The impact of premiums and default deductibles on selection and moral hazard in the car insurance market: Evidence form a randomized field experiment.

We cross-randomize website visitors interested in a car insurance to offers that vary the pre-selected default deductible (4000NOK, 6000NOK, 8000NOK) as well as the insurance premium with mark-ups/downs equal to -8%, -4%, 0, +4%, +8% relative to the prices in the standard menu. The pre-selected deductible is the default option, but customers can easily select another deductible if that is preferred.

2020-09-20

2023-01-31

1. Purchase of insurance
2. Choice of deductible
3. Claimed amount per year (adverse selection)
4. Claimed amount per year for claims above maximum deductible (moral hazard)
5. Customer churn
6. Overall profitability

Claimed amount per year is the sum of all claimed amounts by a customer in the 12 month period after a contract has been signed. It thus captures two different margins in which risk can be affected (number of claims and the size of a claim). We will look at these margins separately as well.

We expect the default deductible to mainly affect which deductible people choose. Although we find it unlikely, the default deductible may, however, also affect who buys insurance. To investigate this possibility we will perform a balance test comparing the means of the background variables we have access to on the final set of customers, across the different default treatments. By random assignment of website visitors we should expect the background variables to balance across the final set of customers unless some type of website visitors were more likely to buy insurance when exposed to a specific default deductible. Hence, in this analysis we will treat the background variables that we have access to as outcome variabels to understand whether the group of final customers are similar across the three default deductibles or not.

If the groups are statistically identical we will simply move on to identify moral hazard (see below). If the groups turns out to be different we will treat it as an unexpected bonus finding, and try to correct for it in the analysis of moral hazard.

We cross-randomize website visitors interested in a car insurance to offers that vary the pre-selected default deductible (4000NOK, 6000NOK, 8000NOK) as well as the insurance premium with mark-ups/downs equal to -8%, -4%, 0, +4%, +8% relative to the prices in the standard menu. This design allows us to study a number of questions in the short term and slightly longer horizon.

In the short term, we will investigate whether the premium and/or default deductible affects the likelihood to purchase insurance. We will also study whether the default deductible affects the choice of deductible, where we predict that a higher default deductible leads to a higher chosen deductible, and thus less insurance cover.

In the long term we will investigate insurance claims, customer churn and overall profitability for the company. A particular focus will be on how the price dimension impacts selection (adverse or advantageous) and how the default deductible dimension impacts moral hazard.

Using the random variation in the price premium, we notice that adverse (advantageous) selection should, ceteris paribus, imply fewer (more) claims, on average, among those who were randomly offered a low price compared to those who got a high price. We will investigate if this is the case.

Moral hazard measures to what extent the coverage of the insurance influences the probability of having a claim. If moral hazard is present we should observe more claims exceeding the maximum deductible - ceteris paribus - among those who have a low deductible. The problem with observational data is that the deductible is chosen and the propensity to choose a low deductible may correlate with non-observed individual characteristics that may also have a separate effect on the probability of having an accident. We aim to get around this problem by using the randomly assigned default deductible to instrument for the chosen deductible. With exogenous variation in the choice of deductible we can investigate moral hazard by comparing the number of claims above the maximum deductible (i.e., 8000NOK) using both an ITT and IV estimation strategy.

The experiment has been running since September 2020 and we will end recruitment in January 2023, based on predictions that we then have reached the desired number of website visitors and customers (see power calculations). The set of customers will be followed for at least another two years in order to reach the desired number of observations to identify effects on claim behavior, customer churn and overall profitability (see power calculations for details).

Important notice: Before September 2021 (i.e. during the first year of the experiment) there was a technical issue that made it impossible to extract data on website visitors that did not proceed to purchase insurance. To study treatment effects on insurance demand we will therefore use two complementary methods. i) First, we will conduct a proportion test, testing whether the observed empirical proportions of customers (i.e. website visitors that purchase insurance) in the respective treatment groups coincide with the expected proportions given the pre-assigned randomization. Based on this test we can, for example, elicit price elasticities of demand. ii) Second, we will restrict the sample to the period September 2021 to January 2023, i.e., where we have complete information on the choices of all website visitors, to estimate how treatment affects the likelihood to buy insurance using standard regression analysis. We expect similar results from the two different methods, and will base our conclusions on the method that turns out to be most powerful ex post.

Not available

Computerized program.

Individual. Website visitors need to provide their social security number to get an insurance offer. We use this information to ensure that the same person gets the same treatment if visiting the website repeatedly.

No

About 130,000 unique website visitors and 8,000 customers (i.e. visitors buying insurance). These are conservative estimates and the actual numbers may turn out to be larger.

About 130,000 unique website visitors and 8,000 customers (i.e. visitors buying insurance). These are conservative estimates and the actual numbers may turn out to be larger.

The default deductible is randomly assigned to all website visitors according to the following proportions:
Low default deductible (4000NOK) = 20%
Medium default deductible (6000NOK) = 40%
High default deductible (8000NOK) = 40%

For each default deductible the premium is varied in the following proportions:
-8% = 10%
-4% = 20%
0 (standard price) = 40%
+4% = 20%
+8% = 10%

The first (but not primary) outcome is the likelihood to buy insurance. We want to be able to refute relatively small treatment effects of the default deductible on this outcome to be in a better precision to analyze and interpret the effects on subsequent outcomes (including choice of deductible and insurance claims). A power analysis in STATA confirmed that with N=15000 in the low default deductible group (4000NOK) and N=30000 in the high default deductible group (8000NOK) we are able to detect a treatment effect of 1.4p.p. (≈0.03SD) from a baseline of 6.25p.p. (t-test, assuming 80% power and 5%-level of significance). Using the more powerful Pearson's chi-squared test we would be able to detect a difference of 0.7p.p. with the same sample size and assumptions. Hence, based on these calculations we aim to recruit a total sample of about 130,000 website visitors, out of which about 75,000 (15000+30000+30000=75000) are recruited after September 2021 when we have complete data on all website visitors. According to predictions we should have reached this number by the end of January 2023. To estimate long term effects on insurance claims we know from historical data that there, on average, is a claim every 4th year. Hence we should expect a 50% chance that an individual reports a claim before 2024-12-31 (two years after the intervention ended). Using the assumption from above (that 6.25% of website visitors decide to buy insurance), we should have a total sample of 8,000 customers, out of which 1600 are in the low default deductible and 3200 are in the high (and medium) default deductible group, assuming no treatment effect on purchase likelihood. With this sample size we have 80% power to detect a treatment effect of 8.58p.p. (≈0.2SD) comparing the fraction reporting a claim within two years in the low and high default deductible groups (5%-significance level). With a Pearson chi-squared test we can detect a difference of 4.28p.p. using the same assumptions. Notice that we will use a slightly different and hopefully more powerful outcome variable in the main analysis (see above). The dummy in this power analysis was used for rough guidance and simplicity.