvency in Japanese property-liability insurance industry and we also test it for whole period, 1986-1996 and 1996-2010.
Table 11 shows the impact of market power on financial stability. For the whole period, the coefficient of Lerner index is positively significant (77.122) at 5 percent level and its quadratic term is negatively significant (-67.572) at 5% level. The inflection point (0.571) covers 60% of the Lerner indices distribution, implying a nearly positive relation existing between market power and firms’ financial stability.
11 We also divide 1997-2010 into 1997-2004 and 2005-2010 according to the peak of mergers and acquisitions before 2005 and the financial crisis after 2005. We find that the competition has positive impact on total risk in 1997-2004. In addition, we introduce merger and acquisition variable and its interaction term with Lerner index, and the result shows merger and acquisition and the interaction term are significant.
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For the period of 1986-1996, we don’t find evidence to prove the existence of relation. For the period of 1997-2010, the Lerner index term is positively significant (99.712) at 5 percent level and its square term is negatively significant (-85.036) at 5% level. The inflection point (0.586) lies in approximately 55th percentile of the distribution, representing a nonlinear relation existing between market power and firms’ financial stability.
For other independent variables, firm size (FS) is positively related to solvency before 1996 but has no influence afterwards. In addition, the results show that if firms take on more long-tailed business, they would have better financial stability and if they arrange more reinsurance, they would suffer worse financial stability. The organization form of insurance company (OF) has impact on financial stability before 1986, indicating that stock firms have better financial stability than mutual firms.
As observed from the result, we infer that firms with higher market power would improve their financial stability at first, but after the threshold obtained, higher market power may decrease financial stability.
To investigate the robustness of the regression for z-index, we also apply three more sets of different instrument variables to test the model. Our finding of the relation between market power and financial stability is consistent to the above-discussed.
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Table 11. The effect of market power on financial stability.
1986-2010 1986-1996 1997-2010 Variable Estimate T value Estimate T value Estimate T value
Intercept -19.826** -2.05 -29.168 -0.78 -21.595* -1.87 Lerner Index 77.122** 2.33 -58.117 -0.70 99.712** 2.49 urqnrq vnsrwf -67.572** -2.44 48.087 0.67 -85.036** -2.55 FS 0.449 0.82 5.413*** 2.76 0.106 0.16 FSS -0.008 -0.44 -0.167* -2.54 0.002 0.09
PLT 6.471*** 3.50 7.356 0.93 7.636*** 2.77
RR -0.888*** -4.60 -3.098** -2.01 -0.974 *** -3.91
DVF -1.913* -1.80 1.943 0.78 -1.971 -1.63
HHI -0.002*** -6.76 0.002 0.40 -0.004*** -8.54
OF 1.018* 1.91 4.281*** 4.93 0.092 0.22 White Test 346*** <.0001 173.8*** <.0001 261.2*** <.0001
Hansen’s J 0.12 0.942 1 0.608 0.69 0.710
Adjusted tf 0.355 0.487 0.306
N 525 213 312
Note: The rejection of White test implies the inexistence of heteroscedasticity .
The rejection of Hansen’s J test implies the invalidity of instrument variables used.
* Statistical significance at 10 % level ** Statistical significance at 5% level *** Statistical significance at 1% level
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