April 09, 2019

### Estimating System Demand for Reserve Balances Using the 2018 Senior Financial Officer Survey

Thomas Keating, Francis Martinez, Luke Pettit, Marcelo Rezende, Mary-Frances Styczynski, and Alex Thorp

Summary
Private sector analysts and researchers have produced a wide range of estimates of the banking system's demand for reserve balances post-crisis, but one feature common to all estimates is a level of reserve demand significantly above pre-crisis levels and below holdings observed over the last five years. Estimating the lowest level of reserves the banking system needs is challenging because most banks currently hold reserves in excess of their operating needs, and historical demand for reserves may not provide an accurate guide in the post-crisis environment.

In this note, we add to this discussion by introducing a range of estimates of the banking system's contemporary demand for reserves based on newly available, confidential micro data from a Senior Financial Officer Survey (SFOS) conducted by the Federal Reserve in September 2018. Among other things, the survey asked senior financial officers from each respondent bank for the approximate lowest level of reserves their institution would feel comfortable holding before taking actions to maintain or increase their reserve balance levels. Using a variety of methods, we extrapolate from survey results to arrive at a range of estimates of the lowest comfortable level of reserves for the whole banking system. Although caution is warranted when interpreting this analysis, we estimate that the aggregate lowest comfortable level of reserve balances in the banking system ranges from about $650 billion to just under$900 billion.

The remainder of this note describes the survey and data, details our estimation methodologies, presents our estimates, and discusses some limitations of our analysis.

Background on the Senior Financial Officer Survey
One of the questions on the September 2018 SFOS asked each responding bank to identify the approximate lowest level of reserve balances, given the prevailing constellation of short-term interest rates, that it would feel comfortable holding before taking active steps to maintain or increase its reserve balance levels.1 Conceptually, if a respondent bank's reserve balances were to fall below this reported 'lowest comfortable level of reserves' (LCLoR), the bank would seek to replenish its reserve balances to its stated lowest level by borrowing funds or otherwise adjusting its balance sheet.

SFOS responses were collected from senior financial officers at 30 domestic banks and 21 U.S. branches and agencies of foreign banking organizations (FBOs). In total, these 51 banks held about $1.37 trillion in reserve balances on average in August 2018, representing slightly over two thirds of the reserve balances in the system at the time. Survey respondents indicated that, in aggregate, their LCLoR was$617 billion, which was a little under half of their August 2018 average reserve balance holdings. As seen in table 1, aggregate LCLoR as a share of total average reserve balances was similar for domestic and foreign institutions.2

#### Table 1: September 2018 SFOS Results and August 2018 Reserve Holdings for Surveyed Banks

Totals ($billions) All Respondents Domestic Foreign Lowest comfortable level of reserve balances1$617.2 $385.0$232.2
Average reserve balances (August 2018)2 $1,368.2$827.5 $540.7 1. As reported in September 2018 SFOS. 2. Federal Reserve data. Return to table The reported LCLoR answers from banks in the SFOS sample provides a new, confidential set of micro data that offers insight into contemporary demand for reserve balances. We next describe how we combine SFOS results with additional data to create a panel suitable for extrapolating from survey answers to the broader universe of banks to estimate the demand for reserves for the whole banking system. Following this description, we present the results of four methods for estimating aggregate system LCLoR. Data The data for our analysis describes 51 banks that participated in the SFOS (SFOS banks) and around 5,300 other depository institutions that did not participate in the survey (non-SFOS banks), but that have accounts at the Federal Reserve. For each bank (SFOS and non-SFOS), we gather data on reserve balances, reserve balance requirements, total assets, and an indicator of whether or not the bank or its holding company is subject to the liquidity coverage ratio (LCR) in the United States.3 In addition, we categorize each bank in our panel into one of four bank categories: (1) U.S. Globally Systemically Important Banks (GSIBs), (2) Other large domestic banks, (3) Small domestic banks, and (4) FBOs. As shown in tables 2 and 3, SFOS banks are noticeably larger than non-SFOS banks, on balance. Summary statistics of panel #### Table 2: Summary Statistics for SFOS banks SFOS Sample N Mean 25th Percentile 75th Percentile Reserve Balances ($ billions) 51 27 3 27
LCLoR (percent of reserve balances) 51 54% 35% 71%
Total Assets ($billions) 51 227 44 198 LCLoR (percent of total assets) 51 8% 1% 10% Reserve Balance Requirement ($ billions) 51 2 0.1 2
Aggregate Reserve Balance Requirements ($billions) 51 94* Subject to U.S. LCR (# of respondents) 25 - - - * Total reserve balance requirements for all institutions described in table. Return to table #### Table 3: Summary Statistics for Non-SFOS banks Non-SFOS Population N Mean 25th Percentile 75th Percentile Reserve Balances ($ billions) 5205 0.1 0.001 0.02
LCLoR (percent of reserve balances) - - - -
Total Assets ($billions) 5299 1.5 0.1 0.8 LCLoR (percent of total assets) - - - - Reserve Balance Requirement ($ billions) 5295 0.01 0 0.0007
Aggregate Reserve Balance Requirements ($billions) 5295 30* - - Subject to U.S. LCR (# of respondents) 16 - - - * Total reserve balance requirements for all institutions described in table. Return to table Estimating System Lowest Comfortable Level of Reserve Balances As noted earlier, SFOS respondents indicated, in aggregate, that their LCLoR was$617 billion. We treat this aggregated amount from the SFOS as given. To arrive at a system LCLoR estimate, we devise four methods of varying complexity for approximating non-SFOS banks' LCLoR, which we then combine with the aggregated LCLoR SFOS responses to calculate a system estimate. We chose to investigate four methods in an effort to convey a range of estimates that somewhat account for the inherent uncertainty in estimating system reserve demand, particularly given the reliance of our analysis on survey data rather than observed behavior.

The rest of this note provides a range of estimates for the aggregate system LCLoR using the four methodologies. The estimates produced by each method are summarized in table 5 at the end of this section.4

Method 1 - Reserve Demand Assuming Non-survey Reserve Balances Equal Reserve Balance Requirements

All banks are required to hold a certain fraction of specified deposit liabilities as reserves at the Federal Reserve to satisfy reserve requirements. For many banks, reserve requirements are small or even zero, while others are required to meet their requirements by holding balances at the Federal Reserve. With this in mind, reserve requirements could be a reasonable lower bound estimate of LCLoR for non-SFOS banks. To approximate non-SFOS banks' LCLoR, in this method we assume that each non-SFOS bank would begin taking active steps to maintain or increase its reserve balance levels only when their reserve balances fell to the level of their reserve balance requirement (RBR), which averaged about $33 billion in aggregate at the time of the survey. Assuming non-SFOS banks' RBR levels remain unchanged, our lower bound estimate of aggregate system LCLoR is thus around$650 billion (aggregated SFOS responses of $617 billion plus non-SFOS banks' aggregate RBR of$33 billion).

The assumption that non-SFOS banks will return to holding just enough reserve balances to meet their RBR is likely too conservative given the changes to liquidity management and the regulatory treatment of reserves post-crisis. Moreover, even pre-crisis, RBR levels were often insufficient to cover day-to-day account payment needs, which led to banks holding more balances than required by mandatory RBR. Thus, we view this estimate as a lower bound.

Method 2 - Reserve Demand using LCLoR to Assets Ratio by Bank Category

In this method, we use LCLoR answers from SFOS banks in aggregate by bank category (U.S. GSIB, Large domestic bank, small bank, FBOs) to create estimates of LCLoR for non-SFOS banks of the same category. To do this, we construct a ratio of survey respondent's aggregate LCLoR to aggregate total assets for all SFOS banks in each bank category. On an individual bank level, we view this ratio as a measure of the minimum allocation to reserves a SFOS bank is willing to bear in its overall portfolio. At an aggregated level by SFOS bank category, we call this ratio the "SFOS bank category ratio." Assuming that the SFOS bank answers are representative of non-SFOS banks in the same category, we estimate non-SFOS bank LCLoR by multiplying this SFOS-bank category ratio by the total assets of individual non-SFOS banks in the same bank category, as shown in equation 1.

$${NonSFOS\ bank\ LCLoR\ estimate}_i = {SFOS\ bank\ category\ ratio} \times \Sigma_i {total\ assets}_i, \ \ \ \ \text{(Equation 1)}$$

where i is an index of non-SFOS banks by bank category that are outside the survey sample. We then sum the non-SFOS LCLoR estimates by bank category and add them to the $617 billion aggregate LCLoR of all SFOS-banks in the survey sample. Using this approach, we estimate a level of aggregate LCLoR in the system of just over$820 billion.

Method 3 - Reserve Demand using Multiple Imputation

For Method 3, we employ "bootstrapping" or multiple imputation to produce a distribution of estimates of aggregate system LCLoR. We create this distribution of estimates by adding the $617 billion aggregate LCLoR from SFOS banks to a large number of simulations of LCLoR for each non-SFOS bank. We construct LCLoR estimates for non-SFOS banks in each simulation by multiplying individual non-SFOS bank's total assets with the ratio of survey reported LCLoR to total assets from a randomly drawn survey respondent of the same bank category. The approach here is effectively the same exercise as the previous method except that the ratio applied to non-SFOS bank asset data is not an aggregate ratio at the bank category level, but rather is a randomly selected survey response to total asset ratio for an individual SFOS bank in the appropriate category. The simulated level of LCLoR for each non-SFOS out-of-sample bank is summed with the reported aggregate LCLoR of$617 billion to arrive at an estimate of total system LCLoR. We ran this simulation 1,000 times to create a distribution of total system LCLoR estimates. In ascending order, the total system LCLoR estimates, the 250th, 500th, and 750th estimates represent the 25th, median, and 75th percentiles of the distribution of estimates, respectively. As shown in table 5, these estimates are about $830 billion,$850 billion, and $870 billion. Method 4 - Reserve Demand based on Fitted Values Using a Regression Equation In this method, we investigate the relationship between reported LCLoR and various SFOS bank characteristics, specifically asset size, bank domicile, and U.S. regulatory treatment. To do this we estimate parameters for a simple regression, defined below in equation 2, which we use to predict the LCLoR of non-SFOS banks.5 Our preferred model specification is defined as: $$\ln⁡(LCLoR)= \beta_0 + \beta_1 \ln⁡(total\ assets) + \beta_2 domestic + \beta_3 LCR + error, \ \ \ \ \text{(Equation 2)}$$ where ln(LCLoR) is the natural log of LCLoR, ln(total assets) is the natural log of total assets for the second quarter of 2018; domestic is an indicator for bank domicile, which is equal to 1 for domestic banks and equal to 0 for foreign banks; and LCR is an indicator for liquidity coverage ratio treatment, which is equal to 1 for banks subject to either the standard or the modified U.S. LCR requirements and equal to 0 otherwise. We include these two indicators in the regression equation because they are frequently cited as important drivers of reserve demand in the post-crisis period. The results in table 4 indicate that domestic banks report a smaller lowest comfortable level of reserves than foreign banks of a similar size and regulatory treatment. Indeed, the coefficient estimate of the region indicator is negative and statistically significant. We believe this reflects the lower complexity of small and mid-size domestic firms, and the fact that foreign firms may not be subject to U.S. LCR, but still subject to foreign liquidity regulations - a facet not captured in this specification. Finally, the coefficient estimate of the LCR indicator is positive, as expected, but it is not statistically significant. When fitted values for each non-SFOS bank predicted using this model are added to the$617 billion aggregate LCLoR of SFOS banks, this approach yields an estimate of aggregate system LCLoR of just under $900 billion. #### Table 4: Estimated Regression Equation of LCLoR Coefficients Standard Errors 1.024* (0.201) -2.222* (0.361) 0.443 (0.483) 0.577 51 Note: The dependent variable is the natural logarithm of the lowest comfortable level of reserves (LCLoR). * Indicates statistical significance at the 5% level. Return to table Summarizing the four estimates By assuming that the answers of survey respondents are representative of non-surveyed banks, the SFOS results provide a means of estimating the aggregate 'lowest comfortable level of reserves' in the system. As we might expect to see increasing competition among banks to retain reserves around the aggregate 'lowest comfortable level of reserves' in the system, these estimates can be thought of as rough measures of the level of reserves at which overnight interest rates might become more responsive to changes in the supply of reserves, indicating points at which the supply of reserves might meet the steep part of the demand curve for reserves. The estimates for aggregate LCLoR produced using the four methods described above are summarized in table 5. Although the estimates range from about$650 billion to roughly $900 billion, three of the four estimates are clustered between$800 and $900 billion. #### Table 5: Estimates of System Lowest Comfortable Level of Reserves (LCLoR) Using SFOS Results Method (1) Assuming non-survey LCLoR equals reserve requirements (2) Extrapolating SFOS sample LCLoR to out-of-sample banks (3) Extrapolating SFOS sample LCLoR to out-of-sample banks using bootstrapping (4) Fitting out-of-sample LCoR using a regression equation estimated from SFOS sample Aggregate LCLoR Estimate$647.7 $821.6$847.7 $895.8 Notes 25th percentile:$829.3; 75th percentile: $869.2 Caveats It is important to note the limitations of these estimates and warn that caution is warranted in interpreting them. Methods 2, 3, and 4 rely on the assumption that answers from SFOS sample banks represent the answers that non-survey banks would have provided if they had participated in the survey. Even though we have taken measures to improve the representativeness of sampled banks, our approach is imperfect and there are certainly cases where this is an inappropriate assumption.6 Furthermore, all of these estimates also assume perfect money market efficiency in distributing reserves within the banking system so that each bank is simultaneously at their LCLoR. These estimates also assume there are no additional factors, such as the Treasury General Account, which affect the supply of reserves on any given day. These assumptions may be unrealistic given signs of frictions in money markets and observed volatility in so called "autonomous factors." As such, these estimates of aggregate LCLoR may be lower than the level of reserves needed to meet system demand. Finally, although survey respondents likely have imprecise measures of their own LCLoR, all of our estimation methodologies treat each bank's self-reported LCLoR at face value. This means that each estimate presented above takes the$617 aggregate LCLoR reported by survey respondents as given, and layers on top various estimates of LCLoR for non-SFOS banks. Given that SFOS banks' business models and balance sheets, as well as external market conditions, evolve, it is likely that banks will periodically reassess and update their LCLoR over time. This introduces further uncertainty into the estimates presented above.

Despite all of these caveats, we think the estimates presented above are informative and provide insight into contemporary demand for reserves.

Conclusion
In this note, we present estimates of the lowest level of reserve balances, given the prevailing constellation of short-term interest rates at the time of the 2018 SFOS, that banks would feel comfortable holding before taking active steps to maintain or increase their reserve balance levels. Although caution is warranted in interpreting this analysis, our estimates of the aggregate lowest comfortable level of reserve balances in the system range from about $650 billion to just under$900 billion.

1. Respondents were asked to assume that the "constellation of short-term rates" referred to the rates on federal funds, Eurodollars, repurchase agreements, and short-dated U.S. Treasury bills. For reference, the average daily rates over the survey window were: Interest on Excess Reserves (1.95 percent), Effective Fed Funds (1.92 percent), Eurodollar (1.91 percent), Overnight Treasury GC repo (1.94 percent), 3-month Treasury bill (2.10 percent). Return to text

3. Reserve balances are from internal Federal Reserve records; reserve balance requirements are based on data from the FR 2900; and total assets are from quarterly reports of condition (FFIEC 002, 031, 041 and 051, FR 2886b, and NCUA 5300). Return to text

4. The estimates presented in this note only consider reserve balances, which are limited to balances of institutions defined as Depository Institutions (DIs) in Regulation D. Return to text

5. The predictions of LCLoR were in log form, which we then transformed into levels using a special case of Duan's smearing estimation to adjust for the bias introduced by exponentiation of the predicted values. Without this transformation, the bias would have resulted in an underestimation of LCLoR. Return to text

6. The assumption of the representativeness of the survey sample to the population is particularly important for the category of small domestic banks because fewer than ten banks of this type were in the SFOS sample, and the answers of those respondents were used to extrapolate to LCLoR for thousands of small, out-of-sample domestic non-SFOS banks. Still, the impact of small, out-of-sample domestic banks on the overall estimate of aggregate LCLoR is quite low because small domestic banks hold a modest share of reserve balances and total bank assets. Return to text