Incurred But Not Reported (IBNR) Explained

Motivation

A lag triangle is a table that shows how medical claims are paid over time. Rows usually represent the month care was received, called the incurred month. Columns show how many months later the claims were paid, called the lag or development month.

This matters because medical claims are not paid all at once. A member may receive care in January, but the provider might submit the claim weeks later, the TPA processes it after that, and payment may not happen until February, March, or later.

IBNR means incurred but not reported, though in medical reserving it often means broader unpaid claim liability: claims that have happened but are not fully paid yet.

For a self-funded medical plan, this is important because the employer, not an insurance carrier, ultimately pays the claims. The TPA administers the plan, processes claims, and provides reporting, but the claim liability belongs to the self-funded plan sponsor.

So IBNR answers a practical finance question:

How much money should the employer expect to pay for care that has already happened, even if the bills have not fully arrived or been paid yet?

That estimate matters for:

Chain Ladder Explained

Chain ladder is a way to estimate unpaid claims using the payment pattern already visible in historical claims data.

The basic idea:

If older claim months usually grow from $100 paid to $120 paid as they mature, then newer claim months probably need similar growth.

That growth pattern is called development.

1. Start with Incremental Paid Claims

This is what was paid in each lag month.

Each row is a claim month. Each column is how many months later the payment happened.

2. Convert to Cumulative Paid Amounts

Chain ladder uses cumulative paid, not incremental paid.

E.g., Jan Age 1 = 100 + 80 = 180

This table shows how claims grow as they mature.

3. Calculate Age-to-Age Factors (aka Link Ratios)

An Age-to-Age factor (aka link ratio) measures growth from one age to the next.

Formula: Age 0 to Age 1 ratio = Age 1 cumulative / Age 0 cumulative

• Average selected factor: (1.80 + 1.75 + 1.77) / 3 = 1.77

• So we select: Age 0→1 factor = 1.77

Meaning: On average, claims at age 0 grow by 77% by age 1.

4. Build Development Factors

Repeat that for every age.

These are the claim growth assumptions.

5. Convert to Cumulative Development Factors (CDF)

A cumulative development factor (CDF) answers the question:

If a month is currently at this age, how much do I multiply paid-to-date by to estimate ultimate claims?

6. Estimate Ultimate Claims

Now apply the CDF to each row’s latest paid amount.

Formula: Ultimate = Latest Paid × CDF

7. Calculate IBNP

IBNP is the unpaid estimate.

Formula:

IBNP = Ultimate - Paid to Date

So the chain ladder estimate says: We have paid $800 so far, expect $978 ultimate, and need $178 of IBNP.

TL;DR

At the end of the day, Chain ladder is simply:

1. Turn incremental paid into cumulative paid.

2. Measure how older months grew from one age to the next.

3. Average those growth ratios.

4. Multiply remaining growth into CDFs.

5. Apply CDFs to newer months.

6. IBNP equals ultimate minus paid.

The method works best when the past payment pattern is a reasonable guide for the future.