In last Thursday’s post, John Kitchen recounted our joint work on what amount of foreign financing would be required to make consistent projections of government debt, and short and long term interest rates. That article from International Finance is now freely available on the Council on Foreign Relations website here.
One issue that people have raised is how our specification for the term premium is consistent with expected inflation.
Figure 1: Nominal and real yield curve for 3/19. Source: US Treasury.
The expectation hypothesis of the term premium would state that the long term rate is equal to the average expected short rates over the relevant period; in that case, higher long rates might be due to the higher short rates associated with anticipated future inflation. However, one can add a liquidity premium for a given maturity, assuming there is a preferred habitat motivation. Then, the yield curve need not necessarily represent merely a measure of expected future inflation. In other words, we assume away complete arbitraging away across maturities.
Figure 1 depicts the entire yield curve. We didn’t estimate the determinants of all the term spreads, only the 10 year – 3 month spread. Specifically, we estimated:
where:
- i10YR is the constant-maturity yield on 10-year Treasury notes;
- i3MO is the secondary market interest rate on 3-month Treasury bills;
- UNGAP is the gap between the unemployment rate and the NAIRU;
- INFL is the deviation of consumer price inflation from the Fed’s target inflation rate;
- STRSURP is the Federal structural budget surplus as a percent of potential GDP;
- FOREIGN is foreign official holdings of U.S. Treasuries as a percent of potential GDP;
- FED is the change in the Federal Reserve’s holdings of long-term Treasury and government securities as a percent of potential GDP.
This approach has been undertaken by Canzoneri, Cumby and Diba (FRBKC, 2002), as well as Brunner (Cato Journal, 1986).
The result should be highlighted in part because it illustrates the point that domestic private demand for government debt, as proxied by the unemployment gap, also comes into play. Those who worry about elevated interest rates shouldn’t stop worrying – but they should keep thinking about whether unemployment is likely to decline rapidly, when doing their worrying.
(Regressions for the levels of long and short interest rates, as well as using debt instead of deficits, are in the appendix to the paper.)
Update, 3/21, 11:30AM Pacific: Reader Jeff wonders about the rationale for the specification. Here is some algebra.
Suppose long term and short term rates are given respectively by:
where:
- i10YR is the constant-maturity yield on 10-year Treasury notes;
- i3MO is the secondary market interest rate on 3-month Treasury bills;
- (u-u*) is the gap between the unemployment rate and the NAIRU;
- π is the consumer price inflation rate;
- (π-π*) is the deviation of consumer price inflation from the Fed’s target inflation rate;
- bus is the Federal structural budget surplus as a percent of potential GDP;
- FOR is foreign official holdings of U.S. Treasuries as a percent of potential GDP;
- FED is the change in the Federal Reserve’s holdings of long-term Treasury and government securities as a percent of potential GDP.
The expression for long term interest rate is used in Chinn and Frankel (2005), and is based on the specification used by Laubach. The short term rate is modeled as a Taylor rule.
Subtract i3MO from i10YR:
For β2 approximately equal to unity (as in Chinn and Frankel (2005)), one recovers the specification used in the paper.
Yes, the yield curve is a mix of inflation expectations and the term premium. No, that does mean that you are assuming away arbitrage across maturities. What ever the term premium and inflation expectations are, a change in the yield on long term bonds will simply cause investors to reallocate between long and short term bonds.
And I don’t get your remark that “Those who worry about elevated interest rates shouldn’t stop worrying – but they should keep thinking about whether unemployment is likely to decline rapidly.” What you are likely picking up with the unemployment term, are times when the Fed is lowering short term rates and investors feel that the move will not lead to higher future inflation, thus the yield curve steepens. Your model does not isolate up the effect of unemployment on the level of long term rates, so I don’t know how you can use it to make such inferences.
The model is derived with a Taylor rule determining short-term interest rates, and the term structure equation also reflects that. As the unemployment gap changes (equivalent to real GDP changing relative to potential) the level of the short term interest rate will change. The term structure equation relationship is relative to the short term rate; so as the level of the short term rate changes, the level of long term rates will change, although not one for one because of the embedded relationships.
Re Menzie’s language, a rapid decline in the unemployment rate (smaller ungap) would result in a rapid rise in short-term rates, and long-term rates would rise as well, although not as much as short rates, as short rates would rise relative to long rates (and the yield spread narrow some) according to the estimated relationship, ceteris paribus. A declining unemployment rate (relative to NAIRU) would raise all interest rates, but short term rates more than long-term rates.
Jeff: See the update for algebra, which is consistent with a Taylor rule for the short rate, and the Chinn-Frankel specification for long term interest rate, and yields the specification used in the Kitchen-Chinn paper.
Right, your equations show my point. I read the last paragraph as; for those worried about i10yr take note of beta1. But you do not estimate beta1.
Jeff: The specification with beta1 is run in Chinn-Frankel, using the output gap instead of the unemployment gap. That yields a positive coefficient estimate.
“Those who worry about elevated interest rates … should keep thinking about whether unemployment is likely to decline rapidly, when doing their worrying.”
I’m not an economist, so I didn’t understand your post fully, but nevertheless I will ask this question.
What about stagflation? Aren’t the 1970’s a counterexample that show that we can have high interest rates and high unemployment?
My uneducated guess is that unemployment won’t decline rapidly, but in spite of that I fear the effect of rising rates on my bond values.
Ned Baker We have seen three Federal Reserve generated crises since 1913. From each a lesson has been learned. The Great Depression was in good part caused by the Fed, especially as they wrongly drained the buildup of excess reserves by banks trying to protect themselves against bank runs which perpetuated the initial plunge all the way to 1933. That mistake was not repeated this time. Then the stagflation of the 70s culminating in the Volcker reversal of money growth from late-1979 to 1983-5. The record since then gives solace that the Fed will not permit the 70s-type profligate money growth ever again. Thirdly, the most recent crisis was one of credit not money. This was not on the Fed’s radar screen until it struck, as the Fed is wedded to a Taylor rule that does not target asset price bubbles (home prices). The jury is still out on whether the Fed has learned this lesson, as Bernanke to this day denies Fed culpability. Let us call these three episodes: debt-deflation, stagflation, and credit bubble collapse. The recovery from the first was badly botched by the Fed and by insufficient knowledge of Keynesian fiscal stimulus. The solution to and recovery from the second episode was admirably implement by Volcker’s switch to tight money. The solution to the current episode is ongoing, and its early stage has benefited much from all that’s been learned since the 1930s. But the law of unintended consequences (to the steps taken up to now) has still to be reckoned with. As does the Fed’s history of all too often botching it.
As for this recovery, will it morph into an admixture of rising inflation coupled with a stagnating economy? As Obama is likely to gain a second term, stagnation is virtually built in. Four years from now, odds are that the current consensus GDP forecast will be seen to have been biased significantly to the upside. Certainly there are no 4% growth years anywhere on the horizon because of household deleveraging still to come, the flurry of inept economic and regulatory policy, the now historic federal debt problem that will constrain any further Keynesian fiscal stimulus, not to mention the element of global competition – anchored by Chinese mercantilism – that is constraining US production via offshoring. This leads us to inflation. Will the slack demand accompanying stagnation constrain inflation?
I have come around to the view that inflation will indeed come back, to 4% or higher versus the Fed’s target of 2%. There are far too many headwinds holding back real growth, and the Fed (no matter its lip service to price stability) is dovishly opposed to hiking the funds rate as much as warranted until they see the economy back at normal growth. Let us not forget that inflation happens with a lag. As we have never experienced anything like present conditions (where the monetary base will have to be shrunk a full 2/3rds), it takes a large act of faith to believe the Fed will be able to manage this along the razor’s edge of nudging growth higher while keeping inflation from going above 2%. Indeed the core PCE index is there now, with all to many leading inflation indicators pointing to even higher.
During the 70s, the output gap averaged 1.3%; the CBO projects a gap of 3 3/4ths% for 2013-17. By 1979 the core rate of the CPI had reached 14%. As first approximation then, inflation could easily reach 5% given (a) the difficult economic environment that will restrain the Fed’s hand, (b) political pressure from the White House to stimulate growth, (c) potentially worse shocks from oil than those of the late-70s, and (d) the unexplored territory the Fed finds itself in regarding the unprecedentedly large monetary base. Partially offsetting will be global downward pressure on wages and hence on domestic prices.
As to your concern about fixed income, look for unremitting erosion of bond values in the years immediately ahead.