October 17, 2019

Approaches to Estimating Aggregate Demand for Reserve Balances

Joseph Andros (Federal Reserve Bank of New York), Michael Beall, Francis Martinez, Tony Rodrigues (Federal Reserve Bank of New York), Mary-Frances Styczynski, Alex Thorp (Federal Reserve Bank of New York)

Summary

Recently, the Federal Reserve has conducted a series of Senior Financial Officer Surveys (SFOS) to gather information on reserve management practices and strategies across different banks. In one survey question, banks were asked to report the approximate lowest level of reserve balances, given the prevailing constellation of short-term interest rates, their institution would feel comfortable holding before taking active steps to maintain or increase their reserve balance levels.1 We interpret banks' responses to this question as a proxy for when banks might start paying higher rates to maintain reserve balances. Throughout this note, we refer to this response as banks' demand for reserve balances.

Based on our interpretation of individual banks' responses to this question on the August 2019 SFOS, we develop a point estimate of the aggregate demand for reserve balances of banks in the system. Additionally, we account for uncertainty around this estimate, using a new approach along with an enhancement from a method in a prior FEDS note.2 Our point estimate for the aggregate demand for reserve balances of banks in the system is $800 billion and ranges between $712 billion and $919 billion, when accounting for two types of uncertainty around the point estimate.3

These uncertainty ranges attempt to address both sampling and non-sampling error, however, they are simply statistical methods applied to survey results and bank assets. These measures do not provide information on the amount of reserves that may be needed above these estimates to overcome distributional frictions in the markets for reserves. Further study is warranted to understand how high-payment flow days, particularly those that result in net reserve drains, can affect the distribution of reserves and thus money market rates.

The remainder of this note describes our approach in estimating aggregate reserve demand using survey-reported data and two methods to account for sampling and non-sampling error, concluding with a discussion of some important items for consideration.

Estimating System Reserve Demand Using Survey Reported Lowest Comfortable Levels

Data4

Seventy-seven survey panel banks (SFOS banks) participated in the August 2019 survey, representing about three-fourths of system reserve holdings at that time. In aggregate, SFOS banks reported a lowest comfortable level of reserves balances (LCLoR) of $652 billion.5 About 5,200 banks with accounts at the Federal Reserve were not included in the survey panel (non-SFOS banks), making up the remainder of system reserve holdings.6 SFOS banks tended to be larger in terms of assets and reserve holdings than non-SFOS banks as can be seen in table 1.

Table 1: Comparison of SFOS and Non-SFOS Banks ($ billions)

  SFOS Respondent Banks Non-SFOS Banks Total
LCLoR 652 To be estimated
Total Reserve Balances7 1,152 334 1,486
Total Assets8 12,943 6,840 19,783

Building the point estimate

The aggregate point estimate for the demand for reserve balances is the sum of the reported aggregate LCLoR for SFOS banks $652 billion plus an estimate of LCLoR for non-SFOS banks. For our analysis, we separated banks into one of four categories: (1) U.S. Global Systemically Important Banks (G-SIBs), (2) Large domestic banks, (3) Small domestic banks, and (4) Foreign Banking Organizations (FBOs).9 The non-SFOS bank LCLoR estimate is constructed using the ratio of the aggregate SFOS bank LCLoR to the aggregate SFOS bank total assets for each banking category multiplied by the aggregate total assets of non-SFOS banks in the respective category.10 Based on the recent survey data, our point estimate of banks' aggregate LCLoR is $800 billion as presented in row one of table 2.

Quantifying uncertainty

Our estimation methods attempt to address two types of errors that could account for uncertainty around the point estimate: sampling error and non-sampling error. Sampling error is the possibility that respondent banks differ randomly from those not in the survey, and that different results would have been generated had a different set of banks been surveyed. Non-sampling error is the possibility that respondent banks' LCLoR does not fully reflect the actual level at which that bank would begin to take action to increase its reserves. SFOS banks provide a single point estimate of their LCLoR, which may be imprecise or for which the bank may have uncertainty to some degree.

A stratified sampling methodology was used as our additional approach to account for sampling error. This methodology sorts SFOS and non-SFOS banks into the four categories previously mentioned and then takes into account that non-SFOS banks are smaller, have lower levels of reserve balances, and potentially lower LCLoRs (see Table 1 above). We estimate the aggregate LCLoR based on the average LCLoR for SFOS banks in each category and a weight to gross up each category's observed sample mean using its respective ratio of population assets to sample assets. This method produces a point estimate identical to the point estimate derived from the procedure described in the prior FEDS Note, but also produces a measure of uncertainty around that point estimate.11 Based on this approach, the 95 percent confidence interval for aggregate demand for reserves accounting for sampling error is estimated to be between $712 billion and $889 billion.

Next, a multiple imputation approach was used to account for some potential non-sampling error.12 With this approach, a representative 95 percent confidence interval is constructed using the 2.5 percent and 97.5 percent quantiles of the multiple imputation aggregate distribution. The multiple imputation approach is applied to all non-SFOS banks and SFOS banks in the large domestic and small domestic categories resulting in a representative 95 percent confidence interval for aggregate demand for reserves to be between $769 billion to $919 billion.13 Our decision to exclude SFOS U.S. G-SIB and FBO banks from the multiple imputation approach is based on our assumption that the heterogeneity in business models among these types of banks makes it less plausible that a bank's behavior would be more accurately described by the behavior of another bank in the same category. If we were to include SFOS U.S. G-SIB and FBO banks in the multiple imputation approach, the representative 95 percent confidence interval would be $778 billion to $1,148 billion.

Given these two methods provided different confidence intervals around our point estimate, and the possibility that the methodologies still may not fully capture all uncertainty, the minimum and maximum values across both confidence intervals are used to construct an estimated range for aggregate demand for reserves between $712 billion and $919 billion. A summary of our point estimate and 95 percent confidence intervals using these approaches can be found below in table 2.

Table 2: Estimates of Aggregate Reserve Demand Extrapolated from August 2019 SFOS Results ($ billions)

Approach Low Point Estimate High Notes
  -- 800 --  
Stratified sampling 712 -- 889 95% confidence interval
Multiple imputation –(estimating uncertainty for large and small domestic bank LCLoRs) 769 -- 919 Representative 95% confidence interval
Estimated Range of Aggregate Reserve Demand 712 800 919 Represents the minimum and maximum estimates

Note: If we were to apply the multiple imputation approach to SFOS U.S. G-SIB and FBO banks, the representative 95 percent confidence interval would be $778 billion to $1,148 billion. We excluded SFOS U.S. G-SIB and FBO banks from the multiple imputation approach because of our assumption that the heterogeneity in business models among these types of banks makes it less plausible that a bank’s behavior would be more accurately described by the behavior of another bank in the same category.

Additional considerations

While the methods in this note address some uncertainties around aggregate reserve demand estimates, they are not comprehensive and challenges remain. One challenge is in estimating potential non-sampling error for U.S. G-SIB and FBO SFOS banks. Exclusion of these banks from the multiple imputation approach suggests that the width of the range of aggregate LCLoR is potentially underestimated, while inclusion may potentially overstate uncertainty given the heterogeneity in these institutions' business models. Additionally, our estimates rely on data reported at a point in time and, as the market environment continues to evolve, banks may continue to refine and revise their LCLoR.

Federal Reserve officials have pointed to additional considerations that would be important in estimating necessary reserve supply in an ample reserves regime.14 However in this note, we do not attempt to quantify any additional factors, such as financial market frictions in reserves re-distribution, beyond our extrapolations of survey results that would be important in estimating necessary reserve supply. Our estimates, however, are likely a useful component for understanding aggregate reserve demand.

Conclusion

In this analysis, we estimated aggregate reserve demand using responses from a question on the August 2019 SFOS and methodologies to account for potential uncertainty around the point estimate. Although there are limitations to this analysis, the methodologies help quantify some forms of uncertainty in the point estimate, and provide a range of $712 billion to $919 billion for the aggregate demand for reserve balances of banks in the system.

References

Cochran, W.G. (1963). Sampling techniques. A Wiley publication in Applied Statistics, 2nd edition, John Wiley & Sons, Inc.

Keating, Thomas, Francis Martinez, Luke Pettit, Marcelo Rezende, Mary-Frances Styczynski, and Alex Thorp (2019). "Estimating System Demand for Reserve Balances Using the 2018 Senior Financial Officer Survey," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, April 9, 2019, https://doi.org/10.17016/2380-7172.2327.

Satterthwaite, F.E. (1946). An approximate distribution of estimates of variance components. Biometrics, 2, 110-114.


1. Respondents were asked to assume that the "constellation of short-term rates" refers to the rates on federal funds, Eurodollars, repurchase agreements, and short-dated U.S. Treasury bills over the survey period of July 2019. Those rates averaged: Interest on Excess Reserves (IOER) Rate (2.35 percent), Effective Federal Funds Rate (2.40 percent), Overnight Bank Funding Rate (2.39 percent), Secured Overnight Financing Rate (SOFR) (2.45 percent), and 3-month Treasury bill rate (2.14 percent). Return to text

2. See Keating, Martinez, Pettit, Rezende, Styczynski, and Thorp (2019). Return to text

3. Sampling error and non-sampling error are two types of uncertainty in the point estimates that will be potentially addressed by these enhanced approaches. See discussion on quantifying uncertainty below for more information. Return to text

4. Please see the August 2019 SFOS Public Summary for additional detail on the survey results: https://www.federalreserve.gov/data/sfos/sfos-release-dates.htm Return to text

5. The survey specifically asked banks: "Given the constellation of short-term interest rates relative to the IOER rate over the past month, what is the approximate lowest dollar level of reserve balances that your bank would be comfortable holding before it began taking active steps to maintain or increase its reserve balance position?" Return to text

6. Non-SFOS banks represent institutions with Federal Reserve master accounts including thrifts, credit unions, and other depository institutions. Return to text

7. This estimate represents the sum of banks' average reserve balances held in master accounts, over July 2019. Return to text

8. Asset data are as of March 31, 2019. Return to text

9. Large domestic banks consist of domestic depository institutions with more than $50 billion in combined assets that are not U.S. G-SIBs, including U.S. banking subsidiaries of foreign banking organizations. Small domestic banks are defined as domestic depository institutions with less than $50 billion in combined assets. The FBO category includes U.S. branches and agencies of foreign banks, Edge Act and agreement corporations, one U.S. banking subsidiary of a foreign banking organization that exhibits reserve management behavior more akin to the behavior of the FBO subgroup than to other similarly-sized domestic banks, and one domestic bank that chose to respond as a consolidated unit with its affiliated U.S. branch of a foreign bank. Return to text

10. See Method 2, Equation 1 $$ (\ {NonSFOS\ bank\ LCLoR\ estimate}_i = {SFOS\ bank\ category\ ratio} \times \sum_{i} {total\ assets}_i \ )$$ from Keating, Martinez, Pettit, Rezende, Styczynski, and Thorp (2019). Return to text

11. The estimates of stratum and overall LCLoR as well as sampling standard errors are derived using results in Cochran (1967), Chapter 5, while the calculation for the degrees of freedom for the confidence intervals is from Satterwaite (1946). This approach assumes that sampling from each subpopulation is random without replacement. Return to text

12. A similar simulation approach was used in Keating, Martinez, Pettit, Rezende, Styczynski, and Thorp (2019) to construct a distribution of aggregate reserve demand estimates. Recall in that approach, a distribution of aggregate LCLoR estimates was created by adding the aggregate survey reported LCLoR to a large number of simulations for LCLoR for each non-SFOS bank. In each simulation, LCLoR estimates are constructed for non-SFOS banks by multiplying individual non-SFOS bank's total assets with the ratio of SFOS bank reported LCLoR to total assets from a randomly drawn SFOS bank of the same category. This approach assumes that non-sampling error is random across banks. Return to text

13. The representative confidence interval is asymmetric around the point estimate because the distribution of LCLoR to asset ratios is skewed. Return to text

14. See Chairman Powell's Press Conference, January 30, 2019. "[T]he ultimate size of our balance sheet will be driven principally by financial institutions' demand for reserves, plus a buffer so that fluctuations in reserve demand do not require us to make frequent sizeable market interventions." See also, "Observations on Implementing Monetary Policy in an Ample-Reserves Regime," Lorie K. Logan, April 17, 2019. Return to text

Please cite this note as:

Andros, Joseph, Michael Beall, Francis Martinez, Tony Rodrigues, Mary-Frances Styczynski, and Alex Thorp (2019). "Approaches to Estimating Aggregate Demand for Reserve Balances," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, October 17, 2019, https://doi.org/10.17016/2380-7172.2459.

Disclaimer: FEDS Notes are articles in which Board economists offer their own views and present analysis on a range of topics in economics and finance. These articles are shorter and less technically oriented than FEDS Working Papers.

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Last Update: October 17, 2019