In early 2013 a third-year economics PhD student at the University of Massachusetts Amherst was given a routine assignment: take a famous empirical paper and try to reproduce it. Thomas Herndon, then 28, picked the most influential macroeconomics paper of the decade. He could not make the numbers come out. He emailed the authors, and to their considerable credit they sent him their original working spreadsheet.
Inside it was a formula that stopped five rows short.
That spreadsheet belonged to Carmen Reinhart and Kenneth Rogoff, two of the most respected economists alive, and the paper was "Growth in a Time of Debt." It reported that once a country's public debt passes 90 percent of GDP, average growth turns slightly negative, minus 0.1 percent. In the years after the financial crisis, few numbers were asked to carry more political weight. It became the evidence base for a cliff: cross 90 percent and your economy falls off it.
The story usually gets told as a punchline. A typo caused austerity. It is a great story, and the interesting part is that it is wrong. The Reinhart Rogoff Excel error is real, and it is the least important thing about the affair.
The claim, and the cliff
Start with what the paper actually said. Sorted into four debt brackets, growth looked healthy up to 90 percent of GDP and then fell off a ledge.
The chart carries a detail the retellings drop. Only one of the three series ever crosses into negative territory. Reinhart and Rogoff published a mean of minus 0.1 percent for the highest bracket, and that is the number the world repeated. They also published a median for the same bracket, in the same table, of positive 1.6 percent. The corrected mean, once Herndon and his supervisors Michael Ash and Robert Pollin had rebuilt the dataset, is 2.2 percent. The median does fall, by about 1.3 points. It never falls off anything.
The 90 percent figure travelled anyway. In February 2010, weeks after the paper appeared as a working draft, the UK's shadow chancellor George Osborne told an audience that "once debt reaches more than about 90% of GDP the risks of a large negative impact on long term growth become highly significant." Paul Ryan's US budget cited the paper as its evidence on debt. The European commissioner Olli Rehn invoked the threshold as recently as six days before the critique broke.
The formula that stopped five rows short
The error itself is almost disappointingly small. In the spreadsheet, the averages were taken over cells in lines 30 to 44 when the data ran to line 49. Five rows, alphabetically ordered, silently outside the calculation: Australia, Austria, Belgium, Canada and Denmark.
Here honesty requires a correction to the popular version. Five countries were dropped, but Austria and Denmark never had a single year with debt above 90 percent of GDP, so their absence could not move the high-debt average by anything at all. Only three of the five mattered. And the one that mattered most was Belgium, which spent 25 years above 90 percent debt while growing at 2.6 percent a year.
No single error did it
So how much did the missing rows actually change the answer? Herndon, Ash and Pollin did the decent thing and published the arithmetic, running every combination of the problems they found so that readers could see each one's contribution separately.
This is the chart the punchline version leaves out. Correctly calculated, growth above 90 percent debt is 2.2 percent. Fix everything except the spreadsheet error and you get 1.9 percent. The famous Excel mistake, on its own, is worth about three tenths of a percentage point out of a gap of 2.3. It never came close to turning a positive number negative.
The top four bars make the point. Each of the three problems, taken alone, lands in the same place, at 1.9 percent. None of them individually does real damage. The collapse happens only when two of them combine: exclude certain years and also weight the countries the way the paper did, and the figure falls from 2.2 percent to 0.3. All three together reach zero. A fourth slip, a transcription error that moved New Zealand's average from minus 7.6 to minus 7.9, takes it the last step to the published minus 0.1. In Herndon, Ash and Pollin's own summary, the exclusions and the weighting account for almost 2 percentage points between them, and the spreadsheet and transcription errors for about 0.4.
Two judgement calls, and the trap between them
If the typo was not the culprit, what was? Mostly an unglamorous decision about arithmetic. Reinhart and Rogoff gave each country equal weight in the average, regardless of how long it spent carrying high debt. The alternative, weighting by country-year, gives a country with two decades of high-debt experience more say than one with a single year. Put the two schemes side by side in the chart below, country by country, and the cost of the choice becomes legible.
Belgium, with its 25 high-debt years, should carry 22.7 percent of the answer. Through the combination of the coding error and the method, it carried none. New Zealand, meanwhile, had its 1946 to 1949 observations excluded, which left it contributing exactly one year to the high-debt category: 1951, a bad year, at minus 7.6 percent. Under equal-country weighting, that single year then carried one seventh of the entire average. One country-year of New Zealand data outweighed a quarter-century of Belgium.
Restored to the full sample, the picture at high debt is unremarkable.
Nine of the ten countries that carried debt above 90 percent of GDP kept growing while they did. Only the United States is negative, and its four high-debt years are the ones immediately after 1945, when wartime output was unwinding.
What the authors said
Reinhart and Rogoff conceded the coding error immediately and without hedging, and published a formal errata a few weeks later. Their own recalculation is worth seeing, because it approaches the same question from the opposite direction.
By their arithmetic, correcting the coding error alone moves the high-debt mean from minus 0.1 to positive 0.3, a shift of four tenths of a point. Herndon, Ash and Pollin, working from the other end, put the spreadsheet and transcription slips together at the same 0.4. Two teams who disagreed about almost everything else landed on the same magnitude for the spreadsheet.
Follow their table to the end and the gap all but closes. With every correction applied, Reinhart and Rogoff's own high-debt mean comes out at 1.0 percent using the Maddison New Zealand series, or 2.0 percent using New Zealand Historical Statistics, against the critics' 2.2. What separates the two camps at that point is which New Zealand data you accept and whether you weight by country or by country-year. Their medians never go near zero at any stage.
They disputed the rest. They argued their weighting choice was defensible rather than an error, and they had never claimed that debt causes slow growth, only that the two go together. On that last point the record supports them: the paper's language is associational throughout, and it explicitly wondered why a threshold might exist rather than asserting a mechanism.
The deeper objection was never about the spreadsheet at all. Slow growth raises a debt-to-GDP ratio by itself, through the denominator, so an association between high debt and weak growth is roughly what you would expect even if debt did nothing to growth. Paul Krugman and others had pressed that point years before anyone opened the workbook. It is the criticism that still stands, and it is the one the typo story buried.
Did a spreadsheet cause austerity?
This is where the viral version overreaches, and where the evidence points the other way. David Cameron's "age of austerity" speech came in April 2009, nine months before the paper existed. When the error surfaced, Olli Rehn responded that the European Commission's recommendations "are not based on any single piece of research." British public opinion did not decisively turn against austerity until around 2018, five years after the number had been publicly demolished. If the policy had truly rested on this paper, knocking the paper down should have knocked the policy down with it. It did not.
The honest reading is that the 90 percent figure was used as ammunition rather than as a foundation. It arrived at a moment when governments had already chosen a direction and were looking for authority, and a crisp number from two of the best-known economists in the field was exactly the authority available.
As for the cliff itself, later work has been fairly consistent. An IMF study found that an apparent threshold shows up over a one-year horizon and then dissolves over five, ten and fifteen years. Eberhardt and Presbitero tested cutoffs at 52, 75 and 90 percent across 105 countries and found the change at each one statistically insignificant. What survives is milder and less quotable: high debt is associated with somewhat slower and more volatile growth, with no magic number where the floor gives way.
The base rate
Underneath the economics is a plainer fact. A spreadsheet that shaped a decade of public argument had a range error in it, and nobody noticed for three years, because nobody looked. Nobody looking is the ordinary state of a spreadsheet.
When auditors have gone looking through real operational spreadsheets, they have found errors in the large majority of them. Panko's pooled figures are 84 percent across 163 spreadsheets and 91 percent across the 55 in his best-methodology set, and the individual audits in the chart run from 11 and 21 percent at the weakest-detection end all the way to 100 percent. The sample sizes are small, so treat the exact percentages loosely. The direction is not in doubt. Worse, review does not save you: a solo checker catches around half of the errors present and a careful team inspection around 80 percent, so roughly one in five survives. Typos in short formulas get caught about nine times out of ten. Logic and omission errors, the kind where a formula simply stops five rows early, get caught far less often. Reinhart and Rogoff made precisely the kind of mistake that review is worst at finding.
In 2020, Public Health England lost 15,841 COVID cases because it was moving contact-tracing data through a legacy file format capped at 65,536 rows, and thousands of contacts went unwarned. In 2022, the UK Ministry of Defence emailed a spreadsheet believed to contain about 150 names that actually held the details of 18,714 Afghan applicants. A flawed financial model forced the Department for Transport to cancel a 9 billion pound rail franchise competition, at a confirmed cost of around 40 million pounds in refunded bid costs. Each one is a small mechanical slip with consequences nobody would have accepted if they had been asked in advance.
What actually went wrong
The satisfying version of this story is that a typo caused austerity, and it is not true. The coding error was minor, the authors owned it, and the policy had its own momentum. What is true is duller and more unsettling: the most consequential economic claim of its decade rested on a working spreadsheet that no one had audited, where two ordinary judgement calls compounded until they had erased almost all of a 2.2 percent average, and a range error plus a mis-copied digit carried what was left across zero. It took a graduate student asking for the file to find out. The tool that produces most working analysis has no version control, no test suite, and nobody whose job it is to check. That is not a scandal about two economists. It is the ordinary condition in which important numbers are made.
References
- Herndon, Ash & Pollin (PERI / Cambridge Journal of Economics). Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff. The corrected 2.2 percent figure, the full error decomposition, the country weights, and the formula that averaged rows 30 to 44 instead of 30 to 49.
- Reinhart & Rogoff (NBER). Growth in a Time of Debt (Working Paper 15639, 2010). The original paper, its published mean of minus 0.1 percent and median of 1.6 percent above 90 percent debt, and its associational language.
- Reinhart & Rogoff. Errata, 5 May 2013. The authors' own recalculation showing the coding error alone moves the high-debt mean from minus 0.1 to 0.3 percent.
- International Monetary Fund (Pescatori, Sandri & Simon). Debt and Growth: Is There a Magic Threshold? (WP 14/34). The apparent debt threshold that dissolves at five, ten and fifteen year horizons.
- Eberhardt & Presbitero (Journal of International Economics). Public debt and growth: Heterogeneity and non-linearity. Finds no statistically significant coefficient change at candidate debt thresholds.
- Raymond Panko (EuSpRIG). Spreadsheet Errors: What We Know. What We Think We Can Do.. Field-audit error rates, inspection detection rates, and the gap between what spreadsheet developers believe and what they do.
- European Spreadsheet Risks Interest Group. Spreadsheet horror stories. The standing index of documented spreadsheet failures; each incident in the article's table was additionally checked against its own press or primary source.
- Wikipedia (with primary policy sources). Growth in a Time of Debt. The paper's use by Osborne, Ryan and Rehn, and the timeline of the April 2013 controversy.
- Conservative Party speech archive. George Osborne, Mais Lecture, 24 February 2010. The "once debt reaches more than about 90% of GDP" passage in full.
- Retraction Watch. Influential Reinhart-Rogoff economics paper suffers spreadsheet error. The contemporaneous account of how the error surfaced in April 2013.
- The Conversation. The Reinhart-Rogoff error, or how not to Excel at economics. Background on Herndon's replication assignment and the public reaction.
- Digital Health. How using Excel may have caused thousands of unreported Covid cases (2020). The 15,841 cases lost between 25 September and 2 October to a legacy XLS file capped at 65,536 rows.
- Wikipedia. United Kingdom government austerity programme. The chronology behind Cameron's April 2009 "age of austerity" speech and the later turn in public opinion.
