Do individuals have consistent risk preferences across domains?: evidence from the Japanese insurance market

Figures & data

Table 1. Descriptive statistics

		Men(N = 924)		Women(N = 984)
		Mean	Std. Dev.	Mean	Std. Dev.
Hold a life insurance policy (Yes = 1, No = 0)		0.768	0.422	0.786	0.411
Age		46.214	12.865	46.188	12.087
Marital status (Married = 1, Unmarried = 0)		0.712	0.453	0.690	0.463
Final education
	Under high school degree	0.445	0.497	0.451	0.498
	College graduate	0.159	0.366	0.356	0.479
	Bachelor’s degree or above	0.396	0.489	0.193	0.395
Employment status
	Working for a private company or public office	0.764	0.425	0.426	0.495
	Self-employed or family worker, or freelance	0.148	0.356	0.106	0.308
	Temporary employee or part-time worker	0.088	0.283	0.468	0.499
Personal income (unit: JPY)
I	less than 1 million	0.024	0.153	0.313	0.464
II	1 million ~ less than 2 million	0.088	0.283	0.276	0.447
III	2 million ~ less than 3 million	0.160	0.367	0.172	0.377
IV	3 million ~ less than 5 million	0.305	0.461	0.169	0.375
V	5 million ~ less than 7 million	0.239	0.427	0.054	0.226
VI	7 million ~ less than 10 million	0.121	0.327	0.012	0.110
VII	over 10 million	0.063	0.243	0.004	0.064
Personal income (unit: JPY 10,000)		489.287	278.333	211.743	175.310

Note) To estimate the mean and standard deviation of personal income with binned data, we used the multimodel generalized beta estimator developed by von Hippel, Scarpino, and Holas (2016). They also made the method available as mgbe commands for Stata.

Table 2. Summary statistics of insurance policies

Insurance premium and ammount (Unit: JPY 10,000)	Mean	Std. Dev.	Min	Max
Total insurance premium per year	17.439	13.863	1	84
Ammount of hospitalization benefit per day
Option 1 (less than JPY 10,000 per day)	0.526	0.148	0.1	0.950
Option 2 (over JPY 10,000)	1.326	0.466	1	3.000
Amount of annuity per year	9.888	25.342	0	150
Amount of death benefits	1048.095	1110.201	0	6000
Percentage of contractors	(%)
Hospitalization benefits
Option 0 (uninsured)	5.4
Option 1 (less than JPY 10,000 per day)	46.1
Option 2 (over JPY 10,000)	48.5
Annuity insurance	26.1
Riders for:
Cancer	47.5
Special diseases	43.1
Nursing care status	9.9

Note) Number of observations = 1370.

Limited to respondents who hold life insurance policies and pay positive insurance premiums.

Table 3. Determinants of total premiums

		(1)	(2)
Hospitalization benefits
Dummy variable of
	Option 1	7.017***	2.876**
		(0.514)	(1.221)
	Option 2	12.256***	8.201***
		(0.687)	(1.318)
Amount of death benefits		0.004***	0.004***
		(0.000)	(0.000)
Amount of annuity insurance		0.181***	0.172***
		(0.016)	(0.016)
Contracting riders for:
	Cancer	1.220*	1.049
		(0.657)	(0.661)
	Special diseases	2.700***	2.706***
		(0.695)	(0.699)
	Nursing care	1.356	1.418
		(1.127)	(1.116)
Age			0.096***
			(0.023)
Sex			−0.276
			(0.625)
Observations		1,370	1,370
Adjusted R-squared		0.724	0.728

Note) Robust standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1

Figure 1. Percentage of respondents who have experience of hospitalization

within the past five years Source) Calculated from the SLP.

Table 4. Hospitalization expenses and number of hospital days

	Mean	Std. Dev.	Min	Max
(a) Total value of direct and indirect costs (unit: JPY 10,000)	21.960	27.990	0.4	200
(b) Number of hospital days	17.875	21.904	1	150
(a) / (b) = Self-paid hospitalization expenses per day	1.984	2.263	0.056	20.000

Source) Calculated from the SLP.

Note) N = 432.

Table 5. Estimated relative risk aversion coefficients by income and insurance options (a) Fixed hospitalization probability (b) Variable hospitalization probability

Income	Option 0	Option 1	Option 2	Age	Income	Option 0	Option 1	Option 2
I	0.5	0.9	1.4	20	I	1.1	1.8	2.4
II	2.0	3.2	4.3		II	4.3	6.0	7.7
III	3.2	4.8	6.4		III	6.8	9.1	11.3
IV	4.5	6.5	8.4		IV	9.5	12.2	14.9
V	5.9	8.1	10.3		V	12.3	15.4	18.4
VI	7.0	9.4	11.8		VI	14.7	17.9	21.0
VII	8.2	10.7	13.2		VII	17.1	20.3	23.5
				30	I	0.8	1.4	2.0
					II	3.3	4.8	6.2
					III	5.2	7.2	9.2
					IV	7.3	9.7	12.1
					V	9.5	12.2	14.9
					VI	11.4	14.2	17.0
					VII	13.3	16.2	19.0
				40	I	0.7	1.2	1.7
					II	2.8	4.2	5.5
					III	4.4	6.2	8.0
					IV	6.2	8.4	10.6
					V	8.0	10.5	13.0
					VI	9.6	12.3	14.9
					VII	11.2	13.9	16.6
				50	I	0.4	0.8	1.3
					II	1.7	2.8	3.9
					III	2.8	4.3	5.7
					IV	3.9	5.8	7.6
					V	5.1	7.2	9.3
					VI	6.0	8.3	10.6
					VII	7.0	9.4	11.8
				60	I	0.1	0.5	0.8
					II	0.7	1.6	2.4
					III	1.1	2.3	3.4
					IV	1.6	3.1	4.5
					V	2.1	3.9	5.6
					VI	2.5	4.4	6.3
					VII	2.9	5.0	7.1

Note) The calibration is executed in increments of 0.1.

The income classes corresponding to the Arabic numerals of I to VII are as follows: I: less than JPY 1 million, II: 1 million ~ less than 2 million, III: 2 million ~ less than 3 million, IV: 3 million ~ less than 5 million, V: 5 million ~ less than 7 million, VI: 7 million ~ less than 10 million, VII: over 10 million.

Figure 2. ${\mathit{\gamma }}_{\mathit{i}}$ for each insurance option by age.

Table 6. Basic statistics for ${\mathit{\gamma }}_{\mathit{i}}$

	(a)	(b)
Mean	5.29	6.22
Std. Dev.	3.09	4.21
Min	0.50	0.10
Median	4.80	5.75
Max	13.20	19.00

Note) N = 1908. Limited to respondents who work with a positive income

Probability of hospitalization is fixed across age groups and variables for (a) and (b), respectively.

Figure 3. Kernel density plot of ${\mathit{\gamma }}_{\mathit{i}}$.Note: Probability of hospitalization is fixed across age groups for (a) and variable for (b).

Table 7. Consistency between ${\mathit{\gamma }}_{\mathit{i}}$ for hospitalization benefits and additional riders

			(1)	(2)	(3)	(4)
			Fixed hospitalization probability		Variable hospitalization probability
Age			−0.013***	−0.005*	−0.174***	−0.163***
			(0.003)	(0.003)	(0.004)	(0.004)
Income			0.010***	0.008***	0.011***	0.009***
			(0.000)	(0.000)	(0.000)	(0.000)
Holding additional schemes for
		Cancer insurance rider (Yes = 1, No Contract = 0)	0.851***	0.796***	1.059***	0.990***
			(0.084)	(0.078)	(0.116)	(0.109)
		Disease-specific rider (Yes = 1, No Contract = 0)	0.774***	0.787***	0.771***	0.789***
			(0.088)	(0.082)	(0.121)	(0.113)
		Nursing care (Yes = 1, No Contract = 0)	0.052	0.089	0.134	0.189
			(0.143)	(0.132)	(0.196)	(0.184)
Marital status (Married = 1, Unmarried = 0)				−0.056		0.071
				(0.077)		(0.106)
Self-employed or family worker, or freelance				−0.577***		−0.961***
				(0.107)		(0.148)
Temporary employee or part-time worker				−1.316***		−1.754***
				(0.093)		(0.128)
Final education (Base case = Under high school degree)
		College graduate		−0.177**		−0.222*
				(0.084)		(0.116)
		Bachelor’s degree or above		−0.318***		−0.420***
				(0.083)		(0.115)
Sex (Male = 1, Female = 0)				0.501***		0.577***
				(0.080)		(0.111)
Constant			2.004***	2.517***	9.889***	10.548***
			(0.144)	(0.150)	(0.199)	(0.208)
Observations			1,908	1,908	1,908	1,908
Adjusted R-squared			0.750	0.784	0.746	0.777

Note) Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1

Figure 4. Response to the general question about risk aversion.

Source) Japan Institute of Life Insurance (2016) Survey on Living Security.

Table 8. Consistency between ${\mathit{\gamma }}_{\mathit{i}}$ for hospitalization benefits and general risk aversion

			(1)	(2)	(3)	(4)
			Fixed hospitalization probability		Variable hospitalization probability
Age			−0.010***	−0.003	−0.170***	−0.161***
			(0.003)	(0.003)	(0.004)	(0.004)
Income			0.010***	0.008***	0.011***	0.009***
			(0.000)	(0.000)	(0.000)	(0.000)
Response for general question regarding risk (Base case = “A” or “Near A”)
		Near B	−0.198	−0.106	−0.352*	−0.259
			(0.148)	(0.139)	(0.198)	(0.187)
		B	−0.231*	−0.127	−0.390**	−0.275
			(0.134)	(0.126)	(0.179)	(0.169)
		I don’t know	−0.303	−0.297	−0.358	−0.352
			(0.237)	(0.222)	(0.317)	(0.299)
Marital status (Married = 1, Unmarried = 0)				−0.023		0.115
				(0.084)		(0.113)
		Self-employed or family worker, or freelance		−0.498***		−0.873***
				(0.117)		(0.158)
		Temporary employee or part-time worker		−1.347***		−1.790***
				(0.102)		(0.137)
Final education (Base case = Under high school degree)
		College graduate		−0.218**		−0.269**
				(0.092)		(0.124)
		Bachelor’s degree or above		−0.380***		−0.492***
				(0.091)		(0.123)
Sex (Male = 1, Female = 0)				0.501***		0.573***
				(0.088)		(0.119)
Constant			2.651***	3.125***	10.725***	11.345***
			(0.190)	(0.193)	(0.254)	(0.260)
	Observations		1,908	1,908	1,908	1,908
	Adjusted R-squared		0.704	0.741	0.714	0.746

Note) Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

von Hippel, P. T., Scarpino, S. V., & Holas, I. (2016). Robust estimation of inequality from binned incomes. Sociological Methodology, 46(1), 212–251.

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Japan Institute of Life Insurance. 2016. Survey on Life Protection.

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