Board of Governors of the Federal Reserve System

October 17, 2019

Approaches to Estimating Aggregate Demand for Reserve Balances

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)

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)

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, 2^nd 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.