台灣商業個人健康保險之核保循環：二階自我迴歸與馬可夫轉換模型

An Analysis of the Underwriting Cycle in Taiwan's Private Health Insurance: The Second-Order Autoregressive Model vs. the Markov Switching Model

10.6226/2012.(22-2).08

林兆欣(Chao-Hsin Lin)；許碩芬(Shuo-Fen Hsu)；陳思竹(Su-Chu Chen)

商業個人健康保險 ； 核保循環 ； 馬可夫轉換模型 ； private health insurance ； underwriting cycle ； Markov switching model

臺大管理論叢

22卷2期（2012 / 06 / 01）

221 - 252

繁體中文

本文主要目的在於探討台灣商業個人健康保險是否存在核保循環及其影響因素，並分析馬可夫轉換模型的損失率兩狀態，是否足以代表核保循環的軟硬市場變化。根據本文實證結果：整體資料期間顯示台灣商業個人健康保險不具二階自我迴歸（Second-order Autoregressive；AR（2））循環。但透過二階自我迴歸馬可夫轉換（Second-Order Autoregressive Markov Switching；MS-AR（2））模型發現台灣商業個人健康保險具備狀態循環。其次，比較線性迴歸與馬可夫轉換迴歸的實證結果發現，加入隱藏的狀態變數時，影響軟／硬市場損失率的變數並不相同，顯示在核保循環的不同階段（狀態）下，影響損失率的變數具時變性，且各項核保循環假說的驗證亦隨之產生差異。

The main purpose of this paper was to validate the underwriting cycle in Taiwan's private health insurance, and to discuss the variables that influence it. The results of the AR(2) model and the Markov switching model are compared to determine the cyclical pattern and to verify if the characteristics of the underwriting cycle remain the same before/after the structure changes and under different regimes. The empirical results show that there is no AR(2) cycle. However, they also show that the cyclical behaviour can be captured by the Markov switching model with the two regimes representing the soft and hard markets of Taiwan's private health insurance market. In addition, we confirmed our hypothesis that the variables affecting the underwriting profit margin differ substantially across the regime switch. The hypotheses regarding the underwriting cycle in the literature cannot be fully explained by the linear model because the latent variable of state is omitted in regression. We demonstrated that the Markov switching regression model is well suited to capture the distinct characteristics of the loss ratio under different cycle stage with estimated time varying parameters.

1. Drechsler, D., & Jütting, J. P. 2005. Private health insurance in low- and middle-income countries: Scope, limitations, and policy responses. Working paper, OECD Development Centre.
2. Lai, G. C., & Witt, R. C. 1990. A microeconomic theory of the commercial liability insurance crisis under uncertainty. Working paper, Department of Finance, University of Texas at Austin.
3. Bloom, T. S.(1987).Cycles and solutions.Best's Review: Property/Casualty Insurance,88(6),20-24.
4. Born, P.,Santerre, R. E.(2008).Unraveling the health insurance underwriting cycle.Journal of Insurance Regulation,26(3),65-84.
5. Cassidy, S. M.,Hardigree, D. W.,Hogan, A. M. B.(1996).Underwriting cycles in health insurance.Journal of Insurance Regulation,14(4),504-517.
6. Chen, R.,Wong, K. A.,Lee, H. C.(1999).Underwriting cycles in Asia.The Journal of Risk and Insurance,66(1),29-47.
7. Chib, S.,Albert, J. H.(1993).Bayesian inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts.Journal of Business and Economic Statistics,11(1),1-15.
8. Choi, S.,Hardigree, D.,Thistle, P. D.(2002).The property/liability insurance cycle: A comparison of alternative models.Southern Economic Journal,68(3),530-548.
9. Chow, G. C.(1960).Tests of equality between sets of coefficients in two linear regressions.Econometrica,28(3),591-605.
10. Cummins, J. D.(Ed.),Harrington, S. E.(Ed.),Klein, R. W.(Ed.)(1991).Cycles and crises in property/casualty insurance: Causes and implications for public policy.Kansas City, KS:National Association of Insurance Commissioners.
11. Cummins, J. D.,Harrington, S. E.,Klein, R. W.(1991).Cycles and crises in property/casualty insurance: Causes and implications for public policy.Journal of Insurance Regulation,10(1),50-93.
12. Cummins, J. D.,Outreville, J. F.(1987).An international analysis of underwriting cycles in property-liability insurance.The Journal of Risk and Insurance,54(2),246-262.
13. Doherty, N. A.,Garven, J. R.(1995).Insurance cycles: Interest rates and the capacity constraint model.Journal of Business,68(3),383-404.
14. Doherty, N. A.,Kang, H. B.(1988).Interest rates and insurance price cycles.Journal of Banking and Finance,12(2),199-214.
15. Engel, C.,Hamilton, J. D.(1990).Long swings in the dollar: Are they in the data and do markets know it.American Economic Review,80(4),689-713.
16. Fields, J. A.,Venezian, E. C.(1989).Interest rates and profit cycles: A disaggregated approach.The Journal of Risk and Insurance,56(2),312-319.
17. Formisano, R. A.(1989).Cyclical behavior of health insurance results: An exploratory analysis.Benefits Quarterly,5(3),51-57.
18. Fung, H.,Lai, G. C.,Patterson, G. A.,Witt, R. C.(1998).Underwriting cycles in property and liability insurance: An empirical analysis of industry and by-line data.The Journal of Risk and Insurance,65(4),539-561.
19. Gabel, J.,Formisano, R.,Lohr, B.,DiCarlo, S.(1991).Tracing the cycle of health insurance.Health Affairs,10(4),48-61.
20. Goldfeld, S. M.,Quandt, R. E.(1976).Studies in nonlinear estimation.Cambridge, MA:Ballinger Publishing Company.
21. Grace, M. F.,Hotchkiss, J. L.(1995).External impacts on the property-liability insurance.The Journal of Risk and Insurance,62(4),738-754.
22. Gron, A.(1994).Evidence of capacity constraints in insurance markets.Journal of Law and Economics,37(2),349-377.
23. Gron, A.(1994).Capacity constraints and cycles in property-casualty insurance markets.The Rand Journal of Economics,25(1),110-127.
24. Grossman, J. M.,Ginsburg, P. B.(2004).As the health insurance underwriting cycle turns: What next?.Health Affairs,23(6),91-102.
25. Haley, J. D.(1993).A cointegration analysis of the relationship between underwriting margins and interest rates: 1930-1989.The Journal of Risk and Insurance,60(3),480-493.
26. Haley, J. D.(1995).A by-line cointegration analysis of underwriting margins and interest rates in the property liability industry.Journal of Risk and Insurance,62(4),755-763.
27. Hamilton, J. D.(1989).A new approach to the economic analysis of nonstationary time series and the business cycle.Econometrica,57(2),357-384.
28. Hamilton, J. D.(1990).Analysis of the time series subject to change in regime.Journal of Econometrics,45(1/2),39-70.
29. Hansen, B. E.(2001).The new econometrics of structural change: Dating breaks in U.S. labor productivity.The Journal of Economic Perspectives,15(4),117-128.
30. Harrington, S. E.,Danzon, P. M.(1994).Price cutting in liability insurance markets.Journal of Business,67(4),511-538.
31. Kim, C. J.(1994).Dynamic linear models with Markov switching.Journal of Econometrics,60(1/2),1-22.
32. Kim, C. J.,Nelson, C. R.(1999).State-space models with regime switching, classical and gibbs sampling approaches with applications.Cambridge, MA:MIT Press.
33. Kim, C. J.,Nelson, C. R.,Startz, R.(1998).Testing for mean reversion in heteroscedastic data based on Gibbs sampling augmented randomization.Journal of Empirical Finance,5(2),131-154.
34. Koop, G.(2003).Bayesian econometrics.Chichester, UK:John Wiley & Sons.
35. Lai, G. C.,Witt, R. C.(1992).Changed insurer expectations: An insurance-economics view of the commercial liability insurance crisis.Journal of Insurance Regulation,10(3),342-393.
36. Lamm-Tennant, J.,Weiss, M. A.(1997).International insurance cycles: Rational expectations institutional intervention.The Journal of Risk and Insurance,64(3),415-439.
37. Leng, C. C.(2006).Stationarity and stability of underwriting profits in property-liability insurance.The Journal of Risk Finance,7(1),49-63.
38. Leng, C. C.,Meier, U. B.(2006).Analysis of multinational underwriting cycles in propertyliability insurance.The Journal of Risk Finance,7(2),146-159.
39. Leng, C. C.,Venezian, E. C.(2003).Underwriting cycles: Are the data consistent with rationally priced cycles?.Insurance and Risk Management,71(3),435-454.
40. Long, J. D.(Ed.),Randall, E. D.(Ed.)(1984).Issues in insurance.Malvern, PA:American Institute for Property and Liability Underwriters.
41. Niehaus, G.,Terry, A.(1993).Evidence on the time series properties of insurance premiums and causes of the underwriting cycle: New support for the capital market imperfection hypothesis.The Journal of Risk and Insurance,60(3),466-479.
42. Rosenblatt, A.(2004).The underwriting cycle: The rule of six.Health Affairs,23(6),103-106.
43. Smith, M. L.(1989).Investment returns and yields to holders of insurance.Journal of Business,62(1),81-98.
44. Urrutia, J. L.(1996).What triggers the underwriting cycle?.International Journal of Finance,8(1),1-14.
45. Venezian, E. C.(1985).Ratemaking methods and profit cycles in property and liability insurance.The Journal of Risk and Insurance,52(3),477-500.
46. Venezian, E. C.,Leng, C. C.(2006).Application of spectral and ARIMA analysis to combined-ratio patterns.The Journal of Risk Finance,7(2),189-214.
47. Winter, R. A.(1991).The liability insurance market.The Journal of Economic Perspectives,5(3),115-136.
48. Winter, R. A.(1988).The liability crisis and the dynamics of competitive insurance markets.Yale Journal of Regulation,5(2),455-499.
49. Winter, R. A.(1994).The dynamics of competitive insurance markets.Journal of Financial Intermediation,3(4),379-415.
50. Zivot, E.,Andrews, D. W. K.(1992).Further evidence on the great crash, the oil price shock, and the Unit-Root hypothesis.Journal of Business & Economic Statistics,10(3),251-270.
51. 韋端(2003)。SARS事件對台灣經濟之衝擊與對策。國家政策論壇季刊，92(秋=Autumn)，19-30。
52. 許文彥(2009)。保險學─風險管理與保險。台北=Taipei, TW:新陸書局=Hsin-Lu Publisher。
53. 賴丞坡(2004)。國立中正大學企業管理研究所=Department of Business Administration, National Chung Cheng University。

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