Reply to Prof. Hamilton regarding “Reinhart-Rogoff Data Problems”

Today Econbrowser hosts this guest contribution from Robert Pollin and Michael Ash of the Department of Economics and Political Economy Research Institute (PERI) at the University of Massachusetts-Amherst.

Reply to Prof. Hamilton regarding “Reinhart-Rogoff Data Problems”
by Robert Pollin and Michael Ash

We appreciate the opportunity to respond to the careful comments posted by Prof. Hamilton concerning our critical replication with Thomas Herndon of the 2010 Reinhart/Rogoff study, “Growth in a Time of Debt.” We will focus on what we see as the three main issues being raised by Prof. Hamilton.

But before we get to these questions, it will be useful to clarify what our paper is about and not about. For starters, let’s just be clear that there is not one word in our paper that suggests that one should never, categorically, worry about high sovereign debt loads. The purpose of our paper is much more focused, and is captured in our paper’s title: “Do high public debt levels consistently stifle economic growth?” RR’s answer to that question was “yes.” But their answer was based on flawed calculations and methodology. We argue that the accurate answer based on a corrected analysis of the RR dataset is “no.” We show, using RR’s own dataset, that there is definitely no threshold point, at 90 percent public debt/GDP, at which countries can anticipate GDP growth dropping sharply on a consistent basis.

Now to the main questions raised by Prof. Hamilton:

1. High sovereign debt loads and long-term interest burdens.

Deficit hawks have been predicting sharp rises in interest rates since the U.S. fiscal deficit rose sharply in 2009 as a result of the financial crisis and onset of the Great Recession. That means they have been badly wrong for four years running. Of course, the interest rate on U.S. Treasuries has been, and now remains, at historic lows, not highs. The deficit hawks may eventually be right. But the fact that they were wrong over these four years also matters a lot. It means that the U.S. has had a great deal of fiscal space to pursue countercyclical measures. Crucially, it also means that the U.S. has been carrying for these past four years—and will continue to carry for at least a few more years—historically low interest payment burdens as a share of total government expenditures. At present, government interest payments as a share of government expenditures are less than half of what they averaged under Presidents Reagan and Bush-1. We consider this an absolutely critical factor to incorporate into the types of discussion Prof. Hamilton has raised. We are not sure why this point is almost universally neglected in current fiscal policy debates. In any case, the basic points are documented in a 2012 paper by one of us (Bob) paper from the Cambridge Journal of Economics Bob has also produced more updated versions of these data. The most up-to-date federal interest payment/expenditure ratio is shown in the figure below. Such figures, of course, are quite easy to obtain and derive.


Moreover, this pattern of low interest payments will almost certainly continue at least until the Fed alters its current monetary policy stance. Chair Bernanke has stated repeatedly that the Fed will continue with its current policy course at least until unemployment falls below 6.5 percent. Meanwhile, the Fed itself is forecasting unemployment to remain between 7.3 – 7.7 percent through 2013.

2. Interpretation of our recalculations from RR data

It is not accurate to say that the main source of the difference in GDP growth was their method of averaging, not their spreadsheet errors and exclusions. It is the combination of these factors that leads to our result that average GDP growth in the +90% public debt/GDP category is positive 2.2 percent, not negative 0.1 percent. If this wasn’t clear enough in the version of the paper we posted last Monday, it should be clearer now in the slightly revised version. Our full narrative around this slightly revised table can be found here.

As for RR’s justification of their averaging technique, it is certainly unusual to, for example, weight the experience of one year in New Zealand equally with 19 years of the UK. It is RR’s obligation as researchers to state clearly in their published work that this is what they have done and to justify their methodology. They did not do so. We do state in our paper that due, for example, to issues of serial correlation, one might not want to give fully 19 times the weight to the UK experience relative to the one New Zealand year. Just to make sure this is clear, here is what we say on pp. 7-8 of our working paper:

RR does not indicate or discuss the decision to weight equally by country rather than by country-year. In fact, possible within-country serially correlated relationships could support an argument that not every additional country-year contributes proportionally additional information. Yet equal weighting of country averages entirely ignores the number of years that a country experienced a high level of public debt relative to GDP. Thus, the existence of serial correlation could mean that, with Greece and the UK, 19 years carrying a public debt/GDP load over 90 percent and averaging 2.9 percent and 2.4 percent GDP growth respectively do not each warrant 19 times the weight as New Zealand’s single year at −7.6 percent GDP growth or five times the weight as the US’s four years with an average of −2.0 percent GDP growth. But equal weighting by country gives a one-year episode as much weight as nearly two decades in the above 90 percent public debt/GDP range. RR needs to justify this methodology in detail. It otherwise appears arbitrary and unsupportable.

In short, doing simple country-year weighting strikes us as more reliable in this case than taking country averages. Beyond this, to be reliable as a guide on important public policy issues, their results need to be robust to alternative defensible averaging methods. We have shown that their results are clearly not robust.

3. Do our overall findings end up close to RR?

RR have said this in their response to us, and Prof. Hamilton seems to agree. We disagree. First, the finding from RR that has driven policy discussions was the idea that countries will consistently experience a sharp, even precipitous, decline in GDP growth once they pass the 90 percent public debt/GDP threshold. This is the message that is conveyed through the average figures they reported: when public debt/GDP is between 60 – 90 percent, GDP growth averages 3.2 percent, but when public debt/GDP exceeds 90 percent, average growth falls to -0.1 percent. Based on our recalculations, we see, on average, a much more mild growth decline with their full 20 country sample over their full set of years. This becomes more evident when we added the 90 – 120 percent public debt/GDP category in our paper. We show that when public debt/GDP is between 90 – 120 percent, average GDP growth is 2.4 percent. This compares with 3.2 percent growth when public debt/GDP ranges between 60 -90 percent.


Still more significant, in our view, are the results we reported in Table 5 of our paper, which we reproduce below.


As we show there, working with the RR corrected data, the GDP drop-off at over 90 percent public debt/GDP declines with time. In particular, over the most recent decade of RR data, 2000 – 2009, we see that the average GDP growth rate when public debt/GDP is over 90 percent is actually either comparable to or higher than when the ratio falls between 30 – 90 percent.

Overall then, from our replication of RR, we conclude that there is no robust evidence showing that countries consistently experience sharp growth declines when public debt level exceed the 90 percent public debt/GDP threshold. We need to emphasize once again: this does not mean that we believe governments can borrow money and pile up debt at will. Considering the U.S. economy specifically, in general, over the course of full business cycles, we believe public borrowing should fall within the historic U.S. range of between 2-3 percent of GDP. However, the 2007 -09 financial crisis and subsequent Great Recession have presented us with extraordinary policy challenges. Under these circumstances, an aggressive program of government deficit spending to combat the downturn was the appropriate policy intervention. Ongoing deficit spending remains the appropriate policy stance now, in combination with expansionary money and credit policies, because we still have not returned the economy onto a healthy growth trajectory, in which we can count on significant declines in mass unemployment.

This post was written by Robert Pollin and Michael Ash


17 thoughts on “Reply to Prof. Hamilton regarding “Reinhart-Rogoff Data Problems”

  1. john jansen

    In the first section of the article the authors make note of the importance of low interest rates.They note that since deficits have increased sharply in 2009 that deficit hawks have been anticipating higher rates and that has not happened. They also note the Federal Reserve purchases which have acted to restrain rates. I think they underestimate that influence as rates are not at some market clearing level but are a function of Open Market Desk manipulation.
    What do you think will happen someday when the Federal Reserve even intimates that it is withdrawing from the market. There will be never before seen carnage and the unwinding will be quick rapid and unprecedented. I think that there will be a one month to (maybe) three month trade in which 10 year yields back up 200 basis points to 300 basis points.
    They will need extra shipments of body bags to Broad and Wall to clean up the mess.

  2. don

    The results do not seem to show causation. Another problem is with the interpretation of results. Looking at the last table, for instance, it seems one could say that the relative size of the effect of debt on growth (if indeed there is such a thing) rises in the later periods, since the growth of high -debt countries declines only from 2.1% to 1.7%, whereas the growth of low-debt countries declines from 4.1% to 2.7%.

  3. river

    “But to-day we have involved ourselves in a colossal muddle, having blundered in the control of a delicate machine, the working of which we do not understand. The result is that our possibilities of wealth may run to waste for a time — perhaps for a long time.”
    This is truer today than it was when it was first spoken. Word to the wise, when Nobel winning economists from Princeton argue with Nobel winning economists from Chicago, or just regular economists from Stanford, and Harvard, and all sides claiming freshman in economics level mistakes by their adversary, it doesn’t instill a great deal of confidence in the lay people watching the discussions in the blogosphere. This latest episode is even worse.

  4. fresno dan

    Its hard for me to understand what the disagree is actually about. The corrected results show that lower debt correlates with higher growth… except that there is something magical between 30/60 and 60/90 debt levels, as greater debt than cause higher growth.
    Of course, like most academic debates about elephants, gnats become the most important thing to argue about. In the second graph, in every period, GDP growth is declining at every debt level.
    Is this DECLINE in growth going to stop?
    Because if growth stops, servicing debt becomes a big problem (unlike most economists, I don’t thing there is infinite oil or infinite oil substitutes…look at economic growth over centuries and there is one reason, and one reason only for economic growth – cheap energy)

  5. ppcm

    Unconvincing is the above paper content with axiomatic data collection contributing to the thesis high debts may not lead to slow growth and high debts may not lead to high interest rates.
    « Deficit hawks have been predicting sharp rises in interest rates since the U.S. fiscal deficit rose sharply in 2009 as a result of the financial crisis and onset of the Great Recession. That means they have been badly wrong for four years running. »
    Those comments are made in abstract of the proverbial (proverbial since more often than none, readers are provided with data and not with the manufacturing process) perennial question of causes and causations.
    They were no compelling reasons to introduce a Fed led ZLB should the target be a zero tangential interest rates. It is worth reminding the trend was built without apparent bottlenecks, the ECB and Fed primary dealers were coupling retention of primary issues, interest swaps and bonds futures. Until rules and regulations are revised or Cauchy, Fourier sequences demonstrate otherwise, this practice will concur with the above paper findings .Causations will be enhanced and causes left in vacuum. Note that the sub prime derivatives debacle should be studied through the prism of Cauchy, Fourier mathematical sequences.
    Fred data
    10-Year Treasury Constant Maturity Rate (DGS10)
    Anecdotic, it seems the financial markets, were left with no guidance, no supervision, no rules. All their faults as no one could question the nature of the yield curves in Europe or USA, Japan. This paper in reference is doing the same.
    “The captains of finance and the public stewards of our financial system ignored warnings and failed to question, understand and manage evolving risks within a system essential to the well-being of the American public,” the Financial Crisis Inquiry Commission wrote in a 545-page book outlining its conclusions »
    Still waiting for the same report from the European commission or ECB.
    Those facts and comments should take care of the faith pronouncement « deficit hawks have predicting sharp rises in interest rates …. »
    The other wedge inserted in the above paper content, that proof is made through blended data
    « average GDP growth in the +90% public debt/GDP category is positive
    2.2 %
    Please provide for the domain of definition of the GDPs deflators during the contemplated time period.
    Mention should be made of few papers with converging conclusion towards « This time is different »
    Pr Ramey paper as introduced through Econbrowser
    « Evolving Views on Fiscal Multipliers »
    After reviewing the macro analysis of the effects of Public debts and multiplier,one may be willing to review the hereunder paper on the
    The real effects of debt – BIS
    Prior to these readings and to comply with the date of issue one may be willing to give due consideration to:
    B Friedman
    « New direction in the relationship of between public and private debts »
    One may as well be willing to read the IMF « what is the damage » introductory report to the great recession.
    Those are only few of those papers as they are numerous deserving papers on the subject,where the conclusion may converge towards a demonstration of the low stable relationship between public debts and growth.

  6. aaron

    What was interest expense relative to GDP minus government spending during the high interest Reagan years? Now? What would happen if interest rates increased to 1, 2, 3, 4%? At what point would interest expense relative to private sector domestic product as high?

  7. Steven Kopits

    I agree entirely with Fresno Dan. This story is about more than debt-to-GDP ratios.
    I would add that I personally would welcome greater exposition of the supply and demand for money. There seems to me an implicit assumption that the supply of money is “normal”, and all problems are arising because money demand is depressed (ZLB).
    It’s not clear to me that this properly characterizes the current situation. Prior to the recession, the low cost of capital appeared to have everything to do with excess savings in China and OPEC petrodollars. Have these gone away? Or does a surplus of dollars remain, with demand for these shifted from the private sector to the government?
    If this latter case, then interest rates must be viewed in light of excess Chinese savings, and that, in turn, as a function of Chinese GDP growth. If China’s economy falters, does excess liquidity go away? What are the risks to interest rates arising from the global supply of funds, and in particular, related to China’s economy and policy?

  8. aaron

    I was not aware of predictions of higher interst rates. JDH says the fed can sustain policy easily for almost 4 years and smooth things out then. While there is no reason to think foreigners will continue their buying of treasuries, relying on it is stupid. How sensitive are interest rates to demand for treasuries?
    I think there is a paradox here. Interest rates will remain low because growth will be low in the private sector while spending is high. If the private sector were to grow demand for treasuries would drop, higher interst on treasuries would stifle growth.

  9. aaron

    Meant to type “There is no reason to expect foreigners will not continue their buying of treasuries…”

  10. Johannes

    Ben Bernanke will retire soon, saying “Hello” to Alan Greenspan, and housing-bubble-Greenspan will say again “No one could see this coming !”
    And the next one in command will say “It was all Ben’s fault !”.

  11. Rick Stryker

    The HAP paper reminds me of the Monty Python sketch “Nobody Expects the Spanish Inquisition” since to me, at least, it reads like a droll, feckless prosecution.
    First, HAP point out a spreadsheet error, which is legitimate. Fair enough. But they then bring up data that was supposedly “selectively excluded,” implying that data that didn’t fit R&R’s worldview was ignored by them. And to top it off, HAP accuse R&R of using some strange estimation method rather than the standard procedure that everybody knows and agrees with (no doubt to skew the results). If the reader is not paying attention, he might easily come away with the impression that HAP have uncovered a hoax.
    But here is some data that HAP selectively excluded:
    1) First, the reason the “selectively excluded” data was left out of the paper was that R&R had not collected it yet. And the only reason that HAP even know about this data is that R&R collected it and give it to HAP. HAP would have a point only if R&R had access to a time machine which they could have used to go back in time and re-write the paper with the new data.
    2) Second, 6 months before HAP’s paper, R&R were already in print in a Journal of Economic Perspectives article with an expanded data set going back to 1800 that fixed the spreadsheet error problem and included the “selectively excluded” data. Moreover, that JEP paper comes up with estimates that are similar to HAP’s.
    3) When you look at HAP’s alternative averaging procedure, you can see immediately that is they and not R&R who are doing something non-standard if not outright wrong. R&R are sensibly assuming that observations from different countries are being drawn from different distributions, as JDH has already pointed out. But HAP assumes that they are from the same distribution, so that the few cases with long time series dominate the analysis while other cases are effectively excluded. There is no reason for R&R to justify what they did since it is standard and makes sense. HAP’s procedure is misleading at best if not just wrong.
    The bottom line is that HAP found a spreadsheet error that was irrelevant since R&R had already addressed the problem in print earlier in a new and expanded paper. The excluded data problem could only be fixed in R&R’s 2010 paper by using a time machine. And HAP’s averaging procedure point can only be resolved by HAP taking a basic statistics course.

  12. 2slugbaits

    Rick Stryker There may well be problems with what HAP did or didn’t do, but I don’t think you’ve correctly identified them. Regarding the R-R weighting issue, there are two problems. The first problem is the weighting itself. That’s open to some reasonable dispute and I don’t think either R-R or HAP got it right. I’ll get to that in a moment. The second problem is that R-R’s explanation of what they actually did does not match what they said they were doing. If you read R-R’s description of what they said they were doing the only sensible and grammatically meaningful interpretation is that they were taking country-year averages and not just country averages. Why else would they even talk about the thousands of observations they used in their study if those observations weren’t given equal weight? What R-R actually used were statistics based on other statistics and not statistics based on observations. There’s a big difference. For example, no one would use Census data statistics and claim that their study was based on 315 million observations! But that’s essentially what R-R did. Again, read how they described their methodology. One of the reasons no one could replicate their results was because no one imagined that there could be such a yawning gap between their description of what they did and what they actually did. At some point we have to expect prominent PhD economists to be able to write coherently.
    As to the way they weighted things…well, let’s break this down into the mean and median. The mean values that they found are meaningless and even they have pretty much given up trying to defend those values. One way to think about it is to understand R-R’s mean analysis as a kind of panel data representation in which they then took the mean of the different intercepts. If you think that’s meaningful, then we live in different worlds. So that takes care of the mean values. The remaining discussion is about the median numbers. And here you have to say that R-R’s approach is a bit bizarre. Why would you take means of country observations and then take the group median of the mean? Afterall, one of the reasons R-R no longer defends the mean estimates is that the raw data is so shot through with extreme skew and variability. That’s why there is such a huge gap between the mean and the median numbers for 90+%. The right way to have weighted things would be to weight by the reciprocal of the standard deviation by country and then take a geometric mean of those weighted observations. Of course, some countries only have one observation and there is no way to know if that one observation was an outlier (e.g., New Zealand), so this best approach probably won’t work. A second best alternative would be to take the median of each country’s experience and then take the group median. Or since there’s good reason to believe there’s some non-linearity (you might want to test the squared residuals for autocorrelation), perhaps a LOWESS approach that weights by neighborhood. In fact, I think I saw where someone might have tried that.
    The larger problem is that at best the R-R analysis only allows you to make predictive inferences, but what was being sold was a causal inference.

  13. Wisdom Seeker

    Sorry, I threw the article out after the first plot. The correct metric for Federal interest payments is as a share of revenues, not expenditures. Deficit spending has artificially suppressed the ratio.Plot it that way, correctly, and the current situation is nearly as bad as the WW2 and Reagan-Bush debt-burden crises.
    And the line “Moreover, this pattern of low interest payments will almost certainly continue at least until the Fed alters its current monetary policy stance.” is just horsefeathers. The Fed cannot alter its current policy stance anytime soon without blowing up both the Federal budget and most of the U.S. and world economy, all of which are dependent on cheap credit at this point. A rise in rates would be a harsher form of austerity than anything dreamed up to date on the fiscal side… since it would also represent an acceleration of the wealth transfer from poor/debtors to rich/creditors which is the root of the whole problem.

  14. urban legend

    What about control of the currency? Doesn’t it matter that one country has no control over it and is beholden to outside forces — no diect control as in the Euro or a local currency’s value pegged to an outside currency or gold — while another country can always create the necessary money and simply pay the debts when they come due? That certainly sounds important to me as far as risk and cost of borrowing are concerned.
    And what about causation? I see none of R & R’s defenders discussing that at all. But let’s see: when the economy goes into decline and unemployment increases, (a) the numerator in the top of the debt-to-GDP ratio gets higher because tax revenue goes down and safety-net expenses increase; and (b) the denominator at the bottom of the ratio gets smaller because GDP goes down. Duh, the ratio gets higher.
    So on the one hand, I have a clear understanding of how the causation goes the other way — i.e., economic decline causes a higher ratio. In contrast, my theory for how the higher ratio causes slower growth is — what? — or even if I can see some possible causal relationship, my theory for why there is a dramatic inflection point at 90% is — double what? Is there a comprehensible theory there?
    Of course, we now see there is no such inflection point at a 90% debt-to-GDP ratio, but instead an apparent gradual slowing of growth the higher the ratio gets. That would be more consistent with reverse causation, or with the growth decline causing the higher ratio as the dominating effect. Without the inflection point, there seems to be no basis for believing there is a spot in the continuum where causation dominance shifts.

  15. mike hughes

    I have come to the informed conclusion that many economists are poorly trained, basically unsupervised, mean hearted, and rather stupid people. They hide behind half-assed math, and sell their souls to the highest bidder.

  16. Tom

    JDH (and Stryker in a well-written comment) have already suitably dismantled HAP, so there isn’t much to add. The argument made here that the data for the 2000s shows the growth disadvantage of debt disappearing is obviously silly, taken during a decade when there were two recessions. Simply put HAP aren’t ready for prime time and if they hadn’t gotten very lucky finding that spreadsheet error no one would have paid them any attention.
    HAP are really ideologists, not scientists. And it’s a weird sort of ideology, which doesn’t seem to care much what the government does or how useful government spending is so long as the government spends increasingly more than it earns. Deficit spending, any deficit spending will supposedly stimulate the economy, and we’re told we don’t really pay for it, because the Fed is printing the money and yet we have low inflation.
    Nevermind the other costs to growth of deficit spending and mismanaged, wasteful government. Looking only at interest costs, there are two possible outcomes to HAP’s ideology. One is that growth returns, and real interest rates normalize back to positive territory, and the Fed stops rolling over or even starts selling its assets, the cycle turns, and then we’re in a recession and a debt crisis. The other is that we remain in this low growth, negative real interest situation forever, a la Japan.

  17. anon2

    I see the comments seem to neatly divide between those who were on the left and the right prior to the post.
    ho hum
    What is it that makes you all hold so tight to your religious beliefs?

Comments are closed.