Hamilton on the Reinhart and Rogoff debt-debate

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Jim Hamilton (his text Time Series Analysis will be familiar to many who have suffered post-grad econometrics) has weighed in on the Reinhart and Rogoff v. Herndon, Ash, and Pollin debt debate (my effort is here)

His bottom line is the same as mine (whatever data set you look at, whatever way, more debt -> lower growth), but he has a great way of explaining the central tendency (mean v. average-average) debate.

Now let’s take a look at the details by which Herndon, Ash, and Pollin 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%. If you further believed that the variance of Greek growth around this mean is the same as the variance of U.S. growth around this mean, then the correct thing to do would be to act as if you have 19 observations on the number of interest 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 Herndon, Ash, and Pollin 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.

One could go a step further and spell out a complete statistical model of the view just espoused, for which the optimal way of combining different observations would weight the Greek average more heavily than the U.S. average (because the Greek average is estimated with greater precision), but not 19/4 times as heavily as Herndon and coauthors want (because the Greek average is estimating something different from the U.S. average). The optimal statistical estimate from that perspective would be somewhere in between the Reinhart-Rogoff number and the Herndon-Ash-Pollin number.

In any case, as seen in the table above, whichever number you used, you would still conclude that higher debt loads are associated with slower growth in the postwar advanced economy data set, just as they were in the postwar emerging economy data set, just as they were in the centuries-long individual country data sets, and as also was found to be the case in separate analyses of yet other data sets by Cecchetti, Mohanty and Zampolli (2011), Checherita and Rother (2010), and the IMF (2012), among others.


  1. For me it seems quite logical that there must be a level of public debt that weights on growth, whatever that level is. Can you imagine a public debt of 1000% of GDP as being sustainable? How could it be paid back? You’d need massive inflation which would definitely weight on growth… this level may not be 90%, but….

    I do think private debt must also have a weight on growth, but the paper does not address this if I am not mistaken.

    Another point that would be interesting to analyze is: is there a level of public debt passed which there’s no way back? Something like, once you go passed X%, you will not be able to cut public debt anymore without causing a GDP contraction.

    On a different note…. RA, it seems Australia will not return to surplus for many years yet.
    What’s the impact on rates and AUD ?

    1. At the margin, the bonds should trade a bit cheaper as if it’s harder to sell our bonds we need to boost the total return. A lower fx rate that was thought to be temporary would do this as well.

      But in all honesty, i think we could sell more bonds, so we are probably not yet at the point where more bonds may mean lower fx. More likely if we make more of the stuff folks want to buy, they will buy more of it — which will push ip the AUD and have a neutral impact on the level of rates.

      Curve ought to steepen a bit.

      1. I feel we are not ready at all for a possible of commodity + dollar collapse (even if remote).

  2. with respect ( and I did add Hamilton’s article to all the rest on Around the Traps) both of you pay little to Konzal’s criticism and completely ignore Dube

  3. I’m a little confused, how do these findings show that the relationship works in the direction of high debt = slow growth. And / or, how does it show that the relationship is NOT: slow growth = high debt. Or is this just another example of findings being generalised to fit a predetermined theory? Where is the proof in these findings of the mechanism being high debt and not slow growth? Aren’t both intrinsically linked i.e. in a period of slow growth tax revenue falls so debt naturally increases if spending isn’t cut. How do these findings show that debt causes slower growth? It is just an association, it is not a mechanism. Isn’t this like saying that higher national suicide rates cause higher national debt levels.

    1. Yes, it is a correlation. Not a mechanism. Now we have a robust correlation, we can start asking the harder questions which you have asked — why do we find that slower debt and lower growth come together? How does it work? One step at a time.

    2. High public debt is usually the result of public spending growing much faster than tax revenues, not simply of lower tax revenues (and usually that’s due to pension/retirement costs and health costs).
      So public debt keeps on growing, always, and not only counter cyclical.

      The problem is that it then grows faster than it should be allowed to. Look at Europe pre-GFC. Yes the economy was growing, but public spending was in many cases out-of-control.

      Right now in Australia, tax revenues are at record high, as far as I know, but the problem is that public spending is growing at a much faster rate.

      It is logical that GDP grows faster when public spending exceeds revenues, i.e. borrowing from the future and when you go from 30% to 60% of public debt the boost to economy is bigger than going from 60% to 90%. When you are at 90%, you gotta double down to 180% or the economy will slow. Then, when you finally try to reduce debt, the economy goes backward. There’s a level where the economy becomes 100% dependent on public spending always increasing, as private investment is reduced to a minimum, see Italy and Japan for examples. The economy is addicted to (often inefficient) public debt.

  4. SSEC,

    you are living in Catallaxy world.

    tax revenues are around where they were in Keating’s time. We would have surpluses if they replicated Howard’s time. Spending has been dropping ever since the Stimulus.

    Why do you think the budget is contractionary?

    1. Are you referring to values as % of GDP ? I am referring to absolute values. They keep spending more than what is coming in. The same as Southern European countries were doing during the pre-GFC credit boom. a surplus is apparently never achievable and there’s always a valid reason.

      1. so your using absolute numbers to make an historical comparison? Correct me if I’m wrong but doesn’t this ignore the fact that the population has grown and that the same amount of money is then spread thinly because more people means more services which equals more money that has to be spent?

        1. The problem is that spending is growing much faster than receipts. So when do we re-align them? As soon as we do, the economy will slow down = less receipts = less spending needed. The longer we wait, the bigger will be the adjustment needed and the bigger the impact to the future economy.

          1. yes that may be true but thats a different issue. Comparing in absolute terms does not help the debate as it is a false comparison. The point is that tax revenues are low so yes spending has to be reduced but why are tax receipts low. If the tax receipts were as high in %GDP terms as they were a few years ago and we were still in the same pickle well then yes we have more of a spending issue but that ain’t so.

          2. “If the tax receipts were as high in %GDP terms as they were a few years ago … ”

            But they are not. So we need to manage our spending. Receipts were at 22.5% in 2011-12. So what’s the reason of estimating 24.0% from 2013 on? A sudden dollar collapse? Commodities to the moon? Credit growth for instance is running at historic lows. Housing has been flat for 5 years, no longer booming. Inflation is low. Dollar high. So what do we do now? Just keep going and hope for the good times to come back, crossing our fingers?

          3. So should policy should just ignore lower tax receipts? Should we just give up on the revenue side of the equation? No of course we shouldn’t. Framing the debate as a spending only problem is a political one…just ask yourself this, if the political party you supported was in power would you be arguing that it was spending only or would you acknowledge that both tax revenues and spending need to addressed?

          4. The political party I would LIKE to support is in power already.
            But I am also a tax payer.
            And I do not like to see my money wasted.

            Yes, I understand it is much easier to get elected if you spend money you do not have. And find all sort of excuses, and make short term promises to make your voters happy… but that’s not real leadership. We do NOT need more govt debt which surely will come with higher taxes shortly after.

          5. Receipts are lower because the global economy is weak, credit growth is not what is used to be, and I would not be surprised if this is the “new normal”. What do you want to do, raise taxes?

          6. so you do admit revenue is a problem…from your first comment it seemed as if you were saying…what was it…”Right now in Australia, tax revenues are at record high…”. So you see honesty in debate is always helpful. Now we can debate why tax revenues are low and not just flip it off as not a problem.

          7. The situation is that spending as a % of GDP is still what it used to be, but revenues are not. And that’s what has been happening in many countries in Europe for the last 20 years until it exploded. And? Solution is more spending? Same spending? I think LESS spending. Cost cuts. Efficiency. When govt see revenues as % of GDP are lower, what do you do, hope they go back higher or adapt your spending to match the revenues?

          8. “what do you do, hope they go back higher or adapt your spending to match the revenues?” nope, i never said that. you said that revenue wasn’t the problem spending was. I said that both were. So the govt should address spending, yes I agree. But it should also investigate ways to raise more revenue. This shouldn’t simply be raising taxes willy nilly but be more sophisticated in its approach. You on the other hand initially dismissed revenue as a problem and have since admitted it is. see what i mean about honesty in debate? we now both agree revenue is a problem…now we can move forward instead of having a phoney political debate.

          9. On the revenue side, I was saying that tax revenues are not “falling”. Revenues are not growing as they used to. I agree it is better to use % values. But if you say “tax revenues are around where they were in Keating’s time”, well, that’s misleading too.

            The problem however is still that both govt and opposition now seem to agree that surplus are a matter for future generations, they do not want to work on “solve” neither revenues or the spending side.

          10. I was simply pointing out that absolute values are phoney in this context. There are lots of ways to look at revenue and each have there advantages and disadvantages. Point is that they are lower now by relevant historical comparisons. Furthermore, whether we like it or not both expenditure and revenue will continue to be a problem because of the population problem. Now yes we can address expenditure to a point but not without looking at revenue.

    2. The more I look at these budget numbers the more they do not make sense.
      Was there a reason to have spending, as a % of GDP, at 25.3% in 2011-12 ? The Economy was growing around trend, so 24% would have been more appropriate. there was no GFC stimulus emergency, was there.
      And receipts were at 22.5% in 2011-12. So what’s the reason of estimating 24.0% from 2013 on? Wishful thinking? This is the most classic example of European govt accounting practices.

  5. @ssec all the things you pointed out are not proven by this analysis. As Ricardo said it is simply a correlation and correlation is not causation, stats 101.

    @RA so we needed a complex model to tell us basically what we already knew. That is, historically speaking, that most governments have in times of slow economic growth borrowed money and gotten into debt to stimulate their economies.

    Also I would point out that you and others have suggested that this paper shows a mechanism of debt retarding growth i.e. your words “His bottom line is the same as mine (whatever data set you look at, whatever way, more debt -> lower growth)” if it were simply an association and you were actually open to the idea that slow growth could conceivably cause high debt or that the two by historical standards are intrinsically linked, then you wouldn’t have said what you said.

    Another thing is that you will have a hard time showing the opposite is true i.e. if the economy slows down and governments reduce their debt they will have higher growth rates. Why because it rarely happens. Which is basically my first point.

    Suggesting this was just a preliminary step is a little disingenuous as all the commentary and support for this article has suggested the findings show their is a mechanism and thus support austerity. To deny this is to deny the politics that surrounds this sort of analysis. The authors of the paper set their analysis up in this way to prove a political point, not as you suggest to simply show a correlation.

    1. Yes, I was not referring to this specific paper analysis. I was just expressing my view that ever increasing public debt does not end up well IMO, and that once you start the always increasing debt cycle it is very hard to come out of it.

      If you are looking for the scientific prove of the best economic model / system you will not find it. We do not know. We do not even know if Capitalism is the best method (probably the best method as of now, but I am sure we will discover much better in the future).

      1. thats my point. The discussion around this paper has been absolute…high debt = slow growth. Where in actual fact there is no evidence to suggest this, it could in fact be the opposite i.e. slow growth = high debt, or it could ,as it often is, extremely complex and different on a case by case basis. The point is, that it seems the debate has moved past the facts and is well into the realm of unfounded opinion.

        1. I think this paper is very good in that it lists factual information. Periods of high debt coincided with slower GDP growth. So if Australia keeps increasing its public debt to GDP for the next 10 years, will we be the exception, and have better GDP growth than now? Maybe yes, maybe our govt is super-efficient and the public debt is going to be very easy to repay!

          1. How are the results of this paper a surprise or novel in anyway? Govts around the world have almost routinely borrowed money in times of slow economic growth. Again why did we need complex statistical models to tell us that Keynesian economics has dominated govt economic policy in post war advanced economies….where is the novel finding? Of course there is a solid correlation it was government policy…it would have been more of a surprise had they not found a correlation.

          2. It has all changed post-GFC. Earth is no longer flat. Even so, there’s people who still advocate more govt spending, more debt, more inefficiencies and short term boosts as the way to get out of this mess. We should all follow the Japanese way.

          3. so your arguing based on a correlation of PRE-gfc data that post gfc world needs something different, keeping in mind that there is no evidence to support you position. Again can you explain what is so informative about this paper that gives credence to austerity programs? Evidence would be nice.

          4. What more evidence do you want? US unsustainable public debt not enough? EU countries going bankrupt? Ireland? Pre-GFC it was a private and public debt party, that lead us to a global crisis. And you suggest we keep doing more of the same?

          5. nope i never said they should do more of the same. I’m simply saying that the paper your so diligently trying to defend offers no evidence in support of your argument. Correlation is not causation. What I am saying is that each country has its own unique situation and they got in their current situations for different reasons.

            Now if you were a doctor and recommending a treatment based on the same type of evidence you are defending I would guess you would lose your medical licence.

    2. If they had only published the means, i think your conspiracy theory would hold more water. Politicians have used the result — as they always will. Our role is to be fair and honest — not to fudge and claim that their results depended on excel ‘errors’, or ‘sub-standard’ or ‘weird’ summary measures. They did not. There is a clear correlation. Let us all agree on this fact.

      As for correlation, it is a grand thing to find a robust correlation. It is suggestive of a deeper relationship, and invites productive research. There are plausible theories as to why slower growth and debt may be causally related in both directions, and my guess is that both are true.

      For long run growth all that matters is the quality of public spending — do you think a government with 150% debt to gdp is more or less likely to be en ‘efficient spender’ than one with debt of 15% of gdp?

      This is a fertile and challenging field for research. I wish everyone would stop carping and lend a hand.

      R+R did a lot of work, and the field owes them gratitude – everyone makes dumb errors … their method was OK.

      1. I don’t think economists can extricate themselves from the consequences of their analysis. The results from this paper were sold as proof of a relationship. But as you say it isn’t proof it is simply an association that we already knew about.

        Too much generalisation, oversimplification and over-exaggeration, not enough caveats and caution.

        And just so we are clear I support neither side of the debate in austerity as I think both sides over simplify things far too much.

        1. Well, you should support one side :) Because a decision must be taken. Austerity or no-austerity? I think Australia is in good shape now, it’s the best time to make tough decisions with a look to our future. It’s too easy now to say we do not want to cut as we want to defend people’s jobs. What about future generation jobs? There’s so many govt program we know are sustainable already next decade (super? health?). Take the medicine now I say.

          1. Errata Corrige: There’s so many govt program we already know are *NOT* sustainable

          2. so is it a binary choice or is there room for subtly and evidenced based policy. Not generalisation and over simplification. Again apart from a correlation that is stating the bleeding obvious what evidence is there to support that an austerity based approach benefits society. Does the misery in parts of europe with harsh austerity programs come into your consideration when you advocate your position. Or is it because you live in a country that is unaffected by such policy decisions that you can advocate for policies that have no evidence to support them apart from correlations that state the obvious.

          3. Yes, I come from a country where govt has been wasting money and happily running deficits for at least the last 20 years and by doing so, it has hidden the real structural problems of the uncompetitive economy. We need to stimulate / support the economy they were saying!

            “Does the misery in parts of europe with harsh austerity programs come into your consideration when you advocate your position.”

            Absolutely, yes. And whatever choice those country make now, it is a painful one. Because it is harder now. Do not think this is going to get resolved in just a couple of years, whatever they do ,austerity or not. Unemployment is at 10% plus. That’s why I do not want to see Australia following the same path of short termism views.

          4. so it is a binary choice then? where do you get such confidence that austerity works? isn’t evidenced based is it.

          5. I am confident that increasing public debt at infinitum is not the right choice. And neither is raising taxes from where we are. I am sure the govt is capable of becoming more efficient, less wasteful, and cut costs as needed.

          6. What do you mean? You think govt can’t get more efficient and do the same with less? You really think there is no waste in govt spending? What do you think a business would do during hard times, when revenues are not what was expected?

            Unless you tell me, look, I want to keep increasing the public debt until it gets to 50% of GDP and then I stop there. That at least we have a target.

        2. “You think govt can’t get more efficient and do the same with less?”
          nope didn’t say that

          “You really think there is no waste in govt spending?”
          nope didn’t say that either

          “What do you think a business would do during hard times, when revenues are not what was expected?”

          exactly what the government is doing now…reduce expenditure and look for ways to increase revenue…oh wait you said revenue wasn’t a problem…would businesses only look at cutting costs? of course they wouldn’t.

          1. I understand you have no proposals or ideas to offer to the discussion….
            We’ll have a laugh when govt releases the May budget. Let’s see how they plan to reduce expenditure and look for ways to increase revenue… it’s going to be fun. I wonder if they’ll postpone returning to surplus indefinitely “in the name of jobs”, it seems to be the latest fashion.

          2. No I’m in the habit of not pretending to be able to offer over generalised, over-simplified solutions that have no evidence to back them up to address complex and unique problems in a few lines on a comment forum. But yes it will be interesting to see how BOTH sides of politics try to justify their equally ridiculous policy positions.

          3. It’s just comments on a blog…. openly discussing helps all forming better opinions.
            You do not need to have won a Nobel prize to vote or to express an opinion.

            The fact remains that countries with higher public debt as % of GDP have experienced lower growth as per paper analysis. But maybe is just like climate change and global warming: it’s just a coincidence and it can’t be proved.

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