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Working Paper Series Stored Value Cards: Costly Private Substitutes for Government Currency WP 96-03 This paper can be downloaded without charge from: http://www.richmondfed.org/publications/ Jeffrey M. Lacker Federal Reserve Bank of Richmond Working Paper 96-3 Stored Value Cards: Costly Private Substitutes for Government Currency Jeffrey M. Lacker* Research Department Federal Reserve Bank of Richmond** April 29, 1996 Abstract: A model in which both currency and stored value cards are used to make payments is presented. I compare steady-state equilibria with and without stored value cards. Stored value cards are beneficial because they help alleviate the deadweight loss due to inflation. When the nominal interest rate is greater than the government’s resource cost of providing currency, the alternative means of payment may have larger real resource costs than the currency it replaces. Stored value results in either a net increase or a net decrease in economic welfare depending upon whether average costs are below or above a certain cut-off. Quantitative restrictions on stored value can be socially beneficial because they reduce the amount of resources absorbed by the most costly stored value applications. *I would like to thank Michelle Kezar for research assistance, James McAfee for useful references, and Urs Birchler, Marvin Goodfriend, Dave Humphrey, Peter Ireland, Bob King, Geoffrey Miller, Ned Prescott, Kevin Reffett, Will Roberds, Stacey Schreft, Bruce Summers, and John Weinberg for helpful comments and conversations. The author is solely responsible for the contents of this article. The views expressed do not necessarily reflect those of the Federal Reserve Bank of Richmond or the Federal Reserve System. **P.O. Box 27622, Richmond, VA 23261, Phone: 804X597-8279, E-mail: eljml02@rich.fib.org. Stored value cards look like credit cards but are capable of storing monetary value. There are a number of stored value card systems being developed in the United States, and some have already been implemented in Europe and elsewhere. Stored value cards are particularly well-suited for transactions that would otherwise be carried out with currency, and thus are a private substitute for government fiat money, like private bank notes. Unlike bank notes, however, stored value cards employ new technologies that are quite different from, and potentially more costly than, the coins and paper currency they are aimed at replacing. This paper explores the basic welfare economics of costly private substitutes for government currency, an important class of payments system innovations2 Consumers and merchants are likely to benefit from the introduction of stored value cards. Many might prefer to avoid the inconvenience and cost of handling paper currency and coins. The usual presumption, in the absence of market imperfection, is that a successful new product must provide social benefits in excess of social costs. Issuers will attempt to cover their costs and earn a competitive return while providing consumers and merchants with a means of payment they prefer. They can do so if consumers and merchants are collectively willing to pay, either directly or indirectly, enough to remunerate issuers for the opportunity cost of the inputs devoted to the alternative means of payment. If stored value thrives, the standard reasoning suggests, it must be because the value to consumers and merchants exceeds the cost of provision. The fact that stored value is a monetary asset provides further reason to believe that it will be beneficial. Currency is subject to an implicit tax due to inflation, which reduces its rate of return relative to other risk-free nominal assets. Like any other tax, the inflation tax distorts economic decisions, giving rise to deadweight costs as people try to economize on the use of currency. Private substitutes for currency provide a means of avoiding the seigniorage tax, alleviating the deadweight loss associated with any given inflation rate. Stored value cards can increase economic welfare by easing the burden of inflation. Stored value cards could be socially wasteful, however. Stored value liabilities compete with an asset, currency, that pays no interest, while issuers are free to invest in interest earning assets.3 Thus one portion of the return to stored value issuers is the spread between market interest rates and the rate of return on currency. This return far exceeds the government’s cost of producing and maintaining the 21 will use the term “currency” rather than “currency and coin” to refer to government supplied notes and coinage; the analysis applies pari passu to government-minted coin. 3Under current U.S. regulations, stored value liabilities are treated as bank deposits; reserve requirements and deposit insurance premia apply. 2 supply of currency--less than two-tenths of a cent per year per dollar of currency outstanding.4 At current interest rates the private incentive to provide stored value exceeds the social benefit by as much as 4 or 5 percent per dollar outstanding. Thus stored value cards, if successful, will replace virtually costless government currency with a substitute that could cost substantially more. In this paper a model in which both currency and stored value are used to make payments is presented. Stored value cards are provided by a competitive intermediary sector and are used in transactions for which the cost of stored value is less than the float cost associated with using currency. Conditions are identified under which the economy with stored value cards does or does not Pareto dominate an otherwise identical economy without stored value cards. The critical condition is a boundary on average cost: stored value is beneficial or harmful depending upon whether, other things equal, average cost is below or above a certain cutoff. If average cost is low, the reduction in the deadweight loss due to inflation will be large and the resource cost will be low. If average cost is high, the resource cost will be large and there will be little effect on the burden of inflation. The fact that costly private substitutes for government fiat money can reduce welfare was demonstrated by Schreft (1992a), and the model presented below is an extension of hers. This fact should not be surprising--as I argue below, we should expect the same result in any model with multiple means of payments5 The interest foregone when holding currency is an opportunity cost to private agents, and they are willing to incur real resource costs to avoid it. The resource cost of a money substitute is a social cost, while the interest cost associated with currency is not. Thus the private incentive to provide a substitute for government currency is greater than the social benefit (Wallace [ 19861). The best policy in the model is one in which the nominal interest rate is zero--the Friedman rule for the optimum quantity of money (Friedman [ 19691). For a given positive nominal interest rate, however, Schreft (1992a) has shown that quantitative restrictions on the use of credit as a means of payment can improve welfare. The same is true here as well, since stored value is just another form of credit as a means of payment; if nominal interest rates are positive, then the right kind of quantitative constraints on stored value cards, if practical, can improve welfare by preventing the most wasteful uses. A noninterest-eaming reserve requirement on stored value liabilities is inferior to quantitative constraints because it imposes an inframarginal tax on 4 Costs are larger but still quite small for lower denominations: see Lacker (1993). ‘For models of multiple means of payment see Prescott (1987), Schreft (1992a, 1992b), Marquis and Reffett (1992, 1994), Ireland (1994), Dotsey and Ireland (1995), and Lacker and Schreft (forthcoming). 3 users of stored value. No attention is paid here to consumer protection, or to the safety and soundness of bank stored value activities (see Blinder [ 19951and Laster and Wenninger [ 19951). The analysis presumes that stored value systems provide relatively fraud- and counterfeit-proof instruments. Historical instances of private issue of small-denomination, bearer liabilities, such as the early nineteenth century U.S. “free banking” era, have raised concerns about fraudulent note issue (see Friedman [196O]). Williamson (1992) shows that a government monopoly in issuing circulating media of exchange may be preferable to laissez-faire private note issue due to asymmetric information about bank portfolios. Others argue that a system of ) private banknote issue can function rather well: see Rolnick and Weber (1983, 1984). In any case, current communications technologies and regulatory and legal restraints are quite different from those of the early nineteenth century. Whether the concerns of Friedman and Williamson are relevant to stored value cards is beyond the scope of this paper; the focus here is the implication of the seigniorage tax for the private incentives to provide currency substitutes. Stored Value Cards Stored value cards--sometimes called “smart cards”--contain an embedded microprocessor and function much like currency for a consumer. Value is loaded onto a card at a bank branch, an automated teller machine (ATM), or at home through a telephone or computer hook-up with a bank. Customers pay for the value loaded onto the card either by withdrawing funds from a deposit account or by inserting currency into a machine. Customers spend value by sliding it through a merchant’s device, which reduces the card’s balance by the amount of the purchase and adds it to the balance on the merchant’s machine. Merchants redeem value at the end of the day through a clearing arrangement similar to those used for “off-line” credit card or ATM transactions. The merchant dials up the network and sends in the stored value, which is then credited to the merchant’s bank account. More elaborate systems allow consumers to transfer value from card to card. The stored value on a stored value card is a privately-issued, bearer liability. It is different than a check because the merchant does not bear the risk of insufficient funds in the buyer’s account. It is different than a debit card in that the consumer hands over funds upon obtaining the stored value, while a debit card leaves the funds in the consumer’s account until the transaction is cleared. Thus a debit card is a device for authorizing deposit account transfers, while a stored value card records past transfers. For consumers, stored value cards can be more convenient than currency in many settings; some consumers are likely to find cards physically easier to handle than coins and paper notes. The technology 4 could conceivably allow consumers to load value onto their cards using a device attached to their home computer, saving the classic “shoe leather” cost of bank transactions. For merchants, stored value cards offer many of the advantages of credit card sales. The merchant saves the trouble of handling coins and notes (banks often charge fees for merchant withdrawals and deposits of currency), and avoids the risk of employee theft. Stored value improves on the mechanisms used for credit and debit cards, however, because the merchant’s device verifies the validity of the card, without costly and time-consuming on-line authorization. Thus stored value cards extend the electronic payments technology of credit card transactions to more time-sensitive settings where on-line authorization is prohibitive. A Model of Currency and Stored Value This section describes a model in which stored value and currency both circulate in equilibrium. Monetary assets are useful in this model because agents are spatiahy separated and communication is costly. In the absence of stored value, agents use currency whenever shopping away from home and the structure of the model reduces to a simple cash-in-advance framework. Stored value is a costly private substitute for currency, similar to costly trade credit in Schreft’s (1992a, 1992b) models. The model is a deterministic, discrete-time, infinite-horizon environment with a large number of locations and goods but no capital. At each location there are a large number of identical households endowed with time and a technology for producing a location-specific good. Each period has two stages. The first takes place before production and, in principle, allows any agent to trade any contingent claim with any other agent. During the second stage production and exchange takes place. One member of the household--the “shopper” --travels to other locations to acquire consumption goods. Simultaneously, the other member of the household--the “merchant”-produces location-specific goods and sells them to shoppers from other locations. Shoppers are unable to bring with them goods produced in their own location, and so direct barter is infeasible. The fundamental friction in this environment is that it is prohibitively costly for agents from two different locations to verify each other’s identities. As a result, intertemporal exchange between agents from different locations is impossible, or, more precisely, not incentive compatible. Meetings between shoppers and merchants away from home thus effectively resemble the anonymous meetings of the Kiyotaki-Wright (1989) model. This provides a role for valued fiat currency. Because agents from the same location are known to each other, households can exchange arbitrary contingent claims with other households at the same location during the “securities market” in the first stage of each period. Households could travel to other locations during the securities markets, but anonymity prevents 5 meaningful exchange of intertemporal claims. me stored value technology is a costly way of overcoming this friction. There are a large number of agents that are verifiably known to all--call them “issuers.” They are price-takers and thus earn a competitive rate of return. Like all other agents they can travel to any other location during the securities market, but since their identities are known they are able to issue enforceable claims. The claim people want to buy is one they can use in exchange in the goods market. The difficulty facing such an arrangement, however, is authenticating the claim to the merchant-in other words, the difficulty of providing the shopper with a means of communicating the earlier surrender of value. Issuers possess the technology for creating message-storage devices-- “stored value cards”-that shoppers can carry, and machines that can read and write messages on these devices. Issuers offer to install machines with merchants, These machines can read, verify and write messages on shoppers’ cards, and can record and store mestiges itself. In principle the stored value technology described here could be configured to communicate any arbitrary messages. In this setting, however, a very simple message space will suffice. The shopper’s device carries a measure of monetary value, and the merchant’s device deducts the purchase price from the number on the shopper’s card and adds it to the measure of value stored on the merchant’s device. During the next day’s securities market, the issuer visits the merchant and verifies the amount stored on the reader. The issuer sells stored value to households in securities markets and then redeems stored value from merchants during the next day’s securities markets. Messages in this case function much like the tokens in Townsend’s (1986, 1987, 1989) models of limited communication. From this perspective, currency and stored value can be seen as alternative communications mechanisms. I will adopt a very simple assumption concerning the cost of the stored value technology. I will assume that the card-reader devices that merchants use are costless to produce but require maintenance each period, and that only issuers have the expertise to perform this maintenance. The amount of maintenance required depends on the location in which the device is installed, and is proportional to the real value of the transactions that were recorded on the device. Some locations are more suited to stored value systems than others. This assumption will allow stored value and currency to coexist in equilibrium, with currency used at the locations that are less well-suited for stored value. The proportionality of costs to value processed might reflect security measures or losses due to fraud that rise in proportion to the value of transactions. I make no effort to model such phenomena explicitly, but merely take the posited cost function as given. There are no other direct resource costs. In particular, stored value cards themselves are costless. 6 The stored value cost function here is quite simple and in many respects somewhat unrealistic. Merchants’ devices and the communications networks used to”clear” stored value are, arguably, capital goods and should be represented as investment expenditures rather than input costs. I am abstracting from capital inputs here, but this seems appropriate in a model with no capital goods to begin with6 Another feature of my cost function is that cost is proportional to the value of the transaction. In practice, the resource cost of electronic storage and transmission might not vary much with the numerical value of the message: transmitting “ten” should not be much cheaper than transmitting “ten thousand.” Thus it seems plausible that a communications system, once built, would be equally capable of carrying large and small value messages.7 The cost function I adopt is the simplest one that is sufficient to demonstrate the claim that the introduction of stored value cards can reduce economic welfare. One critical feature is that the relative opportunity costs of stored value and currency vary across transactions so that both potentially circulate in equilibrium. A second critical feature is that there are constant returns to scale in providing stored value at any given location, so that competition among providers is feasible. It should become clear as I proceed that the results are likely to carry over to settings with more elaborate cost functions. The assumed technology also implies that the choice between currency and stored value takes a particularly simple form. The cost of using currency is the interest foregone while it is in use. The cost of stored value is simply the resource cost described above. Thus I am abstracting from many of the factors mentioned in the previous section such as physical convenience, currency handling costs, and employee theft; I comment on these below. I can now begin describing the model more formally.* Households Time is indexed by ~-0, and locations are indexed by z and h, where z,he[O, 1). For a typical household at location hg[O, l), consumption of good z at time t is given by c,(h,z), and labor effort is given %ee Ireland (1994) and Marquis and Reffett (1992, 1994) for models with private payment technologies requiring capital goods. 71reland (1994) studies a similar model in which cost is independent of the value of the transaction. Also see Prescott (1987). ‘The model is most closely patterned after the environment in Schreft (1992a) and Lacker and Schreft (forthcoming). The main difference is that here the alternative payments medium is used at a subset of locations by all shoppers visiting that location, rather than at all locations but by only a subset of shoppers visiting that location. Also, I allow a general cost function while her cost function is linear in distance. 7 by n,(h). Households are endowed with one unit of time that can be devoted to labor or leisure. The production technology requires one unit of labor to produce one unit of consumption good. Household preferences are m ct-ol-W,@), 1-n,(h)), (1) where u is strictly concave and twice differentiable. Household preferences are thus Leontieff across goods. This assumption implies that the composition of consumption is unaffected by the relative transactions costs at different locations, which considerably simplifies matters. In addition, it implies that transactions costs at a given location are passed on entirely to shoppers, since demand at a given location is inelastic.’ Since all goods will bear a positive price in equilibrium, we can assume without loss of generality that c,(h,z) = c,(h) for all z. In the securities market households acquire both currency and stored value. Since the units in which value is stored are arbitrary, there is no loss in generality in assuming that stored value is measured in units of currency. Thus one dollar buys one unit of stored value. Let c(h,z) and <(h,z) denote the consumption of good z at time t purchased with currency and stored value, respectively. Let m,(h) and s,(h) be the amount of currency and stored value acquired in the securities market at time t. Then the trading friction implies that where pr is the price of goods for currency and p:(z) is the price of goods for stored value at location z. 10 Household h sells y:(h) units of output for currency and g(h) units of output for stored value. In ‘Allowing substitution between goods would imply that the composition of consumption varies with changes in relative transactions costs. Relative prices net of transactions costs would then vary across locations, destroying the symmetry in households consumption and leisure choices. See Ireland (1994) and Dotsey and Ireland (1995) for models which relax the Leontieff assumption. loIn principle the price of goods for currency could vary across locations as well, but symmetry will ensure equality across locations. 8 addition, they sell y:(h) units of output to issuers. Since issuers are well-known, merchants are willing to sell to them on credit and accept payment in next period’s securities market. Feasibility requires ytmVO + y:(h) + y,‘(h) 5 n,(h) (4) units of stored value on their card reader to be At the end of the period, the household has pf(h)$(h) redeemed at t+ 1. Issuers pay interest at the nominal rate it, the market rate on one-period bonds, but deduct a proportional charge at rate r,(h) from the proceeds to cover their costs. Thus the household receives (I-r,(h))( 1+ i,)p#)y#) units of currency at t+ 1 for the stored value they have accepted. l1 Households bring to the securities market: currency from the previous period’s sales, stored value to be redeemed, maturing bonds, and any currency that might be left over from shopping in the previous period. Letting b, be bond purchases at t, households face the following budget constraint at time t+ 1. 1 m,+,(h) + St+l@) + bt+, 5 m,(h) - s 0 p,qm(h,W + (5) 1 s,(h) - s p:(z)c:(Wdz + (1 +i,)b, + pt@tm(h)+y,‘(h)) + (1 -q(h))( 1 +~t)ptS(~)~tS(h) 0 Households maximize (1) subject to (2) through (5) and the relevant nonnegativity constraints, taking prices and interest rates as given. Issuers There are a large number of issuers at location zero, distinct from the households described above. Their preferences depend on their consumption (4(z)) and leisure (1 - $ according to ’ ‘Note that the payment could be thought of as redemption at par plus a premium (1-r,(h))( 1+ it) 1. The form of merchants’ payments to issuers depends on issuers’ cost functions. The payment is proportional to the value redeemed because the issuer costs are proportional to value redeemed. If costs were independent of value redeemed, the equilibrium payment would also be independent of value redeemed. 9 2t-oPf(Cti- n,?, =t i = hf.. cti(z) (6) Issuers sell s,(z) units of stored value per capita in securities market z at time t in exchange for s&z) units of currency, and redeem s;(z) units of stored value per capita from merchants at market z at time t+ 1 in exchange for (1-r,(z))( 1+ iJs;(z) units of currency. All of the stored value they issue will be spent by households and then redeemed from card readers in equilibrium, so issuers face the constraint I s I s,(z)dz = 0 s s;(z) dz (7) 0 Maintenance of the devices on which the stored value at location z is redeemed requires y(z)s~(z)/p~(z) units of labor effort, where y(z) is a continuous, strictly increasing function with y(0) = 0. Total maintenance effort is therefore 1 n, i = s 0 YodwP:o dk (43) The alternative for issuers who are not active is to consume nothing (4(z) = rzi = 0), which can be interpreted as the proceeds of some alternative autarchic activity. The family of an issuer consists of a worker and a shopper. The worker manages the stored value business, while the shopper travels around during the goods market period purchasing consumption. Since issuers are known to all, the shopper can buy on credit, payingp,c’;(z) in the location-z securities market at t+ 1 for goods purchased there at t. Excess funds are invested in bond holdings $ An issuer’s securities market budget constraint is I l(Z)dz J0 St+ (9) I + (1 + Qb,’ - s (1 + i,)(l - rt(z))&) d.z 0 Active issuers maximize (6), subject to (7) through (9) and the relevant nonnegativity constraints, by choosing consumption, bonds, labor effort, and how much stored value to issue and redeem at each location. Because there are a large number of issuers, competition between them will drive the utility of 10 active issuers down to the reservation utility associated with inactivity. Issuers initially have no assets. Government The government issues fiat money Mt and one-period bonds Bt and satisfies MI+1 + B,, = Mt + (1 + i,P, (10) for all t. The government sets a constant money growth rate ‘IC= M,+jM, - 1, where TC1 p - 1. Equilibrium A symmetric monetary equilibrium consists of sequences of prices and quantities along with initial conditions MS1and (1 + i,)B,, such that households and issuers optimize, the lifetime utility of active issuers is equal to the lifetime utility of inactive issuers starting at any date, the government budget constraint (10) holds, and market clearing conditions hold for M,, B,, fl(h), g(h), and y’,(h), for all r and z. I restrict attention to stationary equilibria, in which real magnitudes are constant over time. Where possible, time subscripts will be dropped from variables that are constant over time; variables refer to date t quantities unless otherwise noted. The first order necessary conditions for the issuer’s maximization problem imply r(z)(l + i) = Y(Z)Pt~Pz%) (11) The left side of (11) is the nominal return from issuing one dollar’s worth of stored value at t to be redeemed at location z at t+ 1, with the proceeds invested in a bond maturing at t+ 1. Interest on the bond is paid over to the merchant, with a portion r(z) of the payment is deducted as a fee. The right side of (11) is the nominal cost of enough consumption goods to compensate the issuer for the disutility of maintaining the stored value device at location z. Thus condition (11) states that marginal revenue equals marginal cost for stored value issuers. Merchants consider whether to sell output for currency or for stored value. The first order necessary conditions for the household’s maximization problem imply that if merchants are indifferent between accepting currency and stored value, then 11 = Pt (1 - 4z))U + Qoz) (12) As a result, the last two terms in the household’s budget constraint (5) simplify top~l(h). Households at all locations face identical terms of trade between consumption and leisure despite the difference in transactions costs across locations. Consumption and labor supply are therefore identical across locations and the notation for h can be suppressed. When shoppers consider whether to use currency or stored value to purchase consumption at location z, they compare the unit cost of the former, pt, to the unit cost of the latter, pi(z). Using (11) and (12), shoppers use stored value if Pt ’ P,“(Z) pttl + WMl = + 0 (13) Thus stored value is used where y(z) < i. Because y is strictly increasing, the boundary between the stored value and the currency locations can be written as a function c(i) = y-‘(i). Stored value will coexist with currency as long as i is less than y(l), the cost of stored value at the highest cost location. If i 2 y(l), then stored value drives out currency; in this case C(o is one. The total resource cost of stored value for a given nominal rate is I(0 s y(z)& 5 r(i) (14) 0 Steady-state equilibrium values of c and n can be found as the solutions to the first order condition u,(c,l -n)lu&c,l -n) = 1 = c(1 + l?(i)). + (1 - C(i))i + r(i) (15) along with the feasibility condition n (16) For a given nonnegative nominai interest rate, consumption and employment are determined by (15) and (16). l2 Assuming that neither leisure nor consumption are inferior goods, then v(c, l-n) = 12The reduced form structure in (15) and (16) is identical to Schreft (1992a) and Lacker and Schrefi (forthcoming), although the models are somewhat different. In her model households use credit 12 uI(c, 1-n)lr+(c, l-n) is decreasing in c and increasing in l-n. If in addition we assume that v(c, l-n) goes to infinity as c goes to zero and zero as l-n goes to zero, then we are guaranteed an interior solution; the proof appears in the appendix. The real interest rate is p“ - 1 in all equilibria, and the inflation rate is P(l+O - 1. Without stored value cards the economy has the same basic structure as a standard cash-in-advance model (Lucas and Stokey [ 1983]), and can be obtained as a special case in which C(i) (and thus I’(i)) equals zero. The Welfare Economics of Stored Value An optimal steady state allocation is defined by the property that no other feasible steady state allocation makes at least one type of household better off without making some other type of household worse off. Two features of the model make optimality relatively easy to assess. Even though at some locations goods are sold for currency and at other locations goods are sold for stored value, households at all locations face identical terms of trade between consumption and leisure. As a result, all households at all locations will have the same lifetime utility in any given equilibrium. We can therefore focus our attention on the well-being of a representative household at a representative location. Second, because the lifetime utility of any given issuer is zero in all equilibria, we can effectively ignore the welfare of issuers when comparing equilibrium allocations. This just reflects the fact that issuers receive a competitive rate of return and are indifferent as to how they obtain it; constant returns to scale in providing stored value at any location implies that issuers earn no rents. Given these two facts, we can compare alternative i allocations by considering their effect on the lifetime utility of a representative household. For the version of this economy without stored value the welfare economics are well known. Households equate the marginal rate of substitution between consumption and leisure to 1 + i rather than 1, the marginal rate of transformation, because consumption is provided for out of currency accumulated by working in the previous period and currency holdings are implicitly taxed at rate i. Optimal@ requires that the marginal rate of substitution equal the marginal rate of transformation, which only holds if the nominal interest rate is zero. A positive nominal interest rate distorts household decisions, inducing substitution away from monetary activity (consumption) toward nonmonetary activity (leisure). The when close to their own home location and currency when farther away; thus at every location shoppers from nearby use currency and shoppers from a distance use cash. In contrast, at some locations only stored value is used and at other locations only currency is used in my model. Also, in her model credit costs are linear in distance. 13 resulting welfare reduction is the deadweight loss from inflation in this model. Intuitively, inflation reduces the rate of return on currency, which causes consumers to economize on the use of currency. In a cash-in-advance economy they can do this only by consuming less of the goods whose purchase requires currency. The optimal monetary policy is to deflate at the rate of time preference, x = Q - 1, so that the nominal interest rate is zero and the distortion in (15) is completely eliminated (Friedman [1969]). Note that in the absence of stored value, inflation has no effect on the feasibility frontier (16). I will compare two steady-state equilibria with identical inflation rates, one with and one without stored value. Since the real rate is the same in all equilibria, the nominal rate is constant across equilibria as well. Stored value has two effects on a typical household’s utility. The first is to alter the marginal rate of substitution between monetary and nonmonetary activities. The transactions cost associated with purchases using stored value at a given location z C c(z) is y(z), which is less than i, the private opportunity cost associated with using currency: see Figure 1. Thus stored value reduces the average transactions cost associated with consumption goods. This can be seen from (15), noting that the average cost of stored value, I?(i)lC(z),is less than i. Stored value reduces the right side of (15) by the amount C(i) - I’(& shown as the region A in Figure 1. Therefore, stored value cards reduce the distortion caused by inflation. By itself, this increases welfare. Note that the lower the total cost of stored value r(i), holding constant i and c(o, the larger the welfare gain from stored value. The second effect is through the feasibility constraint. Stored value cards involve real resource costs. Maintenance of the technology requires issuers’ labor time, and consumption at every location must be diverted to compensate issuers for their effort. Currency requires no direct resource costs in this model. l3 The introduction of stored value shifts the consumption-leisure feasibility frontier (16) inward, since resources must be diverted to cover the real costs of stored value. The area under y(z) from zero to C(r) in Figure 1 is equal to r(i), the real resource costs devoted to stored value activities. In contrast, the opportunity cost associated with currency (the area under i) is merely a transfer payment. By itself, the resource cost of stored value reduces welfare; a virtually costless government money is replaced by a costly private money. Note that the larger the total cost of stored value (holding constant i and C(i)), the larger the reduction in welfare. The net effect of stored value cards on economic welfare is indeterminate, and depends on the structure of stored value costs across locations. Since we are comparing two equilibria with the same 13This assumption is for convenience only. The essential property is that the government cost of currency is small relative to government proceeds from the seigniorage tax on currency. See Lacker (1993) for a similar model in which the provision of currency is costly. 14 nominal interest rate, we know that the marginal location has a cost of i. But conditions (15) and (16) tell us that the effect depends on the shape of the cost function. The benefit of stored value in (15) varies positively with the area A in Figure 1. The detrimental effect of stored value in (16) varies positively with r(i). Both effects depend solely on I?(i) for any given i and S(f). If costs are low across most locatior~~but then rise sharply-for example, if y is quite convex-then l?(o will be relatively small. In this case the negative effect through the feasibility condition will be small, and the positive effect through the marginal rate of substitution, c(i)i - I?(i), will be large. If instead costs are large at most locations--for example, if y is quite concave--then r(i) is close to <(i)i, the resource costs will be large, and the gain from reducing the marginal rate of substitution will be small. Thus the greater the convexity of costs across locations, the more likely it is that stored value cards improve economic welfare. This intuition is formalized in the following proposition. (The proof appears in the Appendix.) Proposition 1: Fix i. Compare an economy with no stored value to an arbitrary stored value economy with a given ratio of stored value to currency, C(i)l(l-c(i)). There is a cutof I’* [which depends on i and C(i)] such that if l?(i) > I’* then wel&zreis lower in the stored value economy, and if JI’(o c I’* then wel@re is higher in the stored value economy. The principle described in Proposition 1 appears to be quite general. In any model in which there is a deadweight loss due to the inflation tax, a private substitute for currency will reduce the base on which the tax is levied. The cost of the substitute must be less than the tax it evades--otherwise it would not be introduced. Holding constant the tax rate (the nominal interest rate), the incidence of the tax is lower and so the deadweight loss associated with that distortion will fall. Thus in any model we should expect private substitutes for fiat money should help reduce the burden of a given inflation rate. The negative welfare effect of stored value cards would seem to generalize as well. The spread between the return on currency and the return on interest-bearing government debt is a tax on currency. Absent regulatory constraint, capturing this spread is a component of the return to any private scheme that provides a substitute for currency. Absent market imperfection, participants will adopt stored value if their collective benefits exceed their collective costs. But their net benefits differ from social net benefits in two ways; the capture of seigniorage is not a social benefit, and they do not bear the governmental cost of currency provision. The gap between the nominal interest rate and the government’s per-dollar cost of providing currency thus represents the excess incentive to implement currency substitutes. Private providers will be willing to devote this excess to real resource costs, but these are wasteful from society’s 15 point of view, since they represent costly avoidance of the seigniorage tax. More realistic or elaborate models would also display the principle described in Proposition 1. For example, if stored value costs do not depend directly on the value of messages then the fee an issuer collects from a merchant would be independent of the merchant’s sales.14 The relevant cost comparison is then between the cost of the seigniorage tax, which is proportional to production, and the fixed fee, which is not. In this case the set of locations using stored value would vary with equilibrium consumption, instead of being independent of consumption as in the model above. Nevertheless, stored value would reduce transactions costs where it is used, and the benefit of a reduced inflation tax burden would have to be weighed against the added resource costs. In the absence of stored value, inflation is costly in the model because it distorts the choice between monetary and nonmonetary activities. Some economists have suggested that an important cost of inflation is that it encourages costly private credit arrangements as substitutes for government money (see Ireland [ 19941, Dotsey and Ireland [ 19951, Lacker and Schreft [forthcoming], and Aiyagari, Braun and E&stein [ 19951). Stored value could reduce this cost of inflation by displacing more costly means of payment such as checks or credit cards. The social benefit of stored value would then also include the reduction in payments cost for some transactions, and this benefit would be larger the smaller is the cost of stored value. But again, the benefit of stored value would have to be weighed against the resource cost of substituting stored value for virtually costless currency. Something like Proposition 1 would again emerge; the lower the average cost of stored value cards, the greater the gain from displacing more costly means of payments and the smaller the resources diverted to stored value systems. As I mentioned earlier, stored value seems likely to offer consumers and merchants greater physical convenience or some other advantages over currency that are not captured in the model presented above. Such advantages would not alter the basic feature of Proposition 1, however. If merchants find stored value less costly to handle than currency, their savings will presumably be reflected in their willingness to pay stored value issuers and the social benefit of stored value to merchants will be reflected in issuers’ revenues. Similarly, consumers find stored value more convenient than currency, they should be willing to pay, either directly or indirectly and the benefit of stored value to consumers will be reflected in issuers’ revenues. The intrinsic superiority of stored value cards will provide issuers with added incentive to provide stored value, but the nominal interest rate (minus the resource cost of providing government currency) still measures the excess of the private return to issuing stored value over social “The payments technology in Ireland (1994) has this property. 16 benefits. What if consumers could earn interest on their stored value cards, a possibility that appears to be technologically feasible? In this case issuers’ net interest margin would be the difference between the Tbill rate and the rate paid on stored value. This margin will not exceed the marginal cost to the issuer of providing stored value. But if stored value pays interest and coexists with noninterest-bearing currency, then it must be the case that consumers, at the margin, find stored value less convenient than currency; they are being paid to use stored value. The rate consumers earn on stored value reflects the marginal social cost of the added inconvenience of stored value. The total marginal cost of stored value, aggregating across consumers and issuers in this case, is the nominal interest rate--the sum of the rate paid to consumers and the net interest margin of issuers. The seigniorage tax captured by issuers may be passed on, in part, to consumers in the form of interest on stored value card balances. This would compensate consumers for incurring added costs to adopt stored value. But the nominal interest rate still measures the excess private incentive to adopt stored value. What if stored value completely displaces currency ? In this case the meaning of the nominal interest rate in the model becomes somewhat ambiguous; because currency does not circulate it might not serve as unit of account. Nonetheless, the difference between the real return on bonds and the real return on stored value liabilities will not exceed the marginal cost of providing stored value.15 Unless this difference is less than the government’s cost of providing currency, the principle underlying Proposition 1 still applies. Bryant and Wallace (1984) have argued that different rates of return on different government liabilities can be justified as an optimal tax. If all sources of government revenue require distortionary taxation, then it may be beneficial to raise some revenues from the taxation of currency holders. This consideration is not captured in the model described above, The seigniorage tax merely finances interest payments on government bonds. The reduction in seigniorage revenues was offset by a reduction in outstanding government debt, keeping the nominal rate constant. If instead the loss of seigniorage had to recovered by raising other distortionary taxes, it would strengthen the case against stored value. The additional deadweight burden of the compensating tax increases would have to be added to the resource cost of stored value. Similarly, nonzero government expenditures financed, in part, through seigniorage “This could happen in one of two ways. Currency could remain the unit of account--a “ghost money.” Issuers would pay interest to consumers on stored value, and the net interest margin would not exceed the marginal cost of stored value. Alternatively, stored value could become the unit of account, in which case the nominal interest rate would fall to the marginal cost of stored value. 17 would not change the basic feature Proposition 1. Policy In the presence of one distortionary tax a second distortion can sometimes improve economic welfare. A positive nominal interest rate is a distortio~ry tax on holders of government currency. In the laissez-faire regime with stored value, welfare can be lower because of the costs of stored value, which suggests that constraints on the issue of stored value cards might be welfare-enhancing. This turns out to be true. Restrictions on the issue of stored value can improve welfare, in this second-best situation, by reducing the costly displacement of government currency. Consider first a simple quantitative restriction on the use of stored value. Imagine a legal restriction that limits the quantity of stored value used by households, or, equivalently, that limits the locations at which stored value is accepted. Households can only make a fraction 51of their purchases using stored value, where the government sets r\ between 0 and C(i). Households will continue to use stored value where it is most advantageous to do so-at locations 0 through q. At locations ?J through 1 households use currency. Equilibrium is still characterized as the solution to (15) and (16), except that C(i) is replaced by q. For a given nominal interest rate, consumption and employment are determined as the solutions to tl u,(c, 1-n)/u,(c, l-n) = 1 + (1 - q)i + (17) s Y(W 0 'I n = c[l + s Y(Z)&1 (18) 0 Define C($I and n(q) as the solutions to (17) and (18) for r\~O[,<(i)], and v(q) z u(c(q), l-n(q)). The function v($ is the utility of a representative household under the constraint that no more than a fraction q of purchases can be made using stored value. Proposition 2: v ‘(c(i)) < 0, and therefore there is a binding restriction q c r;(i) on stored value under which steady state utility is higher than under the laissez-faire regime. 18 Reducing q marginally below c(i) has two effects. The direct effect via the resource constraint (18) is to eliminate the most costly uses of stored value, allowing greater consumption at each level of employment. The increase in utility at q = c(i) is proportional to y(i). The second effect via the marginal rate of substitution is to substitute currency (transactions cost r) for stored value (transactions cost y(?j)). The fall in utility is proportional to i - y(q), which vanishes at r\ = C(i) = y“(i), since at the margin stored value and currency bear the same transactions cost. The first order resource savings dominates the negligible increase in the burden of inflation. The net effect of decreasing tl is positive. Therefore there must be a value q c C(i) that results in higher steady state utility than the laissez faire regime. Note that Proposition 2 holds whether or not the stored value equilibrium is worse than the no-stored-value equilibrium; even if store value is welfare-enhancing, quantitative constraints would still be worthwhile. l6 An alternative method of restraining stored value is to impose a reserve requirement. Issuers are required to hold currency equal to a fraction 8 of their outstanding stored value liabilities. Issuers earn (l6)i rather than i on their assets, and the cost of foregone earnings, 6i, is passed on to merchants and ultimately to consumers. Stored value is used at fewer locations for any given interest rate-only where y(i) C (l-6)i. Raising the reserve requirement from zero reduces the amount of resources diverted to stored value. By itself this increases utility by easing the feasibility frontier in (18). The first order condition (15) becomes C&b) u l(C,1 -n)/u,(c, 1-n) = 1 + (1 - C(i,G))i + s 0 (1 -q-‘y(z)dz (19) where C(i,S) = y-*[( I-S)z’J. Increasing the reserve requirement now has two effects on the marginal rate of substitution. First, raising 6 increases the locations at which currency rather than lower cost stored value is used. This effect operates through C(i,b) in (19). Second, raising 6 increases the transactions cost at all locations at which stored value is used. This effect increases the integrand in the last term in (19) and does not vanish at 6 = 0. The first effect is identical to the effect of decreasing the quantitative constraint 11in (17). The quantitative constraint does not involve the second effect in (19), since it leaves inframarginal 16Proposition 2 parallels Proposition 2 in Schreft (1992a). In her model the government issues no bonds and government expenditure depends on the seigniorage collected. Lowering the constraint holding the inflation rate constant increases the demand for money and thus government expenditures. Her proposition requires the condition that government expenditures rise by less than the resource cost of payments services fall when the constraint is tightened. This condition is unnecessary if government spending is held constant and instead the bond supply varies across equilibria. There are no government expenditures in my model. 19 stored value users unaffected. In contrast, the reserve requirement imposes a tax on all stored value users. Therefore, a quantitative constraint is superior to a reserve requirement in this environment. A reserve requirement improves welfare only if the second effect in (19) does not dominate. Concluding Remarks When the nominal interest rate is positive, there is an incentive to develop substitutes for government currency. This incentive is likely to exceed the social benefit of such substitutes because the private opportunity cost of holding currency is larger than the social cost of providing currency. Although stored value can lower the opportunity cost of payments media for inframarginal consumers, the real resources diverted to stored value are wasteful from society’s point of view. For a given nominal interest rate, stored value cards are good or bad for welfare depending upon whether the average cost of stored value is below or above a certain cut-off. Quantitative restrictions on stored value are socially beneficial, in this second-best situation, because they reduce the amount of resources absorbed by the most costly stored value applications. I do not claim to show that such restrictions can be easily implemented--only that if such restrictions were practical, they would enhance welfare. Neil Wallace (1983) pointed out that the U.S. government has effectively prohibited private issue of paper smalldenomination bearer notes, such as bank notes. In the absence of such a ban, he argued, private intermediaries could issue perfect substitutes for government currency backed by default-free securities such as U.S. Treasury bills. In this case one of two things could occur. Either the nominal rate of return would not exceed the marginal cost of such intermediation, which he reckoned at close to zero, or government currency would cease to circulate. Stored value cards are just another way of issuing smalldenomination, bearer liabilities. As a corollary to Wallace’s thesis, then, we should expect one of two things to happen. Either the nominal interest rate will not exceed the marginal cost of an additional dollar’s worth of stored value, or government currency will cease to circulate. All I have added to Wallace’s argument is the observation that since stored value employs a technology that is different from, and potentially far more costly than, the government currency it would replace, it is possible that either outcome could reduce economic welfare. The restrictions that have prevented private paper substitutes for currency were in place since at least the end of the Civil War. As Wallace (1986) notes, “(i)f there is a rationale for that policy.. . then it would seem that it would apply to other payments instruments that potentially substitute for the monetary 20 base.” These longstanding restrictions on paper note issue evidently have been repealed.17 Current policy thus avoids the inconsistency of allowing electronic substitutes for government currency while preventing paper substitutes. t7Title VI of the Community Development Banking Act, P.L. 103-325 (1994) repealed all restrictions on note issue by National Banks except the l/2 percent semi-annual tax on outstanding notes. Section 1904(a) of the Tax Reform Act of 1976 repealed the 10 percent tax on note issue by corporations other than ~ti0~1 banks. De facto restrictions by bank regulators may still prevent private note issue. 21 APPENDIX Existence: Define c(y) and n(y) as the joint solutions to UJC, l-n) = qu2(c, l-n) and qc + (l-n) = y. The assumptions on preferences imply that c(y) and l-n(y) are unique, strictly positive for y > 0, 0 continuous, and monotone increasing. Therefore there exists a unique y such that n@) = q&Q. Proof of Proposition 1: Define c(q,r) and n(q,r) as the unique solutions to u&c,1 -n) = 4 Qc, 1-n) n = rc where attention is restricted to rz 1 and qzr. Define V(q,r) = u(c(q,r),l-n(q,r)). It is easy to show that since neither leisure nor consumption is an inferior good, V is strictly decreasing in q and r. The first-best allocation has a nominal interest rate of zero, so q = r = 1. Economies with positive nominal rates but no stored value have q = 1+i > 1 and r = 1. For given i and C(i), q and r vary positively with the aggregate r(i). This amounts to varying average cost holding constant marginal cost at location 2 = c(i). Note that l?(i) can lie anywhere in the interval (O,C(i)i). Define w(r) = V(l+(l-C(z))i+r,l+r). Then w(0) = V(l+(l-c)i,l) > V(l+i,l), and w([;(i)i) = V(l+i,l+<(i)i) C V(1+i, 1). Since w(r) is strictly decreasing in r, it follows immediately that there exists a unique r* for which w(I@) = V(l+i,l). cl Proof of Proposition 2: Define q(q) as the right side of (17), and r(q) as the bracketed term in (18). With v(rl) = V(q(M,r(W), we have li~,ctij v’01) = Ii%-<(i) V,.y(<(i)) = v,y(<(~J) < 0, since y(C(i)) = i and V,. < 0. lv&’ + V/l = V,[Y(~(OVI + 0 Figure 1 Opportunity Costs for Currency and Stored Value Across Locations costs i 0 GO? Locations, z 22 REFERENCES Aiyagari, S. Rao, Toni Braun, and Zvi E&stein. “Transactions Services, Inflation, and Welfare.” Manuscript, 1995. Blinder, Alan. Statement before the Subcommittee on Domestic and International Monetary Policy of the Committee on Banking and Financial Services, U.S. House of Representatives, October 1I, 1995. Bryant, John, and Neil Wallace. “A Price Discrimination Analysis of Monetary Policy,” Review of Economic Studies vol. 51 (1984): pp. 279-288. Dotsey, Michael, and Peter Ireland. “The Welfare Cost of Inflation in General Equilibrium.” Manuscript, 1995. Friedman, Milton. A Program for Monetary Stability. New York: Fordham Univ. Press, 1960. “The Optimum Quantity of Money,* in The Optimum Quantityof Money and Other Essays. Ckago: Aldine, 1969. Ireland, Peter N. “Money and Growth: An Alternative Approach,” American Economic Review vol. 84 (March 1994), pp. 47-65. Kiyotaki, Nobuhiro, and Randall Wright. “On Money as a Medium of Exchange,* Journal of Political Economy, vol. 97 (August 1989), pp. 927-54. Lacker, Jeffrey M. “Should We Subsidize the Use of Currency ?” Federal Reserve Bank of Richmond Economic Quurterty, vol. 79 (Winter 1993), pp. 47-73. and Stacey L. Schreft. “Money and Credit as Means of Payment,” Journal of Monetary Ekonomics (forthcoming). Laster, David, and John Wenninger. “Policy issues Raised by Electronic Money,” Paper presented to the Conference on Digital Cash and Electronic Money, held at the Columbia Business School, April 21, 1995. Lucas, Robert E., Jr., and Nancy L. Stokey. “Optimal Fiscal and Monetary Policy in an Economy Without Capital,” Journal of Monetary Economics, vol. 12, pp. 55-93. Marquis, Marquis, and Kevin Reffett. “Capital in the Payments System,” Economica 59 (1992), pp. 351364. “New Technology Spillovers in the Payments System,” Economic Journal vol. , and 104 (1994), pp. 1123-1138. Prescott, Edward C. “A Multiple Means of Payment Model,” in William A. Barnett and Kenneth J. Singleton, eds. New Approaches to Monetary Economics. Cambridge: Cambridge Univ. Press, 1987. 23 Rolnick, A., and W. Weber. “New Evidence on the Free Banking Era,” American Economic Review, vol. 73 (1983). “The Causes of Free Bank Failures: A Detailed Examination,” Joutnul of Monetary Econokcs, vol. 14 (1984), pp. 267-292. , and Schreft, Stacey L. “Welfare-Improving Credit Controls,” Journal of Monetary Economics, vol. 30 (1992a), pp. 57-72. “Transactions Costs and the use of Cash and Credit,” Economic 27zeoryvol. 2 (1992b), pp. 283-296. Townsend , Robert M. “Financial Structures as Communications Systems,” in Colin Lawrence and Robert P. Shay, eels., Technological Innovation, Regulation, and the Monetary Economy. Cambridge, Massachusetts: Ballinger, 1986. “Economic Organization with Liited (December 1987), pp. 754-71. Communication,” American Economic Review, vol. 77 “Currency and Credit in a Private Information Economy,” Journal of Political Economy, vol. 97 (December 1989), 132344. Wallace, Neil. “A Legal Restrictions Theory of the Demand for “Money” and the Role of Monetary Policy,” Federal Reserve Bank of Minneapolis Quarter& Review vol. 7 (Winter 1983), pp. l-7. . “The Impact of New Payment Technologies: A Macro View,” in Colin Lawrence and Robert P. Shay, eds., Technological Innovation, Regulation, and the Monetary Economy. Cambridge, Massachusetts: Ballinger, 1986. Williamson, Stephen D. “Laissez-Faire Banking and Circulating Media of Exchange,” Journal of Financial intermediation, vol. 2 (1992), pp 134-167.
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