This paper attempts to explain how cost of intermediation can be reduced. One solution we postulate is subsidizing the cost of intermediation. The model uses ex-ante identical, spatially separated agents in an overlapping-generations framework. Agents receive relocation shock when they become old. We conclude that government cannot subsidize the cost of intermediation completely but it can reduce cost partially

Lahrech, Abdelmounaim

Patil, Hemant

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Southern Illinois University CarbondaleOpenSIUCDiscussion Papers Department of Economics2006Decreasing Cost of IntermediationHemant PatilSouthern Illinois University CarbondaleAbdelmounaim LahrechFollow this and additional works at: http://opensiuc.lib.siu.edu/econ_dpThis Article is brought to you for free and open access by the Department of Economics at OpenSIUC. It has been accepted for inclusion in DiscussionPapers by an authorized administrator of OpenSIUC. For more information, please contact opensiuc@lib.siu.edu.Recommended CitationPatil, Hemant and Lahrech, Abdelmounaim, "Decreasing Cost of Intermediation" (2006). Discussion Papers. Paper 41.http://opensiuc.lib.siu.edu/econ_dp/41Decreasing Cost of IntermediationAbdelmounaim Lahrech and Hemant Patil §May 11, 2005AbstractThis paper attempts to explain how cost of intermediation can be reduced. Onesolution we postulate is subsidizing the cost of intermediation. The model uses ex-anteidentical, spatially separated agents in an overlapping-generations framework. Agentsreceive relocation shock when they become old. We conclude that government cannotsubsidize the cost of intermediation completely but it can reduce cost partially.§ Deaprtment of Economics, Southern Illinois University1 IntroductionFinancial intermediation is a mechanism through which funds are transferred from lenders(savers) to borrowers. This is conventionally accepted to be a very important function. Butmost of the modern macroeconomic theory almost ignores intermediation in that changes inintermediation activity are presumed to be an outcome of changes in real economic activity.The strong correlation between financial intermediation and long-run growth has been em-phasized in the intermediation literature for long time since Gurley and Shaw (1955) firstpostulated it. They argued that both real economic activity and financial intermediationactivity influence each other and the causality runs both ways making both endogenous.But there is a scarcity of any empirical evidence except for few notable exceptions. At thispoint it is sufficient to say that financial intermediation is not looked at seriously by themacroeconomic profession.This paper clsoely follows Bencivenga and Smith (2003) except in one respect, we allow forvariable cost and later we analyse whether government can subsidise cost of intermediation.We use overlapping-generations framework with spatial separation and limited communica-tion between the agents inhabiting the separate locations. We find that government canbring down the cost of inetrmediation partially.The rest of the paper proceeds as follows. Section 1 presents the basic framework of themodel. Sections 2,3,4 and 5 analyse the equilibrium in the economy. Section 6 incorporatesthe governemnt by allowing it to subsidise the cost of intermediation. Section 7 concludes.2 The environmentWe consider an overlapping generations framework with an infinite sequence of two-period-lived agents in each period t ≥ 1. There are two locations across which agents are distributed.1The islands are symmetric in every respect. At each date a continuum of ex-ante identicalagents with unit mass is born at each location.In each location in each period a single final good is produced with constant returnsto scale technology.The production process uses both labor and capital as inputs. Theproduction function has the Cobb-Douglas form F (Kt, Lt) = AKαt L1−αt ,with α ∈ (0, 1).Letting kt = Kt/Lt,the production function becomes f(kt) = Akαt . Also, we assume thatcapital depriciates completely in the production process.Each agent is endowed with one unit of labor which he supplies inelastically. Agentsonly value consumption when they are old. Let ct denote the consumption of agent born att. Then the agent has lifetime utility level u(ct) = c1−ρ/(1 − ρ).All the agents are identicalex-ante.Based on Bencivenga and Smith (2003),we assume that at each date an agent can tradeonly with agents who live at his current location and there is no communication betweenislands. Between dates t and t+1, each agent faces the probability pi ∈ (0, 1)that he will berelocated to the other island.When agents are relocated, they lose contact with agents agentsin their original location. Agents in their new location do not know the capital holdings ofrelocated agents. So, relocated agents need currency in the new location. On the other handnon-relocated agents have both their capital holdings and currency.Stochastc relocation posesa risk for agents: they have to convert capital holdings into currency if relocated. They willrequire insure to cover against relocatio shock.Agents can hold two assets: currency and physical capital. Each unit of final goodinvested at period t becomes capital at period t+ 1.Capital is immobile. Agents lose all thecapital assets if relocated. We assume that young agents can save through banks. Utilizationof bank is costly. We assume that there are two components of cost of intermediation. Thereis a fixed cost and a variable cost which decreases as the savings through banks increase.2For simplicity, we assume the cost that the agents have to face is (φ − gst), where φ is apositive fixed cost. There are various ways in which one can justify the decreasing costof intermediation. The most plausible arguement, however, in the context of developingcountries is that higher savings makes bank penetration better, reducing the costs associatedwith accessing the intermediaries. Agents can also choose to save autarkically. This preventsthem from sharing the relocation risk.the timing of events is as follows: beginning of the period, production takes place. Rentalrate on capital and wages are disbursed. Agents get the prevailig wage rate as they aresupplying labor inelastically. Agents don’t consume when they are young so they saveeverything (their real wage). Agents make two set of choices whether to save the moneyautarkically or to save it through banks. If he chooses autarky, he has to decide how toallocate them between cash and capital assets. If banks are used they make the portfoliochoices. The goods market clear: old agents consume, government makes purchses and finalgoods are invested. Later some young agents suffer relocation shock.1The young relocatedagents have to leave the island immediately. They withdraw cash from the banks and leave.They cannot liquidate the physical capital they hold. Therefore, relocated agents who saveand invest autarkically lose the value of their capital invetsment. Agents who are fortunate tohave escaped the relocation shock do not take any action until the beginning of next period.Both relocated and non-relocated agents make purchases for consumption when they enternext period.Thre is a governmemt in each island which prints money and purchases final good. LetMt be the nominal money supply per young agent at t. Mt evolves acoording toMt+1 = σMt,with σ being chosen once and for all at the beginning of time. Letting pt denote the price1Note that not all the agents receive the relocation shock but all of them have common prior probabilityabout the shock.3level in period t, the seignorage revenue of the government at t is:(σ−1σ)MtptGovernment uses this money to purchase final good. We consider a case where govern-ment does not run contractionary policy.3 Factor MarketsAs noted in the previous section the production takes place at the begiinning of period tand rental rate of capital and wage income is paid. Let wt and rt denote the real wage andreal rate of return on capital.Letting the firms behave competitively gives us following factormarket equilibrium conditions:rt = f′(kt) = αAkα−1t (1)wt = f(kt)− ktf ′(kt) = w(kt) = (1− α)Akαt (2)4 Economy with IntermediationAs mentioned earlier, when young agents save through banks they incur cost which is adecreasing function of their saving. Since agents save all the income through intermediariesthe cost of intermediation will be (φ−gwt). So, effectively they deposit [wt(1+g)−φ] in thebank.Banks,in turn, assure them gross real return of ct if they are relocated and gross realreturn of at for per unit of the final good deposited, if they are not relocated.2Banks allocate2Relocated agents are withdrawing early and non-relocated agents are withdrawing late.4their deposits between currency holdings and capital investment before the relocation shockoccurs. Let γbt be the fraction of total deposits held as currency and (1−γbt) be the fractionof total deposits invested in capital assets. A bank chooses reserve to deposit raio (γbt) tomaximize the expected utility of the representative depositor. The bank faces the followingconstraints:pict ≤ γbt(ptpt+1)(3)The left hand side of this constraint is the expected cost of the bank where pi is theprobability of receiving the relocation shock. And the right hand side is the retuns that thebank gets from holding currency. Note that bank has to hold cash assets in order to pay tothe relocated agent.And pt/pt+1 is simply the gross real rate return of currency.(1− pi)at ≤ (1− γbt)rt+1 (4)The left hand side is again the expected returns that have to be paid to the non-relocateddepositor and right hand side is the returns that bank gets from investment in capital assets.The prices and real rate of return on capital are decided in goods and factor marketsrespectively. For bank they are exogenous. Then the bank’s problem is to maximize expectedutility of the depositor by choosing γbt, ct and dt. More specifically, bank solves the followingproblem:maxγbt(wt(1 + g)− φ)1− ρ[pi(ct)1−ρ + (1− pi)(at)1−ρ](5)subject to the constraints (3) and (4) and non-negativity.Defining gross nominal interest rate It = rt+1(pt+1/pt), the optimal reserve-to-deposit5ratio of a bank at time t is3 :γbt =1(1−pipi)I(1−ρ)/ρt + 1≡ γb(It) (6)We can now derive the returns that bank can can offer to relocated and non-relocatedagents using (3),(4)and (6). More specifically, at = I1ρt ct will be the optimum return. Whenthe nominal interest rate is It > 1, the relocated agent does worse than the non-relocatedagent. Bencivenga and Smith(2003)various properties of the functionγb(I), we are simplyrestating those properties here:(a)γb(I) = pi(b)lim I →∞ = 0(c)Iγ′b(I)γb(I)= −(1−ρρ)[1− γb(I)] < 0Several important conclusions can be drawn from these properties. First of all setting nomi-mal interest rate equal to unity will not make agents (through banks)to hol only currency.Finally, the last property shows that increase in nominal interest will cause banks to moveaway from holding currency.5 Equilibrium with Intermediated SavingLet us first look at the money market. Banks will want to hold a fraction(γb) of their totaldeposits in the form of currency. This gives us the per capita demand for real balances. Themoney market will clear ifMtpt= mt = γb(It) (w(kt) [1 + g]− φ) (7)3Bencivenga and Smith(2003) derive the same expression for γbt with fixed cost of intermediation.6Given that banks will hold rest of their total deposits (1 − γbt)in capital assets, we getthe following per capita rate of capital accumulationkt+1 = [1− γb(It)] [w(kt) (1 + g)− φ] (8)Following condition determines the evolution of gross nominal interest rate.As definedpreviously,It = rt+1(pt+1pt)= rt+1σ(mtmt+1)(9)Substituting (1) and (7) into (9) givesIt =σf ′(kt+1)γb(It) [w(kt)(1 + g)− φ]γb(It+1 [w(kt(1 + g)− φ)]) (10)or,γ(It+1) =σf ′(kt+1)γb(It)It≡ Ω(kt+1, kt, It) (11)This completes our discussion of equilibrium.6 steady stateThe steadys state solution will have It = It+1 = I and kt = kt+1 = k. Substituting it in (10)givesI = σf ′(k) (12)which impliesk =(σαAI)1/(1−α)(13)Now we can express the amount deposited in the bank asw(k)[1 + g]− φ = (1− α)(1 + g)A(σαAI)α/(1−α)(14)7Substituting (14) into (8) and using other conditions we get11− γb(I) = (1 + g)(1− αα)(Iσ)− ν(Iσ)≡ H(I) (15)where ν = φ(αA)1/(1−α). Again, we restate the properties of the function H(I) from Ben-civenga and Smith (2003) with some obvious variations.4(a′) H ′(I) holds if and only ifI ≤ σ[(1−α)2(1+g)αν](1−α)/α≡ Iˆ(b′) H(I) ≥ 0 holds if and only if[(1−α)(1+g)α](1−α)/α≥ I(c′) H(I) is a concave function of I.These properties will yield the steady state solutions which are discussed in detail Bencivengaand Smith (2003).7 Subsidized IntermediationTill this point we have largely followed Bencivenga and Smith(2003). We know that thecost of intermediation has fixed and variable component. Now we argue that governemntsubsidises the agent by making a lumpsum transfer equal to φ while he receives his real wage.Note that we are now allowing only fixed cost of intermediation. We consider two cases. Inthe first case, government subsidises the agent completely by making a trasfer equal to the4The properties of H(I) are slightly different as we use the variable costs.8fixed cost he has to incur in order to save through bank. While in other case governmentsubsidises the agent by offsetting only a fraction of fixed cost.7.1 Complete SubsidizationIn this case we assume that government uses all its seignorage revenue to subsidise a repre-setative agent who incurs the fixed cost of going to bank. This will implyw(kt)g =(σ − 1σ)Mtpt= φ (16)Given the above balanced budget constraint, government can solve for σ or the money growthrate which offsets the fixed cost of intermediation. We getσ =mtmt− φ =MtMt − φPt < 1∀φ > 0 (17)Since pt is subject to change in every time period, we will violate the condition that σ isconstant. Even if we relax the constant σ assumption, we still have to deal with a deflationarysituation.The nominal inetrest rate will be less than one and most importantly since at =I1/ρt ct, the non-relocated agents will have to suffer. Hence, complete subsidization is notfeasible.7.2 Partial SubsidizationNow we look at the situation whether government can offset the fixed cost partially. Here weassume that governemnt does not try to set σ to offset cost but simply passes on whateverseignorage revenue it makes given a predetermined value of σ. This will imply that govern-ment will be able to reduce some of the fixed cost. The exact amout of deposit made byagent will be then[w(kt) +(σ−1σ)mt − φ]. The new money market equilibrium will bemt =γb(It) [w(kt)− φ]1− γb(It)(σ−1σ) (18)9Also, the evolution of gross nominal interest rate will change. We getIt = σf′(kt)(γb(It) [w(kt)− φ]1− γb(It)(σ−1σ) )( 1− γb(It+1) (σ−1σ )γb(It+1) [w(kt+1)− φ])(19)The currency-to-deposit ratio will beγb(It+1) =σf ′(kt+1)γb(It)[w(kt) +(σ−1σ)mt − φ]It[w(kt+1) +(σ−1σ)mt+1 − φ] (20)The steady state value of gross nominal interest rate will remain unchanged. Here increas-ing the growt rate of money will increase capital stock and output as in Bencivenga andSmith(2003).5 However, one can set σ in such a way that it rules out the bad steady state.8 ConclusionIt is often remarked that in developing countries low level of intermediation is caused dueto high cost of intermediation. The argument is based on the lack of penetration of bankingactivity. Here we presented a case where the cost of intermediation can be subsidised by thegovernment. Also, we analysed the case where cost of intermediation is a decraesing functionof the amount of savings.There are various directions in which the present analysis can be extende. One importantissue is why do the banks hold excess reserves of currency when the required reserve level islow. This issue is important even in case of developed countries. One can also try a moresophisticated game-theoretic approach to analyse this. There is also the possibilty that bothagents and banks receive exogenous shocks. The issue of why agents only deposit a fractionof their income in the banks is also important.5Their results are restricted to only certain steady states10References[1] Bencivenga, Valerie and Smith, Bruce D., 1998, Economic Development and FinancialDepth in a Model with Costly Fiancial Intermediation, Research in Economics, 52(4),363-86.[2] Diamond, Douglas W. and Dybvig, Phillip H., 1983, Bank Runs, Deposit Insurance,and Liquidity, Journal of Poliical Economy, 91(3), 401-19.[3] Schreft, Stacey L. and Smith, Bruce D., 1997, Money, Banking and Capital Formation,Journal of Economic Theory, 73(1), 157-82.[4] Schreft, Stacey L. and Smith, Bruce D., 1998, The Effects of Open Market Operationsin a Model of Intermediationand Growth, Review of Economic Studies, 65(3), 519-50.[5] Schreft, Stacey L. and Smith, Bruce D., 2002, The Conduct of Monetary Policy witha Shrinking Stock of Government Debt, Journal of Money, Credit and banking, 34(3,part2), 848-82.[6] Smith, Bruce D., 2002, Taking Intermediation Seriously, Journal of Money, Credit andbanking, 65(3), 519-50.11

Decreasing Cost of Intermediation

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Decreasing Cost of Intermediation

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