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Discount window borrowing and Federal Reserve operating regimes.

I. INTRODUCTION

The borrowing behavior of banks at the Federal Reserve's discount window is a component of most models of the monetary sector, including the model used by the Federal Reserve.(1) As several researchers have noted,(2) however, the policy importance of accurate predictions of borrowing behavior depends on the Federal Reserve's short-run operating procedure. If the Federal Reserve uses a Federal funds rate target to control money growth, as it did in the 1970s, inaccurate predictions of borrowing behavior have no effect on money supply growth. If the Federal Reserve uses a nonborrowed reserves target, as is usually assumed for the October 1979 to October 1982 period, or a borrowed reserves target, as was used after October 1982, then poor predictions of bank borrowing are a potentially significant source of errors in controlling money.(3) Given the importance of accurate borrowing predictions to monetary control under current short-run operating procedures, admissions by the Federal Reserve that its borrowing equation poorly explains recent borrowing behavior are cause for concern.(4)

Part of the problem may lie with inadequate allowance for differences in bank borrowing behavior under different operating procedures. The choice of operating procedure determines not only the importance of accurate borrowing predictions, but also affects borrowing behavior by affecting the stochastic process characterizing the spread between the Federal funds rate and the discount rate.(5) The standard model for aggregate borrowing, typified by Goldfeld and Kane |1966~, assumes a positive relationship between borrowing and the spread. The optimizing model of individual bank borrowing decisions of Goodfriend |1983~, used by Cosimano |1988~ and Dotsey |1989~, among others, suggests that borrowing also depends negatively on banks' expectations about future levels of the spread. Specifically, Goodfriend's model of risk-neutral banks predicts a larger impact on borrowing of a spread change that banks expect to be temporary than one that banks expect to be more persistent. To the extent that banks predict future spreads using an autoregressive model, changes in the stochastic process characterizing the spread should change the impact realizations of the spread have on borrowing.(6) Moreover, if banks are risk-averse, changes in the operating procedures that produce less predictable spreads may affect both banks' borrowing and excess reserve behavior.(7)

Because the spread's stochastic behavior depends on the Federal Reserve's operating procedure, borrowing behavior, in turn, should depend on the Federal Reserve's operating procedure. Consequently, the Federal Reserve should not assume that the borrowing equation in its model is invariant to changes in operating procedure. As Goodfriend notes, such an assumption is another example of the Lucas critique. Bryant |1983~ and Dutkowsky and Foote |1988~ show that borrowing equations estimated during the period when the Federal Reserve targeted the Federal funds rate produce poor forecasts of borrowing after the regime change of 6 October 1979. These papers do not, however, provide evidence on how the borrowing equation changed after October 1979. One purpose of this paper is to investigate whether bank borrowing behavior changed with changes in Federal Reserve operating procedures, leading to estimated borrowing equations that differ significantly under different operating procedures.

In addition to the changes in operating procedures, the Federal Reserve also changed the reserve accounting rules in February 1984, replacing lagged reserve accounting with contemporaneous reserve accounting. Although the effect of this switch on bank reserve management is difficult to predict, the increased uncertainty about reserve needs and the decrease in information about the aggregate demand for reserves make it plausible that banks became more conservative, affecting their excess reserve behavior and their discount window borrowing.(8) Therefore, I also investigate whether bank borrowing behavior changed with the change in accounting rules, again leading to changes in estimated borrowing equations.(9)

The rest of the paper is organized as follows. Section II gives an overview of borrowing behavior during the three alternative operating regimes in effect since 1975. Section III presents the model of discount window borrowing and discusses the econometric problems that may arise in estimating borrowing equations under different operating procedures. Section IV reports estimated borrowing models for the three periods and tests for differences across policy regimes. The final section summarizes the findings of the paper.

II. OVERVIEW OF DISCOUNT WINDOW BORROWING ACROSS OPERATING REGIMES

Borrowing at the Federal Reserve System's discount window is categorized as adjustment borrowing, seasonal borrowing, or extended credit. Adjustment borrowing comprises short-term loans to meet unexpected liquidity needs. Seasonal borrowing, as the name implies, is for recognized seasonal liquidity needs of smaller banks. Extended credit refers to longer-term loans to institutions facing exceptional problems. Consistent with most previous research, I focus on adjustment borrowing.

Three time periods, corresponding to different operating regimes, are examined. The first period runs from 8 January 1975 to 3 October 1979. As discussed in Cook and Hahn |1989, 333~, this period corresponds to an operating regime in which the Federal Reserve framed short-run monetary policy in terms of a tight Federal funds rate target (FFRT). The second period runs from 10 October 1979 to 6 October 1982, the interval in which the Federal Reserve is thought to have used a nonborrowed reserves targeting procedure (NBRT). After 13 October 1982, the Federal Reserve supposedly targeted borrowed reserves (BRT). Fourteen months later, the Federal Reserve switched from lagged reserve accounting (LRA) to contemporaneous reserve accounting (CRA), simultaneously changing the reserve maintenance period from one to two weeks.(10) The third period runs from 15 February 1984 to 25 December 1991, during which borrowed reserves targeting and contemporaneous reserve accounting were in place.(11)

Plots of adjustment borrowing versus the spread between the Federal funds rate and the discount rate show substantial differences across the three periods. Panel A of Figure 1 is the scatter diagram for the Federal funds rate target period, indicating a positive relationship when the spread is positive. All data are weekly averages of daily data with weeks measured from Thursday to Wednesday, corresponding to the reserve maintenance week. During the first half of the period, the spread was usually negative and, not surprisingly, borrowing was quite low. Borrowing levels then rose when the spread became positive in the second half of the period.

Panel B presents the scatter diagram for the nonborrowed reserves target period. Several differences are apparent. First, the range of borrowing levels and the range of the spread are considerably larger. Second, the spread is almost always positive. Third, there appears to be a looser relationship between borrowing and the spread.(12)

Panel C displays the scatter diagram for the borrowed reserves target period with contemporaneous reserve accounting in force. These data are bi-weekly averages of daily data, corresponding to the two-week reserve maintenance period instituted under contemporaneous reserve accounting. During this period, the range of borrowing was generally smaller than in the other periods, while the range of the spread was lower than in the nonborrowed reserves target period but higher than in the Federal funds rate target period.(13) The spread was again almost always positive. The scatter diagram indicates no strong relationship between the spread and borrowing during this period. The borrowing-spread relationship was particularly weak after 1988 when adjustment borrowing was very low despite relatively high spreads.(14)

Table I reports descriptive statistics for the subperiods examined, which also indicate substantial differences across periods. Comparing the Federal funds rate target period to the nonborrowed rate target period, the data reveal that adjustment borrowing more than doubled in the latter period while the average spread (excluding negative spread weeks) increased about eight-fold. Excess reserves also rose in the latter period, from about $208 million to $308 million, despite the higher spread. This is not a scale effect, as indicated by the ratio of excess reserves to total reserves. During the contemporaneous reserve accounting period, average borrowing fell to its lowest level despite the average positive spread being about four times as high as in the Federal funds rate target period. The excess reserves ratio rose to an average of 1.71 percent.(15)

Taken together, the data presented in Figure 1 and Table I reveal notable differences in the spread-borrowing relationship and in banks' holdings of excess reserves across operating procedures and accounting rules. Comparing the two operating regimes under lagged reserve accounting, there was a positive borrowing-spread relationship in each regime, but it appeared weaker when the spread was more volatile. After the switch to contemporaneous reserve accounting, there seemed to be no simple relationship between borrowing and the spread.

III. MODELING DISCOUNT WINDOW BORROWING

To investigate whether changes in policy regimes lead to changes in borrowing behavior, I estimate a borrowing equation for each of the three regimes under study and compare the estimates. I use the standard aggregate borrowing equation in TABULAR DATA OMITTED which adjustment borrowing is a function of the spread between the Federal funds rate and the discount rate, a scale variable (the change in required reserves), and lagged adjustment borrowing. Higher values of the spread are assumed to induce banks with reserve deficiencies to turn to the Federal Reserve rather than to the more expensive Federal funds market. The squared value of the spread is included in the model to allow for a nonlinear relationship. A large increase in required reserves is assumed to increase the need to borrow from the window. The effect of lagged borrowing is less clear. Goodfriend's model of an individual bank predicts that lagged borrowing will have a negative effect on current borrowing, reflecting the perceived increased cost that the Fed imposes on frequent borrowers. Previous studies of aggregate borrowing, however, generally find a positive coefficient.

Time plots of adjustment borrowing indicate that there are end-of-quarter effects on borrowing, particularly after 1982. Given the traditional argument that discount window borrowing is considered a sign of weakness, one might expect borrowing to decline at ends of quarters if banks fear that such borrowing will be revealed when they publicly report their balance sheets. Allen and Saunders |1991~ discuss end-of-quarter window dressing by banks. They argue that banks have had incentives to window dress their balance sheets in both downward and upward directions--leading to temporary end-of-quarter decreases or increases in assets--but that changes in regulations in 1984 reduced incentives to window dress downward. They find evidence consistent with increased upward window dressing after 1984, but their data do not distinguish discount borrowing from other sources of funds. Therefore, in order to test whether borrowing changes in weeks that include ends of quarters, I include a dummy variable in the model. I also estimate models with separate dummies for end-of-quarter and end-of-year weeks to check if there is an additional effect for year-end reports.(16)

Thus the basic model for adjustment borrowing is:

(1) |B.sub.t~ = |a.sub.0~ + |a.sub.1~|B.sub.t-1~ + |a.sub.2~ S|P.sub.t~ + |a.sub.3~ S|P.sup.2~t

+ |a.sub.4~CHR|R.sub.t~ + |a.sub.5~ Q|D.sub.t~ + |u.sub.t~

where

B = adjustment borrowing

SP = spread between the federal funds rate and the discount rate

CHRR = change in required reserves

QD = 1 if week includes the end of a quarter

= 0 otherwise

Changes in the Federal Reserve's operating procedures may introduce a simultaneous equations problem for the estimation of equation (1), as noted by Keir |1981~. If the Federal Reserve adheres strictly to a Federal funds rate target set independently of shocks to borrowing, then OLS estimates of equation (1) should yield unbiased estimates. If the Federal Reserve adheres strictly to a nonborrowed reserves target, shocks to borrowing demand would be correlated with the spread. Specifically, a shock to borrowing demand that raises borrowing at each level of the spread would effectively increase the supply of total reserves and, all else equal, lower the spread. Thus the spread and the error term in equation (1) would be negatively correlated and OLS would yield inconsistent parameter estimates. A similar problem arises if the Federal Reserve adheres strictly to a borrowed reserves target.(17) Blow-by-blow descriptions of open market operations as given in the annual review of monetary policy in the Federal Reserve Bank of New York's Quarterly Review make clear, however, that deviations from targets have been allowed if judgment warranted. In particular, these descriptions suggest that shocks to borrowing often were accommodated with changes in nonborrowed reserves to prevent sharp movements in the Federal funds rate or in borrowing. If the Federal Reserve generally accommodated borrowing shocks, the correlation between the spread and such shocks will be reduced and the simultaneous equations bias decreased.(18) To examine this issue, I estimate borrowing equations for the nonborrowed reserves and borrowed reserves target periods using both OLS and 2SLS and compare the results.

IV. ESTIMATED BORROWING EQUATIONS FOR ALTERNATIVE OPERATING REGIMES

Behavior of the Spread

Before reporting the estimates of the borrowing equation for the alternative operating regimes, the results of an analysis of whether the stochastic process generating the spread changed across these regimes are reported. Evidence of changes implies the likelihood of changes in bank borrowing behavior across regimes. Because only positive spreads are relevant to borrowing behavior, I investigated the subperiod of May 1977 to October 1979 for the Federal funds rate target period. Tests for the presence of a unit root indicate that the spread was stationary over this period. An AR(1) model fits the data adequately with an autoregression coefficient of .73 and a standard error of .15 percentage points. For the nonborrowed reserves target period, the appropriate measure of the spread is unclear because some banks occasionally faced a surcharge added to the basic discount rate. If the surcharge is ignored, unit root tests indicate that the spread is nonstationary with changes in the spread having a standard error of .81 percentage points. If the surcharge is subtracted from the spread, the resulting variable is stationary and is well fit by an AR(1) model with an autoregression coefficient of .91 and a standard error of .78 percentage points. Thus the shocks to the spread were larger and more persistent under the nonborrowed reserves target period.(19)

Unit root tests for the spread under the borrowed reserves target-contemporaneous reserve accounting regime indicate that the spread was stationary, but the estimated autocorrelation coefficient was .96 and the standard error of the AR(1) model, augmented by end-of-quarter and end-of-year dummies, was .23 percentage points.(20) Thus, shocks to the spread during this period were somewhat larger than in the Federal funds rate target period but smaller than in the nonborrowed reserves target period, and more persistent than in the other periods. If the coefficient on the spread in the borrowing equation varies inversely with the size of the autoregression coefficient and with the volatility of the spread, the estimated effect of movements in the spread on borrowing should be substantially less during the nonborrowed reserves target period and the borrowed reserves target-contemporaneous reserves accounting period than during the Federal funds rate target period.(21)

The Federal Funds Rate Targeting Regime

Equation (1) has to be modified slightly for the Federal funds rate target period because the spread was negative for most of the first half of this period. Because banks cannot lend to the Federal Reserve at the discount rate, adjustment borrowing cannot be negative. Thus, the coefficient on the spread should be zero whenever the spread is negative.(22) Hence the spread variable was replaced with the variable PSPR, which equals the maximum of the spread and zero.(23)

Under the assumption that the Federal Reserve was targeting the Federal funds rate, equation (1) can be consistently estimated by OLS. The data are weekly observations on adjustment borrowing and the average daily spread between the Federal funds rate and the discount rate for the period 8 January 1975 through 3 October 1979. Weeks correspond to the reserve maintenance weeks of Thursday to the following Wednesday.

Table II reports estimates of the borrowing equation for this regime.(24) Equation II.1 reports the estimate of equation (1) and indicates that positive spreads have the anticipated positive relationship with borrowing. An increase in the spread of one percentage point is associated with an increase in adjustment borrowing of about $1 billion.(25) There is little evidence of a nonlinear effect for positive spreads during the Federal funds rate target period. Dropping the squared spread variable yields similar results, as indicated by equation II.2. Increases in required reserves have the expected positive effect on borrowing but the effect is imprecisely estimated. The coefficient on QD, the quarter dummy, indicates that borrowing fell by about $100 million, all else constant, in weeks that include the last business day of a quarter. This suggests a desire by banks to reduce end-of-quarter outstanding liabilities to the Federal Reserve. Including separate dummies for year-end and quarter-end produced estimates of a larger decline at year-end, but the estimated coefficients were not statistically different.(26) Similar to the results of other studies, the coefficient on lagged borrowing is always significantly positive, contrary to Goodfriend's prediction for individual banks.(27) Equation II.3 reports the estimated model when end-of-quarter weeks are omitted and indicates that the dummy variable adequately captures the end-of-quarter effects. The model does a reasonable job of accounting for weekly fluctuations in borrowing with no evidence of serially correlated errors.(28)

TABULAR DATA OMITTED

The Nonborrowed Reserves Targeting Period

Estimating the borrowing equation in the nonborrowed reserves targeting regime is more difficult for two reasons. First, as noted above, the spread is not exogenously determined if the Federal Reserve pursues this operating procedure and does not accommodate shocks to the borrowing equation. Second, a surcharge was added to the basic discount rate for large, frequent borrowers.(29) Since the surcharge did not apply to all borrowers, it is added to the model as a separate variable rather than as a deduction from the spread.

Table III reports OLS estimates of the borrowing equation for the nonborrowed reserves target period. Equation III.1 shows the estimate of the borrowing equation with the surcharge (SURCH) variable added. The effect of the spread is again positive but substantially less than for the Federal funds rate target period, and declines as the spread increases. An increase in the spread from, say, zero to 1 percent is associated with an increase in borrowing of about $285 million, roughly one-fourth as large an increase as in the Federal funds rate target period. The surcharge had a significantly negative effect on borrowing, with a 3 percent surcharge reducing borrowing by about $186 million.(30) As in the Federal funds rate target period, the coefficient on lagged borrowing is positive, contrary to the prediction of Goodfriend's model. Neither the scale variable (CHRR) nor the end-of-quarter dummy variable (QD) was significant in this period, and dropping the end-of-quarter observations has little effect, as shown by equation III.2. Estimates using 2SLS are TABULAR DATA OMITTED very similar, implying that shocks to the borrowing equation generally were accommodated so they did not substantially affect the funds rate.(31) The joint hypothesis that the coefficients were equal in the Federal funds rate target and nonborrowed reserves target periods is easily rejected, as is the hypothesis that the effect of the spread was the same across the two periods.(32)

The Borrowed Reserves Targeting Procedure Under Contemporaneous Reserve Accounting(33)

Table IV reports OLS estimates of borrowing equations for the borrowed reserves target-contemporaneous reserves accounting period.(34) Because the squared spread term is never significant, it is dropped from the model. As noted above, TABULAR DATA OMITTED borrowing behavior is thought to have changed after the stock market crash on 19 October 1987, so separate estimates for the pre- and post-crash borrowed reserves target-contemporaneous reserve accounting periods are presented.

Equation IV.1 gives the OLS estimate of the borrowing equation for the pre-crash period, which indicates that borrowing was positively related to the spread in this sub-period but less sensitive to the spread than in the borrowed reserves target-lagged reserves accounting period. An increase in the spread of one percentage point was associated with an increase in borrowing of about $108 million, roughly one-tenth of the estimated effect for the Federal funds rate target period and about 40 percent of the estimated effect for the nonborrowed reserves target period. Once again the coefficients on lagged borrowing are positive. The estimated coefficient on the end-of-year dummy, YE, indicates that borrowing rose by about $400 million in the last settlement period of the calendar year, all else equal. Borrowing also rose at the ends of the other

quarters but only by about $100 million. Equation IV.2 indicates that similar results hold when the end-of-year and end-of-quarter observations are omitted.

Equation IV.3 reports OLS estimates of the borrowing equation for the post-crash period. During this sub-period, borrowing was even less sensitive to the spread, with an increase in borrowing of about $60 million associated with an increase in the spread of one percentage point. Neither lagged borrowing nor the change in required reserves is significant during this period. The estimated end-of-year effect increased, with average borrowing increasing by about $600 million in the maintenance period containing the last day of the year, but borrowing was not significantly higher at the end of the other quarters. Omitting the end-of-quarter observations produces very similar results, as shown by equation IV.4. The hypothesis that the coefficients of the borrowing model are equal before and after the crash is easily rejected.(35)

The estimated borrowing equations for the borrowed reserves target-contemporaneous reserve accounting periods indicate that banks have systematically increased their borrowing at the end of quarters and particularly at the end of years. A closer examination of the borrowing data indicates that, since 1984, banks have been "puffing up" their assets for the end-of-year annual reports by borrowing substantially on December 31. The data show that, except for 1990, bank borrowing is always higher for December 31 than for the bi-weekly average that includes December 31, and the daily Federal funds rate tends to spike at the end of the year as banks strive to borrow to build up asset totals.(36) While there may be incentives for banks to pursue this strategy, as discussed by Allen and Saunders |1991~, it is unclear why the Federal Reserve accommodates these demands.

Comparisons With Previous Work

In a recent paper, Peristiani |1991~ models borrowing as a high-order polynomial in the spread. He reports estimates using weekly borrowing data for 1959 though mid-1988 and finds that the polynomial model holds for sub-periods such as the contemporaneous reserve accounting period, although no formal tests of parameter stability are given. In order to see if the finding that the borrowing equation did change with changes in operating procedures is robust with respect to alternative models, the polynomial model of Peristiani is estimated for the sub-periods examined above.

Table V presents the estimates of the polynomial model. Sequential F-tests to select the order of the polynomial indicate that a fourth-order polynomial is appropriate for the Federal funds rate target period. A maximum likelihood procedure was used to correct for serially correlated errors, consistent with the work of Peristiani.(37) In addition, models were estimated that included a lagged dependent variable. The first two columns of Table V report the estimated models for the Federal funds rate target period. The same models were then estimated for the non-borrowed reserves target period, with the results reported in the third and fourth columns of Table V. Formal tests of the hypothesis that the coefficients on the spread terms were identical across the periods reject the hypothesis for both models.(38) As the parameter estimates indicate, borrowing was less sensitive to the spread in the nonborrowed reserves target period, consistent with the results reported above. For the nonborrowed reserves target period, estimates of the model with a lagged dependent variable indicate that a second-order polynomial in TABULAR DATA OMITTED the spread is appropriate, again consistent with the results in Table III. The reason that a higher-order polynomial is required for the Federal funds rate target period is that there is a kink in the borrowing-spread relationship because the spread only affects borrowing when it is positive. When the polynomial models are re-estimated for the period of positive spreads under federal funds rate targeting, May 1977 to October 1979, the linear model cannot be rejected.

The last four columns of Table V present the polynomial models for the contemporaneous reserve accounting period, pre- and post-crash.(39) As indicated by the F-statistics in the last row of the table, one cannot reject a linear relationship between the spread and borrowing in either period. The estimated coefficients again indicate that borrowing became less sensitive to the spread after contemporaneous reserve accounting was introduced. These results differ from the qualitative statements in Peristiani. One reason for the differences may be that Peristiani's measure of borrowing included seasonal borrowing. A second reason is that Peristiani used weekly data for the contemporaneous reserve accounting period while I use biweekly data matching the reserve maintenance period under contemporaneous reserves accounting.

V. CONCLUSIONS

Several researchers have argued that bank borrowing at the discount window should depend on the operating procedures employed by the Federal Reserve. If the Federal Reserve changes procedures in a way that changes the stochastic process characterizing the spread between the Federal funds rate and the discount rate, the sensitivity of bank borrowing to the spread should change. Intertemporal optimization models of bank borrowing predict borrowing will be less sensitive to the spread if changes in the spread become more persistent. In addition, models that assume risk-averse banks predict that bank reserve management will become more conservative if the spread or reserve needs become less predictable. If, as a result, bank borrowing at the discount window becomes more difficult to predict, operating procedures that rely on accurate predictions of borrowing, such as nonborrowed reserves or borrowed reserves targeting, will be less successful in controlling monetary aggregates.

This paper has provided empirical evidence supporting the hypothesis that bank borrowing behavior did change when the Federal Reserve altered its short-run operating procedures. Under a Federal funds rate target, when the spread was relatively predictable and shocks were less persistent, borrowing was very sensitive to changes in the spread when the spread was positive. Under a nonborrowed reserves target, when the spread was much more variable and shocks to the spread were more persistent, bank borrowing became much less sensitive to the spread. After the switch to contemporaneous reserve accounting under borrowed reserves targeting, shocks to the spread became more persistent and bank borrowing became even less sensitive to the spread, particularly after the October 1987 stock market crash. This last finding, combined with the increase in excess reserves under contemporaneous reserve accounting, is consistent with banks adopting a more conservative approach to reserve management.

These results demonstrate that the Federal Reserve should anticipate that a borrowing equation estimated under one policy regime is unlikely to be an accurate guide to borrowing behavior under a different policy regime. In particular, the systematic connection between borrowing and the spread that existed prior to 1984 has deteriorated, implying that borrowed reserves targeting, which requires a reliable borrowing-spread relationship for success, has become an unsuitable procedure for short-run monetary policy.

1. See Tinsley et al. |1982~.

2. Lindsey et al. |1984~ and Dotsey |1989~, among others.

3. See Dutkowsky and Foote |1988, 601-2~ for an illustration of how errors in predicting bank borrowing affect monetary control. See Wallich |1984~, Gilbert |1985~, Sellon |1986~, Thornton |1988~ and Dotsey |1989~ for descriptions of the alternative operating procedures.

4. The problem of an unreliable borrowing relationship is discussed in "Monetary Policy and Open Market Operations during 1988," Federal Reserve Bank of New York Quarterly Review, Winter-Spring 1989, 98-99 and in Meulendyke |1990, 230~.

5. Walsh |1984~ analyzes a similar interrelationship in which the October 1979 switch from interest rate targeting to nonborrowed reserves targeting changes the variability of interest rates. Because the interest elasticity of the demand for money varies inversely with interest rate volatility in his model, ignoring this effect leads to poor predictions of the resulting volatility of money and interest rates under the nonborrowed reserves targeting regime.

6. Goodfriend argues that banks believe the Federal Reserve will penalize them if they attempt to borrow frequently. Thus banks must trade off the benefits of borrowing this period with the benefits of borrowing next period. If banks think the spread will be lower next period, they will tend to borrow more this period. Accordingly the borrowing equation is

|Mathematical Expression Omitted~

where B = borrowing and S = spread.

If the spread is an AR(1) process, |S.sub.t~ = |Rho~ |S.sub.t-1~ + |u.sub.t~, and if banks forecast spreads using only past spreads, the coefficient on the spread in the usual borrowing equation would be (|c.sub.2~ + |c.sub.3~ |Rho~), which declines with |Rho~ since |c.sub.3~ is assumed to be negative.

7. Ho and Saunders |1985~ develop a model that implies that risk-averse banks facing less predictable interest rates will increase their excess reserves.

8. See Tarhan |1984~ for a discussion of these issues. Sprenkle |1987~ develops a model of bank behavior that predicts that the move to contemporaneous reserve accounting will increase excess reserves. Ho and Saunders |1985~ argue that risk-averse banks will increase their excess reserves if reserve demands become more unpredictable. The Federal Reserve's initial assumption was that the switch would have little effect on reserve management behavior. See "Monetary Policy and Open Market Operations," Federal Reserve Bank of New York Quarterly Review, Spring 1985, 44.

9. Of course other factors may have also affected aggregate borrowing behavior. The 1980 Depository Institutions Deregulation and Monetary Control Act gave nonbank depository institutions access to the discount window, although in practice these institutions were discouraged from using this option. The savings and loan crisis that became evident in the late 1980s may also have affected bank management of reserves.

10. The reserve accounting system is not fully contemporaneous, since the computation period runs from Tuesday to the second Monday and the maintenance period runs from Thursday to the second Wednesday. Thus, on the last two days of the maintenance period, banks know their required reserves.

11. During the period from 13 October 1982 to 1 February 1984, both borrowed reserves targeting and lagged reserve accounting were in place. Because this period has only sixty-six weeks, results for this period are not presented but the qualitative nature of these results are noted below. Estimates for this period are available from the author.

12. As discussed in more detail below, analyzing borrowing in this period is complicated by the occasional imposition of a surcharge added to the basic discount rate for large, frequent borrowers.

13. The very large borrowing by Continental of Illinois in May 1984, which subsequently was classified as extended credit, the loan to the Bank of New York in November 1985, which was necessitated by a computer breakdown, and the borrowing of the Bank of New England in early 1990, which was subsequently classified as extended borrowing, are eliminated from aggregate adjustment borrowing.

14. The Federal Reserve Bank of New York noted that bank borrowing fell substantially after the crash: "In the tumultuous environment, not only did banks generally seem less inclined than normal to use the discount window, but the demand for excess reserves seemed to escalate." ("Monetary Policy and Open Market Operations during 1987." Federal Reserve Bank of New York Quarterly Review, Spring 1988, 41-58.) The savings and loan crisis and the increased frequency of bank failures are often cited as possible causes of low borrowing.

15. The increases in the ratio of excess reserves to total reserves between the Federal funds rate target and nonborrowed reserves target periods and between the nonborrowed and the borrowed reserves target periods are statistically significant at the 5 percent level.

16. End-of-quarter effects would also be reflected in the spread so that the dummies should pick up possible shifts not accounted for by movements in the spread.

17. See Dotsey |1989~ for a model that illustrates these points. An appendix that provides a model of the reserves market demonstrating these conclusions is available from the author.

18. See Thornton |1988~ for evidence suggesting that the Federal Reserve did accommodate shocks to the borrowing equation, at least through 1986.

19. The increase in the autoregressive coefficient is statistically significant with a t-statistic of 2.32, computed using White's correction for heteroskedasticity.

20. For the borrowed reserves target-contemporaneous reserves accounting period there was evidence of spikes in the spread at the ends of quarters and the ends of calendar years. These were taken into account in the unit root tests by including dummy variables as suggested by Dickey, Bell, and Miller |1986~.

21. For the short period during which borrowed reserves targets and lagged reserve accounting were both in effect, October 1982 to February 1984, the spread was stationary with an autoregressive coefficient of .77 and a standard error of .23 percentage points.

22. The observable Federal funds rate is an average, so some banks may face a positive spread when the average spread is negative.

23. In order to test for the asymmetry, models were also estimated that included both positive and negative spreads. In all cases, the estimated coefficient on negative spreads was not statistically different from zero.

24. Peristiani |1991~ argues that aggregating across banks is likely to produce heteroskedastic errors. Formal tests for heteroskedasticity generally support this assertion, so t-statistics are computed using White's heteroskedasticity-consistent estimated covariance matrix.

25. Re-estimating the model for the Federal funds rate target period after May 1977, a period when the spread was always positive, produces results similar to those from the whole Federal funds rate target period using PSPR.

26. Daily borrowing data are not publicly available. Outstanding total borrowing, which includes adjustment, seasonal, and extended credit, is reported for December 31 of each year in Table 2 of the Annual Report of the Board of Governors of the Federal Reserve System. For the years 1975 through 1978, borrowing on December 31 is always about 60 percent of that for the week including December 31, indicating that banks reduced their borrowing on December 31 in these years.

27. The positive coefficient for aggregate borrowing may reflect borrowing by smaller banks that can last for periods exceeding one reserve period. Hamdani and Peristiani |1991~ report evidence that borrowing at smaller banks is positively autocorrelated while borrowing at large banks appears to be negatively autocorrelated. They do not investigate whether borrowing behavior varied across operating regimes.

28. Ignoring the asymmetry in the borrowing equation by using the spread variable rather than PSPR yields the following estimated borrowing equation that is similar to those reported by Keir |1981~:

|B.sub.t~ = 202.38 + .54 |B.sub.t-1~ + 328.98 Spread

(7.47) (8.21) (7.54) + .046 CHRR - 55.27 QD |R.sup.2~ = .77 (2.03) (-1.20)

Including negative spreads as a separate variable yields:

|B.sub.t~ = 286.40 + .29 |B.sub.t-1~ + 1073.40 PSPR

(1.26) (4.44) (10.05) -29.41 NEGSP + .028 CHRR -102.07 QD |R.sup.2~=.84 (-.87) (1.52) (-2.03)

29. "Large banks" were defined as banks with deposits of $500 million or more and "frequent" was defined as borrowing two weeks in a row or borrowing in more than four weeks in a quarter. The surcharge ranged from 0 to 4 percent from March 1980 through November 1981.

30. Estimating the model with PSPR redefined by adding the surcharge to the discount rate yields qualitatively similar results.

31. The instruments for the 2SLS estimates are the predetermined right-hand-side variables, lagged values of the endogenous right-hand-side variables, and the levels of required reserves and nonborrowed reserves, both of which are exogenous under nonborrowed reserve targeting and lagged reserve accounting. The 2SLS results are available from the author.

32. The tests were done using the model that includes a squared PSPR variable and the F-statistics were computed using White's heteroskedasticity-consistent estimated covariance matrix. The computed F for the test that all common coefficients are equal across periods is 9.61 with 6 and 388 degrees of freedom, and the computed F for the test that the coefficients on the spread variables were equal is 21.44 with 2 and 388 degrees of freedom. The analogous F-statistics when the end-of-quarter observations are omitted are 12.11 (5 and 359 degrees of freedom) and 22.42 (2 and 359 degrees of freedom). Tests using models that exclude the squared PSPR variable give identical qualitative results.

33. Estimates of the borrowing model for the borrowed reserves target-lagged reserves accounting period indicate that borrowing became more sensitive to the spread than in the nonborrowed reserves target period but less sensitive than in the Federal funds rate target period. An increase in the spread from zero to 1 percent was associated with an increase in borrowing of about $427 million, roughly one and one-half as much as in the nonborrowed reserves target period but less than half as much as in the Federal fund rate target period. Formal tests indicate statistically significant differences across the three periods.

34. All equations were also estimated by 2SLS using the predetermined right-hand-side variables, lagged values of the endogenous right-hand-side variables, and the borrowings target for seasonal and adjustment borrowing as instruments. The estimates were very similar to the OLS estimates, so they are not reported. This finding is consistent with the Federal Reserve continuing to accommodate borrowing shocks under borrowed reserves targeting and contemporaneous reserves accounting. All estimates are available from the author.

35. The F-statistic for the joint hypothesis that all the coefficients are equal is 8.70 with 6 and 192 degrees of freedom. The corresponding test statistic when the end-of-quarter observations are omitted is 16.31 with 4 and 166 degrees of freedom.

36. The data on December 31 borrowing are reported in the Federal Reserve's Annual Report. I wish to thank Alton Gilbert for a helpful discussion of this issue.

37. All estimates were done using version 6.2 of SHAZAM, see White |1988~.

38. The F-statistic for the model without a lagged dependent variable is 9.13 (5 and 391 degrees of freedom), and the F-statistic for the model with a lagged dependent variable is 9.36 (6 and 389 degrees of freedom). Adding the surcharge to the discount rate yields similar results.

39. The test of equality of parameters across the two sub-periods yields F-statistics of 12.25 (5 and 194 degrees of freedom) and 8.15 (6 and 192 degrees of freedom) for the two models, well above the .05 critical values.

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DOUGLAS K. PEARCE, Professor, College of Management, North Carolina State University. I thank David Dickey, Donald Dutkowsky, Doug Fisher, Don Hester, John Lapp, Karlyn Mitchell, Jim Nason, Vance Roley, Bob Rossana, Ben Russo, Gordon Sellon, Dan Thornton, and Carl Walsh for helpful comments.
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Publication:Economic Inquiry
Date:Oct 1, 1993
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