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Social Inflation and the Bornhuetter-Ferguson Method

Social inflation[1] continues to be on the minds of many actuaries.

We have learned this firsthand over the past year as we have spoken extensively about our paper, “Social Inflation and Loss Development,” published jointly by the CAS and the Insurance Information Institute (III) early in 2022. The paper concluded that rising link ratios at the industry level were consistent with what most commentators called social inflation — an increase in claim severity that is much steeper than standard inflation measures would indicate.

We have received a lot of questions about adapting loss estimates to a social inflation environment. Using standard development methods and picking a three-year or five-year average while social inflation is accelerating will leave one’s cumulative development factors too low, which would leave the ultimate loss estimates too low. We suggest that actuaries should consider selecting link ratios from the most recent development year or consider extrapolating link ratios instead of selecting a multiyear average in an environment of increasing inflation.

At one talk, we received the logical follow up: “How would social inflation affect Bornhuetter-Ferguson (B-F) estimates?” The answer is easy to determine, but we thought it was a nice exercise in working from first principles.

First, the B-F formula, which most of us know by heart for accident year i, evaluated at age of maturity j:

B-F reserveij = a priori loss estimatei * (1 – 1/CDFj), where CDFj is the cumulative loss development factor at age of maturity j.

There are two variables at work here. The first is the cumulative development factor that we previously discussed. If link ratios are affected by social inflation, selecting multiyear averages of link ratios will result in cumulative development factors that are too low. As we explained in our paper: “If losses accelerate, age-to-age factors will increase from accident year to accident year. The process no longer has a stable mean.”

We have received a lot of questions about adapting loss estimates to a social inflation environment.


If one selects individual link ratios that are too low, then the CDF is too low. In turn, 1/CDF is higher than it should be and 1-1/CDF would be lower than it should be. So social inflation’s impact on the CDF makes the B-F estimate lower than it should be.

What about the a priori loss estimate? The situation there depends on the source of this loss estimate. The a priori loss is often estimated by multiplying a selected a priori loss ratio by the earned premium for the period being estimated. Every organization is different, but it is not unusual to use the loss ratio to which the book was priced as the a priori loss ratio for the first year or two. Then the organization moves to the loss ratio derived from the latest reserve review. How does that measure up?

Maybe not so great.

In our paper, we noted there was roughly a three-year lag between losses increasing and pricing increasing in the industry for commercial auto liability. We showed this by comparing both premium and losses to nominal gross domestic product. Nominal GDP is a reasonable exposure proxy at the industry level. The insurance industry is a mature one. It grows over the long term at about the same rate as the overall economy.

The pattern we saw is consistent with the typical narrative of the pricing cycle. It takes time to identify that inflation has increased and is likely to continue increasing. Once it is identified, it again takes time to implement pricing adjustments in the market, including making rate filings, receiving approvals, implementing in systems and communicating to stakeholders. After all that, the actual losses have moved to a new place. If social inflation is present, that place is likely higher than what the rate change anticipated.

So if a company does not make explicit adjustments in its a priori loss ratio in anticipation of increasing inflation, its a priori loss ratio will also be biased low.

In sum, both variables that drive the B-F estimate are likely to be biased low.

It’s also worth looking at the alternative formula for the B-F, wherein the method is effectively a credibility-weighted average of the chain-ladder and the expected loss ratio methods. As a reminder, that formula is:

B-F ultimateij = lossesi*CDFj*(1/CDFj) + net earned premiumi*a priori loss ratioi*(1-1/CDFj). The term before the plus sign is the chain ladder method, weighted by 1/CDFj, which is the credibility complement of 1-1/CDFj.

A moment ago, we established that (1-1/CDF) is biased low when social inflation is present, as is the a priori loss ratio. The CDF would also be too low, meaning the chain-ladder method would also be biased low.

Clearly it is important to understand whether a book of business has something like social inflation baked into it.

The greater challenge is what to do about it. It’s not a difficult exercise to pick separate, higher link ratios to increase the CDF or to adjust the a priori loss ratio based on anticipated trend and rate level changes. For practical as well as professional reasons, it would be important to communicate these changes to anyone using the estimates.

It will also be important to have performed an analysis that identifies the social inflation in the first place. Efforts to increase loss estimates, no matter how laudable, often are skeptically met. Showing that social inflation is affecting a portfolio is the first step toward addressing the issue.

Editor’s Note: The CAS recently published “Social Inflation and Loss Development — An Update,” which is available on the CAS website.

[1]   When we use the term “social inflation,” it can be thought of as shorthand for a confluence of many socioeconomic factors, any or all of which can increase claims costs faster than general inflation. We do not mean to imply that specific excesses are the result of any one individual civil court phenomena. Moreover, the conclusions, formulae and remedies do not rely on any particular cause.

Jim Lynch, FCAS, MAAA, recently retired from his position as chief actuary at Triple-I and has his own consulting firm.
Dave Moore, FCAS, MAAA, CERA, is head of Moore Actuarial Consulting.