Further insights on the Reinhart & Rogoff Research Controversy

James Hamilton at Econbrowser has written a nice summary of the major difference in opinion between the UMass students who challenged the Reinhart & Rogoff paper "Growth in a Time of Debt".   Simply put, if you have a handful of nations that persistently run debt > .9GDP, they will make up a large proportion of the sample.  How to weight them?  Do you weight the sample by incident or by nation?  The students argue by incident;  Reinhart - Rogoff did it by nation.   Is that clear?  Maybe using specific nations will help (quoting Hamilton):


"Now let's take a look at the details by which [the UMass students] come to their numbers. First, they found a dumb error in Reinhart and Rogoff's spreadsheet-- Reinhart and Rogoff left the first 5 countries in the alphabet (Australia, Austria, Belgium, Canada, and Denmark) out of the set of cells selected for averaging. This is a numbskull error, but it turns out it would only have changed the estimate they reported by a few tenths of a percent.

"The major differences come from a difference of opinion about how one should summarize the mean for these data. For example, the U.S. spent 4 years in this sample with debt levels above 90% of GDP, while Greece spent 19 years. How should we combine these two sets of observations?

"One view one could take is that the expected growth rate when a country has a high debt level is a single number across all countries, that is, you expect the real growth rate for Greece when its debt is 90% to be exactly the same number as the real growth rate expected for the U.S. when its debt is 90%. ... the correct thing to do would be to act as if you have 19 observations ... from Greece and 4 observations from the U.S., and take a simple average of those 23 numbers. In other words, you should base most of your inference on the data from Greece, because that is where you have the most observations. This is the approach that [the UMass students] insist is the correct one to use.

"Another view you could take is that the expected growth rates for the U.S. and Greece would be different even if the two countries had the same debt levels. From that perspective, there is a different expected growth rate for each particular country when it gets to the 90% debt level, and our goal is to estimate what that number is for a typical country. That view seems to underlie the method chosen by Reinhart and Rogoff, which was to estimate an average growth rate when debt is greater than 90% for the U.S., a separate average growth rate when debt is greater than 90% for Greece, and then take the average of those averages across different countries."

Seems like a pretty obvious choice to me.

Reinhart & Rogoff's Thesis that High Debt Levels Retard Economic Growth Appear to be Confirmed by Revised Calculations

All over the business and financial media the past 24 hours, and apparently in economics blogs prior to that, there have been stories about a new paper published by three University of Massachusetts (Amherst) economists who found errors in a 2010 paper by Carmen Reinhart and Kenneth Rogoff which supported a thesis that, once a nation's public debt exceeded 90% of GDP, its economy tends to stall.  The R&R paper has been cited as justification for opposing Keynesian-style deficit spending over the past few years, providing evidence that the Keynesian approach won't stimulate the economy as its proponents expect when implemented by a country that is already highly indebted. 

The UMass paper found three errors in the composition and calculation of data behind R&R's 2010 paper that depressed the growth rates of the nations in their study.   R&R  responded and acknowledged the errors, while pointing out that in subsequent papers, they had updated and expanded their analyses. They  also point out that the UMass paper, while deriving different specific numbers, does in fact prove that growth declines as debt increases, so it may  not really support a different bottom line.  This Business Insider link contains their response and a fair summary of the errors found by the UMass researchers.  The New York Times also had a well thought out article on it, albeit with very little in the way of numbers.

The table below, which I've simplified from one prepared by R&R, summarizes the differences between their 2010 study and the UMass corrections.

Debt / GDP ratio	Mean GDP growth, per R&R	Mean GDP growth, per UMass
0 - 30	4.1	4.2
30 - 60	2.8	3.1
60 - 90	2.8	3.2
> 90	-0.1	2.2

Proponents of aggressive government spending are euphoric over the difference that the corrections make at the ">90% debt / GDP " level.  They engage  in the sophomoric chain of reasoning that "a part of your argument has an error; therefore your argument fails entirely; therefore, my argument, opposite to yours, is correct".  That is obviously fallacious, like arguing that, if it can be shown that a mapmaker who drew a map showing the world was round made an error about the size of the Pacific Ocean, the world is in fact flat. 

First, it's clear that the UMass study confirms that increased debt is correlated with slower growth.  There may not be a clear tipping point at 90%, but the trend is unmistakable.  It's argued in response that this doesn't prove causation.  I find that response a little superficial.  Two variables have a correlation.  You can control one of them.  So you should control it in the manner that gives you the better result if the correlation holds.   

Second, and more important from a policy perspective,  the UMass paper shows something very important.  It's very unlikely that a government with a 90% or greater debt / GDP ratio can service that out of a 2.2% growth rate. First, interest has to be paid on all of that debt.  Second,  governments do not have a 100% marginal tax rate; they can only capture some of that growth and apply  it to debt service. Third, a government that has run up a 90% debt / GDP ratio is likely not to be in fiscal balance, but rather is likely running annual deficits that are going to ensure the ratio keeps rising.

 

For example, let's imagine a realistic environment in which real GDP growth of 2.2%  -  the rate calculated by the UMass paper -  might arise,  and see whether it suffices to service the corresponding 90% debt level.    Real GDP growth of 2.2% will arise if, for instance, nominal growth is at 5% and the deflator is 2.8%;  those numbers are reasonably similar to the numbers the US economy has thrown off over the past decade or so when it was functioning normally.  Next, plug in a nominal interest rate  -  say 3%  -  for that government debt at 90% of GDP, and you need 2.7% of GDP just for interest.   Further, let's say the government runs a primary fiscal deficit of 3% of GDP (actually less than what the US federal government has been running recently), so now you need 5.71% of GDP to cover the sum of interest plus deficit spending.  Then, specify the rate at which that government extracts taxes from the economy - say 20% % of GDP, if you want to mirror what the federal government historically tends to extract.   20% of the 5% nominal GDP growth is 1.0%; that's how much new revenue is extracted by the government, so the net increase in federal debt over the year is 4.71%.  Now GDP rose 5%, so the debt balance for that nation grows to 94.71/ 105 or 90.2% of GDP as of year end. Repeat for a few years and you see the hole gets bigger every year through compounding.   Were one to specify tax rates at a Eurozone-like 40% of GDP, you would get a slight decrease in the ratio, assuming the economy grew at nominal 5%.   At nominal 4%, however, the debt / GDP ratio would continue to climb; of course, the Eurozone isn't growing at a 4 or 5% either.  

The UMass paper confirms that high government debt is not sustainable under normal, realistic assumptions.  Eventually the sovereign has to default.  Alternative to a formal default, it can pursue some combination of  (1) inflation to goose up the tax base, (2)  financial repression to keep the sovereign's interest rates down below the rate of inflation, (3)  confiscation of private savings, which are outside of GDP, or (4) higher taxes on GDP, which are likely to stunt the growth rate further. Those are distorting policies and problematic over the long run.  There is one more solution - cut back on other components of government spending to free up money for debt service, or so-called austerity. 

 

It may be fallacious to infer that, once a nation reaches the 90% threshold, austerity will produce growth.  Please do not infer that that is my view. Rather, it may be the case that a high debt burden simply eliminates any chance for growth  under any policy and the right policy is to avoid getting into a high debt position in the first place.  But once a nation gets itself into the debt trap, austerity is likely a necessary part of returning an economy to a healthier condition, if not sufficient by itself. Austerity is just part of the restructuring, part of the default.  And certainly and most importantly, the UMass corrections of Reinhart and Rogoff give no comfort whatsoever that a debt-financed Keynesian stimulus at high debt levels would render the public debt any more serviceable.