Abstract
A theoretical framework and empirical evidence are presented to show the connection between community uniform rating and cross-subsidies in earthquake insurance policy in Japan. Cross-subsidies are defined as the difference between a fair actuarial premium and the community uniform rate. The estimation result shows that the uniform community rating may unintentionally cross-subsidize inhabitants in high-risk areas at the expense of inhabitants in low-risk areas. Our simulation results indicate that replacing the current community rating with the fair actuarial premium would increase the overall subscription rate for earthquake insurance by about 3.7 percentage points, and that the increase is particularly prominent in relatively less risky areas. We propose modifying the Japanese earthquake insurance system by adopting a more refined risk-rating system that more closely reflects regional differences in earthquake risk .
This chapter is adapted from Naoi et al. (2010), Springer Nature.
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Notes
- 1.
For example, subscription rates for earthquake insurance are less than 11% in California (2000) and 19.6% in Turkey (2006). Compared with these two countries and Japan, New Zealand has a compulsory earthquake insurance system with a completely uniform premium setting.
- 2.
This kind of moral hazard is called “charity hazard” in Browne and Hoyt (2000).
- 3.
Standard earthquake insurance rates were last revised in January 2017, and they continue to be based on extremely broad-brush evaluations of the risk in each region.
- 4.
Japan has a government-private shared policy for household risks as does California. Household risks in Japan are all reinsured in the Japanese Earthquake Reinsurance Company (JER) where losses are shared by the insurers, the JER and the government, according to the total cost of damages. So this reinsurance scheme offered by the government serves as an effective subsidy to the private insurance companies.
- 5.
This figure is cited from the website of the General Insurance Association of Japan on June 7, 2008 (http://www.sonpo.or.jp/archive/statistics/disaster/quake.html, accessed 7 June, 2008).
- 6.
This figure is based on the information as of March 1, 2012 by the General Insurance Association of Japan.
- 7.
Insurance premiums also vary according to the structure and construction method of the dwelling.
- 8.
In October 2007, the Japanese government and the Non-Life Insurance Rating Organization of Japan (NLIRO) released a new insurance premium policy based on a new projection of earthquake probability. However, the risk categories are still based on only four rating zones.
- 9.
In reality, loading costs of insurance (administrative cost and cost of capital) might be important factors that make premium levels different from actuarial ones. Introducing loading costs into our model, however, is straightforward and would not change our results below.
- 10.
Solving \(\delta_{L} = 1 - F(\bar{\gamma })\) for \(\bar{\gamma }\), and substituting this into Eq. 11.2 yields a demand-side relationship between \(\delta_{L}\) and \(\bar{P}\) (insurance demand function) in low-risk areas.
- 11.
The parameter values for this example are as follows: \(\lambda = 1/2\), \(F(\gamma )\sim\gamma /(1 + \gamma )\) (log-logistic distribution), \(W = 3,000\), \(D = 1,000\), \(\pi_{H} = 0.10\%\), \(\pi_{L} = 0.05\%\), PH* = 1, PL* = 0.5. The existence of an interior equilibrium, however, can be shown without specifying parameter values. Proof is sent upon request.
- 12.
In this model, we do not allow individuals to move across regions. Allowing for individual mobility with certain costs may yield similar results and is an interesting future extension of the model. Picard (2008) presents a model with individual mobility, but in that insurance purchase is compulsory.
- 13.
The original PSHM data are provided as the ESRI grid format, where grid cells are defined as geographic space of equally sized square grid points. The PSHM data gives the earthquake probabilities for every 1 km × 1 km grid cells in all of Japan. In the following analysis, we aggregate the original data and construct the city-level averages in order to match the PSHM probability with the KHPS. The original data are available at http://www.j-shis.bosai.go.jp/, accessed 27, April, 2008.
- 14.
The JMA seismic intensity scale, which is measured with a seismic intensity meter and is graded from 0 to 7, provides a measure of the strength of seismic motion. For full explanation of the JMA seismic intensity scale, see http://www.jma.go.jp/jma/kishou/know/shindo/explane.html. In general, the relationship between the JMA scale and the Richter scale depends on the distance from the epicenter. Even an earthquake with a small intensity on the Richter scale can have a large JMA intensity at locations near the epicenter.
- 15.
Assuming that the earthquake probabilities are constant over time, \(\pi^{*}\) and \(\pi_{30}\) must satisfy the following relationship. \(\pi_{30} = \sum\nolimits_{t = 1}^{30} {\pi^{*} \left( {1 - \pi^{*} } \right)^{t - 1} }\). This yields our measure of annualized earthquake probability.
- 16.
In a recent study, we carefully examine the empirical validity of this assumption, and find that the bias stemming from the use of objective PSHM probability as a proxy for individual risk assessments is almost negligible (Naoi et al. 2009).
- 17.
Since the actual insurance contracts have high levels of deductions (3% of property value), and a total claim payment limit (5.5 trillion yen), the average premiums of actual contracts tend to be lower than actuarial ones. In consideration of these factors, the actuarial premium is adjusted to have the same sample mean as the observed community rate.
- 18.
These basic rates are as of September 2007. As explained in footnote 8, NLIRO released a new insurance premium policy in October 2007. To check whether this policy change has any influence on our empirical results, we estimated the model without a 2008 sample and found that there are no fundamental changes in our estimates.
- 19.
We also examined the differential effect of our cross-subsidization variable between homeowners and renter households, but found no significant difference between these two groups.
- 20.
See Naoi et al. (2010) Table 3 Models [3] [4] for details.
- 21.
See also Seko and Okuno-Fujiwara (2015).
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Seko, M. (2019). Earthquake Insurance Subscription Rates and Regional Cross-Subsidies. In: Housing Markets and Household Behavior in Japan. Advances in Japanese Business and Economics, vol 19. Springer, Singapore. https://doi.org/10.1007/978-981-13-3369-9_11
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