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The impact of the maturity of US government debt on forward rates and the term premium: New results from old data

The impact of the stock and maturity of government debt on longer-term bond yields matters for monetary policy. This column assesses the magnitude and relative importance of overall bond supply and maturity effects on longer-term US Treasury interest rates using data from 1976 to 2008. Both factors have a significant impact on both forwards and term premia, but maturity of public debt appears to matter more. The results have implications for exit from unconventional policies, and also for the links between monetary and fiscal policy and debt management.

Revisiting the supply effect

The question of the impact of the stock and maturity of net government debt on longer-term US Treasury yields, and the potential implications for central bank balance sheet policies, matters for monetary policy. For Keynes, Tobin, and Milton Friedman, decisions about the maturity of government debt issuance had major implications for the term structure of interest rates (Turner 2011).1 But earlier empirical studies, arguably starting with Modigliani and Sutch (1967), seemed to find limited support for supply effects, with Ben Friedman ([1981] 1992) a notable exception. In any event, the rise of New Classical Macroeconomics and the mainstream New Keynesian model led many economists to ignore portfolio balance effects. Under this new orthodoxy, that inhabited a world of (near-)perfectly elastic demand for government debt, the relative supply of short- and long-dated government bonds had little effect on longer-term interest rates. The yield curve was in turn determined by the current level and expected path of the policy rate. For Ricardian-type reasons, the method of financing a given level of government expenditure would have no impact on the level of consumption, and hence on the path of interest rates. And so the proper focus of monetary policy became solely the assessment of the correct level for the short-term policy rate.

But in trying to assess the prospective and actual impact of large-scale central bank purchases on government bonds, a number of recent studies have attempted to estimate the impact of debt issuance on interest rates. Kuttner (2006) freely admits that his estimates, on quarterly data from 1964–2004, may be ‘too strong’, as he finds that a 2 percentage-point increase in central bank holdings of debt reduces the term premium by around 200 basis points, but they are certainly indicative of the results emerging from several subsequent studies. Greenwood and Vayanos (2013) find that a 1 percentage-point decrease in (maturity-weighted) debt to GDP lowers long-term yields by some 40 basis points.2 D’Amico et al. (2012), estimated on weekly data from December 2002 to October 2008, suggest that a 1 percentage-point fall in the ratio of privately held debt to total outstanding debt will tend to reduce yields by around 5 basis points, and that a decrease in the duration of Treasury securities by 1 year will tend to push 5- to 10-year yields down by around 100 basis points. Krishnamurthy and Vissing-Jorgensen (2012) find on low-frequency long-run data from 1919–2008 that a reduction in debt to GDP by 1 percentage point will tend to reduce long-term yields by some 2 basis points. Greenwood et al. (2014) find in a weekly regression over 1983–2007 that a 1% increase in the ratio of T-bills to GDP may increase the returns on short-term Treasuries by as much as 16 basis points on 2-week paper, and this pari passu will tend to reduce the term premium.

These studies have opened up two questions: what is likely to be the impact of changes in the structure of government debt on interest rates in normal times; and what impact might there be from any future open market operations that change the maturity of government debt? In this note, I summarise some new results from Chadha et al. (2013a and 2013b) and leave the second to subsequent research.

Estimating pre-crisis effects

In Chadha et al. (2013a and 2013b), my coauthors and I want to estimate the impact of both overall supply and maturity effects on the 5-year forward 10-year rate and estimates of the 10-year term premia. First, our work differs from these other studies by following Laubach (2009) in the use of CBO 5-year-ahead projections of public debt and deficits. Second, we focus our estimates on the pre-crisis period by using semi-annual data from 1976 to 2008, thus ensuring that our results do not reflect crisis-induced market illiquidity. Finally, we use a series of the average maturity of federal debt held outside the Federal Reserve. We use a number of business cycle and financial controls, as well as surveys of professional forecasters for long-horizon inflation expectations. Whether we model the 5-year forward 10-year interest rate or the 10-year term premium, the results we obtain are remarkably consistent:

  • A 1 percentage-point increase in the prospective debt to GDP ratio is associated with an increase in the long-term interest rate by around 2 basis points;
  • A lengthening of 1 month in the maturity of public debt held outside the Federal Reserve is associated with an increase in the long-term interest rate by around 10–15 basis points.

The results suggest that supply effects do play a significant role in driving longer-term interest rates. There are two caveats on these results. First, if debt managers seek to increase the maturity of debt when longer-term interest rates are expected to rise in the future, our results may be somewhat upward-biased. But we note that in the period we study, many changes in the maturity of debt were led by legislation, rather than any short-run response to market conditions (e.g. in 1976 and 2001). And, second, if we extend the estimation sample there is some evidence of structural instability from 2008 onwards, which is perhaps hardly surprising, and further motivates the use of the pre-crisis period.

The Greenspan Conundrum and the impact of QE

We run two analyses of the model’s ability to explain changes in longer-term interest rates. In February 2005, Alan Greenspan lamented that long-term interest rates had continued to fall even though the Federal Funds rate had been raised by 150 basis points to 2.5%. In his view, there was no obvious explanation, and he famously called this a ‘conundrum’. In subsequent months, the Federal Reserve continued to raise the Federal Funds rate, which reached 5.25% in July 2006, but the 10-year long-term rate did not increase as much as it had in previous tightening episodes. Our estimates suggest that an important reason for the level of the long-term rate might have been the shortening of the maturity of public debt – average maturity reached a peak of over 70 months in late 2001 and then it steadily declined to reach a trough of 56 months in March 2005. According to our estimates, a decline in the average maturity of almost 58 months would lead to a reduction of over 150 basis points. In Figure 1, we show the cumulative change in the forward rate from 2002H1 and the estimated contribution of expected future debt and average maturity in terms of a 95% confidence band, as well as the point contribution from maturity alone. And we note that any undershoot in forwards seem reasonably well explained by changes in maturity.

Figure 1. Net supply, maturity, and the Greenspan Conundrum

QE1 was announced in November 2008. From then to the end of 2012, marketable debt (including Federal Reserve holdings) rose by 28.5 percentage points of GDP. The Federal Reserve absorbed some 7 percentage points of this increase. And so by buying long-dated bonds, the Federal Reserve also lowered the average maturity of debt by around 7 months. Table 1 shows how much higher the 5-year-ahead 10-year rates and the 10-year term premium would have been if public debt held outside the central bank had been 7 percentage points of debt higher and average maturity 7 months longer. Specifically, the absorption of 7 percentage points of debt translates into a 12–15 basis points lower forward rate and a 0–8 basis points lower term premium, and a 7-month lower maturity translates into an 80–100 basis points lower forward rate and 67–89 basis points lower term premium. Combing these two effects, Fed purchases since November 2008 may have contributed to lowering the 5-year forward 10-year rates by approximately 90–115 basis points and the 10-year term premium by approximately 70–95 basis points.

Table 1. Potential effects of central bank purchases of Treasuries, November 2008 to end-2012

Note: Change in the first column refers to changes in privately held debt which could be attributed to central bank interventions since November 2008

Portfolio balance effects: Segmentation and the limits to arbitrage

Portfolio balance effects are a convenient catch-all for why both the size and maturity of public debt can matter for the determination of interest rates. Preferred habitat theories involve segmented markets in which investors demand bonds at a specific maturity, and the price of that bond is thus determined by local demand and supply at that maturity. For example, pension funds may have a strong preference for longer maturities in order to match their liabilities. Furthermore, Krishnamurthy and Vissing-Jorgensen (2012) have argued that government bonds, particularly those of the US, have such a high degree of liquidity and safety that they are close substitutes for money. And so the prices of government debt may be affected by their relative supply and the demand for money-like debt, rather than simply determined by the expectations hypothesis (e.g. Bauer and Rudebusch 2013). Work by Greenwood and Vayanos (2013) suggests that although inelastic demand and supply for debt at each maturity could be ironed out by arbitrageurs, risk aversion (and liquidity constraints) limit their ability to take on duration risk, and lead them to demand a higher premium when the relative supply of longer-duration government bonds increases. As the price of risk rises, bond prices at all maturities are affected, albeit by more at longer maturities.

Concluding remarks

That our results are estimated in the 30 or so years prior to the financial crisis allows us to exclude the possibility that they have been driven by extraordinary financial market conditions. Our results apply to the market for US government debt. How well overall supply and maturity effects explain longer-term interest rates in other countries remains an open question. However, Iwata and Fueda-Samikawa (2013), applying a very similar methodology to yields on Japanese government bonds, also found significant overall supply and maturity effects. It seems reasonably clear, though, that in any exit from extraordinary policies these effects will complicate the choice of path for the policy rate, as key benchmark longer-term rates will be buffeted by announcements and actual debt sales, which will alter the net supply and maturity of public debt held outside the Federal Reserve. More generally, it would also appear that fiscal policy and its financing may have more substantive implications for monetary policy than was thought a generation ago. Ultimately, if our findings about the importance of maturity are accepted, then the Federal Reserve may also consider making more use of operations that change the maturity of debt held by the private sector and overseas.

Author’s note: I am grateful for comments and support from my co-authors Philip Turner and Fabrizio Zampolli at the Bank for International Settlements.


Bauer, M D and G D Rudebusch (2013), “The Signaling Channel for Federal Reserve Bond Purchases”, Federal Reserve Bank of San Fransisco Working Paper 11-21.

Chadha, J S, P Turner, and F Zampolli (2013a), “The Interest Rate Effects of Government Debt Maturity”, BIS Working Paper 415.

Chadha, J S, P Turner, and F Zampolli (2013b), “The Ties that Bind: Monetary Policy and Government Debt Management”, Oxford Review of Economic Policy 29(2): 548–581.

D’Amico, S, W English, D Lopéz-Salido, and E Nelson (2012), “The Federal Reserve’s Large-scale Asset Purchase Programmes: Rationale and Effects”, Economic Journal, 122(564): F415–F446.

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Greenwood, R and D Vayanos (2013), “Bond Supply and Excess Bond Returns”, London School of Economics Working Paper.

Iwata, K and I Fueda-Samikawa (2013), “Quantitative and Qualitative Monetary Easing Effects and Associated Risks”, Japan Centre for Economic Research.

Krishnamurthy, A and A Vissing-Jorgensen (2012), “The Aggregate Demand for Treasury Debt”, Journal of Political Economy 120(2): 233–267.

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[1]Indeed, “monetary policy determines the composition of the government portfolio” was the first line in Wallace (1981) that expounded the logic of a Modigliani–Miller theorem for central bank market operations.

[2] Note that they calculate that QE1 and QE2 lowered the maturity-weighted debt to GDP ratio by just under 0.7 percentage points. So they suggest that the impact of these operations on longer-term yields was some 30 basis points.

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