# Debt and Interest Rates: Some Empirical Evidence and Implications

Today’s NYT article suggests apocalypse (very) soon:

…the government faces a payment shock similar to those that sent legions of overstretched homeowners into default on their mortgages.

Do we really need to worry so much in the short term?

Figure 1: Ten year constant maturity Treasury yields (blue line), and observation for 11/19 (red square). NBER defined recessions shaded gray; assumes last recession ends June 2009. Source: St. Louis Fed FREDII and NBER.

Six years ago, Jeff Frankel and I examined the implications of the borrow-and-spend policies of the Bush Administration [PDF]. We estimated the following relationship:

(1) it long = 0.001 + 1 × πt + 0.077 E(dt+2) + 0.280 (yt-ytFE) + 0.005 it* – 0.574 intt

Adj.-R2 = 0.51, N=17, Smpl 1988-2004. i is the long term interest rate on ten year bonds, π is the y/y inflation rate, E(dt+2) is the two-year ahead expected debt-to-GDP ratio and (yt-ytFE) is the output gap (both according to OECD), and i* is the foreign interest rate, and int is foreign [correction: official]purchases of US Treasury debt. (This specification was also discussed in this March 2007 post.)

We can use these estimates to do a back of the envelope calculation of what happens in a year, going from end FY2009 to end FY2010, by taking the total differential of equation (1). The change will be given by:

(2) Δ i = Δ π + 0.077 Δ E(dt+2) + 0.280 Δ (yt-ytFE) – 0.574 Δ int

According to the August CBO Economic and Budget Outlook, public debt held by the public two years ahead will rise from 65.2 to 65.9 ppts of GDP (that is, end FY 2011 to end FY2012, in Summary Table 1). The OECD November Economic Outlook reports that the output gap in 2009 was -4.92 ppts of GDP, and is projected to be -5.36 in 2010. If East Asian bank purchases of Treasuries remain constant, then one finds that the inflation adjusted interest rate will rise by:

(0.659-0.652)×0.077 + (-0.0536+0.0492)×0.280 = 0.0005-0.0012 = -0.0007

That is, the interest rate would fall by 7 bps (holding expected inflation constant). In other words, real interest rates would stay roughly constant, ceteris paribus.

Now, what about foreign purchases of US treasury bills and notes? These ran about \$333 billion through September [1], or about 2.3% of nominal GDP. [correction 11/25, 8pm: Now, what about foreign official purchases of US Treasury securities? These ran about \$67.5+320.9= 388.4 billion through September, according to TIC data, or about 2.7 ppts of GDP.] (usual caveats about TIC data apply here.)
Suppose this went to zero (!). Then real rates would rise 1.3% 1.56%. Of course, one needs net foreign official purchases to drop to zero, which seems to me unlikely.

Some caveats: These estimates were obtained using data that spanned a period without extraordinary Federal Reserve credit easing, and in the face of an unprecedented financial collapse. And, the relationship is not precisely estimated. But they’re the estimates we — or at least I — have.

By the way, CBO predicts only a 0.8 ppts increase in the ten year rate going from 2009 to 2010, and an additional 0.3 ppts by 2011 (Summary Table 2).

I’ll further observe that the article gives the impression that the jump in Federal debt was due to the stimulus bill. But in fact, as shown in this post, most of the debt accumulation has been accounted for by the decline in tax revenues associated with the recession.

No doubt, trouble on the fiscal front is real, and has long been brewing — from the tax cuts of 2001 (if extended) to Medicare Part D. And, indeed, I argued for a lot more fiscal restraint when we were near full employment. [2] But, in my view, apocalypse not quite yet.

## 13 thoughts on “Debt and Interest Rates: Some Empirical Evidence and Implications”

1. Cedric Regula

Reasons not to worry:
1) Tbills are a tax write off at the moment.
2) Banks can take their ZIRP deposits and buy treasuries.
3) Forward PE on US stock market is 21.
4) Forward PEs on BRICs % EMs above 20.
5) Foreign CBs still want to peg to the dollar.
6) Commercial real estate, residential real estate problems not over. Some rumors that private equity firms may have leverage problems.
7) Gold and silver is expensive.
8) Commodity prices are expensive.
9) Rental prices dropping, insuring a nice read on the CPI next year.
10) Only problem is now and then we get some decent econ data, but Bernanke will be sufficiently intimidated by next years elections to hold off on rate increases till after November, no matter what the economy is doing by then.
Don’t worry….be happy!

2. Phil Rothman

Menzie: Thank you for this very useful post. I’d like to ask some econometric questions that come to mind: (1) In your paper with Jeff Frankel, you note that a Chow forecast test strongly rejects the no-break null hypothesis for 2003. Doesn’t this imply some sort of misspecification bias when the model is estimated across the full 1988-2004 sample period? (2) Your paper was written four years ago, and more data are now available. Have you estimated the model with an extended sample? If ‘yes,’ it would be interesting to see another back-of-the-envelope calculation of the type you do here. (3) Do you think it would be reasonable to allow for the possibility that the ‘int’ variable is endogenous in the estimated equation? Thanks again.

3. Menzie Chinn

Phil Rothman: Excellent points. (1) Yes, I have no doubt a better specification is feasible, but we were not able to identify it in our paper. (2) Unfortunately, we have not been able to update our results to incorporate data up to 2008. This is what I had available when I saw the NYT article today. (3) Yes, I think int is likely endogenous.

4. ppcm

Do we have the appropriate econometrics models to foresee ?
P6
http://www.brookings.edu/views/Papers/20040910orszaggale.pdf
Do we include all parameters within the econometrics models?
http://www.occ.treas.gov/ftp/release/2009-114a.pdf
Do we measure accurately the side effects of omitted cointegretion?
IMF: Banks are only half way through their loss provision
Is history a reliable tutor of wisedom?
http://www.economics.harvard.edu/faculty/rogoff/files/This_Time_is_Different.pdf
Japan bonds distribution network
http://www.bloomberg.com/apps/news?pid=20601101&sid=awQopeDIR2X8
French revolution assignats
http://en.wikipedia.org/wiki/Assignat
Can we trust our institutions ?
http://www.brookings.edu/views/Papers/20040910orszaggale.pdf
As Rubin, Orszag, and Sinai (2004) note, the effects would be larger if sustained
deficits cause investors to lose confidence in the ability of policy-makers to avoid a fiscal
crisis. Second, because the projected fiscal policy variables are only approximations of
investors’ expectations, rather than investors’ true expectations.
Do we worry on due time? Is it by itself the real cause of worry?

5. Rafael

Hi Menzie,
First, Id like to say that I am a great fan of Econbrowser. Secondly, I have a doubt (off topic): in your calculations of the impact of government spending increases in GDP growth (the debate with Posner), do you consider the deflator of government spending ALONE, or you consider the GDP deflator as a whole?
Rafael.

6. Tom

The main worry for the short-term is that Treasury’s borrowing depends on Fed stimulus, in the sense that without the constant flow of newly created money (about \$120 billion a month this year), Treasury’s borrowing demands (about \$140 billion a month) would overwhelm capital markets and drive up interest rates sharply. That locks the Fed into continuing monetary stimulus at its present scale unless and until revenues dramatically recover. If monetary stimulus is significantly reduced in 2010, we will get a sharp double dip and renewed widespread insolvency. If monetary stimulus is not reduced in 2010, we will get runaway inflation by 2011.
The debt accumulation is mainly an issue for people who do not have enough private retirement savings, as the growth of debt service payments is one more reason why Social Security and Medicare benefits will have to be significantly reduced in real terms.

7. AWH

this is a reasonable result pushing as far as modelling can go. It has no cyclical drivers except inflation.

Big debtors will always be vulnerable to the creditors pulling out. A simple debt variable with linear results cant possibly model this.

A run would likely have a dollar drop in the mix.

Probably the only way to answer the short term question is with confidence measuring data. Does the dollar go down on a bad inflation #? Or up on a good #? Even the latter could show vulnerability. Are bond yields going up on latest unfav. trade or budget deficit data?

8. Get Rid of the Fed

“The OECD November Economic Outlook reports that the output gap in 2009 was -4.92 ppts of GDP, and is projected to be -5.36 in 2010.”

Why do all (or almost all) economists believe that the output gap should be “filled” with more currency denominated debt (future demand brought to the present)?

9. ohwilleke

Iceland was too small to be considered relevant by the markets, but all it would take is one decent sized OECD country default and a rumor that the President was talking to the AG and SecTreas about a default and you’d see the Treasury bond rates triple in a few days.

10. paine

could it be more like 70 basis points ??
in fact i can’t get either of your results
7 basis points or the 1.3%

11. Menzie Chinn

paine: I don’t think so — I just rechecked my math in the equation below equation (2), and replicated my figure. The 1.3% comes from multiplying the int coefficient by 2.3 ppts of GDP, i.e., 0.574×0.023 = 0.013 or 1.3%.

AWH: The output gap is not a cyclical driver?

12. Hitchhiker

“That is, the interest rate would fall by 7 bps (holding expected inflation constant). In other words, real interest rates would stay roughly constant, ceteris paribus.”
When I was in school, one of the theories of interest rates was called the inflation expectation theory. The market simply adds the expected inflation rate to the ‘real rate’. In other words, ‘real rates’ always stay roughly constant.
And if expected inflation does not stay constant? I don’t know about you but, I pay nominal rates of interest on my debt not real rates. I agree with Tom. The fed is between a rock and a hard place. They will either change policy to protect against inflation and protect the dollar or all hell will break loose. Strong economic growth could reduce this risk but, our politicians appear determined to enact policies designed to retard growth and tax revenues.

13. paine

sorry MC
not a gotcha attempt i promise
very generous of you to even recalc
if MC’s formula has rough validity and why not
at least start there..
the punch up from jiggering the E terms variable
by say throwing in a 10% deficit not a 3.something deficit
ie a deficit — in excess of 1.6 trillion —
only pops the rate 7 x .077 = 54 basis points
hardly a spike that
so it must feed in thru inflation not expected but actual
now a sudden t bond dump of roughly a similar magnitude
1.2 trillion dumped plus the 300 assumed in MC’s second
calculation
a 5.75% jump
ie ten times the force
but a suicide run by the peg club ???
but even that loco behaviour
has hardly close to volcker dammerung proportions
so in these dooms day scenarios
the tsunami must feed in thru inflation
recall not expected but actual
only inflation get’s you into a soar
no one sees that comin ’round the bend
do they ???
on second thought
maybe a few von mises epigone
and pq=mv primitives