Welfare cost of inflation considering adoption decisions and interest-bearing deposits

FUNDAÇÃO

GETULIO VARGAS

FGV

EPGE

.

enng

Adoption Decisions and

lnterest-Bearing Deposits

Rubens Penha Cysne

(EPGE/FGV)

Data: 25/1 0/2007(0uinta-feira)

Horário: 16h

Local:

Praia de Botafogo, 1

90-

11° andar

Auditório n• 1

Coordenação:

Welfare Cost of Inflation Considering

Adoption Decisions and Interest-Bearing

Deposits*

Rubens Penha Cysnet

October 25, 2007

Abstract

Attanasio et al. (.JPE, 2002) have used microeconomic data on households to provide new estimates of the welfare costs of infiation using Bailey's unidimensional welfare measure as a basis for their cal-culations. Such a measure does not properly take into consideration lhe fac\ that the majority of households in their sample (58. 7 per-cent) holds not only bank deposits and currency, but also a second type of interest-bearing assct. This work devises alternative formu-las which account for the existence of bank deposits and a sccond interest-bearing asset in the economy, as well as for adoption deci-sions regarding alternative financiai technologies.

1

Introduction

In a rneaningful contribution to the literature, Attanasio et ai. (2002) havc used rnicroeconomic data on households to model and estirnate the dernand for currency accounting for the adoptiou of new transaction technologies. La ter on in that paper, the authors use such results to calcula te new csti-mates of the welfare costs of inflation in an cconorny with currency, interest-bearing deposits and a second type of interest-bcaring asset. A new elernent

*David Turchick provided able research assistencc. Keywords: Welfare, Inflation,

Moncy Demand, Divisia Index, Adoption Decision, Interest-Bearing Deposits, Demand for Currency. JEL: E40, D60

in Attanasio et al.'s calculations, which draws on Mulligan and Sala-i-Martin (2000), is the consideration of adoption decisions by households concerning the different financial technologies available in the economy.

Attanasio et al. use Bailey's (1956) unidimensional1 _{measure of the} wel-fare costs of inflation as a basis for their calculations. The problem with such a procedure, though, is that in the economy considered by these authors 58.7 percent2 of the households hold two monetary assets ( currency and interest-bearing bank deposits), as well as one interest-interest-bearing non-monetary asset (which we shall'call bonds throughout this paper). In such a setting, Bai-ley's unidimensional measure is not appropriate, making the calculations presented in Attanasio

et

al. subject to mistakes.

In this work we suggest an alternative formula to calculate the welfare costs of inflation in such economies, taking into consideration not only the existence of more than one monetary asset, but also adoption decisions by households.

To make our point clearer, make R stand for the interest r ate on bank deposits, R3 for the interest rate on a second interest-bearing asset (this

one non-monetary, with R3 >R), m for the real value of currency, m(R) a

money demand function written as a function of an opportunity cost deter-mined by the holding of bank deposits R, and x for the real value of bank deposits. Bailey's unidimensional welfare formula (Bu3) used by Attanasio

et a1.4 _reads:

Bu(R)

=I~

em'(B)de (1)

Note that the opportunity cost o f currency used in (1) is R, rather than the interest rate on bonds (R3 ). This happens because Attanasio et al.

as-sume, in their welfare calculations, holding bank deposits as the only alter-native to holding currency.

We shall also see in the course of this work that, even when the oppor-tunity cost of holding bank deposits (R3 - R) is constant, as assumed by

Attanasio et al., welfare formulas for households holding both bank deposits and bonds (besides currency) should also take into consideration the effect

1_{The dimension here relates to the number of monetary assets available in the economy.}

See, e.g., Cysne (2003).

2 _{See page 341 in Attanasio et al., regarding the case o f Italy. The main point here is}

that this percentage is usually too relevant not to be properly considered with respect to analytical considerations. Regarding the United States, alternatively, Mulligan and Sala-i-Martin (2000, p. 962) report, following the 1989 Survey of Consumer Finances, that 35 percent of all households hold bank deposits and at least one additional interest-bearing asset.

3_{The subscript} 11

U11

used here stands for 11

unidimensional11_•

of variations of the interest rate paid by bonds on the dernand for bank de-posits (x'(Rs)). Equation (1), therefore, carmot account for ali adoption possibilities in economies like the one considered here.

In the rernainder of this text, we procccds as follows. Sections I I and

I I I derive rncasures of the welfare costs of inflation based, respectively, on a McCallurn-Goodfriend shopping-time dynamic framework and on a rnoney-in-the-utility-function Sidrauski-like framework. Thc measures are developed for households holding currency, bank deposits and bonds5

. In Section IV

we offer an alternatl've way of measuring the welfare costs of infiation in Attanasio et al. 's setting. Section V concludes.

2

The Multidimensional Shopping-Time

Ap-proach to the Welfare Costs of Infl.ation

This scction draws on Cysnc (2003). The consumcr has a (fixcd) time endow-ment equal to the unity and gains utility from the consumption (c = C

I

P,

P standing for the price index) of a single non-storable consurnption good, with preferences deterrnined by:

r=

e-gt U(c)dt

./o (2)

where U (c) is a strictly increasing and concave function o f the consumption good and g >O.

As in the economy considered by Attanasio et al, consumers can accu-mulate three assets: currency

(M),

interest-bearing deposits (X) and and bonds (E). The interest ratcs paid by each one of thesc asscts are, rcspec-tively, 2ero, R and Rs. In this section we shall not consider growth (it makes no difference concerning our results). Make y stand for real output and nor-malize it to 1. Make b

=

BIP, m

=

MIP, x

=

XIP, h= HIP (H indicates the ( exogenous) flow of rnoney transferred by the govermnent to such con-surners). Since output is norrnalized to one, these variables can alternatively bc undcrstood hcre as fractions of GDP. Let s stand for shopping-time and 1r =

P I

P for the inflation r ate ( the dot over the variable represents its time

5_{From anothcr perspective, the welfare formulas obtained in these sections correspond}

to the case in which (i) all such assets are available in the economy; (ii) heterogeneity of

derivative). Then, thc budget constraint reads:

m

+

x

+

b

= 1- c- s +h+ (Rs- n) b +(R-n)x- Rsm (3)

The transacting technology is given by:

c= F(m, x, s) = G(m, x)rf;(s) (4) with Fm

>

O, Fx

>

O and

F., >

O. G is assumed to be concave and first-degree homogenous.

The microfoundations for a transacting technology of the type c = F ( m, x, s) are based ou the inventory-teclmology found in the work:s of Baumol (1952), Tobin (1956) and Miller and Orr (1966). Lucas (2000, p. 265- see, in partic-ular, footnote 13) discuss how this transacting technology can be obtained from the work ofthe authors cited above and mention how it features in some monetary models in the literature. G is a monetary aggregator function.

Households maximizes (2) subject to the budget constraint (3) and to the time-transacting technology (4). In the steady state, assuming interior solutions, Euler equations lead to the necessary conditions:

Rs 1r

+

g

Fm Rs F,

Fx (Rs- R) F,

Make

1 -s = F(m,x,s)

describe equilibrium between demand and supply of output for each class of consumers. When the function rjJ is known, these equations can be used to determine m(Rs,Rs- R), x(Rs,Rs- R) and s(Rs,Rs- R).

As shown in Cysne (2003), in this model the welfare costs of infiation is given in differential form by the Divisia index:

ds = (1-s) [Rsdm

+

(Rs- R)dx]

1 - s

+

Rsm

+

(Rs - R)x (5)

with s(O) = O. In this 2-dimensional context, a reasonable approximation to (5) could be given by the Bailey-like multidimensional (BM6) differential formula:

6 _{As a counterpart to the subscript nun used in (1), the subscript} 11_M11 _{used here stands}

for 11_{multidimensional}11_{• Although we present the model with just two monetary assets,}

(6)

with BM(O) = O. Note that, upon intcgration, s(Rn) ---> BM(RB) when

Rum+ (RB- R)x---> OT

3

The Money-in-the-Utility-Function Approach

For the sakc of investigating the robustncss of the results we have shown above, in this Section we derive the same type of 2-dimensional Divisia index and I3ailey formula in a Sidrauski-type framework. Our results in this Section draw upon Cysne and Turchick (2007) and extend those regarding the l-dimensional analysis provided by Lucas (2000) in Section 2 of that paper. We consider a positive rate of growth o f the real output y : y( t)

=

e0_{', where}

y(O) is normalized to one. This assumption does not changc the welfare measures which emerge frorn the model.

Make c, rn and x stand, like in the previous Section, for the fractions of output of, respectively, currency, bank deposits and bonds. Assume the utility function, written in terrns of cy, rny and xy, to be given by:

1-a (

(G(

)))1-a

U(c,rn,x)=~-IJ

Cip :,x

whcre 17

>

O, 'P is an increasing function with 'f!( oo) = oo and G, as in the previous section, is a first-degree homogenous rnonetary aggregator function. Given thc ( 1 - 17 )-degree homogeneity of U, the consurner maximizes:

i

+=

rnax e-(g-(1-a)"y)tU(c, m, x )dt

. o

(Psn)

subject to:

Euler equations for this problern are:

{

[b]: (RB - 1 r -1))U, = 1i( -U,)

+

(g

-1(1-!7))Uc

[m]: (

-7>: -I)Uc +Um,=

f,(-.

Uc)

+

(g -1(1-!7))Uc ,

[x]:

(R -1': -I)Uc

+

Ux, = 1i(-Uc)

+

(g -1(1-!7))Uc

7_{Lucas (2000) shows in the unidimensional case and in a general-equilibrium context}

These equations imply:

(8)

Make

M

stand for the maximum possible value of G (O

<

M

<

oo) and define the domains:

2

-D~ := {(m, x)E ~+ : G(m, x)

S:

M}

and

D := {(m,x)E ~~: G(m,x) = M}

The points d E D are those which give the maximum available value for

G.

Repeating the procedure used in Cysne (2003), here we shall initially work with the welfare-cost function w defined as a function of the vector of monetary aggregates, rather than as a function of the interest rates. The initial condition reads w (d) = O for any d E D. We shall be specifically interested in paths

x

:t --+ (m, J;) such that x(O)

=

d E D (note that each coordinate di of d E D can be equal to infinity) and 8₈';'

<

O, 8₈';'

<

O. We

take x(O) = d because this is how we get the lowest possible values for the opportunity costs, making this the benchmark used for measuring the welfare cost of inflation.

Making c= 1, (8) gives:

{

RB =

'P(G(m,x)(cg/:::,:/)~'(G(m,x))Gm(m,x)

:= 1/Jm(m,x)

R _R_ '{J1(G m,x)) G ( ) ._ ~J,x( )

B - <p(G(m,x))-G(m,x)'P'(G(m,x)) x m, X . - '!" m, X

(9)

Note that (9) gives us the opportunity cost of holding each asset as a function of m and x. Cal! this function

1/J :

D~ --+ ( +oo, +oo ), with

1/J

:=(1/Jm(m,x),.,Px(m,x)).

Let <p' := supm>O,x>o'P(G(m,x)) = <p(M). Note that <p' can be equal to infinity. Write down the equations defining Lucas' measure of the welfare cost o f inflation using the definition o f <p':

{

U((1

+

w(m, x)), G(m, x)) = U(1,

NI),

or

Partially differentiating thc first of these equations with respect to m,

and dividing through by '(!1

(C (

₁

;;;·;,;,x))),

we obtain:

_

'P(cC;;;~,xll))

[

_

(

(m,x) )]

'Wm(m,x) ( (. ))+ Cm(m,:r)-wm(m,x)C _( ) =0.

d C (m,x) ) 1

+

'I1J m, X

r l+w(rn,x)

But (9) givcs us:

1

(c (

_{(m,x) ) )}

i.p l+w(m,x)

'P

(c (

(m,.x) ) )

l+w(m,x) _{Cm(m,x) ( (rn,x) )}

"'' ( (m,x) )

+

C 1

+

·w( m,

X)

'

'+'m 1+w(m,x)

so we get the cxpression:

_ ( ) m( (m, x) )

111m m, X = -1/J

1

+

w rn,x ( ) ,

By analogy:

_ ( ) x( (m, x) )

'Wx m, X = -1/J ( )

1

+w

m,x

(ll)

(12)

Similarly to the case based on the shopping-time model (sce (??) above), the welfare costs of inflation are now given in diffcrential form by the Divisia index:

dw = -

[1/Jm(

(m, x) )dm

+

1/Jx( (m, x) )dx]

l+w(m,x) l+w(m,x) (13)

Note that, since 1/Jm((m,x) = RB and 1Jx((m,x)) = RB- R, w-+ EM when

w -+ O. Again, as found out by Lucas (2000) concerning the unidimensional case, when w -+ O the welfare measure which emerges from the money-in-the-utility-function multidimensional approach lcads to an expression very close to the one which would emerge from a generalization, to the same multidimcnsional setting, of Bailey's formula.

The conclusion to be drawn from this Section and from the previous one is that anyone of the tlnee measures (5), (6) and (13) can be used as welfare measures for households holding currency, bank deposits and bonds, at least when welfare !asses are low~.

R For an ordering of such mcasures, as well as for an cstimate of thc maximurn rclative

error which can emerge when one uses one or another measure (including three others), see Cysne and Turchick (2007).

,

-4

Welfare and Adoption Decisions

Attanasio et ai. assert in page 340 that: "In principie, the evaluation of the welfare cost of inflation should also take into account the distortions involved in the managernent of other monetary assets, not only currency". Later on,

in the same paragraph, the authors justify not doing so in their calculations based on the follqyving line of reasoníng: i) (page 325, last paragraph): R8 - R

"ís roughly constant, suggestíng that the wedge between the nominal ínterest rate on Treasury bílis and bank deposíts ís índependent of ínflatíon; íí) (page 326, first paragraph) " ... thís property ís crítica! for the computíng of the welfare costs of ínflatíon-" and; ííí) (page 340, last paragraph): "íf R8 -R

ís índependent of ínflatíon, to compute the welfare costs of ínflatíon ít ís suflicíent to consíder the effect of changes in the nominal ínterest rate on the demand for currency".

One of the reasons why Attanasío et ai. end up wíth a measure of the welfare cost o f ínflatíon ( equatíon 10, p. 338) whích does not allow for the íncorporatíon of ali the varíety of households in theír sample ís that statement ( iii) above, whích thoy assume to be true, ís actually not correct. It overlooks the fact that the effect of changes in the nominal ínterest rate R8 on the demand for bankíng deposíts also has to be taken ínto consíderatíon in the welfare calculatíons, even whcn R8 - R ís constant.

Indeed, we have seen in the prevíous two sectíons that, in an economy as the one consídered by Attanasío et ai., three alterna tive formulas ( whích lead to very dose numerícal values) can be used to calculated the welfare costs of inflation for households holding currency, bank deposíts and bonds: (5), (6) o r (13). By assumíng R8 - R = K constant in thcsc formulas one obtaíns,

respectívely, the followíng particular cases:

s(Rs) = -

rB

(1-s)

[em'(e)

+

Kx'(e)] de

0

1-

s +em+

Kx when the shopping-time model is taken as reference;

BM(R8 ) = -~~B

[em'(e) +

Kx'(e)j de

when a multi-dimensional Baíley-líke formula ís taken as reference and;

w(RB)

= {

_ j'RB ( 7/Jm( m(B,K),x(B,K) )m' (e)

O Hw(m(B,I<),x(B,I<))

+1/Jx (

m(O,K),x(B,K) )x' (e) )de l+w(m(B,K),x(O,K)

(14)

(15)

when a money-in-the-utility-function approach is takcn as refcrence9.

Note three important differences of the formulas above (14), (15) and (16)) relatively to (1), used by Attanasio et al, regarding consumers adopting a financia! tcclmology including bank deposits and bonds.

First, the relevant opportunity cost to hold currency in economies with banking deposits and bonds is given by R8 , rather than by R.

Second, even when R_{8 -} R is assumed to be constant, one has to take into consideration (in contrast to what is assumcd by Attanasio et al. in the last paragraph 'üf page 340) the effects of R8 on the demand for bank dcposits. This stems from the fact that bank deposits also perform rnonetary functions.

Third, all functions are evaluated at (RR, R8 -R), rather than just at

(R).

4.1

The Bias From the Use of

Bu

We have seen above that two important differences betwcen our underlying measurcs (14), (15) and (16) and (1), used by Attanasion et al (still without considering adoption decisions).

First, by integrating from zero to R, rather than from zero to RB, anyone of the three measures (14), (15) and (16) lead to a lower value of the integral with respect to m' ( 8) ( which is certainly nega tive) and to a greater o r lower value of the integral with respect to x' ( B), depending on the signal of this term, if, respectively, negative or positive.

Second, consider the integrais from zero to R. Anyone of the formulas above, (14), (15) or (16), presents an integral involving the term x'(B) (eval-uated for a fixed value of R8 -R (equal to K)), whereas (1) does not. Again, the measures (14), (15) and (16) willlead to welfare figures greater of lower than (1) if x' ( B) is, respectively, negative or positive.

For these two rcasons, it is interesting to study the signal x' ( B) which can emerge of the shopping-time or of the money-in-the-utility-funciton model. When it is negative, Attanasio et al.'s measure will not be adding (twice, as descrived in the two points above) a positive cost, thereby underestimating the total wclfare costs of inf!ation. The opposite, of course, may occur for positive values of x' ( B).

9_{To simplify the notation, the derivativcs m'(B) and x'(B) above omit the second}

Let us analyze this point in the context of the money-in-the-utility-funciton model. In the following developments, we omit the arguments of the functions for clarity.

An application of the lmplicit Function Theorem to the equilibrium equa-tions (9) yields:

dx 'P'P"GmGx

+

('P (G) ~ Gtp' (G)) tp'Gmx

dRB tp'2 _(G;,x ~ _GmmGxx) ~ 'P(Gf'f(j~,(G) _(G;,Gxx ~ _2GmGxGmx

₊

_a;Gmm).

Let 's analyze the sign o f this expression. First of all, since G is concave, we know that a;,x ~G,m,Gxx ::; O. Using the facts that Gm is 0-homogeneous and

Gmm < O, we get by Euler's formula, for any ( m, x) E lll:.~+' Gmm (m, x) m

+

Gmx ( m, x) x

=

O* Gm ( m, x)

=

O, so that Gmx

>

O. Therefore, the numerator of the above expression for ~~ has an indefinite sign, whereas its denominator is surely negative. This means that, for a given equilibrium triple ( m*, x*, r*),

we have:

~xl( _{r m ,x ,r}

, ,

'l :::0: O iffB(tp,G,m*,x*)

:= 'P (G (m*, x')) tp11 _{(G (m*, x*)) Gm (m*, x*) Gx (rn*, x*)}

₊

+

(tp(G(m',x*)) ~ G(m*,x*) tp' (G(m*,x*))) tp1 _{(G(m*,x*)) Gmx (m*,x*)::; O.}

We can specialize the math above for the log-log case m = Ar-a (a E

(0, 1)), with G (m, x)

=

m~x~-~ (also

f3

E (0, 1)). By using10: G

'P (G) = " '

(A'(

a+

a'-:.")

1-o

we get the following expression for checking of nonnegativity:

B(tp,G,m,x) =

~{3

(1

~

{3) Klfa

m2~-lx1-2~

(Kl(a + G (m, x) '-;.") ,::.:,

l~a

*[G(m,x)~(l~a)G(m,x)':"].

That is,

~~

:::0: O iff G(m,x)2

-±::;

1

~a.

This means that ifwe take, for instance, a= 0.5 (as in Lucas (2000)), we automatically get ~: <O.

This would correspond to a case in which the use of (1), as carried out by Attanasio et al., would tend to understimate the true welfare cost of inflation of consumers holding currency, bank deposits and bonds. It is not difficult, given the general result (??), to obtain cases in which the opposite is true.

4.2

Attanasio et al. 's Welfare Measure Considering

Adop-tion Decisions

After introducing (1) as the basic measure of the welfare cost of inflation in their economy, Attanasio et ai. consider thc decision to aelopt bank eleposits anel ATM carels by plugging Eu into their cquation 10 on page 338, which leaels to the value o f the total welfare loss consielereel in that paper (cal! it WA11

):

In this equation, Bu is given by (1), Fv(R) anel FH((R) rcpresent, respec~ tively, the probability that a householel has a bank account anel the probabil~

ity that a household has an ATM card, both evaluated at interest rate

R.

The dummy variable D is equal to 1 when the household has a bank account and cqual to zero othcrwise; the second dummy variable H is equal to one when the household has an ATM card and equal to zero otherwise. Thc reason for the term Fn(R) in (17) is the following assumption made by Attanasio et ai.:

Assumption 1: (Attanasio et ai., p. 338): "To compute the welfare cost of inflation we do not need to look at the behavior of those without bank accounts11

•

vVhile Assumption 1 may be questionable undcr a more encompassing analysis12 , we shall not qucstion its validity in this text.

The rcason for the term FH(R) (the probability that the household has an ATM card) in (17) is that the money~demand elasticities (and, therefore, the numbers which emerges from (1), in Attanasio ct al.'s calculations) are empirically observcd to be different for consumers with and without access to such a technology. The welfare costs calculated in (17), as one can observe, are a weighed average of the welfare costs of households with and without ATM cards.

5

Main Result

1111 _A 11 _{herc stands for Attanasio et al.}

12_{The subjaccnt idea comes from Mulligan and Sala-i-Martin (p. 986): consumers}

with-out access to altcrnative monetary assets (respectively, bank dcposits in Attanasio et al. and bonds in J\.1Iull1igan and Sala-i-Martin) would not incur in shopping-time or adoption costs, thereby having no welfarc costs stcmming from infiation. A1tcrnative allocation of rnoney in consnmption goods, rather than on other assets, generating consumption dis-tortions and other typcs of welfare losses, are ignored both by Mulligan and Sala-i-Martin

Our purpose here is to revise (17) taking into consideration ali types of households considered by Attanasio et ai.

Let us begin with those holding only currency and interest-bearing de-posits. Make Fs(Rs, R3 - R) represent the probability that a household

has a financiai asset other than a bank account (here, bonds), conditional on having a bank deposit13

; and F;{ stand for the probability that a

house-hold has a ATM card conditional on having a bank account but not bonds. Consider the modification of (17), which we shall cal!

w.;:,

given by:

W' (R R -R). = { (1- Fs(Rs- R))FD(Rn, Rs- R){F;I(Rs)Eu(R)D~t,H~t

T, 3' 3 · +[1- FÊ(R3 , Rs- R)]Eu(R, Rs- R)D~t,JI~o}

(18) Note that (18) differs from (17) in the following points: (i): It substitutes FH for F;I; (ii) it recognizes the fact that ali probabilities must be functions of the two spreads Rs and R3 - R, rather that a function just of R, as

assumed by Attanasio et ai. and; (iii) it takes into consideration, by using the multiplicative factor 1-F3 (R3 - R), that (17) can only be used with

respect to households holding bank deposits, but no bonds.

Now let us consider households holding currency, bank deposits and bonds. Start making

r

indicate anyone of the welfare measures we have obtained in Sections 2 and 3 above (s, EM or w). Use (14), (15) or (16) if (as considered in Attanasio et ai.), R3 - R can be assumed to be constant;

otherwise, use the values of either s, EM or w given, respectively, by more

general versions (5), (6) and (13). Next, let Fj,'(Rs, Rs- R) represcnt the probability that the household has an ATM card conditional on having a bank account and a second interest-bearing asset (bonds). J ust to follow the notation in Attanasio et ai. (see their equation 11 in page 342), denote by

E a dummy variable which is equal to one when the household has a bank account and an interest-bearing financiai asset other than a bank account

(bonds) and equal to zero otherwise. Make

{

Fs((Rs, Rs- R))FD(Rs, Rs- R)* WT,(Rs, R2-R) := {Fj,'((Rs, Rs-R))r((Rs, RB- R))s~l,H~I

+[1-FÊ'((Rs, Rs- R))]r((Rs, Rs- R))B~I,H~o}

(19) Equation (19) considers the welfare losses of a fraction F3((R3 , R3

-R))FD(R3 , R3 - R) of households (equal to58.7 percent of ali households in

Attanasio et ai.) who have both bank accounts and bonds. Following our

previous calculations of Sections 2 and 3, as well as the considerations made by Attanasio et al regarding the possession or not of ATM cards, thc welfare cost for these honseholds should be given by

vV

r2 . This second componcnt of

the we!fare calculations is based on

r

(which stands for either s, EM or w), rather than on Bailey's unidimensional measure Eu, as in Attanasio et al.'s calculations.

Proposition 1 gives the main point of our work

Proposition 1 Consider an economy with cv.rrency, bank deposits and bonds,

subject to adoption decisions, as the one described in Atta.nasio et al., and suppose tha.t Assumption 1 is valid. Then, the welfare costs of inflation in this economy, associated with the pai r o f opportunity costs (RB, R - RB), and taken into consideration adoption decisions, is given by:

(20)

6

Conclusion

Attanasio et a!. (2002) have used microeconomic data on households to providc new estimates of the welfare costs of inflation using Bailey's unidi-mensional welfare measure as a basis for their calculations. Such a measure does not properly take into consideration economies in which (!ike theirs) the majority of households holds not only bank deposits and currency, but also a second type of interest-bearing asset.

In this work we have devised alternative formulas to calculate welfare losses which account for the existence o f interest-bearing deposits and a o f second interest-bearing asset in the economy, as well as for adoption decisions of the households regarding alternative financia! technologies.

References

[1] Bailey, Martin J., (1956) "Welfare Cost of Inflationary Finance. (1956) "Journal of Política! Economy 64, 93-110.

[3] Cysne, Rubens P. (2003): "Divisia Index, Inflation and Welfare". Jour-nal of Money, Credit and Banking, Vol 35, 2, 221-239.

[4] Cysne, Rubens P. and Turchick, David (2007): "An Ordering of Mea-sures o f the Welfare Cost of Inflation in Eco no mies with Interest-Bearing Assets". Working Paper, EPGE/FGV.

[5] Cysne, Rubens P. and Thrchick, David (2007a): "Wbich Money De-mands are jointly Consistent with Weakly-Separable Versions of the Sidrauski and Shopping-Time Models?" Working Paper, EPGE/FGV.

[6] Lucas, R. E . .Jr., (2000): "Inflation and welfare". Econometrica 68, No. 62 (March), 247-274.

[7] Miller, Merton H. and Daniel Orr. (1966): "A Model of the Demand for Money by Firms." Quarterly Journal o f Economics 77: 405-422.

[8] Mulligan, Casey. B and Sala-i-Martin, Xavier (2000): "Extensivo Mar-gins and the Demand for Money at Low Interest Ratos", .J o urna! of Political Economy, Vol. 108, N. 5, 961-991.

[9]

Simonsen, Mario

H.

and Cysne, Rubens P. (2001): "Welfare Costs of Inflation and Interest-Bearing Deposits". Journal of Money Credit and Banking, February, 33-1, 90-101.