Board of Governors of the Federal Reserve System

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.
3. Full runoff: Shrink the balance sheet through the full runoff of all Treasury securities as well as maturing and prepaid agency MBS starting in June 2022, without any phase-in period (about $105 billion per month, on average over the runoff period).

The top-left and top-right panels of figure 1 report the total value of assets held by the Federal Reserve in current dollar terms and as a share of nominal GDP, respectively, in the scenarios. In all three scenarios, it is assumed that the ratio of reserves to nominal GDP declines to the average level of reserves held in December 2019 as a share of nominal GDP. Net asset purchases then resume to maintain the ratio at this illustrative value and grow other Federal Reserve liabilities in line with nominal GDP, consistent with a ratio of total assets to nominal GDP of about 21 percent. The no-runoff scenario provides a counterfactual benchmark to assess the overall effect of balance sheet reductions in the other two scenarios.

Figure 1. Illustration of the substitutability between policy rate and balance sheet actions

To determine the substitutability between policy instruments implied by the model, we first combine the baseline balance sheet scenario with an illustrative economic projection—including the policy rate, employment, and inflation—that is consistent with the median policy rate assumptions and economic projections in the March 2022 editions of the Survey of Primary Dealers and Survey of Market Participants conducted by the Open Market Trading Desk of the Federal Reserve Bank of New York.⁷ We then find, for each of the no-runoff and full-runoff balance sheet scenarios, the path of the federal funds rate that leaves the outcomes for employment and inflation essentially unchanged from those in the illustrative economic projection, restricting, for simplicity, the policy rate path to be a roughly parallel shift of the baseline path.⁸ We view this shift in the policy rate path as a measure of the substitutability between policy instruments.⁹

Table 1 reports some key simulation statistics for 2024:Q3, an illustrative date that corresponds to the resumption of asset purchases under the full-runoff scenario. For the full-runoff scenario, total asset holdings in 2024:Q3 are roughly $0.8 trillion (2.8 percent of GDP) lower than for the baseline. The macroeconomic effects of this smaller balance sheet are offset through a small reduction in the level of the federal funds rate of only 9 basis points, reflecting the modest difference in term premiums between the two scenarios. In other words, the differences in interest rates and economic effects of allowing full runoff of the balance sheet as opposed to the capped runoff in the FOMC's plans are, by this calculation, very small. For the no-runoff scenario, the level of assets is $2.1 trillion (7.7 percent of GDP) higher in 2024:Q3 than in the baseline balance sheet scenario, a difference that widens to about 2.5 trillion by the time the balance sheet size under the baseline scenario reaches its trough in mid-2025; the policy rate is 56 basis points higher in our reference quarter. Put differently, the balance sheet reduction in the baseline scenario is equivalent to a bit more than two sustained 1/4 percentage-point hikes in the policy rate when measured against the no-runoff scenario.

Table 1: Differences relative to baseline balance sheet scenario in 2024:Q3

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

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