# A Bit More on Debt and Growth

Here is a bit more analysis of the data set used by Reinhart and Rogoff (R-R) and by Herndon Ash and Pollin (HAP) in their critique, and in particular the stata data set RR-processed.dta with data on public debt to GDP ratios and real GDP growth in 20 developed countries since 1946. This post is a minor addition to my earlier post and, especially adds little not shown by Arindrajit Dube.

In general macroeconomists have a problem that we non experimental data so we observe correlation but we want to know about causation. We don’t know what to do about this problem, so we almost all do the simplest thing which is look at timing — the cause comes before the effect. This is what Dube did showing a much stronger relationship between the public debt to gdp ratio and real GDP growth in the preceding 3 years than between the ratio and growth in the following three years. Also the non parametric estimate suggest a much stronger relationship between higher debt and lower subsequent growth for low levels of debt (up to 30% of GDP) than for higher levels — the opposite of what policy makers guessed given the original Reinhart and Rogoff analysis which really didn’t address that issue.

I redo Dube with parametric regressions which have the nice feature that there are standard statistical tests of null hypotheses concerning parametric point estimates (that’s fancy talk for STATA gives me t-statistics). The very first standard way to look at causality using post hoc ergo propter hoc is caused a Grander causality test. It is just a regression of one variable on lagged values of the explanatory variable and lagged values of the dependent variable. This is definitely the first thing macroeconomists do does if he she or they wonder about the direction of causality.

Recall the basic regression which notes that a debt to GDP ratio 1% higher is associated with a real GDP growth rate which is 0.02% lower (this is in fact a big deal).

dRGDP is the rate of growth of real GDP in the country, debtgdp is the ratio of public debt to gdp.

Now l1drgdp is the rate of real GDP growth lagged one year.

Including that variable appears to show a striking decline in the coefficient on the debt to GDP ratio, but really one should calculate the long term effect of a permanent increase in the debt ratio using

(1-0.3793671)(new steady state growth rate) = constant -0.089041(debt to GDP ratio) so the estimated long term effect is about -0.015 not much smaller than the simple coefficient.

The t-statistic is calculated assuming that the disturbance to growth is independent across countries (no global recessions or oil shocks) and that all structure within a country is captured by the simple lagged term. STATA is very willing to recalculate standard errors assuming, for example, that disturbances in the same year may be correlated.

. reg dRGDP debtgdp l1drgdp, cluster(Year)

gives a t-statistic on the debt to GDP ratio of -2.45 (the point estimates are exactly the same the cluster option just calculates more robust estimates of the standard errors). No big change.

Now I can get the t-statistic to be insignificant (you can always do this). I do this by definining a new lagged variable al3drgdp which is the average of the growth rate of real GDP lagged one, two, and three years. When I toss that in the regression and calculate standard errors allowing correlation in the same year across countries I get the t-statistic insignificant.

There is nothing wrong with this regression, except that I fiddled till I got the absolute value of the t-statistic under one (the added variable is due to Dube so there is that). The point estimate of the effect on growth isn’t much lower. the long run guess is a bit below 0.01 so slightly less than half the estimate based on the simple regression.

There is nothing much to see here. Neither strong evidence that the original estimate is due to reverse causation nor strong evidence that high debt causes low growth.

In contrast, the hypothesis that low growth causes a high debt to gdp ratio is not just obviously true but also strongly supported by the data. Here l1debtgdp is the lagged ratio of public debt to GDP.

. reg debtgdp l1drgdp l1debtgdp, cluster(Year)

Note the t-statistic is robust to correlation across countries within a year. Similarly, if STATA allows correlation of disturbances for the same country at different years (but not across countries within a year) the t-statistic is still huge being -6.21.

This shows that you just can’t interpret the simple coefficient as a measurement of the effect of debt on growth. But we knew that (R-R never denied that there was some reverse causation).

Now for something slightly different. How about non linearity ? A lot of interest in R-R was due to the unreasonable interpretation that their analysis showed a threshold near a debt to gdp ratio of 90%. I am going to go back to regressing real GDP growth on lagged real GDP growth and data on the debt ratio but cut the data on the debt ratio to debtgdpto90 which is rounded down to 90 if the ratio is over 90%

gen debtgdpto90 = debtgdp + (90-debtgdp)*(debtgdp>90)

and gen debtgdpmin30 = debtgdp-debtgdpto30 which is zero if the ratio is less than 90 and the ratio minus 90 if the ratio is greater than 90

The results correspond to the pattern reported by Dube (as they must) the point estimate of the effect of debt over 90% is lower and only borderline statistically significantly different from zero.

reg dRGDP debtgdpto90 debtgdpmin90

Now how about both considering non-linearity and including a lagged dependent variable for Granger “causality”

reg dRGDP debtgdpto90 debtgdpmin90 l1drgdp

There is no evidence at all that increasing the debt to GDP ratio above 9o% has a negative causal effect on real GDP growth. In my heart, I am sure that debt still does have such an effect even if it is over 90% but there is just no evidence for this effect in R-R’s famous data set which was interpreted as including strong evidence that the effect is very large.

Finally out of respect for Dube, I consider debt ratios rounded down to 30% debtgdpto30 and above 30% debtgdpmin30

. reg dRGDP debtgdpto30 debtgdpmin30

As we know from Dube 2013, debt appears to make a huge difference up till a ratio of 30% then much less.

Finally (really finally the end at last) the null of no Granger “causality” is not rejected for ratios above 3o% . The evidence is that having very low debt ratios has a good effect on growth, but above that low level, there isn’t statistically signficant evidence of a causal effect.

reg dRGDP debtgdpto30 debtgdpmin30 l1drgdp

here is the do file I used to generate the regressions I just cut and pasted

clear

use C:\rjw\Papers\Peri\RR-processed.dta

quietly tab Country,gen(count)

gen cntry = count1+2*count2+3*count3+4*count4+5*count5+6*count6 + 7*count7 + 8*count8+9*count9+10*count10+11*count11+12*count12+13*count13+14*count14+15*count15+16*count16+17*count17+18*count18+19*count19+20*count20

quietly tab Year, gen(yr)

sort cntry Year

gen debtcat = 1 + floor(debtgdp/30)

replace debtcat = 4 if debtcat>4

gen episode = 1 in 1/1

replace episode = episode[_n-1]+1-(debtcat==debtcat[_n-1])*(cntry==cntry[_n-1]) in 2/1175

gen debtct1 = debtgdp<30

gen debtct2 = (debtgdp<60)*(debtgdp>=30)

gen debtct3 = (debtgdp<90)*(debtgdp>=60)

gen debtct4 = debtgdp>90

gen debtm90 = (debtgdp-90)*(debtgdp>90)

gen l5debtgdp = debtgdp[_n-5] if cntry==cntry[_n-5]

tab debtcat,sum(dRGDP)

tab debtcat,sum(debtgdp)

reg dRGDP debtgdp debtm90

reg dRGDP debtgdp

reg dRGDP debtgdp if l5debtgdp!=.

reg dRGDP debtgdp l5debtgdp if l5debtgdp!=.

reg dRGDP debtgdp l5debtgdp if l5debtgdp!=., cluster(cntry)

reg dRGDP l5debtgdp if l5debtgdp!=.

reg dRGDP l5debtgdp if l5debtgdp!=.,cluster(cntry)

gen l1drgdp = dRGDP[_n-1] if cntry[_n-1]==cntry

gen l2drgdp = dRGDP[_n-2] if cntry[_n-2]==cntry

gen l3drgdp = dRGDP[_n-3] if cntry[_n-3]==cntry

gen al3drgdp = (l1drgdp+l2drgdp+l3drgdp)/3

gen l1debtgdp = debtgdp[_n-1] if cntry[_n-1]==cntry

gen debtgdpto90 = debtgdp + (90-debtgdp)*(debtgdp>90)

gen debtgdpmin90 = debtgdp-debtgdpto90

gen debtgdpto30 = debtgdp + (30-debtgdp)*(debtgdp>30)

gen debtgdpmin30 = debtgdp-debtgdpto30

reg dRGDP l1drgdp l2drgdp l3drgdp

reg dRGDP debtgdp l1drgdp

reg dRGDP debtgdp l1drgdp, cluster(cntry)

reg dRGDP debtgdp l1drgdp, cluster(Year)

reg debtgdp l1drgdp l1debtgdp

reg debtgdp l1drgdp l1debtgdp, cluster(cntry)

reg debtgdp l1drgdp l1debtgdp, cluster(Year)

reg dRGDP l1debtgdp al3drgdp

reg dRGDP l1debtgdp al3drgdp, cluster(cntry)

reg dRGDP l1debtgdp al3drgdp, cluster(Year)

reg dRGDP debtgdpto90 debtgdpmin90

reg dRGDP debtgdpto90 debtgdpmin90 l1drgdp

reg dRGDP debtgdpto30 debtgdpmin30

reg dRGDP debtgdpto30 debtgdpmin30 l1drgdp

Robert – way above my head. Will read, and read to see if I can wrap my head around this.

My one nit with the RR paper is they compare sovereign free floating countries to non-sovereign, and pegged countries. Even countries that may have been sovereign, and switched.

I wonder how the results look if you segment countries.

robert

could be above my head too, but i wonder about that debt/gdp ratio of 30% and why there should be a negative effect on growth when the ratio is lower than that.

Coberly, accounting for some other factors such as trade surpluses, it could be contractionary, draining financial assets from an economy.

Here is an exchange between Warren Mosler and Al Gore that explains it nicely:

Early in 2000, in a private home in Boca Raton, FL, I was seated next to then-Presidential Candidate Al Gore at a fundraiser/dinner to discuss the economy. The first thing he asked was how I thought the next president should spend the coming $5.6 trillion surplus that was forecasted for the next 10 years. I explained that there wasn’t going to be a $5.6 trillion surplus, because that would mean a $5.6 trillion drop in non-government savings of financial assets, which was a ridiculous proposition. At the time, the private sector didn’t even have that much in savings to be taxed away by the government, and the latest surplus of several hundred billion dollars had already removed more than enough private savings

Matt

what you are saying could very well be true. but i can’t wrap my head around it. i think i have a fairly good head, so i am going to suggest you need to explain this more carefully, slowly. but i should also say that i am extremely leery of magic tricks.

i think robert said that below 30% there was a POSITIVE relation between debt/GDP and lower growth. which raises the question “lower than what?”

you seem to be saying that there is a NEGATIVE relation between debt/GDP and lower growth… that is more debt leads to higher growth, which is what i would expect up to a point.

the point being the point where the money borrowed (or printed?) by the government can no longer draw out more growth because some limiting factor (resource) is in short supply… that is, it cannot be “produced” without drawing more other resources out of other production than it can replace with more productivity of its own.

this may be as hard to understand as you and robert are to me. maybe we could clear it up if it was worth the time.

i don’t think words like “savings” are much help unless they are very clearly defined in terms of the subject of discourse.

Coberly, one of my favorite topics right now, and worth discussion. Depending on the circumstances governments may need to continuously accumulate debt to have growth. So yes, more debt is associated with long term growth – in a sovereign currency. Pegged currencies can have all sorts of limiting factors, which is another problem in the paper as it compares apples to oranges. I don’t even remember if their paper included current accounts.

There are several other factors at play, for example, running a trade surplus means you can have low debt/deficit to GDP and do quite well. Resource inflation is a constraint. Debt has no control over the amount of oil in the ground, though can effect how much we can buy. The limiting factor on debt is high inflation, which I certainly do not define as 2%, and under certain circumstances 5 or 6% may be no big deal either, but that is a whole other discussion.

All the depressions and many recession in the U.S. were preceded by debt/deficit reduction. In Europe their attempts to reduce debt and deficits is making their economies worse – and actually increases debt – which flies in the face of the RR paper.

Savings is a horrible word to use, and means too many things to different people. I’ll try to describe/define “savings” that I refer to here:

Lets say there is no money in the economy and the government buys $1,000 in stuff from two people, and they deficit spend. Government “debt” is $2,000 and the private sector has $2,000 in savings.

The national debt is nothing more than dollar balances in savings accounts at the Federal Reserve Bank. The accounts, along with checking accounts at the same Federal Bank (reserves’) and the actual cash in circulation constitute the total net dollar savings in our economy, to the very penny. When the U.S. government spends more than it taxes, those extra dollars it spent first go into our checking accounts, and then some gets exchanged for actual cash as needed, and some goes into those savings accounts at the Fed called Treasury securities. Technically, nothing is really borrowed.

See this chart showing national debt and NGDP:

http://static.seekingalpha.com/uploads/2010/12/14/saupload_a_us_annual_gdp_national_debt_1791_2010.png

Sorry about being over heads. Partly I am reporting pretty much every regression I run (no data dredging). The bottom line of this post is that there is no (zero, 0, nada, niente) evidence that a debt/gdp over 90% does any harm once you take into account the past year’s rGDP growth. As far as STATA can tell, all (100% tutto) of the association between debt/gdp rising over 90% and slow real GDP growth is due to slow growth causing a high ratio.

No evidence of an effect doesn’t mean no effect. In my heart, I am sure that public debt is bad for growth except when the economy is in a liquidity trap when it is good for growth. The data on my hard disk provide no support for this conviction in my heart.

I don’t think the apparent wonderfulness of a ratio of 0 compared to 30% is meaningful let alone evidence of causation. The regression considers only the last years real GDP growth. My heart is sure that the apparent wonderfulness of extremely low debt to GDP ratios is reverse causation in which prolonged booms cause extremely low ratios. Again, this belief is not based on the data set.

Robert

thank you. that is much clearer.

i am not sure that public debt should be bad for growth. the government can borrow money that someone otherwise is not using, and use it to create real jobs or encourage real investment, or both by investing directly in, say, public roads. even “investing’ in defense is arguably making possible economic growth that might be more difficult if we had to learn chinese to get a job in middle management.

i don’t go so far as McOsker… probably because my heart believes in the law of diminishing returns. At some point government debt would “crowd out” other investments. i don’t believe we are anywhere near that point. rather the opposite.

then we have “pointless debt” where we just don’t pay for stuff so we can give “tax breaks” to people who are not investing their money in anything useful, but are using it in gambling and swindles that destroy the economy.

Matt

let me let that percolate until i am less tired. in the meanwhile my reply to Robert above may mean something.