Inflation and Financial Sector Size

Preliminary,commentswelcome INFLATIONAND FINANCIAL SECTOR SIZE* William B. English Federal Reserve Board 20th and C Streets,NW Washington,DC 20551 May 1991 Revised: April 1996 ABSTRACT Traditionallythe cost of expected inflationhas been seen as the “shoeleathercost” of going to the bank more often. This paper focuses on the other side of these transactions--i.e., on the increased productionof financial servicesby financial firms. I construct a model in which householdsmust make purchaseseither with cash or with costly transactionsservicesproducedby firms in the financial services sector. One can think of these servicesas being the use of a credit card or other method of paying without cash. In the model, a higher inflation rate leads householdsto substitute purchasedtransactionsservices for money balances. As a result, the financial services sector gets larger. A test of the model using cross-sectionaldata finds that the size of a nation’s financial sector is strongly affected by its inflation rate. The empirical results provide an alternativeway to measure the costs of inflation. These costs appear to be large. JEL Classification:E31 * The analysis and conclusionin this paper are mine alone and do not indicate&oncurrenceby other members-ofthe research staffs,by the Board of Governors,or by the Federal Reserve Banks. I thank seminar participantsat the University of Pennsylvania,the Universityof Maryland, Johns Hopkins University,and the Federal Reserve Board for useful comments on earlier drafts of this paper. Mauricio Fernholz provided excellent researchassistance. All-remainingerrors are mine.

-2- Introduction Traditionally,the cost of expected inflationhas been viewed primarilyas the “shoeleathercost” of going to the bank more often, as in the familiar Baumol-Tobinparable (Baumol,1952; Tobin, 1956). In this view, households reduce their average holdings of cash by making smallerwithdrawalswith greater frequency,and the cost of the inflation is the utility loss associatedwith trips to the bank, waiting in line, etc. This paper focuses on the banks’ side of these transactions:in order to satisfy the increasedcustomer activity, banks may need to hire additionaltellers, build more and larger branches, or make other costly investmentsin automationor technology. Thus, the cost of inflation can be viewed, at least in part, as the result of resourcestransferredto the financial sector to accommodatethe increasednumber of transactionschosen by households as they attempt to shift the cost of holding currency onto others. These resourcesare a social loss because if inflationwere lower, the resourcescould be used directly to increase productionof consumer goods. This focus on the effects of inflationon the size of the financial sector is not new. Bresciani-Turroni, in his history of the German hyperinflation,notes that inflationcaused a ‘hypertrophyof the banking system~ in late 1922 and 1923 (Bresciani-Turron,i 1937, p. 215). For example he reports that more than 400 new banks were established.in1923, the peak year of the hyperinflation. This was more than four times the number establishedin 1922, and six times the number establishedin 1920 and 1921. At the same time, existingbanks were extendingtheir branch networks and greatly increasingtheir employment. There were 30,489 employeesat the ‘DV banks (Deutsche

-3- Bank, Diskonto-Gesellschaft, DarmstadterBank, and Dresdner Bank) in 1920. By 1922 there were more than 45,000 employees,and by the fall of 1923, when the inflationwas at its peak, almost 60,000. Bresciani-Turroninotes that the increase in banking activity reflecteda higher volume of financialtransactionsrather than an increase in real activity. Indeed, the number of current accounts at the three largest “D” banks rose from less than 1.5 million at the end of 1920 to an estimated 2.5 million at the end of 1923. The rapid expansionin the banking sector generatedby the German hyperinflationreversed sharply following stabilization. The number of new banks establishedfell by more than 80 percent in 1924, to just 74. The number of employeesat the four ‘Dn banks declinedby nearly a half by the end of 1924, and the number of current accounts at the three largest “D” banks fell by three-quartersover the same period, A similar pattern of decline in the size of the financial sector following stabilizationwas noted by Weber (1986)in his study of the ends of hyperinflationsin Eastern Europe in the 1920s. He cites one estimate that 4,000 of 12,000bank officialsin Budapest became unemployedfollowingthe stabilizationin Hungary, and he estimatesthat 10,000 bank employees lost their jobs following the Austrian stabilization. In order to address this issue, I constructa model in which households can make purchaseswith cash or with purchasedtransactions services. A number of recent papers (e.g.Cole and Stockman, 1992; Schreft, 1992; Gillman, 1993; Dotsey and Ireland, 1993) present models in which households can transactwithout money at some cost in terms of labor. While these models allow for alternativemethods of transacting,the focus on labor costs seems to capture primarilythe cost of household “home production”of financial services. In

-4contrast,the approach taken here is to allow agents to make purchases with “transactionsservices~ suppliedby banks or other financial firms as in Fischer (1983),Prescott (1987),and Aiyagari et al. (1995). In the model, households are constrainedto make purchases either with cash or with purchasedtransactionsservices.1 One can think of these servicesas interest-bearingchecking accounts,money market mutual funds, overdraft services,or credit cards. An increase in the inflation rate induces householdsto substitutetransactions services for real balances. As a result, increasesin the inflation rate increase the size of the financial sector. I test this implicationof the model using cross-sectional data on financial sector size and inflation rates. The results suggest that the effect of inflationon the size of the financial sector is significantboth economicallyand statistically. The empiricalmodel indicatesthat the effect of a 10 percent inflationin the United States would be to increasethe share of GDP produced in the financial sector by almost 1-1/2 percentagepoints. This estimate of the cost of inflation is larger than those found in earlier studies, such as those of Fischer (1981)and Lucas (1981),although it is similar to that found in a recent study by Lucas (1994). I. The Model The economy contains a continuumof identicalagents, indexed by ic[O,l], each with infinitehorizons. Each period they supply a 1. One could also require firms to transactwith cash or transactionsservices. This issue is discussedbelow. In practice, firms’ purchases of cash management servicesare likely very important.

: -5unit of labor inelasticallyand receive a wage, w.2 They hold two assets: capital and money. Each period the capital is rented to firms at a rental rate r. Agents must purchase their consumptionfor the period using their start-of-periodmoney balances or by purchasing transactionsservices. One could motivate this constraintby assuming that households include two individualagents, one of which works while the other shops (see,for example,Lucas and S-tokey, 1987). At the end of the period, households receive their wage and a cash transfer from the government,and they pay for the purchasesmade with transactionsservices as well as for the servicesthemselves. Then they choose their money and capital holdings for the start of the next period, and the period ends. The economy has three types of firms. Firms in the consumptiongoods sector produce one of a continuum of consumption goods. The market for each of the goods is competitive. Firms in the capital goods sector produce capital. Firms in the transactions services sector produce transactionsservices. As discussedbelow, capital and transactionsservices can be purchasedwithout cash or transactionsservices. Firms in all three sectors are competitive, and productionin each sector requiresboth capital and labor. A. The TransactionsTechnology There is a continuum of goods in the economy indexed by j, je[O,l]. Each good is assumed to be purchasedwith a separate transaction. Agents can pay cash, or incur a fixed cost, q, to make the purchasewithout cash. Because the cost of making a purchase 2. If labor supply were not inelastic,then inflationwould affect labor supply. Since my focus here is on the effects of inflationon the size of the financial sector, I do not take account of this possible effect. See Aiyagari et al. (1995)for a relatedmodel that includes an effect of inflationon labor supply.

-6without money is independentof the size of the transaction,agents will make small transactionswith cash and large ones with transactionsservices. This approach is similar to that taken by Whitesell (1989,1992) in studies of the optimal use of alternatives to cash purchases,althoughWhitesell (1992)allows for more than one alternativeto cash and both a fixed and a proportionalcost of transactingwithout cash. Other recent models take a variety of approachesto get a margin along which agents adjust to reduce cash transactionsin the face of higher inflation. In Gillman (1993)and Aiyagari et al. (1995)the cost of making a purchasewithout cash is assumed to be proportionalto the size of the transaction,and the size of the cost differs exogenouslyacross goods. In Schreft (1992)and Dotsey and Ireland (1993),the cost is assumed to be larger for goods purchased farther from the agent’s location on a unit circle. The cost structureassumed here has the intuitivelyappealing implicationthat cash transactionstend to be smaller than check or credit purchases. Evidence on actual household transactionscan be obtained from the preliminaryresults of the 1995 Survey of Consumer TransactionsAccounts Usage, commissionedby the Board of Governors of the Federal Reserve System and conductedby the Universityof Michigan Survey Research Center. This survey, conductedin May 1995, showed that the mean size of household check transactionswas $80, the mean size of credit card purchaseswas $54, and the mean size of debit card transactionswas $24. By contrast,the mean cash purchasewas $11. The pattern of transactionssizes is similar to the one prevailingin the mid-1980s, as reportedby Whitesell (1992). The 1995 survey showed that on average householdsused checks to make 15 purchasesa month, credit cards to make 4 purchases,debit cards to make 1

“purchase, and cash to make 29 purchases. Thus, cash was used for nearly 60 percent of purchases,but those purchases accountedfor less than 20 percent of the dollar volume of expenditures. The nature of the cost of transactingwithout cash differs across the papers in this area. Gillman (1993),Dotsey and Ireland (1993),and Schreft (1992)all assume that the cost is a labor cost-perhaps focusing on the purchaser’snuisance costs of writing a check, keeping records,waiting while the store verifies the check, etc. By contrast,this paper, like Prescott (1987)and Aiyagari et al. (1995), focuses on the productionof transactionsservicesby financial firms. The model in Fischer (1983)allows for both household productionof transactionsservicesand purchases of transactionsservicesfrom banks, with their marginal costs equalized in equilibrium. Whitesell (1989)suggests a number of types of costs, includingnuisance costs, seller charges, and bank charges,but his model does not focus on the productionof transactionsservicesor their welfare implications. It would be straightforwardto add to the model an additionalnuisance cost of using transactionsservices. Doing so would clearly raise the welfare cost of inflation,but would not greatly change the results of 3 the model. In the model presentedhere agents pay a fixed cost for transactionservices. In practice,of course, the purchaser generally does not actually pay the fixed cost of the transaction. While some banks do have per-checkfees on some accounts,and some sellershave different prices for cash and credit purchases,these direct payments 3. The nuisance costs could even be negative, especiallyfor large transactions,owing to the possibilitythat large amounts of cash could be lost or stolen.

-8are the exception.4 More commonly,the costs of transacting without cash are implicit--feesand lower interest rates paid on checkableaccounts, for example. In addition,decisionsmade by retailers,who absorb a part of the transactionscost, likely generate effects much like those of a fixed cost. For example, some stores have a minimum size for credit card purchases. Alternatively,stores selling products that generallyyield small transactionsizes (e.g., newsstandsor coffee shops) are presumablyless likely to accept checks or credit cards because the associatedcosts would require too large a percentageincrease in prices. The assumptionthat the cost of transactingwithout cash is independentof transactionsize may not be strictlytrue for very large transactions,but it seems more reasonablethan the assumption that the cost is proportionalto the transactionsize. The cost of clearing a personal check through the payments system, for example, is likely the same virtually regardlessof the amount of the purchase. For example, the Federal Reserve System’s functionalcost analysis reports a fixed estimatedcost for individualcheck transactions regardlessof size (FederalReserve System, 1995). The same should be true for credit card transactions. For retailers,the costs of verifying checks and credit card accounts as well as the subsequent paperwork should not depend on the size of the transaction (although retailersmay be more likely to verify large transactions). As for purchasers,the nuisance costs of writing the check or waiting for the clerk to handle the transactionare likely very similar for widely different transactionsizes. 4. Of course, a higher credit price would amount to a proportional, rather than a fixed, cost of transactingwithout cash (seeAiyagari et al., 1995, p. 9).

-9- 1 assume that capital goods can be purchasedwithout cash at 5 no cost. Not doing so would generatean investmentdistortionas in Stockman (1981). Aiyagari et al. (1995)assume that households augment their capital holdings by purchasingequal amounts of each consumptiongood. As a result, capital is purchasedin part with cash and in part with transactionsservices. Purchasesof capital are likely very large, however, compared to the average household purchase. For example, the average size of a check purchase, includingpurchasesby businesses,is about $1150,while the average size for households,as noted above, is only $80 (Humphrey,et al., 1995). Thus the assumptionin Aiyagari et al. may greatly overestimatethe cash portion of capital purchases. One could model purchases of capital in a manner similar to that used for consumption goods here--allowingthe size distributionof capital goods purchases to differ from that for consumptiongoods. Implicitly,I am assuming that capital goods purchasesare so large that they can be made without cash at negligible cost. B. The Household’sProblem The representativehousehold gets utility in a given period based on consumptionof the various consumptiongoods: 1 @(j)cjl-y u= J dj o l-y where c. is the consumptionof good j, y is the inverse of the J intertemporalelasticityof substitution,and ~(j) is a weighting function. I assume that ~(j) is increasingin j, and that ~(l) is 5. I also assume that firms do not need to pay cash in advance for labor and capital services.

-1o- 6 equal to 1. I will also assume that ~ is continuousand strictly increasingin j. Given my assumptionsabout ~(j), and the fact that all goods have the same price in equilibrium,householdswill choose a cutoff * value of j, j , and purchase goods O through j* (i.e.,those goods it consumes relativelylittle of) with cash. The remaining goods are purchasedwith transactionsservices,hence the household purchases (1-j’) units of transactionsservices. Thus the household’smaximizationproblem is: j* ~(j)cjl-y (1) V(k,M) = Max J dj .,k’,M’,j* O l-y CJ $(j)cjl-y 1 + J dj + ~V(k’,M’) j* l-y Subject to a budget constraint: * (2) w+rk+k+~+ ? =k’ +“’ + ~ j c.dj + ~ 1 *cjdj+ qt PP ‘POJj and two transactionsconstraints: (3) * (4) ~= l-j where w is the wage, r is the rental rate for capital,k is this period’s capital stock, M is nominal money holdings,X is a cash transfer from the government,P is the price of all of the consumption goods and capital, q is the relative price of transactionsservices, T is the quantity of financial servicesbought, and a prime denotes the values of variablesnext period. The transactionsservices 6. The latter assumptionis not simply a normalization. It has the plausible implicationthat consumptionof good 1 is finite, but this means that sufficientlylow positive nominal interest rates will eliminatethe inefficientuse of transactionsservices. See the discussionon this point at the end of Section II.

-11constraintsrequire that a good either be purchasedwith cash, or with a transactionsservice costing q, as discussedabove, Assuming that that equation 3 holds with equality,the firstorder-conditionsfor an interior solutionto this problem are the three constraintsand: O(j)c:y = ~ for j > j* Cj: J @(j)c~Y=L+pfor j <j’ M’: P(L’+P’)/p’ = ~,p where ~ and p are the multipliers on (2) and (3) respectively,c.* and Jare the levels of consumptionof good j* approachingfrom above Cj*+ and from below, and I have substitutedout for the multiplier on (4).7 The condition for j* shows that the budget constraintand the transactionsconstraintare related. Using the conditionsfor k’ and M’, one can show that: P’ =~’i’ where i is the nominal interest rate: l+i’ = (l+r’)(l+m’) and n is the inflation rate: 1+~’ = P’/P Substitutioninto the conditionsfor consumptionyields the intratemporalrelationshipbetween levels of consumptionof each good: lly 1 (5a) ~(j)cl for j <j’ Cj = {1l+i 7. Note that it does not matter whether the household consumes c.*- * J of good j , paying with cash, or c+’+ of good j* paying with * transactionsservices. I have arbitrarilyassumed that good j is purchasedwith cash.

-12and = (5b) Cj ~(j) Cl for j > j* where So the profile of consumptionacross goods looks like the that shown in Figure 1. Note that equations 5a and 5b imply that: Cj$= (l+i)l/yC j-. * Eliminatingc.*and p from the the conditionfor j yields, (5) q=cj${filf~+i)y- 1} To interpretthis equation,note that the product of the terms in brackets on the right hand side is less than i (for small values of i it is approximatelyequal to i). The cost of purchasingan amount q/i of a consumptiongood using cash exactly equals the cost of purchasing it with a transactionsservice. Thus C .* is just larger than this J+ level. Similarly,one can show that c.* is just below this level. J- Thus j* is, roughly speaking,the index of the good that is consumed at a level equalizingthe two types of transactionscosts. For goods with j>j’ it is cheaper to use transactionsservices,while for goods * with j<j it is cheaper to use cash. The growth rate of consumptionof good 1 can be derived from 8 the condition for k’: ‘y = (7) c1 ~(l+r’ )c 1 ~“Y Equations (2)-(7)determinethe optimal time paths for k, M, cl’ Cj (j#l),j*, and ~, given time paths for r, w, q, n, and X/P plUS initial holdings of real money balances and capital. 8. Note that the assumptionof an interior solutionfor j* implies that good one is purchasedwith transactionsservices. If this were not the case, then the economywould look like a simple cash-inadvance model.

-13c. The Firms’ Problems The firms in each sector maximize profits given the levels of wages and prices. All consumption-goodsproducershave identical productionfunctions,eF(kj,lj),as do capital-goodsproducers. The first order conditionsfor producersof consumptiongoods are: (8) r = Of’(Kj) for all j (9) w = 9f(Kj) - rKj for all j where = k./l. for all j ‘j J J is the capital-laborratio chosen by the firm. The first order conditionsfor capital-producingfirms are the same: (8’) r = ef’(Kk) (9’) w = 6f(Kk) - rKk where = kk/lk ‘k Since consumptionand capital producershave the same production functions and face identicalfactor prices, their prices will be the same, as was assumed above. Firms producingtransactionsserviceshave a production function e(l/~)F(kz,lz),for some fixed ~. Note that the production function differs from that of the goods producing sectors only by a constant. As a result, shifts in the size of the transaction-services sector have no effect on the relative returns to capital and labor. This is a convenient simplification. In addition,productionof transactionsservices is assumed not to require the use of money. There is little effect on the results of the model if transaction services productiondoes requiremoney--as in Fischer (1983)--solong as the share of money in productionis small. One measure of that

-14share would be the interest lost on bank holdings of (interestfree) reserves as a fraction of GDP in the banking sector. Since total bank reserves (includingvault cash) are only about $60 billion and shortterm nominal interest rates are currentlyunder 5-1/2 percent, the foregone interest amounts to roughly $3-1/2 billion a year, or less than two percent of banking sector GDP. Given the assumed productionfunction,the first order conditionsfor a transactionssector firm are: (8U) r = qe(l/~)f’(K~) (9”) w = qe(l/&)f(Kz)- rKt where Notice that (8)-(9”)imply that: (lo) q=g (11) K = = K for all j T ‘k = ‘j – D. GovernmentPolicy The governmenthas a simple policy of increasingthe money supply by a constant fraction,a, each period. Hence: (12) X = GM As noted above, these increases in the money supply are achievedvia lump-sum cash transfers. E. Equilibrium An equilibriumfor this economy consists of sequencesfor prices (r,w, q, and P) and quantities (c., z, 1., lk, lt, k., k , J J J kk z’ and M) such that: the households’first order conditionsare satisfied,firms’ first order conditionsare satisfied,and the

-15markets for each of the consumptiongoods, money, transactions services,capital, and labor clear. Market clearing in the consumptiongoods markets is: (13) = eljf(K) for all j Cj Market clearing in the transactionssector is given by: (14) l-j* = 6(1/~)l~f(K) Market clearing in the money market is: (15) M’ = (l+o)M Market clearing in the rental market for capital is: (16) ~lkjdj+ kk + k = k T o and market clearing in the purchasemarket for capital is: (17) k’ - k = elkf(K) Market clearing in the labor market is: (18) Because of Walras’ law, one of the market clearing conditionswill be redundant. F. Steady-stateConditions In the steady state equations (2)-(7), (8)-(12),and (13)- (18)will hold with constantvalues of c., j*, T, K, M/p, Ik, I I J T’ j’ Let these constantvalues be indicatedby ‘k’ ‘I’ ‘j’ “ “ “ and q“ bars, =. , etc. J Market clearing in the money market, equation 15, implies that: The first-orderconditionfor consumptionof good 1, equation 7, implies that in steady state the marginal product of capital must equal the rate of time preference:

-16- (20) ef’(i) = s where K = kll Equation (20)yields the steady-statecapital stock. Note that it is not affectedby the level of inflation. The economy is not super-neutral,however, because a change in ~ will affect ~., ~*, and J m. Substitutioninto the household’sbudget constraint,equation 2, yields the feasibilitycondition: (21) which shows that total output must be equal to total consumptionof the various consumptiongoods plus purchasesof financial services. In steady state, the relativeconsumption of the various goods can be obtained from equations5a and 5b: ‘orjsj* ‘22a) ‘j={(l+3);l+a,}1’y~(j):l and (22b) ‘. = ~(j)=1 for j > j* CJ * The steady state conditionfor j is given by: y-1 (23) - * ‘Y ((1+5)(1+0))~- 1 = ~ Cj+ v { }{ } The steady-state levels of ~~ and ~* are jointly determinedby (21) and (23), after substitutingfor the c.‘s using (22a) and (22b). Then J the steady-state levels of the c.‘s can be obtained from (22a) and J (22b). Finally, the level of the steady-state real money stock is given by:

-17” (24) II. GraphicalAnalysis Using equations (22a)and (22b),one can rewrite (21) and (23) as: (21‘) ef(K) (23‘) Y {}y-1 Equation (21’)defines a locus in c1-j* space that is feasible given K and ~. This locus is upward-slopingbecause an increase in j* reduces the productionof transactionsservicesand so allows an increase in I call this locus BB; it is shown in Figure 2. Equation (23‘) c1“ also defines a locus in c 1-j* space along which the marginal cost of *th purchasingthe j good with cash is balanced against the cost of an additionalfinancial service,for each value of c This locus is 1“ downward slopingbecause an increase in c1 raises the amount of each good purchasedand so raises the cost of purchasingeach good-- ‘th includingthe j good--withcash. Thus the marginal condition is * satisfiedat a lower j . This locus is also shown in Figure 2, and it is labeled FF. The intersectionof these two loci provides the * steady-statevalues of c~ and j . It is useful to define a third locus. Equation (24) can be rewrittenas: r~(j)dj ‘24’) ‘n=c,{(l+b,;l+a)l’’y

-18- Equation (24’)defines a locus along which the steady-statelevel of real money balances are constant. This locus is downward sloping since an increase in c~ would raise money holdings unless fewer goods were purchasedwith cash. In general,this line can be either steeper or flatter than than FF; it is labeledMM in Figure 2. Steady-state real money balances are higher above and to the right of MM. This figure can be used to explore the effect on the steady state of this economy of changes in the technologyand government policy parameters. A. The Effect of an increase in 0 An increase in productivityin all industries,e, raises output, thereby shiftingthe BB line up. It has no effect on the other curves. As a result, c1 rises and j* falls (seeFigure 3). Not surprisingly,increasedproductivityraises consumption. It also increasesthe use of financial servicesbecause more goods are consumed in large enough quantitiesto make purchasingthem with financial services preferableto paying the inflationtax. Note that if the MM locus is steeper than the FF locus, then real money balances decline. In fact, as long as O(O) is strictly positive,a large enough increase in e will make this economy cashless, since consumptionof good O will eventuallybe sufficientlyhigh than it will be optimal to purchase it with transactionsservices. * Nonetheless,if~(j) is steep at j , then there would be little substitutionof transactionsservicesfor cash transactionsowing to a rise in e, and the steady-statelevel of real balances would rise since the increased consumptionof goods purchasedwith cash would outweigh the small reductionin the number of goods purchasedwith cash.

-19- B. The Effect of a Decrease in ~ An improvementin the transactionstechnology (whichis a decline in ~) shifts the BB line up since for a fixed j*, fewer resourcesneed to be employed in the financial services sector. The fall in { also shifts the FF line to the left because at the margin it is now cheaper to transactwith financial services,thereby reducing j* for each cl. Thus the decrease in ~ causes a fall in j*--i.e. a larger financial sector--andcould cause a rise or fall in c1 (see Figure 4). The change in & has no effect on the MM line, and so the steady state money stock likely falls. If the shift in the FF locus is large enough, then the improvementin the transactionstechnologycould reduce welfare. This result is not as surprisingas it may seem. If ~ is very large, then no financial services are used. In this case, the economy is super- 9 neutral, and the steady-stateoutcome is first best. It is also the same steady-stateoutcome that would occur with { equal to zero-i.e., free financial servicesand no money holding. For ~ between the two extremes,the dead-weightcost of using the transactionsservices sector reduceswelfare, and the effect on welfare of a change in & is ambiguous. Indeed, the governmentin this model could raise welfare by eliminatingthe financial sector through regulation. Of course attemptingto do so in a real economywould lead to the substitution of home-producedfinancial services or a foreign currency for financial services producedby the domestic financial services sector, with a likely loss in efficiency. 9. This outcomewould not be first best if inflationaffected the labor supply and savings decisions. See Gillman (1993)and Aiyagri et al. (1995)for discussions.

-20- i C. The Effect of an Increase in c An increase in a raises inflationand the nominal interest rate. The increase in the nominal interest rate raises the BB line because it cuts consumptionon cash goods for a fixed cl. An increase in the nominal interest rate shifts the FF line to the left because, with the higher inflation,transactingwith cash is more costly, inducinghouseholdsto purchasemore financial services. As a result, an increase in 6 reduces j* (seeFigure 5). It also reduces total consumptionexpenditurebecause output is divided between the productionof consumptiongoods and transactionsservices and the latter rises. It could increase or decrease c1 because with the higher inflation rate consumptionwill shift toward the goods purchasedwith transactionsservices. The increase in the nominal interest rate causes the consumptionof cash goods to fall. The lower consumptionof cash goods, coupledwith the reductionin the number of goods purchasedwith money, causes a decline in the steady-statemoney stock. The cost of higher inflationhas two componentsin this model. The first, familiar from Lucas and Stokey (1987),is the distortionin the distributionof consumptionacross goods purchased with cash and those purchasedwith credit (seeFigure 6). In this model, however, which goods fall into each category is endogenous. The cost of this distortionis likely small for low rates of inflation since the lower consumptionof goods purchasedwith cash is partially compensatedby increased consumptionof goods purchasedwith transactionsservices. The second cost is the waste of resources resultingfrom the use of transactionsservices rather than money. This loss could be large because the resourcesshifted to the productionof transactionsservicesare completelylost.

-21- The optimal monetary policy in this economy is clearly to set ~ sufficientlylow that all purchasesare made with cash. If ~(j) is bounded, as assumed above, this policy will not correspondto a zero nominal interest rate, as in the Friedman rule. So long as the nominal interest rate is low enough that it is cheaper to buy good 1 with cash than with purchasedtransactionsservices,there will be no cost to the inflation. If one allowed~(j) to go to infinity as j 10 goes to 1, then the usual Friedman rule would obtain. III. Empirical Evidence In the Introduction,I noted the evidence from the 1920s on the effect of hyperinflationon the size of the financial sector. A similar effect has been noted in the cases of Brazil and Israel in the 1980s. Dornbusch et al. (1990,p. 25) note that in Brazil “financial markets substantiallyadapted [tohigh inflation]. As a result, the velocity of Ml rose more than in other countries,while that of M 4 increasedless. The sharp rise in the velocity of Ml reflectsa well organized payment system by check (evenfor a lunch snack) drawn on overnightaccounts.~ Presumablythis “well-organized”payment system required increasedcapital and labor in the financial sector. Marom (1988),presents an empirical study of the effects of inflation on the size of the banking sector in Israel in the early 1980s. He notes that while the share of banking in Israeli GDP in 1970 was smaller than in any of the six OECD countriesfor which 10. The Friedman rule would also obtain, regardlessof the boundednessof ~, if inflationaffected the labor or savings decisions. Aiyagari et al. (1995)and Cooley and Hansen (1991)argue that these distortionscould be important.

-22comparabledata are available,it was larger than in all of the six OECD countriesby 1982. Over the period 1970-82 inflation in Israel averaged 33.9 percent,more than three times the highest average rate among the OECD countries. Marom estimatesa time series econometric model to assess the effect of inflationon the size of the Israeli banking sector. The effects are statisticallysignificantand indicatethat high inflation (definedby Marom as inflation over 10 percent per year) nearly doubled the share of banking in GDP in the early 1980s. Similar equations estimatedusing banking’s share in total employmentand total wages show smallerbut statistically significanteffects. Work by Kleiman (1989)provides informationon the effect of the 1984 stabilizationprogram on employmentin the banking sector. After expandingfurther in 1983, employmentdeclined through 1987, by which time it had returned to its 1979 level. As noted by Kleiman, however, the immediate cause of the declinewas a banking crisis that occurred in late 1983. The governmentintervenedto provide assistance,but the banks were requiredto cut costs. Nonetheless, the pattern of banking sector expansionand contractionis broadly consistentwith the model. Aiyagari et al. (1995)present time series data on the size of the banking sector in Brazil, Israel, and Argentina, noting that high inflationhas been reflectedin the size of the financial sector in all three countries. The Argentine data, however, is somewhat problematical: The banking sector’s share in employmentpeaked around 1980 and then declined,while the inflationrate spiked sharply in the mid-1980s, and then even more forcefullylater in the decade. The decline in the relative size of the financial sector in the early 1980s likely reflectedthe effects of a financial crisis at that time,

-23which followed a period of financial liberalizationin the late 1970s (Balino,1991). As a result,when inflationpicked up in the mid- and late-1980sArgentineansappear to have reacted, at least in part, by shiftingto U.S. dollars rather than making greater use of domestic financial firms (Dornbuschet al., 1990, p. 25).11 Currency substitutionof this sort is, of course, another form of costly adjustmentto high inflation--albeitone of a sort not contemplatedin the model. A. A Cross-CountryComparison As an alternativetest of the model, similar to Marom’s (1988)comparisonof Israel to six OECD countries,I consider a cross-countrycomparisonof inflation rates and financial sector size. The model presented above suggeststhat the share of output devoted to the financial sector should be a function of the level of inflation,output per capita, and relativeproductivityin the financial sector. While higher inflationshould cause the financial sector to expand, the effects of the other two variables are not clear on theoreticalgrounds. As noted in section II, above, higher productivitywill raise consumptionof all goods, causing an increase in the number of transactionsthat are made without cash. It is not clear, however, whether the proportionalincrease in the financial sector will be larger or smaller than that of GDP. Similarly,more transactionswill be done with financial servicesif the financial 11. The resultingdifferencein the method of domestic payments is noted in a recent Economist survey of Latin American Finance (Dec. 9- 15, 1995). Kamin and Ericsson (1993)present an empirical study of dollarizationin Argentina. They conclude that holdings of U.S. dollar currency in Argentinawere nearly as large as the total of dollar-denominateddomestic deposits and all peso-denominatedmonetary assets by the early 1990s. They also note that the effect of inflation on the use of dollars appears to be long lived.

-24sector becomes more efficient,but the relativeprice of these serviceswill fall. Thus, the net effect of the productivityincrease on the financial sector’s share is uncertain. Because of the difficultyof obtainingcomparableinformation on the relative size of the banking sector for a large number of countries,I focus on the broader sector includingfinance, insurance, and real estate. I use two measures of the size of the financial sector: its share in GDP and its share in employment (bothin percent). These shares can be used to calculatethe relative productivityof labor in the financial sector. Because data on capital inputs are not available,a more comprehensivemeasure of total factor productivitycannot be constructed. The GDP, employment, and labor productivitydata are for 1985.12 Wherever possible, I measure annual average percentageinflationusing the GDP deflator. Where this is not available,the consumer price index has been substituted. Because the model presentedabove focused on steady states, I use the average annual inflation rate over the ten years from 1975 to 1985.13 To account for differencesin the level of income across countries,I use GNP per capita at world prices from the Penn World Table (Summersand Heston, 1991). For details on the data used, see the data appendix. B. EmpiricalResults The first column of table 1 shows the results of a regression of the share of the financial sector in GDP on per-capitareal output, average inflationover the previous 10 years, and relative labor 12. In some cases the employmentdata were not available for 1985, and so data from 1984, 1986, or 1987 were substituted. 13. I experimentedwith the average inflation rate over 1980-85 and obtained similar results.

-25productivityin the financial sector. The results show that higher levels of per-capitaincome and average inflationare reflectedin increasedfinancial sector size. By contrast,there does not appear to be a significanteffect of relative labor productivityon this measure of financial sector size. This result suggeststhat the two offsettingeffects noted above cancel out. Dropping the productivity variable from the regression,as shown in the second column, does not greatly affect the other parameters. The strong and statisticallysignificanteffect of real income per capita on the size of the financial sector should not come as a surprise. Kuznets (1971,p. 107) notes that ‘the share of banking, insuranceand real estate shows a striking rise as we shift from low to higher income countries.” The strong result found here suggests that either the effect of higher income on the share of goods purchasedwithout cash is large, or the model fails to capture another effect of higher income that leads to increaseduse of the financial system. It is not hard to think of such effects. For example, if higher income households purchase a larger number of goods, as well as more of each good, higher incomes would lead to a larger number of transactionsand likely to an increasedneed for financial services (aswell as cash). Alternatively,if householdsdo their own cash management,they may choose to do less of it as incomes rise, owing to the higher opportunitycost of household time. As a result, householdswould increase their purchasesof transactionsservices producedby financialfirms. The effect of inflationon the size of the financial sector, as shown in columns 1 and 2, is economicallyas well as statistically significant. Given that countrieswith higher per-capitaincomes generallyhave larger financial sectors,however, it seems likely that

-26- i the effect of inflationon financial sector size is larger in high income countriesas well. To test this hypothesis I interact the inflationterm with per capita income in the regressionreported in 14 column 3. The use of the interactionterm improves the fit of the regressionfairly substantially,suggestingthat the effect of inflationon the size of the financial sector is smaller for lowincome than for high-incomecountries. The results of an alternativetest are shown in table 2. Here the countriesare divided into three groups based on income per capita, and for each group a separate regressionis run of financial 15 sector size on income and average inflation. The coefficienton the inflation rate is small and insignificantfor the poorest countries,moderate and marginally significantfor the middle-income countries,and large and significantfor the high-incomecountries. The theoreticalmodel suggeststhat the effect of inflation on financial sector size should be nonlinear. In particular,if inflation gets sufficientlyhigh, virtually all transactionsare done without money. Further increasesin inflationwill then have no effect on the size of the financial sector. Experimentationwith a number of nonlinear specifications,however, did not yield statisticallysignificantnonlinearities. The remainingcolumns in table 1 show regressionresults for the share of the financial sector in total employment. One difference between the GDP share and employmentshare results is the significance of the productivityvariable in the employmentregressions,especially 14. If the level of inflation is included as well as the interaction term, it is insignificantand does not affect the other parameters. 15. The income categorieswere defined, arbitrarily,as under $2000, between $2000 and $9000, and over $9000. The mean income level in the sample is about $4800. Modest changes in the cutoff levels of income do not affect the results appreciablyso long as Israel (witha 1985 per capita income of $9293) remains in the high income group.

-27when it is interactedwith the level of income (column5). Given the insignificanceof this variable in the GDP regression,the significancehere may not be a surprise. Since countrieswith higher financial sector labor productivitydo not generallyhave a larger share of GDP in the financial sector, they must have a smaller share of employmentin the sector. The inflationinteractionterm is significantin the employmentregressions,although the coefficientis less than 1/3 the size of the comparableterm in the GDP regressions. The smaller parameteris not surprisingbecause, on average, the share of the financial sector in employmentis about 1/3 as large as its share in GDP, suggestinga similar proportionaldecline in the size of the parameter. C. Caveats There are two caveats to the empirical results shown above. First, it is possible that the relativelylarge effect of inflationon the GDP measure of financial sector size reflectsinflation-induced measurementerror. The measurementof output in the financial sector is difficultbecause output is often hard to quantify. (SeeTriplett, 1993, for a brief discussionof the difficultiesin measuringbanking sector output.) If, for example,high inflation led to an upward bias in the measurementof financial sector output, then the regression resultswould reflect, in part, the measurementproblem rather than a real effect of inflation. Such a bias should be apparent in the labor productivity measure used in the regressions,since the share of the financial sector in GDP would be boosted by the measurementerror while the

-28- 16 share of the financial sector in employmentwould not be. To test for this effect, I regress the productivitymeasure on per capita income, inflation,and inflationtimes per capita income. The results, shown in table 4, show no significanteffect of either inflationvariable on relative labor productivityin the financial sector. Table 5 shows the results of regressionslike those in table 1 when the GDP measure of financial sector size is adjusted to remove the effects of inflation on relative financial sector productivity shown in table 4. These adjusted results differ very little from the baseline results in table 1.17 A second caveat is simply to point out the importancein the empirical results of a relativelysmall number of countries. Figure 7 shows a plot of the GDP measure of financial sector size versus inflationtimes per capita income. (A constant and per capita income have been partialed out of both variables.) The upward slope found in the regressionsis clearly evident in the figure. It is also clear, however, that the result depends a great deal on a small number of countrieswith very high inflation rates. The five most inflationary countries in the sample--Israel,Argentina, Brazil, Bolivia, and Peru--comprise5 of the 6 observationsin the upper-rightquadrant of 16. The relative labor productivitymeasure is: (FinancialSector GDP)/(FinancialSector Emt)lovment) (TotalGDP)/(TotalEmployment) which can be rewrittenas: (FinancialSector GDP)/(TotalGDP) (FinancialSector Employment)/(TotalEmployment) which is the ratio of the financial sector share in GDP to the financial sector share in employment. 17. To do the adjustment,I startedby adjustingthe relative productivityvariable by evaluatingthe two inflationterms in the regressionand subtractingthem from the relativeproductivity measure. Then I multiplied this adjusted productivitymeasure by the share of the financial sector in employmentto get the adjusted measure of the financial sector in GDP.

-29- 18 the figure. If they are excluded from the regressions,the inflationterms are no longer significant. However, excludingthem is surely wrong, since high inflationcountriesare exactly the ones with the most informationabout the effects of inflation on financial sector size. Nonetheless.it is unfortunatethat the effect of inflation on financial sector size does not stand out in the lower inflation countries. Evidently,other factors contributeimportantlyto variation in the size of countries’financial sectors. In part, this variation likely reflectsthe effects of regulationand past financial sector difficulties. In addition,the regressionsemploy data on the productionof financial services,while it is consumptionof financial servicesthat should be affectedby inflation. Clearly, if a country purchases financial services from firms in a neighboringcountry, its financial sectorwill appear to be unexpectedlysmall, while that of its neighborwill appear to be large. The geographicalpattern of the residuals suggeststhat this differencemay be significantin some cases. For example, the residualfor Belgium in the regressionshown in column 3 of table 1 is -8.3 percent, the financial sector in Luxembourgis more than 9 percent larger than the equationwould lead you to expect (becauseof its small population,Luxembourgwas excluded from the regression). By contrast,the standard error of the regressionis only 3.6 percent. Similarly,the residual for Ireland is -5.8 percent,while that for the United Kingdom is +3.6. In some cases there appear to be regional financialcenters reflecting relative political or economic stability. In particular,Jordan and Kenya have unexpectedlylarge financial sectors (residualsof 6.2 and 18. The other one is Chile, which had the seventh highest inflation rate in the sample.

-30- 6.0 percent respectively), while some of their neighborshave unexpectedlysmall ones. Note that to the extent that low inflation allows a country to export financial servicesto its neighbors, low rather than high inflationwould be associatedwith a large financial sector, biasing downward the estimatedeffect of inflationon the size of the financial sector. D. Discussion The regressionsshown in table 1 suggest a larger cost of inflationthan might have been expected. A 10 percent rise in the inflation rate in the U.S. (1985real per-capitaincome, $16,779) would be expected to increasethe share of the financial sector in GDP by about 1-1/2 percent, and its share in employmentby about 1/2 percent. The 1-1/2 percent share of GDP is a measure of the resources lost owing to the inflation. Fischer (1981)and Lucas (1981) calculatethat the welfare loss of a 10 percent inflationamounts to .3 to .45 percent of GNP, based on estimates of the area under a money demand curve. However, Lucas (1994)reports a welfare loss similar to that reportedhere, 1.3 percent,based on a different paramaterizationof the money demand curve. It is straightforwardto show that, in the model presentedabove, the area under the compensatedmoney demand curve is approximatelyequal to the size of 19 the financial sector. Thus the results presentedhere do not differ conceptuallyfrom the measures employedby Fischer and Lucas. To assess whether the large costs of inflationfound here are credible,table 5 presents informationon the two measures of financial sector size, inflation,and per-capitaincome for the five 19. The two are exactly equal if inflation is not allowed to distort the pattern of consumptionacross goods. For a proof of a similar result, see Aiyagari et al. (1995).

-31countrieswith the highest inflation rates over 1975-85. Also reported in the table are the average values of these variables for other countrieswith real per-capitaincomes between 50 and 150 percent of each of the five countries. As shown in the table, both Brazil and Israel have financial sector shares in GDP more than 10 percentagepoints larger than other comparablecountries. By the same measure, Argentina,Bolivia, and Peru have financial sectors that roughly 6, 3, and 1 percentagepoint larger than their peers. With the exceptionof Bolivia, there is a similar pattern to the employment shares of the financial sector,with financial sector employment3 percentagepoints higher in Argentina,Brazil, and Israel, and 1 percentagepoint higher in Peru. It is not surprisingthat the effects of inflation on financial sector size are largest for Brazil and Israel, and smaller in the other three countries. As noted above, a larger share of the adjustmentto inflationin Argentina took the form of dollarization. The same appears to have been the case in Bolivia (Melvin,1988; Melvin and Afcha, 1989) and Peru (Rojas-Suarez,1992). The experience in these countries suggeststhat high inflationmay not lead to as large an expansionin the financial sector if currency substitution takes place instead. Which method of adjustmentpredominates presumablydepends on the regulatoryenvironmentas well as the quality of financialfirms at the start of the inflation. In any case, the likely importanceof dollarizationin limiting the size of the financial sector in some of the high inflationcountries suggests that the regressionresults reportedabove will provide underestimates of the effects of inflationon financial sector size for countries where growth in the financial sector is not constrainedby regulation or financialcrises.

-32- The evident large effects of inflation shown in table 3 are consistentwith the large costs of modest inflationsimplied by the regressions. For example, Israel,with 110 percentagepoints of “extra” inflation relativeto its peers, had a financial sector share about 11 percentagepoints higher, implying a cost of about 1 percent of GDP for each 10 percent of inflation. For the U.S., with per capita income about half again as large, an increase of 1-1/2 percent for a 10 percent inflation seems plausible. Aiyagari et al. (1995)report that the effects of inflation on the banking sector appear to be limited to a few percent of GDP. Thus the larger effects found here for the broader finance, insurance, and real estate sector likely reflect,in part, increases in other subsectorsas well as in banking. This implicationseems plausible: other intermediaries, such as insurancecompaniesand securities dealers will have to handle more transactionsas businessesand householdsincrease their efforts to conserve on cash. Moreover, such firms will also be boosting their own efforts to limit cash holdings. Of course institutionalinertia or nonlinearitiescould limit the expansion of the financial sector in responseto moderate inflations,reducingthe cost of such inflationsto levels below those implied by the estimatedequations. There are other reasons,however, to believe that the increase in the size of the financial sector understatesthe total costs of inflation. For example,this measure does not take account of the unremuneratedcosts of increased “home production”of financial services--e.g.the traditionalshoeleather costs of inflation--nor does it account for the productionof financial servicesby nonfinancialfirms. Bresciani-Turroni(1937) notes that during the German hyperinflationnonfinancialfirms had to

-33greatly increasethe amount of “unproductive”work time--i.e., work requiredto manage financialflows. The increase in the size of the financial sector also does not take account of a variety of other inflation-relateddistortions. For example, the wedge driven between the marginal utility of cash and non-cash goods in consumptionreduceswelfare directly. Similar distortionsin labor supply and investmentdecisions reduce welfare indirectlyby reducing either current or future output. Even if consumptionand investmentwould otherwisenot be affected, if reservespay no interest,inflation serves as a tax on intermediation, reducingthe efficiencyof resourceallocation. Finally, there is some evidence (seeFischer, 1993) that inflation reduces the growth rate of total factor productivity,which would have a potentially large effect on welfare.

-34- Data Appendix The data on the size of the financial sector are taken from two United Nations sources. The data on GDP by sector are from the United Nations National Accounts:Main A~~re~ates and Detailed Tables volumes (table1.11). The data for 1985 were not availablefor every country in the 1986 volume, and so later volumes were used in some cases. The employmentdata by sector are from the United Nations StatisticalYearbook. Because of lags in data availability,several volumes from the late 1980s were used. The numbering of the tables in the yearbooks changes from year to year. As noted in the text, employmentdata for 1985 were not always available,and data for 1984, 1986, or 1987 have been substitutedwhere necessary. These data are used to calculatethe shares of the finance, insurance,and real estate sector in GDP and employment,and relativelabor productivity in that sector. The inflationdata is taken from the country tables in the InternationalMonetary Fund’s InternationalFinancial Statistics volume (1992). Where possible the GDP deflator (line 99bi) is used, Where this is not reported,consumer price index data (line64) have been substituted. For a few high inflationcountries,the deflator grew by so much that it cannot be reportedin the country tables. In these cases, the inflation rates, as reportedin the inflationtables (pp. 152-155 for the deflator,pp. 104-107for the cpi) have been used instead. The per capita income at world prices data is from the Penn World Table (Summersand Heston, 1991). Robert Summers kindly provided this data on diskette. I exclude countrieswith populationsbelow three million. These countriesare very noisy since some are offshore or regional banking centers (e.g.Panama, Luxembourg,Hong Kong, and Singapore) while others are not. The data used in the regressionsis availablefrom the author on request. Descriptivestatisticsare shown below: Table Al Variable Number of Mean Std. Dev. Minimum Maximum Observations Financial Sector Share in GDP (%) 73 10.38 5.11 2.26 24.22 Per-Capita Income ($1000s) 73 4.82 4.41 .33 16.78 Inflation (%) 73 22.80 39.88 3.23 252.95 Inflationo(Per- Capita Income) 73 91.41 178.73 2.13 1117.11 Share in Employment (%) 49 5.34 3.10 0.77 14.09 Relative Labor Productivity 49 2.99 2.02 0.40 8.82

-35- Table 1 RegressionsExplainingthe Size of the Financial Sector (t-statisticsin parentheses) DependentVariable: Share of the Financial Sector (1) (2) (3) (4) (5) Share Measure: GDP GDP GDP EmploymentEmployment Sample Size: 49 73 73 49 49 ExplanatoryVariable Constant 5.53 5.92 6.32 5.40 3.43 (3.71) (8.21) (9.86) (8.17) (7.89) Per-Capita Income 0.76 0.77 0.67 0.32 0.78 (6.07) (7.68) (6.77) (5.68) (9.86) Inflation 0.04 0.03 (2.78) (2.88) (Inflation)o(Per Capita Income) 009 .002 .003 (~.80) (1.80) (2.21) Financial Sector Productivity 0.32 -0.75 (1.10) (5.65) (FinancialSector Productivity)o(per Capita Income) -0.21 (6.07) R2 0.44 0.46 0.50 0.67 0.69

-36- Table 2 RegressionsExplainingthe Size of the Financial Sector (By Level of Per-CapitaIncome) (t-statisticsin parentheses) DependentVariable: Share of the Financial Sector in GDP (1) (2) (3) Income Level: Low Medium High Sample Size: 27 28 18 ExplanatoryVariable Constant 5.90 6.85 1.90 (4.28) (2.42) (0.34) Per Capita Income 1.32 0.50 1.04 (1.11) (0.74) (2.26) Inflation 0.01 0.03 0.11 (0.42) (1.86) (3.17) R2 -0.01 0.07 0.36

-37- Table 3 RegressionExplainingRelative Productivityin the Financial Sector (t-statisticsin parentheses) DependentVariable: Relative Labor Productivityin the Financial Sector Sample Size: 49 ExplanatoryVariable Constant 3.81 (6.92) Per-Capita Income -0.13 (1.79) Inflation .001 (0.03) (Inflation)o(Per Capita Income) -.001 (0.15) R2 0.04

-38- Table 4 RegressionsExplainingthe Size of the Financial Sector (t-statisticsin parentheses) DependentVariable: Adjusted Share of the Financial Sector (1) (2) (3) Share Measure: GDP GDP GDP Sample Size: 49 49 49 ExDlanatorvVariable Constant 5.26 6.42 7.04 (3.35) (6.20) (7.77) Per-CapitaIncome 0.81 0.77 0.64 (6.19) (6.20) (5.48) Inflation 0.05 0.05 (3.61) (3.58) (Inflation)o(Per Capita Income) 0.01 (4.56) Financial Sector Productivity 0.30 (0.99) R2 0.48 0.48 0.54 Note: The GDP measure of the size of the financial sector has been adjusted to remove the effects of inflationon measured productivityin the financial sector.

-39- Table 5 Financial Sector Size and Average InflationRates for High InflationCount~iesin 1985 Financial Sector Average Inflation Per-CaDitaGDP Share 1975-1985 GDP EmRlovment Argentina 14.7% 6.5% 252.9% $3,982 Comparable Countries 9.0 3.6 17.6 3,742 Bolivia 10.6 .-a 197.8 1,566 Comparable Countries 7.7 3.1 15.8 1,506 Brazil 20.0 5.7 98.4 3,995 Comparable Countries 9.0 3.6 17.6 3,742 Israel 24.2 9.6 120.2 9,293 Comparable Countries 12.9 6.7 10.6 9,264 Peru 9.8 4.5 77.6 2,730 Comparable Countries 8.8 3.6 16.1 2,468 a The United Nations data indicate that the share of the financial sector in Bolivian employmentwas 0.9 percent in 1987, the year closest to 1985 for which data are available. This is lower than all but three countries in the sample, and implies a very unlikely level of relativeproductivity in the sector. I have assumed that the number is an error and excludedit from the regressions. Includingit does not greatly affect the results presented in the last two columns in table 1. In particular,the effect of inflation is still statisticallysignificant. Note: Comparablecountriesare selected separatelyfor each country shown based on per capita income. “Comparablenis defined to be those countries with incomes between 50 and 150 percent of the country to which comparisons are being made. The comparablecountriesexclude the five countries shown and those with populationsof 3 million or less. There are between 20 and 25 comparablecountriesin each case, although only about half generally have data on the share of employment.

-40- REFERENCES Aiyagari, S. Rae, and Zvi Eckstein, “Interpreting Monetary Stabilizationin a Growth Model with Credit Goods Production,H Federal Reserve Bank of MinneapolisWorking Paper No. 525, 1994. , and Toni Braun, “TransactionsServices, Inflation:and Welfare,n Federal Reserve Bank of MinneapolisWorking Paper No. 551, July 1995. Balino, Thomas J. T., “The Argentine Banking Crisis of 1980,” in SundararajanV., and Thomas J. T. Balino, Banking Crises: Cases and Issues, Washington,D.C.: InternationalMonetary Fund, 1991. Baumol, William J., “The TransactionsDemand for Cash: An inventory theoretic approach,”Quarterly Journal of Economics, 1952, pp. 545- 556. Bresciani-Turroni, Costantino,The Economics of Inflation:A Studv of Currencv Depreciationin Post-War Germanv, translatedby Millicent E. Sayers, London: George Allen and Unwin, Ltd., 1937. Cole, Harold L. and Alan C. Stockman, “Specialization,Transactions Technologies,and Money Growth,U InternationalEconomic Review, 1992, PP” 283-298. Cooley, Thomas and Gary Hansen, ‘The Welfare Costs of Moderate Inflations,”Journal of Money, Credit. and Banking, 1991, pp. 483-503. Dornbusch,Rudiger, Federico Sturzenegger,and Holger Wolf, “Extreme Inflation:Dynamics and Stabilization,nBrookin~sPaDers on Economic Activitv 2, 1990, pp. 1-64. Dotsey, Michael and Peter Ireland, “On the Costs of Inflationin General Equilibrium,”Mimeo. Federal Reserve Bank of Richmond, 1993. Federal Reserve System, FunctionalCost and Profit Analvsis: National Avera~e ReDort. CommercialBanks 1994, 1995. Fischer, Stanley, “The Role of MacroeconomicFactors in Growth,n Journal of Monetarv Economics, 32(3), December 1993, pp. 485-512. “A Framework for Monetary and Banking Analysis,nEconomic Journal, 1683, pp. 1-16. . “Towardsan Understandingof the Costs of Inflation:11,” Carne~ie-RochesterConferenceSeries on Public Policy 15, 1981, pp. 5-41. Gillman,Max. “The Welfare Cost of Inflationin a Cash-in-Advance Economy With Costly Credit,” Journal of Monetary Economics, 1993, pp. 97-116. Humphrey, David B., Lawrence B, pulley, and Jukka Vesala, ~Cash, Paper, and Electronic Payments:A Cross Country Analysis,~Mimeoo, Florida State University, 1995.

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-42- Triplett, Jack E. “BankingOutput” in Newman, peter, Murray Milgat~, and John Eatwell, eds., The New Pal~rave Dictionaryof Monev and Finance, 3v, London: MacMillan, 1992. United Nations, StatisticalYearbook, New York: United Nations: various years. United Nations, National Accounts:Main A~Qre~ates and Detailed Tables. 2v, New York: United Nations: various years. Whitesell,William C., “The Demand for Currency versus Debitable Accounts,” Journal of Money, Credit, and Banking, 1989, pp. 246-251. “Bank Deposits and the Market for Payment Media,” Journal of Monev, ~redit, and Banking, 1992, pp. 483-498. Wicker, Elmus “TerminatingHyperinflationin the DismemberedHapsburg Monarchy,”American Economic Review, 1986, pp. 350-64.

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