Saturday, May 4, 2013

Is There a Debt/GDP Threshold at 90 Percent? (Part 1)

In January of 2010, Harvard economists Carmen M. Reinhart and Kenneth S. Rogoff released an NBER working paper titled "Growth in a Time of Debt". The paper's abstract states:

Our analysis is based on new data on forty-four countries spanning about two hundred years. The dataset incorporates over 3,700 annual observations covering a wide range of political systems, institutions, exchange rate arrangements, and historic circumstances. Our main findings are: First, the relationship between government debt and real GDP growth is weak for debt/GDP ratios below a threshold of 90 percent of GDP. Above 90 percent, median growth rates fall by one percent, and average growth falls considerably more.

This 90 percent threshold was cited by a number of public figures. For example, Paul Ryan stated the following on page 80 of the House Fiscal Year 2013 Budget Resolution titled "The Path to Prosperity: A Blueprint for American Renewal".

Even if high debt did not cause a crisis, the nation would be in for a long and grinding period of economic decline. A well-known study completed by economists Ken Rogoff and Carmen Reinhart confirms this common-sense conclusion. The study found conclusive empirical evidence that gross debt (meaning all debt that a government owes, including debt held in government trust funds) exceeding 90 percent of the economy has a significant negative effect on economic growth.

As another example, a Washington Post editorial stated the following:

The CBPP analysis assumes steady economic growth and no war. If that’s even slightly off, debt-to-GDP could keep rising — and stick dangerously near the 90 percent mark that economists regard as a threat to sustainable economic growth.

A number of other positive references to the 90 percent threshold are mentioned in this article. However, there were some criticisms of this 90 percent threshold as in this article from the Economic Policy Institute.

In any case, a very interesting thing happened in April of 2013, over three years after the Reinhart and Rogoff paper was released. The event is described in Planet Money podcast titled "Episode 452: How Much Should We Trust Economics?". The following is from a summary of the show:

Reinhart and Rogoff looked at what had happened in many different countries over many years. And they found a what looked like a clear debt threshold: 90 percent. Average growth was much, much slower in countries with debt-to-gdp ratios over 90 percent.

The paper got a lot of coverage in the press. Politicians cited it in the U.S. and Europe.

Then, this week, a 28-year-old grad student and his professors published a startling finding: Reinhart and Rogoff [hereafter called RR] had made a simple Excel error in one part of their study. The authors of the new critique also questioned other elements of the study and argued that, in fact, there is no debt threshold.

The new critique was published by Herndon, Ash and Pollin (hereafter called HAP) and is titled "Does High Public Debt Consistently Stifle Economic Growth? A Critique of Reinhart and Rogoff". The error that was most widely reported was the simple Excel error, shown in the following image:

Rogoff and Rinehart Excel error

As seen, the formula for cell L51 is given as AVERAGE(L30:L44), the cells within the blue box. In fact, the formula should have been AVERAGE(L30:L49). This mistake served to omit the data for Denmark, Canada, Belgium, Austria, and Australia. In the case of column L, only the Belgium omission mattered since the other four omitted countries did not have data for that column. However, the same mistake was made in columns I, J, and K which did contain data for those other four countries.

However, the HAP critique pointed out two other issues. One was data exclusion which it described as follows:

More significant are RR's data exclusions with three other countries: Australia (1946-1950), New Zealand (1946-1949), and Canada (1946-1950). The exclusions for New Zealand are of particular significance. This is because all four of the excluded years were in the highest, 90 percent and above, public debt/GDP category. Real GDP growth rates in those years were 7.7, 11.9, -9.9, and 10.8 percent. After the exclusion of these years, New Zealand contributes only one year to the highest public debt/GDP category, 1951, with a real GDP growth rate of -7.6 percent. The exclusion of the missing years is alone responsible for a reduction of -0.3 percentage points of estimated real GDP growth in the highest public debt/GDP category. Further, RR's unconventional weighting method that we describe below amplifies the effect of the exclusion of years for New Zealand so that it has a very large effect on the RR results.

The other was the unconventional weighting method mentioned at the end of the above excerpt. As an example, Great Britain had 19 postwar years (1946 to 1964) when it's debt to GDP was above 90 percent and the average growth in real GDP over this period was 2.4 percent. According to RR, however, New Zealand had just one year above 90 percent (1951) and the growth in real GDP for that year was -7.6 percent. RR give the -7.6 percent the same weight as Great Britain's 2.4 percent despite the fact that the former is for one year and the latter is for 19 years. HAP, on the other hand, gives the latter 19 times as much weight as the former.

In an April 25th New York Times editorial, RR responded to these criticisms, saying the following:

Last week, three economists at the University of Massachusetts, Amherst, released a paper criticizing our findings. They correctly identified a spreadsheet coding error that led us to miscalculate the growth rates of highly indebted countries since World War II. But they also accused us of “serious errors” stemming from “selective exclusion” of relevant data and “unconventional weighting” of statistics — charges that we vehemently dispute. (In an online-only appendix accompanying this essay, we explain the methodological and technical issues that are in dispute.)

In an April 29th New York Times editorial, Pollin and Ash responded, saying:

(Ms. Reinhart and Mr. Rogoff have substantial disagreements with us about the proper selection and weighting of data. They elaborated on these points in their Op-Ed appendix. We have presented all our data, calculations and methodological arguments on the Web site of the Political Economy Research Institute at the University of Massachusetts, Amherst, where we teach.)

The given Web site points to a page for the HAP critique which points to a zip file containing "Data and code files upon which the results are based". This zip file contains an Excel spreadsheet named RR.xls which contains all of the data on which the HAP critique is based, including the original RR data. I added three tabs labeled A, B, and C to the beginning of this spreadsheet on which I used this data to examine the HAP criticisms. I have posted that spreadsheet at and will refer to it in the following post.

Is There a Debt/GDP Threshold at 90 Percent? (Part 2)

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About Me

I became interested in U.S. budget and economic matters back in 1992, the first time that I remember the debt becoming a major issue in a presidential election. Along with this blog, I have a website on the subject at I have blogged further about my motivations for creating this blog and website at this link. Recently, I've been working on replicating studies such as the analysis at this link.

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