# Financial innovation, price smoothing, and monetary policy.

FINANCIAL INNOVATION, PRICE SMOOTHING, AND MONETARY POLICY

I. INTRODUCTION

In a monetary economy, the volume of nominal transactions fluctuates with the level of economic activity. Empirical evidence suggests that the supply of nominal transaction assets (such as currency and bank deposits) also fluctuates with the level of economic activity. Some researchers have attributed these observations to the phenomenon of money endogeneity.'(1) One explanation for this endogenous supply response is a systematic monetary policy as described by Black [1972] under which the central bank "passively" adjusts the money supply to accommodate the changes in money demand. Alternatively, King and Plosser [1984] and Saving [1979] stress the role of the private banking system in producing this endogenous response. They argue that exogenous changes in real activity elicit sympathetic changes in the demand for transaction services that may be partially or fully accommodated by the banking system through its supply of "inside money." In either case, this endogenous supply response tends to mitigate the price adjustment that accompanies a real supply shock.(2)

In the long-run, however, the price level is ultimately determined by the central bank in the market for the nominal quantity that it controls, e.g., currency, bank reserves when deposit accounts are subject to reserve requirements, or the monetary base.(3) This suggests that if the private banking system does not fully accommodate the real shock, and if the shock exhibits a well-defined persistence, then endogenous price adjustments that are fully anticipated may be further damped by a passive supply response by the central bank. In addition, if price expectations affect real interest rates, then current period price level smoothing via a passive monetary policy may also be possible.(4)

In addition to employing transaction assets (currency and checkable bank deposit accounts) to meet their transaction requirements, agents may purchase non-deposit transaction services directly. For firms, these services include the tools available to the modern corporate cash manager such as lockbox collection systems, repurchase agreements, and zero balance accounts. In the household sector, they take the form of ATMs, debit and credit cards, and overdraft privilages on checkable accounts, among others. These non-deposit transaction services represent an increasingly important medium of exchange. Their supply by the banking system is not directly controlled by the central bank, and also offers another avenue by which the economy may respond endogenously to fluctuating transaction requirements associated with real shocks, thereby further mitigating the price adjustment.(5)

The production of non-deposit transaction services is subject to technology shocks in the form of financial innovations. These innovations alter the economy-wide demand for currency and checkable bank deposit accounts, and prices adjust. As with the introduction of new technology into the production of goods, financial innovations are not fully adopted immediately due to the fixed costs of adjusting individual cash management practices, but are instead assimilated over time. This implies that their effects on transaction asset demands persist. If the rate of adoption has a forecastable component, the central bank can smooth expected prices by passively accommodating these innovations. As with aggregate productivity shocks, this persistence may also enable the central bank to damp the disturbances to the current period price level that these innovations create, through the impact of price expectations on real interest rates.

This paper examines a non-deposit transaction services market in a model economy that is developed in section II. It has the following features. Transactors can meet their transaction requirements by allocating wealth to currency or to bank deposit accounts that pay a market-determined interest rate, or by purchasing non-deposit transaction services directly at a market-determined price. The decision is based on minimizing the costs of conducting the quantity of real transactions determined in the output market. There is an economy-wide credit market, with commercial banks, the central bank, and households supplying credit to firms. Commercial banks are profit-maximizers that supply bank deposits and non-deposit transaction services, in addition to credit. They also demand base money in the form of bank reserves in order to meet reserve requirements. The central bank conducts open market operations that determine its supply of base money and credit. There is no fiscal government. Output is determined by an aggregate Lucas-type supply function (see Lucas [1973]) with an autoregressive error structure reflecting persistence in productivity shocks (see Kydland and Prescott [1982] and Long and Plosser [1983]), and a stochastic aggregate demand that responds inversely to the real interest rate that clears the credit market.

Section III adds a base money supply equation where the central bank's policy passively adjusts each period in response both to forecasts of real output (which determines the quantity of real transactions to be conducted during the upcoming period), and to the anticipated technology in the provision of non-deposit transaction services (which affects the market for these unregulated substitutes for currency and bank deposits). The model is solved for the optimal policy rule that smooths prices by minimizing a weighted sum of the variances of current period price level shocks and expected inflation. Section IV discusses the results.

II. THE MODEL ECONOMY

The economy has financial markets for base money, currency, bank deposits, and credit. In addition to bank deposit accounts and credit, profit-maximizing banks produce non-deposit transaction services that households can purchase in lieu of larger currency holdings and/or bank deposit balances. The production of non-deposit transaction services by banks provides an avenue beyond price adjustment by which the economy responds endogenously to changing transaction requirements that accompany a real shock to the goods market.(6)

The Real Sector

The economy produces a single, homogeneous nondurable good that is fully consumed within the period. Output is determined by a short-run aggregate Lucas [1973] supply function that is subject to productivity shocks. Firms raise output above anticipated levels in response to positive price shocks.(7) A positive productivity shock also raises output in the current period, and these shocks generate persistent effects.(8) The aggregate supply function is specified as

[Mathematical Expression Omitted]

where [y.sup.s.sub.t] is the log of real output, [p.sub.t] is the log of the aggregate price level, and [E.sub.t-1] is the mathematical expectations operator based on full contemporaneous information available at time t-1. This variable [epsilon.sup.s.sub.t] is is the cumulative productivity shock at time t whose stochastic properties are characterized by an AR(1) process(9) given by

[Mathematical Expression Omitted]

Short-run aggregate demand fluctuates inversely with the real interest rate in the credit market and contains a stochastic component;

[Mathematical Expression Omitted]

There [y.sup.d.sub.t] is the log of the aggregate demand for goods, [r.sup.b.sub.t] the nominal interest rate in the credit market, and [epsilon.sup.d.sub.t] the random term.

The market clears period by period, or

[y.sup.s.sub.t] = [y.sup.d.sub.t].

(Hereafter, since the model is only concerned with equilibrium values of output, the superscripts on [y.sub.t] are dropped.)

The Financial Sector: The Banks

The banking sector adapts the models in Saving [1977;1979]. Identical profit-maximizing pricetaking banks supply credit, deposit accounts with transaction privileges, and non-deposit transaction services. They receive a market-determined rate of interest on credit, pay a market-determined rate of interest on deposits, and charge a market price on non-deposit transaction services. They employ a single factor to service deposit and credit accounts, and to produce non-deposit transaction services. Banks demand base money to meet reserve requirements and hold no excess reserves.(10) The aggregate bank profit function for period t is given as

[Mathematical Expression Omitted]

where [pi.sub.t] is nominal profits. [S.sup.s.sub.t] is the quantity of non-deposit transaction services provided, measured as the number of transactions performed. For simplicity, the average size of these transactions in real terms (N) is assumed constant.(11) The average unit price the banks charge for non-deposit transactions is [q.sub.t]. The nominal volume of credit banks extend to firms this period is [L.sup.b.sub.t]. The nominal supplyof bank deposits is [D.sup.s.sub.t]. The deposit rate is [r.sup.d.sub.t] and is net of the activity charges associated with check-clearing.(12) The unit cost of the bank factor input is [W.sub.t],and [X.sup.T.sub.t], [X.sup.D.sub.t], and [X.sup.S.sub.t] are the quantities of the bank factor input employed in servicing the credit and deposit accounts, and in producing the non-deposit transaction services.

Banks maximize profits by choosing the quantities of credit, deposits, and services to supply. Central bank reserve requirements fix the relationship between banks' demand for reserves [R.sup.d.sub.t] and supply of deposits to be

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the reserve requirement ratio. The banks' balance sheet constraint is

[R.sup.d.sub.t] + [L.sup.b.sub.t] = [D.sup.s.sub.t].

Assume factor input use depends solely upon the real quantities of credit and deposits being serviced:

[Mathematical Expression Omitted]

where [P.sub.t] is the current period price level (the prime and double-prime represent first and second derivatives). The banks' production function for transaction services is

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] represents a (positive) technology parameter at time t. Financial innovations take the form of positive shocks to [Mathematical Expression Omitted]. Due to the fixed costs of adjusting individual cash management programs, these innovations are assimilated over time, and any effects that they produce on asset demands exhibit persistence. This is modeled by expressing [Mathematical Expression Omitted] in terms of the following (IMA) stochastic process:

[Mathematical Expression Omitted]

with:

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the financial innovation and [Mathematical Expression Omitted] represents the average rate of technological improvement in the production of non-deposit transaction services in the current period due an innovation.

Carrying out the optimization yields the following set of supply functions for the banks.

[Mathematical Expression Omitted]

where [D.sup.s.sub.t], [L.sup.b.sub.t], and [S.sup.s.sub.t] represent the banks' supply of nominal deposits, credit, and non-deposit transaction services. Note that the supply schedules of real deposits and credit, and services are homogeneous of degree zero in [W.sub.t], [P.sub.t], and [q.sub.t], implying that a general increase (that, say, caused [W.sub.t], [P.sub.t], and [Q.sub.t], to double) leaves the quantities of each supplied unaffected.

The Financial Sector: Transaction Demand

The total real value of transactions, [T.sub.t], conducted in the economy during one period is assumed to be proportional to the value of real output in the goods market, i.e., [T.sub.t] = [upsilon] [Y.sub.t], [Y.sub.t] is real output and [upsilon] [is greater than] 0. For simplicity, all transactions are assumed to be of equal size (N) and fixed in real terms (see footnote 11). This implies that the total number of transactions that are conducted per period equals ([upsilon] Y/N). Transactors can meet these transaction requirements by employing currency or bank deposits, or by purchasing non-deposit transaction services from the banks. They are assumed to have identical preferences with respect to all choices regarding the use of transactions media. (See footnote 12 for the implications of relaxing this assumption.) The transactors' decision regarding the numbers of transactions conducted using currency, deposits, and services, respectively, is based on minimizing the total cost of conducting these transactions. This total cost includes the opportunity costs of holding a portion of the transactors' wealth in currency and deposits rather than extending credit to firms, and the cost of the services that are purchased from the bank. Note that the model developed below is consistent with requirements that currency or bank deposits be used exclusively in specific transactions, but it assumes that transactors can freely substitute between currency, deposits, and services at the margin.

The transaction cost function is expressed in real terms as

[Mathematical Expression Omitted]

where TC([T.sub.t]) is the total cost of meeting the transaction requirements for the period in real terms, [C.sup.d.sub.t] and [D.sup.d.sub.t] are the average per period nominal stocks of currency and bank deposits demanded by the public, and [S.sup.d.sub.t] is the demand for non-deposit transaction services. To obtain expressions for the numbers of transactions conducted using currency and deposits, household production functions are postulated that treat real currency and deposit holdings as factor inputs. They yield interior solutions, assuming diminishing marginal returns to increased factor use. This gives the following relationships:

[Mathematical Expression Omitted]

where [T.sup.C.sub.t] and [T.sup.D.sub.t] represent the number of transactions per period conducted using currency and deposits. The following equation is the adding up constraint on total transactions per period.

[Mathematical Expression Omitted]

Carrying out the optimization yields the following set of demand relationships. (The numerical subscripts represent partial derivatives.)

[Mathematical Expression Omitted] [Mathematical Expression Omitted]

Note that the argument in these demand functions that transmits financial innovations to the real economy is [q.sub.t], the unit price of non-deposit transaction services. A financial innovation raises the productivity of the bank factor input in the production of services. This precipitates a decline in [q.sub.t] that induces a portfolio-type adjustment by transactors in their selection of transaction media. That is, they reduce their (real) demand for currency and bank deposits, and increase their demand for services. Persistence in the rate of adoption of financial innovations by the banks elicits persistence in this portfolio adjustment.(13)

The Financial Sector: The Credit Market

Households, commercial banks, and the central bank extend credit to firms for expansion of new plant and equipment.(14) The demand for credit by firms is inversely related to the real interest rate, and positively related to output.

[Mathematical Expression Omitted]

The supply of credit by households is positively related to the real interest rate and to real income (or real output).

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the nominal supply of credit by households to firms.

The supply of credit by the central bank is determined by its open market operations policy, and is equal to the supply of high-powered, or base money. From the central bank's balance sheet constraint, this is given as

[Mathematical Expression Omitted]

where [H.sub.t] is the nominal base money supply, and [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the nominal supplies of reserves and currency.

Assuming the credit market clears period by period, the following equilibrium condition results:

[Mathematical Expression Omitted]

A Quasi-Solution for the Price Level

Assuming the markets for currency, deposits, credit, non-deposits transaction services, and bank reserves clear each period, the financial sector can be collapsed into two equations that represent equilibrium conditions in the markets for base money and credit. A (semi-) log-linear approximation yields the following expressions:(15)

[Mathematical Expressions Omitted]

where [h.sub.t] is the log of the monetary base, and the parameters [d.sub.i], [c.sub.i], and [Mathematical Expression Omitted] represent the absolute values of the elasticities (or (semi-elasticities) of the following demand and supply equations with respect to the "ith" arguments:

[Mathematical Expression Omitted]

and

[Mathematical Expression Omitted]

Combining equations (26) and (27) with equations (1) - (4) from the real sector yields the following expression for the price level.

[Mathematical Expression Omitted]

where:

[Mathematical Expressions Omitted]

In general, the signs of [PI.sub.2] and [PI.sub.4] are indeterminate. However, [c.sub.2] is the indirect effect of a change in [Mathematical Expression Omitted] on the demand for currency resulting from a substitution toward or away from non-deposit transaction services. This indirect effect is much smaller than [d.sub.2] which incorporates the direct effect of a change in the own rate of return on the demand for bank deposits. The implications are that ([d.sub.2] - [c.sub.2]) is positive and the term (phi [d.sub.2] - [c.sub.2]) is small. Therefore, the likely signs of [PI.sub.2] and [PI.sub.4] are positive.

The availability of the unregulated non-deposit transaction services market for transactors provides an alternative to currency and bank deposits that affects the adjustment of prices to disturbances originating in the real sector. This reduces the interest rate and real income elasticities of the demands for currency and bank deposits, i.e., [c.sub.1], [d.sub.1], [c.sub.2], [d.sub.2], [c.sub.4], and [d.sub.4] are all smaller than they otherwise would be.(16) Therefore, [PI.sub.1], [PI.sub.2] and [PI.sub.4] are smaller than they otherwise would be, with [PI.sub.2] more affected than [PI.sub.1] and [PI.sub.4], provided that (the absolute value of) the interest rate [Mathematical Expression Omitted] elasticity of aggregate demand ([beta.sub.1]) is less than unity. In the absence of this market, financial innovations do not occur, and [c.sub.3] and [d.sub.3] are both zero, implying that [PI.sub.3] is zero. The implications that these observations have for price smoothing are discussed below.

III. PRICE SMOOTHING AND AN OPTIMAL `PASSIVE' POLICY RULE

This section specifies a passive policy rule under which the central bank supplies base money in an amount that is consistent with its forecast of the future transaction requirements of the economy during the upcoming period. This rule is combined with equation (28), and the final reduced form expression for the price level is derived. Optimal values for the choice parameters in the policy rule are then determined based on a price smoothing objective by the central bank.

The Reduced Form Expression for the Price Level

The price level adjusts to aggregate demand and supply disturbances that originate in the real sector, and to financial innovations. This adjustment occurs as a result of a temporary disequilibrium that these disturbances produce in the markets that yield transaction services, i.e., the currency, bank deposit, and non-deposit transaction services markets. The central bank may be able to smooth these price movements by adjusting the supply of base money in anticipation of the future transaction requirements for the upcoming period. Expectations of these future transaction requirements are based on forecasts of output and the level of technology that is to be employed in the production of non-deposit transaction services. If the central bank chooses to conduct this passive, or accommodative, policy by controlling the supply of base money, then the following policy rule would result. [h.sub.t] = [mu.sub.1] [E.sub.t-1] [Y.sub.t] + [[mu].sub.2] [E.sub.t-1 [THETA.sub.t] (29) where [mu.sub.1] and [mu.sub.2] are policy parameters to be optimally chosen by the central bank.

Upon substitution of equation (29) into (28), the resulting expression can be solved by the method of undetermined coefficients for the price level, [p.sub.t].

[Mathematical Expression Omitted]

where

[Mathematical Expressions Omitted]

Note that [GAMMA.sub.4] is positive (assuming [Pi.sub.2] and [Pi.sub.4] are positive) and is independent of the policy parameters. This implies that an aggregate demand shock raises the price level by an amount that is independent of the policy rule. This independence from the policy rule is due to the lack of persistence in the shock. However, if the interest elasticity of aggregate demand ([beta.sub.1]) is less than unity (in absolute value), then the magnitude of the price response is damped by the availability of non-deposit transaction services, i.e., the reductions in [c.sub.i] and [d.sub.j] (i,j = 1,2,4) discussed above lower [GAMMA.sub.4].

The Optimal Passive Policy Rule

A passive monetary policy that is designed to accommodate future transaction requirements is successful to the extent that it is able to smooth prices. In a model economy where expectations play a major role in price level determination, price smoothing objectives could focus on minimizing the variances of both the current period price level shocks, and the expected inflation rate. This corresponds to the following loss function (L).(17)

L = A var [[p.sub.t] - [E.sub.t-1] [p.sub.t]] + B var [[E.sub.t] [p.sub.t+1] - [p.sub.t]],

A,B > 0,

(31) where A and B are the weights attached to the two price smoothing objectives.

The optimal values of the policy parameters, [mu.sub.1] and [mu.sub.2], that minimize the loss function (L) are given below.

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted]

If the persistence in the productivity shocks is sufficiently great, i.e., [rho] is sufficiently large (and assuming that [Pi.sub.1] and [Pi.sub.2] are positive), then [Mathematical Expression Omitted] is positive. Therefore, as the central bank raises its forecast of output, it anticipates greater transaction requirements, and increases the supply of base money in order to avoid a decline in the price level. The term [Mathematical Expression Omitted] is unambiguously negative. If the central bank anticipates improved technology in the provision of non-deposit transaction services, it expects transactors to substitute away from currency and bank deposits, and reduces the base money supply in order to avoid a price increase.

The optimal policy rule represented by equations (32) and (33) can be examined under certain special "cases". Allow p [right arrow] 1, which implies that the cumulative productivity disturbance term, [Mathematical Expression Omitted], follows a random walk. Next, let the relative weights in the loss function (L) vary from (B/A) [right arrow] 0 to (A/B) [right arrow] 0. This gives the following optimal values for [Mathematical Expression Omitted].

If the central bank is concerned with minimizing the variance of current period price level forecast errors only, the elasticity of the base money supply response to the forecast of output for the upcoming period is given by equation (34), i.e., (B/A) [right arrow] 0. Two elements of this equation are noteworthy. First, as the interest elasticity of aggregate demand ([beta.sub.1]) increase (in absolute value), the base money supply becomes less responsive to changes in output forecasts, i.e., [Pi.sub.2] is smaller. This is due to the additional price smoothing effect produced by the greater damping of aggregate demand by interest rate movements that are responding to aggregate real shocks. Second, as long as the interest elasticity of aggregate demand ([beta.sub.1]) is less than unity (in absolute value), the availability of the non-deposit transaction services market also reduces the supply response to changes in output forecasts, i.e., [Pi.sub.2] is reduced by a greater amount than [Pi.sub.1]. This is the result of the endogenous supply response in this market mitigating the price adjustment that accompanies a real shock.

If the central bank is concerned exclusively with minimizing the variance of expected inflation, then its optimal response to changes in the output forecast is given by equation (35), i.e., (A/B) [right arrow] 0. The two elements that were just discussed with respect to equation (34) are also true in this case. That is, the persistent effects of aggregate supply shocks and financial innovations imply that factors which smooth current period price shocks also smooth expected inflation. In addition, an increase in the elasticity of output with respect to the current period price level forecast error ([alpha.sub.1]) increases the central bank's optimal base money supply response to changes in output forecasts. This results from the greater anticipated swings in transaction requirements that would accompany the more volatile output induced by current period price shocks.

A similar examination can be made of the optimal base money supply response to the anticipated level of technology in the production of non-deposit transaction services [Mathematical Expression Omitted]. Allow [PHI] [right arrow] 0, in which case the level of technology used to produce non-deposit transactions services, [THETA.sub.t], follows a random walk, and allow (B/A) [right arrow] 0, followed by (A/B) [right arrow] 0.

[Mathematical Expression Omitted]

When the central bank is concerned solely with current period price level forecast errors, equation (36) applies. In this case, a financial innovation that is unaccompanied by a sympathetic base money supply response would raise the price level. The greater the share of transactions that are being conducted by non-deposit transaction services prior to the innovation, the greater is the effect of a given innovation on the price level, i.e., [Pi.sub.3] would be larger and [Pi.sub.1] (and [Pi.sub.2] would be smaller. This would require a larger base money supply response by the central bank

If the central bank were concerned only with expected inflation, then equation (37) would indicate the optimal base money supply response to a financial innovation. As just discussed, as non-deposit transaction services assume a larger share of the total transactions being conducted, the magnitude of the required base money supply response to a financial innovation would increase, i.e., [Pi.sub.3] increases and [Pi.sub.2] declines by more than [Pi.sub.1]. In addition, a financial innovation that is unaccompanied by a base money supply response would have a greater effect on inflation expectations as the interest elasticity of aggregate demand ([beta.sub.1]) rises (in absolute value), implying that aggregate demand is more damped by interest rate movements, and as the elasticity of output with respect to current period price shocks ([alpha.sub.1]) falls. Both of these factors imply that price movements rather than changes in output (or the volume of real transactions) absorb a greater share of the increased supply of transaction services that accompany the financial innovation. Therefore, the central bank's optimal base money supply response to a financial innovation would increase in magnitude.

IV. CONCLUSIONS

Non-deposit transaction services have assumed an increasingly important role in the U.S. economy's payments system over the past two decades. The growth of this market was not always foreseen, and was often understood only in retrospect.(18) The significance that this has for monetary policy is in its impact on the demand for aggregate measures of money. The inability of the central bank to identify these changes, and to take them into account when setting policy, causes fluctuations to occur in the price level as transactors adjust to changes in transaction requirements and to the availability of transaction services. These price level fluctuations can be minimized by a monetary policy that forecasts future transaction needs in the economy and engages in a passive policy that is designed to accommodate these needs.

This paper explores some of the major policy implications of a dynamic unregulated market for financial services whose product(s) competes with the transaction assets that are subject to central bank control. Under very general conditions, the existence of this market has the positive effect of smoothing prices as the production of these non-deposit transaction services responds endogenously to disturbances originating in the real sector.

As this market continues to expand, this price smoothing effect will become more pronounced. If the real disturbances exhibit a well-defined persistence, as the real business cycle theorists stress, then the central bank is able to anticipate changes in transaction requirements and further smooth prices by accommodating these needs.

The negative effect of this unregulated market is the impact of financial innovations on prices. A financial innovation raises the supply of transaction services and acts as a monetary shock. This causes an unanticipated price response as transactors adjust their transaction asset demands. If the financial innovation is absorbed slowly, and the central bank fails to adjust its supply of these assets to the rate of adoption of the new technology, the price response will persist. Again, the optimal policy is one that anticipates the change this produces on transaction needs and accommodates the new environment.

This paper has focused on some of the more significant effects that this growing unregulated market for transaction services has on the economy, and on the significance of the market for monetary policy under the current regulatory structure. Additional work in this area seems warranted. In particular, financial innovations are not purely exogenous. For example, the pace of financial innovation accelerates during periods of high and volatile inflation and interest rates. An important issue is how significant this market is for economic stability under various regulatory regimes, particularly when financial innovations are largely endogenous. A fractional reserve banking system may not be optimal. The removal of supply constraints on transaction assets may enhance the ability of the economy to absorb real shocks as well as financial innovations without large unanticipated swings in the price level.

VARIABLE LIST

[Mathematical Expression Omitted] = log of real output

[P.sub.t] = log of aggregate price level

[Mathematical Expression Omitted] = cumulative productivity shock

[n.sub.t] = current period productivity shock

[Mathematical Expression Omitted] = log of aggregate demand for goods

[Mathematical Expression Omitted] = nominal interest rate in the credit market

[Mathematical Expression Omitted] = current period aggregate demand shock

[Y.sub.t] = log of current period output and log of current income

[pi.sub.t] = aggregate bank profits

[Mathematical Expression Omitted] = quantity of non-deposit transaction services produced

(number of transactions)

N = average size of transactions

[q.sub.t] = unit price of non-deposit transaction services

[Mathematical Expression Omitted] = average nominal volume of credit extended to firms by banks

[Mathematical Expression Omitted] = average nominal supply of bank deposits per period

[Mathematical Expression Omitted] = nominal deposit rate

[W.sub.t] = nominal unit cost of the bank's sole factor input

[Mathematical Expression Omitted] = quantity of bank factor input employed in servicing credit

accounts

[Mathematical Expression Omitted] = quantity of bank factor input employed in servicing deposit

accounts

[Mathematical Expression Omitted] = quantity of bank factor input employed in producing

non-deposit

transaction services

[Mathematical Expression Omitted] = banks' demand for reserves

[Mathematical Expression Omitted] = reserve requirement ratio for bank deposits

[Theta.sub.t] = technology parameter in the production function for non-deposit

transaction services

[xi.sub.t] = current period financial innovation

[delta] = magnitude of the financial innovation when it occurs (from

the binomial distribution of [xi.sub.t]

k = probability (each period) that a financial innovation of size [delta]

will occur

[Z.sub.t] = cumulative effect of financial innovation on [THETA.sub.t]

[t.sub.t] = total real value of transactions

u = number of transactions per dollar of output

[Y.sub.t] = nominal output or nominal income

[T.sub.C] = total cost of meeting transaction cost for the period

[Mathematical Expression Omitted] = average per period nominal stock of currency demanded by

the public

[Mathematical Expression Omitted] = average per period nominal stock of bank deposits demanded

by the public

[Mathematical Expression Omitted] = average per period demand for non-deposit transaction services

[Mathematical Expression Omitted] = total number of transactions made using currency

[Mathematical Expression Omitted] = total number of transactions made using bank deposits

[Mathematical Expression Omitted] = nominal demand for credit by firms

[Mathematical Expression Omitted] = nominal supply of credit extended to firms by households

[H.sub.t] = nominal supply of high-powered (or base) money by the

central bank

[h.sub.t] = log of nominal supply of high-powered (or base) money by the

central bank

[Mathematical Expression Omitted] = nominal supply of currency by the central bank

[Mathematical Expression Omitted] = nominal supply of bank reserves by the central bank

[mu.sub.1],[mu.sub.2] = central bank policy parameters

(1.) See Sims [1980; 1983].

(2.) King and Plosser have suggested the possibility that the observed procyclical movements of prices may be the result of an excessive endogenous supply response by the banking system [1984, 372]. This type of response can be rationalized only in the presence of endogenous financial innovation or incomplete information. Our model takes financial innovation as exogenous. Hester [1981] discusses the likely endogeneity of financial innovation during the 1970s. Saving's partial equilibrium model of the money market takes prices as exogenous. However, the comparative statics of his money supply equation are consistent with the accommodative response described above. Specifically, the money supply rises with output and falls with prices, both of which would accompany a real supply shock.

(3.) See Fama [1980].

(4.) See Litterman and Weiss [1986] for empirical evidence.

(5.) Non-financial businesses may also choose to produce these transaction services "in-house" by allocating resources (capital and labor) to their internal cash management program. This adds a new dimension to the non-financial business sector's demand for money as discussed in Marquis and Witte [1989]. For the purposes of this paper, it is immaterial whether firms exercise this option or the banks are assumed to be the sole providers of these services.

(6.) Adjustments in the currency/deposit ratio are also possible. This represents a principal source of money endogeneity in Saving [1979].

(7.) This is a common feature of the incomplete information models of Lucas [1972; 1973; 1975] and Barro [1976; 1980], as well as the Fischer [1977] and Taylor [1980] models that incorporate long-term nominal wage contracts. Of these models, only Lucas [1972; 1975] generates persistent effects that result from mistakes in investment decisions. Our model does not have this feature since all output is fully consumed within the period, which is similar to the Barro and Fischer-Taylor models.

(8.) In the real business cycle models of Kydland and Prescott [1982], Long and Plosser [1983], and King and Plosser [1984], this represents the sole source of short-run aggregate fluctuations. Rationales for the persistent effects of productivity shocks include the "time-to-build" character of realizing investment decisions in the form of new plant and equipment (Kydland and Prescott) and the desire of households to smooth the additional consumption flows over time (Long and Plosser).

(9.) This allows the model to accord well with the empirical observations that output follows a low-order autoregressive process. This is discussed in Lucas [1977] and Nelson and Plosser [1982], in addition to the real business cycle literature previously cited.

(10.) Adjustments in excess reserves could also provide a means for an endogenous response of the banking system in meeting the change in transaction requirements of the economy associated with a real shock. In practice, the growth of the federal funds market over the past twenty-five years has substantially reduced the quantity of excess reserves in the banking system as a percentage of total assets. This ratio is now less than 1 percent and is relatively stable over the course of a business cycle, which suggests that it plays a very limited role in providing this kind of endogenous response to real shocks.

(11.) This assumption is also made for the size of transactions conducted via currency and bank deposits. This removes (at least) one degree of freedom in the choices made by transactors.

(12.)] Since the nationwide legalization of NOW accounts, it is common practice for depository institutions to offer their depositors explicit choices on the pricing structure of their accounts that include various combinations of interest income, minimum balance requirements, and per check transaction fees. As Sweeney (1988, 182-3, 197-9) points out, even if pricetaking, quantity-setting banks are interested only in the "net interest rate on bank money" (i.e., the variable [Mathematical Expression Omitted] in this model) when making their quantity decisions, an optimal mix of interest income and per check transaction fees is determined by the households' preferences in the use of bank money for transactions purposes. There may be additional price-smoothing effects in response to exogenous shocks that the model does not capture. Banks could hold [Mathematical Expression Omitted] constant while raising both the deposit rate and transaction fee. These changes would have differential effects across transactors with those having the stronger preferences for using bank money in transactions more affected by the higher transaction fees than by the higher deposit rate. To fully capture the aggregate price-smoothing effects would therefore require explicit modeling of the pricing decisions as well as the households preferences. We have chosen to abstract from these considerations in order to focus on the principal implications that the unregulated non-deposit transaction services market has for monetary policy. For additional discussions of the pricing decisions from the bank's perspective, see Saving [1979], Mitchell [1979; 1988], and Merris [1985].

(13.) This assumes that households continuously optimize in their selection of transaction media. This assumption is a potential problem only when a financial innovation involves a new financial services product. In this case, it might be argued that there is some degree of "habit-persistence" on the part of households that produces a sluggish adjustment in the rate at which they assimilate the new technology. However, if the banks accurately perceive this, it would be incorporated into their decision on the rate at which the new technology is introduced to the public. This is captured by [PHI] in equation (11). Mistakes made by the banks in this regard could lead to additional supply shocks that are not included in the model. However, if these mistakes are purely random and are correctable period-by-period, they would have no persistence, and therefore no relevance for a passive monetary policy that pursues price-smoothing objectives.

(14.) In this model, open market operations are conducted in the private versus the government securities market. It would be a trivial matter to include a fixed stock of government securities in the model that the central bank could draw on for its open market operations.

(15.) The following two assumptions were also required in order to sign the coefficients in equations (26) and (27): (1) Nominal factor costs, [omega.sub.t], are homogeneous of degree one in prices. (2) Direct effects of changes in [Mathematical Expression Omitted], and [Y.sub.t] on the demand for bank deposits, and of changes in [Mathematical Expression Omitted] and [Y.sub.t] on the demand for currency dominate the indirect (or feedback) effects that are due to substitution toward or away from non-deposit transaction services. Details of this derivation, as well as the other mathematics of the paper, are contained in an appendix that is available from the authors upon request.

(16.) For the income elasticities of the demands for currency and bank deposits to be reduced by the availability of this unregulated market, the income elasticity of the supply of non-deposit transaction services must exceed the income elasticity of demand. This is discussed in the appendix.

(17.) See Goodfriend [1987] for a discussion of this loss function.

(18.) This was an important factor contributing to Goldfeld's [1976] famous "case of the missing money." See Porter, Simpson, and Mauskopf [1979].

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MILTON H. MARQUIS and STEVEN R. CUNNINGHAM(*)

(*) Assistant Professor, Florida State University, and Assistant Professor, University of Connecticut. We would like to thank Richard Sweeney and two anonymous referees for their numerous insightful comments that vastly improved the quality of this paper. They, of course, bear no responsibility for any remaining errors or omissions.

I. INTRODUCTION

In a monetary economy, the volume of nominal transactions fluctuates with the level of economic activity. Empirical evidence suggests that the supply of nominal transaction assets (such as currency and bank deposits) also fluctuates with the level of economic activity. Some researchers have attributed these observations to the phenomenon of money endogeneity.'(1) One explanation for this endogenous supply response is a systematic monetary policy as described by Black [1972] under which the central bank "passively" adjusts the money supply to accommodate the changes in money demand. Alternatively, King and Plosser [1984] and Saving [1979] stress the role of the private banking system in producing this endogenous response. They argue that exogenous changes in real activity elicit sympathetic changes in the demand for transaction services that may be partially or fully accommodated by the banking system through its supply of "inside money." In either case, this endogenous supply response tends to mitigate the price adjustment that accompanies a real supply shock.(2)

In the long-run, however, the price level is ultimately determined by the central bank in the market for the nominal quantity that it controls, e.g., currency, bank reserves when deposit accounts are subject to reserve requirements, or the monetary base.(3) This suggests that if the private banking system does not fully accommodate the real shock, and if the shock exhibits a well-defined persistence, then endogenous price adjustments that are fully anticipated may be further damped by a passive supply response by the central bank. In addition, if price expectations affect real interest rates, then current period price level smoothing via a passive monetary policy may also be possible.(4)

In addition to employing transaction assets (currency and checkable bank deposit accounts) to meet their transaction requirements, agents may purchase non-deposit transaction services directly. For firms, these services include the tools available to the modern corporate cash manager such as lockbox collection systems, repurchase agreements, and zero balance accounts. In the household sector, they take the form of ATMs, debit and credit cards, and overdraft privilages on checkable accounts, among others. These non-deposit transaction services represent an increasingly important medium of exchange. Their supply by the banking system is not directly controlled by the central bank, and also offers another avenue by which the economy may respond endogenously to fluctuating transaction requirements associated with real shocks, thereby further mitigating the price adjustment.(5)

The production of non-deposit transaction services is subject to technology shocks in the form of financial innovations. These innovations alter the economy-wide demand for currency and checkable bank deposit accounts, and prices adjust. As with the introduction of new technology into the production of goods, financial innovations are not fully adopted immediately due to the fixed costs of adjusting individual cash management practices, but are instead assimilated over time. This implies that their effects on transaction asset demands persist. If the rate of adoption has a forecastable component, the central bank can smooth expected prices by passively accommodating these innovations. As with aggregate productivity shocks, this persistence may also enable the central bank to damp the disturbances to the current period price level that these innovations create, through the impact of price expectations on real interest rates.

This paper examines a non-deposit transaction services market in a model economy that is developed in section II. It has the following features. Transactors can meet their transaction requirements by allocating wealth to currency or to bank deposit accounts that pay a market-determined interest rate, or by purchasing non-deposit transaction services directly at a market-determined price. The decision is based on minimizing the costs of conducting the quantity of real transactions determined in the output market. There is an economy-wide credit market, with commercial banks, the central bank, and households supplying credit to firms. Commercial banks are profit-maximizers that supply bank deposits and non-deposit transaction services, in addition to credit. They also demand base money in the form of bank reserves in order to meet reserve requirements. The central bank conducts open market operations that determine its supply of base money and credit. There is no fiscal government. Output is determined by an aggregate Lucas-type supply function (see Lucas [1973]) with an autoregressive error structure reflecting persistence in productivity shocks (see Kydland and Prescott [1982] and Long and Plosser [1983]), and a stochastic aggregate demand that responds inversely to the real interest rate that clears the credit market.

Section III adds a base money supply equation where the central bank's policy passively adjusts each period in response both to forecasts of real output (which determines the quantity of real transactions to be conducted during the upcoming period), and to the anticipated technology in the provision of non-deposit transaction services (which affects the market for these unregulated substitutes for currency and bank deposits). The model is solved for the optimal policy rule that smooths prices by minimizing a weighted sum of the variances of current period price level shocks and expected inflation. Section IV discusses the results.

II. THE MODEL ECONOMY

The economy has financial markets for base money, currency, bank deposits, and credit. In addition to bank deposit accounts and credit, profit-maximizing banks produce non-deposit transaction services that households can purchase in lieu of larger currency holdings and/or bank deposit balances. The production of non-deposit transaction services by banks provides an avenue beyond price adjustment by which the economy responds endogenously to changing transaction requirements that accompany a real shock to the goods market.(6)

The Real Sector

The economy produces a single, homogeneous nondurable good that is fully consumed within the period. Output is determined by a short-run aggregate Lucas [1973] supply function that is subject to productivity shocks. Firms raise output above anticipated levels in response to positive price shocks.(7) A positive productivity shock also raises output in the current period, and these shocks generate persistent effects.(8) The aggregate supply function is specified as

[Mathematical Expression Omitted]

where [y.sup.s.sub.t] is the log of real output, [p.sub.t] is the log of the aggregate price level, and [E.sub.t-1] is the mathematical expectations operator based on full contemporaneous information available at time t-1. This variable [epsilon.sup.s.sub.t] is is the cumulative productivity shock at time t whose stochastic properties are characterized by an AR(1) process(9) given by

[Mathematical Expression Omitted]

Short-run aggregate demand fluctuates inversely with the real interest rate in the credit market and contains a stochastic component;

[Mathematical Expression Omitted]

There [y.sup.d.sub.t] is the log of the aggregate demand for goods, [r.sup.b.sub.t] the nominal interest rate in the credit market, and [epsilon.sup.d.sub.t] the random term.

The market clears period by period, or

[y.sup.s.sub.t] = [y.sup.d.sub.t].

(Hereafter, since the model is only concerned with equilibrium values of output, the superscripts on [y.sub.t] are dropped.)

The Financial Sector: The Banks

The banking sector adapts the models in Saving [1977;1979]. Identical profit-maximizing pricetaking banks supply credit, deposit accounts with transaction privileges, and non-deposit transaction services. They receive a market-determined rate of interest on credit, pay a market-determined rate of interest on deposits, and charge a market price on non-deposit transaction services. They employ a single factor to service deposit and credit accounts, and to produce non-deposit transaction services. Banks demand base money to meet reserve requirements and hold no excess reserves.(10) The aggregate bank profit function for period t is given as

[Mathematical Expression Omitted]

where [pi.sub.t] is nominal profits. [S.sup.s.sub.t] is the quantity of non-deposit transaction services provided, measured as the number of transactions performed. For simplicity, the average size of these transactions in real terms (N) is assumed constant.(11) The average unit price the banks charge for non-deposit transactions is [q.sub.t]. The nominal volume of credit banks extend to firms this period is [L.sup.b.sub.t]. The nominal supplyof bank deposits is [D.sup.s.sub.t]. The deposit rate is [r.sup.d.sub.t] and is net of the activity charges associated with check-clearing.(12) The unit cost of the bank factor input is [W.sub.t],and [X.sup.T.sub.t], [X.sup.D.sub.t], and [X.sup.S.sub.t] are the quantities of the bank factor input employed in servicing the credit and deposit accounts, and in producing the non-deposit transaction services.

Banks maximize profits by choosing the quantities of credit, deposits, and services to supply. Central bank reserve requirements fix the relationship between banks' demand for reserves [R.sup.d.sub.t] and supply of deposits to be

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the reserve requirement ratio. The banks' balance sheet constraint is

[R.sup.d.sub.t] + [L.sup.b.sub.t] = [D.sup.s.sub.t].

Assume factor input use depends solely upon the real quantities of credit and deposits being serviced:

[Mathematical Expression Omitted]

where [P.sub.t] is the current period price level (the prime and double-prime represent first and second derivatives). The banks' production function for transaction services is

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] represents a (positive) technology parameter at time t. Financial innovations take the form of positive shocks to [Mathematical Expression Omitted]. Due to the fixed costs of adjusting individual cash management programs, these innovations are assimilated over time, and any effects that they produce on asset demands exhibit persistence. This is modeled by expressing [Mathematical Expression Omitted] in terms of the following (IMA) stochastic process:

[Mathematical Expression Omitted]

with:

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the financial innovation and [Mathematical Expression Omitted] represents the average rate of technological improvement in the production of non-deposit transaction services in the current period due an innovation.

Carrying out the optimization yields the following set of supply functions for the banks.

[Mathematical Expression Omitted]

where [D.sup.s.sub.t], [L.sup.b.sub.t], and [S.sup.s.sub.t] represent the banks' supply of nominal deposits, credit, and non-deposit transaction services. Note that the supply schedules of real deposits and credit, and services are homogeneous of degree zero in [W.sub.t], [P.sub.t], and [q.sub.t], implying that a general increase (that, say, caused [W.sub.t], [P.sub.t], and [Q.sub.t], to double) leaves the quantities of each supplied unaffected.

The Financial Sector: Transaction Demand

The total real value of transactions, [T.sub.t], conducted in the economy during one period is assumed to be proportional to the value of real output in the goods market, i.e., [T.sub.t] = [upsilon] [Y.sub.t], [Y.sub.t] is real output and [upsilon] [is greater than] 0. For simplicity, all transactions are assumed to be of equal size (N) and fixed in real terms (see footnote 11). This implies that the total number of transactions that are conducted per period equals ([upsilon] Y/N). Transactors can meet these transaction requirements by employing currency or bank deposits, or by purchasing non-deposit transaction services from the banks. They are assumed to have identical preferences with respect to all choices regarding the use of transactions media. (See footnote 12 for the implications of relaxing this assumption.) The transactors' decision regarding the numbers of transactions conducted using currency, deposits, and services, respectively, is based on minimizing the total cost of conducting these transactions. This total cost includes the opportunity costs of holding a portion of the transactors' wealth in currency and deposits rather than extending credit to firms, and the cost of the services that are purchased from the bank. Note that the model developed below is consistent with requirements that currency or bank deposits be used exclusively in specific transactions, but it assumes that transactors can freely substitute between currency, deposits, and services at the margin.

The transaction cost function is expressed in real terms as

[Mathematical Expression Omitted]

where TC([T.sub.t]) is the total cost of meeting the transaction requirements for the period in real terms, [C.sup.d.sub.t] and [D.sup.d.sub.t] are the average per period nominal stocks of currency and bank deposits demanded by the public, and [S.sup.d.sub.t] is the demand for non-deposit transaction services. To obtain expressions for the numbers of transactions conducted using currency and deposits, household production functions are postulated that treat real currency and deposit holdings as factor inputs. They yield interior solutions, assuming diminishing marginal returns to increased factor use. This gives the following relationships:

[Mathematical Expression Omitted]

where [T.sup.C.sub.t] and [T.sup.D.sub.t] represent the number of transactions per period conducted using currency and deposits. The following equation is the adding up constraint on total transactions per period.

[Mathematical Expression Omitted]

Carrying out the optimization yields the following set of demand relationships. (The numerical subscripts represent partial derivatives.)

[Mathematical Expression Omitted] [Mathematical Expression Omitted]

Note that the argument in these demand functions that transmits financial innovations to the real economy is [q.sub.t], the unit price of non-deposit transaction services. A financial innovation raises the productivity of the bank factor input in the production of services. This precipitates a decline in [q.sub.t] that induces a portfolio-type adjustment by transactors in their selection of transaction media. That is, they reduce their (real) demand for currency and bank deposits, and increase their demand for services. Persistence in the rate of adoption of financial innovations by the banks elicits persistence in this portfolio adjustment.(13)

The Financial Sector: The Credit Market

Households, commercial banks, and the central bank extend credit to firms for expansion of new plant and equipment.(14) The demand for credit by firms is inversely related to the real interest rate, and positively related to output.

[Mathematical Expression Omitted]

The supply of credit by households is positively related to the real interest rate and to real income (or real output).

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the nominal supply of credit by households to firms.

The supply of credit by the central bank is determined by its open market operations policy, and is equal to the supply of high-powered, or base money. From the central bank's balance sheet constraint, this is given as

[Mathematical Expression Omitted]

where [H.sub.t] is the nominal base money supply, and [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are the nominal supplies of reserves and currency.

Assuming the credit market clears period by period, the following equilibrium condition results:

[Mathematical Expression Omitted]

A Quasi-Solution for the Price Level

Assuming the markets for currency, deposits, credit, non-deposits transaction services, and bank reserves clear each period, the financial sector can be collapsed into two equations that represent equilibrium conditions in the markets for base money and credit. A (semi-) log-linear approximation yields the following expressions:(15)

[Mathematical Expressions Omitted]

where [h.sub.t] is the log of the monetary base, and the parameters [d.sub.i], [c.sub.i], and [Mathematical Expression Omitted] represent the absolute values of the elasticities (or (semi-elasticities) of the following demand and supply equations with respect to the "ith" arguments:

[Mathematical Expression Omitted]

and

[Mathematical Expression Omitted]

Combining equations (26) and (27) with equations (1) - (4) from the real sector yields the following expression for the price level.

[Mathematical Expression Omitted]

where:

[Mathematical Expressions Omitted]

In general, the signs of [PI.sub.2] and [PI.sub.4] are indeterminate. However, [c.sub.2] is the indirect effect of a change in [Mathematical Expression Omitted] on the demand for currency resulting from a substitution toward or away from non-deposit transaction services. This indirect effect is much smaller than [d.sub.2] which incorporates the direct effect of a change in the own rate of return on the demand for bank deposits. The implications are that ([d.sub.2] - [c.sub.2]) is positive and the term (phi [d.sub.2] - [c.sub.2]) is small. Therefore, the likely signs of [PI.sub.2] and [PI.sub.4] are positive.

The availability of the unregulated non-deposit transaction services market for transactors provides an alternative to currency and bank deposits that affects the adjustment of prices to disturbances originating in the real sector. This reduces the interest rate and real income elasticities of the demands for currency and bank deposits, i.e., [c.sub.1], [d.sub.1], [c.sub.2], [d.sub.2], [c.sub.4], and [d.sub.4] are all smaller than they otherwise would be.(16) Therefore, [PI.sub.1], [PI.sub.2] and [PI.sub.4] are smaller than they otherwise would be, with [PI.sub.2] more affected than [PI.sub.1] and [PI.sub.4], provided that (the absolute value of) the interest rate [Mathematical Expression Omitted] elasticity of aggregate demand ([beta.sub.1]) is less than unity. In the absence of this market, financial innovations do not occur, and [c.sub.3] and [d.sub.3] are both zero, implying that [PI.sub.3] is zero. The implications that these observations have for price smoothing are discussed below.

III. PRICE SMOOTHING AND AN OPTIMAL `PASSIVE' POLICY RULE

This section specifies a passive policy rule under which the central bank supplies base money in an amount that is consistent with its forecast of the future transaction requirements of the economy during the upcoming period. This rule is combined with equation (28), and the final reduced form expression for the price level is derived. Optimal values for the choice parameters in the policy rule are then determined based on a price smoothing objective by the central bank.

The Reduced Form Expression for the Price Level

The price level adjusts to aggregate demand and supply disturbances that originate in the real sector, and to financial innovations. This adjustment occurs as a result of a temporary disequilibrium that these disturbances produce in the markets that yield transaction services, i.e., the currency, bank deposit, and non-deposit transaction services markets. The central bank may be able to smooth these price movements by adjusting the supply of base money in anticipation of the future transaction requirements for the upcoming period. Expectations of these future transaction requirements are based on forecasts of output and the level of technology that is to be employed in the production of non-deposit transaction services. If the central bank chooses to conduct this passive, or accommodative, policy by controlling the supply of base money, then the following policy rule would result. [h.sub.t] = [mu.sub.1] [E.sub.t-1] [Y.sub.t] + [[mu].sub.2] [E.sub.t-1 [THETA.sub.t] (29) where [mu.sub.1] and [mu.sub.2] are policy parameters to be optimally chosen by the central bank.

Upon substitution of equation (29) into (28), the resulting expression can be solved by the method of undetermined coefficients for the price level, [p.sub.t].

[Mathematical Expression Omitted]

where

[Mathematical Expressions Omitted]

Note that [GAMMA.sub.4] is positive (assuming [Pi.sub.2] and [Pi.sub.4] are positive) and is independent of the policy parameters. This implies that an aggregate demand shock raises the price level by an amount that is independent of the policy rule. This independence from the policy rule is due to the lack of persistence in the shock. However, if the interest elasticity of aggregate demand ([beta.sub.1]) is less than unity (in absolute value), then the magnitude of the price response is damped by the availability of non-deposit transaction services, i.e., the reductions in [c.sub.i] and [d.sub.j] (i,j = 1,2,4) discussed above lower [GAMMA.sub.4].

The Optimal Passive Policy Rule

A passive monetary policy that is designed to accommodate future transaction requirements is successful to the extent that it is able to smooth prices. In a model economy where expectations play a major role in price level determination, price smoothing objectives could focus on minimizing the variances of both the current period price level shocks, and the expected inflation rate. This corresponds to the following loss function (L).(17)

L = A var [[p.sub.t] - [E.sub.t-1] [p.sub.t]] + B var [[E.sub.t] [p.sub.t+1] - [p.sub.t]],

A,B > 0,

(31) where A and B are the weights attached to the two price smoothing objectives.

The optimal values of the policy parameters, [mu.sub.1] and [mu.sub.2], that minimize the loss function (L) are given below.

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted]

If the persistence in the productivity shocks is sufficiently great, i.e., [rho] is sufficiently large (and assuming that [Pi.sub.1] and [Pi.sub.2] are positive), then [Mathematical Expression Omitted] is positive. Therefore, as the central bank raises its forecast of output, it anticipates greater transaction requirements, and increases the supply of base money in order to avoid a decline in the price level. The term [Mathematical Expression Omitted] is unambiguously negative. If the central bank anticipates improved technology in the provision of non-deposit transaction services, it expects transactors to substitute away from currency and bank deposits, and reduces the base money supply in order to avoid a price increase.

The optimal policy rule represented by equations (32) and (33) can be examined under certain special "cases". Allow p [right arrow] 1, which implies that the cumulative productivity disturbance term, [Mathematical Expression Omitted], follows a random walk. Next, let the relative weights in the loss function (L) vary from (B/A) [right arrow] 0 to (A/B) [right arrow] 0. This gives the following optimal values for [Mathematical Expression Omitted].

As p [right arrow] 1 and (B/A) [right arrow] 0, [Mathematical Expression Omitted ] (34) As p [right arrow] 1 and (A/B) [right arrow] 0, [Mathematical Expression Omitted ] (35)

If the central bank is concerned with minimizing the variance of current period price level forecast errors only, the elasticity of the base money supply response to the forecast of output for the upcoming period is given by equation (34), i.e., (B/A) [right arrow] 0. Two elements of this equation are noteworthy. First, as the interest elasticity of aggregate demand ([beta.sub.1]) increase (in absolute value), the base money supply becomes less responsive to changes in output forecasts, i.e., [Pi.sub.2] is smaller. This is due to the additional price smoothing effect produced by the greater damping of aggregate demand by interest rate movements that are responding to aggregate real shocks. Second, as long as the interest elasticity of aggregate demand ([beta.sub.1]) is less than unity (in absolute value), the availability of the non-deposit transaction services market also reduces the supply response to changes in output forecasts, i.e., [Pi.sub.2] is reduced by a greater amount than [Pi.sub.1]. This is the result of the endogenous supply response in this market mitigating the price adjustment that accompanies a real shock.

If the central bank is concerned exclusively with minimizing the variance of expected inflation, then its optimal response to changes in the output forecast is given by equation (35), i.e., (A/B) [right arrow] 0. The two elements that were just discussed with respect to equation (34) are also true in this case. That is, the persistent effects of aggregate supply shocks and financial innovations imply that factors which smooth current period price shocks also smooth expected inflation. In addition, an increase in the elasticity of output with respect to the current period price level forecast error ([alpha.sub.1]) increases the central bank's optimal base money supply response to changes in output forecasts. This results from the greater anticipated swings in transaction requirements that would accompany the more volatile output induced by current period price shocks.

A similar examination can be made of the optimal base money supply response to the anticipated level of technology in the production of non-deposit transaction services [Mathematical Expression Omitted]. Allow [PHI] [right arrow] 0, in which case the level of technology used to produce non-deposit transactions services, [THETA.sub.t], follows a random walk, and allow (B/A) [right arrow] 0, followed by (A/B) [right arrow] 0.

[Mathematical Expression Omitted]

When the central bank is concerned solely with current period price level forecast errors, equation (36) applies. In this case, a financial innovation that is unaccompanied by a sympathetic base money supply response would raise the price level. The greater the share of transactions that are being conducted by non-deposit transaction services prior to the innovation, the greater is the effect of a given innovation on the price level, i.e., [Pi.sub.3] would be larger and [Pi.sub.1] (and [Pi.sub.2] would be smaller. This would require a larger base money supply response by the central bank

If the central bank were concerned only with expected inflation, then equation (37) would indicate the optimal base money supply response to a financial innovation. As just discussed, as non-deposit transaction services assume a larger share of the total transactions being conducted, the magnitude of the required base money supply response to a financial innovation would increase, i.e., [Pi.sub.3] increases and [Pi.sub.2] declines by more than [Pi.sub.1]. In addition, a financial innovation that is unaccompanied by a base money supply response would have a greater effect on inflation expectations as the interest elasticity of aggregate demand ([beta.sub.1]) rises (in absolute value), implying that aggregate demand is more damped by interest rate movements, and as the elasticity of output with respect to current period price shocks ([alpha.sub.1]) falls. Both of these factors imply that price movements rather than changes in output (or the volume of real transactions) absorb a greater share of the increased supply of transaction services that accompany the financial innovation. Therefore, the central bank's optimal base money supply response to a financial innovation would increase in magnitude.

IV. CONCLUSIONS

Non-deposit transaction services have assumed an increasingly important role in the U.S. economy's payments system over the past two decades. The growth of this market was not always foreseen, and was often understood only in retrospect.(18) The significance that this has for monetary policy is in its impact on the demand for aggregate measures of money. The inability of the central bank to identify these changes, and to take them into account when setting policy, causes fluctuations to occur in the price level as transactors adjust to changes in transaction requirements and to the availability of transaction services. These price level fluctuations can be minimized by a monetary policy that forecasts future transaction needs in the economy and engages in a passive policy that is designed to accommodate these needs.

This paper explores some of the major policy implications of a dynamic unregulated market for financial services whose product(s) competes with the transaction assets that are subject to central bank control. Under very general conditions, the existence of this market has the positive effect of smoothing prices as the production of these non-deposit transaction services responds endogenously to disturbances originating in the real sector.

As this market continues to expand, this price smoothing effect will become more pronounced. If the real disturbances exhibit a well-defined persistence, as the real business cycle theorists stress, then the central bank is able to anticipate changes in transaction requirements and further smooth prices by accommodating these needs.

The negative effect of this unregulated market is the impact of financial innovations on prices. A financial innovation raises the supply of transaction services and acts as a monetary shock. This causes an unanticipated price response as transactors adjust their transaction asset demands. If the financial innovation is absorbed slowly, and the central bank fails to adjust its supply of these assets to the rate of adoption of the new technology, the price response will persist. Again, the optimal policy is one that anticipates the change this produces on transaction needs and accommodates the new environment.

This paper has focused on some of the more significant effects that this growing unregulated market for transaction services has on the economy, and on the significance of the market for monetary policy under the current regulatory structure. Additional work in this area seems warranted. In particular, financial innovations are not purely exogenous. For example, the pace of financial innovation accelerates during periods of high and volatile inflation and interest rates. An important issue is how significant this market is for economic stability under various regulatory regimes, particularly when financial innovations are largely endogenous. A fractional reserve banking system may not be optimal. The removal of supply constraints on transaction assets may enhance the ability of the economy to absorb real shocks as well as financial innovations without large unanticipated swings in the price level.

VARIABLE LIST

[Mathematical Expression Omitted] = log of real output

[P.sub.t] = log of aggregate price level

[Mathematical Expression Omitted] = cumulative productivity shock

[n.sub.t] = current period productivity shock

[Mathematical Expression Omitted] = log of aggregate demand for goods

[Mathematical Expression Omitted] = nominal interest rate in the credit market

[Mathematical Expression Omitted] = current period aggregate demand shock

[Y.sub.t] = log of current period output and log of current income

[pi.sub.t] = aggregate bank profits

[Mathematical Expression Omitted] = quantity of non-deposit transaction services produced

(number of transactions)

N = average size of transactions

[q.sub.t] = unit price of non-deposit transaction services

[Mathematical Expression Omitted] = average nominal volume of credit extended to firms by banks

[Mathematical Expression Omitted] = average nominal supply of bank deposits per period

[Mathematical Expression Omitted] = nominal deposit rate

[W.sub.t] = nominal unit cost of the bank's sole factor input

[Mathematical Expression Omitted] = quantity of bank factor input employed in servicing credit

accounts

[Mathematical Expression Omitted] = quantity of bank factor input employed in servicing deposit

accounts

[Mathematical Expression Omitted] = quantity of bank factor input employed in producing

non-deposit

transaction services

[Mathematical Expression Omitted] = banks' demand for reserves

[Mathematical Expression Omitted] = reserve requirement ratio for bank deposits

[Theta.sub.t] = technology parameter in the production function for non-deposit

transaction services

[xi.sub.t] = current period financial innovation

[delta] = magnitude of the financial innovation when it occurs (from

the binomial distribution of [xi.sub.t]

k = probability (each period) that a financial innovation of size [delta]

will occur

[Z.sub.t] = cumulative effect of financial innovation on [THETA.sub.t]

[t.sub.t] = total real value of transactions

u = number of transactions per dollar of output

[Y.sub.t] = nominal output or nominal income

[T.sub.C] = total cost of meeting transaction cost for the period

[Mathematical Expression Omitted] = average per period nominal stock of currency demanded by

the public

[Mathematical Expression Omitted] = average per period nominal stock of bank deposits demanded

by the public

[Mathematical Expression Omitted] = average per period demand for non-deposit transaction services

[Mathematical Expression Omitted] = total number of transactions made using currency

[Mathematical Expression Omitted] = total number of transactions made using bank deposits

[Mathematical Expression Omitted] = nominal demand for credit by firms

[Mathematical Expression Omitted] = nominal supply of credit extended to firms by households

[H.sub.t] = nominal supply of high-powered (or base) money by the

central bank

[h.sub.t] = log of nominal supply of high-powered (or base) money by the

central bank

[Mathematical Expression Omitted] = nominal supply of currency by the central bank

[Mathematical Expression Omitted] = nominal supply of bank reserves by the central bank

[mu.sub.1],[mu.sub.2] = central bank policy parameters

(1.) See Sims [1980; 1983].

(2.) King and Plosser have suggested the possibility that the observed procyclical movements of prices may be the result of an excessive endogenous supply response by the banking system [1984, 372]. This type of response can be rationalized only in the presence of endogenous financial innovation or incomplete information. Our model takes financial innovation as exogenous. Hester [1981] discusses the likely endogeneity of financial innovation during the 1970s. Saving's partial equilibrium model of the money market takes prices as exogenous. However, the comparative statics of his money supply equation are consistent with the accommodative response described above. Specifically, the money supply rises with output and falls with prices, both of which would accompany a real supply shock.

(3.) See Fama [1980].

(4.) See Litterman and Weiss [1986] for empirical evidence.

(5.) Non-financial businesses may also choose to produce these transaction services "in-house" by allocating resources (capital and labor) to their internal cash management program. This adds a new dimension to the non-financial business sector's demand for money as discussed in Marquis and Witte [1989]. For the purposes of this paper, it is immaterial whether firms exercise this option or the banks are assumed to be the sole providers of these services.

(6.) Adjustments in the currency/deposit ratio are also possible. This represents a principal source of money endogeneity in Saving [1979].

(7.) This is a common feature of the incomplete information models of Lucas [1972; 1973; 1975] and Barro [1976; 1980], as well as the Fischer [1977] and Taylor [1980] models that incorporate long-term nominal wage contracts. Of these models, only Lucas [1972; 1975] generates persistent effects that result from mistakes in investment decisions. Our model does not have this feature since all output is fully consumed within the period, which is similar to the Barro and Fischer-Taylor models.

(8.) In the real business cycle models of Kydland and Prescott [1982], Long and Plosser [1983], and King and Plosser [1984], this represents the sole source of short-run aggregate fluctuations. Rationales for the persistent effects of productivity shocks include the "time-to-build" character of realizing investment decisions in the form of new plant and equipment (Kydland and Prescott) and the desire of households to smooth the additional consumption flows over time (Long and Plosser).

(9.) This allows the model to accord well with the empirical observations that output follows a low-order autoregressive process. This is discussed in Lucas [1977] and Nelson and Plosser [1982], in addition to the real business cycle literature previously cited.

(10.) Adjustments in excess reserves could also provide a means for an endogenous response of the banking system in meeting the change in transaction requirements of the economy associated with a real shock. In practice, the growth of the federal funds market over the past twenty-five years has substantially reduced the quantity of excess reserves in the banking system as a percentage of total assets. This ratio is now less than 1 percent and is relatively stable over the course of a business cycle, which suggests that it plays a very limited role in providing this kind of endogenous response to real shocks.

(11.) This assumption is also made for the size of transactions conducted via currency and bank deposits. This removes (at least) one degree of freedom in the choices made by transactors.

(12.)] Since the nationwide legalization of NOW accounts, it is common practice for depository institutions to offer their depositors explicit choices on the pricing structure of their accounts that include various combinations of interest income, minimum balance requirements, and per check transaction fees. As Sweeney (1988, 182-3, 197-9) points out, even if pricetaking, quantity-setting banks are interested only in the "net interest rate on bank money" (i.e., the variable [Mathematical Expression Omitted] in this model) when making their quantity decisions, an optimal mix of interest income and per check transaction fees is determined by the households' preferences in the use of bank money for transactions purposes. There may be additional price-smoothing effects in response to exogenous shocks that the model does not capture. Banks could hold [Mathematical Expression Omitted] constant while raising both the deposit rate and transaction fee. These changes would have differential effects across transactors with those having the stronger preferences for using bank money in transactions more affected by the higher transaction fees than by the higher deposit rate. To fully capture the aggregate price-smoothing effects would therefore require explicit modeling of the pricing decisions as well as the households preferences. We have chosen to abstract from these considerations in order to focus on the principal implications that the unregulated non-deposit transaction services market has for monetary policy. For additional discussions of the pricing decisions from the bank's perspective, see Saving [1979], Mitchell [1979; 1988], and Merris [1985].

(13.) This assumes that households continuously optimize in their selection of transaction media. This assumption is a potential problem only when a financial innovation involves a new financial services product. In this case, it might be argued that there is some degree of "habit-persistence" on the part of households that produces a sluggish adjustment in the rate at which they assimilate the new technology. However, if the banks accurately perceive this, it would be incorporated into their decision on the rate at which the new technology is introduced to the public. This is captured by [PHI] in equation (11). Mistakes made by the banks in this regard could lead to additional supply shocks that are not included in the model. However, if these mistakes are purely random and are correctable period-by-period, they would have no persistence, and therefore no relevance for a passive monetary policy that pursues price-smoothing objectives.

(14.) In this model, open market operations are conducted in the private versus the government securities market. It would be a trivial matter to include a fixed stock of government securities in the model that the central bank could draw on for its open market operations.

(15.) The following two assumptions were also required in order to sign the coefficients in equations (26) and (27): (1) Nominal factor costs, [omega.sub.t], are homogeneous of degree one in prices. (2) Direct effects of changes in [Mathematical Expression Omitted], and [Y.sub.t] on the demand for bank deposits, and of changes in [Mathematical Expression Omitted] and [Y.sub.t] on the demand for currency dominate the indirect (or feedback) effects that are due to substitution toward or away from non-deposit transaction services. Details of this derivation, as well as the other mathematics of the paper, are contained in an appendix that is available from the authors upon request.

(16.) For the income elasticities of the demands for currency and bank deposits to be reduced by the availability of this unregulated market, the income elasticity of the supply of non-deposit transaction services must exceed the income elasticity of demand. This is discussed in the appendix.

(17.) See Goodfriend [1987] for a discussion of this loss function.

(18.) This was an important factor contributing to Goldfeld's [1976] famous "case of the missing money." See Porter, Simpson, and Mauskopf [1979].

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MILTON H. MARQUIS and STEVEN R. CUNNINGHAM(*)

(*) Assistant Professor, Florida State University, and Assistant Professor, University of Connecticut. We would like to thank Richard Sweeney and two anonymous referees for their numerous insightful comments that vastly improved the quality of this paper. They, of course, bear no responsibility for any remaining errors or omissions.

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Author: | Marquis, Milton H.; Cunningham, Steven R. |
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Publication: | Economic Inquiry |

Date: | Oct 1, 1990 |

Words: | 6983 |

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