Islands of Stability Firm survival
Young firms die far more often than old ones. Does a firm become safer as it ages, or do the fragile ones simply die first?
The founding essay of this site is about organizations: firms that find a way of working, hold it for a while, and have to cross to another when the world changes. Proposition 3 once had an organizational reading, that a firm's age says nothing about how long it has left. It was withdrawn after an objection that this page makes visible with real data.
How often firms die, by age
Averaged over 2004 to 2023, 18.7 percent of American firms in their first year of age died within the year, against 5.0 percent of firms aged 26 or more: 3.7 times as often. Most of the fall comes in the first five years, and at the average rates only about 51 percent of new firms would reach their fifth year.
Memory or frailty?
The falling bars look like firms growing safer with age: learning, building customers, gathering reserves. But the same shape appears without any firm changing at all. Suppose some firms are fragile and some are sturdy, and each keeps the same chance of dying every year, forever. The fragile ones die first, so the older the group, the more of it is sturdy, and the group's death rate falls. The red curve is exactly such a population: every firm in it is memoryless. Move the sliders and see how close it comes.
The best fit has 35 percent of new firms fragile, each with a 40 percent chance of dying every year, and the rest sturdy, each with a 5.8 percent chance, and it comes within 1.2 percentage points of every real average. Make all firms alike and the curve goes flat: without differences between firms, memoryless firms produce no liability of newness.
This is the objection recorded against proposition 3's organizational reading: a death rate that falls with age may be frailty, the weak leaving first, rather than memory, each firm growing safer. The two cannot be told apart from counts like these without a measure of each firm's depth that does not depend on how long it has survived, and no public record supplies one. The same trap waits in any domain where islands differ in depth: supercooled water droplets, lakes, and agent systems.
Cost line and fragility line
Cost line. A firm stays in business only by paying for it continuously: wages, rent, suppliers, interest. Its island is a flow, as proposition 4 describes, and it ends when the money to keep paying runs out.
Fragility line. Cash: most firms that die run out of it, whatever else went wrong first. Young firms have the least of it, which is one of the reasons offered for the liability of newness, alongside frailty.
How the propositions meet the firms
| Proposition | On the firms | Status |
|---|---|---|
| P3 Exit statistics | The death rate falls with age. That would meet the proposition's falsifier only among firms of the same depth, and the data cannot say whether it is memory or frailty. Version 0.2 names frailty in the proposition's wording. This is why the organizational reading was withdrawn. The page shows the objection, not a test. | objection illustrated |
| P1 Sparsity | About half of new firms do not reach their fifth year: the ways of working that last are fewer than those attempted. A resemblance, not a test. | resemblance |
| P4 Cost | A firm's survival is paid for continuously and ends when the payments stop. Illustration. | illustration |
| P2, P5, P6 | Not applied here. Proposition 6's era ratio needs data on how fast firms reconfigure, which these counts do not hold. | not applied |
Source and method
Data: US Census Bureau, Business Dynamics Statistics, 2023 release, firm age (bds2023_fa.csv), from the Census Bureau, retrieved 2026-09-29, 86,502 bytes, SHA-256 52a36e61791aacfaedc0466a4d9b8c1c94a8b0dfbe05e967840119bf6d5695a1. A class's yearly death rate is its firm deaths over its firms counted that year plus its deaths, since the firms counted are the survivors. Rates are averaged over 2004 to 2023, when every age class exists. The two-kind model is fitted by least squares at each class's nominal age (26 and over at 30). It describes what the data cannot rule out and tests nothing.