## _wp14189

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---

### Unconventional monetary policy (UMP) and transmission to long rates
- After the short-term interest rate is constrained by the zero lower bound (ZLB), long-term borrowing costs decompose into:
  - an expectations component (average of expected future short-term rates)
  - a term premium
- Two principal UMP tools:
  - Forward guidance: lowers the expectations component by guiding market expectations of future short-term rates.
  - Large Scale Asset Purchases (LSAP) / Quantitative Easing (QE): lowers the term premium via portfolio balance effects (market segmentation/duration removal).
- Interaction: forward guidance can lengthen expected LSAP persistence and thus amplify portfolio-balance effects; LSAP purchases can signal revised FOMC outlooks and affect expected short rates.

### Construction of a real-time LSAP measure
- Core notion: LSAP policy strength depends on size of purchases and length of time assets remain on the Fed’s balance sheet.
- Measure constructed from market projections of the future path of the Federal Reserve’s SOMA balance (excluding short-term Treasury holdings), using Survey of Primary Dealers and policy announcements.
- Calculated as the present discounted value of current and future SOMA balances expressed as a ratio to potential GDP, in excess of historical normal level (γ = 3.94 percent).
- Normalization: a reading of 100 percent ≡ average excess SOMA balance of 100 percent of potential GDP for a year; factor 0.9967 chosen so the implied annualized discount rate is 4 percent.
- LSAP_N: a counterfactual measure assuming market participants do not update expected holding periods for already-purchased assets; LSAP − LSAP_N captures “forward guidance”–related extensions of projected holding periods.
- Key announcements and marker readings:
  - QE I purchases (Nov 2008–Mar 2010): excess SOMA ≈ 11 percent of U.S. potential GDP by end-2009.
  - QE II: excess-SOMA-to-potential-GDP ≈ 14 percent.
  - Operation Twist: longer-term holdings >16 percent of potential GDP as of August 2012.
  - QE III (since Sep 2012): purchases at a pace of $85 billion per month as of September 2013; market expectation of tapering to zero around mid-2014 implies peak excess SOMA ≈ 23 percent of potential GDP in first half of 2014.

### Model specification, data, and estimation sample
- Yield decomposition: i^τ_τ = (1/τ) ∑_{κ=0}^{τ−1} E_τ i_{1,τ+κ} + τπ^τ_τ; under affine term structure, yields and term premiums are linear in state vector X_τ.
- Econometric specification (equation (5)):
  - i_τ = α + X^I_τ β_I + X^{II}_τ β_{II} + X^{III}_τ β_{III} + LSAP_τ β_LSAP + ε_τ
  - Dependent variable i_τ: either the ten-year term premium or the expectations component (average of expected future short rates).
- Controls:
  - Macroeconomic fundamentals: unemployment rate gap; consumer confidence; ten-year-ahead CPI inflation expectation; one-year-ahead short-run inflation expectation; 12-month core PCE inflation.
  - Uncertainties: SPF dispersions for growth, unemployment, and inflation.
  - Financial volatilities: Merrill Lynch MOVE index, VIX, six-month Eurodollar implied volatility.
  - LSAP measure (PDV of excess SOMA-to-potential-GDP).
- Term premium decompositions used: Kim-Wright (KW), D’Amico-Kim-Wei (DKW), Adrian-Crump-Moench (ACM).
- Estimation sample: monthly data January 1992 to September 2013 (261 months); subsamples for pre-crisis (Jan 1992–Aug 2008) and crisis (Sep 2008–present).

### Empirical findings: LSAP, forward guidance, and the ten-year term premium
- Model fit: R^2 of 85 to 90 percent for term premium regressions.
- Macroeconomic fundamentals:
  - Term premiums tend to be counter-cyclical.
  - A 1 percentage point increase in 10-year-ahead CPI inflation expectation → 1.26 percentage point rise in 10-year term premium (significant at 1 percent).
  - Crisis sample shows increased sensitivity to short-run inflation outlook.
- Uncertainty and volatility:
  - Growth and labor-market uncertainty increase term premium (significant at 1 percent).
  - Bond-market implied volatility (MOVE) increases term premiums (significant at 1 percent).
  - VIX coefficient slightly negative and insignificant (possible flight-to-quality).
- LSAP measure effects on term premium:
  - 100 percentage point increase in LSAP measure ≡ immediate increase in SOMA balance of 20 percent of nominal potential GDP (about $3.4 trillion as of 2013) with assets held about five years before disappearance.
  - Estimated impacts:
    - Full-sample: 100 percentage point increase in LSAP → 1.12 percentage point reduction in the 10-year term premium (significant at 1 percent).
    - Crisis-sample: effect ≈ 0.62 percentage point reduction (significant at 1 percent).
- Observed (September 2008 → May 2013):
  - 10-year Treasury yield change: −217 basis points.
  - 10-year term premium change (KW): −114 basis points.
  - Contribution of constructed LSAP measure to term premium decline: −113 basis points.
  - Phase-specific LSAP contributions (KW):
    - QE I: −35 basis points
    - QE II: −9 basis points
    - Operation Twist: −19 basis points
    - QE III: −26 basis points

### Decomposition of LSAP vs. “forward guidance” effects
- Forward guidance announcements can lead markets to extend projected holding periods for already-purchased LSAP assets, raising LSAP readings.
- At the constructed LSAP peak of 104 percent of GDP in early 2013, over 45 percentage points come from gradual extensions of holding periods (the LSAP − LSAP_N difference), primarily due to forward guidance.
- Estimated coefficients: forward-guidance–related component of LSAP statistically significant at 1 percent.
- Examples:
  - Initial direct effect of $1.725 trillion QE I purchases reduced the 10-year term premium by 45 basis points in early 2009 (dissipating over time).
  - Extension of the projected “exit” date for QE I assets contributed almost 40 percentage points to the LSAP reading in early 2013 and implied a 34-basis point reduction in the 10-year term premium as of early 2013.
- Cross-phase variation:
  - LSAP effectiveness similar across QE I, QE II, and Operation Twist, but substantially weaker during QE III.
  - QE III dummy coefficient ≈ one-third to slightly more than one-half of other QE dummies; likelihood ratio tests reject all dummies = 0 at 1 percent but cannot reject equality of first three dummies against QE III.

### Signaling channel: LSAP and expected short rates
- Average of expected future short rates is strongly pro-cyclical and reacts to consumer confidence and inflation expectations.
- Near-term short-rate uncertainty (six-month Eurodollar volatility) causes average expected short rates to decline (coefficients significant at 1 percent).
- LSAP effect on expected short rates:
  - LSAP coefficient negative and significant at 1 percent, indicating LSAP lowers market projections of future short-term rates.
  - Decomposition (Sep 2008 → May 2013): 107-basis point decline in average expected future short rates:
    - 25 basis points from changes in macroeconomic fundamentals.
    - 84 basis points from changes in the LSAP measure.
  - Using LSAP_N to isolate pure purchase signaling:
    - LSAP_N coefficient only slightly smaller than LSAP and significant.
    - Implied LSAP_N contribution: at least 45 basis points of the 107-basis point decline (coefficient −0.0076 times LSAP_N = 59 percent).
    - Implied signaling effect of QE I on the ten-year average expected short rates: 27 basis points (Table 4) or 30 basis points (Table 5).

### “Tapering” myth, market reactions, and exit simulations
- QE III open-ended purchases ($85 billion per month as of Dec 2012) made markets especially sensitive to “tapering” news.
- Mid-May to June 2013: about 100 basis point rise in 10-year Treasury yield in a few weeks; market advanced projected lift-off from Q3 2015 to Q1 2015 per surveys.
- Quantitative experiment: two-quarter earlier lift-off
  - If federal funds rate rises to long-run pre-crisis average level of 4 to 4.5 percent with unchanged slope, a two-quarter earlier lift-off generates a 20 to 25 basis point increase in the average expected short rate over next ten years.
- June 2013 decomposition of a 48-basis point term premium increase:
  - 18 basis points: strengthening consumer confidence.
  - 18 basis points: heightened bond-market volatility (MOVE).
  - 12 basis points: changes in market projection of future SOMA path (earlier exit/tapering).
- Additional scenarios:
  - Faster “exit” (three years instead of five years for balance sheet normalization) would add 17 basis points to the ten-year term premium.
  - A “rush to exit” raising elasticity of term premiums to LSAP by one standard deviation would add 13 basis points.
- Magnitudes contextualized:
  - Total stock of LSAP assets already purchased by then: over $3.6 trillion.
  - Difference in total QE III purchases if tapering expected to start Sep 2013 vs Dec 2013: at most $150 billion.

### Robustness checks, alternative decompositions, and stability
- Alternative regressors: real GDP gap for unemployment gap; eight-quarter trailing SD for growth uncertainty; 24-month trailing SD for inflation uncertainty — results very similar.
- Expanded crisis sample (Aug 2007–Aug 2008 included) yields similar or slightly larger LSAP effects.
- AR(1) and differenced specifications: LSAP coefficients remain substantial and significant.
- Adding variables such as outstanding Treasury quantities yields statistically insignificant coefficients.
- Alternative term structure decompositions (KW, DKW, ACM):
  - Results very close across decompositions for term premiums, expected short rates, and LSAP effects.
  - QE I LSAP effect on 10-year term premium:
    - KW: 35 basis points
    - ACM: 41 basis points
    - DKW: 33 basis points
  - Total LSAP effects (Sep 2008 → May 2013) PDV of excess SOMA:
    - KW: 113 basis points
    - ACM: 132 basis points
    - DKW: 106 basis points

### Policy implications and recommendations
- Forward guidance and LSAP are interlinked and generate spillovers:
  - Forward guidance can extend market projections of LSAP holding periods, making LSAP effects more persistent.
  - Continued LSAP enhances credibility of forward guidance and helps keep projected future short-term rates low (signaling effect).
- As FOMC approaches exit, market turbulence may reoccur due to difficulty in firmly anchoring expectations under uncertainty.
- Recommended focus: enhance policy communications on format, procedures, criteria, and principles behind exit actions to de-link correlations between “tapering” and “exit strategy”; improved transparency should ease short-run market jitters and support timely, smooth withdrawal of unconventional monetary policy.

### Technical appendix: construction assumptions (selected)
- Data: FOMC announcements and real-time market information, especially Survey of Primary Dealers.
- Key imputation assumptions:
  1) Markets expect FOMC to implement announced purchases at steady pace within announced time frames (example: $600 billion Nov 3, 2010 → assumed pace $75 billion per month Nov 2010–Jun 2011).
  2) Markets anticipate a steady sell-off during “exit”; imputed schedules:
     - Throughout QE I: markets anticipated sell-off returning Fed balance sheet to normal by Q1 2016.
     - H2 2010/H1 2011 expectations: passive runoff in 2012, sell-off beginning early 2013 and taking five years.
     - Post-June 2011 “exit principle”: passive runoff begins six months prior to lift-off; active sell-off begins nine months after lift-off; sell-off takes five years.
  3) Unless new purchases announced, assume no expectation of new purchases.
  4) Use median survey responses when ranges reported.
- LSAP definition used in regressions:
  - LSAP_τ = sum_{i=0}^{∞} β^{i} E_{τ}( SOMA_{τ+i} / GDP^{POT}_{τ+i} − γ )
  - SOMA_τ: SOMA balance excluding Treasury bills.
  - GDP^{POT}_{τ}: CBO potential nominal GDP.
  - γ = 3.94 percent; β normalization discussed above (0.9967).

*Source: _wp14189*

### 1.   Introduction .............................................................................................3

### _wp14189 - 1.   Introduction .............................................................................................3

### Major Sections
- 1.   Introduction .............................................................................................3
- 2.   A Real-Time Measure of the Federal Reserve’s LSAP Program.................................6
- 3.   Model Specifications ................................................................................11
- 4.   Portfolio Balance Channel: The UMP and Term Premiums ...................................14
- 5.   Signaling Channel: The UMP and Short-Rate Expectations ....................................20
- 6.   The “Tapering” Myth and the “Exit” of UMP.....................................................23
- 7.   Robustness and Stability Check.....................................................................26
- 8.   Concluding Remarks .................................................................................28

### Annexes and Supplementary Materials
- References.................................................................................................29
- Technical Appendix: Construction of the Real-Time LSAP Measures ............................44

### Tables (listed)
- 1.  Determination of Ten-Year Term Premium ......................................................32
- 2.  Decomposition of Changes in Ten-Year Term Premium: September 2008 to May 2013..................................................................................................33
- 3.  Effects of LSAP and “Forward Guidance” on Ten-Year Term Premium.....................34
- 4.  Determination of the Average of Expected Future Short Rates ..............................36
- 5.  Determination of the Average of Expected Future Short Rates: Alternative LSAP Measure............................................................................................... 37
- 6.  Determination of Ten-Year Term Premium: Robustness Check.............................. 38
- 7.  Decomposition of Changes in Ten-Year Term Premium: September 2008 to May 2013, Alternative Bond Yield Decompositions ........................................................ 39
- 8.  Determination of the Average of Expected Future Short Rates: Robustness Check.... 40

### Figures (listed)
- 1.  Evolution of Market-Projected Path of Excess SOMA Holding...............................41
- 2.  Present Discounted Value of Market's Projected SOMA Balance......................41
- 3.  Ten-year Treasury Bond Yield and Term Premium Estimates..................................42
- 4.  Real-time and Counter-Factual LSAP Measures................................................................42

*Source: _wp14189 - 1.   Introduction (PDF chapter/section) — canonical URL provided in source metadata.*

### 5.  Simulations of Ten-Year Term Premium.................

### _wp14189 - 5.  Simulations of Ten-Year Term Premium.................

### Unconventional monetary policy (UMP) and transmission to long rates
- After the short-term interest rate becomes constrained by the zero lower bound (ZLB), a central bank can affect aggregate demand by influencing long-term borrowing costs, which decompose into an expectations component (average of expected future short-term rates) and a term premium.
- Two principal UMP tools discussed:
  - Forward guidance: attempts to lower the expectations component by guiding market expectations of future short-term interest rates.
  - Large Scale Asset Purchases (LSAP) / Quantitative Easing (QE): aims to lower the term premium by affecting supply-demand balance in bond markets.
- Federal Reserve LSAP activity since late 2008:
  - Cumulative purchases of about $4 trillion of long-term Treasury securities and Mortgage-backed securities (MBS).
  - Examples of guidance chronology: “some time” (January 28, 2009), “an extended period” (March 18, 2009), “at least through mid-2013” (August 9, 2011), “at least through late 2014” (January 25, 2012), “at least through mid-2015” (September 13, 2012), then switch to threshold-based guidance linking lift-off to economic indicators.
- Interaction and channels:
  - Portfolio balance channel (market segmentation/duration removal): central bank purchases change relative supplies and risk premia.
  - Signaling channel: purchases signal revised views on economic outlook or policy preferences, affecting expected future short rates.
  - Forward guidance and LSAP interact: changes in LSAP may signal changes in FOMC outlook; extensions of forward guidance may lengthen expected LSAP persistence and affect term premiums.

### Construction of a real-time LSAP measure
- Key concept: LSAP policy strength depends on (i) the size of purchases and (ii) the length of time purchased assets remain on the central bank’s balance sheet.
- Constructed measure:
  - Based on market participants’ projections of the future path of the Federal Reserve’s SOMA (System Open Market Account) balance, using survey data (notably the Survey of Primary Dealers) and policy announcements.
  - Calculated as the present discounted value of current and future SOMA balances (excluding short-term Treasury holdings), expressed as a ratio to potential GDP, in excess of historical normal level.
  - Changes in this real-time measure capture market expectations of size and persistence of LSAP over time and serve as a proxy for QE strength.
- Historical markers in the constructed series:
  - November 25, 2008 initial LSAP announcement: purchase up to $100 billion in agency debt and up to $500 billion in agency MBS.
  - QE I (November 2008 to March 2010): $1.25 trillion MBS, $300 billion longer-term Treasury, $175 billion agency debt → excess SOMA ≈ 11 percent of U.S. potential GDP by end-2009.
  - QE II (November 2010 to June 2011): additional $600 billion Treasury purchases → excess-SOMA-to-potential-GDP ≈ 14 percent.
  - Operation Twist (September 2011 to December 2012): re-composition, raised SOMA longer-term Treasury holdings to >16 percent of potential GDP as of August 2012.
  - QE III (since September 2012 and ongoing as of text): purchases at a pace of $85 billion per month as of September 2013; market expectation of tapering to zero around mid-2014 implies a peak excess SOMA ≈ 23 percent of potential GDP in the first half of 2014 (Bernanke September 18, 2013).
- Purpose: enable separate empirical analysis of LSAP effects on expectations vs. term premium components and to assess interactions with forward guidance (e.g., forward guidance extensions shifting projected SOMA path upward).

### Model specification and data
- Yield decomposition framework:
  - Yield to maturity of a τ-period zero-coupon bond i^τ_τ = (1/τ) ∑_{κ=0}^{τ−1} E_τ i_{1,τ+κ} + τπ^τ_τ, i.e., expectations component plus term premium.
  - Under an affine term structure, yields and term premiums are linear functions of state vector X_τ: i^τ_τ = A^τ + B^τ X_τ; τπ^τ_τ = A^{τπ} + B^{τπ} X_τ.
- Econometric model (equation (5)):
  - i_τ = α + X^I_τ β_I + X^{II}_τ β_{II} + X^{III}_τ β_{III} + LSAP_τ β_LSAP + ε_τ
  - Dependent variable i_τ represents either the term premium component or the expectations component of the ten-year Treasury bond yield.
- Variables included:
  - Macroeconomic fundamentals:
    - Unemployment rate gap (unemployment rate − CBO potential unemployment rate)
    - Consumer confidence (expectations component of Conference Board’s Consumer Confidence)
    - Long-run inflation expectation (ten-year-ahead CPI inflation forecast from SPF)
    - Short-run inflation expectation (one-year-ahead from Reuters/University of Michigan Surveys of Consumers)
    - Short-run actual inflation (12-month changes in core PCE)
  - Macroeconomic uncertainties:
    - Growth uncertainty (SPF four-quarter-ahead real GDP forecast dispersion)
    - Labor market uncertainty (SPF four-quarter-ahead unemployment forecast dispersion)
    - Inflation uncertainty (SPF four-quarter-ahead GDP deflator inflation forecast dispersion)
  - Financial market volatilities:
    - Merrill Lynch MOVE index (implied volatility in longer-term U.S. Treasury market)
    - VIX (implied volatility from S&P 500 options)
    - Implied volatility from six-month-ahead Eurodollar futures options (uncertainty re near-term policy rate)
  - The constructed LSAP measure (present discounted value of projected excessive SOMA holdings to potential GDP; solid black line in Figure 2).
- Term premium decomposition methods used:
  - Kim-Wright (KW) decomposition (Federal Reserve Board)
  - D’Amico, Kim, and Wei (DKW)
  - Adrian, Crump and Moench (ACM)
- Estimation sample: monthly data January 1992 to September 2013 (261 months). Subsamples: pre-crisis (January 1992–August 2008) and crisis (September 2008–present) used for stability checks.

### Empirical findings: LSAP, forward guidance, and ten-year term premium
- Model fit:
  - Model (5) fits the term premium data well with R^2 of 85 to 90 percent.
- Macroeconomic fundamentals and term premiums:
  - Term premiums tend to be counter-cyclical; unemployment gap coefficient not always statistically significant in full/pre-crisis samples, but becomes significant in the crisis sample.
  - Long-run inflation expectations: a 1 percentage point increase in 10-year-ahead CPI inflation expectation → 1.26 percentage point rise in 10-year term premium (statistically significant at 1 percent).
  - Short-run inflation expectations and realized 12-month core PCE inflation have much smaller effects on term premium in full/pre-crisis samples; crisis period shows increased sensitivity to short-run inflation outlook.
- Uncertainty and volatility effects:
  - Growth uncertainty and labor market uncertainty increases term premium (statistically significant at 1 percent).
  - Inflation uncertainty: statistically insignificant pre-crisis, significant in crisis sample (negative coefficient discussed as possibly episode-specific).
  - Rise in bond market implied volatility (MOVE) increases term premiums (significant at 1 percent).
  - VIX coefficient slightly negative and insignificant (possible flight-to-quality effect).
  - Near-term short-rate volatility uncertainty has little effect on long-term term premium.
- LSAP measure effects on term premium:
  - Interpretation: a 100 percentage point increase in LSAP measure = immediate increase in SOMA balance of 20 percent of nominal potential GDP (about $3.4 trillion as of 2013) with assets held for about five years before disappearing.
  - Estimated effects:
    - Full-sample (column 1, Table 1): 100 percentage point increase in LSAP measure → 1.12 percentage point reduction in the 10-year term premium (statistically significant at 1 percent).
    - Crisis-sample (column 3, Table 1): effect ≈ 0.62 percentage point reduction (statistically significant at 1 percent).
- Overall observed market movements (September 2008 to May 2013):
  - 10-year Treasury bond yield declined by 217 basis points.
  - Decline in 10-year term premium over this period: 114 basis points (KW decomposition).
  - Decomposition of drivers of term premium change (Sep 2008 → May 2013):
    - Changes in macroeconomic fundamentals increased term premium by 26 basis points (largely due to unemployment rate remaining 1.5 percentage points higher than in Sep 2008).
    - Declines in macroeconomic uncertainties lowered term premium by 19 basis points.
    - Improvements in financial market stability contributed a similar decline in term premium (magnitude similar to 19 basis points).
    - Changes in the constructed LSAP measure reduced the term premium by 113 basis points (substantial persistent LSAP effect).
  - Phase-specific LSAP contributions to term premium decline:
    - QE I (November 2008 to March 2010): −35 basis points
    - QE II: −9 basis points
    - Operation Twist (September 2011 to August 2012): −19 basis points
    - QE III (September 2012 to May 2013): −26 basis points
- Example event:
  - January 25, 2012 FOMC extension of forward guidance from “at least through mid-2013” to “at least through late 2014”:
    - 10-year Treasury yield declined by 17 basis points on the announcement day and the following day.
    - Decomposition of that 17 basis point decline: 12 basis points from term premium decline, 5 basis points from decline in average of expected future short-term rates.
- Interpretation and caveats:
  - LSAP effects are primarily evaluated through “stock effects” (persistent changes in prices from movements along Treasury demand curves) rather than “flow effects.”
  - Forward guidance can affect term premiums indirectly by revising market expectations of LSAP persistence (exit timing), thereby generating portfolio balance effects in addition to its direct effect on expected short-rate path.
  - Different term structure decompositions (KW, DKW, ACM) are used for robustness; Section 7 reports largely consistent findings across methods.

*Italic: Source — _wp14189 - 5.  Simulations of Ten-Year Term Premium..................*

### Section 2, a “forward guidance” announcement of a later federal funds rate “lift-off”notonly

### _wp14189 - Section 2, a “forward guidance” announcement of a later federal funds rate “lift-off”notonly

### Decomposition of LSAP and “forward guidance”
- A “forward guidance” announcement of a later federal funds rate “lift-off” not only lowers the market projection of future short-rate path and thus the expectations component of long-term interest rates, but may cause market participants to speculate on a later “exit” of the LSAP program and generate an upward revision to their projected path of future SOMA balance and the  measure.
- Example: a pure FOMC announcement in early August 2011 (intention to keep the federal funds rate at exceptionally low levels “at least through mid-2013”) resulted in a 20 basis point decline in the 10-year term premium according to the model estimate.
- To isolate LSAP purchases per se from “forward guidance” effects, a counter-factual 
  
  measure is constructed assuming market participants never revise expectations of holding periods for already-purchased assets; the difference between the original  and 
  
  captures “forward guidance”-related extensions of projected holding periods.

### Quantitative findings on LSAP vs. “forward guidance”
- Constructed 
  
  measure and its difference from the original  reveal substantial contributions from “forward guidance.”
- At the height of the constructed  measure at 104 percent of GDP in early 2013, over 45 percentage points come from gradual extensions of the length of the holding period of LSAP assets (the difference between the two lines in Figure 4), primarily affected by “forward guidance.”
- Model estimation (Table 3) indicates the “forward guidance”-related component of the  measure has a coefficient estimate statistically significant at the one percent level.
- Estimated effects:
  - Initial effect of the $1.725 trillion QE I purchases per se was to reduce the 10-year term premium by 45 basis points in early 2009; this effect tends to dissipate over time.
  - Extension of the projected “exit” date for QE I assets contributed almost 40 percentage points to the  reading in early 2013 and implied a 34-basis point reduction in the 10-year term premium as of early 2013.
- Decomposition conclusion: reported quantitative figures for different QE phases should be interpreted as combined effects of both LSAP and “forward guidance,” not LSAP per se.

### Variation in LSAP effectiveness across QE phases
- The model allows the pure purchases (
  
  ) and the “forward guidance”-related term ( − 
  
  ) to change over QE phases (QE I, QE II, Operation Twist, QE III).
- Estimation results:
  - Substantial variation across QE phases, notably QE III: estimated coefficient for the QE III dummy is about one-third of that of other QE dummies in the first exercise and slightly more than half in the second exercise.
  - Likelihood ratio tests:
    - Null that all dummies equal zero rejected at the one percent significance level.
    - Null that the first three QE-phase dummies are equal and jointly different from the QE III dummy cannot be rejected at any commonly used significance level (p-value is greater than 25 percent in both cases).
- Summary points:
  - LSAP program since late 2008 has been effective in reducing term premiums, by more than 100 basis points as of mid-2013.
  - Both pure bond purchases and gradual extensions of projected holding periods (closely related to “forward guidance”) contributed substantially to declines in term premiums.
  - Effectiveness of LSAP and “forward guidance” in lowering term premium exhibits substantial variation over time, with much weaker effects during the QE III phase.

### Signaling channel: LSAP, “forward guidance,” and expected short rates
- Theoretically, perfect “forward guidance” that pins down the future short-rate path would make the expectations component of long-term yields independent of LSAP. In practice, uncertainties, threshold-type guidance (e.g., unemployment rate at 6.5 percent described as a “threshold” rather than a “trigger”), lack of information on post-lift-off path, and diverse FOMC preferences prevent this.
- Replacing dependent variable in equation (5) by the expectations component of the 10-year Treasury yield yields:
  - The average of expected future short rates is strongly pro-cyclical (rises when unemployment gap diminishes or consumer confidence strengthens).
  - Strong responses to increases in long-run or short-run inflation expectations.
  - Mild response to macroeconomic uncertainties; correlations with financial volatility measures are smaller than for term premiums.
  - Heightened near-future short-rate uncertainty (e.g., 6-month Eurodollar volatility) causes average expected short rates to decline; coefficients significant at the one percent level.
- LSAP effect on expected short rates:
  -  coefficient estimate is negative and statistically significant at the one percent level, indicating substantial negative effect of LSAP on market projections of future short-term interest rates.
  - Decomposition of a 107-basis point decline in the average of expected future short rates from September 2008 to May 2013:
    - 25 basis points attributed to changes in macroeconomic fundamentals.
    - Changes in macroeconomic uncertainties and financial market uncertainties are small and largely offsetting.
    - Changes in the  measure contribute 84 basis points to the total decline.
- Isolating pure LSAP signaling effect using 
  
  :
  - Coefficient on 
    
    is only slightly smaller than on  and remains statistically significant.
  - Implied changes in 
    
    account for at least 45 basis points in the 107-basis point decline (coefficient estimate of -0.0076 in column 1 of Table 5 times an 
    
    reading of 59 percent).
  - Implied “signaling” effect of QE I purchases on average expected future short rates over next ten years is 27 basis points (based on Table 4) or 30 basis points (based on Table 5).

### “Tapering” myth, market reactions, and “exit” simulations
- QE III context:
  - Since December 2012 QE III is open-ended: FOMC purchases $85 billion of long-term Treasury and other securities each month without announcing termination date.
  - Market more sensitive to “tapering” news than anticipated: 10-year Treasury yield jumped by about 100 basis points in a few weeks after mid-May 2013, particularly around the June 19 FOMC meeting.
  - Chairman Bernanke noted puzzlement over the magnitude of the move at his June 19, 2013 press conference.
- Market linkage hypothesis:
  - Market participants likely assume high correlation among “tapering,” federal funds rate “lift-off,” and timing of LSAP asset unloading (“exit”).
  - Surveys indicate market moved projected lift-off forward from the third quarter of 2015 to the first quarter of 2015.
- Quantitative effects of a two-quarter earlier lift-off:
  - If federal funds rate rises steadily after lift-off to long-run pre-crisis average level of 4 to 4.5 percent and slope unchanged, a two-quarter earlier lift-off generates a 20 to 25 basis point increase in the average of expected short rate over next ten years.
- Effect of earlier “tapering” on term premiums via SOMA path revision:
  - Example hypothetical experiment (Figure 5): assume fundamentals and volatilities return to long-run pre-crisis averages over three years beginning in June 2013; model predicted values match May 2013 actual.
  - Model-implied 10-year term premium path as of June 2013, assuming market anticipates a two-quarter earlier “exit,” rises to -22 basis points (almost identical to actual reading of -24 basis points).
  - Decomposition of the 48-basis point term premium increase observed that month:
    - 18 basis points attributable to strengthening in consumer confidence.
    - 18 basis points attributable to heightened bond-market volatility (MOVE index).
    - 12 basis points attributable to changes in market’s projection of future SOMA path.
  - Market perception of earlier lift-off/exit, stronger confidence, and higher bond volatility accounted for the majority of the observed rise in long-term yields in June 2013.
- Additional scenarios and sensitivities:
  - If market projects a faster “exit” process (three years instead of five years for Fed’s balance sheet to return to normal) in June 2013, the 10-year term premium would have increased by another 17 basis points.
  - If heightened uncertainty generates a “rush to exit” effect by increasing the elasticity of term premiums to changes in the  measure by one standard deviation, the 10-year term premium would have jumped by another 13 basis points.
- Contextual magnitudes:
  - Total stock of LSAP assets already purchased by then was over $3.6 trillion.
  - Difference in total QE III purchases if tapering expected to start in September 2013 instead of December 2013 would be at most $150 billion.

### Policy implications and communication
- Forward guidance and LSAP are intimately intertwined and generate spillovers:
  - “Forward guidance” can extend the market’s projected holding period for LSAP assets, making LSAP effects more persistent.
  - Continued LSAP enhances credibility of “forward guidance” and helps keep projected future short-term rates low (signaling effect).
- As FOMC approaches exit, market turbulence may reoccur because expectations are difficult to firmly anchor amid heightened uncertainty and discretionary future policy.
- Recommended focus:
  - Enhance policy communications on format, procedures, criteria, and principles behind exit actions to de-link correlations between “tapering” and “exit strategy.”
  - Improved transparency should help ease short-run market jitters and support a timely and smooth withdrawal of unconventional monetary policy.

*Source: _wp14189 - Section 2, a “forward guidance” announcement of a later federal funds rate “lift-off”notonly*

### conclusions. First I estimate the model using alternative definitions of the underlying regressors,

### _wp14189 - conclusions. First I estimate the model using alternative definitions of the underlying regressors,

### Robustness checks and alternative specifications
- Replaced unemployment rate gap by the real GDP gap; replaced survey measures of real growth uncertainty by an eight-quarter trailing standard deviation of the real GDP growth rate; replaced inflation uncertainty by a 24-month trailing standard deviation of core PCE price index inflation. Estimation results are very similar to those reported in Tables 1 to 5.
- Expanded the crisis sample to include August 2007 to August 2008 (first stage of the most recent financial crisis). Estimation results based on this sample period are very close to those in Tables 1 and 4; estimated LSAP effects become slightly larger.
- Experimented with AR(1) specifications and differencing regressions. The estimated LSAP coefficients remain substantial and statistically significant.
- Adding other potential determinants (e.g., quantity of outstanding Treasury securities) produced coefficient estimates that are not statistically significant. Foreign official purchases of U.S. Treasury securities were noted as a possible determinant, but previous studies have not found a large and significant effect on bond yields (Rudebusch, Swanson, and Wu 2006).

### Alternative bond-yield decompositions (robustness)
- Re-estimated using D’Amico, Kim, and Wei (2010, DKW) and Adrian, Crump and Moench (2012, ACM) decompositions; compared to Kim-Wright (KW).
  - DKW: 4 factors including an observable inflation factor; uses nominal and real zero-coupon Treasury yields.
  - ACM: 5 factors (first five principal components of term structure); uses nominal zero-coupon yields and constant maturity Treasury yields that bear coupons; estimation via 3-step OLS.
  - KW: 3 latent factors; full-scale non-linear maximum likelihood estimation; uses nominal zero-coupon Treasury bond yields.
- Estimation results based on alternative decompositions are very close to KW results (Tables 6 to 8).
  - Term premiums are counter-cyclical and react strongly to changes in consumer confidence, long-run inflation expectations, macroeconomic uncertainties, and financial market volatilities (Table 6).
  - Estimated LSAP effects are strikingly similar across KW, ACM, and DKW, both quantitatively and in statistical significance.

### Quantitative LSAP effect comparisons across decompositions
- During “QE I” phase, estimated LSAP effect on 10-year term premium:
  - KW sample: 35 basis points
  - ACM: 41 basis points
  - DKW: 33 basis points
- Total LSAP effects from September 2008 to May 2013 (PDV of excess SOMA balance):
  - KW sample: 113 basis points
  - ACM: 132 basis points
  - DKW: 106 basis points

### Determination of average future short rates (robustness)
- Estimates of the average of expected future short rates are very similar across bond-yield decompositions (Table 8).
  - All three decompositions suggest average future short rates are counter-cyclical, reacting strongly to long-run and short-run inflation and inflation expectations, and less so to macroeconomic uncertainties and financial market volatilities than term premiums.
  - The estimated LSAP effect in signaling future short-term interest rates is substantial and statistically significant in all decompositions.

### Main conclusions on channels and dynamics
- Both the “signaling” channel and the “portfolio rebalance” channel are important in the transmission of unconventional monetary policy.
- Additional spillover effects documented:
  - “Forward guidance” leads to a gradual extension of the market’s projected length of the holding period of LSAP assets, generating a more persistent LSAP effect on term premiums.
  - Continuing LSAPs enhance the credibility of “forward guidance” and help guide market expectations of future short-term interest rates, generating a “signaling” effect.
- Effectiveness of LSAP:
  - Similar during QE I, QE II, and Operation Twist phases.
  - Declined substantially during QE III phase.

### Decomposition of changes in 10-year yields and term premiums (selected figures)
- Changes in 10-year Treasury Bond Yields (September 2008 to May 2013): -217.1 basis points (Table 2; Table 7 shows same -217.1 across KW, ACM, DKW).
- Changes in 10-year Term Premium (same period):
  - KW: -114.0 basis points
  - ACM: -93.9 basis points
  - DKW: -79.9 basis points
- Changes in the PDV of Excess SOMA Balance (same period):
  - KW: -112.8 basis points
  - ACM: -131.5 basis points
  - DKW: -106.0 basis points
- Breakdown of PDV of Excess SOMA Balance by phases (KW / ACM / DKW):
  - “QE I” Phase: -34.9 / -40.6 / -32.7 basis points
  - “QE II” Phase: -8.6 / -10.0 / -8.0 basis points
  - “Operation Twist” Phase: -19.1 / -22.2 / -17.9 basis points
  - “QE III” Phase: -26.1 / -30.4 / -24.5 basis points
- Periods without active purchases (examples: April-October 2010, July-August 2011): contribution about -24.1 / -28.3 / -22.9 basis points (KW / ACM / DKW).
- Residuals: 10.9 / 27.9 / 38.0 basis points (KW / ACM / DKW).

### Policy simulations and exit dynamics
- Model simulations (Figure 5) illustrate scenarios for ten-year term premium under:
  - Actual path
  - Model prediction in May 2013
  - Model prediction in June 2013
  - Faster Sell-off
  - Rush to Exit
- Simulations underscore the importance of policy transparency in minimizing unnecessary market turbulence and ensuring a timely and smooth exit of unconventional monetary policy stimulus.

### Limitations and avenues for future research
- This study focuses on U.S. Treasury yields; broader assessment requires analyzing how declines in private borrowing costs translated into real activity.
- The constructed real-time LSAP measure is useful for further quantitative analyses and can be extended to study similar policies in other countries.
- Future research: assessing transmission to private borrowing costs and real activity; applying methodology to other countries.

### Technical appendix: construction of the real-time LSAP measures (selected steps, assumptions)
- Data sources: official FOMC policy announcements and real-time market information, especially the Survey of Primary Dealers from the Federal Reserve Bank of New York.
- Key assumptions and observations used to impute market projections of future excess SOMA balance:
  1) Market participants anticipate the FOMC will implement announced asset purchases at a steady pace within the announced time frame (example: November 3, 2010 announcement of “a further $600 billion of longer-term Treasury securities by the end of the second quarter of 2011” → assumed purchasing pace about $75 billion each month from November 2010 to June 2011).
  2) Market participants anticipate a steady pace for the FOMC to sell off LSAP assets during the “exit.” Specific imputation assumptions:
     - Throughout QE I (November 2008 to March 2010), market participants generally anticipated the purchased assets would be sold off and the Fed’s balance sheet would return to normal by the first quarter of 2016.
     - In second half of 2010 and first half of 2011, market participants expected passive runoff to occur “at some point in 2012,” sell-off to begin in early 2013 and take five years to finish (as reflected in the Survey of Primary Dealers).
     - Since the FOMC announced its “exit principle” in June 2011, assumed market expectation: passive runoff begins six months prior to the “lift-off,” active sell-off begins nine months after the “lift-off,” and the sell-off takes five years to finish.
  3) Unless the FOMC explicitly announces a new purchasing plan, assume market participants do not expect new purchases beyond announced ones.
  4) Use median responses of surveyed projections when Survey results provide a range.
- Definition of the LSAP measure:
  - LSAPτ = sum_{i=0}^{∞} β^{i} E_{τ}( SOMA_{τ+i} / GDP^{POT}_{τ+i} − γ )
  - SOMAτ: SOMA balance excluding holdings of Treasury bills.
  - GDP^{POT}_{τ}: Congressional Budget Office’s estimates of potential nominal GDP.
  - γ: average of SOMA-to-potential-GDP ratio from 2003 to 2008 = 3.94 percent.
  - β: time discount factor (value set in the paper; specific β value not included in supplied excerpt).

*Italic: Source — _wp14189 - conclusions. First I estimate the model using alternative definitions of the underlying regressors,*

### 0.9967 so that the implied annualized discount rate is 4% (choosing a different value implies

### _wp14189 - 0.9967 so that the implied annualized discount rate is 4% (choosing a different value implies

### Construction and normalization of the LSAP measure
- The LSAP measure is normalized so that a reading of 100 percent is equivalent to an average excess SOMA balance of 100 percent of potential GDP for the period of a year.
- The normalization uses a factor of 0.9967 so that the implied annualized discount rate is 4% (choosing a different value implies almost no changes to the estimated magnitude of the LSAP effect).

### Definition and role of the LSAP_N measure and forward guidance
- The LSAP_N measure is constructed similarly to the LSAP measure, with a key difference in expectations updating timing:
  - At each point in time, it is assumed that market participants do not update the expected length of the holding period of the LSAP assets that have already been purchased.
  - Example: After the completion of QE I purchases in March 2010, even if market participants have gradually updated their expectations of the unloading schedule of all LSAP assets, the assumption is that market participants will only update their expectations of the length of the holding period for assets to be purchased going forward, but not the QE I assets.
- Implications:
  - The LSAP_N measure only captures the effects of asset purchases per se.
  - LSAP_N is not affected by the Fed’s “forward guidance” over time.
  - The difference between LSAP and LSAP_N captures the influences of “forward guidance” in extending the holding period of purchased LSAP assets.

### Key LSAP announcements: November 2008 to September 2013 (selected chronology)
- November 25, 2008: The Federal Reserve announced that it would initiate a program to purchase up to $500 billion mortgage-backed securities (MBS) and up to $100 billion government-sponsored enterprises (GSE) direct obligations. The purchases would begin “before year-end,” and the purchases are expected to take place over several quarters.
- December 16, 2008: The FOMC indicated that “it stands ready to expand its purchases of agency debt and mortgage-backed securities as conditions warrant. The Committee is also evaluating the potential benefits of purchasing longer-term Treasury securities.”
- March 18, 2009: The FOMC announced that it would “increase the size of the Federal Reserve’s balance sheet further by purchasing up to an additional $750 billion of agency mortgage-backed securities, bringing its total purchases of these securities to up to $1.25 trillion this year, and to increase its purchases of agency debt this year by up to $100 billion to a total of up to $200 billion. Moreover, to help improve conditions in private credit markets, the Committee decided to purchase up to $300 billion of longer-term Treasury securities over the next six months.”
- August 12, 2009: The FOMC eliminated the “up to” phrase in its intended purchase amount of Treasury securities. It also stated that it would slow the pace of these transactions and anticipates that the full amount will be purchased by the end of October.
- September 23, 2009: The FOMC eliminated the “up to” phrase in its intended purchase amount of the MBS, as well as its plan to “slow the pace of these purchases in order to promote a smooth transition in markets and anticipates that they will be executed by the end of the first quarter of 2010.”
- November 4, 2009: The FOMC clarified that the intended purchase amount of agency debt would be $175 billion, instead of the previously announced “up to $200 billion.”
- August 10, 2010: The FOMC announced that it “will keep constant the Federal Reserve’s holdings of securities at their current level by reinvesting principal payments from agency debt and agency mortgage-backed securities in longer-term Treasury securities. The Committee will continue to roll over the Federal Reserve’s holdings of Treasury securities as they mature.”
- November 3, 2010: The FOMC announced that it “intends to purchase a further $600 billion of longer-term Treasury securities by the end of the second quarter of 2011, a pace of about $75 billion per month.”
- September 21, 2011: The FOMC announced that it “intends to purchase, by the end of June 2012, $400 billion of Treasury securities with remaining maturities of 6 years to 30 years and to sell an equal amount of Treasury securities with remaining maturities of 3 years or less.”
- June 20, 2012: The FOMC announced its intention “to continue through the end of the year its program to extend the average maturity of its holdings of securities.”
- September 13, 2012: The FOMC announced that it plans to “increase policy accommodation by purchasing additional agency mortgage-backed securities at a pace of $40 billion per month.”
- December 12, 2012: The FOMC announced that it “will continue purchasing additional agency mortgage-backed securities at a pace of $40 billion per month. The Committee also will purchase longer-term Treasury securities after its program to extend the average maturity of its holdings of Treasury securities is completed at the end of the year, initially at a pace of $45 billion per month.”
- September 18, 2013: The FOMC decided to “continue purchasing additional agency mortgage-backed securities at a pace of $40 billion per month and longer-term Treasury securities at a pace of $45 billion per month.”

*Source: _wp14189 - 0.9967 so that the implied annualized discount rate is 4% (choosing a different value implies*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14189.pdf_