Expiration Dates in Automobile Insurance Contracts: The Curious Case of Last Policy Month Claims in Taiwan

Data

The data used in this study is unique. We obtained the entire data set of private automobile vehicle damage insurance contracts in Taiwan for the calendar years from 2003 to 2005. In this heavily regulated industry, insurers are required to report the sale of all individual policies to the Taiwan Insurance Institute, a semi-official organisation responsible for collecting insurance statistics and financial data for insurers. The data set includes complete car insurance information from insurers, including characteristics of policyholders, vehicles, claim drivers and contract details. Unfortunately, there is no information available about distribution channels. Therefore, we are not able to directly examine trends in policies secured through direct writers, independent agents or DRAs.

Taiwan's automobile insurance policies are usually valid for one year. As a new policy can become effective any day of the year, we reorganise claim data, originally reported by calendar year, by policy year. This reorganisation is necessary to investigate possible policy period effects in the data.

Preliminary analysis

Figure 1a illustrates the calendar time distribution of claim frequency—the ratio of claims each month to total policies in that calendar year—for three types of automobile insurance contracts in Taiwan from 2003 to 2004. There is little variation in the share of claims across months for Forms A and B. Claim frequencies for these two policies appear to be slightly higher in December (Forms A, 8 per cent; Form B, 7 per cent) and January (Form A, 8 per cent), as compared to other months (4 per cent∼6 per cent), perhaps due to seasonal conditions. Form C, which covers collision only, reveals a relatively lower ratio of claim frequency (around 1 per cent) for all months.

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In contrast, Figure 1b presents the period time distribution of claim frequency—the ratio of claims each month to total policies in that policy year—for the three types of contracts in the same years. Claim shares are noticeably different when viewed on the policy time scale instead of on the calendar time scale.⁷ In the 2003 policy year, Forms A and B exhibit high peaks in the last policy month, reaching 7.0 per cent and 7.9 per cent, respectively (vs. 1.5 per cent∼2.5 per cent for Form A and 1.2 per cent∼2.3 per cent for Form B in the first 11 months). Form C displays a much lower claim tendency (0.2 per cent∼0.6 per cent) in all policy months. Similar phenomena are even more evident in the 2004 policy year. For Form A and Form B, claim frequencies are 14.1 per cent and 23.2 per cent, respectively, in the last policy month, compared with 2.4 per cent∼5.7 per cent in other months.

As different policy forms provide different coverage, we expect that the explanation for the high peak in claims during the last month of the policy year is different for each form. If these claims result from small losses accumulated over the policy year, we would expect fewer Form C claims, as collisions involve two drivers. This phenomenon is apparent in Figure 1c, which shows the differences in monthly shares of total claims between policy forms A and B vs. C. The claim shares are indeed much higher for Forms A and B than they are for Form C. This positive difference is consistent for all policy months and reaches its highest level in the last month of the policy year.

Comprehensive Form B policies, the most common policy type, have the highest frequency of claims. This policy is very popular as the premium for comprehensive Form B is approximately half of that of Form A, and also because Form C provides less coverage, as shown in Table 1. The period time distributions of claim shares in Figure 1b are consistent with these expectations.

On the basis of Figure 1, we may predict that the highest average claim payment (in terms of total policies sold) is in the last policy month. Figure 2a shows the expected tendency. Interestingly, while claim shares spike in the last month of each policy year, we find that claim severity (average payments per claimed policy) is lowest in this month, as illustrated in Figure 2b. For example, the average claim payment per claimed policy for Form B is NT$26,760 for the first 11 policy months in policy year 2003, but only NT NT$19,300 in the last policy month—a 28 per cent reduction.⁸ Similar patterns appear in Forms A and C, as well as in the policy year 2004.

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Conjectures

Two major conjectures can be made based on the environment of this regulated automobile insurance market to explain some of the irregular claim patterns. First, the designation of BMS in Taiwan might provide incentive for the insured to file a claim before the end of the policy period. There are three related issues contained in the BMS: filing one claim, accumulating small losses and recouping the paid premium. Since a single claim in a given year does not change the claim coefficient, this creates an illusion that there is no cost involved in filing just one claim (we discuss the real cost of filing one claim in a latter section). In addition, since the claim coefficient depends on the number of claims and not on the claim amount, there is a structural temptation to file a single claim for reimbursement of several small losses. Under the BMS, a policyholder might not report small claims because he or she does not feel that the claim payment sufficiently offsets higher future premiums.³ In particular, Lemaire⁹ calculates the average optimal retention and compares the efficiency of BMS in various countries. Although accumulation and retention are similar but not exactly the same, the existence of both situations is possible. As the retention of policyholders is not observable, we focus on the accumulation of small losses.

Another possible reason for excessive claims in the final policy month is the designation by BMS for the recouping of paid premiums; in other words, filing a claim to effectively be reimbursed for the premium already paid. It is common for some insureds to question whether the protection provided by insurance is worthwhile. It is difficult to distinguish between an excessive claim filed as reimbursement for accumulating small losses, and that filed for the recouping of paid premiums. For policyholders who file more than one claim in a policy year, accumulated small losses is a less likely explanation. For these cases, recouping of paid premiums is a more likely explanation, especially when the realised total claim payment is smaller than the premium paid.

The second conjecture is the auto-dealer incentive issue. The DRA, as described in the section “Taiwan's automobile insurance market”, might play an important role in claim patterns. Since providing insurance is an integral part of the car marketing and sales system in Taiwan, car dealers are directly involved with DRAs who sell automobile insurance in show rooms. The car salesperson, acting as the DRA, occupies a key position in the insurance system. After buying a car and an insurance policy together, a policyholder contacts the salesperson when an accident occurs or a repair is needed. We expect that new cars are closely connected with excessive claims in the last policy month. In practice, purchasing insurance from a DRA together with a new car may form the basis of a short-term relationship that is mutually beneficial, as it provides repeat business for the DRA and is convenient for the policyholder in terms of claim services. The problem is that the salesperson might suggest or even encourage unnecessary repairs, which may or may not be a part of an implicit contract, as an incentive to buy a policy from the DRA. The situation here is similar to that in recent studies focusing on collusion between policyholders and providers.¹⁰

However, as policyholders rarely renew a policy with DRAs after the first two years, one might hypothesise that the role of DRAs in excess claims decreases with car age and reaches the highest tendency within the first year after a new car is purchased.

In an extension of the role of the DRA, as discussed above, the salesperson contacts the policyholder when the insurance policy approaches expiration, in addition to brokering regular insurance services. Renewing a policy secures additional commissions for the salesperson. Filing a claim in the last policy month and then renewing the policy might signal excess claims induced by DRAs.

In sum, the potential factors related to irregular claims filed in the last policy month are twofold: (1) the designation of BMS without explicitly penalising the claim coefficient for the first claim, which might lead to the accumulation of small losses and the recouping of paid premiums; and (2) the auto-dealer incentives, which are related to an implicit contract with DRAs and a new car. We establish econometric models to examine the impact of these factors on excess claims in the next section.

Variables and descriptive statistics

An average car has a 1,893c.c. engine capacity, which is not unusual in Taiwan (the most popular cars have a capacity of 1,600–2,000c.c.). The average claim coefficient is −0.098 (ranging from −0.6 to 2.8), indicating that most policyholders have relatively low claim coefficients. For claimed policies, the average claim payment is NT$29,735 (ranging from 600 to 4,300,000).

A policyholder's claim coefficient reflects his or her claim history over the past three years. Figure 3 suggests that claim shares in the last policy month peak for policyholders with zero claim coefficients. While this peak is not particularly pronounced, it might reflect the common misperception among policyholders that a claim in one policy year will not affect his or her future policy terms. Although the claim coefficient for a policyholder who files a single claim in a given year remains unchanged, he or she forgoes the 20 per cent discount in the next year's premium. In fact, the percentage change in future premiums grows linearly with claims in a given policy year (Figure 4).

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To obtain a general understanding of claim distribution before formal testing, we examine the claim frequency pattern between new and old cars, and between single claims and more than one claim. Figure 5a shows that both new and old cars have a much a higher ratio of claims that occur in the last policy month during the periods this research examines. In particular, the last month claim ratio for new cars is larger than that for old cars. In 2004, there are twice as many claims on new cars than there are on old cars. A similar situation exists for cases involving one claim vs. cases with more than one claim. For example, in Figure 5b there is high spike in claims filed in the last month both for cases of one claim and for cases of more than one claim. However, the claim ratio for one-claim cases is more than double of that of cases with more than one claim.

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Figure 5c provides a further observation on the average claim payments for cases of one claim and more than one claim. The average claim amount is consistently higher for one claim than for more than one claim in each month and reaches the lowest amount in the last policy month of 2003 and 2004. This fact might partly fit with the conjectures mentioned above. For example, a higher amount of one claim might have a connection with the designation of BMS. The lower severity of cases with more than one claim might be partly due to the intended reclaiming of the premium paid.

Methodology

To verify the conjectures regarding the factors affecting last policy month claims, we use two different regression models. In the first model, we define a binary response variable, Claim in last policy month, as the indicator of whether a claim is filed in the last policy month, and then consider the probit model:

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where Φ represents the standard normal cumulative distribution function. We include six major variables to test the conjectures discussed in the section “Data, preliminary analysis and conjectures”. All other available policy details are included in the predictor matrix X: car size, policy type and deductible choice. To control for possible effects of insurers, regions, car brands and time, we include dummy variables to reflect 16 insurers, 4 regions, 7 car brands and the policy year 2003.

In the second model, we use the same explanatory variables to examine factors associated with payments of claimed policy in the last policy month. We take the log of claim payments (in NT$) as the response variable and consider the variables directly related with claims together with Claim in last policy month. The model is:

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where β _i is the parameter of primary interest, and ɛ is an independent and normally distributed error term. We run the log-linear model using claimed data.

Estimation results

The role of the BMS

As discussed in the section “Data, preliminary analysis and conjectures”, the BMS in Taiwan might strongly encourage a policyholder to file only a single claim because this will not change the claim coefficient. Coincidentally, Lemaire argues that a good BMS should “introduce penalties for the first claim as severe as commercially possible, especially in the lower classes … Never forgive the first claim, whatever the pressure of the marketing department (p. 681).”⁹ Lemaire’s view does provide an interesting concept for the designation of BMS.

Theoretically, a minimal level of benefit is needed for both parties for the incentives of collusion to be worthwhile. This threshold is likely met in Taiwan when a policyholder can obtain excess claim payments to recoup paid premiums, while a salesperson can receive additional revenue in the form of commissions for renewed contracts as well as directly from car repair garages.¹⁴ However, this explanation of incentives for policyholders is incomplete since there are both positive and negative effects for policyholders. Some policyholders may feel that the policy is not worth the premium if there is no accident. For these policyholders, filing an excess claim to partially recoup paid premiums may be attractive. Nevertheless, Taiwan's BMS penalises the policyholder for the additional claim by increasing his or her claim coefficient, and thereby increasing future premiums. Therefore, the benefit of the excess claim is diminished so that this penalty serves as a partial deterrence for excess claims. In practice, however, some policyholders might be under the illusion mentioned in previous sections that a single claim will not bear any cost. Some policyholders might not understand this aspect of the BMS, and it is possible that an unscrupulous salesperson exploits this information asymmetry. For these reasons, the deterrent effect of the BMS is weakened.¹⁵ In sum, it is plausible that at least some policyholders feel there is a net positive incentive to report unnecessary claims.

At first glance, this observation seems consistent with the results of Dionne and Gagné,² namely that the probability that a car is stolen significantly increases with the endorsement of a replacement contract, confirming evidence of opportunistic fraud. However, the nature of the incentive mechanism at play in our study is somewhat different from the one they describe. The case in Dionne and Gagné² is one-way fraud, in which the origin of cheating comes from policyholders and has nothing to do with other participants in the market. In contrast, the excess claims in our study come from several different sources: the self-motivated insured and perhaps a kind of soft collusion between agent (including DRAs) and car owner. Nevertheless, it is not easy for the insured to independently file an unsubstantiated claim in the last policy month.

Who is responsible?

It is debatable whether policyholders or insurance agents are more often responsible for initiating excess claims, whether or not soft fraud or collusion is involved. While the inter-relationships among auto-insurer, insurance agent and policyholder are very similar to those for medical insurer, physician and patient in the situation of “induced demand” in standard medical insurance literature,¹⁶ an important difference is who is the decision-maker. Patients usually have insufficient knowledge to judge if a specific treatment is needed without the guidance of doctors. Therefore, doctors are responsible for much, if not all, of the induced demand for unnecessary medical care. In contrast, policyholders know if their cars have been in accidents and if consequent repairs are required. Even if insurance agents suggest or encourage policyholders to file excess claims, the final decisions are made by the insured. While there may be a grey area for the utility of an extra medical test, lying about the date of an accident or filing accumulated small losses as a single claim constitutes a breach of good faith inherent in the insurance contract.

How do the insurers react?

There is a missing part of the story: Why do rational insurers tolerate excess claims, if any? Several explanations are possible: high monitoring costs, revenue maximisation, equilibrium contractual provisions and regulated pricing rule.

First, as Mayers and Smith¹⁷ stated, “Various ways of verifying the incidence and loss amount are available. Effective competition among insurance firms assures that the monitoring procedures employed will be provided in the least costly form (p. 412)”. In this sense, insurers do not audit suspicious cases when costs are high enough, representing costly state verification in the standard theoretical framework.¹⁸ As we have shown, average claim amounts are relatively low in the last policy month and do not attract additional attention from insurers. This situation is consistent with characteristics of the incentive-compatible contract,¹⁹ in which policyholders intentionally adjust claim amounts to evade verification and auditing. Even if only sometimes successful, this strategy helps to explain how the expiration date effect persists without triggering more investigations from insurers.

Second, premium revenue is one of the key performance indicators of insurers. From the viewpoint of some managers, maximising revenue is perhaps preferred to maximising profit,²⁰ as the former is a daily pressure while the latter is only reviewed after a specific period, and there is no clear-cut chain of responsibility for suboptimal profits. In addition, although excess claims are generally known to exist, automobile insurance remains a major product line in property insurance.

Third, by relying on agents as one of their largest distribution channels, insurers are more likely to look the other way as long as general loss ratios fall in an acceptable range. Jou and Hebenton²¹ observe the case in Taiwan where the insurers “have no motivation or ready capacity to further investigate the relatively ‘small’ amount of suspicious claims (p. 124)”. In our case, accepting some excess claims from agents forming contractual provisions to maintain business relationships with agents and policyholders seems to create equilibrium in this market.

Fourth, the fact that insurance pricing during the study period has been determined by authorities might also play a role. On the basis of the standard pricing formula, although insurers do not compete over prices, the pricing authorities must set prices that allow insurers to earn a normal rate of return.²² In this situation, the official pricing rule must contribute to insurers’ willingness to permit the claiming practices.