Shoe-Leather Costs of Inflation and Policy Credibility

1 Shiller (1996).

2 Karni (1974), McCallum andGoodfriend (1987).

FEDERAL RESERVE BANK OF ST. LOU IS

37

NOVEMBER/DECEMBER 1998

Shoe-LeatherCosts ofInflationand PolicyCredibilityMichael R. Pakko

Most people recognize that inflation issomething to be avoided, but the popularpublic perception of inflation’s harmfuleffects can be rather vague. In responsesto survey questions about inflation, forexample, most people express concernsabout prices rising (defining inflationitself) or that it somehow erodes standardsof living.1 When economists discuss thecosts of inflation, however, they have morespecific concerns in mind. One generalclass of inflationary consequences is some-times referred to as the “shoe-leather” costsof inflation: In an effort to minimize theeffect that inflation has on eroding thepurchasing power of money, people haveto spend more time and effort protectingthe value of their nominal assets—wearingout their shoes on the way back and forthto the bank.

Of course, this quaint notion representsa much broader and more serious problemthan simply the cost of wearing out onesshoes. To protect assets against inflation,societal resources are channeled away fromproductive activities and toward inflation-hedging activities. In countries that haveexperienced hyperinflation, these resourcemisallocations are readily apparent; butthey are also present for less extreme casesof inflation.

This article discusses the nature ofshoe-leather costs in the context of a theo-retical model economy. The shoe-leather

costs themselves are represented by a“shopping-time” feature embedded in themodel: It is assumed that individuals mustspend time conducting transactions andthat carrying money reduces the timerequired. The incentive to economize onmoney balances in the face of highinflation then implies that individualsincur a time-cost that rises in response toan increase in the inflation rate.

Using the U.S. experience of the post-World War II (WWII) era to calibrate themodel, I show that the shopping-timemodel implies shoe-leather costs that arebroadly consistent with estimates derivedby other researchers using a variety ofapproaches. In the previous literature,these costs have been presented as a com-parison between two specific long-runinflation rates. In this article, I use theshopping-time model to take this analysisa step further, demonstrating how thetransition from one inflation rate toanother might be expected to proceed, andevaluating the importance of uncertaintyabout the commitment of the monetaryauthority to keep inflation in check. Thisanalysis suggests that the credibility of themonetary authority is an important factorin evaluating the welfare gains that accruefrom policies to reduce inflation.

SHOE-LEATHER COSTS INTHEORY

The nature of shoe-leather costs in ashopping-time approach to modelingmoney can be thought of as a general-equilibrium version of the inventoryapproach to money demand pioneered byBaumol (1952) and Tobin (1956).2 In theBaumol-Tobin model, individuals trade offthe convenience of using money to conducttransactions against the opportunity costof holding non-interest-bearing money;that cost being represented as the nominalinterest rate. The cost of managing moneybalances is represented by a specific

Michael R. Pakko is a senior economist at the Federal Reserve Bank of St. Louis. Gilberto Espinoza provided research assistance.


38

3 Bresciani-Turroni (1937),Cagan (1956).

4 One of Bresciani-Turroni’s impor-tant points about the effects ofthe German hyperinflation wasthat wealthier members of soci-ety who had access to inflationhedges were at a huge advan-tage. This type of distributionaldistortion can be associatedwith costs, which are distinctfrom the shoe-leather costs thatare the focus of this analysis.(Page 216.)


brokerage fee which is charged for visiting afinancial intermediary. Individuals balancethe cost of making many trips to the “bank”against the cost of going infrequently andcarrying around large money balances thatearn no interest.

The outcome of this decision is anoptimal number of trips to the bank and acorresponding level of money holdings,which depends (inversely) on the nominalinterest rate. The shoe-leather costs ofinflation emerge through the interest ratesrole in money demand. In particular, con-sider the standard Fisher equation, whichrepresents the nominal interest rate asbeing comprised of two components: thereal interest rate, and a term that compen-sates for expected inflation:

(1) .

When inflation and inflation expecta-tions rise, so does the nominal interestrate. As a result, individuals economizeon their money holdings, requiring moretrips to the bank. The brokerage costsassociated with these trips representshoe-leather costs.

Although modeled as a specific fee, thebrokerage cost in the Baumol-Tobin modelcan be interpreted more broadly as encom-passing all of the various resource and

time costs of managing ones financialassets and facilitating money payments.To gain some insight into the nature ofthese costs, it is informative to considerhistorical experience with extreme episodesof inflation, known as hyperinflation.

AN EXTREME EXAMPLEThe most famous episode of hyperin-

flation occurred in Germany in the 1920s.From mid-1922 through mid-1923, pricesincreased by a factor of 100. By November1923 the price level was over one billiontimes its level in August 1922.3

Anecdotes of the distortionary effectsof this hyperinflation abound. Workerswere paid two to three times per day,rushing out to spend their pay before themoney became worthless. At the pubafter work, patrons ordered two beers atonce in fear of the price rising before theyhad finished the first one. Shopkeepersposted prices as multiples of a base,changing the multiplication factor hourlyafter consulting with banks, which hadset up phone lines to give the latestexchange rate quotes.

Indeed, the banking system expandedand took on crucial importance—especiallyfor those with the resources to beat the dev-astating effects of inflation by holdingforeign currency and precious metals. Bres-ciani-Turroni (1937) documented that thenumber of persons employed by Germanbanks rose from about 100,000 in 1913 to375,000 in 1923. His description of thisphenomenon provides a summary of thewastefulness of the financial sectors roleduring hyperinflation: “The increase inbanking business was not the consequenceof a more intense economic activity . . .The banks did not help in the productionof new wealth; but the same claims to wealthcontinually passed from hand to hand.”4

Of course, the effects of hyperinflationmust be recognized as extreme examplesof the destructive effect of inflation. It isnot unreasonable to suppose, however,that costly distortions emerge on a smallerscale during more moderate periods ofinflation. While the costs of hyperinflation

i rt t te= +π

Figure 1

Costs of Inflation as the Area Under the Money Demand Curve

Interest Rate

Hri π+=′

Lri π+=

P

M

P

M

P

Md′

Real MoneyBalances0


39


are enormous and obvious, the smallercosts associated with more mild inflationare more subtle and more difficult to mea-sure empirically.5 An alternative approachis to calibrate a theoretical model economyand derive estimates from the modelsimplications. We now turn to an examina-tion of some estimates of inflations coststhat are measured this way.

MEASURING SHOE-LEATHERCOSTS

One approach to measuring the costsof inflation in less extreme circumstancesexploits the role of the nominal interestrate in the money demand equation. Asdescribed in the context of the Baumol-Tobin model, an increase in expectedinflation leads people to economize ontheir money balances and other nominalassets. It is the cost of minimizing moneyholdings which gives rise to shoe-leathercosts. Hence, one way to measure thecosts is to estimate the effects of a givenrise in inflation on the demand for money.Because inflation can be thought of as atax on money, demand analysis used tomeasure the welfare costs of taxation canbe used to evaluate the costs of inflation.6

Figure 1 shows the effects of a changefrom a low inflation rate, πL, to a higherinflation rate, πH.7 As Equation 1 shows, thisis associated with an increase in the nominalinterest rate. The inverse relationship betweennominal interest rates and the demand formoney implies that individuals will respondby holding less money. The shaded area underthe demand curve represents the resource-cost incurred when individuals economizeon money-holding after the rise in the nom-inal interest rate, and represents the shoe-leather costs of inflation.8

Note that the only nominal interestrate at which there are no costs of holdingmoney is the point where the money demandcurve crosses the horizontal axis—the satia-tion point for money balances, which isreached when the nominal interest rate iszero. From Equation 1, a zero nominalinterest rate requires that expected inflationbe negative. This property, known asFriedman's rule, is a property of many the-oretical models of money demand, and istrue of the shopping-time model of moneydemand to be introduced in the nextsection.9 The proposition that there aregains to be had by taking inflation to verylow or even negative levels is controversial,and we have relatively little evidence on

Some Estimates of the Costs of In ation

Inflation Welfare CostsStudy Features Comparisons (percent of GDP)

Fischer (1981) Welfare triangle 10% vs. 0% 0.3

Lucas (1981) Welfare triangle 10% vs. 0% 0.45

Cooley/Hansen (1989) RBC model with cash in advance 10% vs. optimal* 0.387motive for money demand

Imrohoroglu (1992) Precautionary, consumption-smoothing 10% vs. 0 1.07motive for money demand 5% vs. 0 0.57

Dotsey/Ireland (1996) Endogenous growth with cash in 10% vs. 0% 1.73advance and financial intermediation 4% vs. 0% 1.08

Lucas (1994) Welfare triangle—with general 10% vs. optimal* 1.3equilibrium motivation

*Comparisons with the optimal refer to the Friedman rule of a slight deflation such that nominal interest rate is zero.

Table 1

5 For example, the effects ofinflation measured in cross-country comparisons by Barro(1996) and Bruno and Easterly(1996) are largely attributableto the inclusion of high-inflationeconomies in their samples.

6 Baily (1956).

7 Carlstrom and Gavin (1993)illustrate this derivation using aBaumol-Tobin model of shoe-leather costs.

8 The rectangle to the left of thetriangle is the increase in taxrevenue gained by the govern-ment or monetary authority.The governments revenuegained from inflationary financeis known as seigniorage.

9 Friedman (1969).


40

10 Mulligan and Sala-i-Martin(1997) show that small modi-fications of the theoretical satia-tion point can alter the optimalinflation rate and the relativecosts of low inflation.

11 Studies that have attempted toestimate the distortionaryeffects of interactions betweeninflation with the tax code,such as Altig and Carlstrom(1991), Feldstein (1996) andBullard and Russel (1997),have found much higher costs.In this paper, I limit my analy-sis to shoe-leather costs.

12 The model is fully specified inthe Appendix and in Pakko(1998).


which to base empirical estimates of moneydemand at such rates.10 Hence, it is notunusual for inflation costs to be measured rel-ative to zero.

Some of the estimates found inprevious studies of the welfare cost ofinflation are listed in Table 1. The firsttwo lines in the table represent the area-under-the-demand-curve approach toestimating the costs of inflation. Fisher(1981) suggested that the cost of goingfrom zero to 10 percent inflation amountedto the equivalent of three-tenths of 1 per-cent of Gross Domestic Product (GDP).Lucas (1981) argued that the numbermight be closer to one-half of a percent.While these might seem like smallnumbers, at today’s level of output andprices, they represent somewhere between$25 billion and $40 billion.

Another approach to estimating thecosts of inflation is to specify a theoreticalmodel of the economy, and then to calcu-late the effects of changes in the inflationrate on individuals in the model. Forexample, Cooley and Hansen (1989) speci-fied a basic real business cycle model withthe demand for money motivated by acash-in-advance constraint. They foundthat the costs of inflation were along thesame order of magnitude as suggested inprevious studies. Other researchers haveintroduced additional features of the

money demand specification, and foundthat the costs of inflation are higher. Imro-horoglu (1992) examined a model wherethe demand for money includes a precau-tionary, income-smoothing motive formoney. Dotsey and Ireland (1996)consider an endogenous growth with cash-in-advance money demand and financialintermediation. Lucas (1994) discussedthe welfare costs of inflation in the contextof a shopping-time model of moneydemand similar to the one examined inthis article. These studies estimated thecosts of 10 percent inflation to be as highas 1 to 2 percent of GDP.11

A SHOPPING-TIME MODELTo demonstrate the way that shoe-leather

costs can be calculated using a model-basedapproach, I examine a general-equilibriummodel where the costs of managing moneybalances are represented by a shopping-timefunction.12 In principle, the costs of inflationcould be specified literally as a resourcecost (shoe-leather), or as a time cost. Inthe model examined here, I choose thelatter approach, exploiting the relationshipbetween inflation and increased time spentcarrying out financial activities.

Specifically, individuals are assumed tohave a motivation to economize on moneybalances in the face of rising inflation, andthey weigh this incentive against theincreased time cost of managing moneyor shopping. We assume that these timecosts, St, are increasing in the level of con-sumption purchases, Ct, and decreasing inthe quantity of real money balances (pur-chasing power) held by individuals, Mt/Pt;specifically:

(2) ,

with µ1>0 and µ2>0. The parameter µ1determines the average amount of timespent shopping, while µ2 measures thecurvature of the shopping-time function.Figure 2 illustrates the nature of therelationship between real money balancesand shopping time: For a given amount of

SC

M Ptt

t t

=

µµ

1

2

/

Figure 2

The Shopping-Time Function

Shopping Time

Real Money Balances


41

expenditure, individuals can reduce thetime spent shopping by holding moremoney. The time remaining to individualsafter subtracting shopping-time is spentworking, Nt, or enjoying leisure, Lt:

(3) .

Firms hire labor and rent capital, Kt,from the households. They use the avail-able technology for producing goods andservices, Yt, which they sell to thehouseholds,

(4) .

In Equation 4, Xt represents an indexof labor productivity that increases overtime, determining the rate of long-runeconomic growth.

Output is allocated to consumptionand investment, It, the latter providing forchanges in the capital stock as:

(5) .

A central bank provides the moneyused in transactions, increasing the moneybalances of individuals each period by anamount Tt, so that total real moneybalances evolve over time by:

(6) .

Individuals in the model are assumedto value consumption and leisure now andin the future. Their optimization problemcan be used to find efficient allocations,which we consider to represent theoutcome of an undistorted marketeconomy—the equilibrium of the model.

By adjusting the values of money andprices by the average growth rate of moneyimplied by T—and adjusting the levels ofproduction, consumption and investmentby the growth rate of technologicalprogress implied by X—trends in the

model are removed. Equilibrium then canbe expressed in terms of relative levels ofeconomic activity that depend on trendgrowth rates—including the inflation rate.13

These equilibrium solutions dependon some of the parameters of the modeleconomy such as the relative returns tocapital and labor, the long-run interestrate, long-run growth rates, and individualsattitudes about consumption and saving.The parameters used in this study arebased on U.S. economic data during thepost-WWII period and are selected to beconsistent with previous specifications ofsimilar models.14

One of the key relationships thatemerges from the detrended solutions(represented now in lower case) is amoney demand relationship,

(7) ,

where w represents the wage rate.15

Note that the relationship between realmoney balances and the interest rate, con-sumption, and wages crucially depends onthe parameters of the shopping-time func-tion, µ1 and µ2. For the purposes ofsubsequent analysis, values of these twoparameters are selected by considering thegrowth of the financial sector during the

m

p

w c

it

t

t t

t

+

+

+ ++

=

1

1

1 2 1 1

1

12 2µ µ µ µ

M

P

M

P

T

Pt

t

t

t

t

t

+ = +1

t+1 t tK = (1- )K + Iδ

Y X N Kt t t t= ( ) −1 α α

1 − = +S N Lt t t


Figure 3

Inflation and FIRE Employment as a Percentage of Aggregate Weekly HoursPercent Percent

7.0

6.5

6.0

5.5

5.0

4.5

4.01964 1972 1976 1984 1988 1992

13

11

9

7

5

3

11968 1980 1996

CPI Inflation(3 Year MA right scale)

FIRE Employment Ratio(left Scale)

Source: Bureau of Labor Statistics

13 Technically, the model is trans-formed to a stationary equilibri-um, in which levels ofeconomic variables depend onthe average values of thegrowth parameters. See theAppendix for details.

14 Specific values of the keymodel parameters are listed inthe table accompanying theAppendix.

15 As Lucas (1994) points out,relationships derived from ageneral-equilibrium model, suchas this one, are not truedemand equations in the sensethat the right-hand variablesdetermine the quantity ofmoney demanded directly.Rather, Equation 7 summarizesa relationship that characterizesthe jointly determined equilibri-um values of money, prices,consumption and interest rates.


42


period of rising U.S. inflation during the1960s and 1970s.

As discussed in the context of Germanhyperinflation, rising rates of inflation areassociated with an increasing role for thefinancial sector as individuals seek toprotect the value of their nominal assetsfrom inflation. This relationship also hasbeen observed in more recent high-inflationenvironments. For example, Lamb (1993)reported that the financial sector in high-inflation Brazil during the early 1990saccounted for 15 percent of GDP—muchhigher than in most countries. Yoshino(1993) found a similar positive relationshipbetween the size of the financial sectors andinflation rates for several countries.

In the U.S., the increase in inflationfrom the 1960s to the early 1980s wasalso associated with an increase in the rel-ative size of the financial sector. Forexample, the fraction of the labor forceemployed in the finance, insurance, andreal estate (FIRE) sector—plotted inFigure 3—rose from about 4.6 percent in1965 to just over 6.7 percent during themid-1980s. The growth of this measureslowed and turned downward following thedisinflation of the 1980s.

The average value of the FIRE employ-ment share over the sample period wasapproximately 6 percent. Obviously, notall activity in the FIRE sector is associated

with shoe-leather costs of inflation, but nei-ther are all shoe-leather costs associatedwith activity in that sector (or in themarket, in general). Technologicaladvances and deregulation are often cited asbeing particular factors related to financialsector growth throughout this period. Evenso, technological innovation and regulatoryinitiatives were, to an extent, undertaken inreaction to the distortions emerging in anincreasingly inflationary environment.

In an attempt to not overstate the shareof shopping time represented by this admit-tedly crude measure, we cut the estimate inhalf: The scale parameter of the shopping-time function, µ1, is set to yield a value of 3percent of total work effort on average (atthe 5 percent average inflation rate that pre-vailed during the sample period).

The efficiency conditions derived fromthe optimization problem of the modelimply that shopping time is relatedinversely to the inflation rate. This can beused to pin down the curvature parameter(i.e., the elasticity) of the shopping-timefunction, µ2. The model predicts that theFIRE employment ratio will vary over itsobserved range in response to movementsof trend inflation during the sample period(i.e., inflation rates of between about 2 and10 percent) if the curvature parameter hasa value near one. The parameterizationµ=1.0 is also consistent with empirical evi-

Effects and Welfare Costs of In ation in the Steady-StateRelative to Zero Inflation (percent)

Inflation Percent change in*: Welfare Cost as a percent of:Rate (percent) Consumption Leisure Consumption Output

-r** 1.90 0.06 -2.05 -1.59

1 -0.22 -0.01 0.24 0.19

3 -0.61 -0.02 0.65 0.50

5 -0.93 -0.03 0.99 0.77

10 -1.61 -0.05 1.70 1.32

*Output, investment and capital all adjust in the same proportion as consumption.

**An inflation rate of -r implies a nominal interest rate equal to zero (the Friedman rule).

Table 2


43


dence that the interest elasticity of moneydemand is about one-half (as representedin Equation 7).

SHOE-LEATHER COSTS INTHE SHOPPING-TIMEMODEL

With the calibrated version of themodel in hand, we can calculate the wel-fare costs of changes in the trend rate ofinflation. Specifically, the system of equa-tions that define the models equilibrium canbe solved for cases in which macroeconomicvariables have settled at their long-runvalues, e.g., yt = yt-1 = yt-2, etc. This type ofpath is known as a steady state. Anyparticular long-run growth rate of moneyand prices will be associated with aspecific steady state.

Table 2 provides a comparison ofsteady states for various inflation rates,showing the welfare costs of inflation atselected inflation rates. These costs aremeasured as the percentage of steady-stateconsumption (or output) that individualswould have to forego at zero inflation tomake them indifferent about moving to ahigher inflation rate.16 The estimatesshown in Table 2 are broadly consistentwith previous studies.

Table 2 also demonstrates the sourcesof these costs. As increases in the inflationrate induce people to economize on moneybalances, they increase their shopping timeand decrease their consumption purchases.Leisure and work effort both decline toaccommodate more shopping time, so pro-duction also falls. The economy contracts,including a decrease in the stock ofproductive capital.

The responses to changes in the inflationrate shown in Table 2 represent changes inthe levels of economic activity. However,the effects of inflation often are consideredin terms of sacrifices in economic growth.Although long-run economic growth inthe model is independent of inflation,depending ultimately only on the rate oftechnological advance, the transition adjust-ments of the economy following a change inthe inflation rate can give rise to adjustments

over time, which can temporarily changemeasured growth.17 This happens becausethe capital stock cannot be adjusted immedi-ately; an increase in inflation results in lowerinvestment, which (as shown in Equation 5)lowers the level of the capital stock over time.

DYNAMIC ADJUSTMENT TOCHANGES IN THE INFLA-TION TREND

Figure 4 shows the simulated transitionpath of the model economy following anincrease in the rate of money growth andinflation from 5 percent to 10 percent.18

Prior to the change, output grows at itslong-run productivity-driven rate (set hereto equal 2.5 percent), as it also will be afterthe economy has adjusted fully to thechange in the inflation rate. During theperiod of transition, however, measuredgrowth declines as the economy contractsover time. In Figure 4, during the twoyears following the increase in inflation, theaverage growth rate of the economy falls to2.2 percent. During the first year after thechange, growth is only 1.9 percent. Afterthe brief period of adjustment, growthreturns to near its long-run rate.

This analysis suggests that at least aportion (albeit small) of the measuredgrowth decline observed during the infla-tionary 1970s might reflect this type of

16 Specifically, the required com-pensation in terms of steady-state zero-inflationconsumption, κ, is defined bythe relationship:

U[(1-κ) co, Lo] = U(c, L)

where the subscript 0 refers tosteady state values at zeroinflation.

17 The notion that inflation affectsthe level of economic activity—but not the growth rate—issupported by empirical evidencecited in Bruno and Easterly(1996), who find that countriesexperiencing a temporary boutof high inflation (over 40 per-cent) tend to return to their orig-inal growth trends after theinflation crisis is removed.

18 The models dynamic solutionsare found using a log-linearapproximation (around the ini-tial steady state). The solutiontechnique for the approximatedsystem follows the approachdescribed by King, Plosser andRebelo (1988).

Figure 4

Transition Path of Output Following an Increase in Inflation From 5% to 10%Index

0.92

0.96

1.00

1.04

1.08

1.12

2.50% 2.20% 2.49%

Quarters from Change-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16-8


44

adjustment. Similarly, because the costs ofhigher inflation are symmetric to the bene-fits of lower inflation, at least a small shareof increased economic growth experiencedin the period following the early 1980smight be attributed to disinflation.

One problem with this explanation,however, is the rapid adjustment illustratedin Figure 4, in which over half of the changein output is complete after only one quarter.In response to the shift in the inflation trend,consumption and output immediately fall,and the remaining transition involves theadjustment of the capital stock to the newlower-equilibrium value. The fact that economic activity falls off so quickly is due largely to the assumption, made thusfar, that the change in the trend rate of inflation is fully known to the public—andfully believed.

In fact, evidence suggests that some-times the inflation expectations of thepublic are quite slow to adjust to actualchanges in the inflation trend. Figure 5shows one measure of these expectations,the mean estimate from an inflation surveyconducted by the University of Michigan.19

Throughout the 1980s, this measure ofexpectations considerably lagged behindthe decline in actual inflation.

This suggests an additional feature ofthe adjustment process that might be

important: the formation of expectationsabout the inflation trend. In this regard,the credibility of the monetary policy-making authority also becomes a factor. Inthe simulation shown in Figure 4, it isassumed that individuals are fully aware ofthe change in the inflation trend and respondaccordingly. Suppose, however, thatchanges in the trend rate of inflation arenot fully anticipated. In particular, let usassume that increases in the money stocksometimes reflect changes in the growthtrend of money and inflation, and sometimesjust reflect transitory movements of themoney stock around the growth trend.When observing a particular change in themoney supply, individuals attach a proba-bility of less-than-100-percent to thelikelihood that the inflation rate has actu-ally changed, delaying adjustment untilthe weight of evidence supports a changein the trend rate of growth. People mightattach a low probability to changes in theinflation rate when the implementation ofsuch policies by the monetary authorityare announced explicitly—if the policy-maker has less-than-perfect credibility.

In the model, the formation of expec-tations can be represented by assumingthat the trend of money growth can followeither a high-growth or a low-growthpath.20 We also will assume that themoney supply is subject to transitory fluc-tuations—complicating the process ofdeducing the true growth trend.21

Policy credibility is likely to be bothparticularly important and elusive whenthe monetary authority is attempting toimplement a disinflationary policy followinga surge of inflation. For the purposes ofthis illustration, therefore, we will considerthe benefits derived from reducing the rateof inflation.

If the economy begins at the highmoney growth rate, the key parameter thatdetermines expected inflation is the proba-bility that the growth trend will change tothe lower level. Equivalently, we can con-sider the probability that the inflationtrend will not fall to the lower trend in anyparticular period, q.22 A relatively highvalue of q implies a low probability that


19 University of Michigan SurveyResearch Center.

20 This approach is an applicationof the Hamilton regime-shiftingmodel (Hamilton, 1989,1994).This representation has beenused to demonstrate the pro-tracted adjustment of inflationexpectations by Andolfatto andGomme (1997) and Duekerand Fisher (1998).

21 The latter source of innovationsto the money supply is pre-sumed to follow a first-orderautoregressive process, with anautocorrelation coefficient of0.72 (estimated from M2growth, 1960 to1996). Thestandard deviation of theexogenous shock is set so thattransitory shocks to the moneysupply growth rate account forabout half of the overall vari-ance of M2 growth over thesample period.

22 It is assumed that once thetrend growth rate has fallen, itremains at the lower level withprobability 1 (the low-growthtrend is therefore known as anabsorbing state).

Figure 5

Inflation and the Michigan Survey of Inflation Expectations (Mean)Percent

1980 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 970

2

4

6

8

10

12

14

Expected

Actual

Source: Bureau of Labor Statistics and University of Michigan Survey Research Center, Mean expected price change.


45


inflation will decline in any given timeperiod, and can therefore be interpreted asreflecting, in part, the credibility of a mon-etary authority’s disinflation policy. Theunconditional probability of a change inthe growth trend in any particular periodshould be considered quite low on average—after all, shifts in inflation trends do nothappen all the time—so the value of qshould be high. The shading of theseprobabilities to reflect policy credibility isthen a matter of degree.

Figure 6 shows the paths of theeconomy following a decline in theinflation rate from 5 to 3 percent. Thepaths are calculated assuming that theprobability of the inflation trend remaininghigh, q, takes on a higher (0.999), medium(0.99) or a lower (0.96) value. The higher

value of q is associated with the greatestdegree of skepticism about the policymaker’sintentions to lower the inflation rate. Inorder to illustrate clearly the effects ofexpectations on the adjustment process,the adjustment paths of economic quanti-ties in Figure 6 are illustrated withouttrend growth.23

Notice that for each of the values ofq, the adjustment process is more protractedthan when the shift in the inflation trend isknown with certainty. In the three caseswith uncertainty, output reaches 90 percentof its ultimate increase only after 17, 22, and30 quarters have passed. In the certaintycase, only 11 quarters are required.24

For the upper value of q, notice thatthe lower inflation is initially associatedwith a decline in output and investment.

Figure 6

Transition Paths Following a Permanent Reduction in the Inflation Rate From 5% to 3%

Investment

-20 -10 0 10 20 30 40 50 60 70 80-0.1

0.0

0.1

0.1

0.2

0.2

0.3

0.3

0.4

-20 -10 0 10 20 30 40 50 60 70 80-0.10.0

0.1

0.1

0.2

0.2

0.3

0.3

0.4

-20 -10 0 10 20 30 40 50 60 70 80-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

-20 -10 0 10 20 30 40 50 60 70 80-0.015

-0.001

-0.005

0.000

0.005

0.010

q=.990

q=.999

Certainty

q=.960

Percent Percent

LeisureConsumption

Quarters from Change Quarters from Change

Output

q=.990

q=.999

Certainty

q=.960

q=.990

q=.999

Certainty

q=.960

Certainty

q=.960 q=.999

q=.990

23 The values used for inflation inthe high and low regimes areadjusted for different values of qto normalize steady-state values.

24 In the three cases where theshift in the inflation trend isunknown, individuals are 90percent certain that they are inthe low-inflation regime after11, 17 and 26 quarters.

This happens because the shift in themoney growth trend is initially mistakenfor a transitory decline in the moneysupply, implying relatively higher moneygrowth as money reverts back to its trend.It is only after observing the lower growthrate for several quarters that individualsare certain that the growth trend haschanged and that economic variables beginthe complete transition to the new steadystate. Consequently, the temporary boostto economic growth is not as sharp, but itis more protracted.

The gradual adjustment to the newinflation trend also means that the welfaregains from a lower rate of inflation—aspresented in Table 2—take time to be real-ized fully. Although individuals benefitfrom higher consumption and leisure asthe economy adjusts, the cumulative gainsfrom lower inflation will be considerablyless than those associated with changes inthe steady state—less, that is, than thebenefits of lower inflation enjoyed bypeople who are born after the transitionperiod is complete. Figure 7 shows thefraction of total cumulative benefits thatare realized during periods subsequent tothe actual change.25 Even after 10 yearshave passed, the cumulative benefits oflower inflation are 75 percent of thesteady-state total for the case of complete

certainty about the change in the inflationtrend. When learning and credibility areissues, the cumulative gains after 10 yearsare only 64 percent, 54 percent and 37 per-cent of the total for the three values of q.For the lowest-credibility case, the initialdecline in consumption and output takestime to offset, so cumulative welfare effectsare negative for 11 quarters. It should benoted that although the cumulative bene-fits of lower inflation might be smaller andmore drawn out over time, nevertheless,they are positive after only a few quarters.Moreover, it should be remembered thatfuture generations benefit by the full mag-nitude of the welfare gains described inTable 2.

Many theoretical monetary modelsimply that short-run monetary contractionsresult in real economic contractions, even ifthey might eventually yield benefits oflower shoe-leather costs. The mechanismpresent in the shopping-time model,which is evident in the low-credibilitycase in Figure 6, is much weaker than insome other model frameworks. Manyeconomists would argue that the short-run costs of disinflation are larger thanshown here.26 Nevertheless, this analysishas illustrated how the credibility of mon-etary policy-makers’ commitment to lowerinflation can mitigate those losses andaccelerate the accrual of benefits fromlower inflation.

CONCLUSIONInflation can be harmful to an economy

for many reasons. This article has discussedone of the most direct and pervasive ofthose costs, known as shoe-leather costs.Representing the time and effort devoted toprotecting the value of one’s purchasingpower from the ravages of inflation, shoe-leather costs are apparent in high-inflationeconomies. For more moderate inflation,the costs are more subtle and more difficultto measure, but still harmful nonetheless.

This article has demonstrated oneapproach to estimating the magnitude ofshoe-leather costs using experiments from ageneral-equilibrium model of money

25 We calculate these figures bycomparing a discounted sum ofthe gains over the first n yearswith a similar discounted sumof the new steady-state values.The discount factor we use isthe one assumed for the indi-viduals in the model.

26 Even in models where theshort-run costs of disinflationare fairly high, the long-runbenefits of lower inflation areultimately considered to belarger. For examples of suchcalculations, see Carlstrom andGavin (1993) and Neely andWaller (1997).



46

Figure 7

Cumulative Benefits of Lower Inflation As a Percent of Steady-State Welfare GainsPercent

Quarters from Change0 10 20 30 40 50 60 70 80

-100

102030405060708090

Certainty

q=.960

q=.990

q=.999

demand. When calibrated to the U.S.economy, the long-run costs of inflationimplied by the model are consistent with avariety of previous estimates. These long-runcosts—and the associated benefits of lowinflation—are generally calculated withoutconsidering the transition effects from oneinflation trend to another. This paper hasdemonstrated that these transitional effectscan be important, delaying and limiting theultimate welfare effects of inflation ratechanges. An important feature of a successfulpolicy of reducing inflation is credibility ofthe monetary authority—particularly whenindividuals in an economy have incompleteinformation about emerging inflation trends.When people are slow to understand orbelieve the permanence of lower inflation, thetransition effects are larger and more pro-tracted. Hence, policy credibility is not onlyimportant for achieving low inflation, it isalso crucial for fully exploiting the potentialbenefits of low inflation.

REFERENCESAndolfatto, David and Paul Gomme. “Monetary Policy Regimes and

Beliefs,” Institute for Empirical Economics of the Federal ReserveBank of Minneapolis, Discussion Paper 118 (July 1997).

Baily, Martin J. ”The Welfare Cost of Inflationary Finance,” Journal ofPolitical Economy 64 (April 1956), pp. 93-110.

Barro, Robert J. ”Inflation and Growth,” this Review (May 1996), pp.153-169.

Baumol, William J. ”The Transactions Demand for Cash: An InventoryTheoretic Approach,” Quarterly Journal of Economics 66 (November1952), pp. 545-556.

Bresciani-Turroni, Costantino. The Economics of Inflation: A Study ofCurrency Depreciation in Post-War Germany 1914-1923, Translated byMillicent E. Sayers, New York (1937).

Bruno, Michael and William Easterly. ”Inflation and Growth: In Searchof a Stable Relationship,” this Review (May 1996), pp. 139-146.

Bullard, James and Steven Russell. ”How Costly is Sustained LowInflation for the U.S. Economy?” Working paper 97-012B, FederalReserve Bank of St. Louis (1997).

Cagan, Phillip. ”The Monetary Dynamics of Hyperinflation,” in MiltonFriedman (ed.) Studies in the Quantity Theory of Money, Chicago:University of Chicago Press (1956), pp. 25-117.

Carlstrom, Charles T. and William T. Gavin. ”Zero Inflation: TransitionCosts and Shoe Leather Benefits.” Contemporary Policy Issues 11(January 1993), pp. 9-17.

Cooley, Thomas F. and Gary D. Hansen. ”The Inflation Tax in a RealBusiness Cycle Model,” American Economic Review 79 (September1989), pp. 733-748.

_______. and _______. ”The Welfare Costs of ModerateInflations,” Journal of Money, Credit and Banking 23 (August 1991,Part 2), pp. 483-503.

Dotsey, Michael and Peter Ireland. ”The Welfare Cost of Inflation inGeneral Equilibrium,” Journal of Monetary Economics 37 (February1996), pp. 29-47.

Dueker, Michael and Andreas Fisher. ”Switching Persistence Parametersin a Monetary Business Cycle Model,” Manuscript, Federal ReserveBank of St Louis (1998).

Feldstein, Martin. ”The Costs and Benefits of Going from Low Inflationto Price Stability” National Bureau of Economic Research WorkingPaper 5469 (February 1996).

Fischer, Stanley. ”Towards an Understanding of the Costs of InflationII,” Carnegie-Rochester Conference on Public Policy 15 (Autumn1981), pp. 5-42.

Friedman, Milton. The Optimal Quantity of Money and Other Essays,(Chicago: Aldine Publishing, 1969).

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Hamilton, James D. Time Series Analysis, Princeton: Princeton UniversityPress (1994).

Imrohoroglu, Ayse. ”The Welfare Cost of Inflation Under ImperfectInsurance,” Journal of Economic Dynamics and Control 16 (January1992), pp. 79-91.

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King, Robert G., Charles I. Plosser, and Sergio T. Rebelo. ”ProductionGrowth and Business Cycles: I. The Basic Neoclassical Model,” Journalof Monetary Economics 21 (March/May 1988), pp. 195-232.

Lamb, Christina. ”A Rollercoaster Out of Control,” Financial Times,February 22, 1993.

Lucas, Robert E., Jr. ”Discussion of: Stanley Fischer, ‘Towards anUnderstanding of the Costs of Inflation: II,’” Carnegie-RochesterConference on Public Policy 15 (Autumn 1981), pp. 43-52.

_______. ”On the Welfare Cost of Inflation,” Center for EconomicPolicy Research, Stanford University, Publication 394 (February1994).



47

McCallum, Bennett T., and Marvin S. Goodfriend. ”Demand for Money:Theoretical Studies,” in The New Palgrave: A Dictionary of Economics,John Eatwell, Murray Milgate, and Peter Newman, eds. London:MacMillan; New York: Stockton Press (1987), pp. 775-781.

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48

THE SHOPPING-TIME MODELPreferences and Technology

A single representative agentmaximizes a discounted stream of utilityderived from consumption, C, and leisure,L:

(A1) ,

where the utility function defines acomposite good using a Cobb-Douglasfunction in Ct and Lt, and displaysconstant relative risk aversion with respectto the composite:

(A2) .

The time endowment and shopping-time technology are described in the text.The agent faces a sequence of budget con-straints given by:

(A3) ,

where investment, It, is gross capital accumulation as shown in Equation 5 in the text.

Output is produced using capital andlabor via a constant returns-to-scale,Cobb-Douglas function:

(A4) ,

where Xt represents labor augmentingtechnical progress, which is assumed togrow at a constant rate γ.

The money stock evolves over timewith fluctuations, vt, around a growthtrend, Gt:

(A5) ,

where Gt = gGt-1 and, vt = ρvvt-1 + εt with εta normally distributed random variable.

Stationary TransformationsIn order to examine the model’s

dynamics, the problem is first transformedto a stationary representation. This involvesadjusting the real variables for trend produc-tivity growth (γ) and the nominal variablesfor trend money growth rate (g).

To adjust for productivity growth,divide all quantity variables by Xt. Withthis modification, the capital accumulationequation becomes:

(A6)

where lower case is used to represent the transformed stationary variables. A1

The growth rate of nominal variables isdetermined by the growth rate of Gt, g.Dividing Mt′ and Pt by beginning-of-periodmoney balances Gt (yielding transformedvariables mt′ and pt ), the nominal side ofthe model is rendered stationary. Thismodifies the budget constraint to be:

(A3′) .

The first-order condition for theagent’s choice of money balances to carryforward, which can be expressed as:

(A7)

reflects the trade-off of the opportunity cost of holding a dollar, the nominal interestrate, against the marginal benefit of lowerfuture shopping time. Equation A7 can berearranged to yield the money demand rela-tionship in the text.

CalibrationParameters of the dynamic system are

calibrated by matching long-run character-istics of the U.S. economy to the modelssteady state solutions. Table A1 lists the

1 1 1 1+( ) = + ⋅( ){ }+ +i E w St t t M t ,

ym

p

t

pc i g

m

ptt

t

t

tt t

t

t

+ ′ + = + + ′+1

γ δk k it t t+ = −( ) +1 1 ,

M G et tvt=

Y F K X N K X Nt t t t t t t= ( ) = ( ) −, α α1

YM

P

T

PC I

M

Pt

t

t

tt t

t

t

+ ′ + = + + ′+1

U(C ,L ) = 1

1- (C L )t t t t

1- 1-

σθ θ σ

max ,β tt t

tU C L( )∑

=

∞

0

A1The transformation of consump-tion also alters the effective rateof time preference. See King,Plosser and Rebelo (1988).



49

Appendix

key model parameters. Most have beenselected to be consistent with previous cal-ibrations of equilibrium business cyclemodels.A2 The steady state per-capitagrowth rate and the inflation rate are set attheir long-run average values of 1.6percent and 5 percent annually. Capital’sshare in production, α, is set to 0.3 and thecapital depreciation rate, δ, is 10 percentper year. The discount factor is 0.99, andthe coefficient of relative risk aversion isset to equal 2. Leisure’s share in overallutility, (1-θ), is selected to yield steady-state work effort as a fraction of the totaltime endowment at 0.3. Selection of theparameters of the shopping time functionis discussed in the text.

A2King, Plosser and Rebelo (1988);Cooley and Hansen (1989);and others.



50

Baseline Parameter Values

Description Symbol Value

Preferences Discount factor β 0.99

Intertemporal substitution σ 2

Consumption share θ 0.322

Technology Capital’s share α 0.3

Capital depreciation rate δ 0.025

Shopping Time Scale parameter µ1 0.0111

Curvature parameter µ2 1

Growth Trends Technology growth γ 1.004

Money growth g 1.012

Table A1

Documents

Shoe-Leather Costs of Inflation and Policy Credibility