Werner's Blog — Opinion, Analysis, Commentary
The cost components of automobile insurance and the bonus-malus system

In my recent commentary on the planned ICBC auto insurance reforms, I had mentioned the multiplicate nature of contributing cost factors. The risk premium that we pay as insured motorists can be disaggregated as follows:

\[ \mathrm{TC} \equiv \left(\frac{\mathrm{TC}}{\mathrm{NC}}\right)\cdot \left(\frac{\mathrm{NC}}{\mathrm{NA}}\right)\cdot \left(\frac{\mathrm{NA}}{\mathrm{NI}}\right)\cdot \mathrm{NI}\]


  • TC: total cost of claims
  • NC: number of claims
  • NA: number of accidents
  • NI: number of insurance contracts (insured motorists)

The three ratios in parentheses are the average cost of claim (TC/NC), the accident rate (NA/NI), and the claims rate (NC/NA). The latter is not equal to one. In some cases damage is sufficiently small that parties do not pursue insurance claims. The claims rate is also endogenous to the insurance regime. If there are lucrative rewards for "pain and suffering" for minor bodily injuries, injured parties may decide to pursue such claims if there are no apparent costs to pursuing such claims. This in turn drives up average cost of claim.

The risk (insurance) premium paid by individual motorists is based on the expected value so that \[\mathrm{RP}= \widehat{\mathrm{TC}}/\mathrm{NI}\]

The above calculations are based on aggregate data and therefore only represent the average. The risk premium for the individual motorist hinges crucially on the prediction of frequency and severity of accidents caused by that motorists. How can one predict these measures? There are many proxies—mostly demographics that reveal that the worst drivers are young and male. However, proxies are proxies, and even among young male drivers there are some good and careful drivers. The best way to determine risk is to monitor behaviour: ex ante before an accident occurs (telematics) or ex post after an accident occurs (established driving history and claims record). The latter is precisely what ICBC has turned to last year when it improved the way riving record is taken into consideration. The underlying idea is a bonus-malus system.

What is a bonus-malus system?

With a bonus-malus system (BMS) for auto insurance, the insurer is obliged to consider the loss history and discount the premium in case of a claim-free history (bonus) or add a surcharge in case of payment of an indemnity (malus). Policyholders are placed on a premium scale based on the information available in their (standardized) claims history statement. BMS rewards low-risk drivers and punishes high-risk drivers. Academic research suggests that the optimal BMS follows a path for the premium factor \(\Theta\) in period \(t\) \[\Theta_{t+1}=\lambda\cdot\Theta_{t}+(1-\lambda)\cdot\Phi_t \quad\mathrm{with}\quad\Theta_0=1\] where \(0<\lambda<1\) is a weight and \(\Phi_t\) is the standardized number of claims in year \(t\). Each claim-free year is rewarded by reducing the premium factor by \((1-\lambda)\cdot100\%\), and the premium increase after a claim is approximately a fixed amount. The optimal \(\lambda\) can be estimated and is typically in the 0.80-0.90 range. In practice, most bonus-malus systems consist of a fixed number of levels and each level has its defined rate. Many variations and modifications of BMS have been developed over the years. See for example Lemaire (1998) for a discussion.

The quest for an optimal bonus-malus system has led to many research papers. BMS can and does provide strong incentives for safe driving, but it can also encourage non-reporting of claims (or repayments of costs) in order to avoid the malus. In order to avoid distortions of this type, as of September 2019 ICBC no longer allows claims to be repaid unless the claim amount is less than $2,000. Other variations of BMS adjust for claims size. Many forms of BMS introduce varying deductibles that prevent malus evasion. ICBC has so-called escalating deductibles that increase for customers with multiple claims. In September 2019, ICBC also moved to a more comprehensive bonus-malus system by recognizing up to 40 years of driving experience. With each year of driving experience, policyholders earn additional discounts, while previously discounts maxed out after nine years.

So how does ICBC calculate premiums in practice in British Columbia? The base premium rate is multiplied by driver category (based on driving experience, crash history, and listed drivers) and by vehicle category (accounting for where one lives, how a car is used such as commuting or pleasure, and applicable discounts).

The path to low insurance premiums

So what keeps insurance rates low in the end? Three things. First, low accident rates. This is a combination of incentives for good driving behaviour, safe road infrastructure, and targeted and effective enforcement. Second, low claims cost. This is a combination of reducing the severity of accidents (such as through lower speeds in urban areas) and reducing claims overhead (less litigation, more focus on recovery and recuperation). And third, public policy and institutions that support all of the above. I have stated the case for public auto insurance previously, because a public insurer is in a better position to internalize the benefits of improved road safety. Let me say it again: privatizing auto insurance doesn't make our roads safer. It is reassuring to see that ICBC introduced many improvements last year, and is introducing care-based insurance next year to get a handle on claims cost that had spiraled out of control. There is much to do still. The best way to keep auto insurance costs low is to make accidents less frequent and less severe—the best insurance is one that needs to be relied upon rarely.

Posted on Saturday, February 29, 2020 at 09:30 — #Economics | #Transportation | #BC
© 2020  Prof. Werner Antweiler, University of British Columbia.
[Sauder School of Business] [The University of British Columbia]