Reinhart and Rogoff’s defense is misleading and here’s why

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Economics calls itself a “science”, but it’s pretty much always a political proxy war. Which helps explain the bone-crunching social media pile-on that Harvard economists Ken Rogoff and Carmen Reinhart received in recent days after some other researchers questioned their influential findings that high government debt is a drag on economic growth.

The source of those questions was a paper by University of Massachusetts economists Thomas Herndon, Michael Ash and Robert Pollin, hereinafter HAP. And today Reinhart and Rogoff (R+R) issued a pretty stark acknowledgement of errors  that was remarkable for its candor.

For instance: “Herndon, Ash and Pollin accurately point out the coding error that omits several countries from the averages in figure 2. Full stop. HAP are on point.” In the world of economics, that’s about as straightforward a mea culpa as you get. (Check out this post for a full list of the links on the affair.)

But while admitting this mistake, R+R contend that their conclusion of slower economic growth for high-debt countries still holds up if you look at other metrics. They also suggest that HAP reach the same conclusion, namely that countries with debt-to-GDP ratios over 90% will have slower growth:

Do Herndon et al. get dramatically different results on the relatively short post war sample they focus on? Not really. They, too, find lower growth associated with periods when debt is over 90% (they find 0-30 debt/GDP , 4.2% growth; 30-60, 3.1 %; 60-90, 3.2%,; over 90, 2.2%. Put differently, growth at high debt levels is a little more than half of the growth rate at the lowest levels of debt.

R+R go on to argue that while the above differences in GDP growth may not look like very much, they add up:

It is very misleading to think of 1% growth differences without recognizing that the typical high debt episode lasts well over a decade (23 years on average in the full sample.) … It is utterly misleading to speak of a 1% growth differential that lasts 10-25 years as small. If a country grows at 1% below trend for 23 years, output will be roughly 25% below trend at the end of the period, with massive cumulative effects.

But those statements are pretty misleading themselves. That’s because HAP’s key point isn’t that the decline from 3.2% growth to 2.2% growth for countries over 90% debt-to-GDP is small. It isn’t small. If your country grew at 1% less a year, it would indeed, as R+R say, be a good deal poorer two decades hence.

No, HAP’s point is that 1% is statistically insignificant. That, given the statistical margins of error that arise when you do a calculation like this with a limited set of data, “[d]ifferences in average GDP growth in the categories 30-60 percent, 60-90 percent, and 90-120 percent cannot be statistically distinguished.”

If that’s true, you can’t even really speak of a 1% growth difference for high and low debt countries. Why? Because statistically speaking there is not enough evidence to suggest it really exists, even with average growth data that the economists collected.

Think about it in terms of public opinion polling during election season. A typical opinion poll canvasses about 1,000 people. The “margin of error” for asking that many people if they’ll vote for person A or person B is about 3% either way. So if person A polls 51% and person B polls 49%, person A’s lead isn’t statistically significant. There’s no confidence that person A will actually win when all the votes are counted.

In other words, R+R seem to be claiming that even though their lead shrank considerably after redoing the math—so much so that it now falls within the margin of error—they’re still clearly in the lead. But statistically speaking, according to the new paper, that’s just not true.