強制汽車責任保險理賠風險分析－－Malmquist指數之應用

A RISK ANALYSIS OF COMPULSORY AUTOMOBILE LIABILITY INSURANCE AN APPLICATION OF MALMQUIST PRODUCTIVITY INDEX

強制汽車責任保險屬強制性質之政策性保險，任何車輛都應納入投保範圍，並採「無過失主義」及「無盈無虧」方式經營，以所有車主繳納的保險費，承擔共同的理賠風險，然而目前相關文獻大多僅考量從人因素或從車因素，甚少從理賠風險的變動來源探討保費之合理性。本研究利用資料包絡分析法前緣的概念，已受測單位與風險前緣的相對距離作為度量其相對風險高低之依據，並利用Malmquist生產力指數易於拆解的優點，區別不同風險的來源，建立一新的汽車責任保險風險評估模式。本文先將總風險變動拆解為個別車種風險變動與行車風險變動，由於個別車種風險變動代表在固定風險前緣下，保險費收入不變而理賠金額增加，或是理賠金額不變但保險費收入減少之狀態，為了探討個別風險來源，本研究進一步將其區分為純車種風險及規模風險兩類。研究結果顯示，近五年汽車強制責任險的總風險呈微幅上升的趨勢，其主要來源是規模風險的增加，因此建議調降理賠金額與調高汽車使用燃料費，以降低風險，至於行車風險則呈現下降的現象，顯示政府修法以導正駕駛人的行車習慣已經達到某種程度的效果。

The compulsory automobile liability insurance is a mandatory government program in which all automobile owners are required to buy the policy under the no fault liability principle. The premiums are based on the goal of “zero-profit-zero-loss” by spreading the risks among domestic co-insurers. Most literature evaluates the fairness of the premiums based on either the personal or vehicle factors, without due consideration of the dynamic relationship among various sources of risks and premium payments. This study integrates the concept of data envelopment analysis (DEA) and mean-variance portfolio frontier into a distance-function-based premium-indemnity efficient frontier. Premium (the insurance cost) is treated as an input while indemnity (the risk coverage) is treated as an output for each vehicle type. The efficient frontier is established to select the most preferred premium-indemnity combination among its boundary points by either maximizing total indemnities under given premiums or minimizing total premiums under given indemnities. The Malmquist index decomposition is then adopted to decompose the changes of total risks across two periods into the vehicle risk and travel risk components. The vehicle risk component measures the efficiency changes of the premium-indemnity combination and represents how much the risk coverage can be increased without changing the premium or how much the premium can be reduced without affecting the coverage. It can be further decomposed into changes of pure vehicle risk and scale risk. The empirical results indicate that the vehicle risk has increased over the past five years due to the sharp increase of scale risk, but travel risk has decreased at the same time due to better enforcement of safe driving habits. Therefore, a coupling of lower indemnity with higher fuel tax to reduce travel intensity is proposed as a policy solution to improve the efficiency of the compulsory insurance program.