Islands of Stability Economy
Booms, pegs and growth: which economic states last, what holds them up, and how they end.
Economics has studied islands of stability for longer than most sciences, under other names: regimes, equilibria, pegs, traps. The theory page lists economists as prior owners of five of its six propositions. This page takes four economic islands in turn, each with public data: the business cycle, the calm before 2008, the currency peg, and the long-run spread of incomes across countries. It mostly describes. One test has run: X1, on expansions in 42 countries, deposited and run on 30 September 2026. Its verdict is unresolved.
On this page: Do expansions die of old age? · The quiet years · How long does a regime last? · A peg and its runway · A sea between rich and poor? · The propositions
Do expansions die of old age?
Since the middle of the nineteenth century, the National Bureau of Economic Research has dated every turn of the American economy: the month an expansion peaked and the month the contraction that followed hit bottom. If an expansion is an island in the sense of proposition 3, an expansion's age should say nothing about how long it has left.
The NBER has dated 35 expansions since December 1854. They have grown longer: from 1854 to 1919 they averaged 26.6 months, from 1919 to 1945 35.0, and since 1945 64.2, the longest 128 months, from June 2009 to February 2020. Contractions shrank, from 21.6 months to 18.2 and then 10.3. The expansion that began in April 2020 had not been declared over when the dates were retrieved. It counts here as lasting at least 65 months, to September 2025, since the committee has announced every peak since 1980 within a year of it.
A Weibull fit sums up in one number, its shape, how the chance of ending changes with age: 1 for a chance that stays the same, above 1 for one that rises. Measured from the fifth month, expansions before 1919 have a shape of 2.47 (95 percent interval 1.63 to 3.48) and contractions since 1945 1.70 (95 percent interval 1.01 to 2.60), leaving out the two-month contraction of 2020: both grew more likely to end as they aged. Expansions since 1945 come out at 1.64 (95 percent interval 0.98 to 2.49), an interval that just includes 1, and contractions before 1919 at 1.32 (95 percent interval 0.88 to 1.83). Measured from month zero every shape is higher: postwar expansions, for instance, come out at 1.84 (95 percent interval 1.11 to 2.79).
A shape above 1 means the chance of ending rises with age. Part of that is built into the dating: the committee does not call phases much shorter than half a year, so no phase can end in its first months, and a curve fitted from month zero rises by construction. The fits above start each phase's clock at the fifth month, the minimum of the rule written to reproduce the committee's choices (Bry and Boschan, 1971), as the economists who first asked this question did. Daniel Sichel reported in 1991 significant evidence that expansions before the Second World War and contractions after it grow more likely to end as they age. The data since then tell the same story.
For proposition 3 this is description, not a test. The dates are public and well studied, and nothing separates one expansion's depth from another's, so a rising rate could be exhaustion, something used up as the expansion runs, and a falling one could be frailty. Version 0.2 counts neither as evidence until the reserve or the depth is shown. Test X1 asked the same question of expansions in 42 countries, comparing each country's expansions only with each other and allowing for each decade. Its data were downloaded and only their structure read before the freeze, and it ran once after its deposit.
Test X1: the result
Test X1 ran once, on 30 September 2026, after its frozen rules were deposited as 10.5281/zenodo.23066598. It draws no random numbers, and the verdict follows the deposited rules.
| Test | Bears on | Verdict | What was found |
|---|---|---|---|
| X1. Do expansions age? | P3 | unresolved | Within each country and decade, an expansion's chance of ending rose with its age: the shape was 1.38 (1.15 to 1.63), where memoryless is 1, over the 142 expansions that ended, of 169, in the 40 of 42 countries that had one. Memoryless is ruled out (p = 0.001), but a departure needed the interval's lower end above 1.25, and survival needed an interval that holds 1. |
Reported without a verdict, as the rules require:
- Without decade effects: 1.23 (1.02 to 1.45).
- Without country effects: 0.94 (0.76 to 1.12). Pooling countries whose expansions run long with ones whose expansions run short hides the aging, which is why the test compares each country only with itself.
- Contractions: 1.54 (1.18 to 1.92).
- Through the latest quarter, pandemic included: 1.48 (1.28 to 1.69). The pandemic ended expansions everywhere at once, whatever their age, which is why it was kept out of the test.
- The sample as first drafted, estimated quarters included: 1.23 (1.07 to 1.40).
The quiet years
From the mid-1980s, American output grew more steadily than ever before. Economists called it the Great Moderation, and in a 2004 speech of that name Ben Bernanke, then a Federal Reserve governor, weighed how much of it better policy had earned. Proposition 2 says that looking stable is not evidence of an island. Only recovery from a push is. The quiet years are its standard economic example.
From 1960 to 1983 the annualized growth of US output swung around its average with a standard deviation of 4.3 points. From 1984 to mid-2007 the swings shrank to 2.0, 2.1 times smaller. Then, in the fourth quarter of 2008, output fell at an annualized rate of 8.9 percent.
The calm measured how quietly output moved, not how hard the economy was to push off course. Hyman Minsky had argued that stability itself breeds the borrowing that ends it. Whether he was right about 2008 is argued still. What the record shows is that twenty-three calm years were not evidence of depth.
How long does a regime last?
Proposition 6 turns on how long the world stays in one regime before it changes. In 1989 James Hamilton showed how to estimate that from a series alone: let the economy switch at random between a regime of growth and a regime of decline, each with its own average, and find the switching chances that best explain the data. A regime that stays with chance p each quarter lasts, on average, 1 / (1 − p) quarters. The theory page names his method as the candidate instrument for proposition 6. Here it is, built and run on the series Hamilton used, US output, in its simplest form: two averages, one spread, no lags.
In Hamilton's own window, 1951 to 1984, the fit finds a low regime, with output shrinking 0.18 percent a quarter on average, that lasts 4.0 quarters, and a high one, growing 1.32 percent a quarter, that lasts 9.3. It never saw the NBER's dates, yet it puts 92 percent of their recession quarters in the low regime, and 14 percent of the other quarters. From 1985 to 2019 the high regime's expected length is 59.0 quarters, 6.3 times as long, and the fit puts 55 percent of recession quarters in the low regime and none of the others.
Hamilton's original form, with four lags, reaches two different optima from the 18 starting points tried on today's revised data for 1951 to 1984, and the highest is not a recession regime: its low regime lasts 1.1 quarters and holds 12 percent of recession quarters. Started from his published estimates, the same model settles at 4.2 and 9.3 quarters, close to his own, at a slightly lower likelihood. The answer depends on the specification as well as the series.
What this is not. Proposition 6 bets that AI shortens the regimes of AI-exposed sectors. US output is not such a series, and the author has not named one. Were US output the series, the lengthening shown here would count against the proposition, since "era proxies stable or lengthening" is one of its falsifiers. So the instrument is built, and its series is still to be chosen and frozen, together with its specification, before any estimate on it counts.
A peg and its runway
A country that fixes its currency to the dollar has made an island: the exchange rate stays put while everything around it moves. The island is not free. Whenever more money wants to leave than to come in, the central bank must sell dollars from its reserves to hold the rate. That is proposition 4's picture exactly: depth bought by continuous spending against a drift, and a stabilizer, the reserves, that becomes the weak point. Version 0.2 of the theory defines the runway for such an island: how long the reserves would last at the rate they are being spent, measured before, and apart from, how the island ends.
Paul Krugman's 1979 model of a currency crisis turns this into a clock. Below, the central bank starts with some reserves and loses a steady amount each month. Speculators know the peg cannot outlast the reserves, so they do not wait for the last dollar: they attack when what is left equals what can leave at once.
The two stories are proposition 3's two cases in one currency. On a clock, the peg ends by exhausting a reserve, and its age tells you how long it has left: version 0.2 names exactly this as no counterexample. At any moment, the end is memoryless, and a peg that has held for five years is as likely to fall next month as one set up last month. Real crises have mixed the two.
Real runways can be measured. The World Bank records, for most low- and middle-income countries, their reserves and their short-term foreign debt, the money that can leave within a year if lenders stop rolling it over. Reserves divided by that debt is a runway in years. The chart counts, for every year in which a currency had held within 2 percent against the dollar for two years, whether a crash followed within two years: a fall of at least a quarter of its value in a year, by Frankel and Rose's 1996 definition.
The World Bank's data give 986 years in which a currency had held within 2 percent against the dollar for two years and the country's short-term debt is recorded. Where reserves covered less than half a year of that debt, a crash followed within two years in 15 of 92 years, 16.3 percent, and where they covered two years or more, in 15 of 591, 2.5 percent. In between, 10.2 percent and 7.7 percent. Counted in months of imports, the runway shows no such gradient: 4.4 percent under three months, 2.1 percent from three to six, 3.7 percent above six.
The runway that predicts is the one measured against the outflow that threatens: for a peg, money leaving, not imports arriving. That is the definition's point, a reserve against its own net outflow, and it is an illustration, not a test. The pattern has been known to economists since the crises of the 1990s, and nothing here was fixed before looking.
A sea between rich and poor?
Over the long run, is there an island of wealth, with a sea around it that countries cross only rarely? In the 1990s Danny Quah found the world's income distribution splitting into two peaks, a rich club and a poor one. Later decades brought fast growth to many poor countries. The Maddison Project's estimates of income per person, back to 1950 for 141 countries, show what happened.
The Maddison estimates cover 141 countries in every one of the years shown. With the smoothing used here, every year has three or more peaks: in 1950 near 7, 19 and 57 percent of US income per person, in 2022 near 3, 19 and 67 percent. The band between a quarter and a half of US income held between 12 percent and 18 percent of the countries in every year. From one year shown to the next, 92 percent of countries below the band stayed below it and 94 percent of those above stayed above. Of those in the band, 66 percent were still there, 19 percent had moved up and 15 percent had fallen back.
Twelve countries crossed from below a quarter of US income per person in 1950 to above half in 2022: Singapore, Saudi Arabia, Taiwan, Oman, South Korea, Bahrain, Japan, Puerto Rico, Malta, Spain, Cyprus and Seychelles. One fell the other way: Venezuela, from 56 percent to 9.
The middle band is thinner than either side but never empty, and it holds its countries less firmly: that is a passage more than a sea. Proposition 5 says survival is decided in the crossing, not on either shore. The growth miracles made the crossing in a generation or two. Others started it and fell back. What decided each crossing, whether institutions, oil, education or luck, is what growth economists argue about, and this chart cannot say.
Cost line and fragility line
Cost line. A peg is paid for in reserves whenever money leaves, and in high interest rates when reserves run short. An expansion is paid for in credit and confidence that must keep being renewed. A rich country's place is kept by continuous investment. The oil states that crossed on oil rents hold it only while the oil flows.
Fragility line. For a peg, the runway: reserves against the money that can leave within a year. For an expansion, what builds up while it runs, which the dates alone cannot show.
How the propositions meet the economy
| Proposition | In the economy | Status |
|---|---|---|
| P1 Sparsity | Incomes cluster: countries sit mostly in three groups, and the ends keep more than nine in ten of their countries from one decade to the next. The band between is thinner, not empty. A resemblance of form. | resemblance |
| P2 The evidence rule | The Great Moderation: swings in output halved for twenty-three years, then 2008. Calm was measured, depth was not. The canonical false island among the proposition's economics precedents. | illustration |
| P3 Exit statistics | Before 1919, expansions grew more likely to end with age, and since 1945 contractions have. Postwar expansions are borderline. No depth measure, and public, well-studied dates: description. Test X1, on expansions in 42 countries and the first written against version 0.2's wording, ran after its deposit: expansions aged, short of the bar set in advance. | described, X1 unresolved |
| P4 Cost | A peg is held by a throughput, reserves spent against a drain, and in the World Bank's data a short runway, measured beforehand, was followed by crashes more often. The model shows the reserve as the weak point. Illustration: the pattern was known and nothing was fixed before looking. | illustration |
| P5 Transit | A dozen countries crossed from below a quarter of US income per person to above half since 1950, and one fell the whole way back. The middle band holds its countries less firmly than either end. | illustration |
| P6 The era ratio | The instrument is built: Hamilton's model estimates how long regimes last, shown on US output, where the high-growth regime's expected length rose several times over after 1984. Not the proposition's series, which is not named. | instrument built, series not named |
Source and method
Business-cycle dates: the NBER's Business Cycle Dating Committee, from the NBER, business_cycle_dates.json, 2,303 bytes, SHA-256 675edfab232057b6d05dc460afee504013d40d12dd206ea70bb73a79e6481551, copied with attribution, as the NBER permits. Output: US real GDP, quarterly, from the Bureau of Economic Analysis via FRED, 1947Q2 to 2026Q2, 6,527 bytes, SHA-256 519d65c05941022da119fdcbc95976d6865e94b9cc4a8248239e20d7b898e5fc, public domain. Reserves, short-term debt and exchange rates: the World Bank's World Development Indicators (updated 2026-07-13), three files of 69,340, 95,745 and 68,087 bytes, CC BY 4.0. Incomes: the Maddison Project Database 2023 (Bolt and van Zanden, 2024), in Our World in Data's copy with its minor processing, 567,429 bytes, SHA-256 3764bd2ceff342198e539a27a87ec85bc2679ed8fc40c09f430a70a21fcdf27b, CC BY 4.0. All retrieved 2026-09-29. Every file's checksum is recorded, and the code refuses any other file.
Method. Phases are counted in months from the NBER's dates. Weibull shapes are maximum-likelihood estimates with profile-likelihood intervals, the running expansion treated as censored. Growth is the quarterly change in log output. Hamilton's model is fitted with statsmodels from 18 fixed starting points, keeping the highest likelihood. A crash is a loss of at least 25 percent of a currency's value against the dollar in a year, at least 10 points more than the year before, and the first in three years (Frankel and Rose, 1996). Incomes are relative to the United States in the same year, smoothed with one Gaussian kernel for all years. All of it is description: the data are public, and nothing was fixed before looking.