Guest Post: Reinhart/Rogoff and Growth in a Time Before Debt

Apr 17, 2013Arindrajit Dube

[Mike Konczal here.  Yesterday I wrote about a paper by Thomas Herndon, Michael Ash and Robert Pollin of University of Massachusetts, Amherst. They replicated the influential Reinhart/Rogoff paper Growth in a Time of Debt. There were many responses on the internet, including Jared Bernstein, Matt YglesiasDean Baker, Paul Krugman, and many, many others. Reinhart and Rogoff have since responded with a statement. They believe that the findings do not "affects in any significant way the central message of the paper or that in our subsequent work." What is that message? That higher debt is associated with lower growth.

From the beginning many economists (Krugman, Bivens and Irons) have argued that their paper probably has the causation backwards: slow growth causes higher debt. But now that Herndon, Ash and Pollin have made the data used public, perhaps a talented econometrician could actually answer this? Arindrajit Dube was up for the challenge. Dube is an assistant professor of economics at the University of Massachusetts, Amherst.]

Growth in a Time Before Debt…

Recent work by my colleagues at UMass Thomas Herndon, Michael Ash and Robert Pollin (2013)—hereafter HAP—has demonstrated that in contrast to the apparent results in Reinhart and Rogoff (2010), there is no real discontinuity or "tipping point" around 90 percent of debt-to-GDP ratio.

In their response, Reinhart and Rogoff—hereafter RR—admit to the arithmetic mistakes, but argue that the negative correlation between debt-to-GDP ratio and growth in the corrected data still supports their original contention. Taking the Stata dataset that HAP generously made available as part of their replication exercise, I first reproduced the nonparametric graph in HAP (2013) using a lowess regression (slightly different than the specific method they used). The dotted lines are 95 percent bootstrapped confidence bands.

There is a visible negative relationship between growth and debt-to-GDP, but as HAP point out, the strength of the relationship is actually much stronger at low ratios of debt-to-GDP.  This makes us worry about the causal mechanism. After all, while a nonlinearity may be expected at high ratios due to a tipping point, the stronger negative relationship at low ratios is difficult to rationalize using a tipping point dynamic.

In their response, RR state that they were careful to distinguish between association and causality in their original research. Of course, we would only really care about this association if it likely reflects causality flowing from debt to growth (i.e. higher debt leading to lower growth, the lesson many take from RR's paper).

While it is difficult to ascertain causality from plots like this, we can leverage the time pattern of changes to gain some insight. Here is a simple question: does a high debt-to-GDP ratio better predict future growth rates, or past ones?  If the former is true, it would be consistent with the argument that higher debt levels cause growth to fall. On the other hand, if higher debt "predicts" past growth, that is a signature of reverse causality.

Below I have created similar plots by regressing current year's GDP on (1) the next 3 years' average GDP growth, and (2) last three years' average GDP growth. (My .do file is available here so anyone can make these graphs. After all, if I made an error, I'd rather know about it now.)

Figure 2:  Future and Past Growth Rates and Current Debt-to-GDP Ratio

As is evident, current period debt-to-GDP is a pretty poor predictor of future GDP growth at debt-to-GDP ratios of 30 or greater—the range where one might expect to find a tipping point dynamic.  But it does a great job predicting past growth.
 
This pattern is a telltale sign of reverse causality.  Why would this happen? Why would a fall in growth increase the debt-to-GDP ratio? One reason is just algebraic. The ratio has a numerator (debt) and denominator (GDP): any fall in GDP will mechanically boost the ratio.  Even if GDP growth doesn’t become negative, continuous growth in debt coupled with a GDP growth slowdown will also lead to a rise in the debt-to-GDP ratio.
 
Besides, there is also a less mechanical story. A recession leads to increased spending through automatic stabilizers such as unemployment insurance. And governments usually finance these using greater borrowing, as undergraduate macro-economics textbooks tell us governments should do. This is what happened in the U.S. during the past recession. For all of these reasons, we should expect reverse causality to be a problem here, and these bivariate plots are consistent with such a story.
 
Of course, these are just bivariate plots. To get the econometrics right, when looking at correlations between current period debt-to-GDP ratio and past or future GDP growth, you should also account for past or future debt-to-GDP ratio.
 
A standard way of doing this is using a "distributed lag" model - which just means regressing GDP growth on a set of leads and lags in debt to GDP ratio, and then forming an "impulse response" from, say, a hypothetical 10 point increase in the debt-to-GDP ratio (where 100 is when the debt level is equal to GDP).
 
Figure 3 below reports these impulse responses. What we find is exactly the pattern consistent with reverse causality.
 
The way to read this graph is to go from left to right. Here “-3” is 3 years before a 10 point increase in the debt-to-GDP ratio, “-2” is 2 years before the increase, etc.   The graph shows that GDP growth rates were unusually low and falling prior to the 10 point increase in the debt-to-GDP ratio.  If you average the growth differentials from the 3 years prior to the increase in debt, (i.e., the values associated with -3,-2,-1 on the X-axis), it is –0.6 (or 6/10 of a percent lower growth than usual) and statistically significant at the 5 percent level. In contrast, the average growth rates from years 1, 2 and 3+ after the 10 point increase in debt-to-GDP ratio is 0.2 (or 2/10 of one percent) higher than usual. 
 
Figure 3: Impulse Response of GDP Growth from a 10-point increase in Debt-to-Income Ratio

So what does this all show?  It shows that purely in terms of correlations, a 10 point increase in the debt-to-GDP ratio in the RR data is associated with a 6/10 of a percentage point lower growth in the 3 years prior to the increase, but actually a slightly larger than usual growth in the few years after the increase. During the year of the increase in debt-to-GDP ratio, GDP growth is really low, consistent with the algebraic effect of lower growth leading to a higher debt-to-GDP ratio.

All in all, these simple exercises suggest that the raw correlation between debt-to-GDP ratio and GDP growth probably reflects a fair amount of reverse casualty. We can’t simply use correlations like those used by RR (or ones presented here) to identify causal estimates.

[Aside:  For those who are more econometrically inclined, here is the picture with country and year fixed effects to soak up some of the heterogeneity.  Not much different. By the way, the standard errors in the panel regressions are clustered by country.]

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Addendum.
 
Labor economists have long recognized that falling values of the outcome can sometimes precede the treatment. In the job training literature this is known as an "Ashenfelter dip." Those with a fall in earnings are more likely to enter training programs, creating a spurious negative correlation between training and wages. This has similarity to the problem of debt and growth studied here.
 
One way in which economists control for such dips is by including the lagged outcome as a control.  In this case, we can control for a 1-year lagged GDP growth using a partial linear model. This still allows for a nonlinear relationship between GDP growth and debt-to-GDP ratio like in the bivariate case, but in addition controls for last period's growth.
 
Here's the picture:
Controlling for the previous year's GDP growth largely erases the negative relationship between debt-to-GDP ratio and GDP growth, especially for the range where debt is 30 percent or more of GDP.  This is because a fall in GDP precedes the rise in Debt-to-GDP ratio. This is yet another demonstration that the simple bivariate negative correlation is driven in substantial part by reverse causality.

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