Term Structure Modeling with Supply Factors and the Federal Reserve's Large-Scale Asset Purchase Programs
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Does the sheer quantity of bonds outstanding, and not just expected interest rates, move Treasury yields? Fitting a yield-curve model to United States data from 1994 to 2007 in which bond and mortgage-security supply affects yields only through the extra compensation investors demand for holding long maturities, this paper finds a one percentage point fall in the supply-to-output ratio lowers the ten-year yield by about 10 basis points. Applied to the Federal Reserve's 2008 to 2012 purchases, the combined effect is roughly 100 basis points. It matters because that figure anchors how far bond buying can substitute for rate cuts, though signalling is excluded by construction.
What this paper finds — and why it matters
This 2013 International Journal of Central Banking paper by Canlin Li and Min Wei asks whether changes in the supply of Treasury securities and agency mortgage-backed securities (MBS) affect nominal Treasury yields, and uses the answer to evaluate the Federal Reserve’s large-scale asset purchase (LSAP) programs. The authors build a no-arbitrage affine Gaussian term-structure model, motivated by the Vayanos-Vila (2009) preferred-habitat framework, whose state vector consists of two observable yield factors (the level, proxied by the 5-year yield, and the slope, the 5-year-minus-1-month spread, which together capture over 99% of yield variation) plus three observable supply factors: the Treasury ten-year-equivalents-to-GDP ratio, the agency-MBS par-to-GDP ratio, and MBS average duration. The model is deliberately restricted so the short rate loads only on the yield factors and supply factors carry zero own risk premium, meaning supply shocks affect yields only through the term premium and not through interest-rate expectations (the signaling channel is shut down by construction); the model is estimated by a two-step Ang-Piazzesi (2003) procedure on monthly pre-crisis data from March 1994 to July 2007. In-sample, supply factors are significantly and positively related to the term premium (reduced-form R-squared up to 0.89), a one-percentage-point decline in the Treasury ten-year-equivalents-to-GDP or MBS par-to-GDP ratio lowers the 10-year Treasury yield by roughly 10 basis points, a one-year shortening of average MBS duration lowers it by roughly 7 basis points, and supply factors account for about 9% (5-year) and 20% (10-year) of conditional term-premium variance at a 60-month horizon. Applying the estimated model out-of-sample to evaluate the Fed’s 2008-2012 asset purchases, and using the authors’ preferred approach that treats each program as a gradually implemented supply shock that investors expect to be partly reversed by future asset sales, the paper finds LSAP1 lowered 2-/5-/10-year Treasury yields by about 16/52/60 basis points, LSAP2 by about 2/13/19 basis points, and the Maturity Extension Program (MEP) by about 2/13/19 basis points, for a combined 10-year effect of roughly 100 basis points — the paper’s headline number. The authors are explicit that the model captures only the term-premium channel of LSAPs by construction, that estimates are sensitive to assumptions about the pace and timing of expected future asset sales, and that the model is fit on a pre-crisis sample and then applied out-of-sample to the very different 2008-2012 period.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What question does the paper ask, and what is its headline finding?
The paper asks whether the supply of Treasury securities and agency mortgage-backed securities (MBS) affects nominal Treasury yields, and finds that the Federal Reserve’s first and second large-scale asset purchase programs (LSAP1 and LSAP2) together with the Maturity Extension Program (MEP) lowered the 10-year Treasury yield by a combined total of roughly 100 basis points. The authors describe their contribution as being, “to our knowledge, … the first to use an arbitrage-free term structure model to evaluate the effects of LSAPs” (p. 6), embedding supply effects directly into a no-arbitrage pricing framework rather than relying on event-study or reduced-form regression approaches alone.
Q2. What is the term-structure model, and how does it embed supply effects?
The model is a no-arbitrage affine Gaussian term-structure model in the tradition of Duffie-Kan (1996), Dai-Singleton (2000), and the Ang-Piazzesi (2003) macro-finance approach, with a state vector of two observable yield factors (a level factor, proxied by the 5-year yield, and a slope factor, the 5-year-minus-1-month spread, which together explain over 99% of yield variation) augmented with three observable supply factors: the Treasury ten-year-equivalents-to-GDP ratio, the agency-MBS par-to-GDP ratio, and MBS average duration. The setup is motivated by the Vayanos-Vila (2009) preferred-habitat model, in which preferred-habitat investors and risk-averse arbitrageurs interact with a risk-neutral Treasury/Fed, so that changes in the quantity of duration risk arbitrageurs must absorb move the compensation (term premium) they require.
Q3. How is the model restricted so that supply operates only through the term premium, not through interest-rate expectations?
The short rate is specified to load only on the two yield factors, not on any supply factor, so supply shocks cannot affect investors’ expectations of future short rates — by construction they can only affect yields through the term premium. Supply factors are further assumed to carry zero own risk premium, but they still affect term premiums indirectly by altering the market prices of risk attached to the yield factors. This modeling choice deliberately shuts down the “signaling” channel through which asset purchases might otherwise affect yields by conveying information about the future path of policy, isolating the term-premium (portfolio-balance) channel that is the paper’s object of interest.
Q4. What data and sample period does the paper use, and how are supply shocks identified?
The model is estimated on monthly U.S. data from March 1994 to July 2007 — a pre-crisis sample — using Treasury zero-coupon yields (3, 6, 12, 24, 60, 84, and 120 months) built from the Svensson (1995) curve maintained at the Federal Reserve Board, with a 10-year term-premium target from the Kim-Orphanides (2012) three-latent-factor model. Supply variables (Treasury par-to-GDP, par-weighted average maturity, ten-year-equivalents-to-GDP; agency-MBS par-to-GDP and average duration) are constructed from total outstanding securities (Treasury MSPD data; Barclays for MBS) net of Federal Reserve (SOMA) holdings. Estimation proceeds in two steps following Ang-Piazzesi (2003): first the factor VAR and short-rate equation are estimated by OLS, then risk-premium parameters are chosen to minimize the gap between observed and model-implied yields and term premiums at 6-month, 1-, 2-, 7-, and 10-year maturities. Supply shocks are identified via a lower-triangular (Cholesky-type) volatility matrix, reflecting that Treasury and MBS issuance responds to the business cycle, so that a supply shock orthogonal to yield-factor shocks has no effect on yield expectations.
Q5. What do the reduced-form regressions and the model’s estimated term-premium loadings show about the relationship between supply and the term premium?
Reduced-form motivating regressions show supply factors are significantly and positively related to the 10-year term premium, with R-squared values as high as 0.89, and the estimated model assigns substantial term-premium loadings to each supply factor: 10.16% per percentage point for the Treasury ten-year-equivalents-to-GDP ratio, 9.73% per percentage point for the MBS par-to-GDP ratio, and 6.79 per year of MBS duration. These loadings translate directly into the marginal effects and LSAP calculations described below.
Q6. How large are the estimated marginal effects of supply changes on yields, and how much of term-premium variance do supply factors explain?
A one-percentage-point decline in the Treasury ten-year-equivalents-to-GDP ratio, or in the MBS par-to-GDP ratio, lowers the 10-year Treasury yield by approximately 10 basis points; a one-year shortening of average MBS duration lowers it by approximately 7 basis points. In a variance decomposition at the 60-month horizon, supply factors account for about 9% of conditional term-premium variance at the 5-year maturity and about 20% at the 10-year maturity, with the Treasury supply factor dominating and the supply contribution rising with both maturity and horizon.
Q7. How does the paper translate these estimates into effects of LSAP1, LSAP2, and the MEP, and what two approaches does it use?
The paper reports two sets of LSAP estimates: a “one-period shock” calculation that treats each program as an instantaneous supply shock that then mean-reverts (Table 6), and a “sequence of shocks” calculation that instead models the gradual implementation of each program together with investors’ expectations about future exit sales (Table 7) — the authors’ preferred approach. Under the one-period-shock approach, LSAP1 (calibrated as roughly a 1.2% Treasury ten-year-equivalents shock plus an 8.9% MBS-par shock, corresponding to about $300 billion in Treasury purchases and $1.25 trillion in MBS purchases) lowers 2-/5-/10-year yields by about 27/64/99 basis points; LSAP2 (a 2.7% ten-year-equivalents shock) lowers them by about 3/14/26 basis points; and the MEP (a 2.6% ten-year-equivalents shock) lowers them by about 3/13/25 basis points.
Q8. Why does the preferred sequence-of-shocks approach give different, generally smaller, estimates, and what is the combined headline effect?
Under the sequence-of-shocks approach, which assumes investors expect asset sales to begin two years after each program ends and to finish five years after, LSAP1 lowers 2-/5-/10-year yields by about 16/52/60 basis points, LSAP2 by about 2/13/19 basis points, and the MEP by about 2/13/19 basis points, for a combined 10-year effect of about 98, or roughly 100, basis points — the paper’s headline figure, and one the authors note is similar in magnitude to Chung et al. (2012). The gap between the two approaches reflects that the term-premium effect of a supply shock depends not just on the purchase amount but on how far away, and how gradually, investors expect the resulting reduction in outstanding supply to be reversed by future sales: “the further away and the slower the future exit sales, the bigger the term premium effect” (pp. 30-31).
Q9. What limitations and alternative channels does the paper explicitly acknowledge?
The authors flag that the model is estimated on a pre-crisis sample (1994-2007) and then applied out-of-sample to the very different 2008-2012 LSAP period; that the one-period-shock estimates “may overstate or understate the true effect” by ignoring possible deviations of shock persistence from historical norms; and that the sequence-of-shocks estimates depend materially on assumptions about the expected timing and pace of future unwinding. More fundamentally, the model captures only the term-premium channel by construction and does not speak to other channels the literature has proposed for LSAP effects: the safety/clientele channel of Krishnamurthy and Vissing-Jorgensen (2011), the localized-scarcity channel of D’Amico and King (2012), and the signaling channel of Bauer and Rudebusch (2012). The authors state plainly that “disentangling the various channels remains a challenge and is left for future research” (Conclusion, p. 33). They also note that a fully specified MBS prepayment model is “beyond the scope” of the paper, so MBS duration is approximated as a linear function of its own lag and the lagged yield level rather than modeled structurally.
Key terms in this paper
Definitions below follow the paper's own usage.
- Term premium
- in this paper, the component of a long-term bond yield in excess of the expected average of future short rates over the bond's life, as extracted from the Kim-Orphanides (2012) three-latent-factor model for the 10-year target and from the paper's own affine model at other maturities; it is the sole channel through which supply factors are allowed to affect yields, since the short rate itself is specified to be independent of supply.
- Preferred-habitat / arbitrage channel (Vayanos-Vila 2009)
- the paper's motivating theoretical mechanism, in which "preferred-habitat" investors have fixed maturity preferences and risk-averse arbitrageurs must be compensated to bear the interest-rate risk of absorbing the residual supply of duration; reducing the supply of long-duration securities that arbitrageurs must hold lowers the compensation (term premium) they require, and effects spread across close substitutes such as Treasuries and agency MBS.
- Ten-year equivalents (TYE)
- the paper's supply metric for aggregate Treasury duration exposure, converting the outstanding stock of Treasury securities of varying maturities into an equivalent quantity of 10-year notes based on their relative sensitivity to a change in the 10-year yield, then scaled by GDP; it is the primary Treasury-side supply factor in the model and the metric used to calibrate the size of each LSAP program's shock.
- Signaling channel (shut down by construction)
- the alternative channel, emphasized elsewhere in the literature (e.g., Bauer and Rudebusch 2012), through which asset purchases could affect yields by signaling the future path of the policy rate; the authors' model rules this out by specifying that the short rate loads only on the yield factors and not on supply, so any yield effect the model attributes to LSAPs in this paper is, by assumption, a term-premium effect rather than a signaling effect.
- One-period shock vs. sequence-of-shocks calibration
- two ways the paper translates an LSAP program's purchase size into a path of the supply factors feeding the model — the one-period-shock approach (Table 6) treats a program as a single shock that then decays according to its estimated historical persistence, while the sequence-of-shocks approach (Table 7, the authors' preferred method) instead builds in the program's gradual implementation and an assumed future schedule of exit sales beginning two years after completion and ending five years after, which the authors show materially changes the estimated yield effects.