Opinion

# Felix Salmon

## Chart of the day, reverse-causality edition

April 18, 2013

This chart comes from Arindrajit Dube, who has a fantastic post chez Rortybomb on whether high debt causes lower growth or whether it’s the other way around. What you’re looking at is the famous Reinhart-Rogoff dataset, as made available by their critics (and Dube’s colleagues), Herndon, Ash and Pollin. Reinhart and Rogoff are the poster children for the statement that high debt loads cause lower growth, especially once those debt loads exceed 90%. But do they?

There does seem to be an inverse correlation between debt and growth, but Dube shows that the correlation is strongest at low levels of debt, below 30% of GDP, rather than at high levels of debt. Countries with debt of 30% of GDP have a significantly lower growth rate, on average, than countries with debt of 10% of GDP, while the numbers at debt ratios above 90% have much wider error bars and are much less useful.

But let’s grand the correlation, for the sake of argument: the next question is whether the correlation implies causation, and if so, which way the causation flows. Here’s Dube:

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.

That’s what you’re seeing in the charts. Both of them have the same axes: GDP growth on the y-axis, and debt/GDP on the x-axis. Both of them plot the correlations in the dataset, with the dark line being the signal and the dotted lines showing the 95% confidence interval. And just as in the main dataset, the correlations are much clearer at low levels of debt/GDP than they are at higher levels.

But the two charts are different, all the same, especially at levels of debt/GDP above that 90% level. If you look at the left-hand chart, it shows that it really doesn’t matter how much debt you have: you’re likely to average about 3% GDP growth a year over the next three years. On the other hand, if you look at the right-hand chart, it shows that the more debt you have, you’re significantly more likely to have experienced low growth in the past three years.

In other words, the causation here seems about as clear as causal analysis can ever be: low growth causes high debt, rather than high debt causing low growth. Indeed, once you get past 90% of GDP, your debt load doesn’t seem to have any significant effect on future growth at all!

RE: Left graph

The confidence interval blowing up a high debt/gdp probably has to do with the fact that there are so few data points up there in the R-R dataset. It doesn’t mean there isn’t a correlation at high levels, just that we can’t say for sure because there’s simply no data on which to draw inference.

I drew a histogram of the distribution of the Debt/GDP variable in the R-R dataset: https://dl.dropboxusercontent.com/u/4002 8/rr_debtgdp.jpg

Posted by VincentMI | Report as abusive

Sorry, but that is a bit of a “no-brainer” really. In layman’s terms, the size of your mortgage is pretty illiquid and static; the same is not true of your salary. Same pretty much with an economy, only using ‘Debt’ and ‘GDP’.

Nice find Felix.

Posted by FifthDecade | Report as abusive

There isn’t a finance person worth his or her salt who wouldn’t be able to figure that out.

If you borrow too little, you can’t find enough projects worth the investment. That may be because (a) everyone has access and no one has desire or (b) a constricted peerage has access and is at their capacity or some combination thereof, but in any of those cases, growth will be suboptimal. (The sign is clear; the magnitude is worth checking.)

As you expand access to capital, you will get more growth on average. (You will also have more investments that don’t return better than their expected RoE; this is a side effect of “creative destruction”–a feature, not a bug.)

I believe this is what DeLong et al. mean when they refer to an “equity premium” (though I will stipulated that the original Mehra-Prescott paper’s definition varies).

If your credit markets are fully available but still prudent, periods of “excessive” borrowing–borrowing to enter new markets, for instance, in a non-closed economy–now fall into the Law of Large Numbers.

All of the above is intuitive if you’re not innumerate or convinced this is already the Best of All Possible Worlds (i.e., using a Ramsey model).

It’s why R&R’s “90% is a cliff! A cliff I say!” never made sense to anyone who looked at Japan’s demographics and its actual growth in the late 1990s and early Naughties. For such an “old” population, they didn’t underperform expectations by much, despite being well beyond the 90% Pale (Horse).

Posted by klhoughton | Report as abusive

The 800 pound gorilla in this room is Europe. If debt to GDP ratios don’t matter then why is Europe experiencing a near depression is not an actual depression?

Posted by thesafesrufer | Report as abusive

“If debt to GDP ratios don’t matter then why is Europe experiencing a near depression is not an actual depression?”

Oh, come on, are you seriously that ignorant, or are you just a troll? This has been talked about ad nauseam by Felix, Paul Krugman, and numerous other econ-bloggers. (1) Europe’s periphery, thanks to years of capital inflows, has costs that are out of whack with its importers; (2) The periphery can’t adjust via currency depreciation like Iceland has, because they’re on the Euro; (3) The ECB won’t tolerate higher average inflation (say, tolerating a 5-6% inflation rate in Germany for a few years, while the periphery’s costs and wages stay constant); (4) Even the core countries are running austerity policies.

When every player in your economy cuts spending simultaneously, you get a depression. This is Macro 101 stuff.

Posted by Auros | Report as abusive

Also, it’s worth remembering that Spain came into the crisis with relatively low debt, and a surplus in their gov’t budget. To believe that gov’t debt caused the EZ crisis, you have to be both stupid AND blind.

Posted by Auros | Report as abusive

Weren’t Reinhard and Rogoff talking about long-term growth (~20 years)?

3-year forward growth seems a red herring.

Posted by WCVarones | Report as abusive

“The 800 pound gorilla in this room is Europe. If debt to GDP ratios don’t matter then why is Europe experiencing a near depression is not an actual depression?”

Also maybe because Europe, unlike the U.S., actually tried implementing austerity?

Nobody is arguing that debt to GDP ratios don’t matter. Reinhart and Rogoff make a very specific and very strong claim (not in the paper itself, but in their op-eds and talks with Congress citing the paper) that there is a tipping point where debt higher than 90% of GDP causes low GDP growth. That is the argument that has been debunked thoroughly.

Posted by perfctlyGoodInk | Report as abusive

No where do you make mention of the 800-lb gorilla in the room … namely, unproductive and unsustainable levels of social expenditures among Europe’s periphery, as you refer to them.

The evidence of “Macro 101″, as you attempted to condescendingly tell us, in fact reveals that the Keynesian-Krugman model of ever higher deficit spending is sub-optimal at best and perilous at its worst. Debt and deficit spending only work when they are married with rigorous requirements for high return on capital (viz., an interstate highway system, an improved power grid, but only with strict cost management).

Furthermore, it is not true that reducing spending necessarily leads to a depression. That is utter nonsense. Canada, New Zealand, Switzerland and a host of other countries have disproven that Krugman-esque bunk.

Posted by mm463 | Report as abusive

Examining this issue without reference to private debt levels seems a pretty pointless exercise.

Take Spain, since it’s been mentioned. Between 2000 and 2008, its household and non-financial corporate debt rose by 103% of GDP, most of it the consequence (and cause) of a real estate boom. Financial institutions added another 58% of GDP. The cumulative current account deficit for those years was 56% of GDP. In other words, it was primed for disaster.

Except for outliers like Greece (and to a lesser degree Portugal), high sovereign debt isn’t generally a primary contributor to crisis. Instead, unsustainable growth brought on by excessive private-sector credit finally stumbles, and sovereign debt rises rapidly as a direct consequence.

Posted by Basho | Report as abusive

Examining this issue without reference to private debt levels seems a somewhat pointless exercise.

Take Spain, since it’s been mentioned. Between 2000 and 2008, its household and non-financial corporate debt rose by 103% of GDP, most of it the consequence (and cause) of a real estate boom. Financial institutions added another 58% of GDP. The cumulative current account deficit for those years was about 56% of GDP. In other words, it was primed for disaster.

Except for Greece (and to a degree Portugal), sovereign debt wasn’t a primary contributor to the recent crises. Instead, unsustainable growth based on excessive private sector credit finally stumbled, and sovereign debt rose rapidly as a direct consequence.

Posted by Basho | Report as abusive

Its not government debt as much as the whole suite of government policies. I think people who don’t like the policies use the debt as a straw man and it leads them into intellectual trouble.

There is nothing magic about 80% debt/GDP, or 90% or 100%.

Each situation is different and what matters is whether you are making good use of that debt and whether your growth prospects warrant it.

Posted by QCIC | Report as abusive

It makes perfect sense that higher debt would cause slower growth. It also makes sense that slower growth causes higher debt. The data bear both out to be true. The idea that only one can be true is a false paradigm.

Your analysis shows that “>90% debt level hardy effects growth”. A ridiculous result should cause you to take a more careful look.

I suspect that the analysis is flawed because nations whoutout a strong economic base and tradition tend to not be able to extend their borrowing much beyond 90%. For example, the US may be able to achieve a 200% debt level, while Greece has a crisis at 125%. Data from Greece will thus never be represented on the right side of those graphs.

It is also likely that the majority of the astronomical debt levels on the right side of those graphs represented debt accumulated during each world war. Reinhart-Rogoff concluded that war debt did not have as strong negative effect on growth. That makes your left graph consistant with their findings.

Posted by Kennen | Report as abusive

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