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BANKS REFINANCING WITH THE CENTRAL BANK Re-examination of Its Interest Rate Elasticities for Belgium 1960-1973 Herwig LANGOHR* IN SEAD, F-77305 Fontainebleau, France Received February 1979, final version received July 1979

This paper reports evidence that bank refinancing with the central bank is highly interest elastic, particularly with respect to the discount rate. It shows that banks fully adjust actual to desired refinancing within three months and that the apparent negative association of refinancing with a need variable is a spurious one. Discount rate changes are found to be largely effective as a policy instrument.

1. Introduction In a recent article, D. Heremans, A. Sommariva and A. Verheirstraeten (1976, p. 193) henceforth HSV, reported 'not (to) find . . . a significant relationship for the discount rate with domestic refinancing of the banks'. Furthermore, the authors (p. 203) found that domestic refinancing by Belgian banks was highly inelastic with respect to a government securities interest rate, the Eurodollar rate and the discount rate. The results shown by the authors were disturbing insofar as they reported an elasticity of refinancing with respect to its own cost lower than the refinancing cross interest rate elasticities. Refinancing appeared to be dominated by unborrowed reserves I-HSV (1976, p. 183)1. This is what the authors (p. 172) postulated. In their (p. 172) view, 'banks resort to the discount window of the National Bank when they are in short supply of money base to finance their credit'. To sum up, in both, specifications and findings, HSV appear to support the residual theory of bank refinancing. As discussed elsewhere I-Langohr (1980)] this theory states that banks refinance from the central bank, not to profit but out of need. For explaining bank refinancing, this theory assigns only secondary importance to interest rates. The adherence of HSV to this view is particularly illustrated by the absence of the forward premium from the HSV (equation 14, p. 172) refinancing function. *I express special gratitude to Michele Fratianni who probed, corrected and encouraged the research that led to this paper. The suggestions of an anonymous referee are acknowledged. Any remaining errors are mine.

H. Langohr, Banks refinancing with the central bank

176

The purpose of this paper is to report evidence supporting the profit theory of refinancing and invalidating some of the HSV results and conclusions. It lends support to the policy of the Belgian central bank, as presented by governors R. Vandeputte (1976, pp. 209-219) and C. de Strycker (1978, pp. 311-312), to actively use discount rate changes as a policy instrument. It confirms the statement of Fourgans (1976, p. 224) that ' . . . in a monetary system where banks' borrowing from the authorities is very important, the cost of this borrowing should significantly affect the behavior of commercial banks'. The empirical results to be reported respond further to a call made by Plasschaert (1976, p. 229) who commented on the pessimistic conclusions of HSV about the efficacy of monetary policy in Belgium that 'unless these conclusions are reversed or substantially qualified by subsequent research, the outlook is not comforting at all. The monetary instruments that have been traditionally used appear to be dull. Discount rate c h a n g e s . . , are said to be largely ineffective'. This paper is divided in three parts. Section 2 briefly reviews profit theory formulations appearing in the empirical literature on monetary policy. The estimation of the alternative specifications for each of the closed and open economy are reported in section 3. Policy implications of the findings are discussed in section 4. The appendix gives detailed data sources.

2. The profit theory of refinancing The profit theory of refinancing was first formalized for the United States closed economy by Meigs (1962) in connection with free reserves, x De Leeuw (1965), Goldfeld (1966) and Silber (1970) used the Meigs framework to formulate and test directly the profit hypothesis on refinancing. Frost and Sargent (1970) refined the measuring technique of the cost variable and the partial adjustment path. The profit hypothesis is further adopted by Brunner and Meltzer (1964a, b,c) and more recently also by Burger (1971), Sutch and Thurston (1976) and Korteweg and van Loo (1977). The profit theories postulate that refinancing AD is homogeneous of degree 1 in total deposits D, responding positively to the market rate of interest i,, and negatively to the discount rate p. If the adjustment processes are rapid relative to the time period implied by the model, the desired refinancing ratio is equal to

AD/D=z(i,,,p) with z l > 0 > z 2 ,

(1.1)

or alternatively,

AD=fl(i,,,p)D

with

~1 >0>f12,

(1.2)

1As in the United States, Belgian banks can seek refinancing either through the money market or through the discount window and the usual distinction between borrowed and unborrowed reserves applies.

H. Langohr, Banks refinancing with the central bank

177

In the case of only partial adjustment of actual to desired refinancing during the interval under consideration and given a set of interest rate conditions, the function becomes

AD/O=?(i,,,,p, (AD/D)_I),

(1.3)

with ~1 > 0 > ~ 2 and 0<~, 3 <1, and

AD=3(im, P, AD_I)'D, with 61 > 0 > 3

2

(1.4)

and 0<33 < 1, where

33 = 1 - ~,

0 < ~ < 1,

fii=fli~

i=land2.

for

~ = adjustment coefficient,

The higher the adjustment relative to the time period allowed for the adjustment, the smaller 63. A full adjustment hypothesis from actual to desired refinancing is equivalent to setting ~ equal to one. Meigs and subsequent authors modified the profit hypothesis as stated by eqs. (1.1) through (1.4) by including in the refinancing function, elements of the reserve position doctrine [e.g. Meigs (1962, pp. 45-46 and 53-57)]. 2 This doctrine argues that central banks cannot have effective control of total bank reserves, and hence of deposit expansion, because bank refinancing would automatically offset open market operations intended to change total reserves. 3 In contrast, it proposes to control, at the level of the central bank, the ratio between bank refinancing and government securities or, equivalently, at the level of the banking system, free reserves (excess reserves minus refinancing). Under the reserve position doctrine, bank refinancing is essentially interest inelastic and open market operations determine, through the manipulation of banks need for funds, the level of refinancing. Meigs incorporates this view of the monetary mechanism by introducing in the refinancing function the change of unborrowed reserves AR". He recognizes though that this argument of the borrowing function does not account for desired refinancing on behalf of the banking system. Formally, one can write,

AD/D=og(im, P, ARU/D, (AD/D)_I) with o91,o9, >0>o92, oga, (1.5) and

AD=ck(im, P, ARU,AD_i)D with ¢1,¢4>0>¢2,¢3,

(1.6)

2For an excellent discussion of the free reserves doctrine for implementing monetary policy, see Brunner and Meltzer (1964b). aFor a recent discussion of this offset issue in the context of a structural model, see Aftalion and White (1977, 1978), Vuchelen (1978) and Langohr (1979).

178

H. Langohr, Banks refinancing with the central bank

The profit theory of refinancing is extended to the open economy by introducing the arguments reflecting the cost of the foreign substitute. This cost is equal to the foreign interest rate i~ for banks not covering against foreign exchange risk; when they do cover, the forward premium (or discount when negative) y should also be included as an argument with the same sign as i~. To illustrate, define X = amount banks want to borrow in domestic currency, F X ~ =number of dolXnestic currency units per unit of foreign exchange for spot payment and delivery, F X : = number of domestic currency units per unit of foreign exchange for payment and delivery in three months, y = F X : / F X ~ - 1 forward premium of foreign currency. The amount to borrow in foreign exchange to satisfy the demand X is equal to X / F X ~. At maturity, banks have to repay in foreign exchange, (X/FX~)(1 + ie). The domestic currency amount of forward foreign exchange banks are purchasing now to cover against foreign exchange risk is equal to (X/FX~)(1 + ie) FX:. The cost of this operation equals therefore (FX:/FX~)(1 + ie) or, in forward premium terms, (1 + ie)(1 +y). Considering that the term i~-y is of secondary importance and can be neglected, the refinancing cost under covering is equal to i~ + y. A system refinancing function aggregates individual banks that do cover with individual banks that decide not to cover. Constraining the refinancing response of the banking system to i~ to be equal to its response to y by introducing the sum ie+y as a single argument of the system refinancing function would be unduly restrictive. I't is more general to introduce both i~ and y separately into the refinancing function. Refinancing the amount of domestic currency X through the foreign exchange market is a substitute for refinancing the same amount from the monetary authorities AD. Its costs ie and y therefore appear in the domestic refinancing function with a sign opposite to the own cost p of domestic refinancing AD,

AD/D=2(i,,,,p, ie, y),

(2.1)

with 2 I, 2 3 and 24 > 0 > 22, or

AD=gJ(im, p, ie, y ) ' D , with 711, tP s and ~ 4 > 0 > tP 2

(2.2)

The reader can easily draw the parallel between (2.3) through (2.6) not

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179

written out here, and (1.3) through (1.6) for the case of partial adjustment with or without incorporating elements of the reserve position doctrine.

3. Empirical estimation of refinancing The equations are estimated on end of quarter, seasonally unadjusted, data from 19601 through 1973IV. All arguments of the refinancing function are considered to be parametrically given. 4 The LS estimates are all Feasible Aitken estimators obtained with the Cochrane-Orcutt technique [see Johnston (1972, pp. 208-211 and 261-265)]. Table 1 reports the results for the closed economy and table 2 for the open economy. The appendix provides detailed data sources.

3.1. Resolution of some measurement problems There is a one-to-one correspondence between the specified refinanc!ng equations and the estimated ones, but several empirical identification problems had to be solved. Refinancing could be interpreted as borrowing strictu-sensu ADb: advances from the central bank and bankers acceptances in its portfolio. Alternatively, it could mean commercial bills and promissory notes rediscounted by the banking system at the central bank ADp. Lastly, as both AD b and ADp are determined by commercial bank behavior, refinancing can be defined as the sum of the two, AD. A case can be made to differentiate between ADb and AD r F r o m a bank behavior point of view, even if present in AD~, any reluctance effect should be absent from ADp [see Langohr (1977, pp. 29-30)]. From the viewpoint of the money supply process, AD b is a liability of the banking system, whereas ADp one of the non-bank public. 5 However, the sample correlation coefficient between ADp and ADb is 0.88. They are about equally relevant empirically with sample period means of 6.2 BBF for ADb and 5.5 BBF for ADp, both demonstrating the same coefficient of variation of 0.8. H S V (1976) used AD. It is concluded to measure refinancing by AD. Six different discount rates applied during the sample period: the basic discount rate DR, the export discount rate DRX, the rate for accepted domiciled bills DRCBAND, the rate for unaccepted domiciled bills DRCBNAD, the rate on promissory notes and unaccepted undomiciled bills DRPN, and the rate on direct advances DRBORR. Three institutional changes occurred. The first made D R = D R X and the second made 4This standard assumption is not tO deny possible interdependenciesbetween the explanatory variables and the error term, with the consequential limited sample bias in one- or two-stage least squares coefficientestimates. SFollowing result follows from this distinction: an increase of the ADb discount rate unambiguously decreases the monetary base B, whereas the impact on B of an increase in the AD~,rate is in general ambiguous [see Langohr (1978, pp. 37-38)].

180

H. Langohr, B a n k s refinancing with the central bank

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DRCBAND=DRCBNAD=DRPN from July 31, 1969. The third one made D R C B A N D = D R C B N A D = D R P N = D R B O R R from March 2, 1972. At this point, an identification problem arises. No single discount rate applies exclusively to either borrowing or rediscounting. An empirical criterion must be followed. The rate selected is the one that explains refinancing best according to the minimization of the standard error of the estimate. This rate corresponds to DRCBNAD which is therefore chosen. There are several ways of measuring the interest rate i,,. It can be considered as a return index of bank earning assets in general. In another view, im can be interpreted as the yield of whatever instrument that is used for short-run portfolio adjustments. Lastly, i,, could be the interest cost of the nearest substitute to borrowing from the monetary authorities. A rate that a priori should combine characteristics of all three interpretations is the market rate of interest on three month bankers acceptances, as determined in the private market for bankers acceptances organized by the Rediscount and Guarantee Institute. 6 The existence in Belgium of a two-tier foreign exchange market creates a problem for the identification of the appropriate forward premium of foreign currency y. Compartmentalization between spot markets is carried over to the forward foreign exchange market where exist the regulated commercial premium and the market determined financial premium. The latter one is chosen.

3.2. Analysis of empirical results The bracketed items under the regression coefficients in tables 1 and 2 represent t-statistics. DQ4 is a binary variable equal to one in the fourth quarter. The other quarters seasonal d u m m y variables were statistically insignificant and the regressions were rerun without including them. The last two columns report the adjusted coefficient of determination R 2, the standard deviation of the estimated error term SE, the Durbin-Watson Statistic D - W and the degrees of freedom DF. The interest rate coefficients in eqs. (1.1), (1.5), (2.1) and (2.5) were multiplied by 100 for reporting purposes. Contrary to the results reported by HSV (1976, p. 184), the interest and discount rate coefficients reported in tables 1 and 2 are all statistically highly significant (5 percent or better) with the correct sign. This is confirmed for all cases examined: the closed economy (table 1) and the open economy (table 2), the linearized or ratio forms (the first versus second panels of both tables, respectively), with allowance for partial adjustment [eqs. (1.4) through (1.5) and (2.4) rhrough (2.5),1 or without l-eqs. (1.1), (1.2), (2.1) and (2.2)'!, 6This Institute exercises, among others, the functions of a Discount House centralising as a broker, dealer and on principal the market in commercialbills and bankers acceptances.

H. Langohr, Banks refinancing with the central bank

183

with inclusion of unborrowed reserves (1.5), (1.6), (1.6a), (2.5), (2.6), (2.6a) or without (the others). Table 3 reports elasticities associated with the regression coefficients of tables 1 and 2. In contrast with the findings of HSV (1976, p. 203) this shows that bank refinancing is highly interest elastic. The absolute value of all elasticities is larger than one. Furthermore, the own price elasticity, the one with respect to the discount rate, is larger in absolute terms than any of the cross price elasticities, as predicted by relative price theory. Table 3 Refinancing elasticities a

e(AD, x)= (dAD/~x ) . (~/AB ). X

AD

im

(1.1) (1.2) (2.1) (2.2)

2.67 3.31 1.98 2.03

p -3.01 - 3.42 -3.24 - 3.82

i~

y

1.01 1.80

0.11 0.15

D

0.67 0.67

~Elastiticies are calculated around the sample period mean.

H S V (1976, p. 187) ascribe their lack of significant results to a large extent

to 'the high degree of covariance' among the interest rates. Any statistical test would confirm the substantial degree of collinearity among the interest rate series. But the genesis of such collinear time series results from strong and significant quantity responses of the market transactors to minor changes in relative interest rates. The observed collinearity among the interest rate time series is exactly the result of the interest rate equilibrating market mechanism. Were it not for highly significant and elastic portfolio adjustment responses to initial changes in relative interest rates, the ex post collinearity would not be observed in the time series. One is led therefore to explain the surprising results of HSV to variable measurement and equation specification rather than to actual interest inelastic behavior of the Belgian banking system. One such important difference in specification between (2.1) [or (2.2),1 and HSV relates to the role assigned to 'need' and 'partial adjustment' variables in shaping banks demand for refinancing. According to HSV, these variables are crucial in explaining bank refinancing as evidenced by the inclusion of the unborrowed base BU as an argument of the refinancing function. This view appears to be strongly corroborated by the statistical significance level 4.34 of its regression coefficient -0.39 [HSV (1976, p. 184)-I, the goodness of fit of the regression (R 2 of 0.824), the extreme elasticity of AD with respect to

184

H. Langohr, Banks refinancing with the central bank

B U - - 7.42 and the interest inelastic response of AD with respect to a credit

rate (0.36) and the foreign rate (0.39). Of course, bank refinancing cannot simultaneously be interest elastic (as indicated by table 3) and interest inelastic (HSV). To solve the paradox, eqs. (2.6) was tested. The 'need' for funds is .represented by A R u, and the introduction of AD_ 1 allows for 'partial adjustment'. When this evidence is taken at face value, the offset coefficient is large indeed (-0.90), adjustment occurs slowly (only 31 percent during the current quarter), and refinancing is, in the short run, inelastic with respect to im (0.81) and ie (0.74). The results of HSV appear to be corroborated. Belgium appears to satisfy the setting for the reserve position doctrine. Such a conclusion, however, would be completely spurious. The direct introduction of an offset variable, in casu AR", blurs the genuine underlying response structure. The regressor d R ~ is incorporated in A D through the identity: A R - A D + A D _ I . This constrains the estimated coefficient of A R" to be highly negative (at the limit - 1 ) and forces the estimated coefficient of AD_~ upwards (at the limit +1). It biases the coefficient on the interest variables toward zero in the limit. It decreases the standard error of the estimate without adding to the explanatory power of the hypothesis. The magnitude of the biases introduced by the offset variable can be illustrated by comparing (2.6) with (2.4). The latter examines the partial adjustment profit hypothesis. According to (2.4), and contrary to (2.6), the hypothesis cannot be rejected that banks fully adjust actual to desired refinancing within three months and that refinancing is interest elastic. In summary, the results of (2.4) re-inforce these of (2.2) [(2.1)] and illustrate the spuriousness introduced by the offset variable in (2.6)[(2.5)]. The results reported in table 2 are further differentiated in specification from those of HSV by the inclusion of y and D as arguments of the refinancing equation. The coefficients on both arguments are highly significant statistically with the correct sign. It should be no surprise that the elasticity of A D with respect to y is low (around 0.10 to 0.15), as this elasticity should be considered in conjunction with the one on ie. Regarding the elasticity e(AD, D) of 0.67, this suggests the existence of some economies of scale in the reliance of the banking system upon the discount mechanism as the system expands. The explanatory power of the profit hypothesis is remarkably high. In the closed economy case, as reported with (1.2), it explains 77 percent of the variation in AD; adding i, and y to allow for the open economy case increases this explanatory power to 83 percent. This is marginally larger than the result obtained by HSV. To allow for a fuller comparison with HSV, regression results that drop the scale variable D [(1.2a), (1.4a), (1.6a), (2.2a), (2.4a) and (2.6a)] are reported. This illustrates that none of the results previously discussed are due to the particular inclusion of D. It tends to re-inforce them. The explanatory

H. Langohr, Banks refinancing with the central bank

185

power of im and p alone is shown in (1.2a) to be 73 percent. The case that best compares with HSV in terms of incorporating the reserve position doctrine without an additional scale variable, eq. (2.6a), yields an 'apparent' explanatory power of 90 percent, to be compared with the 'apparent' 82.4 percent in the case of HSV.

4. Summary and conclusions The purpose of this paper was to report evidence that strongly supports the profit theory of bank refinancing and that re-examines its interest rate elasticities for Belgium 1960-1973. The evidence presented indicates that the profit theory explains up to 83 percent of the variation in bank refinancing during the sample period. Refinancing responds strongly and statistically significantly to interest rates. It is highly interest elastic, but particularly so with respect to the discount rate. Banks fully adjust actual to desired refinancing within three months. The negative association of refinancing with a need variable such as unborrowed reserves is a spurious one which leads to inappropriate inferences and potentially wrong policy conclusions. These findings substantially reverse the ones reported in a recent article by Heremans, Sommariva and Verheirstraeten (1976). They provide empirical support to the statement made by Fourqans (1976, p. 224) that 'in a monetary system where banks' borrowing from the authorities is very important, the cost of this borrowing should significantly affect the behavior of commercial banks'. The main conclusion of this paper is that the outlook for policy-making should be comforting. Monetary policy instruments that have been traditionally used appear to be well-conceived: discount rate changes . . . are found to be largely effective. This conclusion substantiates the opinion expressed by Plasschaert (1976, p. 230).

Appendix: Data description The publications of the National Bank of Belgium, 'Belgische Economische Statistieken 1960-1970' and 'Tijdschrift van de Nationale Bank van Belgie' are the main sources of the data. Table numberings and arrangements of the two publications are different and, unless otherwise stated, all table references are to 'Belgische Economische Statistieken 1960-1970'. A substantial amount of unpublished series was provided by the research Department of the National Bank of Belgium. They are referred to as NBBRD. The series obtained from the 'Centrum voor Ekonomische Studi~n' of the Katholieke Universiteit Leuven are referred to as C.E.S. Unless otherwise

186

H. Langohr, Banks refinancing with the central bank

indicated, all data are seasonally unadjusted end of quarter figures in billions of Belgian frances. Interest rates are stated in percent. =Banking system indebtedness to the monetary authorities. Table XIII-2: Actif, A4, B2b, B2c, C3a, C3b, C3c, C3d, C3e, C5. D =Total bank deposits (demand, time and equivalents) in Belgian francs: Table XIII-4, Passif, A3b, A4, B2b, C2a, C3al, C3a2, C5b, C5d, C5e; plus NBB-RD: netto bankers' acceptances liabilities in Belgian francs minus bankers' acceptances held by the NBB. DQ 4 = Dummy binary variable for the fourth quarter. ie =Eurodollar depos!t rate, prime bank bid rate in London (source: Morgan Guaranty Trust Company, World Financial Statistics). im =Market rate of interest for three-month bankers' acceptances, in percent; Table XIX-5; since 1970: NBB-Annual Report. p = N B B discount rate for not-accepted domiciled bills: NBB-Bulletin, Table XIX-1. R =Bank reserves: Table XIII-4: Actif, B1, B2a; plus C.E.S.: Bank deposits with Postal Checking Office. R e = Total required reserves: Table XII-4, Actif B2al. R" = Unborrowed reserves: R - AD. y =3-month financial forward prehaium on the U.S. Dollar (source: through 1969-1, C.E.S.; since 1969-11, NBB-Bulletin, Table X-4). AD

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Frost, P.A. and T.J. Sargent, 1970, Money-market rates, the discount rate, and borrowing from the Federal Reserve, Journal of Money, Credit and Banking 2, 56-82. Goldfeld, S., 1966, Commercial bank behavior and economic activity (North-Holland, Amsterdam). Heremans, D., A. Sommariva and A. Verheirstraeten, 1976, A money bank credit model for Belgium, in: M. Fratianni and K. Tavernier, eds., Bank credit, money and inflation in open econbmies, Supplements to Kredit und Kapital, Heft 3 (Duncker and Humblot, Berlin) 155208. Johnston, J., 1972, Econometric methods, 2nd ed. (McGraw Hill, New York). Korteweg, P. and P.D. van Loo, 1977, The market for money and the market for credit (Martinus Nijhoff, Leiden). Langohr, H., 1977, Domestic and international borrowing by the banking system and the ability of the monetary authorities to control monetary base: The Belgian case (University of Michigan microfilms, Ann Arbor, MI). Langohr, H., 1978, Domestic and international borrowing and the determination of the monetary base: A credit market view, Mimeo. (Money and Banking Theory Workshop of the European Institute of Advanced Studies in Management Sciences, Brussels). Langohr, H., 1979, Banking system's refinancing and base determination: Belgium 1960-1973, tenth Konstanz Seminar in Monetary Theory and Policy, Mimeo. Langohr, H., 1980, Banks borrowing from the central bank and reserve position doctrine: Belgium 1960-1973, Journal of Monetary Economics 6, forthcoming. Meigs, J.A., 1962, Free reserves and the money supply (Chicago University Press, Chicago, IL). National Bank of Belgium, Report presented by the Governor in the Name of the Council of Regency, 1960-1974 (National Bank of Belgium, Brussels). Nationale Bank van Belgie, 1971-1975, Tijdschrift van de Nationale Bank van Belgie (Nationale Bank van Belgie, Brussel). National Bank van Belgie, 1975, Belgische economische statistieken, 1960-1970 (Nationale Bank van Belgie, Brussel). Plasschaert, S.R.F., 1976, Comments on the paper of D. Heremans, A. Sommariva and A. Verheirstraeten, in: M. Fratianni and K. Tavernier, eds., Bank credit, money and inflation in open economies, Supplements to Kredit und Kapital, Heft 3 (Duncker and Humblot, Berlin) 227-230. Silber, W.L., 1970, Portfolio behavior of financial institutions (Holt, Rinehart and Winston, New York) 35--44. Sutch, R.C. and T.B. Thurston, 1976, Member bank borrowing from the federal reserve system and the impact of discount policy, Quarterly Review of Economics and Business 16, 7-23. Vandeputte, R., 1976, Objectives and tools of monetary policy in Belgium, in: M. Fratianni and K. Tavernier, eds., Bank credit, money and inflation in open economies, Supplements to Kredit und Kapital, Heft 3 (Duncker and Humblot, Berlin), 209-219. Vuchelen, J., 1978, A study of a monetary system with a pegged discount rate under different market structures: Comments on the article by F. Aftalion and L. White, Journal of Banking and Finance 2, 339-350.