«Research Division Federal Reserve Bank of St. Louis Working Paper Series Understanding the Accumulation of Bank and Thrift Reserves during the U.S. ...»
The larger the stock of reserves, the lower the probability that withdrawals will be larger than reserves and that the bank will have to pay the penalty rate rp on borrowed funds. On the right-hand side of equation (3), the marginal cost of increasing reserves is determined by the forgone revenues of investing at larger-than-rIOR returns on alternative assets net of the beneﬁt of relaxing the constraint, λ. When the optimal ∗ reserve holding Ri exceeds the required reserves, then λ = 0 and the constraint is not binding. The constrained solution, in which λ 0, identiﬁes situations in which the bank accumulates only the required reserves δDi.
Intuitively, the demand for reserves increases when the ratio between the interest +∞ 10 Ifwe consider this cost, C(Ri ), the expected cost of a liquidity shortage, to be a convex function C(Ri ) = rp Ri (x− Ri )f (x) dx, then C (Ri ) = −rp Pr [Li ≥ Ri ] and C (Ri ) = −rp f (Ri ) 0.
rate diﬀerential rA − rIOR and the penalty rate rp rises. Ogawa (2007) uses a version of this model (following Freixas and Rochet, 1997) to interpret the increase of excess reserve holdings in the Japanese experience during the Lost Decade. The situation in which banks in poorer ﬁnancial health hold larger reserves—for example, to limit the possibility of a bank run—is captured by an increase of P r [Li ≥ Ri ] in the model. The model can be easily transformed to a log-linearized version that facilitates reduced-form estimation using bank-level data.
We can assume that banks perceive deposit withdrawals Li as draws from a Pareto distribution with density function
where L0,i 0 denotes the location parameter and θ 0 the shape parameter for the distribution. The location parameter shifts the distribution right and left, while the shape parameter governs the variance of withdrawals.
Under this speciﬁcation, the probability that withdrawals exceed reserves becomes
Under this speciﬁcation, reserves depend negatively on the ratio between the interest rate and penalty rate scaled by a parameter, θ, that governs the variance of deposit withdrawals. A larger location parameter, L0,i, translates into a right shift of the withdrawal distribution: For a given level of the ratio of interest to penalty rates, the i-th bank desires to keep larger reserves when L0,i is higher. We assume that this scale parameter depends on the strength of a bank’s precautionary motive and is positively correlated with the ﬁnancial weakness of the bank. Financial weakness can be approximated by a variety of measures. In this paper, we assume that ﬁnancial
weakness (F Wi ) shifts the location parameter, L0,i, as follows:
We assume that ﬁnancial weakness is a composite measure of bad loans (BLi ) and bank capital (Ki ). Using the speciﬁcation for the precautionary motive captured in equation (7) by L0,i, we obtain
that can be estimated using censored regression methods.
4. The determinants of reserves accumulation
4.1 Data and descriptive statistics We create two datasets, one for commercial banks and one for thrifts. Our primary sources of ﬁnancial information on banks and thrifts are the quarterly Reports of Condition and Income database (commonly called the Call Reports [CRs]) and the Thrift Financial Reports [TFRs].
The CRs contain regulatory information for all banks regulated by the Federal Reserve System, the Federal Deposit Insurance Corporation, and the Comptroller of the Currency. In this dataset, banks report their individual-entity activities on a consolidated basis for the entire group of banks owned by the reporting entity at the end of each quarter. Entities typically belong to bank holding companies (BHCs).11 For 11 The most frequent proprietary structure is an individual BHC controlling an individual bank. In many instances, however, an individual BHC may control many banks or a combination of banks and thrifts.
our estimation procedures, we use data for the quarters between 2008:Q3 and 2010:Q2 and include 2008:Q2 as a pre-IOR quarter for comparison.12 The number of entities in the CRs fell from 7,769 in the pre-IOR quarter (2008:Q2) to 7,182 in 2010:Q2 as a result of failures, mergers, and acquisitions. We use the National Information Center’s ﬁles on bank and thrift mergers, acquisitions, and failures to remove the eﬀects of these discrete events.
For this period, the TFRs contain similar but less-detailed information. Because there is no one-to-one correspondence between CRs and TFRs for the particular variables required for our analysis, we cannot merge the data; instead, we perform two parallel sets of analyses when possible. The number of thrifts reporting in 2008:Q2 was 829; by 2010:Q2, this number was reduced to 753.
We make several adjustments to the data to deal with complications generated by particular entities. We ﬁrst remove investment banks and ﬁnancing arms of large corporations that acquired charters in the 2008-09 period from our dataset and exclude them from our analysis of reserves accumulation. These “new” commercial banks are ﬁnancial entities not historically regulated as banks (and hence did not ﬁle CRs), but they acquired charters in 2008-09 because they either applied for a charter or were acquired by regulated commercial banks.13 These “banks” are likely to have reserves accumulation patterns signiﬁcantly diﬀerent from other commercial banks due to the distinct nature of the intermediation function they perform. In addition, we omit foreign-owned banks. There is evidence that international banks managed intragroup liquidity within their internal capital market very diﬀerently from other banks during the crisis (see Cetorelli and Goldberg, 2011).
In order to estimate the model derived in Section 3, we construct an empirical counterpart using information from the CRs and the TFRs.14 Our measure of ER is computed as a diﬀerence between total cash, including reserve balances at the Fed, and required reserves calculated as a percentage δ of deposits according to the reserves requirements for the period under consideration (listed in Table 1).15 This is our key dependent variable and the empirical counterpart of variable Ri − δDi in the model.
Cash and reserves can be maintained in various forms, not necessarily as deposits at the Federal Reserve Bank. We calculate required reserves based on information on reserves 12 Problems in the commercial banking system, including thrifts, did not become apparent in the lending data until 2008:Q3.
13 Namely, Goldman Sachs, Morgan Stanley, Merrill Lynch, American Express, CIT Group Inc., Hartford Financial Services, Discover Financial Services, GMAC Financial Services, IB Finance Holding Company, and Protective Life Corporation.
14 Table 13 describes the matching between the relevant variables in the CRs and TFRs.
15 Total cash and reserve balances at the Federal Reserve is variable rcfd 0010 in the Reports of Income and Condition.
requirements from the Board of Governors (also reported in Table 1). Since we cannot calculate required reserves precisely as the basis for their calculation changes daily, we consider our dependent variable to be cash including ER as any holdings greater than 110 percent of calculated required reserves for each bank.
Accurate measurement of the dependent variable is important for the robustness of our analysis. There are three ways it could be mismeasured. The ﬁrst two ways involve our calculation of reserves requirements: We may have under or overestimated reserves requirements. If we underestimated reserves requirements, then some ER are actually required reserves. In this case, a change in deposits would automatically produce a change in “ER.” To the extent that our covariates are correlated with deposits, increases in deposits could bias the coeﬃcients upward. We check whether the reserves requirements calculated on end-of-quarter deposits are underestimated and ﬁnd they are to some extent: 174 entity-quarter observations have negative ER; of these 125 are small bank observations, 33 are large banks, and 82 are thrifts. The solution for this is simple: We calculate ER as cash and reserves holdings 110 percent above calculated reserves requirements. Using this restriction, there are zero observations with negative ER. Alternatively, if we overestimated reserves requirements, then our measure of cash and ER holdings would be systematically too small. Since this is a level eﬀect—that is, constant cross-sectionally and over time—it is not clear there would be any systematic bias on our coeﬃcients. Provided this overmeasurement did not aﬀect cross-sectional or time-series variation in a heterogeneous manner (e.g., disproportionately aﬀecting large banks), we would not expect any meaningful impact on our coeﬃcients except the possibility of downward bias. Since we have no evidence of diﬀerential impact, we conclude that any overestimation of required reserves has only a level eﬀect, which should be reduced by scaling ER by total deposits (banks with similar amounts of transaction deposits should have the same estimated required reserves).
Finally, as noted earlier, our measure of ER includes cash and other cash-equivalents in addition to reserves holdings at the Federal Reserve. How this type of mismeasurement aﬀects our coeﬃcients is not easy to determine. Since our estimation equation is derived from the ﬁrst order conditions of the bank’s reserves management problem, not a portfolio allocation problem, we are possibly not capturing all the determinants for holding non- or low-interest-bearing assets. If DIs are holding more cash than strictly ER, then for a given change in a covariate that aﬀects ER but not cash in excess of excess reserves, the observed eﬀect would be smaller. In that case, our coeﬃcient estimates provide a minimum bound for the measurement of the relationship between these covariates and ER.
Fig. 6 plots the cross-sectional distribution of our measure of the cash plus ERR ratio between the quarter before our sample begins, 2008:Q2, and 2010:Q2, the last quarter in our sample. Each histogram represents one quarter and is left-censored at zero (as no bank holds less than the required reserves) and right-censored at 75 (as our data contain some ratios in excess of 75).16 Over the 2008:Q3–2010:Q2 period, the distribution of the ERR became more dispersed (less peaked and with a fatter tail; see Fig. 6) compared with 2008:Q2, indicating that more banks have accumulated larger amounts of ER, in conjunction with the expansion of the Federal Reserve budget. This outward movement is also documented by Ennis and Wolman (2012), who focus on large banks, but the explanation for the more-disperse distributions represents an open research question that we shed some light on in our study.
Using the theoretical model developed in Section 3 as a guide for choosing appropriate covariates, we choose a set of proxies available in the data. Table 2 displays a set of descriptive statistics for each covariate discussed below.
We use total deposits (Di ) as a scale variable and to correct for the heterogeneity in bank sizes. Deposits include (i) total transactions and non-transactions accounts, (ii) non-interest-bearing and interest-bearing deposits, and (iii) money market deposit accounts.
We use the interest diﬀerential between 1-year Treasury bills and the IOR as the opportunity cost institutions face for holding ER and cash. We considered a variety of other measures, including the rate on 3-month Treasury bills and the eﬀective federal funds rate, but believed that the 1-year rate best captured alternative low-risk investment opportunities. Fig. 7 displays each of the interest rate variables in the empirical model. We discuss other measures of the opportunity cost of holding cash and ER in Section 5.2.3.
For a measure of the penalty rate—the rate banks would theoretically pay for maintaining insuﬃcient cash and reserves—we use an index of daily rates on (30-day) Treasury bill repurchase (repo) agreements aggregated to a quarterly basis using either averaging over the quarter or choosing the last observation in each quarter.17 16 For each of the 9 quarters reported in these histograms, we counted the following number of banks exceeding an ERR of 75: 38, 45, 77, 107, 114, 143, 126, 3, and 4.
17 This index, called the DTCC GCF Repo Index, is created by the Depository Trust & Clearing Corporation (DTCC).
According to the DTCC website, the index tracks the average daily interest rate paid on the most-traded general collateral ﬁnance repo contracts for U.S. Treasury bonds, federal agency paper, and mortgage-backed securities (MBS) issued by Fannie Mae and Freddie Mac. The index’s rates, according to the website, are par-weighted averages of daily activity in the GCF repo market and reﬂect actual daily funding costs experienced by banks and investors.
We then construct the following three measures of bank loan health, each progressively more inclusive of less-distressed loans. The ﬁrst measure (nonaccruing loans, labeled “bad loans 1” in the regression tables) contains the category of loans most likely to turn into permanent losses. Nonaccruing loans are deﬁned as the outstanding balances of loans and lease ﬁnancing receivables the bank has placed in nonaccrual status, as well as all restructured loans and lease ﬁnancing receivables in nonaccrual status.18 The second measure of bad loans (nonperforming loans, labeled “bad loans 2” in the regression tables) includes both nonaccruing loans and loans that are due and unpaid for 90 days or more in addition to all restructured loans and leases.