# The Most Costly Excel Error Ever?

Efficient computing tools are essential for statistical research, consulting, and teaching. Generic packages such as Excel are not sufficient even for the teaching of statistics, let alone for research and consulting (ASA, 2000).

### Introduction

Back early in 2009 we published a post on the risk of spreadsheet errors. The reference above is taken from that post, but it seems even more relevant today as show in the following.

### Growth in a Time of Debt

**In 2010**, economists Reinhart and Rogoff released a paper, “Growth in a Time of Debt.” Their “main result was:

- Average growth rates for countries with public debt over 90% of GDP are roughly 4% lower than when debt is low (under 30% of GDP).
- Median growth rates for countries with public debt over 90% of GDP are roughly 2.6% lower than the when debt is low (under 30% of GDP).
- Countries with debt-to-GDP ratios above 90 percent have a slightly negative average growth rate (-0.1%).

The paper has been widely cited by political figures around the world, arguing the case for reduced government spending and increased taxes and ultimately against government efforts to boost the economy and create jobs. All based on the papers conclusion that any short-term benefit in job creation and increased growth would come with a high long-term cost.

**Then in 2013**, Herndon, Ash and Pollin (Herndon et. al., 2013) replicated the Reinhart and Rogoff study and found that it had:

- Coding errors in the spreadsheet programming,
- Selective exclusion of available data, and
- Unconventional weighting of summary statistics.

All this led to serious errors that inaccurately estimated the relationship between public debt and GDP growth among 20 advanced economies in the post-war period. Instead they found that when properly calculated:

That the average real GDP growth rate for countries carrying a public-debt-to-GDP ratio of over 90 percent is actually 2.2 percent, not -0:1 percent as published in Reinhart and Rogoff.

That is, contrary to the Reinhart and Rogoff study – average GDP growth at public debt/GDP ratios over 90 percent is not dramatically different than when debt/GDP ratios are lower.

### Statistics and the use of Excel

Even if the coding error only accounted for a small part of the total error, “everyone” knows that excel is error-prone in a way that any programming language or statistical package is not; it mixes data and code and makes you do things by hand that would be automatically done in the other settings.

Excel is good for ad-hoc calculations where you’re not really sure what you’re looking for, or for a first quick look at the data, but once you really start analyzing a dataset, you’re better off using almost anything else.

Basing important decisions on excel models or excel analysis only is very risky – unless it has been thoroughly audited and great effort has been taken to ensure that the calculations are coherent and consistent.

One thing is certain, serious problems demands serious tools. Maybe it is time to reread the American Statistical Association (ASA) endorsement of “Guidelines for Programs and Departments in Undergraduate Mathematical Sciences”

### References

Herndon, T., Ash, M. and Pollin, R. (April 15, 2013). Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff, PERI, University of Massachusetts, Amherst. http://www.peri.umass.edu/fileadmin/pdf/working_papers/working_papers_301-350/WP322.pdf

American Statistical Association (ASA) (2000). Endorsement of the Mathematical Association of America (MAA): “Guidelines for Programs and Departments in Undergraduate Mathematical Sciences” http://www07.homepage.villanova.edu/michael.posner/sigmaastated/ASAendorsement2.html

Baker, D. (16 April 2013) How much unemployment did Reinhart and Rogoff’s arithmetic mistake cause? The Guardian. http://www.guardian.co.uk/commentisfree/2013/apr/16/unemployment-reinhart-rogoff-arithmetic-cause

Reinhart, C.M. & Rogoff, K.S., (2010). Growth in a time of Debt, Working Paper 15639 National Bureau of Economic Research, Cambridge. http://www.nber.org/papers/w15639.pdf

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