fundmentally on t reserve ratios than terms of ‘liquidity latter function int

formal- and inform&sector financial instmments.

The fundamental thesis advanced i

and Shaw (1973) was that financial associated reforms in exchange-rate, improve the allocation of resources thereby help to optimize their pry

innon and Shaw - with the the ‘neo-structura

referees for My for the views exp

03043878/92/W% c 1992~Elsevier ts r

Most commonly associated with the Wijnbergen (1982, 1983), and BufEe (1 the consideration that commercial ba nent of the formal financial sector in ’

to legal reserve requirements, in contrast to en informal credit markets of t financial liberalization, essentially invoIvi of administratively im in the formal sector, away from informal-sector institutions (Raving 2ero or low reserve ratios), and towards formal-sector institutions ( aving significantly higher reserve ratios), and as a result the total voI e of productive lending in the economy will be reduced, contrary to the express intentions of the fan liberalization proponents.

The neo-structuralists have recognized that their criticism wou hold if the above-mentioned effect were to be dominated either by an increase in the level of total saving in the economy (in res deposit rate increase) or by a concomitant shift away fro currency (or other ‘unproductive’ assets such as gold) and towards formal- sector deposit-holdings. Other investigators have advanced further criticisms, both empirical [Fry (1988)] and theoretical [Chang and Jung (1984), Owen and Solis-Fallas (1989), Kapur (1989)]. The theoretical criticisms take issue with the implicit neo-structuralist supposition that informal-sector enterprises eflcien@ allocate all the funds they receive to productive activities. In this paper, we argue that the neo-structuralist thesis is based on an inadequate accounting of the ‘seignorage’ gain accrluing to the govern znt as a result of a financial liberalization. We also contend that the economic role performed by the ‘central actor’ in the neo-structuralist critique - the reserves held by commercial banks - deserves far closer micro-theoretic examination than it has hitherto received. Such an examination, which forms the analytical base of the paper, leads to the result that a financial liberalization is unambi- guously welfare-enhancing, and also points up an important flaw in previous portfolio-theoretic models of the financial sectors of LDCs.

. ity a em

Before embarking on the formal analysis, it would be he1 contemplate the essential purpose served by bank reserves. this is to enable banks to meet immediate c in excess of any concurrent cash inflows.

e also receives an endowment at the

financial intermediary (IFI henceforth): the remainder of his wealth would then be deposited with a commercial bank (CB), all other forms of wealth- holding being abstracted from.4

‘It should be noted that this function is also served by reserves that are legally required to held. To quote Luckett (1984, pp. 212-213), ‘The bank is not expected to hold the exact amount of its required reserves every minute of every day, but instead is only required t d average reserves as a percent of average deposits, where these items are averaged over a or more. Thus, on any given day a bank may pay off depositors completely out of its requr reserves as long as it makes up such a deficiency within the next few days.’

3This follows from their small sca!e and local&d (and generally unsupervised) character. As a consequence: (a) they are unlikely to be linked by a market as extensive as the interbank market, whose existence permits reserve-holding to be minim&d because (abstracting from general&d bank panics, which would in any event certainly affect informal credit well) banks that unexpectedly experience reserve ‘deficits’ can tedly experience surplu synchronisation betwee whole does in the tour then essentially serves the purpose of bridging any short gaps that may arise wi! hhwak arid li~c: ,iyts.

4Van Wijnbergen ( 1983) also allows fcornote i(I), do-- e * c3 ilot rnves!:gzi; :i;c h postulates. A referee has suggested t stochastic expenditures’: this is likely to de one could, at the cost ‘cash goods’ and currency and ather

an LDC context, it is rfzalistic to assu insured against. The cxmsumer his bank account, or by bsras

derived by him from his en od consumption of goods and services? we turn next to the on of the consumer’s utility functi

the purpose of intertemp analysis, the most commonly employed cation in economics has been that of additively separable utility, in conjunc- tion with a usually constant rate of time preference. While the first- and second-order conditions for an optimal solution in a model incorporating such a utility function can be fairly readily determined, any further character- ization of the solution is rather problematic [see, for exa Mirman and Zilcha (1980)]. For our purposes, however, it is essential that such a further characterization be developed. As such, we propose to adopt here the much more tractable ‘fixed coefficients” function:

U=min[E(CI),E(C,) ,..., E(C,)], (1)

where Ci =consumption at the end of period i (i = 1,2,. . . , T), E is the expectation operatar, and c’ is the utility function. e for analytical simplicity the absence of a bequest motive, and of an intertemporal discount

‘As will be subseq uently evident, the optimised value of the consumer’s utility function is bounded from above. An ‘unacceptable decline in utility’ could therefore be formally modelled as a decline which, should it occur, would in absolute value exceed this upper bound.

6This characterization anpears to be formally equivalent to the assumption, initially made by Lucas (1980) and subsequently adopted by other investigators into the analytics of the liquidity

[reference issue, that consu

preferences: however, our treatment is

random expense, ich he can defray either by dra

may or may not be the same C

‘The latter is also motivated by our desire to abstract as fz as possible from changes in the level of total savings in response to parameter changes.

*A referee has questioned our choice of utility function on the grounds that, for example, it implies that the consumer would be indifferent between a ‘fiat’ and a rising consumption profile, as long as both have the same initial level of consumption. While this is correct in an sense, in an ‘ex ante’ sense (which is our concern in this paper) a corzmer whose budget constraint permitted a rismg consumption profile would but would instead ‘tilt’ it to obtain a flat profile yielding hi periods and lower consumption (than otherwise) in the later Mall’s ( 1988) empirical i~vestjgat~ intertemporal substitution) have also employed the R

of period i, so that (Ai- denote the expense thr: consumer has Xi IS assumed to be a time, with continuous probability density function f(Xi) (t all i), and we also assume that Xi is al an upper limit X. The issue of h

subsequently. FinalSy, we assuine no interest on that part ot his C meet his expenses: since the ‘margm between an IFI term deposit and a reasonable assumption. l0

We then have

E(W;A)=(1+d)D$(l+i)(A- 0

-(1 +&X-D)f(X)dX-(1 +d)&(X)dX, (2) I) D

where, since we are for the time being focusing on the one-period problem, all time subscripts have been suppressed.

A brief explanation of eq. (2) is perhaps called for. The sum of the first two terms on the right-hand side constitutes the end-of-period wealth if X were zero, and the remaining terms reflect the deductions from this amount nco~c;nn~A by the set of values that X may possibly assu VU~U0&Y&IYU “J e. The third right- hand side term is the expected value of the deductions occasioned by (probabilistic) values of X in the (0,D) interval (such values being ‘paid for’ by the consumer drawing upon his CB deposit), while any alternative value of X between II) and X will be paid for by his completely drawing down his bank deposit (thus explaining the last term on the right-hand side) and by his borrowing at the rate h the amount required to defray the remaining ex ses (X-D) (thus accounting for the penultimate term).

fferentiating eq. (2) successively with pect to D [and for notational convenience suppressing the parameter A i W; A)], we have

“Bank nolicies in regards to premature withdrawals of time deposits vary from country to country but in any event it is unlikely that payment of interest will be exactly pro-rated (for example, a 3-month deposit, withdrawn after one-and-a-half months, is likely to receive at most only the one-month interest payment). Moreover, it is still reasonable to assume that h (a half- period borrowing rate) exceeds d and i (one-period deposit rates) when one ap includes the usually quite substantial transacti0r.s costs (such as the costs of ne preparing the requisite documentation, and the like) which have to see Ahmed ( 1989), and also Ng ( 1985).

Since ddeh, we

t

c

i-- th . If we further assume negative for all DE ( established below) i Correspondingly, at (A -D*) in an IFI deposit.

There are a couple of features of the foregoing solution that are wo~hy of note. First, implicitly differentiating eq. (5) with respect to d, holding h an constant, we obtain

i?D” 1 -=-• (h-0 >o

?d f(D*) (h-d)2 l

Thus, as one would expect, D* varies positively with d. Correspondingly, denoting the optimised value of E(W) by E( )*, it can be easily shown, using eq. (2) and the envelope theorem, that

dE( W)*

Zd = -y(X-D*)_f(X)dX

h, i corm. 0

ell as on the density

70 B.K. Kapur, Financiai liberalization strategy

consider first of all a consumer situated at the beginning of period 1 of his life. Let G1 denote the endowment he receives at the beginning of period 1: as mentioned earlier, hc also receives a fixed income of W at the beginning of each period of his working life. Now, an inspection of the entire right-hand side of eq. (2) reveals that it can be expressed as (1-t i)A -H, say, where H is the expected cost of financing the within-period random expense. For example, if D were zero, it is readily determined that H would reduce to (1 + h)~, where p = $ Xf(X) dX is the mean of X: the consumer finances his entire random expense by borrowing at the rate h, and repaying such borrowing at the end of the period out of his maturing IF1 deposit. However, increasing D above zero permits H to be reduced below (1 + h)p (even after allowing for the fact ihat H includes the opportunity cost - which is ‘extractable’ from the first two terms on the right-hand side of eq. (2) - of holding D at the expense of foregone IFI deposit-holding). In fact, we can substitute from eq. (5) into eq. (2) and manipulate terms to derive the optimal value, H”, of H (corresponding to D = D*):

H*=(l +h)/r-(h-d)qxf(X)dX. 0

(8)

It follows that the discounted present value of the consumer’s expected life-time wealth, denoted by L1, is

&zGl+/il -!!- t=o (1 +i)’

(9)

- . . r ram eq. (I), it 3 ev:uvnnr. ‘Ann+ that the consumer would seek ex ante to attain the highest possible constant value of E( Ci) (i = 1,2,. . . , T), &~td E(CS

The discounted present value of his expected consumption plan, denoted by K, would then be

Equating L, and K and manipulating terms, we are able to solve for

“The choice of i as the discount rate will be justified shortly. Note that the first summation on the right-hand side of eq. (9) is across N terms (since he works for N periods), and the second summation is across T terms (since he incurs the random ex his life).

nditures in ai] periods of

12This term denotes the value of (c)* as at the be term with the h superscript omitted denotes the value of

B. K. Kapur, Financial liberalizarion strategy 71

E(C)*[;= 1= (11)

Having characterized the optimal plan of the individual at the beginning of his life, it is necessary next to consider how his plan is modified as he gro older (and equivalently - assuming that X is distributed inde only across time but also across individuals - to characterize plans of individuals of all ages). Since the procedure involved is closely analogous to that described above, and to conserve space, we shall details are obtainable from the author upon request. Essentially, involved is a simple sequential updating procedure: at the end of each the actual realization of X during that period (as well as in all preceding periods) is known, and hence the actual end-of-period wealth is known. This becomes a datum: the individual then deter-r-nines his actual consumption at that time (equal to his expected consumption at all subsequent dates14) by equating the discounted value of his expected wealth over his remaining lifetime with the discounted value of his expected remaining consumption stream. Thus, our preceding present-value formulae continue to apply, mutatis mutandis, and noting also that after retirement (at age N) the individual recives no further income payments: he then finances his consump- tion and deposit-holding out of his accumulated wealth and interest earnings thereon.’ 5

’ 3The foregoing derivations help to indicate that i is the correct discount rate: since, as pointed out earlier, D* in each period does not vary with variations in total asset-holdings A (as long as A > D*), each period’s consumption induces only a lower level of IF1 deposit-holdings in

net of expected ex

72 B.K. Kapur, Financial liberalization strategy

3. The banking system

Having characterized the optimal behaviour of the individual asset-holder, we proceed now to consolidate the activities of all asset-holders. We assume that asset-holders can be partitioned into two equal groups, A and B. Group A places its CB deposits at ‘integer’ dates, namely times 1, 2, 3,. . . This group comprises T sub-groups of equal size, each comprising individuals born at the same (integer) date, who will die T periods later. Thus, at each integer date one sub-group will go out of existence, and another sub-group of equal size will come into existence.

Group B has exactly the same characteristics, except that its members are born (and die) at the non-integer dates 13, 23,. . . They also place their CB deposits at these dates. The working members of Group A receive their income payments (assumed the same for all working individuals in both groups) at dates 1,2,. . . , and those of Group B at dates 14, 24, : o i The individual optimization exercise conducted in the preceding section is equally applicable to individuals in Group B, except that various time subscripts pertaining to their situation will, obviously, take on non-integer values, examples being C 1 +,C2+, . . . , and so on. We also assume that the distribution function of X is the same for all individuals (although X varies indepen- dently across individuals).

Lastly, we assume that the size of each group is large, in a sense to be made clear subsequently. The notable feature of our group demarcation is that at dates 1, 13, 2, 23,. . . , one group is in the middle of its ‘transactions period’ and is therefore having to meet its random expenses, and the other group has completed one transactions period (its IF1 deposits have matured and it can thus repay outstanding loans incurred earlier to meet its random expenses), and initiates the next period (by placing new deposits with IFIs and CBS). As such, the asset-and-liability position of commercial banking system as a whole has a stationary structure, as foll At, for example, an integer date (the same kind of argument applying in resiect of integer-and-a- half dates), members of one group, in this case Group A, will be withdrawing their outstanding IF1 and CB deposits,16 repaying outstanding loans, and placing new IF1 and CB deposits (the total value of the latter being D* times the number of individuals in the group). At the same time, members of the other group will be drawing upon their CB deposits and (in respect of those individuals whose realizations of X exceed D*) borrowing from CBS to finance their random expenditures. From the law of large numbers it readily shown that the average (in other words, per member of each amount of deposits withdrawn and loans incurred at each ha1

“The total amount of outstanding Croup A C deposited one period earlier minus the amount

&posits at that date is eq

wit random expenses.

B.G. Kapur, Financial liberalization strategy 73

meet the random expenses can be made arbitrarily close *co their respective expected values [jr X$(X) dX + D* pb f(X) dX] and if the size of each group is made sufficiently large.’ ’ to any desired degree of accuracy approximate these averages by the corresponding expected values.’ * At each integer date, therefore, the average inflow of new deposits, D*, would equal the average outflow, [lr X f (X) dX + D* Sf f(X) dX] of withdrawals per Gro [D*-jrXf(X)dX-D*rif(X)dX] of withdrawals per (since the latter is liquidating the balance of his earlier after his withdrawal a half-period earlier). In addition, the average amount of loans issued to Group B members to finance their random ex G(X-D*)f(X)dX will be equal to the average repayments of sue contracted a half-period earlier by Group A members. Thus, at each integer date (and correspondingly for non-int r dates), after transactions have completed, the average size of Group deposits will be D*, and of Gro deposits will be [D* -jr Xf(X) dX- D* s; f(X) dX], so that the average deposit size across both groups, denoted by 6, will be

6=f[2D*-jrXf(X)dX-D*$f(X)dX]. (12)

Moreover, the average (across both groups) volume of outstanding loans (issued for the purpose of financing the random expenditures), denoted by fi, is

ff=#&(X-D*)f(X)dX. (

It is assumed [in view of eq. (5) above] that the values of i, d, and h are such that D* is sufficiently close to X that exceeds f? by more than the av size of bank reserves held.” s that not all bank loans are i for the purpose of financing the random expenditures: the remainder will be issued to firms to finance their productive activities?’ This completes the ‘profile’ of the banking system induced by our theoretic analysis, and we proceed next to examine the effects of a fi liber&ization within this framework.

74 B.K. Kapur, Financial liberalization strategy

. Effects of a financial liberalization

Given the above liquidity-theoretic characterization of the banking system, which is the center-piece of our argument, the remainder of the discussion can in fact be easily apprehended in informal terms. Owing to space rionstraints, we omit here a complete formal treatment (obtainable upon request), and focus instead on the essential logical links in the argument.

Since D in eq. (12) above is easily shown to be an increasing function of D*, it follows that dD/dd ~0. Likewise, since R dd CO. Now, per capita bank lending to firms denoted by z, is, as indicated earlier, given by

2=(14)&i?,

is decreasing in D*, dk?/ for productive purposes,

(14)

where k is the reserve ratio maintained by CBS, and is assumed for simplicity to be fixed. We assum:, as is common in LDCs, that the government pegs the interest rate, 1, on L at a level below the ‘equilibrium’ rate [see Fry (1988, Section l--4)], and that all firms which cannot obtain (suficient) bank financing turn to the IFIs for their (remaining) credit requirements.

A financial liberalization can then be represented simply as a policy decision to increase 1, which enables CBS to increase d as well. The resulting change in D is given by dD/dd, and in per capita CB lending by (I- k)(dB/

dd). However - and surprisingly - the corresponding change in average IFI deposit holdings, even at an unchanged level of each consumer’s total asset- holdings, is not - dD/dd, but instead - dD*/dd.21 Neo-structuralist analyses - as well as empirical studies such as that of Burkner (1982) - have typically imposed ‘adding-up’ constraints which imply that, with all other asset- holdings unchanged, changes in IFI and CB deposit holdin s must be exactly

offsetting, an implication that our more detailed investigation shows to be incorrect.22

It turns out, though, that the above result strengthens the neo-structuralist ‘case’, since the reduction in D* exceeds the increase in D, Against this, however, we have to counterpose the associated reductioh in ff: because

21Eollowing upon section 3’s analysis, a typical Group A asset-holder wouldi after transac- tions have been completed at an integer date, hold (A -D*) worth of IF1 deposits, where A denotes his total assets at that date. A half-period later, he would draw upon his CB deposits to help meet his random expenses, but this would not affect his IFI deposit-holdings. Similarly for Group B asset-holders. Thus, across all Group A and B asset-holders, average CB deposit- holdings at any date would, as shown earlier, be fi, but average IFI deposit-holdings would be A-D* (where A denotes average asset-holdings across all persons in both a-6.

221t may appear that our analysis illegitimately violates the adding-up const however, is not so: when an asset-holder draws upon his CB d sit expense, he has to incur less borrowing than he otherwise would. minus liabilities) position remains t~nchan~ed.

us, ur liquidii y- t keoret dc appr

that any portJi,lir,-huscd mcrlysis should not ignore the liutilities side CVJ‘ consu

B.K. Kapur, Financial liberalization strategy 75

asset-holders have more CB deposits to draw upon, they need to borrow less, and the resulting funds are, as eq. (14) indicates, ‘freed’ for lending to productive enterprises. Thus, the net change in total lending by both C and IFIs to firms is

dD* 1 i-d dD* -P dd +?‘h-d’ dd l

Now, it can be shown that the entire right-hand expression is in fact negative: total productive lending does indeed decline. structuralists conclude that their argument is validated, how noted that the entire right-hand side would be zero were it not for the term

_p-4+(h-i).dD* 2(h-d) dd

_-

that is a part of the first term on the right-hand side. Now, this term is none other than the increase in the economy’s demand for high-powered a result of the liberalization (since asset-holders switch from IFI deposits, having zero reserve backing, to CB deposits having a reserve backing of bc In meeting this increased demand, the government received a ‘windfal seignorage gain (in the sense of a seignorage gain that is over and above its existing seignorage requirements, reflected in the size of the pre-exist monetary base). The government thus has the option of utilising this wind gain for the purpose of productive lending, by channelling the newly-create high-powered money to ‘development banks’, or to the

If the government does exercise this option, which have totally overlooked, then their critique is entire right-hand side of eq. ( 15) is reduced to zero. ___ ___.. - made the same p consideration of the economic role o insights into the e

posits, then the

he fundamental thesis evaluation of the m2o-strUC be arrived at unt

final generaI print, namely informal financial market liberalized financial system.

mistaken belief that only by doing so can the economy re oRered by the informal financial system.

24An increase in d can be easily shown to reduce H* my the same amcaunt as, in eq. (?), it raises Q&V)*], and hence raises the life-time wealth (and consumption) of asset-holders. It is important to emphasize that the reduction in consumer borrowing R is not a consequence of an increase in h 01” of the imposition of credit rationing: it is simply a concomitant of increased asset-holder liquidity resulting from increased holdings of CB deposits (whose liquidity is a resultant of CB holdings of reserves). The welfare gain also partly arises from the fact that the increase in the bank leading rate I induces a reallocation c.” oank loans to hig activities [see Fry (1988, pp. M-19)].

“SThe casz of currency holdings is quite different, since a reduction in the public’s currency holdings will, analogously to our argument above. impose a windfall seignorage ‘loss’ on the government. This supports the point made by Owen and So!is=Fa!!as (!9@;, that al! unproduc- tive assets should not be viewed alike, and also suggests that fiscal considerations should receive nlorc attention from botl- I I”,;;zzriz! Yiberatizationists and their critics.

Ahmed, Z-U., 1989, Effective costs of rural loans in Bangladesh, World Development 17, 357-363.

Burkner, HP., 1982, The portfolio behaviour of indiv . nalysis of the Philippine case, Oxford Bulletin of e, E.F., 1984, Financial repression, the new stru

mdustrialized economies, Journal of evelopment Economics

York).

Iicies: A ~~~ti~tive

Waldo, D., 1985. Bank runs, the deposit-currency ratio, and the interest rate, formal of Mmetary Economics f 5,269-278.

Williamson. SD., E988, Liquidity, banking, and ban failures, International Economic 29, 25-43.