*[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 Yglesias, Dean 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.*

*F**rom 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**

**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.]

*Follow or contact the Rortybomb blog:*

*[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 Yglesias, Dean 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.*

*F**rom 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**

**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.]

*Follow or contact the Rortybomb blog:*