June 03, 2022

### Substitutability between Balance Sheet Reductions and Policy Rate Hikes: Some Illustrations and a Discussion1

Edmund Crawley, Etienne Gagnon, James Hebden, and James Trevino

This note explores the substitutability between policy rate hikes and reductions in the size of the Federal Reserve's balance sheet for the removal of policy accommodation. We do so using a version of the FRB/US model augmented to incorporate the effects of changes in the Federal Reserve's asset holdings on term premiums. We illustrate how the equivalence between policy rate hikes and balance sheet reductions in the model depends on assumptions about the evolution of the balance sheet over an extended period. Overall, the model predicts that reducing the size of the balance sheet by about $2.5 trillion over the next few years, as opposed to maintaining the size at its peak level, would be roughly equivalent to raising the policy rate a little more than 50 basis points on a sustained basis. However, this estimate is associated with considerable uncertainty. #### Economic context In response to the pandemic-driven recession, the FOMC lowered the target range for the federal funds rate rapidly to its effective lower bound (ELB) of between 0 and 0.25 percent. The Committee also purchased Treasury securities and agency mortgage-backed securities (MBS) to support smooth market functioning and progress toward its maximum employment and price stability goals. At the conclusion of the asset purchase program, the Federal Reserve's balance sheet size had increased by roughly$4.8 trillion (20 percent of annual GDP).

Policymakers have since turned to removing policy accommodation. In March 2022, they started raising the target range for the federal funds rate and conveyed their anticipation that ongoing increases in the policy rate would be appropriate at future meetings. In May 2022, the FOMC released its Plans for Reducing the Size of the Federal Reserve's Balance Sheet, with reductions beginning on June 1 of this year.2 Both the policy rate and balance sheet tools are expected to contribute to a firming of the stance of monetary policy.

#### The relationship between balance sheet reductions and policy rate hikes

In the model we use, the policy rate and balance sheet tools influence the economy primarily through their effects on the medium- and longer-term interest rates that drive economic activity.3 Policy rate actions and communications do so by affecting the cost of short-term borrowing and expectations about the path of short-term interest rates. Balance sheet policies primarily influence the term premiums embedded in medium- to longer-term yields by changing the supply—current and expected—of longer-term securities held by the public. In the model, the two tools are substitutes in terms of their ability to affect medium- and longer-term interest rates, employment, and inflation when the ELB constraint is not binding. Because of this substitutability, the model can be used to translate balance sheet reductions in terms of equivalent increases in the path of the federal funds rate that would lead to similar macroeconomic outcomes.

The model implies that a one-time permanent reduction in the Federal Reserve's holdings of 10-year equivalent Treasury securities equal to 1 percent of nominal GDP raises the term premium on a 10-year Treasury security by about 10 basis points, all else equal.4,5 In the model, this amount of policy tightening can also be achieved by raising the average expected path of the federal funds rate over the coming decade by about 10 basis points. Together, these relationships provide a simple rule of thumb for the substitutability between balance sheet reductions and policy rate hikes in the model when the economy is away from the ELB. However, as we discuss next, the translation of dollar amounts of balance sheet reductions into equivalent policy rate hikes depends on the evolution of the size and maturity composition of the balance sheet.

#### Illustrative balance sheet scenarios

We consider three illustrative balance sheet scenarios:

1. Baseline: Shrink the balance sheet starting in June 2022 in a manner consistent with the FOMC's Plans for Reducing the Size of the Federal Reserve's Balance Sheet, as captured by the illustrative baseline balance sheet scenario featured in the 2021 SOMA annual report.6 After a three-month phase-in period, let up to $60 billion in Treasury securities and up to$35 billion in agency MBS run off the balance sheet per month.
2. No runoff: Keep the balance sheet size constant in dollar terms by rolling over Treasury securities and agency MBS until growth in the demand for Federal Reserve liabilities provides a basis for resuming organic growth of the balance sheet.

##### Table 1: Differences relative to baseline balance sheet scenario in 2024:Q3
Balance Sheet Scenario Full runoff -0.79 2.14 -2.8 7.7 8 -60 -9 56 11 26

Source: Staff simulations of the FRB/US model augmented to incorporate term premium effects arising from the Federal Reserve’s asset holdings.

Table 1 also shows that the differences in policy rate paths across scenarios are roughly equal (but with an opposite sign) to the corresponding differences in 10-year term premiums. These offsetting effects on term premiums leave the 10-year real and nominal Treasury yields little changed. However, as the addendum to table 1 shows, there is no fixed relationship in the model between dollar reductions in the balance sheet at a point in time (or, alternatively, in terms of the peak-to-trough reduction) and offsetting changes in the federal funds rate. The reason is that the effects of balance sheet policies in the model depend on the public's exposure to changes in longer-term interest rates over extended periods: The larger the public's holdings of long-duration assets, the greater the compensation that the public will require for holding the underlying duration risk. Therefore, the term premium effects of balance sheet policies in the model depend not only on the size of the Federal Reserve's asset holdings but also on how these asset holdings influence the maturity composition of assets held by the public. In the no-runoff scenario, the public holds less duration risk than in the baseline scenario through the end of the next decade, whereas the duration risk held by the public in the full-runoff scenario converges to that of the baseline scenario in 2027. Accordingly, a given dollar difference from the Federal Reserve's baseline asset holdings in the medium term is associated with larger macroeconomic effects—and, thus, calls for a larger policy rate offset—under the no-runoff scenario than under the full-runoff scenario because it has a larger effect on the public's exposure to duration risk.

#### Discussion of the results and related considerations

We note that balance sheet reductions in the model may not have the same effects as balance sheet expansions. At the time of runoff, the macroeconomic effects of asset holdings may be reduced because these holdings form a smaller share of nominal GDP than when they were purchased. In addition, as noted above, the effects of balance sheet actions in the model depend not only on the change in total assets, but more generally on the change in the duration of assets held by the public. For example, the duration of Treasury securities purchased in response to the Global Financial Crisis was notably longer than the duration of Treasury securities subsequently taken on by the public because of runoff.10 By contrast, in the current episode, the average duration of Treasury securities purchased by the Federal Reserve is expected to be similar to the duration of Treasury securities taken on by the public during runoff.

In a similar vein, we emphasize that our analysis only features portfolio balance effects (as captured by the duration risk channel) and, thus, does not take account of other possible transmission channels, such as those associated with flow effects or with signaling of the intended course of the policy rate.11 Notably, in the early months of the pandemic, asset purchases played an essential role in supporting smooth market functioning, an aspect not captured by the model. As policymakers turn to reducing asset holdings, market functioning and financial conditions are much improved, which, all else equal, could make the effects of asset reductions smaller than those of asset purchases. On the other hand, if financial markets were to find it difficult to absorb large amounts of runoff, then the effects on yields could be larger than we assume. Our modeling exercise also abstracts from possible complementarities between the policy rate and balance sheet tools. Researchers have notably stressed the importance of asset purchases for giving the public confidence that the federal funds rate will remain at the ELB for an extended period in response to economic downturns.12

Finally, we stress that there is significant uncertainty regarding the transmission of balance sheet and policy rate actions to medium- to longer-term interest rates, as well as the transmission of the resulting yield curve movements to the broader economy.13 For example, the term premium estimates used in the model are based on data prior to the Global Financial Crisis when interest rates were farther above the ELB than they are today.14 However, a number of authors, including King (2019) and Gagnon and Jeanne (2020), have argued that the effects of balance sheet purchases on term premiums are likely to be attenuated when medium- to longer-term interest rates are close to the ELB, in contrast to our modeling assumption that these effects are invariant to this factor. Furthermore, there is some evidence that increases in longer-term interest rates may have smaller effects on macroeconomic outcomes when they originate from increased term premiums than when they originate from increased expectations of the policy rate.15

#### References

Andrés, Javier, David López-Salido, and Edward Nelson (2004). "Tobin's Imperfect Asset Substitution in Optimizing General Equilibrium," Journal of Money, Credit, and Banking, vol. 36 (4), pp. 665‒90.

Bonis, Brian, Ihrig, Jane and Wei, Min (2017). "The Effect of the Federal Reserve's Securities Holdings on Longer-term Interest Rates," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, April 20.

Chung, Hess, Cynthia Doniger, Cristina Fuentes-Albero, Bernd Schlusche, and Wei Zheng (2018). "Simulating the Macroeconomic Effects of Unconventional Monetary Policy," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, July 20.

Doniger, Cynthia, James Hebden, Luke Pettit, and Arsenios Skaperdas (2019). "Substitutability of Monetary Policy Instruments," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, July 19.

Fuhrer, Jeffrey C., and Glenn D. Rudebusch (2004). "Estimating the Euler Equation for Output," Journal of Monetary Economics, vol. 51 (6), pp. 1133‒53.

Gagnon, Joseph E. (2016). "Quantitative Easing: An Underappreciated Success," Policy Brief Number PB16–4. Washington: Peterson Institute for International Economics, April.

Gagnon, Joseph E. and Olivier Jeanne (2020). "Central Bank Policy Sets the Lower Bound on Bond Yields," Working Paper 20–2. Washington: Peterson Institute for International Economics, January.

Kiley, Michael T. (2014). "The Aggregate Demand Effects of Short- and Long-Term Interest Rates," International Journal of Central Banking, vol. 10 (4), pp. 69‒104.

King, Thomas (2019). "Expectation and Duration at the Effective Lower Bound." Journal of Financial Economics, vol. 134 (3), pp. 736‒760.

Krishnamurthy, Arvind and Annette Vissing-Jorgensen (2013). "The Ins and Outs of LSAPs (PDF)," in Global Dimensions of Unconventional Monetary Policy, proceedings of the Jackson Hole Economic Policy Symposium. Kansas City: Federal Reserve Bank of Kansas City, pp. 57–111.

Li, Canlin and Min Wei (2013). "Term Structure Modeling with Supply Factors and the Federal Reserve's Large Scale Asset Purchase Programs," International Journal of Central Banking, vol. 9 (1), pp. 3‒39.

Smith, A. Lee, and Victor J. Valcarcel (2022). "The Financial Market Effects of Unwinding the Federal Reserve's Balance Sheet," Research Working Paper no. 20‒23. Kansas City: Federal Reserve Bank of Kansas City, January.

Woodford, Michael (2012). "Methods of Policy Accommodation at the Interest-Rate Lower Bound (PDF)," in The Changing Policy Landscape, proceedings of the Jackson Hole Economic Policy Symposium. Kansas City: Federal Reserve Bank of Kansas City, pp. 185‒288.

1. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. The authors thank Erik Bostrom, Ally Lamb, Philippa Marks, and Jake Scott for their research assistance. The note benefited from comments and suggestions by Alyssa Anderson, Jim Clouse, Rochelle Edge, Chris Gust, Ben Johannsen, David López-Salido, Trevor Reeve, Zeynep Senyuz, and Bob Tetlow. Return to text

2. The FOMC's Plans for Reducing the Size of the Federal Reserve's Balance Sheet, released on May 4, 2022, are available at https://www.federalreserve.gov/newsevents/pressreleases/monetary20220504b.htm. Return to text

3. The model we use is a combination of the FRB/US model of the U.S. economy and a model of the Federal Reserve's balance sheet holdings and their effects on term premiums based on Li and Wei (2013). See Chung and others (2018) for a description of this augmented model and Bonis and others (2017) on the modeling of the balance sheet and associated financial effects. Return to text

4. The 10-year equivalent of a fixed-income portfolio is calculated as the par amount of on-the-run ten-year Treasury notes that would have the same par value times average duration as the portfolio under consideration; see Li and Wei (2013) for a mathematical characterization. Return to text

5. The strength of this effect in the model is within the range of estimates derived from time-series models and event studies of asset purchase program announcements. For a review of such estimates, see Gagnon (2016). Return to text

6. The assumptions underlying the report's baseline balance sheet scenario reflect the FOMC's Plans for Reducing the Size of the Federal Reserve's Balance Sheet; the median economic projections of respondents to the Survey of Primary Dealers and Survey of Market Participants conducted in March 2022 by the Open Market Trading Desk of Federal Reserve Bank of New York; and a number of illustrative auxiliary assumptions about elements such as usage of the Federal Reserve's liquidity facilities, the evolution of the Treasury General Account, and the longer-run size of the Federal Reserve's balance sheet. For details on the construction of the baseline balance sheet scenario, see Federal Reserve Bank of New York (2022), Open Market Operations during 2021, a report prepared for the Federal Open Market Committee by the Markets Group of the Federal Reserve Bank of New York, May 24, https://www.newyorkfed.org/markets/annual_reports. Because we use a different economic model and interpolation scheme, the values in the balance sheet and macroeconomic projections in our baseline scenario can differ slightly from the values reported in the annual report. Return to text

7. The degree of substitutability between balance sheet reductions and policy rate hikes in the model is somewhat insensitive to the economic projection, provided that the policy rate is not constrained by the ELB. Return to text

8. Specifically, we assume that the economic projection is underpinned by the assumptions in the baseline balance sheet scenario. Then, for each of the other two scenarios, we compute the term premium paths implied by the balance sheet side of the model when economic outcomes are identical to those in the economic projection. Treating the difference in term premium paths relative to the baseline balance sheet scenario as economic shocks, we then use the FRB/US model to find the path of the federal funds rate such that, in equilibrium, the outcomes for employment and inflation are close to those in the economic projection. In doing so, we constrain the path of the federal funds rate that supports those outcomes to be nearly parallel to the path in the baseline scenario from the simulation start in 2022:Q2 until 2030:Q4. The assumption of a uniform shift in the path of the federal funds rate offers a simple way to assess the average differences in policy rate space across scenarios over the next many years. In principle, other policy rate paths could underpin similar outcomes for employment and inflation in the model as long as these paths give rise to similar movements in medium- and longer-term real interest rates. We conduct the simulations assuming that the expectations determining financial variables, prices, and wages are model-consistent. Return to text

9. See Doniger and others (2019) for a previous illustration of the substitutability between policy rate hikes and balance sheet reductions using the FRB/US model augmented with term premium effects from the Federal Reserve's asset holdings. Our approach to computing a counterfactual policy rate path in the absence of balance sheet reductions differs modestly from the approach followed by these authors in that we consider a parallel shift in the baseline policy rate path whereas they penalize movements in the policy rate path over time, except for a one-time initial shift. The two approaches lead to similar estimates of the average difference in policy rates over the next many years across balance sheet scenarios. Return to text

10. For a discussion of the possibly smaller financial effects of balance sheet reductions than balance sheet expansions in the previous tightening episode, see Smith and Valcarcel (2022). Return to text

11. For a discussion of these other transmission channels, see, for example, Krishnamurthy and Vissing-Jorgensen (2013). Return to text

13. See Bonis and co-authors (2017) for an illustration of the sampling uncertainty attending the effect of asset purchases on term premiums in the Li and Wei (2013) model. While there is less uncertainty about the effects of policy rate decisions than balance sheet actions, the connection of policy rate actions to medium- to longer-term interest rates is loose. During the 1994‒95 tightening episode, the 10-year Treasury yield rose roughly one for one with the policy rate for a time, before retracing much of that rise. By contrast, during the 2004‒06 tightening episode, longer-term interest rates rose little as the policy rate was hiked, a situation known as the "Greenspan conundrum." In the current policy tightening episode, medium- and longer-term interest have so far risen more than the policy rate, reflecting in a large part the expectation that policymakers will raise the federal funds rate promptly toward neutral levels. Return to text

14. The subsequent period, which covers the Committee's large-scale asset purchase programs and maturity extension program, includes large public debt issuance, safe-haven flows associated with the Global Financial Crisis, the euro-area debt crisis, Brexit, and other factors that make estimation of the model challenging. Estimating the financial effects of purchases of agency mortgage-backed securities is further complicated by the difficulties in measuring the expected duration of the underlying securities because of mortgage prepayments. Return to text

15. Kiley (2014) considers both a micro-founded model with financial market segmentation (based on Andrés, López-Salido, and Nelson (2004)) and a reduced-form model (based on Fuhrer and Rudebusch (2004)). Both approaches suggest that movements in term premiums have approximately one-quarter to one-third of the effect on macroeconomic outcomes as movements in the expected path of the policy rate leading to equal changes in longer-term interest rates. Return to text