The H Theory of Money Supply

7/24/2019 The H Theory of Money Supply

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The H theory of Money Supply

Concepts and measures of money supply relate to the supply of ordinary money (M),

referring to money, as people generally understand it. Monetarists often distinguish it fromwhat they call the high-powered money (H) while discussing the theories of money supply.

According to them, the single-most factor determining money supply is the high-powered

money (H), defined as money produced by the central bank and the goernment and held by

the public and the banks. !t consists of

(i) Currency, C, including coins and notes in circulation with the public"

(ii) Cash reseres, #, held by commercial banks as ault cash"

(iii) $ther %eposits, $%, of the central bank High-power money (H) can thus be e&pressed

as

Money supply is thus directly proportional to the high-powered money, H. %ifferentiating the

e&pression for M with respect to H, we hae (dM'dH) m, defined as the ratio of increase in


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money supply (M) per unit increase in high-powered money (H) and known as the money

multiplier.

!n short run analysis, % may be treated as insignificant. *&pression for money supply can

now be e&pressed as

M (+ c) ' (c r) H

*&pression for money multiplier would then change to

dM ' dH m (+ c) ' (c r)

!n either case, when increase in H is not infinitesimally small, increase in M may be gien as

M (m) H

his shows that change in money supply (M) is directly proportional to the change in high-

powered money (H).

!nferences drawn from */uations 0.+1 and 0.+2 support the statement that high- powered

money (H) is the single-most determinant of money supply (M), gien c, r and t. !t is for this

reason that high-powered money (H) is at times called the money base.

*/uilibrium of the market of high-powered money refers to e/uilibrium of demand and supply

of high-powered money.

At a gien stock of high-powered money, its supply,

Hs H

!n the same way, demand for high-powered money can be e&pressed as

H%

C%

#d

H% can thus be obtained by ertical summation of C% and #%, where C% and #% represent

demands for currency and cash reseres. 3ig. 0.+ demonstrates the e/uilibrium of the H-

market.


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o demonstrate the money multiplier process, let us hae an illustration.

Illustration 7.1:

4oernment purchases goods and serices from public worth #s. 56.66 crores. Currency-

deposit ratio is 6.76 and resere-deposit ration is 6.+6. %etermine deposit and moneymultipliers and hence calculate the additional olumes of deposits and money created in

conse/uence of an increase in high-powered money by #s. 56.66 crores.


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he mechanism can also be e&plained without the use of the formulae deeloped aboe.

As soon as public receies the che/ue of #s. 56.66 crores from goernment for goods and

serices sold by it and deposits the same with its bank, the che/ue is sent for collection by

the bank.

he amount becomes aailable to the public in a few days8 time. Currency deposit ratio

being 6.76, public diides the amount between currency held and deposit made in such a

way that 769 of the deposit forms the currency withdrawn by the public. As result, C 16

crores and % :6 crores so that C'% +';. hus bank deposits increase by #s. :6 crores in

conse/uence.


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As soon as the bank of deposit comes to know of it, resere-deposit ratio being 6.+6, it holds

+69 of the deposit (#s. :.66 crores) as ault cash and lends out the rest (#s. 72.66 crores)

to borrowers, who in turn split it between cash held and deposit made in the ratio +


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Theory of Money Supply: Ordinary Money and High-Powered Money!

?o far we hae assumed money supply to be policy @ determined. his is

not true, because the supply of money is determined ointly by the

monetary authority, banks, and the public. Bo doubt, most of the time, in

this determination the monetary authority plays the actie and also the

dominant role. ut the role of the public and banks cannot be ignored, nor

een taken for granted. Droper recognition and understanding of this role is

important for a successful policy of monetary control.

s a preliinary to the study of the theory of oney supply" it is

essential to understand the distin#tion $etween two %inds of oney:

(a) $rdinary money (M) and

(b) high-powered money (H).

hey are all measures of ordinary money (M), or money as generally

understood. here it was also stated that in this book we shall define M

Enarrowly8 as the sum of currency and demand deposits of banks (including

the #!) held by the public" and that since Eother deposits8 of the #!

included in the measure of M are a ery small proportion (less than one per

cent) of the total supply of M, no harm will be done if in our future

discussion we ignore these Eother deposits8 of the #!. 3or simplification ofour theoretical discussion, this is what we shall do. Accordingly, for our

theoretical analysis, we define

MC %% (+7.+)


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High-powered money (H) is money produced by the #! and the

4oernment of !ndia (small coins including one-rupee notes) and held by

the public and banks. he #! calls H Eresere money8.

H is the su of:

(i) Currency held by the public (C),

(ii) Cash reseres of banks (#), and

(iii) $ther deposits8 of the #! ($%).

Again, for simplicity, we leae out of our theoretical analysis $%, as they

constitute only about one per cent of total H. Accordingly, for our theoretical

analysis, we define

H C #. (+7.;)

he empirical definition of H in H C #. (+7.;) is by its uses or by its

holders, not by its producers (the #! and the goernment). At a later

stage, we shall find it fruitful to look at H from the latter angle. $n

comparing e/uations M C %% (+7.+) and H C #. (+7.;) we find that C

is common to both M and H and that the only difference between the latter

two is due to the second component of each, namely %% in M and # in H.

his difference is of crucial importance for the theory of money supply.

!t arises from the presence of banks as the producers of demand deposits,

which are counted as money at par with C. ut to be able to produce %%,

banks hae to maintain #, which is a part of H, produced only by the

monetary authority and not by banks themseles.


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?ince in a fractional-resere banking system, %% are a certain multiple of

#, which are a component of H, it lends to H the /uality of high-powered-

ness (as compared to M) the power of sering as the base for the multiple

creation of %%. 3or this reason, H is also called Ebase money8.

The H Theory of Money-Supply &'(plained )ith *iagra+!

here is near- unanimity among monetary economists around the theory of

money supply that says, that the single most important and dominant factor

that determines money supply is H. 3or short, we shall call it the H theory

of money supply. 3or reasons that will become clear in the se/uel, it is also

called the Emoney-multiplier theory of money supply8. ut we prefer to call it

the H theory, because the entire theory is built around the demand and

supply of H and the money-multiplier is only an outcome of this approach,

not its starting point.

Calling it the H theory focuses attention on the key ariable in the whole

drama of money-supply changes. !t also proides the theory the standard

techni/ue of demand-supply analysis. Fe shall discuss the H theory in a

ery simple form. his will be enough to bring out the main contours of the

theory and its basic analytical thrust.

As a first appro&imation and proisionally, it is assumed that the supply of H

(Hs) is policy-determined. Gater on, we shall e&amine how far this is a

correct assumption to make in the !ndian conte&t and in what sense. hisassumption gies us


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H?H (+7.1)

where the bar aboe H signifies that it is gien e&ogenously to the public

and banks.

he analysis of the demand for H (Hd) is much the more important for the H

theory. he key insight of the theory is to relate it to %% or M. Get us see

how this is done.

Fe hae already said aboe that H is demanded partly by the public as

currency (C) and partly by banks as reseres (#). hese are the only two

sources of demand for H in our model.

he demand for C (Cd) as a component of M is affected largely by the

.same factors as affect the demand for M, such as the leel of income and

the rate of interest, among other things. he same is true of the demand for

%% (%%d).herefore as a first appro&imation, it is reasonable to assume

that Cd and %%d will be highly correlatedthat will be (say) a proportional

function of %%. his may be e&pressed as

Cd c. %%. (+7.2)

c, then, is the ratio of Cd Eto %%. 3or short, we shall call it the (desired)

currency-deposit ratio of the public c itself will e&press the preferences of

the public as between currency and demand deposits of banks.

As such, this itself will be affected by seeral factors which in turn reflect

the relatie adantages (and costs) of the two forms of money.

Conse/uently it can ary oer time, not only secularly but also from one

season to the other. herefore, c is a behaioural ratio. ut for simple

e&position of the H theory, we shall assume it to be a constant.

Fhat about the bank8s demand for reseres (#d)I he reseres of banks

are usually diided under two heads (a) re/uired reseres (##) and (b)


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e&cess reseres (*#). #e/uired reseres are reseres which banks are

re/uired statutorily to hold with the #!. anks hae no choice about them.

Jnder the law, the #! is empowered to stipulate the statutory resere

ratio, which may be aried between 1 per cent and +7 per cent of the total

demand and time liabilities of a bank. *ery scheduled bank is re/uired to

maintain all its ## as balances with the #!. All reseres in e&cess of ##

are called *# anks are free to hold them as Ecash on hand8 (also called

Eault cash8) with themseles or as balances with the #!.

anks hold *# oluntarily. hey are held to meet their currency drains (i.e.

net withdrawal of currency by their depositors) as well as clearing drains

(i.e. net loss of cash due to cross-clearing of che/ues among banks).

hese drains may be partly e&pected and partly une&pected, giing rise to

what may be called banks8 transactions demand and precautionary demand

for cash reseres.

hus, the standard theory of the demand for money can be applied to the

banks8 demand for e&cess reseres as well, which alone is their disposable

cash. $ur obectie here is not to go into a detailed discussion of the banks8

demand for e&cess reseres (*#d). Fe only hypothesise that *#d will be

determined largely by the banks8 total liabilities.

hus, both ## and *#d and so become increasing functions of the total

demand and time liabilities of banks. Fe can introduce a further

simplification here. he demand and time liabilities of banks are

predominantly (about 5; per cent of them) due to the demand and time

deposits from the public.

Moreoer, this ratio between liabilities and deposits has remained stable

oer the past ;6 years.


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Therefore" as a siplifi#ation" we #an re,ise our earlier hypothesis

and say that d is largely a proportional fun#tion of the total deposits

of $an%s:

#d r.%. (+7.7)

r, then, is the ratio of #d total deposits of banks. 3or short, we shall call it

the resere-deposit ratio.

Get us now introduce in our model the important fact that bank deposits are

of two kinds demand deposits (%%) and time deposits (%). he former

are counted as money" the latter not. ?ince we are interested in deeloping

a theory of money supply, we must decide how to treat %.

he diision between %% and % is decided by the public, gien the terms

and conditions on which banks are willing to sell the two kinds of deposits

to the public. !n other words, it is the public who decides how much % to

hold in relation to %%.

gain" as a siplifi#ation" we hypothesise that T*d is an in#reasing

proportional fun#tion of **:

%d t. %% (+7.:)

t, then is the ratio %d to %%. 3or short, we shall call it the time-deposit

ratio. ?ince, by definition,

% %% %, the use of %d t. %% (+7.:) gies us

% (+ t)%%. (+7.0)

3rom #d r.%. (+7.7) and n % (+ t)%%. (+7.0) we hae

#d r (+t). %% (+7.=)

#ecalling that Hd Cd #d, from (+7.2) and #d r (+t). %% (+7.=) we hae

Hd Kc r(+t)L%% (+7.5)

hus, Hf has been e&pressed as a function of %% and three behaioural

ratios c,t, and r.


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he market for H will be in e/uilibrium when Hd Hs or from Hs H (+7.1)

and Hd Kc r(+t)L%% (+7.5) when

Kcr(+t)L. %% H.

he aboe e/uation can be soled for %% to gie

%%+'(c r(+ t) H (+7.+6)

he aboe e/uation gies us the e/uilibrium alue of %% in terms of H and

the three behaioural ratios c, t, and r1. !n the literature on money supply,

the e&pression l' c r(+t) is called the demand-deposit multiplier.

Be&t, from M C %% (+7.+) and Cd c. %% (+7.2) and assuming that C

Cdwe hae

M +c 'c r(+t) H. (+7.++)

he aboe, ultimately, is the key e/uation of the H theory of money supply.

!t makes the supply of money a function of H and the three behaioural

ratios c,t, and r. he *&pression + c 'c r (+t) gies the alue of what is

known as the money multiplier. Fe shall denote it by m. hen, e/uation M

+c 'c r(+t) H. (+7.++) can be more simply written as

M m () H. (+7.+;)

he aboe e/uation sums up briefly, but ery well, the main message of the

H theory of money supply. 3rom its form it can be seen why this theory can

be and has been more popularly called the money-multiplier theory of

money supply.

More iportant" the euation says that the deterinants of the supply

of M #an $e eaningfully #lassified under two ain heads:

(a) hose that affect H and


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(b) hose that affect m.

hus, in the first instance, the e/uation seres well one of the useful

functions of a theorythat of proiding a filing or classificatory deice for

arious factors affecting a dependent ariable, as, for e&ample, is done by

the well-known theory of demand and supply of price determination under

perfect competition.

Fhether the classificatory deice suggested by the theory of e/uation M

m () H. (+7.+;) is empirically meaningful or not can be known only after a

detailed e&amination of the factors goerning H and the factors goerning

m and the e&tent to which the former can be meaningfully separated from

the latter. Fe hae already summed up the pro&imate determinants of m in

e/uation M +c 'c r(+t) H. (+7.++). hey are the three behaioural ratios

c. t, and r.

3rom this discussion we shall see that whereas changes in H are largely

policy-controlled, changes in m are largely endogenous, i.e. are such as

depend mainly on the behaioural choices of the public and banks. his is

a useful distinction, analytically as well as for monetary planning. !t implies

that, for policy purposes, the monetary authority will do well to take the

behaiour of m as something outside its control and to concentrate its

efforts on controlling H to control M.

Fe shall comment on e/uation (+7.+;) later in this article, because it is

high time that we e&plain the economics of what we hae already done. Fe

shall do so with the help of diagrams. he discussion will throw much-

needed further light on the forces determining money supply and its

correlates8 (such as currency, demand deposits, and time deposits held by

the public and reseres held by banks), gien the supply of H.


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*ither of the two 3igures +7.+ and +7.; can be used to show the

determination of money supply under the H theory. 3irst consider figure

+7.+. !n it H is measured ertically and %% are measured- horiNontally.

?ince the supply of H is a Mumed to be gien e&ogenously by the monetary

authority at H (e/uation +71), the H cure is drawn parallel to the horiNontal

a&is at the height ft., showing that H is perfectly inelastic to %%. he three

demand cures in the market for H are upward-sloping straight lines going

through the origin in accordance with the hypotheses of e/uations Cd c.

%% (+7.2), #d r (+t). %% (+7.=), and Hd Kc r(+t)L%% (+7.5).

he Cd cure represents e/uation Cd c. %% (+7.2), with its slope e/ual to

c. (!n !ndia at present the alue of c is about one. ?o the cure has been

drawn to make an angle of about 27O with the horiNontal a&is) the #d cure

represents e/uation #d r (+t). %% (+7.=). !ts slope has the alue of r (+

t). he Hd cure is simply the ertical summation of the Cd and #d cures.

hus, it represents e/uation Hd Kc r(+t)L%% (+7.5).

he intersection of the Hd cure with the Hs cure gies the e/uilibrium of

the H market. hat is, at this point the public and banks are fully happy to

hold all the amount of H the monetary authority chooses to place in the H

market. !n this situation, the e/uilibrium amount of %%, is that shown by

%%o" the public holds Coamount of currency and leaes the balance of H,that is, HCo#o. for banks to hold. 3or %%oamount, this is e&actly e/ual


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to banks8 #d. !t will also be noted that, gien the Cd function, Co is e&actly

the amount of currency the public would like to hold when %% %%o

he same story is told in 3igure +7.;, though in a different way- his figure

depicts the e/uilibrium of the market for reseres and the conse/uent

determination of the e/uilibrium amount of %%. he participants in this

market are also the monetary authority, the public, #d banks. $n the

demand side, the demand for reseres coming from banks is represented

by the #d cure #d r (+t). %% (e/uation +7.=), as in figure +7.+.

he supply of # to banks is determined ointly by the monetary authority

and the public. he monetary authority does so by fi&ing the total supply of

H. 4ien H, the public determines how much of H it would like to hold in the

form of currency and how much to leae for banks to sere as their

reseres.

he decision is reflected in the Cd function Cd c. %% (+7.2). !t is

reasonable to assume that the public has first claim on H to meet its

demand for currency, because banks always stand ready to conert their

demand deposits into currency at par. herefore, it is assumed that actual

C held by the public is e/ual to their Cd. his makes banks only residual

claimants for reseres. Conse/uently the supply of reseres to them is

simply the e&cess of Ms

oer Cd

.


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#s Hs -Cd (+7.+1)

his is represented in 3igure +7.; by the downward @ sloping #s cure

which is the ertical subtraction of the Cd cure from the Hs cure in 3igure

+7.+. he intersection of the #dand #d cures in * (3igure +7.;) gies the

e/uilibrium of # market. his e/uilibrium is attained when the amount of

%% is %%othe same e/uilibrium amount of %% we had in 3igure +7.+.

his is as it should be, because 3igure +7.; has been deried from 3igure

+7.+ as e&plained aboe. !n the former figure the amount of C is not shown.

!t has to be determined with the help of e/uation Cd c. %% (+7.2), gien

the e/uilibrium amount of %%o.

Beither of the two figures shows the e/uilibrium amount of M produced or

supplied. !n 3igure +7.+ it can be easily inferred, because we know the

e/uilibrium alues of Co, and %%o, that will be produced, gien H, and Mo

Co %%o.

he cru& of the aboe demonstration is the role the secondary e&pansion of

money supply plays ia the production of %%. he role of banks in money-

supply changes also inheres in this. his will come out well when we study

the money-multiplier process. ut preparatory to this discussion and also to

throw further light on what has preceded, we undertake the stability

analysis of the e/uilibrium of the Markets for H and #. his will also bring

out clearly one crucial assumption of the H theory.

he stability analysis offers an opportunity for studying the dise/uilibrium

behaiour of the system. 3or this, let us ask what will happen if, other

things being the same, the public comes to hold %%, amount of demand

deposits which are less than the e/uilibrium amount %%o.

At this alue of %%, both #d and Cd, and so their sum Hd will be lower than

before (3igure +7.+). Hs remaining the same, there will be e&cess supply of

H in the H market. Correspondingly, there will be e&cess supply of # in the


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# market, as can be easily seen in 3igure +7.;. Fhat will be the

conse/uences of this e&cess supply of #I

efore- answering this /uestion, it needs to be pointed out that the e&cess

supply of # is not the same thing as e&cess reseres (*#), because

desired e&cess reseres at each leel of %% are already included m the

#d function. herefore, the e&cess supply of # is called undesired *#.

*&cess reseres, whether desired or undesired, do not earn banks any

interest income. herefore, banks try to get out of undesired e&cess

reseres and moe into earning assets (*A) as fast as they can.

'arning assets are $roadly su$-di,ided under two heads:

(i) !nestment and

(ii) loans and adances.

!nestments are made in marketable securities, whether goernment or

priate. he implicit assumption of the H theory of money supply is that the

supply of earning assets to banks is ery highly elastic around preailing

rates of interest and that banks are generally not deterred from moing into

earning assets out of undesired e&cess reseres.

!n sum, one important assumption of the H theory is that banks restore

e/uilibrium to their resere holding pretty fast.

here was a time when the bulk of earning assets of banks consisted of

loans and adances and inestments in securities were negligibly small,

because such securities had not grown in olume. he latter was the result

of low leel of corporate deelopment as well as of goernment debt and

securities market. !n such a world, during depressions the demand for bank

loans and adances could decline sharply and banks could stay loadedwith undesired e&cess reseres.


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hey did not hae enough bankable earning assets to buy. he situation

has been substantially different in recent times. 3or arious reasons, most

of the time the market for bank Moans suffers from e&cess demand rather

than e&cess supply. hen, the inestment market has grown significantly.

*en if good corporate securities are in short supply, goernment bonds

and bills are not. *er since the goernment adopted the policy of planned

economic deelopment through the public sector in the early +576s, it has

been hard pressed for funds.

hat is, it has stood irtually eer ready to borrow from banks and others in

the open market. he #! as the manager to public debt has tried hard to

widen the market for goernment debt as much as it can. o that end it has

tried to keep orderly conditions in the market for goernment securities,

aoid fluctuations in the prices of such securities, and een support it in

time of need.

his has meant irtual perfectly elastic supply of goernment securities of

different maturities. herefore, without any risk of capital loss in the short

run, banks can afford to inest large amounts of funds in at least short-term

goernment securities, especially treasury bills. his means that een if the

demand for bank loans and adances slackens significantly, banks are not

constrained to stay in undesired cash reseres" they can moe intogoernment securities as earning assets. ecause of the stable conditions

in the market for goernment securities (and the borrowing facilities against

goernment securities as collateral e&tended by the #! to banks), banks

are not een encouraged to hold on to their surplus cash on grounds of

speculation.


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All this is confirmed strongly by releant empirical eidence for !ndia. he

ratio of e&cess reseres to total demand and time liabilities of scheduled

commercial banks declined continuously oer the period of the +576s from

the high of :.=2 in +576-7+ to the low of ;.5+ in +5:6-:+. he reasons of

this decline were many and we need not go into them here. ut the fact of

continuous decline in the said ratio is important for our argument.

3urther, oer the period +5:6-:++501-02, this ratio stabilised around the

mean alue of ;.01, with only minor fluctuations. !t fell continuously oer

the ne&t three years from ;.7= in +501-02 to +.50 in +50:-00. All this goes

to support our theoretical assumption about the capacity of banks to moe

into earning assets when they hae undesired e&cess reseres and keep

actual e&cess reseres e/ual to desired e&cess reseres. !f this were not

true we would hae found large fluctuations in the e&cess reseres ratio.

After this rather lengthy digression spread oer three paragraphs, we come

back to our /uestion of the fourth preceding paragraph< what will the banks

do with their undesired *#I Bow we can confidently answer that they will

inest and'or lend such *#. he borrowers from banks as well as sellers of

securities (the goernment and others) will spend the funds receied from

banks.

he recipients of funds so spent will retain a part in the form of currencyand deposit the rest with banks, partly in demand deposits and partly in

time deposits. How this diision is made will depend upon the c ratio and

the t ratio. he interesting thing to note is the conse/uent increase %% in

# dand Cd. hus, there will be a moement towards %% from %%+.

his moement will continue so long as banks possess undesired e&cess

reseres. he moement will stop and the process of adustment

completed only when the original e/uilibrium is restored at %%6leel of


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demand deposits. he reerse will happen when the banks are short of

reseres


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In simple terms High Powered Money (HPM) is the net or total liability of the monetary

authority of any nation......in India it is the liability of RBI .

It is simply the sum of all currency in circulation with the people of country , cash ept in

the commercial ban !aults along with the deposits of go!t. of the country and

commercial bans.

"he term liability basically means that when people#go!t#commercial bans produce the

currency#claims....the RBI has to pay !alue e$ual to currency#claim.

"he RBI uses this H.P.M. for regulation of money supply in the economy . By controlling

the money supply RBI regulates (i.e tries to regulate) the inflation in eco.

RBI uses the H.P.M for process of money creation . Money creation will increase the

supply of money in eco.

%hen RBI needs to pump e&tra money in eco. it in'ects a certain amount of high

powered money (ay H) into eco.(by purchase of go!t bonds#assests etc).

"his money increases the total money supply in nation ....... but by what amount**It

increases money supply( say M) by not +H+ , but by a larger amount.

"his increased addition of money supply (o!er the in'ected !alue of H) is due to the

factor called Money Multiplier

"he !alue of money multiplier is determined by two factor , which are. -R/ i.e cash0to0deposit ration. It is the ratio of amount of money people tend to eep

with themsel!es as cash and the amount they deposit in ban acc.

1. RR/ Reser!e0to0deposit ratio. It is the ratio of amount of money that a ban will eep

in its !ault(or as reser!e with RBI) to the amount of the deposits rece!ied by them.

-R is a beha!ioral patter of people which can+t be regulated by RBI( eg people will sa!e

more during festi!e season or for upcoming marriage in familty etc) .Howe!er,RR can

be regulated by RBI.

epending upon the !alues of RR and -R , the amount of money supply increased ineco. is determined.

Money multiplier is gi!en as

Money Multiplier= (1+CDR)/(CDR+RDR)

2"heoretically, Money multiplier is ratio of money in economy i.e money supply (M) to

the amount of high powered money(H) 3

o when RBI in'ects H amount as HPM, the actual increase in money supply is

Money Multiplier*H.


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4

5ote/ 6alue of money multiplier is greater than one as the !alue of RR is less than .

7

"hus when RBI needs to reduce inflation it will reduce HPM in eco to slow down money

creation by commercial bans ."his will reduce the o!erall money supply leading to low

purchasing power .....which in turn lower the demands and hence cut inflation.

imilarly to increase the price le!els in eco RBI will in'ect more of HPM to increase

money supply(which will increase purchasing power of the people....thereby increasing

demand).

P.. HPM is only one of the ways used by RBI to regulate economy.Its has many

powerful ways lie 8R , -RR etc etc to regulate economy.

P..1 /-ommercial bans play a !ery important role in the process of money creation.(By

gi!ing out loans for further in!estments etc)

The H Theory of Money Supply

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