COSTLY INTERMEDIATION AND CONSUMPTION SMOOTHING

COSTLY INTERMEDIATION AND CONSUMPTION SMOOTHING

ANTONIO ANTUNES, TIAGO CAVALCANTI and ANNE VILLAMIL∗

This paper studies quantitatively how intermediation costs affect household con-sumption loans and welfare. Agents face uninsurable idiosyncratic shocks to laborproductivity in a production economy with costly financial intermediation and a bor-rowing limit. Reducing intermediation costs has two effects: (1) For a given decreasein the interest rate on borrowing, agents’ ability to smooth consumption over timeimproves. (2) The demand for loans increases, which increases the interest rate. The netwelfare gain of reducing intermediation costs from 3.927% (U.S. level) to 1% is about1.14% of equivalent consumption in the baseline economy for an endogenous interestrate and 1.90% for an exogenous interest rate. The gains are distributed unevenly:households at the bottom wealth decile improve welfare by 3.96% and 5.86% of equiv-alent consumption, while those at the top decile have welfare gains of 0.35% and 0.2%,respectively. Sufficiently high intermediation costs eliminate borrowing and hence thewelfare gain of reducing costs is not substantial. The welfare analysis includes transi-tional dynamics between steady states. (JEL D91, E60, G38)

I. INTRODUCTION

Financial intermediaries play an essential rolein economies, transferring funds from agentswho do not wish to use them immediatelyto those who do, improving the allocation ofresources with consequences for efficiency and

*We thank the associate editor, Gian Luca Clementi,two anonymous referees, Kartik Athreya, Gabriele Cam-era, Dean Corbae, Jonathan Heathcote, Hashem Pesaran,Facundo Piguillem, Drew Saunders, Gustavo Ventura, andRui Zhao for comments, and Rui Castro for conversa-tions about computing the model transitional dynamics. Wealso benefited from comments at the SED Meeting, Euro-pean Economic Association Congress, Latin American andCaribbean Department of the World Bank, IMT Institute forAdvanced Studies in Lucca, Cambridge Finance Workshop,Purdue University, University of Iowa, and the University ofIllinois. Villamil thanks the Said School of Business at theUniversity of Oxford where she was the Peter Moores Fel-low. Financial support from Fundacao para a Ciencia andTecnologia, grant PTDC/EGE-ECO/108858/2008, is grate-fully acknowledged. We are responsible for any remainingerrors.Antunes: Departamento de Estudos Economicos, Banco

de Portugal, Av. Almirante Reis 71, Lisbon 1150-012,Portugal. Phone 351 213128246, Fax 351 213128114,E-mail [email protected]

Cavalcanti: Faculty of Economics, University of Cambridgeand PIMES/UFPE, Sidgwick Avenue, Cambridge CB39DD, UK. Phone 44 1 223 335262, Fax 44 1 223 335475,E-mail [email protected]

Villamil: Department of Economics and Finance, Universityof Illinois Urbana-Champaign and University of Manch-ester, 1407 South Gregory Street, Urbana, IL 61801.Phone 1 217 244 6330, Fax 1 217 244 6571, [email protected]

welfare. As Hahn (1971) pointed out, financialintermediation is not a costless activity: Ituses real resources, such as labor and capi-tal, and governments often tax such activity.This generates a wedge between the deposit andborrowing rates and consequently implies thathouseholds face different interest rates, depend-ing on whether they are savers or borrowers.We construct a neoclassical growth model withcostly intermediation, in order to analyze twopositive questions: (1) What are the quantitativewelfare implications of intermediation costs? (2)Are the welfare effects evenly distributed acrossindividuals with different levels of wealth?

Individuals in our neoclassical growth modelface uninsurable idiosyncratic shocks to laborproductivity, an endogenous borrowing limit,and costly intermediation. Households smoothconsumption over time by making deposits at afinancial intermediary in good times and run-ning down credit balances or getting loansin bad times. Intermediation costs generate awedge between loan and deposit rates, withinterest payments on loans higher than the

ABBREVIATIONS

GDP: Gross Domestic ProductNIPA: National Income and Product AccountsSCF: Survey of Consumer Finances

1

Economic Inquiry(ISSN 0095-2583)

doi:10.1111/j.1465-7295.2012.00471.x© 2012 Western Economic Association International

2 ECONOMIC INQUIRY

return on deposits. We assume that financialinstitutions provide all the intermediation, andtherefore abstract from direct borrowing andlending between households.1 As in Martins-da-Rocha and Vailakis (2010), the intermedi-ary has a labor-intensive technology, maximizesprofit, is remunerated by the marginal productof labor, and takes regulation as given.2 SeeHahn (1971), Dıaz-Gimenez et al. (1992), andMehra, Piguillem, and Prescott (2011) for simi-lar approaches.

Our goal is to analyze the effects of inter-mediation costs on agents’ intertemporal abilityto smooth consumption and insure against laborincome shocks. As a consequence, we focus onunsecured consumption loans such as personalloans and credit card debt, and abstract from theeffects of intermediation costs on entrepreneur-ship and productivity. Unsecured consumptionloans, while only a subset of the total creditmarket, allow us to construct a direct mea-sure of intermediation costs for our quantitativeexercise. In addition, the fraction of unsecuredcredit over all credit in the data provides anotherdimension on which we can assess the perfor-mance of our model.

We use our model to measure key statisticsof the U.S. economy, including intermediationcosts, and perform counterfactual experiments.Reducing intermediation costs leads to twoeffects. First, for a given interest rate, decreasingborrowing costs expands net borrowers’ con-sumption possibility frontiers and even currentsavers may benefit (with positive probabilitythey may need to borrow to smooth consump-tion in the future due to bad labor productiv-ity shocks). Second, there is an indirect effect:lower intermediation costs imply an increase inthe demand for loans, which raises the interestrate. This offsets part of the decrease in bor-rowing costs and also increases interest income,improving savers’ welfare. Determining the netimpact of these effects requires a quantitativeanalysis.

We interpret a reduction in intermediationcosts as an improvement in the financial

1. This is optimal, for example, when monitoring iscostly and there is no double coincidence of wants. Banksintermediate by bundling deposits together to make loansand diversify risk.

2. Townsend (1978) and Greenwood and Jovanovic(1990) build economies in which financial institutions ariseendogenously to share risk and smooth consumption bycollecting information, pooling risk, and allocating resourcesto high return investments. See also Diamond and Dybvig(1983), Krasa and Villamil (1992a, 1992b).

intermediation technology or a reduction intaxes on financial transactions. The welfare anal-ysis focuses on stationary equilibria and tran-sitional dynamics. The transition is slow, andabstracting from it can lead to misleading wel-fare calculations. Also, mobility in wealth meansthat comparing, for instance, the agent withmedian wealth in two stationary equilibria maynot involve the same household. We find threemain quantitative results:

First, intermediation costs have a large effecton welfare. For the U.S. economy, the averageaggregate welfare gain of all agents from reduc-ing intermediation costs from 3.927% (U.S.level) to 1% (the level observed in the 10thpercentile of countries with the lowest inter-mediation costs) is about a 1.14% consumptionequivalent increase in the baseline economy.The indirect general equilibrium effect is alsosubstantial. When we assume that the economyis integrated in the world capital market, andhence the interest rate does not adjust after achange in intermediation costs, the aggregatewelfare effect is larger, about 1.90% of con-sumption equivalent to the baseline economy (a66% increase over the endogenous interest ratecase). When the interest rate is endogenous, thelowest wealth decile has an average welfare gainof 3.96% of baseline consumption, while thehighest decile has an average welfare gain ofroughly 0.35%. Therefore, inefficient intermedi-ation affects heavily poor households that facebad income shocks.

Second, the welfare effects of intermediationcosts are not linear and depend on the size ofthe interest rate wedge. To illustrate this, weincrease intermediation costs from the U.S. levelto the level observed in Mexico (6.5%) andBrazil (12%). Surprisingly, the effect of thiscounterfactual increase in intermediation costs isnot substantial: aggregate welfare decreases byonly 0.12% and 0.30% of consumption equiv-alent to the baseline level, respectively. Thisoccurs because when intermediation costs arehigh, agents do not borrow to insure againstincome shocks and instead accumulate assets toself-insure. When households hold little debt,the scope for welfare gains is small. As inter-mediation costs fall, more households rely ondebt to smooth consumption and the scope forwelfare improvements from reducing the wedgerises.

Third, we find that introducing an interest ratewedge improves the ability of Bewley modelsto match the left tail of the wealth distribution.

ANTUNES, CAVALCANTI & VILLAMIL: COSTLY INTERMEDIATION AND CONSUMPTION SMOOTHING 3

Bewley models are a class of models withexogenously incomplete markets and agents thatare ex ante identical but heterogeneous ex postdue to uninsurable idiosyncratic income shocks.Risk averse agents use an asset (e.g., a risk-free bond, capital, or private borrowing andlending) to self-insure, adjusting their hold-ings of the asset to smooth consumption. Themodel is widely used in quantitative macroe-conomic analyses. We obtain a better matchbecause Bewley models without intermediationcosts generate more borrowing than the amountobserved in the data. Our model also bettermatches household consumption loan data.

The quantitative effects of intermediationcosts on the ability of agents to use con-sumption loans to insure against labor incomeshocks and the associated welfare consequenceshave been largely neglected. An exception isChia and Whalley (1999), but they use atwo-period exchange economy, while we con-sider an infinite horizon production economyand use standard calibration techniques. Ourresults show that for the United States, thewelfare effects of reducing intermediation costsare substantial compared to other supply-sidereforms,3 with poor households benefiting most.

The paper proceeds as follows. Section IIcontains facts on intermediation costs and inter-est rate differentials. Section III describes themodel and defines the competitive equilibrium.Section IV calibrates the model and performspolicy experiments to evaluate the welfare eff-ects of changes in intermediation costs. SectionV concludes.

II. INTERMEDIATION COSTS AND INTEREST RATEDIFFERENTIALS

This section reports measures of intermedia-tion costs and interest rate differentials for theUnited States and other economies. In the stan-dard Bewley model, agents borrow and lenddirectly and such activity is costless. How-ever, financial intermediation entails transactioncosts to process applications, verify informa-tion, taxes, and so on. We measure intermedi-ation costs directly, but first comment on analternative approach—the net interest margin,which is related to the wedge between bor-rowing and deposit rates. Demirguc-Kunt and

3. See Lucas (1990, 2000), Aiyagari (1995), Erosaand Ventura (2002), Cavalcanti and Villamil (2003),among others.

Huizinga (1999) show that the net interest mar-gin can be decomposed into the sum of aftertax bank profit, overhead costs, loan loss provi-sions, and taxes, minus non-interest income, alldivided by total assets:

NIM = After tax profits/TA + OVC/TA

+ LLP/TA + Taxes/TA − NII/TA.

We construct a direct measure of intermediationcosts based on overhead and bank taxes insteadof an indirect measure based on interest ratespreads for two reasons: (1) no measure ofintermediation costs for unsecured consumptionloans only is available; and (2) interest ratespreads contain bank profit, default risk, and“other activities” that are accounted for in ourmodel.4 Thus, we focus on overhead costs andtaxes over total assets.

Figure 1A reports financial intermediaries’noninterest expenses (i.e., overhead costs) rela-tive to total assets in the United States from 1999to 2008. This corresponds to salaries and bene-fits paid by banks, as well as banks’ expenditureson capital and services, such as advertising, dataprocessing, and consulting. The average valuefrom 1999 to 2008 is 3.365% of total assetsheld by financial institutions. This is a signif-icant amount, since, as Mehra, Piguillem, andPrescott (2011) report, the amount intermedi-ated in 2007 was about 1.72 times the grossdomestic product (GDP) and data from NationalIncome and Product Accounts (NIPA) show thatthe value added of the financial sector as a shareof GDP is over 7%. This figure also reports taxespaid by banks over total assets and the averagevalue from 1999 to 2008 is about 0.562% of totalassets. Therefore, the average sum of taxes andnoninterest expenses of financial intermediariesin the United States is roughly 3.927% of totalbanks’ assets. Figure 1B shows that when weconsider all financial intermediaries’ assets andliabilities in the United States, the average valueof the wedge between deposit and borrowingrates from 1999 to 2008 is over 3.5 percentagepoints and highly persistent, consistent with ourmeasure.

We model unsecured consumption loans,which are only a fraction of all loans. Fed-eral Reserve Statistical Release Table G.19 onconsumer revolving credit outstanding, which

4. We assume free entry (hence economic profit is zero)and default is offset by loan loss provisions. Our modelabstracts from “other activities” in NII (gains in foreignexchange holdings, fiduciary services, etc.).

4 ECONOMIC INQUIRY

FIGURE 1Intermediation Costs and Interest Rate Differentials in the United States. (A): Noninterest

Expenses (NIE) Relative to Total Assets (TA) and Taxes Relative to Total Assets. (B): InterestRates on Financial Intermediaries’ Assets and Liabilities.

1998 2000 2002 2004 2006 20080

0.5

1

1.5

2

2.5

3

3.5

4

Year

%

A

1998 2000 2002 2004 2006 20080

1

2

3

4

5

6

7

8

9

10B

Year

%

NIE/TA

Taxes/TAiL on assets

iD on liabilities

Source: The 2009 Federal Reserve Bulletin (Bech and Rice 2009, page A88, table A.1).

excludes loans secured by real estate and auto-mobiles, shows that unsecured loans are roughly7.7% of output in the United States on averagefrom 2004 to 2008. As we shall see in the cal-ibration, our model produces a result close tothis number and does not overestimate borrow-ing. The Bewley model with a natural borrow-ing limit but no interest rate wedge, produces amuch larger figure for unsecured loans. There-fore, the introduction of a wedge between thedeposit and borrowing rates improves the abilityof Bewley models to match household consump-tion loan data.

In addition, the wedge for unsecured loansis larger than for total intermediary assets andliabilities: Data from the Board of Governors ofthe Federal Reserve system, Table G.19, showsthat the average interest rate on (unsecured)

credit card loans is roughly 12% per year,which is about 8 percentage points above theaverage deposit rate.5 As a consequence, wemight underestimate intermediation costs forunsecured household loans, as total assets istoo broad a measure, for example, securitiesand government bonds are unlikely to requirethe same resource expenditures as loans toindividuals.6

5. The wedge between deposit and loan rates is persis-tent in the United States. Using data for the 1980s, Dıaz-Gimenez et al. (1992) show that for collateralized loans theaverage interest rate is nearly 4 percentage points higherthan the return on bank deposits and for uncollateralizedloans the spread exceeds 10 percentage points.

6. Our value for intermediation costs is consistent withother sources. Data reported from Beck, Demirguc-Kunt,and Levine (2000) show that overhead costs over totalassets in the United States is 3.4% and Demirguc-Kuntand Huizinga (1999) show that banks’ taxes over total


III. THE MODEL

There are three sectors: households, bank-ing, and production. The continuum of infinitelylived households are ex ante identical and faceidiosyncratic shocks to their labor productivity,and there is no aggregate uncertainty. Banks’only role is to intermediate among households,and intermediation is costly. The productiontechnology exhibits constant returns to scale.The produced good can be used for consumptionor investment.

A. The Production Sector

In any time period t , a production technologyconverts capital, K

yt , and labor, N

yt , into output

Yt according to:

Yt = (Kyt )α(N

yt )1−α.(1)

Parameter α ∈ (0, 1) is the capital income share.Capital depreciates at rate δ ∈ (0, 1) per period.Households competitively rent units of efficientlabor and capital to firms and input rental pricesare given by their net marginal productivity:

wt = (1 − α)(Kyt )α(N

yt )−α,(2)

rt = α(Kyt )α−1(N

yt )1−α(3)

Because the production function is homoge-neous of degree one, profits are zero and firmownership is unimportant.

B. The Banking Sector

Banks lend to households that wish to bor-row, accept deposits from those that wish tosave, and bundle small deposits together to makeloans. In period t , let Db

t be households’ depositsand Lb

t be loans, with iD,t and iL,t the respec-tive interest rates on deposits and loans. Let τrepresent the tax paid on financial intermedia-tion. Banks use capital and labor to intermedi-ate among households. Define the intermediarytechnology by the Leontief function:

Lbt = η−1 min{ν−1Kb

t ,Nbt }.(4)

Parameter η−1 > 0 measures intermediary effi-ciency. A small η implies that banks are very

assets is 0.5%. Using these indirect sources would lead tointermediation costs of 3.9%. Using numbers reported byEvans and Schmalensee (1999) on the net cost of servicingaccounts, Athreya (2002) sets the value of intermediationcosts in the United States to be 3.4%, which is also close toour calibrated value.

efficient in intermediation. When η goes to zero,banks do not need labor and capital to interme-diate among households. Parameter ν−1 is theimportance of capital relative to labor in theintermediary technology. Assume there is freeentry into the banking sector.

The problem of the representative bank isto choose deposits, loans, labor and capital(Db

t , Lbt , N

bt ,Kb

t ) to maximize profit:7

max{(1 + iL,t )Lbt − (1 + iD,t )D

bt

− τLbt − wtN

bt − rtK

bt },

subject to

Dbt ≥ 0,Db

t ≥ Lbt ≥ 0, and

Lbt = η−1 min{ν−1Kb

t ,Nbt }.

Free entry and competition in the banking sectorimply zero profit in equilibrium. Thus,

iL,t − iD,t = τ + η(wt + νrt ) = τt .(5)

The wedge between lending and deposit ratescan be decomposed into two factors:

1. intermediary taxes τ; and2. overhead costs η(wt + νrt ).

Equation (5) shows that the wedge is deter-mined endogenously by policy parameter τ,technology parameters η, ν, and factor prices.

C. The Household Sector

Households inelastically supply one unit oflabor per period, and face idiosyncratic shocksto labor productivity. A household with shockzt ∈ Z receives labor income wtzt , where the zt

follow a finite state Markov process with supportZ and transition probability matrix P(z, z′) =Pr(zt+1 = z′|zt = z). The Markov chain gener-ating zt has just one ergodic set, no transientstates, and no cyclically moving subsets. House-hold preferences are defined over stochastic pro-cesses for consumption, ct , and given by thefollowing utility function:

E0

[ ∞∑t=0

βt u(ct )

], β ∈ (0, 1).(6)

One-period utility, with inverse intertemporalelasticity of substitution θ > 0, is

u(c) = (c1−θ − 1)/(1 − θ).

7. Notice that there is no uncertainty at the aggregatelevel.

6 ECONOMIC INQUIRY

The Credit Market and Budget Constraint.Agents own capital, kt , make deposits, dt+1, andget loans, lt+1 from financial intermediaries. Aloan is a promise by a household in period t − 1to pay back (1 + iL,t )lt to the bank at the begin-ning of period t , against the immediate deliveryby the bank to the household of lt units of finalgood. A deposit is a promise by the bank todeliver (1 + iD,t )dt units of the final good atthe beginning of period t against a deposit by ahousehold of dt units of final good during periodt − 1. Let γt denote lump-sum transfers.8 Com-petition among banks drives interest rate iD,t

to a level such that households are indifferentbetween making a deposit or investing in cap-ital. One unit of consumption good invested incapital in period t − 1 yields 1 + rt − δ units ofthe consumption good in period t . If householdsdeposit one unit of consumption good in periodt − 1, they will have available 1 + iD,t units ofconsumption good in period t . Therefore:

rt − δ = iD,t .(7)

If the wedge τt is positive and agent networth at+1 is negative, then kt+1 + dt+1 = 0and lt+1 > 0; likewise, at+1 > 0 implies lt+1= 0. Using this fact and arbitrage condition (7),the agent’s budget constraint can bewritten as

ct + at+1 ≤ at (1 + i∗t ) + wtzt + γt ,(8)

where i∗t (at ) = iD,t + τtI(at < 0). Indicatorfunction I(at < 0) is 1 if at < 0 and 0 other-wise. The agent’s position in period t is entirelydescribed by asset holdings and current laborshock, xt = (at , zt ).

Borrowing Limit and Households’ Problem. Toavoid a Ponzi game, we follow Aiyagari (1994)and use a natural borrowing limit.9 Aiyagari(1994) defines a “natural” borrowing limit asa situation where in an agent’s worst possi-ble state, z, interest payments do not exceedlabor income (i.e., current debt can at least be

8. The lump-sum transfers are important in the welfarecalculations. We assume the proceeds from the interme-diation tax, τ, are rebated back to households. Therefore,welfare numbers indicate only the inefficiency generated bycostly intermediation, which affects agents’ ability to smoothconsumption over time.

9. We also used an endogenous borrowing limit, asin Kehoe and Levine (1993) where agents always keeppromises in equilibrium. The welfare implications of inter-mediation costs are roughly the same. We report only thenatural borrowing limit, but endogenous borrowing limitresults are available upon request.

rolled over after a long spell of low produc-tivity shocks). The natural borrowing limit isgiven by:

at+1 ≥ aNBt+1 = −

∞∑j=0

(wt+1+j z)/

×j∏

s=0

(1 + iLt+1+s).

We assume a very large upper bound forassets, a.10 Define X = [a, a] × Z and let χbe the associated Borel σ-algebra. For eachB ∈ χ, λ(B) is the mass of households whoseindividual state vectors lie in B. An agent’svalue function depends on the current idiosyn-cratic state and aggregate variables such as thewage and interest rate, which are affected bythe current measure λt . To compute this mea-sure in the next period, households must knowthe current period’s entire measure λt , and anaggregate law of motion, which we call H ,such that λt+1 = H(λt ). We will define H(·)shortly and use standard dynamic programmingnotation to denote future variables (e.g., a′ =at+1 and λ′ = H(λ)). Since our focus is notonly on the stationary equilibrium, but also onthe transition to this equilibrium, we should alsoinclude a time index in the value function andan aggregate measure. For the sake of notation,we omit it.

The value function of a household with networth a and labor productivity z is defined bythe following maximization problem:11

v(a, z,λ) = maxa′ {u(a(1 + i∗) + wz

(9)

+ γ − a′) + βE[v(a′, z′,λ′)|z]}subject to the natural borrowing limit12

a′ ≥ aNB,(10)

and

λ′ = H(λ).(11)

10. Such that if at > a, then agents choose to decreaseasset holdings, that is, at+1 < a.

11. Here we use budget constraint (8) in the one-periodutility function.

12. Since X = [a, a] × Z is bounded, value functionv(a, z,λ) is a contraction mapping. Thus, there is aunique fixed point such that v(a, z, λ) is the solutionof (9).


D. Equilibrium

Let x = (a, z) be the individual state vec-tor of a particular agent. The policy functionassociated with problem (9) is a′ = h(x,λ).Given policy function h(x,λ) we can com-pute l′ = hl(x,λ) and c = hc(x,λ). DefineQ(x,λ, B;h) as the endogenous transition prob-ability of the households’ state vector, whichdescribes the probability that a household withstate x = (a, z) will have a state vector lying inB next period, given current asset distribution λand decision rule h. Therefore,

Q(x,λ, B;h) =∑

(h(x,λ),z′)∈B

Pr(z′ ∈ Z|z).

The aggregate law of motion implied by tran-sition function Q is an object T (λ,Q) thatassigns a measure to each Borel set B, withλ′(·) = T (λ,Q)(·), computed as

T (λ,Q)(B) =∫

X

Q(x,λ, B;h)dλ.(12)

The resource constraint and market clearingconditions for loans, capital, and labor are

K = Ky + Kb(13)

N = Ny + Nb(14) ∫X

hc(x,λ)dλ + K ′ + τ

∫X

hl(x,λ)dλ(15)

= A(Ky)α(Ny)1−α + (1 − δ)K∫X

hl(x,λ)dλ = (Lb)′(16) ∫X

h(x,λ)dλ = K ′(17) ∫X

zdλ = N.(18)

Equation (17) takes into account that loans anddeposits net out to zero. Moreover,

γ

∫X

dλ = τ

∫X

hl(x,λ)dλ.(19)

DEFINITION 1. An equilibrium is an initialdistribution λ0, a vector of prices (w, r, iD, iL)and a pair (h,H) such that: Equations (2), (3),and (5) are satisfied; h is the policy functionassociated with Equation (9) given H ; H(λ)coincides with T (λ,Q); all markets clear; andEquation (19) holds with equality.

DEFINITION 2. A stationary equilibrium is anequilibrium where the probability measure λ isstationary, that is, λ(B) = T (λ,Q)(B) for allB ∈ χ.

IV. QUANTITATIVE EXPERIMENTS

The purpose of the quantitative analysis isto assess numerically the impact of intermedi-ation costs on welfare, including distributionaleffects. The exercises require us to calibrate thetheoretical model (i.e., determine values for aset of parameters for preferences, technology,the stochastic process on labor productivity, andintermediation costs). We choose parameter val-ues consistent with empirical observations in theUnited States and then perform counterfactualanalyses by investigating the effects of alterna-tive intermediation costs on the economy andwelfare.

A. Calibration and Computation

Table 1 summarizes the parameter values andwe describe how they were set. The modelperiod is 1 year.

Utility and Production Technology. Risk aver-sion coefficient θ is set at 2.0, consistent withmicro evidence in Mehra and Prescott (1985).Utility discount factor β and depreciation rateδ are chosen jointly such that the real risk-free interest rate is 2% and the capital to out-put ratio is 3, numbers consistent with theU.S. economy (see Castaneda, Dıaz-Gimenez,and Rıos-Rull 2003). We obtain β = 0.962 andδ = 0.08. The capital income share α is set to0.30, which is in the range estimated by Gollin(2002).

Stochastic Process on Labor Productivity. Wefollow Heathcote, Storesletten, and Violante(2010) and assume that the labor process is acomposition of a permanent and a transitorycomponent, such that:

ln(zt ) = ut + εt ,

ut = ρut−1 + υt ,

where εt and υt are drawn from identically inde-pendent distributions with mean zero and vari-ance σ2

ε and σ2υ, respectively. Using U.S. data,

Heathcote, Storesletten, and Violante (2010)estimate the persistence parameter to be equalto ρ = 0.973 and the average variance from1985 to 2000 of the transitory component andstochastic component to be equal to σ2

ε = 0.0728and σ2

υ = 0.0176, respectively. We use identicalnumbers for our labor process. We approximateeach component with a Markov chain with sevenstates.

8 ECONOMIC INQUIRY

TABLE 1Parameter Values, Baseline Economy

Parameters Values Comment/Observations

θ 2 Risk aversion coefficient based on micro evidence in Mehra and Prescott (1985)α 0.30 Capital income share based on estimations by Gollin (2002)β 0.962 Discount rate of utility such that real interest rate on risk-free asset is 2%δ 0.08 Capital depreciation rate such that capital to output ratio is K/Y = 3ρ 0.973 Persistence parameter of the labor process estimated by Heathcote, Storesletten, and Violante

(2010)σ2

ε 0.0728 Variance of the transitory component estimated by Heathcote, Storesletten, and Violante (2010)σ2

υ 0.0176 Variance of the persistence component estimated by Heathcote, Storesletten, and Violante (2010)η 0.026 Calibrated to match banks’ noninterest expenses over total assets based on Bech and Rice (2009)ν 3.017 Calibrated to match banks’ expenses on capital over banks’ expenses on labor, based on Bech and

Rice (2009)τ 0.00562 Bank taxes over total assets based on Bech and Rice (2009)

Intermediation Costs. We use the direct mea-sures described in Section II to estimate inter-mediation costs. Bech and Rice (2009, pageA88, table A.1) show that in the UnitedStates the average non-interest expenses overassets from 1999 to 2008 is about 3.365%.In our model, this corresponds to overheadcosts, therefore η(w + νrK) = 0.0365. Theyalso show that expenses with occupancy (fixedassets) over expenses with salaries, wages, andemployee benefits is roughly 0.27% from 1999to 2008, which implies that νrK/w = 0.27.13

This implies that in equilibrium ν = 3.017 andη = 0.026. Finally, the same study reports thatthe average value for taxes over total assets paidby banks during the same period was 0.562%,which implies that τ = 0.00562. The total levelof intermediation costs in equilibrium is there-fore equal to τ = 0.03927.

B. Baseline Economy

This section analyzes the properties of thebaseline economy. Table 2 reports the statis-tics for the United States and model economy.The model underestimates the wealth and earn-ings Gini index, but notice that in the model allinequality comes from idiosyncratic shocks tolabor productivity, while in the data part is alsodue to observed differences in individual char-acteristics, such as schooling and experience. As

13. This is the ratio of rKKb/wNb = rKνηLb/wηLb =rKν/w = 0.27. Noninterest expense also contains a thirdcategory (other), which includes a wide range of itemsthat are not reported separately, such as expenses foradvertising and marketing, data processing, and consulting.We assume that the ratio of expenses for capital andlabor for this third category is similar to the remainingnoninterest expenses. Results are not sensitive to smallvariations in ν.

the model abstracts from such households char-acteristics, it should yield lower inequality thanin the data. The model also misses the top tail ofthe wealth distribution. The first row of Table 2shows that in the data, the top 1% of householdshave 29.6% of all wealth. In the baseline model,the top 1% of households hold only 10% of totalwealth.14 The baseline model does a good jobat the lower tail with households at the bottom20% of the wealth distribution holding about−0.4% of total wealth in the data and −0.3% inthe model. Households at the bottom 60% holdabout 8% of all wealth in the data and 7% inthe model.

Interestingly, the model with intermediationcosts does a much better job matching the lefttail of the wealth distribution than the modelwithout intermediation costs (third and fourthrows).15 This occurs because there is much moreborrowing in the model without intermediationcosts than there is in the data. Some studies (e.g.,Castaneda, Dıaz-Gimenez, and Rıos-Rull 2003;Huggett 1993) use an ad hoc borrowing limit tomatch the lower tail of the wealth distribution.Our exercises show that a similar outcome canbe achieved by using a positive wedge between

14. Quadrini and Rıos-Rull (1997) and Castaneda, Dıaz-Gimenez, and Rıos-Rull (2003) note that this is a commonfeature of neoclassical growth models with heterogeneousagents and uninsurable idiosyncratic shocks to earnings.Quadrini (2000), for instance, shows that entrepreneursaccumulate more assets because they face risk associatedwith business activities and higher returns on savings thanworkers. Therefore, entrepreneurs play an active role inshaping the top tail of the wealth distribution.

15. The difference between the third and fourth rows isthe following: In row three, we use all parameters of thebaseline economy reported in Table 1, except for τ, whichwe set to zero (i.e., τ = 0 and η = 0); in row 4, we also setτ to zero, but we adjust the subjective discount factor suchthat the capital to output ratio is similar to the one in thebaseline economy.


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the deposit and borrowing rates. However, themodel with a positive wedge still misses theconcentration of wealth in the upper tail ofthe wealth distribution, as in “standard” Bewleymodels.16

In our model, banks accept deposits and makeloans to households. Because the loans in themodel are unsecured, bank assets correspond toa small fraction of all loans in the data. It isimportant that we do not overestimate such loansin our baseline economy, otherwise, we mightoverestimate the effects of intermediation costson welfare. Section II reports that consumerrevolving credit outstanding, which excludesloans secured by real estate and other securedloans (e.g., automobile loans), is roughly 7.7%of output in the United States.17 In our base-line model, the ratio of unsecured debt to outputis about 1.3%. In the model without intermedia-tion costs, outstanding unsecured consumer debtis roughly 49% or 13% of output, dependingwhether we adjust or not the subjective dis-count factor to match the capital to output ratio(Table 2).

Data from the 2007 Survey of ConsumerFinances (SCF) show that roughly 6% of allhouseholds have negative net worth. In ourbaseline economy about 10% of householdshave a negative asset position. However, in thedata due, for instance, to liquidity issues, somehouseholds with positive net wealth also relyon unsecured debt to smooth consumption andshocks. In fact, according to the 2007 SCFroughly 46% of all households have outstand-ing credit card debt. Therefore, our model doesnot seem to overestimate unsecured consumerlending. Quite the opposite. This implies thatour exercises are likely to generate conservativenumbers on the welfare implications of interme-diation costs.18

In summary, a change in intermediation costshas two effects: a direct effect on the cost

16. When parameter ρ in the stochastic process for laborproductivity is smaller than the 0.97 value we use, the fit ofthe wealth distribution improves. However, the labor processis usually very persistent, sometimes approaching a unit root.

17. We use revolving credit from the Federal ReserveStatistical Release G.19 and divide it by the NIPA value ofGDP. The average over 2004–2007 excludes atypical creditmarket volatility that began in 2008.

18. We abstract from life-cycle behavior. Erosa (2001)shows costly intermediation distorts the life-cycle profileof consumption. Since the age-profile of earnings increasesover the life cycle, agents would like to borrow to increaseconsumption when young. Intermediation costs reduce wel-fare by making consumption “smoothing” over the life cyclemore costly. Hence, our results are likely to underestimatethe true welfare costs of costly intermediation.

10 ECONOMIC INQUIRY

of borrowing and an indirect effect throughgeneral equilibrium price adjustments. Whenintermediation costs are reduced, for a giveninterest rate, the net borrowers’ consumptionpossibility frontier expands, since it is cheaperto borrow to smooth consumption over time.Even net savers might be affected by this directeffect, since in period t they face a positiveprobability of becoming a net borrower in thefuture. In addition to this direct effect, thereis an indirect one: lower intermediation costsimply an increase in the demand for loans, andtherefore the interest rate rises. This affects allagents, increasing borrowing costs and the returnon deposits, and implies a fall in the capital tooutput ratio and wages. Wealth becomes moreunequal. See rows 2 and 3 of Table 2.

We focus solely on the effects of intermedia-tion costs on unsecured consumption borrowingand abstract from entrepreneurial activities.Thus, changes in intermediation costs have rel-atively small effects on long run output. Resultsmight be different if entrepreneurs are creditconstrained and intermediation costs affect theirability to borrow. Antunes, Cavalcanti, and Vil-lamil (2008), for instance, show that inter-mediation costs have a negative effect onentrepreneurial productivity and output evenwhen the interest rate is endogenous. Whenentrepreneurs rely on bank loans to produce(rather than retained earnings or personal funds),intermediation costs may decrease firm size andproductivity.

C. Welfare

We now analyze the quantitative welfareimplications of intermediation costs in theUnited States. We measure the welfare impli-cations by the average permanent consumptionsupplement (e.g., Lucas 1987) that makes house-holds in an economy with benchmark inter-mediation costs (3.927%) as well off as in aneconomy with no intermediation costs. If inter-mediation costs were zero, banks would not needto use labor and capital to intermediate amonghouseholds.19 We also evaluate the case inwhich intermediation costs are reduced but stillpositive and then conduct two counterfactualexercises where costs are above the U.S. level.

19. We set τ = η = 0. This experiment approximatesthe smallest overhead cost of 0.2% observed in the sample,in Ireland in 1994 (see Beck, Demirguc-Kunt, and Levine2009) and provides a check on our model (i.e., τ = 0 shutsdown the wedge friction and returns us to the “standard”Bewley model).

FIGURE 2Interest Rate: Transition from the Baseline

Economy (τ = 3.927%) to an Economy withZero Intermediation Costs

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Welfare Transition Dynamics. One caveat isimportant: In evaluating the welfare effects ofintermediation costs, we cannot focus on steady-state equilibria. The median agent, for instance,in the initial stationary distribution is not nec-essarily the same median agent in the finalstationary distribution, and this is true for allagents ranked according to the wealth distribu-tion. There is social mobility in the economyand comparing value functions of two differ-ent steady states for agents at the same pointof the wealth distribution might be misleading.We calculate each agent’s value function con-sidering the transition from one steady state toanother. This guarantees that we are evaluatingthe welfare of the same agent with and without apolicy change.20 Also, τL is redistributed backto households as a lump-sum transfer, isolatingthe effect of the inefficiency generated by costlyintermediation on welfare, which affects agents’ability to smooth consumption over time.

Figure 2 plots the adjustments of the interestrate from the baseline economy to an economywith no intermediation costs. As discussed pre-viously, the interest rate rises when intermedi-ation costs decrease due to higher demand forunsecured loans.

Welfare Distributional Effects. Figure 3 displaysa three-dimensional graph of the welfare gains

20. If the transition from one stationary equilibrium toanother is fast, one might abstract from transitional effects.However, Figure 2 shows that it takes about 12 years forthe interest rate to reach about 85% of the distance betweenthe first and the second steady-state values.


FIGURE 3Distribution of Welfare Gains: ChangeIntermediation Costs from 3.9% to 0%

2 4 6 8

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of decreasing intermediation costs from 3.927%to 0%. The welfare gains are on the z-axis, whilethe x-axis and y-axis contain the labor shocks(wz) and agent net worth (a), respectively.21

Qualitatively, all agents have positive welfaregains. Borrowing costs are lower since the lend-ing rate decreases from 5.95% to 2.29%. Thisincreases the ability of agents to smooth con-sumption over time, which increases welfare notonly in the lower tail of the wealth distribution,but even for agents with positive net worth.22 Inaddition, a higher interest rate increases incomefrom deposits,23 which increases welfare in theupper tail of the wealth distribution. In the lowertail of the asset distribution, as productivityshocks improve, welfare gains are reduced. Inthe next section we will decompose the over-all welfare effect of intermediation costs into adirect effect and a general equilibrium effect.

Quantitatively, the welfare gains are largerfor agents with negative net worth and persis-tently bad labor productivity shocks. Table 3part (a) reports the average welfare gain perincome percentile. For agents at the bottomdecile of wealth, average welfare gain fromreducing intermediation costs from 3.927% to0% are roughly 7% of baseline consumption.However, welfare gains are substantial even foragents at the top of the wealth distribution. Atthe top decile, the average welfare gains are

21. We use the shocks and the net worth of the eachagent in the period before the policy change.

22. There is a positive probability that an agent withpositive wealth might experience negative labor shocksresulting in negative net wealth.

23. The deposit interest rate increases from 2.02%to 2.29%.

about 0.72% of baseline consumption, which ishigher than the average welfare gains of thoseat the top 25% of wealth.24 The average wel-fare gains for households with the median levelof wealth is roughly 0.60% of baseline con-sumption. The weighted average of the welfaregains of all agents in the economy is 2.05%of consumption equivalent of the baseline econ-omy,25 a substantial amount.

In our model, a reduction in intermediationcosts can be explained by two factors: (1) animprovement in the intermediation technology,and (2) a reduction in intermediation taxes. Animprovement in the intermediation technologyleads to a welfare gain since it implies areduction in the resources “wasted” on financialintermediation. There is also a second effect dueto the fact that a reduction in spreads allowshouseholds to better smooth consumption overtime. We run two experiments to decomposethe importance of the two effects. In one allthe spread is explained by taxes, and the taxrevenue is rebated back lump sum to households.As a consequence, no resources are wastedin intermediation. In a second experiment thewedge between the borrowing and the depositrates is explained by the cost of intermediation.The welfare gains of reducing intermediationcosts are roughly the same for the two case,26

which suggests that most of the welfare gains aredue to improvements in the ability of householdsto smooth consumption over time.

When intermediation costs decrease to 1%instead of 0%,27 the results are qualitatively

24. The non-monotonicity in welfare for endogenousinterest rate case (a) occurs because a higher interest ratebenefits current savers (agents at the top of the wealthdistribution). This non-monotonicity disappears when theinterest rate is fixed; see part (b) of Table 3 and thediscussion in the welfare decomposition below.

25. We could instead calculate an “aggregate valuefunction” as a weighted average of the value function of eachagent. Then, we could calculate the aggregate consumptionequivalent for the baseline economy and for the economyafter the policy change. The welfare gains in this case aresomewhat larger, so we use the method described in thetext. For instance, the aggregate welfare gains using thisalternative measure is about 3.88% when τ decreases fromits baseline value to zero.

26. Notice that total transfers are quite small: less thana third of 1% of income. The case in which intermediationcosts are not rebated back to households leads to largerwelfare gains from reducing intermediation costs than inthe case in which transfers are rebated back to households.However, the difference between the average welfare gainsof the two experiments is less than 5%.

27. Data from Beck, Demirguc-Kunt, and Levine (2009)show that from 1993 to 2006 the average overhead costs overtotal assets for the 10% of countries with the smallest costis 1.1%.

12 ECONOMIC INQUIRY

TABLE 3Welfare Effects: United States

Average Welfare Gain Wealth Percentile

Average Welfare Gain 10% 25% 50% 75% 90%

Benchmark, τb = 3.927%Part (a): Endogenous interest rate

τ = 0% 2.05 7.02 3.17 0.60 0.25 0.72τ = 1% 1.14 3.96 1.73 0.41 0.21 0.35τ = 6.5% −0.12 −0.46 −0.12 −0.02 −0.02 −0.05τ = 12% −0.30 −1.18 −0.24 −0.04 −0.03 −0.08

Part (b): Exogenous interest rateτ = 0% 2.97 7.83 4.38 1.66 0.53 0.18τ = 1% 1.90 5.87 3.07 1.18 0.49 0.2τ = 6.5% −0.16 −0.57 −0.20 −0.02 −0.02 −0.02τ = 12% −0.32 −1.20 −0.25 −0.07 −0.07 −0.07

similar but smaller; see row 2 of Table 3,part (a). In this case, we decrease τ from itsbaseline value of 0.562% to 0% and changeη, such that overhead costs over total assets(η(w + νrK) = 0.01) is equal to 1%.28 Thisexperiment is similar to a boost in productivityin the intermediary sector. The average welfaregain is 1.14% of consumption equivalent to thebaseline and welfare effects are larger in thelower tail of the wealth distribution. The bottomdecile of wealth has an average welfare gain of3.96% of consumption equivalent.

As one would expect, the results depend onthe coefficient of risk aversion. When σ = 1 andτ decreases from 3.927% to 1%, average welfaregains are only 0.1% of consumption equivalentto the baseline economy.29 This is much smallerthan when σ = 2. Agents at the bottom decile ofwealth would still have an increase in welfare ofroughly 0.61% of the consumption equivalentto the baseline. At the upper tail of the wealthdistribution, welfare gains are positive but small.When σ decreases agents are less risk averse andthe cost of consumption fluctuations decreases.

Counterfactual Experiments. We conduct twocounterfactual experiments to investigate whatwould happen to welfare in the United Statesif intermediation costs were higher, that is, weincrease τ = 3.927% to 6.5% and 12%, roughlythe levels in Mexico and Brazil, respectively.30

The last two rows in Table 3 parts (a) and (b)

28. We could also keep τ at its baseline value andchange η such that τ + η(w + νrK) = 0.01. Results areroughly the same.

29. In order to match the same moments of the datadescribed in Table 1, we set the values of β and δ to 0.9738and 0.08, respectively.

30. See Beck, Demirguc-Kunt, and Levine (2009): over-head costs over total assets in Mexico are about 6.2%, while

show that average welfare declines by −0.12%of consumption equivalent to its baseline levelfor the case that corresponds to Mexico, and by−0.30% of consumption equivalent for Brazil,when the interest rate is endogenous. The resultsare roughly similar when the interest rate isexogenous. The point of these experiments isto show that when the wedge between the bor-rowing and deposit rates is large, the welfareeffects of intermediation costs are small. Thisoccurs because households hold little debt whenthe wedge is large, and thus there is little scopefor welfare gains, which accrue largely throughincreased borrowing.31 As intermediation costsdecrease and more households rely on debtto smooth consumption, the scope for welfareimprovements from reducing the interest ratespread increases. Overall, Table 3 shows that thewelfare effects of reducing intermediation costsare nonlinear.

Welfare Decomposition. As explained previ-ously, there are two effects on welfare aftera change in intermediation costs: a directeffect and a general equilibrium one. Here wedecompose the welfare change into these twoeffects. When intermediation costs decrease,for a given interest rate, households’ abilityto smooth consumption over time improves.There is also an indirect effect on price adjust-ment as lower intermediation costs increase the

bank’s tax over total assets is roughly 0.3%. The counterfac-tual exercises are not designed to capture the welfare gainsof reducing intermediation costs from the Mexican or Brazil-ian level to the U.S. level, since this would require one tore-calibrate all parameters of the model economy to matchstatistics of the Mexican or Brazilian economy.

31. When τ = 6.5% (12%), then the debt to outputratio is only 0.27% (0.23%) and the percent of agents withnegative net worth is 3.19% (2.25%).


FIGURE 4Average Welfare Gain Per Asset Value from

Changing Intermediation Costs from 3.927%to 0%.

−2 0 2 4 6 8 10 12 14 16−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

assets (a)

aver

age

wel

fare

gai

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ExogenousEndogenous

Notes: Black solid line: endogenous interest rate; dottedblack line: exogenous interest rate.

demand for loans and therefore the interestrate. Such adjustments offset in part the bene-fits of lower intermediation costs for those withnegative net wealth, but they increase interestincome for those in the upper tail of the wealthdistribution.

Table 3, part (b) reports the welfare gainsfrom reducing intermediation costs for an exoge-nous interest rate. At the aggregate level, wel-fare gains are about 45% and 60% larger foran economy with an exogenous interest ratethan for an economy with endogenous priceadjustments when intermediation costs decreasefrom the baseline value to 0% and 1%, respec-tively. Figure 4 shows the average welfare gainfor each asset value when the interest rate isexogenous (dotted line) and endogenous (solidline), and intermediation costs decrease fromthe baseline level to 0%. For the lower tail ofthe wealth distribution, welfare gains are largerwhen the interest rate is exogenous, but forthe right tail of the wealth distribution, dueto higher interest income, welfare gains arelarger for the endogenous interest rate case.The two effects are quantitatively significant.Therefore, as in Antunes, Cavalcanti, and Vil-lamil (2008) and Castro, Clementi, and Mac-Donald (2004), policy reforms aimed at improv-ing intermediary efficiency would have strongerimpacts in economies open to financial capitalflows.

V. CONCLUDING REMARKS

This paper developed a growth model inwhich agents face uninsurable idiosyncraticshocks to labor productivity, a borrowing limit,and costly financial intermediation. Intermedia-tion costs generate a wedge between the loanand deposit rate. We calibrated the model tomatch key statistics of the U.S. economy andperformed counterfactual experiments. Reduc-ing intermediation costs leads to two effects. Fora given interest rate, borrowing costs decrease.The net borrowers’ consumption possibilityfrontier expands, and even households with pos-itive net wealth can benefit because they mayneed to borrow in the future to smooth con-sumption. There is also an indirect effect: lowerintermediation costs imply an increase in thedemand for loans, and therefore the interest raterises. Such price adjustments offset part of thedecrease in borrowing costs and increase interestincome.

Quantitatively, we show that the welfareimplications of intermediation costs for theUnited States are large. The average welfaregain from reducing intermediation costs from3.927% (the U.S. level) to 1% (the 10th per-centile of countries with the smallest overheadcosts) corresponds to about 1.14% of consump-tion equivalent of the baseline economy whenthe interest rate adjusts and 1.90% for a smalleconomy integrated in world financial markets.We also show that there are important distribu-tional effects. For agents at the bottom decile ofwealth, welfare gains are about 3.96 (5.87)% ofconsumption equivalent when the interest rateis endogenous (exogenous). At the top decile ofwealth, welfare gains are 0.35% and 0.2% whenthe interest rate is endogenously and exoge-nously determined, respectively. For economieswith large wedges such as Mexico or Brazil,we show that there may be no welfare gainsfrom modest reductions in intermediation costsbecause when the spread between deposit andborrowing rates is large, households do notinsure against idiosyncratic income fluctuationsby borrowing.

Our model with an interest rate wedge alsoprovides insight into the Bewley model. Weshow that the wedge allows us to match bet-ter additional dimensions of U.S. consumptiondata, as well as the lower 60% of the wealthdistribution. The model continues to miss theupper tail when the labor productivity processis highly persistent. We also check sensitivityto the coefficient of risk aversion and find that

14 ECONOMIC INQUIRY

welfare is much lower when σ is low. The rea-sons are twofold: First, a lower σ implies alower preference for consumption smoothing.Second, in equilibrium there is less borrowingand the direct impact of a reduction in interme-diation costs affects fewer households. Finally,we abstracted from default risk, but conjecturethat welfare gains from reducing intermediationcosts would be lower in a model with endoge-nous default because default would increase theinterest rate. Of course, the quantitative magni-tude of this effect remains an open question.

Our exercises show that policies aimed atreducing financial sector taxes and inefficiency,such as those related to bank entry restrictions,government ownership of banks, and regula-tion, can have a large impact on consumptionloans and household welfare, especially for poorhouseholds, when credit markets are active. Weuse our model to compute the welfare gains froma reduction in intermediation costs and abstractfrom the political and operational costs of suchpolicies. While the net effect is crucial fordetermining the desirability of a given policy,our model provides useful benchmark estimatesfor the welfare implications of costly financialintermediation.

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