Welfare costs of inflation: the case for interest-bearing money and empirical estimates for Brazil

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We1fare Costs of IDfIation

The Case for Interest-Bearing Money and Empirical Estimates for

BraziI

Mario Henrique Simonsen and

Rubens Penha Cysne* ProfessoIS at the

Getulio Vargas Foundation Graduate SchoolofECononUcs

TeUFax:55-21-552S099

Praia

de Botafogo 190 8° Andar, Sala 821 Rio de Janeiro - RJ. - Brazil

April,1994

Abstract

We provide in this paper a closed fonn for the Welfare Cost of Inflation which we prove to be closer than Bailey's expression to the correct solution of the corresponding non-separable differential equation. Next. we extend this approach

to ao economy with interest-bearing money, once again presenting a better appoximation than the one given by Bailey's approach. Fmally, empirical estimates for Brazil are presented.

Keywords: Inflation, Near-Money, Welfare Cost. Classification Code: E 42

*Tbis paper wu iniúa1ly conceived al lhe time wben ODe of tbe autbors was visiúng lhe University of Chicago. He1rful discussions witb Robert Lucas Ir. and a scholarsbip from CNPq are bereby :\Clmnwlrrlgrrl.

Welfare Costs of IDfIation:

The Case for Interest-Bearing Money and

Empirical

Estimates

for BraziI

1) Intro<iuctiQn

Mario Henrique Simonsen· Rubens Penha Cysne·

Starting with Manin Bai1ey in 1956, the literature on welfare costs of inflation

has recendy becn fostered by contributions by Lucas (1993 and 1994), Correia and Telles (1994), Cooley and Hansen (1989), Eckstein and Leiderman (1992) and GiUman

(1993). A tentative analysis of the role of

me

hanking sector in this process bas becn made by Yoshino (1993)", as well as by Lucas (1993).

In this paper we derive tbree importaot results. First, we depart from the basic

theoretical work by McCallum and Goodfriend (1987) and Lucas (1993 and 1994) to derive an approximate solution for lhe non-separable differential equation only numerically solved by Lucas (1993 or 1994) in the fourth section of bis work. Given Lucas' hypothesis of a constant retums to scale time-transacting technology, we prove lhat this approximate solution is a better ODe tban BaiIey'

s.

and actuaIly lies between

the correct welfare cost and Bailey' s approximation. An estimate of the maximum relative errar of our solution is also presented.

Second1y, we provide an extension of the basic model for an economy with n different kinds of money, for an integer n. As in the previous cJassical case, we present an appoximate solution to lhe underlying non-separable differential equation, proving once more lhat tbis approximate solution lics between lhe correct ODe and lhat wbich

would be generated had one extended Bailey's approach to this case. We also show lhat accounts the higber the banking income share in GDP, lhe less accurate Bai1ey's appoximation. For countties like Brazil in the nineties, where the financial system accounts for a share over ten percent of GDP, the use of Bailey's approximation can rum out to be very misleading.

Thirdly, we re-interpret the previous medel to conclude that in the basic medel money should stand not only for the cunency held by tbe public, but also for the non-interest-bearing demand deposits, that is to say, Ml. Finally, we derive sufficient conditions which allow lhe use the basic fonnulas derived in lhe first section of lhe paper even in the presence of interest-bearing near monies. This is the case when lhe real demand for such deposits does not depend on the inflation rate.

2) The McCallum-Goodfáend Framework

The McCallum-Goodfriend frarnework assumes an cconomy where the representative houschold gains utility from the consumption of a singlc non-storable consumption good. its preferenccs bcing dctcnnincd by:

(2.1)

where U (c) is a concave funetion of lhe consumption c = c( t) at instant t. The houschold is endowcd with one unit of time mat ean bc uscd to transact or to produee the consumption good with constaot retums to scale:

. y + s = 1 (2.2)

where y stands for lhe produetion of lhe consumption good and s for lhe fraction of the initial endowment spent as transacting time.

Households can accumulatc two assets. moncy (M) and bonds (B), the lattcr yielding a nominal intcrest rale equal to r. Indicating by P = p( t) the priee of the consumption good. the houschold faces the budget constraint:

M+B=rB+p(y-c}+H

H indicating lhe (exogenous) tlow of moncy transferred to the houschold by the govemment Making = p/p (inflation rale), m = MIP , b =BIP , h = HIP, the budget constraint reads:

ril+b = y-c+h+(r-x)b-xm or, taking into aceount (2.2):

ril+b= l-(c+s)+h+(r-1t)b-1tm (2.3)

Compared to money, bonds are obviously preferable from the poiot of view of intcrest yield. Yet money is useful because it saves transacting time, as cao bc describcd by the technology function:

c = F (m. s) (2.4)

where F is ao increasing function of both m and s. That means mal, by usiog higher cash balances (io real tcnns) the household cao consume the sarne with less transacting time.

The household is supposed to maximize (2.1) subject to

me

budget consttaint

(2.3) and to the time-transacting technology (2.4). DefiDing

me

expenditure z = c + s we obtain fram (2.4) lhat c = F(m.z-c) and since FI i* -I we can apply the implicit funcúon theorem to defme V(z. m) as:

v

(z. m)

=

U (c) (2.S)

which expresses the fact that money is useful because it saves time spent on transacúons. The representaúve household will choose

me

path of its money and asset holdings so as to maximize:

r

e-tl V(z.m) d t

where. according to (2.3). :

z=c+s= l+h+(r-x)b-xm-b-m

This is a standard variational problem, where Euler equations yield

dV (r-x-g)V =-~ • dt dV (x+g) V. = V. +~ dt

We are interested in steady-state solutions where

m.

b and z converge to constant figures. In tbis case. the equilibrium equations are:

r

=

x+ g (2.6) rV.=V. (2.7)

Equaúon (26) states lhat tbe equilibrium real interest rale r- equals the discounl rale on fulure utilities. Equaúon (2.7) haJann:s

me

marginal utility of money

with the marginal u1ility of expenditure times lhe nominal interest rale. a classicallaw. now expressed in tenns of indirect utilities. One should remember tbal in equilibriwn. since the consumption good is non-storable and since ali households are equal:

y=c or. equivalently:

z

=

c + s

=

1 (2.8)

Equaúon (2.7) can be rewritten in tcmlS of

me

time-transacting technology

Now, since c = z-s = F (m, s)= G (z, m):

as can be checked by implicit differentiation. Hence. (2.7) can be replaced by:

r

F.

= F.. (2.9) Moreover. (2.4) and (2.8) yield:

l-s=F(m,s) (2.10)

nus

completes lhe description of lhe McCallum-Goodfriend framework. In spite of its dramatic simplific$ions. it addresses two really important issues. Fust, it

shows that the utility of money is to save time spent on traDsactions. Second, it

provides a natural measure for lhe welfare costs of inflation, the time s spent on such transactions. For a given nominal interest ra1C r the demand for money m = m{ r) and the welfare cost s=s{r) can be detennined by equations (2.9) and (2.10)1. We sbaJl assume that such solutions yicld m = m{r) as a decreasing function. and consequendy s = s{r) as, an iDcreasing function of the nominal interest ra1C r. Hence. the higber the

nominal interest nue. the lower the consumption 1-s(r) of the representative household. lbis leads to Fricdman's optimum monetary role. that of keeping the (lominal interest nue as low as possible. presumably at r = O. Moving the equilibrium nominal interest nue from O to r causes a welfare loss s{ O) - s{ r ), measured in tenns of reduction in individual consumption. As the nominal interest rale increases, the opponunity cost of holding cash balances increases too. As a resulto individuais will reduce transaction balances and spend more time on such transactions. The overall

effect wil1 be a reduction in time employed productively, and hence in consumption. For empirical purposes. lhe problem with the McCallum-Goodfriend framework ia that s(r). namely lhe time spent on transactions. is not directly measurable. 1be advantage of lhe BaiJey consumer surplus construction is that it derives s(r) from m(r). although through an approximation role. To do the same in the McCallum-Goodfriend framework. an additional assumption must be introduced.

nus

leads to Lucas' hypothesis:

c=F{m.s)= mcl»{s)

(2.11)

(,'(s)

> O and

,"'(s)

S O)

which assumes a time-transacting technology with constant returns to scale. as in the

1 A sufflCieDt conditioa for tbis determiDatioa to be possible is thal me fuDctioa F salisfies

-{l+

1;)

(r

F.. -

F .. .) + F .. (r

F.. -

F_ ) ;tO.

Baumo1 analysis, where F{m,s) = k MS. Lucas sbows how, under hypothesis (2.11),

s(r), m(r) and ,(s) are inter-related, and analyses in detail lhe timc-transacting function

F(

m,s) = k m

sI'",

where O.S S J.1 S 1. With lhe Lucas assumption (2.11), equations (2.9) and (2.10) are rep1aced by:

,(s)

= rm,' (2.12)

l-s=m,{s) (2.13)

If the time-transacting function ,(s) is known. lhe demand for money m(r) and

the welfare cost s(r) can be determined by the above equations. For instance, , ( s) = ks implies:

1 r=--,--~ m{l+km) 1

5 =

-l+km

In practice. ,(s) can not be direcdy estimated from statistical data, what is known from empirical studies is the money demand m = m{ r) or its inverse funcion r = r{m). 'The problem of deriving s(r) from m(r) without knowing ,(s) can be easily solved as follows: We fll'St differentiare (2.13), which leads to:

We then eliminate (s) and " (s) combining the above equation with (2.12) and (2.13). The result is the differential equation:

-ds= r(1-s) dm

rm+{I-s) (2.14)

which determines the welfare cost ser) as a function of the money demand m(r). Once ser) is thus determined. the implied ,(s) can be found by equation (2.13).

From the computational point of view, the trouble with (2.14) is mat it is not a separable equation. 1bis suggests the use of some approximation formula to case practical calculations. Bailey's graphic constmction. corresponding to the formula:

-ds=rdm (2.1S)

is one possible approximation, as 10ng as the interest rale r times the real stock of money m can be neglected when compared to l-s. Moreover, Bailey's construction

provides an upper bound to the welfare eost s, since (2.14) obviously imp1ies -d s > r d m. Yet a better approximation formula. based on the fact that 0< s < 1. is

provided by the doub1e-sided inequality=

ds r - - < dm<-ds (2.16) l-s rm+1 or. sinee d m = m'(r) dr= d s<- rm'(r) d r < -ds rm(r)+l l-s

Defming F(r) as the integI:3l:

d)

rr

pm'(p) d

.l"\r =

Jo

-

pm(p)+ 1 p (2.17) the above inequalities yield:

(2.18)

nus

shows that F(r) is an upper bound to the welfare cost of inflation. with a

maximum relative errar of approximate1y F{r )/2.

In fact:

F{r) -( 1_e-Ftr

»)

s(r)

Thus. F(r)= 0.0 I means that O.OO99S < s{ r) < O, O 1. F(r)

=

0,1 S implies 0.1393 < s{r) < O, IS. For practieal purposes, F(r) ean be taken as an adequate measure of the welfare eosts of inflation. given the simplifications invo1ved in the theoretical analysis of the prob1em. One should note tbat F(r) is a better esâmate 01 s(r) tban Bailey's approximation:

B{r) =

r

-pm'(p) dp

In f~ since m'(r)<O. F(r)<B(r), as results immediately from the expression above aDd (2. 17). As F(r) is aIso a upper bound to s(r), this inequality shows tbat it is a better approximation to tbe wellare cost 01 inOation than the

one provided by Bailey's fonnulL

As an exampleior the money demand equation:

expression (2.17) yie1ds:

F(r) = _a_ 10g(1 + Krl-a) (2.19)

l-a compared to Bailey'5 approximation:

B( r) =

2.-.

K· rl-a (2.20) . . l-a

3) Interest-Beariol Money

Let us extend the model of the preceding section assumiog the existence of two kinds of money, currency bills and interest-bearing demand deposits. lhe real quantities of which will be indicated by m and x, respectively. 1be nomiDal yieJd of currency bills is equal to zero, that of demand deposits equal to L 1bis implies replacing the budget constraÍDt (2.3) by:

ril+x+ b = 1-(c+5)+h+(r-1t)b+(i-1t)x-1tm or, equivalently:

z =c+s = 1+ h+(r-1t)b+{i-1t)x-1tm- b-x-ril (3.1)

The time-uansacting technology is now described by:

c

=

F(m,x,s) (3.2)

and lhe indirect utility function by:

V(z, m, x)

=

U (c) (3.3)

Market clearing requires:

z

=

c + 5

=

F (m, x, s) + 5=1 (3.4) The marginal utility conditions (2.6) and (2.7) being replaced by:

r=1t+g Vf4 = rVz V .. =(r-i)Vz

(3.S.a)

(3.S.b)

(3.S.e)

In tenns oí the time-transacting technology function, lhe last two equations above are equivalent to:

rf.=F .. (r-i)F. = Fz

(3. 6. a)

(3.6.b)

With two kinds oí money, Lucas' assumption (2.11) reads: F(m, x, s)= O(m, x) , (s) (3.7)

where O (m, x) is differentiabte. homogeneous oí degree one, increasing in each oí its variables and with decreasing marginal retums with respect to each one. 1bis

transíorms equations (3.6) into:

O .. ,(s) = rO{m,x) ,'(s) Oz ,(s)=(r-i)O(m,x),'(s)

Oiven lhe hypotheses about O(m,x), the marginal rale oí substitution O ..

lO

z is an increasing function oí the asset ratio xJm. Taking lhe inverse function

x

-= J(G"./G,.)

m

J'(.) > O

the derivative oí lhe log oí J with respect to the log oí its variable indieating the elasticity oí substitution between currency bills and demand deposits. According to the preceding analysis. utility maximization leads to

.!.=

J(r/(r-i)

m

(3.8)

Moreover, since O(m,x)= mO .. +xO z (Euler's theorem):

~s) =(rm+(r-i)x) ,'(s) (3.9) Fma1ly,the market elearing eondition (3.4) ean be rewritten as:

l-s=O(m,x),(s) (3.10)

Assuming the time-transacting technology fuDction (5) to be known. equations (3.8), (3.9) and (3.10) detennine the asset holdings

m.

x and the welfare cost of inflation s as a function of r and r - i. 'Ibroughout the following discussion we sball assume the banking spread r - i on demand deposits to be a constant (except for very

small lending cates). 'Ibi!f is to say that the real interest yiekl of demand deposits

i -1t = r -1t - (r - i) = g - (r - i) is a constant toa. In tbis case. the asset ratio xlm ~ an increasing function of r, as well as the welfare 1055 s(r), wbile the demand for currency bills declines with the increase of the interest cate r. As to lhe demand for interest-bearing deposits, it can eilher increase ar decrease with r, depending on the signal of the sum of the elasticity of substitution between x aod m with lhe elasticity of the demand for m with respect to r. An important reference case is wbere the sum of these two elasticities is equal to O. Here the demanei for interest-bearing deposits does not depend on r, but only on their real interest yield, wbich is a constanL 1bis is the same as saying that the real demand x for such deposits does not depend on lhe

inflation rate. 'Ibe case will be referred to in lhe following discussion as that of inflation-neutral deposits ..

For empirical purposes. ODe should note that lhe specification of lhe function

q, (s) is usually unknown. 1be problem can be dealt with by the same method adopted in the preceding section. We fust differentiate (3.10):

-ds =G_m q,(s)dm+G_II q, (s)dx+G (m,x)

q,'

(s) ds ar equivalendy:

-ds = G(x.m) q,'(s) (rdm+(r-i)dx+ds)

We now use (3.9) and (3.10) to eliminare (s) and

q,'

(s). 1bis leads to:

(J-s)(rdm+(r-i) dx) -ds=---~--~--~­

l-s+rm+(r-i)x (3.11)

which can be interpreted as a two-dimensional ver5ion of (214). In lhe denominator, r m is the seigniorage collected on currency bills held by lhe public, (r - i) x lhe

banking spreads on demand deposits. both measured as a proportion of GDP. 'Ibe sum r m + (r - i) x is the total banking income. that is. lhe income received by financial

intermediaries for financing medium- and long-term assets with immediately callable liabilities also measured as a ratio to GDP. lt corresponds to lhe income share of financiai intennediation in GDP. measured by national accounts. \Vith the exclusion of revenues not related to the art of borrowing shon for lending longo

Differential equation (3.11) may be solved direcdy ar, more easi1y, approached by a separable differential equation. by noting tba1:

d s< - rdm+(r-i)dx < -ds

l+rm+(r-i)x l-s

Defming F(r) as the integral:

r m'(r) +(r - i) x'(r)

-~...;-:--..:....,..~ d r

l+rm+(r-i)x

(3.12)

one concludes. as in the preceding section, lhat the welfare cost of inflation lies in the interval:

Bailey's consttUction formula is In approximation to F(r) lhat treats as infwresimal lhe banking income share in GDP, namely. substituting 1 for lhe

denominator of the integrand of (3.12):

F{r) - S(r)

= -

1

(rm'(r)+(r-i)x'

(r))

dr (3.14)

The preceding results can be more concise1y restated in vector notalion. For that purpose. let us introduce the cash-holdings vector M = (m,x) as well as the opportunity-cost vector R

=

(r, r-i), noting lhat lhe inner product R. M = rm+(r-i)x indicateS total banking income as a propomon of GDP. Equation

(3.11) cao be rewritten as:

the estimating function F(r)

as:

(l-s)R·dM

-ds=---~-­

l-s+R·M

F(r)

=-1

R· M'(r)

_1+R·M dr a.nd Bailey's approximation as:

B(r)

=

-1

R· M'(r) dr

These concise expressions are quite important. less for their elegance than for

the fact that lhey bold for a medel with n different kinds of money: for any integer n.

For empirical investigation we shall he interested in a model with tbree types of money, currency biDs, non-interest-bearing demand deposits and intercst-bearing deposits, which are essential to deserihe payment systems after lhe financial innovations of the

late 1970's and 1980's. lbe three assets must he treated as imperfect substitutes, to malte possible the coexistence of both types of demand deposits, interest- and non-interest-bearing' .). Yet since the flI'St two bave zero nominal interest ~ their som can be aggregated as if they were one single asset, wbich brings us back to the (m, x)

model with one reinterpretation: m no 10nger stands for currency beld by lhe public, but for its sum with the balance of non-interest-bearing demand deposits. In short, m now means MI' while x stands for interest-bearing demand deposits.

With this understanding, the problem of estimating lhe welfare cost of inflation

. is reduced to solving differential equation (3.11), ar more simply to calculare eitbcr F(r) in (3.12) ar B(r) in (3.14).

For that purpose,

hesides

the knowledge of lhe banking spread r - i, estimares

should he available for lhe demand m(r) of M₁ and x (r) of interest-bearing demand deposits, as a function of the nominal interest rale.

Estimations are considerably simplified in lhe case of intlation-neutral interest-bearing deposits. Here dx

=

O, and since lhe total bank spreads (r -

i)x

on such deposits can be neglected when compare<! to GDP plus lhe intlationary tax r m, F(r)

can be approximated by:

F{r)

=_rr

rm'{r) dm

Jo

l+rm

which is equivalent to equation (2.17). In short, with intlation-neutral interest-bearing deposits the welfare waste s(r) can be calculated as if there were no other kind of money besides M_{I .}

Additional infonnation on lhe welfare cost of intlation results from lhe assumption that lhe time-transactions technology function can be specified as:

,(s)

= ks" (3.15)

where 0.5 < J.l < 1, as suggested by Lucas. 1bis parametrization emerges in the inventory-theoretical literature on money demand. following Baumol's seminal work. lbe latter implies

=

1, while the Miller and Orr stoChastic version leads to economies of scale that malte J.l

=

0.5. Introducing cp{s)

=

k~ in (3.9) yields:

s = J.l(rm+{r

-i)x)

(3.16)

(-) A more promisiDl aoa1ysis wou1d perhaps treal

me

twO types of deposits as twO parts of a salDe

product suppüed UDder a tedmoIogy iDvolviDl fixed oosu. Ia fact. imerest is ooly paid for demaDd

which is to say that lhe welfare cost of inflation is ~ times lhe total banking income, measured as a proportion of GDP.

nus

conclusion is very much in line with the perception that intlation leads to excess fmancial intemediation.

In the particular case where interest-bearing demand deposits are inflation-neutral, one may establish a simple approximate relation between ~ and the interest cate elasticity -a of the money (M1) demand Differentiating (3.16), since (r - i) x is a constant:

d s = ~(r d m

+

m d r)

Since the interest rate elasticity of the demand for M I is equal to -a as in m(r) = Kr-a;

m dm=-a-dr

r

Now, since dx = O, Bailey's approximation formula implies: ds=-rdm

Combining lhe last-lhree relations:

a=...L

~+ 1 (3.17)

a very important re1ation that COMCCts lhe Baumol case ~ = I, where the welfare cost of inílation equals lhe total banking income, with an interest rate elasticity of the money demand equal to ~.S, as empiricaJly supported in many countries. An elasticity with absolute value a

=

0.33 corresponds to lhe case described by Miller and Orr.

4) Some EmlÚrical

&dmata

Cor

dai

Wd'are çgst ollnflation in IM'

Empírical estimares of lhe welfare cost of intlation in Brazil have been provided by Dias (1993). Cysne (1994a and 1994b) and Pastore (1993). Dias' work unfortunately presents strong evidence of misca1ibration of lhe parameters. Indeed, the values obtained for lhe elasticity of lhe money demand. lhe intlation taxo as well as for the welfare costs of inflation. are very far from thase which one would theoretically expecl The figures presenteei by Cysne (1994a and 1994b) are preliminary to those obtained here. and were still base<! on BaiJey's approximation, which we prove here to

be a worse approximation to the tnle welfare cost than those provided by the approximation we suggesl Pastore's work , also based on Bailey's approximation,

prescnts a welfare wastc of about 8,5% of GPD for a 4()CI montbly intlauon rale. 1bis figme, however, ia overestimated. Fust bccause of lhe use of Bailey's formula, whose

innacuracy ia relatively high for a countty Iike Bram. which presents a bloated finaDcial sector of around 10,5% of GDP. Secondly, becausc Pastore used lhe periodic valuea of lhe intcrest rale, whcn lhe correct ODCS would bc lhe 10garithmic. This ia to say that

Pastore's estimare of a welfare cost of 8,5% of GDP actually refers to a 48,18% «exp 0,4) - 1) monthly inflation rale, and not to a 4()CI monthly inflation. This correction makes Pastore's estimares very close to lhosc prescntcd in tablc 1.

The empirica1 results here derivcd wcre bascd on monthly and annual data on lhe means of payment, ovemight intcrest rale, GDP, industrial production indcx and

lhe IGP-FGV pricc indeXo The original sourccs were, respectively, Central Bank (for M₁ and for lhe ovemight rale), FIBGE (for GDP and lhe industrial production indcx) and Getulio Vargas Foundation (for lhe IGP pricc indcx).

According to tcsts prescntcd in Cysnc and Issler (1993), whcre this hypotbesis proved not to bc rejectablc, we workcd wilh an unitary income elasticity of lhe money demand function.

The choicc bctwccn a semi-Iog and a log-Iog moncy demand spccification was

decided upon by empirical criteria, in favor of lhe latter. As can bc concludcd from figures 1 and 2, lhe log-Iog demand function, as was also lhe case in Lucas' work for U

.s.

data., prescnts a much bctter filo

Our first goal was to use lhe results derived in section 3 of lhe paper to estimare lhe welfare costs of inflation, sincc Brazil ia a countty which very easily falIs

into lhe caregory of intcrest-bcarlng demand deposits.1 _{In order to do so, howevcr, we}

5hould have empirical estimares of lhe function x(r). But this ia ccrtainly not an easy task in an economy Iike Brazil's, which in many cases prescnts interest controis as well

as heavy taxation on some finaDcial transactioDS.3 _{We lhen decided to assume lhe}

hypothcscs hcre derivcd which provide sufficient ConditioDS for lhe cstimation of welfare costs bascd only on lhe knowlcdge of m(r). In doing 50, lhe only bcnefit we couJd get from lhe tbeoretical results hcre dcrivcd was relatcd to lhe use of our approximalion F(r), bcsides Bailcy' s B(r), in order to evaluate lhe wclfare figures.

We tben applied lhe formulas (2.19) and (2.20) derived in lhe text using lhe

paramcters obtaincd from lhe empirica1 estimation of lhe moncy dcmand specification:

Thc parameters for Bram. whcre R ia sclected 50 lhe curve passes the geometric mcans of lhe last five-year data pairs, are:

lActuaDy, danand depoIill ia Brazil are DOt aIIowed 10 . . y iDIaest, but we are referriDg bere 10 sbort-nm fuods wbic:b are automatjcally lDIIIferred 10 tbe demaDd-deposit aa:ouDlS in case. ri

overdraw.

3Lucas reportEd to UI tbal be bad tbe same difficulty ia tryiDJ to estimare sudl a fuDcliOll (li' tbe

k

=

0,0368 and a

=

0,525 from which we obtain

F{r) = 1,10510g(1 +0,0368· rD.475) B( r) = 0,0407. rO.475

The following table compares the figures for the welfare cost of Brazilian inflation using our approximation F(r) and Bailey's B(r). As. we mentioned before in

this section, the interest rale to be used in these calcuIations is the 10garitlunic rather

than the periodic. In table 1, colwnns two (M.1N11 and tbree (A.IN1) stand,

respectively, for the monthly and yearly periodic inflation rates. Column 4 (LA.IN1)

presents the 10garithmic annual intlation, to be used in the above formulas. Column 5 shows the 10wer bound- (l-exp(-F(r» for the welfare cost wbich is presenteei in

incqua1ity 2.18. Fina1ly, colwnns 6 and 7 present the welfare cost of inflation as a fraction (not percentage) of GDP, the ~ one using the formula here derived F(r),

and the other Bailey's expression B(r).

As. one can observe, the estimations using Bailey's formula always Iead to higber welfare costs.

nus

is also visible in figure 3, wbich shows lhe 10wer bound for

the welfare cost (l-exp(-F(r» as well as our approximation F(r) and BaiJcy's B(r). Theoretically, lhe differences between F(r) and B(r) are particularly high for bigh inflation rates, when lhe value added by lhe tinancial system is not insignificant compareci to lhe GDP. It is important tô notice. however. that given lhe formulas we are using. deduced in section 2 of lhe paper, lhe differences between F(r) and B(r) alise only from part of lhe value added by the tinancial system (the total inflationary transfers on lhe means of payment m(r).r), the remaining part «r-i).m) not being considered.

An inference on lhe value added by the tinancial institutions issuing interest-bearing deposits can be made from our estimares. The elasticity of lhe money demand we are dealing with. 0,525, is very close to Baumol's theoretical prediction. As. we show in section 3 of lhe paper (equation (3.16», in this case we bave a transacting technology of lhe type t(s)

=

Im, and the welfare cost is equal to lhe value added by

me

part of lhe fiDancia1 system which issues means of payment and interest-bearlng deposits (mr + (r-i)x). The tirst part of this total. mr. standing for lhe total inflationary transfers on lhe means of payment, represents something around 6CJ1 of GDP. The remaining 1,98CJ1 can be consequent1y accrued to the value added by the financial

institutions issuing interest-bearing demand deposits.

It is also worthwhile noticing that for lhe leve1 of inflation around 45% per month existing at lhe time when this paper was being written, lhe evaluated welfare cost (7,98CJ1 of GDP) corresponds very closely to lhe difference between the size of the fmancial system in Brazil (around 1O.5CJ1 of GDP) and the size of a financial system one would expect for a low-inflation country (around 2.5CJ1 of GDP, to late an average of the German and American parameters).

Particu1arly interesting is lhe fact thal. at lhe time when tbis paper was written. lhe levei of inflation in Brazil, around 45% per month. cost lhe COUDtry sometbing

around 7.98% af its GDP. that is to say, sometbing in lhe area of 33,9 billion dollars peryear.

BibliarrqphjcaI

Ikferencu:

Bailey, Martin 1; 1956, Welfare Cost of Inflationary Fmance, loPIDaI of Politicaf Economy ,64,93-110.

Chang, Fwu-Rang, 1992, Homogeneity and the Transactions Demand for Money. Indiana University working paper.

Cooley, Thomas F. and Gary D. Hansen,1989, The Inflation Tax and the Business Cycle; The

American

Economic Review 79 , 733-748.

Correia. I. and Telles. P .• 1994, Money as an Intennediatc

G<lOd

and the Welfare Cost of the Intlation Tax,

Mimeo.

Portuguese Catholic University. Cysne. Rubens P. and Issler,loão Victor. 1993. Forecasting Ml with Monthly Data. Annals of the 1993 Meeting of the Brazilian Econometric Society, 1993. Belo Horizonte.

Cysne. Rubens Penha. 1994a. Quanto Custa a Inflação Brasileira; lomal Folha

de São Paulo (12102194).

Cysne • Rubens Penha. 1994b,

"O

Custo Social da Inflação - R~plica" lornal Folha de São Paulo (15/05/94).

·Dias. Maria H. Ambrosio.1993. The Welfare Costs of Inflation and Seigniorage in Brazi1: A Medel with Leisure.

Annuals

of the Meeting of the Brazilian Economic Association (ANPEC), Belo Horizonte.

Eckstein. Zvi. and Leonardo Leidennan.1992. Seigniorage and the Welfare CoastofInflation; Joumal ofMopetary Economics 29. 389-410.

Gillman.

Max.

1993. The Welfare Costs of Inflation in a Cash-in-Advance Economy with Costly Credit, JoumaI of MonetJuy Economjçs. 31 97-116. Guidoti. P.

E.

and Veigh. Carlos A. 1993. The OptimaI Inflatioo Tax when Mooey Reduces Transactioo Costs. JOUDJal of MonetaJy Economics. 31. 189-205.

Irnrohoroglu. Ayse.1989. The Welfare Costs of Inflatioo under Imperfect Insurance. University of Southem Califoroia working paper.

Lucas. Robert E .• Jr. 1993.

00

the Welfare Cost of Inflation. University of Chicago worldng paper.

Lucas. Robert E .• Jr, 1994.

00

the Welfare Cost of Inflation. University of 16

Chicago worlcing paper.

McCallurn, Bennett T. and Marvin S. Goodfriend. 1987, Demand for Money: Theoretical Studies, The New Palgrave: A Dictionary of Economics, John Eatwell Milgrate, and Peter Newman, eds. (London: Mcmillan) , 775-781. Pastore, Afonso Celso, 1993, D6ficit Póblico, a Sustentabilidade do Crescimento das Dívidas Interna e Externa, Senhoriagem e Inflação : Uma Análise do Caso Brasileiro; Mimeo, São Paulo.

Simonsen, Mario Henrique e Cysne, Rubens Penha, 1989, Macrpecooomia. Ao Livro Técnico Editora, Rio de Janeiro.

Yoshino, Jce A, 1993. Money & Banldng Regulation : 'lbe Welfare Costs of Inflation. PhD Dissertation, University of Chicago.

Tablel

OBS

M.INT

A.INT LAINT X F

B

1 .0100 .1268 .1194 .0146 .0147 .0148 2 .0200 .2682 .2376 .0202 .0204 .0206 3 .0300 .4258 .3547 .0243 .0246 .0249 4 .0400 .6010 .4706 .0277 .0281 .0285 5 .0500 .7959 .5855 .0306 .0311 .0316 6 .1000 2.1384 1.1437 .0416 .0425 .0434 7 .1500 40.3503 1.6771 .0495 .0508 .0520 8 .2000 7.9161 2.1879 .0558 .0575 .0590 9 .2500 13.5519 2.6777 .0611 .0631 .0650 10 .3000 22.2981 3.1484 .0657 .0680 .0702 11 .3500 35.6442 3.6013 .0698 .0723 .0748 12 .4000 55.6939 4.0377 .0734 .0762 .0790 13 .4500 85.3806 4.4588 .0767 .0798 .0828 14 .5000 128.7463 4.8656 .0797 .0830 .0863 18

FIGURE 1

Semi-1og Specificationl P10t on Interest Rates, Actua1 x Fitted

48.6188

..

1.~.&&79

14.7179

I-~---1

7678

· .. ··· ....

· · . H H H _ _ • I I _ .... H •

. 8122

.2816

.5518

.0285

Log Log Specification: Plot on Interest Rates, J\ctual x Fitted

662848.8

461367.1

268686.

(i888S

.

...

~.~.~ ...

. 5

.8121

.2878

20 \ (I.

cng

<~ t,;-.;; ~ ~tJ <"":; ;;> .. c~ :t .., '.11

~ª

f:~ ... o :': c~ -<to( u-~

~~

~~

~

\ \ é

_{, 'tL}

ENSAIOS ECONÔMICOS DA EPGI

200. A VISÃO TEÓRICA SOBRE MODELOS PREVIDENCIÁRIOS: O CASO BRASn.EJRO -Luiz Guilherme Schymura de 0Iiwira -Outubro de 1992 (eagotado)

201. HlPERINFLAçÃO: CÂMBIO, MOEDA E ÂNCORAS NOMINAIS - Fcmmdo de Hoa..da

Barbou - Nowmbro de 1992 -(eagotado)

202. PREVID~NCIA SOCIAL: CIDADANIA E PROVISÃO -CIcMI de FIlO - Nowmbro de 1992 203. OS BANCOS ESTADUAIS E O DESCONI'R.OLE FISCAL: ALGUNS ASPECTOS - Sérgio

Ribeiro da Costa Wcdaoa e ArmfDio Frap Neto - NCM:mbro de 1992 -(eagotado)

204. TEORIAS ECONÔMICAS: A MEIA-VERDADE TEMPORÁRIA - Antoaio Maria da

Silvara-Dczanbro de 1992

205. TIfE RICARDIAN VICE AND TIfE INDETERMINATION OF SENIOR - Antoaio Maia da SiMira - Dezembro de 1992

206. HIPERINFLAçÃO E A FORMA FUNCIONAL DA EQUAÇÃO DE DEMANDA DE MOEDA -FCII"DIIIdo de}Wancla BarboIa -JIDCiro de 1993 (eagotado)

207 REFORMA FINANCEIRA - ASPECTOS GERAIS E ANÁlJSE 00 PROJETO DA LEI

COMPLEMENTAR -Rubem Pcaba Cymo -fCWII'Ciro de 1993.

208. ABUSO ECONÔMICO E O CASO DA LEI 8.002 - Luiz Guilherme Schymura de 0IMira e Séqpo Ribeiro da Costa Wedq -fncrciro de 1993 (eagotado)

209. ELEMENTOS DE UMA ESTRATÉGIA PARA O DESENVOLVIMENTO DA AGRICULTURA BRASILEIRA -AIdoDio S"'zw Peaoa BnndIo e FJiIeu AI\a -Fewcciro de 1993

210. PREVID:blCIA SOCIAL PÚBUCA: A

EXPERItNCIA

BRASILEIRA - Hélio Portocamro de

Castro, Luiz GuiIIII:ImD SdIyDn de 0IiYcim, RaIMo F . . . . CardoIo e Urid de M . . .

-Março de 1993.

211. OS SISTEMAS PREVIDENCIÁRIos E UMA PROPOSTA PARA A REFORMULACAO 00 MODELO BRASlLElRO -Helio Portocam:ro de Castro, Luiz Guilherme Schymura de Oliveira, Reuto FrageIIi CardoIo e Uriel de MapIh" -Março de 1993. (eagotado)

212. THE INDETERMINATION OF SENIOR (OR THE INDETERMINATION OF WAGNER) AND SCHMOlLER AS A SOCIAL ECONOMIST - Antoaio Maria da Silveira - Março de 1993.

213. NASH EQun.IBRIUM UNDER KNIGlfllAN UNCERTAINTY: BREAKlNG OOWN BACKW ARD INDUCTION (E.DmiwIy RcMIecI Venioa) - 1 _ _ Dow e Séqpo Ribeiro da

Costa WerlaDg -Abril de 1993 •

214. ON TIfE DIFFERENTIABn..rrY OF THE CONSUMER DEMAND FUNC110N - Paulo

K1iDger MontciI:o, Mário Rui PiIcoa e Séqpo Ribeiro da Costa Wedq - Maio de 1993

215. DETERMINAÇÃO DE PREÇOS DE ATIVos, ARBrnlAGEM, MERCADO A TERMO E MERCADO FUrURO - Sérgio Ribeiro da CoIta Wc:dIDa o FINo AuIer - Apto do 1993

(CIIOfado ).

216. SISTEMA MONETÁRIO VERSÃO REVISADA -Mario Hcmiquo Simomca o Rubem

Pcuha Cymo -Agosto de 1993 (CIIOfado).

217. CAIXAS DE CONVERSÃO - Fcmando Antônio Hadba -Apto do 1993.

211. A ECONOMIA BRASILEIRA NO PERÍODO MILITAR. - Rubem Ponha Cymo - Apto do 1993 (CIIOfado).

219. IMPÓSTO INFLACIONÁRIO E TRANSFERÍNCIAS INFLACIONÁRIAS - RuboIII Pcuha Cymo -Apto do 1993 (CIIOfado).

220. PREVISÕES DE Ml COM DADOS MENSAIS - Rubem Ponha Cymo c Joio VICtoI' IIIIer

-Setembro de 1993.

221. TOPOLOGIA E cÁLCULO NO Rn - RuboJII Pcaba Cymo c Humberto Morára - Setembro do 1993.

222. EMPRÉSTIMOS DE MÉDIO E LONGO PRAZOS E INFLAçÃO: A QUESTÃO DA INDEXAÇÃO - CkMI do F." -Outubro do 1993.

223. ES1lJOOS SOBRE A INDETERMINAÇÃO DE SENIOR, wl. 1 - NcIIoD IL BarboIa, Fábio N.P. FrcitaI, Carb F.LR. LopcI, ~ B. MUDteiao, ADtoaio Maria da Silwira (CoonIcDador) c MIIiaa V CIDCIIF -Outubro do 1993. (CIIJOUIdo)

224. A SUBS1TIlJIÇÃO DE MOFDA NO BRASn.: A MOEDA INDEXADA - Fcmmdo do Holanda BIl'boIIa c Pedro Luiz Vali Pu • • -NOYaDbro do 1993.

225. FINANCIAL INTEGRATION AND PUBUC FINANCIAL INSnnrnONS -WaIIcr NOYICI c

Sérgio Ribeiro da CoIta WcdIag - Nawmbro do 1993.

226. LA WS OF LAROE NUMBERS FOR. NON-ADDITIVE PROBABIUI1ES - Jamea Dow c

Sérgio Ribeiro da CoIIa WcdIag -Dezembro do 1993.

227. A ECONOMIA BRASILEIRA NO PERfODO MILITAR. - VERSÃO REVISADA - R.uboaI

Ponha Cymo -

J"-'"

do 1994. (CIIl*do)

228.

nm

IMPACT OF PUBUC CAPITAL AND PUBUC INVESTMENT ON ECONOMIC

OROWIH: AN EMPIRICAL INVESTIOATION - Pedro ~ Ferreira - FeYCRiro do

1994.

229. FROM

nm

BRAZILIAN PAY AS VOU GO PENSION SYSTEM TO CAPITALlZATION:

BAlLlNG

our nm

GOVERNMENT -

J_

Luiz do CarwIbo c ClIMa do F." - Fewniro do

1994.

230. ESTIJOOS SOBRE A INDETERMINAÇÃO DE SENIOR - vol. fi - Brcaa PIUIa Mapa

FCI1IIDdcz, Maria Tcroza Garcia nu.tc, Scqio GrumJwth, ADtoaio Maria da SiMira

(CoonIcDador) -Fevereiro do 1994. (CIIOfado)

231. ESTABILIZAÇÃO DE PREÇOS AOlÚCOLAS NO BRASIL: AVAliAÇÃO E

PERSPECTIVAS -CIoYiI do F." o JOIé Luiz Carvalho -Março do 1994.

232 ESTlMATING SECTORAL CYCLES USING COINTEORATION ANO COMMON

233. COMMON CYCLES IN MACROECONOMIC AGGREGATES - Joio VICtor lIIIcr e FIIIhid

Vabid - Abri de 1994.

234. BANDAS DE CÂMBIO: TEORIA, EVIDblcIA EMPÍRICA E SUA POSsjvEL APUCAÇÃO NO BRASIL -AIoiIio PCIIOa de Araújo e Cypriaao LopeI Feij6 Filho - AId de

1994.

235. O HEOOE DA DÍVIDA EXTERNA BRASn.EIRA - Aloisio PCIIOa de Araújo, TúIio Luz Barbosa, AméIia de FMima F. SembImo c Maria HaycWe MoraIeI-AbrI de 1994.

236. TESTlNG

nm

EXTERNAllTIES HYPOTHESIS OF ENDOGENOUS GROWIll USING

COINTEGRA1l0N - Pedro CavaIcaati Fc:m:ira e Joio VICtor _ _ -AbrI de 1994.

237.

nm

BR.AZIL1AN SOCIAL SECtJRITY PROGRAM: DIAGNOSIS ANO PROPOSAL FOR

REFORM - Renato FrapIIi; UrieI de M . . . ; Helio Portoçam:ro e Luiz GuiIhamc Schymura

- Maio de 1994.

238. REGIMES COMPLEMENTARES DE PRE~NCIA - Hélio de 0IMira Portocarrero de

Castro, Luiz GuiJbcnne Schymura de 0IMira, Renato FragdIi Cardoeo, Sérgio Ribeiro da Costa

Wcdang e UrieI de M . . . - Maio de 1994.

239. PUBUC EXPENDI11JRES, TAXAll0N AND WEl..FARB MEASUREMENT - Pedro

CavaIcaati Ferreira -Maio de 1994.

240. A NOTE ON POLICY, lHE COMPOSmoN OF PUBUC EXPENDI11JRES AND

ECONOMlC GRowm -Pedro CavaIcaati Fc:m:ira -Maio de 1994.

241. INFLAçÃO E O PLANO FHC -Rubem Penha Cyme -Maio de 1994.

242 INFLAll0NARY BIAS AND STATE OWNED F1NANCIAL INSnnmONS - WIItcr

NOYICI Filho e Sérgio Ribeiro da Coá

Wcdaaa -

Juabo de 1994.

243. INTRODUÇÃO

A

INTEGRAçÃO ESTOCÁS11CA - Paulo

KJiDaer

Moatcim -JUDbo de 1994. 244. FURE ECONOMlC nIEORIES:

nm

TEMPORARY HALF-

muni -

ADfoDio M. Silw:ira

-JUDbo de 1994.

245. WELFARB COSTS OF INFLA110N - lHE CASE FOR INTEREST-BEARING MONEY

AND EMPIRICAL ESTIMATES FOR BRAZJL - Mmo Hemique SimaaIco c RubcaI Pcaha

- Julho de 1994.