### Why Did Reinhart-Rogoff Become Such an Influential Paper?

**Matthew Martin**4/19/2013 06:44:00 PM

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Don Taylor's take on the R&R disaster reminded me of something I wanted to say about the paper. Taylor confesses:

"When asked at myriad speeches, presentations and the like the past 3 years how much debt:GDP is too much, I have many times said something like “no one knows for sure, but when you are getting around 100% of public debt:GDP you will harm economic growth.” This diddy was based largely on an influential paper by Carmen Rinehart and Kenneth Rogoff "I think that gets at the heart of why R&R was so influential. Rather than expend the mental energy required to go through cost-benefit analysis of how much to spend, when to spend it, and how and how much to tax, R&R provided us with a rule of thumb to use instead--keep debt to less than 90% of GDP--that appealed to the intellectual laziness that, let's be honest, we are all guilty of from time to time.

Strictly speaking, if you are following a rule of thumb, then you are almost certainly not optimizing. Optimizing requires an assessment of all the specifics of each case individually, not a one-size-fits-all rule applied indiscriminately. Even if debt does hurt growth, which R&R did not prove, you still have to do a cost-benefit calculus before deciding what the optimal debt level should be.

I'm not sure that it was originally R&R's intent for the 90% threshold to be interpreted as a structural break or point-of-no-return. When I skimmed the paper when it first made news, I interpreted them as using 90% as an arbitrary threshold around which to estimate the local, rather than average, correlation between debt and growth. Why would you want to estimate the correlation like that? I'll explain in a graph:

Suppose the red line is the relationship between debt and GDP we observe in the data (note, I'm not claiming this is a causal relationship). We can interpret the correlation between debt and GDP as being the slope (also called first derivative) of the red line. If we simply pool the data and compute a correlation, what we get is a weighted average slope of the red line, which corresponds to the slope of the green line in the data--but, this correlation is weighted by the distribution of our data, which consists mostly of much lower levels of debt than we have currently. Thus, the object R&R wanted was not this average correlation, but rather the specific slope of the red line at debt levels close to what the US currently has, around 90% of GDP. Their methods, had there been no excel errors and weighting problems, would have done exactly that, and given us the slope of the blue line.

In that regard, the R&R paper would have made a slight contribution to the debate, since had they done the computation correctly, they would have shown that the correlation between debt and GDP growth is slightly worse at current levels of debt than in normal times. That says nothing about whether increasing debt further causes GDP growth to fall, so pundits like Krugman and Yglesias were right to question its relevance to the debate. But as long as we are talking about correlations, might as well use the right one, right?

*(*

**Update**: I fell for a misrepresentation R&R made in their rebuttal--it turns out that if you correct their mistakes, the difference is no longer statistically significant. That means it isn't even correct for them to argue correlation, let alone causation.)Anyway, that was how I read the paper, and I think that's what R&R originally intended. But the austerians took it and ran with it, and Reinhart and Rogoff unfortunately mistook their personal credibility as evidence that the causal claim was credible. Bad mistake. Very, very bad mistake.