Chapter 4 Methodology
4.2 Model description
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Chapter 4 Methodology
4.1 Sample Selection
This paper chooses Japanese domestic general insurance company as the objective in the research, and data is collected from The Statistics of Japanese Non-life Insurance Business and annual financial statements of non-life insurance companies from 1986, 25 sample years in total.
Owing to cases of mergers and acquisitions in Japanese insurance industry, the number of firms in each year is inconsistent, which creates an unbalanced panel data for us. After deleting missing data and abnormal samples, there are totally 535 sample numbers adopted in this research1. The sample companies in every year are listing in the appendix.
Since the sample period includes 25 years, nominal variables are divided by consumer price index in every year and thus we adopt real variables in the research to avoid the impact of price inflation. Annual CPI are collected from the website of Statistics Japan.
4.2 Model description
We apply fixed- effect GMM (Generalized method of moments) model developed by Lars Peter Hansen in 1982 to examine the relation between market power and risks in insurance
1 Our initial sample size is 551. After deleting ten units of abnormal and missing observations, we have 535 samples using in the model. Abnormal and missing data are listed as follows: YKFG lacks net claim paid in 2000 and 2001.
Taisei lacks data in 2001. SJFG lacks net claim paid in 2002 and data for diversification in 2003 and 2004. Anicom lacks data for diversification in 2008, 2009 and 2010. Taisho lacks data for reinsurance ratio in 1989, 1990 and 1991.
Allianz has negative net premium income in 2010. Unum has negative Lerner index in 1997 and 1998. Hitachi C has abnormally large reinsurance ratio in 2005.
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industry. The model is set as follows:
= + + + + ∀ i, t (1)
From the literature review, we get the conclusion that the degree of competition has a certain relation with risks. Boyd and De Nicole (2005) suggest that lower competition would bring about higher risk in banking industry. On the contrary, Keeley (1990), Salas and Saurina (2003) and Liu (2009) suggest that lower competition would bring about lower risk in banking industry. Our research focuses on Japan and Liu (2009) focuses on Taiwan, both belonging to Asia and experiencing similar economic environment as well as similar industrial structure, we therefore expect lower competition would bring about lower total risk and underwriting risk according to Liu (2009). We also examine the impact of competition on investment risk due to the fact that it’s one of the main risks insurers face, yet it might not be significant because investment is not directly relevant to competition in general. We choose Lerner index as our measure to evaluate market competition for Japanese non-life insurance companies, and how it is calculated will be defined as below.
However, Martínez Miera and Repullo (2010) prove that there is a U-shaped relation between the degree of competition and bankruptcy risk in banking industry. In view of the above, we also add the square of as another variable in this model to test whether U-shaped relation exists, and this model reflects the correlation between competition and risks in insurance
industry. represents the risk variable of the i company in t year and risks includes total risk, underwriting risk and investment risk. represents a set of control variables and will be
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discussed in detail later.
In the analysis of our results, we will discuss where the inflection point for the distribution of Lerner index locates to investigate if the relation between competition and risks is U-shaped or linear. If Lerner index and its quadratic term are both significant, indicating the existence of U shape, we would see our observations mainly locate below or above inflection point to infer it is a positive or negative relation. On the other hand, if the inflection point locates close to half of the distribution of Lerner index, we would say it is an upwardly or downwardly U-shaped relation.
Moreover, many regulations had been amended and mergers and acquisitions had appeared since Japanese Big Bang in 1996, we further separate the whole sample period (1986-2010) into two periods (1986-1996 and 1997-2010). Chang (2008) studies if the operating efficiency improves after merger and acquisition. The result shows that both profitability and business performance are better before merger and acquisition than after. Merger and acquisition usually brings about higher market power and we expect firms with higher market power (lower competition) might face higher risks during 1997-2010.
The next step is to test the competition-financial stability relationship for Japanese
property-liability insurance industry. The model is set as:
= + + + + ∀ i, t (2)
In formula (2), represents the financial stability for the firm in year t. The Z-index is an inverse measure of firm’s overall risks, combining profitability, leverage, and return volatility in a single ratio, which will be defined as below. We specifically follow Fernández and
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Garza-Garcíab (2015) to use the natural logarithm of the Z-index ( ) as the financial stability variable.
To address the likely endogeneity of measures of market power, we employ an instrumental variable technique with a Generalized Method of Moments (GMM) estimator. A common problem in using empirical data is heteroskedasticity, and we test for its presence by white test.
Although the instrumental variables coefficient estimates remain consistent in the presence of heteroskedasticity, the estimates of their standard errors are inconsistent, preventing valid inference and rendering the estimator inefficient. The usual diagnostic tests for endogeneity and overidentifying restrictions will also be invalid if heteroskedasticity is present. Such estimation issues can partially be addressed by using heteroskedasticity consistent or robust standard errors, but the usual approach when facing heteroskedasticity of an unknown form is to use the GMM estimator. We apply the Hansen J statistics to test the overidentifying restrictions. If the J statistic is too small to reject the null hypothesis that J =0, the overidentification restrictions are valid, giving us the confidence that our instrument set is appropriate.
Dependent variable
Risk is the most concern to all insurers. Due to the professional knowledge and technique, insurance companies afford risks the public transfer by selling insurance policies and earn profit only when they deal with different types of risks well. In this model, represents risk of
the i company in year t. Risk variables we use here include total risk, underwriting risk, investment risk in this research.
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We evaluate total risk by the standard deviation of ROA (return on asset) in previous three sample years2. ROA is the ratio of net profit to asset representing how efficient the insurance companies make use of their assets. If the ROA ratio fluctuates too much, it means the company would face higher total risk and instable operation3. Firms with high market power are usually stable and experienced on their operation to minimize the possibility of loss. We expect the relation between market power and total risk is negative.
Underwriting risk is the risk of unanticipated loss generated from business solicitation, writing policy or relevant cost. Underwriting risk is evaluated by the standard deviation of loss ratio in previous three sample years and loss ratio is calculated as losses incurred divided by premiums income. Firms with low market power may be less careful with underwriting policy in order to earn business so we expect the effect of market power upon underwriting risk is negative.
After gathering premiums from the public, insurance companies have to make profitable investment to ensure that their fund can afford claims when incurring losses and therefore investment risk is important for insurance companies. We evaluate investment risk by the standard deviation of ROI ratio (return on investment) in previous three sample years and ROI ratio is calculated as investment income divided by total investment assets, which represents
2 We use year%&, year% and year% to calculate the standard deviation of ROA in year .
3 Because many mergers and acquisitions happened in Japanese insurance industry in our sample period, the total risk of firms going through a merger is calculated by the weighted average of standard deviation of its previous entities. For example, if firm A and frim B merge with each other and become frim C in 2001, in order to get firm C’s total risk, we calculate firm A and firm B’s standard deviation of ROA in 1998-2000 respectively and calculate the weighted average of firm A and B’s total risk with the weight as firm’s total assets. The underwriting risk and investment risks are also calculated in this way.
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whether insurance company’s investment is in stable status or not. Because insurers with higher market power gather greater premium volume, they may make investment decision more carefully to reduce risk. We expect a negative relation between market power and investment risk.
In addition, we also introduce Z-index as a proxy for financial stability. It is estimated as:
Z =
()*+,1-./0*+,+,234
(3)
Where 56 is the return on assets for each firm in year t, 7/86 represents the ratio of
equity to total assets for each firm in year t. 9()* is the standard deviation for return on assets for a period of every three years for each firm and this is the total risk we calculate for insurance companies as mentioned previously. As observed in formula (3), the Z-index increases when the level of return on assets and the degree of capitalization increase. However, it is reduced when the return volatility widens. We use Z-index to examine the relation between the market competition and financial stability.
Independent variable
Lerner suggests a method to quantify the level of market competition in 1934, which is called Lerner index. We calculate the degree of the price deviating from marginal cost to evaluate
the strength of the market power, and the definition of Lerner index is as follows:
=
:+,%;<: +,+,
(4)
where
=
represents the unit price of output of the i insurance company in t year and is evaluated by total income total asset, and total income includes net premium income and‧ 國
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investment income.
>?
is the marginal cost of the i insurance company in t year, meaning that the cost occurs when additional unit output is produced.From the formula (3), we know the Lerner index is between 0 and 1, and the Lerner index has a negative relation with market competition. When Lerner index is smaller, the gap between the market price and the cost is smaller, which means the firms have smaller power to determine market price and thus have less market power, and vice versa. If the market is in perfect competition, the output price is equivalent to the marginal cost and therefore the Lerner index is zero.
Fernandez de Guevara and Maudos (2007) adopt Lerner index as a proxy for the degree of competition in European banking industry. With regards to the calculation, they choose the ratio of the total income divided by the total assets as the output price and the total income includes interest and non-interest income. Therefore, we here use the total assets to evaluate the output of insurance industry, and the output price is calculated as the total income divided by the total asset.
The total income includes the net premium income and investment income that are two major revenue sources for insurance industry.
We adopt the translogarithmic cost function approach used by Fernandez de Guevara and Maudos (2007) to estimate the marginal cost of insurance company. Assuming that total cost of insurance company is a function comprised of total outputs, labor unit price, capital unit price and funds, the model is set as follows:
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five different periods categorized by Japanese economic situation4.Total cost is the sum of personnel expense, commission and general operating expense. G is calculated as personnel expenses divided by number of the staffs. G is the ratio of commission plus general operating expense to number of policies. We evaluate G& by ROE (return on equity), and ROE is estimated by the ratio of net profit for the year to total net worth.
Notice that we have imposed the following restrictions in the translog cost function in order to obtain a valid cost function. Homogeneous of degree one should be satisfied in factor prices, that is ∑ λF F = 1, ∑ λF FH= 0 ∀ , ∑FJF = 0 and ∑F∅F = 0, and symmetry restriction should be
4 Japan was in a good ecomonic staus during 1986 to 1990 and thus we set the trend as 1. Owing to the burst of economic bubble during 1990 to 1996, risks may become higher and thus we set the trend as 2. Risks may grow during 1996 to 2000 because of Big Bang and the liberalization of rate, and thus we set the trend as 3. The peak of mergers and acquisitions occurred during 2000 to 2005 and thus we set the trend as 4.and we set the rest of the time period equals 5.
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satisfied, that is
E
FH= E
HF,
in formula (5).Table 4 shows the statistics of variables in translog cost function model. The mean of total asset is 11,384,581 thousand yen and the distribution is left-skewed, indicating that the majority of the non-life insurance companies are large-scale.
After obtaining the estimators, we are able to further estimate the marginal cost by regression equation as follows:
>? =
[0<[0*+,+,=
0<0*+,+,( + 86 + ∑
&FIJ
FG
F,+ K
&8 L)
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Table 4. The statistics of variables in translog cost function model
Variable definition Calculation Mean Medium Minimum Maximum Standard
Deviation
TC Total cost personnel expense + commission
+ general operating expense 1,330,823 790,972 8,529 7,260,194 1,595,211
TA Total asset 11,384,581 6,005,292 20,314 98,121,787 16,121,433
\ Unit input price of labor personnel expense
number of staffs 101.286 100.600 1.550 189.620 21.147
f Unit input price of capital commission + general operating expense
number of policies 0.124 0.137 0.005 0.694 0.073
Unit input price of fund ROE -0.018 0.038 -2.120 0.587 0.238
Note: 1. TC, TA, W1 and W2 are in thousand Japanese yen.
2. Nominal sample data are divided by annual consumer price index and thus transformed into real variables.
3. The sample number is 535 in total.
4. We increase all the ROE for 2.12 to have the minimum ROE equal zero to deal with the problem that ROE are negative.
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Control variable
As mentioned before, we introduce a set of control variables (Kj ) in model (1). Firm size (FS), percentage of long-tailed business (PLT), reinsurance ratio (RR), the degree of business diversification (DVF), Herfindahl-Hirschmani index (HHI) and the organization form of insurance company (OF) are selected as the control variables in the model.
Firm size reflects how much business volume an insurance company is able to accept. The larger the company is, the more business volume the company can take. If an insurance company owns larger asset, when severe event occurs, it would afford absorbing risk in comparison with small companies. Fernandez de Guevara and Maudos (2011) show a negative relation between bank size and financial stability, but beyond a threshold, greater bank size decreases the possibility of
bankruptcy. Craig and Dinger (2013) find humped shape of the relation between bank size and bank risk, we thus also add the square of total asset as a control variable to test if the U-shaped relation exists between firm size and risks in insurance industry. We apply the natural logarithm of total assets as the firm size in our model.
According to Lee and Urrutia (1996), the proportion of premiums written in long-tailed lines has statistically significant impacts on the probability of insolvency of a property-liability insurer in their logit model. If the percentage of long-tailed business of a general insurance company is high, it has to take the longer responsibility, which represents the longer duration that insurer has to face uncertain risk than insurers with low percentage of long-tailed business. The proportion of
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premiums written in long-tailed lines is measured by the ratio of long-tailed lines5 net premiums written to total net premiums written.
Berger, Cummins, and Tennyson (1992) suggest that profitability is improved by the ceding of reinsurance, consistent with a view of reinsurance as an alternative to other risk diversification devices. Shiu (2011) and Aunon-Nerin and Ehling (2007) show that increasing use of reinsurance leads to higher risk-taking. Reinsurance ratio of a company reflects the degree of risk transferred to other insurer or reinsurer. When loss occurs, companies can be compensated by reinsurance to stabilize their operation, and thus insurers doing reinsurance arrangements incline to face lower risk. The reinsurance ratio is calculated as reinsurance premium expense to net premiums income.
Odesanmi S. and Wolfe S. (2007) find that diversification across and within both interest and non-interest income generating activities decreases insolvency risk. When a huge loss occurs for a certain kind of insurance policy, insurers with high degree of revenue diversification can be compensated from other kinds of insurance business, and therefore their risk is relatively smaller.
We sum the square premium of every line first6, dividing it by the square of total premium and then minus the value by 1 to obtain the diversification for every firm in every year.
Fernandez de Guevara and Maudos (2009) use HHI as a proxy for market concentration and they find that increases in concentration lead to a lowering of financial stability. HHI indicates the
5 Long-tailed lines include Compulsory Automobile Liability Insurance and General Liability Insurance. Short-tailed lines include Fire Insurance, Savings-type Fire Insurance, Hull Insurance, Cargo Insurance, Transit Insurance, Automobile Insurance, Personal Accident Insurance and Savings-type Personal Accident Insurance.
6 According to The Statistics of Japanese Non-life Insurance Business, we select Compulsory Automobile Liability Insurance and General Liability Insurance, Fire Insurance, Savings-type Fire Insurance, Hull Insurance, Cargo Insurance, Transit Insurance, Automobile Insurance, Personal Accident Insurance and Savings-type Personal Accident Insurance to calculate diversification as our variable.
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level of concentration, evaluating whether the market share is highly-concentrated on some specific companies, and risk may vary across different degree of market concentration. The HHI index is calculated by squaring the market share of each firm competing in a market, and then summing the resulting numbers.
Organization form of insurance company represents whether insurance company is a stock or mutual company. Investment decision and operation can be affected to some extent according to the way insurance company being hold and thus insurance companies face different degree of risk. Lamm-Tennant and Starks (1993) find that stock firms face higher total risk (measured by the variance of loss ratio) than mutual firms in the U.S. property-liability insurance industry. In our model, if the insurance company is held as a mutual firm, the dummy variable is set as 0, otherwise it is set as 1.
Table 5. The definitions and calculations of control variables
Variables Definition Calculation
FS Firm Size natural logarithm of total assets
FSS Square of FS square of natural logarithm of total assets
PLT percentage of long-tailed business Premiums of long-tailed lines / Total Net Premiums RR reinsurance ratio Reinsurance Premium Expense / Net Premiums Income DVF degree of business diversification 1-( ∑((Premiums of lines)^2) / (∑Premiums of lines)^2 ) HHI
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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
lnTA -0.253 -1.43 lnTATrend -0.029*** -3.72