Self inflicted paranoia - The "secret" of insurance deductibles

It is a well known fact (or at least strong belief) that most people make very wrong choices with respect to buying insurance products. The majority of people over-insure, that is, pay much more than they should, or just neglect to purchase insurance altogether.

This post turned out to be a bit long and somewhat technical, but here's my promise - if you can keep with it until the end, the chances are you will feel fooled by insurance companies, but will also be able to save lots of money in the future.

As someone who studies consumer decisions, buying insurance is one of the most fascinating phenomena to study, for several reasons:

  1. Insurance is a complex product, containing many details, but at the end, there is just one price (premium) to pay.
  2. Consumers buying insurance need to make many decisions about many "parameters" of the product they buy.
  3. Insurance sells something in the future (coverage against negative events), that might happen or might not - who can predict his own future with accuracy?
  4. The product sold is very emotional - it is related to negative events with big and bad impact. Most people have a hard time entangling their emotion about the event itself and the decision of how much coverage to buy.
  5. The insurance industry (in the US) is rather competitive, so the products are abundant, advanced and should be fairly priced.
  6. People make the decision to buy insurance over and over again, many times annually for a period of 30-40 years. This means there is ample time and information for learning from past mistakes.
I am fascinated by this phenomenon, since it shows how firms produce a complex, emotional product and profit on consumers' inability to understand too many details, or their plain fear from negative events.
A very interesting and roughly "simple" parameter of insurance where consumers make almost unanimous mistakes is how much deductible they would like to pay in case of an insurance event.
A paper by Justin Sydnor analyzes the case of homeowners insurance, where this paradox is sometimes stronger than in the case of other insurances.
To have a clear example, let's take auto insurance deductibles for instance.
A deductible is a sum of money that someone pays from his/her own pocket before the insurance kicks in. For example, if a car was involved in an accident with damage worth $2000, and the insurance policy has a $500 deductible, the insured will pay $500 from his/her own pocket, and the insurance company will pay the remaining $1500 to fix the damages.
If the damage was less than $500, the insured person pays for all the damages from his/her pocket.
Why are deductibles interesting? Deductibles are interesting because they come with a clear menu of options. 
A typical auto insurance offer will have the option (for example) to select deductibles of $250, $500 and $1000. In addition, a change in the choice of deductible affects the price of auto insurance greatly.
Every time a person chooses a lower deductible, they need to pay a higher premium for that. That is, the price of having to pay less out of pocket in the future, costs more today.
The second interesting point about deductibles is that the difference between one option to the other is very clear - the value of a $500 deductible vs. a $1000 deductible is at most $500 per year.
If you don't see why, think about it for a minute - buying a lower deductible just gives you the option to pay less of the difference in that year.
Let's focus on the choice of a $500 vs. a $1000 deductible. Here comes the interesting part (if I haven't lost you by now) - how much are people willing to pay for the option to pay less in the event of an accident?
That depends only on one parameter - their beliefs about their probability of being involved in an accident with damages over $1000.
(To simplify things. This is very close to the actual reality).
It is important to understand this does not depend of how much damages will be created to the car (once they are above $1000), since everything above $1000 is covered anyway by the insurance company.
If you go to your car insurance provider, and ask them for two quotes for the same insurance policy, with just one difference, one quote for a $1000 deductible, and one for a $500 deductible, the difference in annual (yearly) premium will probably be on the order of $150-$250. Let's suppose it's $150.
I urge you to go and check. This difference can be very different for many people.
What does this mean? It means that if you believe you will have a 150/500 chance of an accident (30%) with damages above $1000, you should buy the lower deductible. 
Why? Because you are paying $150 extra every year for the chance of getting $500 in return (or the chance of not paying $500 in the event of an accident). If this chance is higher than 30% (say 40%), you will get back 500*40% = $200 back, thus having a "profit" of $200-$150=$50. If this chance is lower than 30%, you will get back less than what you paid, on average.
Is 30% chance a lot or a little for having an accident? Think about it - if you are involved in a car accident with big damages roughly every 3 years, 30% is about right (100/30). If you are not (and I hope most people are not), then you shouldn't get the lower deductible. To make things worse, if the difference of the two quotes was $250, and you bought the lower deductible option, it implicitly means you believe you will be involved in such an accident every second year (250/500 = 50% chances of an accident each year). Assuming you and most people around you are decent drivers, this is clearly a self inflicted paranoia.
Another way to look at it is as a savings scheme - get the higher deductible, and put the savings from insurance price in a savings account, and call it "emergency car repair fund". Use these funds only to pay for deductibles. I would assume this "fund" will pass the value of $500 quite fast.
There are essentially only two cases where buying a lower deductible is worth it:
1. You cannot afford the $500 in one time - In case of an accident, if you cannot afford to spend $1000 (but can afford to spend $500), then get the lower deductible. In this case you are basically paying the insurance company a very high interest rate (roughly 15%-20% is my estimate) on having not to save $500 on the side.
2. You are a very reckless driver - If you are prone to accidents, get the lower deductible. Insurance companies are smart as well, though. The chance your entire premium won't raise once you have a bad driving history is zero, so you will be paying for being reckless anyway.
This anomaly can happen in any industry where insurance is sold, but I have a hunch it happens the most where the  negative events might have large financial consequences - health insurance, home insurance, earthquake insurance and such, and also when recent negative events have happened. If you've paid attention, however, you should be able to say by now that the choice of deductible should depend on the size of the "average" damage and not the "extreme" damage, since both deductible options will cover the extreme damages.
Hopefully after reading this, some of you went to check out what their deductibles are, and some of these some, saved roughly $500-$1000 per year on unnecessary over-insurance.

9 replies on “Self inflicted paranoia - The "secret" of insurance deductibles”

  1. I've known several car accidents lawyers who have handled different accident cases over the past years. If you ask me, I'm still quite confused on how insurance policies measure the amount of cost. Don't get me wrong but sometimes, I feel like we're being cheated by insurance agencies when it comes to accident cases.

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