A Note on Inflation and the Saving Rate (Brookings Papers on Economic Activity, 1972, No. 3

F. THOMAS JUSTER* NationalBureau of EconomicResearch

PAUL WACHTEL* NationalBureau of EconomicResearch and New York University

A Note on Infation and the Saving Rate

IN AN EARLIER PAPER FOR BrookingsPapers on EconomicActivity, we presentedfindings on the relationbetween price inflationand consumer saving in the context of examiningthe role of expectationalvariables in consumerspending and savingdecisions.' The paperfocused primarily on durablegoods expendituremodels, and presentedevidence on the useful- ness of explicitlyexpectational variables in such models. We also looked brieflyat a relativelysimple saving function to see if the sameexpectational variablesthat were associatedwith durablegoods expendituredecisions also had an impacton savingdecisions. This reportfocuses entirely on saving, and is concernedprimarily with modelsthat can be usedto predictthe personalsaving rate. In this report,we examinethree sets of variablesfor theirimpact on the saving rate. The first is personaltaxes and transferpayments, which the evidencesuggests have a stronginitial impact on observedsaving behavior. Second, we includeboth the levels of and changesin the unemployment

* Supportfor the computerwork in the paper was providedby Rapidata, Inc., and for research assistance by the Commercial Credit Corporation. Teresita Rodriguez helped with the computations.The researchgrows out of earlierwork supportedby the National Science Foundation,the U.S. Bureauof the Census, and the National Bureau of Economic Research. 1. "Inflationand the Consumer,"Brookings Papers on EconomicActivity (1:1972), pp. 71-114. 765 766 Rrnnkins,v Panprs on Economic Activitvy 3:1972 rate; the formerrepresents the effect of diminishedactual resources,the latterthe effectof uncertaintyabout incomeprospects. Third, we measure the influenceof inflation, both anticipatedand unanticipated,and ask whetherconsumer expectations and attitudes,as measuredby household surveys,have any net influenceon savingbehavior after these otherfactors have been taken into account. The predictiveability of the model developedusing these explanatory variables,referred to as the forecastmodel, is then comparedwith that of a model developedby Houthakkerand Taylor that is more typical of the recentliterature.2 The Houthakker-Taylormodel also incorporatesa stock adjustmentor distributedlag process,and emphasizesthe influencesof tax changes and the composition of personal income changes on saving behavior.

The ForecastModel

Before turningto a more detailedexamination of empiricalresults, a summaryof the variablesused in the forecastmodel, and the reasonsfor their inclusion,may be useful.

TAXES AND TRANSFERS The role of both taxes and transfersin the model is straightforward.In- creasesin personalincome taxes reducedisposable income relative to personal income.The same is true of payroll taxes, which we combinewith personalincome taxes becauseof the absenceof any strongevidence that the influenceof the two is different.The questionis how much of the impact of tax changesfalls on saving and how much on consumption.We find, as othershave before us, that changesin transferpayments have a verylarge and positiveinitial impact on saving,suggesting that people re- ceivingtransfers have a very high short-runmarginal propensity to save.3 Since most transferpayments are social securitybenefits, which accrueto lower-incomeindividuals with, presumably,high marginalpropensities to

2. H. S. Houthakker and Lester Taylor, ConsumerDemand in the United States, 1929-1970: Analysesand Projections(2nd ed., HarvardUniversity Press, 1970). 3. Lester Taylor, "Saving out of Different Types of Income," BrookingsPapers on EconomicActivity (2:1971), pp. 383-407. F. Thomas Juster and Paul Wachtel 767 spend,this findingpresents a continuingpuzzle. However, a variationof the forecastmodel that allowsfor lag effectsindicates that this high propensity to save out of transferincome does not exist in the long run.

UNEMPLOYMENT RATES When the unemploymentrate is high, a relativelylarge fractionof the populationis receivingsubstantially less income than normal.Given the stickinessof consumptionpatterns, one would anticipatea reductionin the aggregaterate of personalsaving as a result.Thus the direct influenceof high unemploymentin reducingdisposable income suggests that the unemploymentrate will have a negativesign in a savingequation. But changesin unemploymentrates may play an entirelydifferent role. If unemployment is rising, the fear of becomingunemployed is probablyrising too. For people who continueto hold jobs and thereforesuffer no actualdecline in disposableincome, this fear implies a retrenchmenton spendingand a buildingup of reservesvia saving.When unemploymentrates are declining, concernabout job securitywill also be declining,and with it the need to build financialreserves. In the empiricalwork we find evidencefor both a directnegative influence of the unemploymentlevel on saving and an indirectpositive influence of unemploymentchange on saving.

PRICE INFLATION In our previouspaper, we arguethat therehas been a markeddifference betweenthe effectsof anticipatedand unanticipatedinflation.4 Traditional economictheory suggeststhat a fully anticipatedrate of inflationhas no effect on real economicbehavior in the long run. For unanticipatedinflation, our basic argumentis that it generatesan increasedvariance of expectedreal income that has asymmetricaleffects on behavior;that is, a rise in the rate of priceinflation above the anticipatedrate tends to mean that consumerswill be less certainthan before about prospectivechanges in theirreal income.In decisionsabout whetherto spend or save, the proba- bility that real incomewill be improvedis not accordedthe sameweight as the probabilitythat real income will deteriorate.The reason is that the consequencesof guessingwrong are not symmetrical:If consumersre- trenchon spendingand it turns out that real incomerises because money 4. "Inflationand the Consumer." 768 Brookings Papers on Economic Activity, 3:1972 incomerises more rapidly than prices, nothing is lost exceptan opportunity to consumenow at favorableprices rather than laterat less favorableones. But if people act on the assumptionthat real incomewill rise and, in fact, it does not because prices outstripmoney incomes, the financialconse- quencescan be unpleasant.The argumentthat the increasedvariance in real income expectationsleads to increasedsaving can be made for anticipated as well as unanticipatedinflation if the varianceof inflationexpecta- tions increaseswith the level. The empiricalevidence associates positive saving effects only with unanticipatedinflation. However, comparison of the actualand expectedseries reveals that periodsof high inflationin the United Stateshave neverbeen fully anticipated. An alternativeexplanation, which is consistentwith the same empirical results,is that consumerexpectations are biased: Becausepeople do not generallyanticipate money income increasesto the same extent as they anticipateprice increases,a rapid rate of inflationis taken to be synony- mous with a declinein expectedreal incomeby the majorityof consumers. The expecteddecline in real incomeinduces increased saving as the expectations are not realized.Survey data provide some evidencethat a bias towardpessimistic mean expectationsabout real income when pricesrise relativelyrapidly is not characteristicof consumers;hence the first inter- pretationseems more consistentwith the availableevidence, although un- fortunately,no directevidence exists to supportit.

EXPECTATIONS AND ATTITUDES Thereare severaldirect survey measures of consumerexpectations and attitudesthat are often allegedto have an influenceon saving behavior. The questionis whetherthese measures simply duplicate the informationon plansand perceptionsalready reflected in the economicvariables discussed above, or captureinformation that thesevariables fail to pick up.

EmpiricalEstimates

Estimatesof the forecastmodel for the period1954:1-1972:3 are shown in Table 1. The dependentvariable is the ratio of personalsaving to personal income. Personalrather than disposableincome is used becausethe effectsof tax changeson savingare includedin the equation.Estimates for four versions of the model are shown: equation(1) is the basic model; F. ThomasJuster and Paul Wachtel 769 equation(2) drops the interestrate term from the basic model; equation (3) addsa surveyindex of expectedpurchases; and equation(4) repeatsthe variablesof equation(1) but uses a serialcorrelation adjustment in estimation. All the coefficientsof the basic model, equation(1) in the table, have the expectedsigns and all but the interestrate are significant at the 5 percent level. The equationexplains over 70 percentof the variancein savingrates over a nineteen-yearperiod. The equation does exhibit positive serial correlationof the residuals.In general,the savingrate model is relatively robust in the specificationof income composition and unemployment effects,but the role of both expectedand actualprice inflation is muchless satisfactory.When the equationis estimatedfor time spansbeginning later than 1954and continuingthrough 1972, the role of pricesbecomes erratic: The effect of interestrates is larger,and the effect of actualprice inflation becomes smallerand in some cases disappearsentirely. The interestrate coefficientsseem implausiblylarge. When the equationis estimatedfor the periodthrough 1967, the inflationeffects are unchanged.Actual, as well as expected,price inflation should be correlatedwith long-terminterest rates, and we have not been able to devisea structurethat is not sensitiveto the time period of estimation. The partialeffects of unemployment,U, unemploymentchange, AU, and interestrates, R, are all sizable: The impliedunemployment elasticity of the savingrate from equation (1) is -0.6, whilethe interestrate elasticity is +0.28. An interestrate elasticityof this size seems implausibleto us, but the standarderror of the coefficientis also large.The unemploymentelas- ticity also seemslarge, but the changein U is beingheld constant;when U is risingor falling,the net effectson savingare mutedbecause AU has the opposite sign. The effects of transferincome and tax and social security payments,while powerful,tend to be offsetting. In equation(2) of Table 1, the interestrate is droppedfrom the basic model on the groundsthat thereis little a priorireason to expectany effect of interestrates on saving, net of inflationeffects.5 Doing this raises the 5. The interest rate variablein equation(1) is actuallya nominal rate, but the coefficient is exactlythe same as if it were a real rate. It can be shown that an equationinclud- ing the real rate (R - CPI) and CPI has the same R coefficientas that shown in Table 1, and a larger CPI coefficient.An equation using the real rate of interest S = a, (R - CPI) + a2 CPI + ... (where S = saving) implies S=a, R + (a2-a,) CPI+ ..., which is our nominal rate equation. V C f * 1O%0 V} . * * * N- en r- 00 C - 4 C * 5 o o --o o** I I I

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4)ESo!=tWi? a . 5 13J1 11 1 8 4?;Qa 772 Brookings Papers on Economic Activity, 3:1972 standarderror of estimateby 0.0077 and makes the inflationvariables, CPI* and CPI, somewhat stronger. In equation (3) the expected automobile purchaserate, A*, is addedto equation(2). The variableshows up strongly, but weakensthe importanceof the inflationvariables. We also tried the index of consumersentiment as an explanatoryvariable; it enteredthe equationwith the appropriatenegative sign, but its t-ratiowas less than one. The interpretationof the coefficientson actualand expectedinflation is discussedin our earlierpaper.6 When both variables are in the equation,the effectof anticipatedinflation is the sumof the two coefficients,and the effect of unanticipatedinflation is the coefficientof CPI. The preferredequation (2) impliesthat anticipatedinflation has only a smallpositive effect on saving and unanticipatedinflation has a large positiveeffect. As noted, the data indicatethat inflationis rarelyfully anticipated. In equation(4), the basic model is reestimatedusing a serialcorrelation correctionbased on the Cochrane-Orcutttransformation. The standard errordeclines by almost 15 percent,but the inflationcoefficients are reduced.Their standard errors are unchanged,but their impliedt-ratios fall below conventionalacceptance levels.

Long-runCharacteristics

The forecastmodel estimated here is static,yet manyof the determinants of the savingrate are expectedto have a lagged influencethat variesover time. This is particularlytrue of the two income ratios, whose large estimated effectson saving shown in Table 1 are plausibleas short-runphe- nomenaonly. Thereis no reasonto think that a changein the proportion of incomereceived as transfersshould have a permanentinfluence on saving exceptthrough changes in the distributionof income,while a changein tax rates might be expectedto changethe ratio of saving to personalincome, but not by as much as equation(1) suggests. In orderto test the effectof thesevariables on savingin the long run, the modelwas reestimatedusing eight-quarter, third-degree Almon lags on the two incomeratios.7 The initiallag coefficientsare of the sameorder of mag- nitude and significanceas the coefficientsin Table 1. The sums of the lag

6. "Inflationand the Consumer." 7. Program limitations required that these estimates exclude R and AU from the basic equation. F. Thomas Juster and Paul Wachtel 773 coefficientsare alwayssmaller and not significantlydifferent from zero at the 5 percentsignificance level. These resultsindicate that the Table 1 coefficientsare impacteffects and that the effectof taxes and transferson the savingrate is negligiblein the long run. Almon lags on the inflationvariables indicatethat their long-runeffects are somewhatstronger than the impacteffects shown in Table 1.

The Houthakker-TaylorModel

The secondmodel used to test the effect of inflationon personalsaving is that developedby Houthakkerand Taylor from a simple behavioral hypothesis.8 TheHouthakker-Taylor model is basedon the followingsaving function:

n (l) ~~~St=ae + OKt+ E ajYj,, i=l where S = personal savings K = stock of assets Y; = componentsof incomeand any othervariables entering the saving function. The reduced-formequation of the model,(3), is derivedfrom (1), the stock identity(2), and a discretetime approximation: (2) kt= St

(3) St = I St__, + ?- A3 Yg

The reducedform includes lagged saving and the firstdifferences of all the variablesin the savingfunction (1). Thereis no constantterm when assets are consideredto be nondepreciating. Estimates of the Houthakker-Taylormodel for the period 1954:1- 1972:3 are shown in Table 2. Equation(1) in that table follows Taylor's

8. Houthakker andjraylor, ConsumerDemand, and Taylor, "Saving out of Dif- ferent Types of Income." 774 Brookings Papers on Economic Activity, 3:1972 specificationand all variablesare in constant prices and expressedper household.Income is dividedinto the followingcomponents: L = labor income P = property income TR = transfer payments SI = personalsocial securitycontributions T = personaltax and nontaxpayments. The disaggregationof incomeis highlysignificant and leads to largediffer- ences in the estimatedmarginal propensity to consume out of different types of income.These results are similarto Taylor'sfor the periodending with 1969 and have been analyzedextensively before. For all estimatesof the Houthakker-Taylormodel, the hypothesisof zero autocorrelationof the residualsis rejectedat the 1 percentconfidence level by the Durbintest. Whenthe rate of inflationis addedto the behavioralequation (1), it too appearsin the reducedform as a firstdifference. Experimentation with the inflationvariables in the Houthakker-Taylorspecification was not success- ful. Of the nonincomevariables tested, only AR (and not ACPIor ACPI*) enteredthe equationsignificantly. However, the impliedlong-run elasticity of interestrates is so large-0.42 when evaluatedat the means-that we regardedthe inclusionof either inflationor interestrate variablesin the long-runbehavioral specification of the Houthakker-Taylormodel as an unsettledissue. We thereforetested variousspecifications of actual and expectedinflation rates in the reduced-formHouthakker-Taylor equation. When the level of expectedor actualinflation was addedto the equation,AR became insignificant.The actual inflation rate was more powerfulthan the ex- pectedrate, and the expectedpurchase variable did not entersignificantly.

ALTERNATIVE SPECIFICATIONS Equation(2) in Table 2 reestimatesthe model with the formalspecifica- tion relaxedto allow a constantterm, and with inflation,but not interest rates,included as an explanatoryvariable. This formulation yields a modest improvementin the explanatorypower of the model.The structuralincome coefficientsare unchangedand both the constantterm and the actualrate of inflationenter significantly.The actualrate of inflationhas a beta coefficientof 0.12 in equation(2), while AR has a beta coefficientof 0.06 in * e, r P-.O 00 t . * * * n t- \.0 00 en t . . . * c o0o 00 '. r en

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i~~~~~C ?, S9 R ( 776 Brookings Papers on Economic Activity, 3:1972 equation(1). Accordingto equation(2), an increasein the rate of inflation of one percentagepoint will raisesaving per householdby $8.17, or by 1.8 percent.

TrackingRecent Saving

The standarderror of estimatefrom the forecastmodel can be compared with the standarderrors from the Houthakker-Taylormodel by multiply- ing by the mean level of real incomeper householdover the sample. The standarderrors in real savingper householdas impliedby the savingrate forecast equations(Table 1) are $38.92, $39.56, $37.40, and $33.50, respectively.Only when the serialcorrelation correction is made is the standard errorlower than that of the Houthakker-Taylormodel. This is not surprising,for that model includesa lagged dependentvariable while the forecastequation does not. A better comparisonis found in Table 3, where predictedand actual

Table 3. Estimates of Predicted and Actual Saving, Houthakker-Taylor and Forecast Models, First Quarter 1970 through Third Quarter 1972 Personalsaving as a percentof Real savingper household, personialinicome, Year Houthakker-Taylormodel Forecastmodel and quar- Actual Predicted Error Actual Predicted Error ter (1) (2) (3) (4) (5) (6) 1970:1 $576.9 $601.2 -4.2% 5.89%0 5.76% 2.3% 2 686.7 684.4 0.3 6.93 6.87 0.9 3 703.1 713.9 -1.5 7.13 7.01 1.7 4 704.5 665.2 5.6 7.22 6.81 5.8 1971:1 695.5 724.9 -4.2 7.08 7.09 -0.1 2 741.6 750.4 -1.2 7.47 6.54 -0.8 3 698.3 709.6 -1.6 7.03 6.99 0.5 4 672.7 661.7 1.6 6.73 6.72 0.1 1972:1 623.4 591.6 5.1 6.14 5.51 10.2 2 554.1 618.5 -11.6 5.43 5.37 1.1 3 554.8 561.9 -1.3 5.40 5.61 -3.8 Sources: Column 1, Survey of CurrentBusiness, various issues; U.S. Bureau of the Census, CurrentPopula- tion Reports, Series P-20, Nos. 218 and 233, "Household and Family Characteristics, March 1970" (1971) and ". . . March 1971" (1972), respectively; column 4, Economic Indicators(December 1972) and preceding relevant issues. Column 2 is calculated from Table 2, equation (2), and column (5) is calculated from Table 1, equation (2). The errors are calculated from data before rounding. F. Thomas Juster and Paul Wachtel 777 values from the Houthakker-Taylormodel and the forecastequation are presentedfor 1970:1-1972:3.The forecastmodel has a slightlybetter ex post performancein explainingthe erraticsaving behavior of recentyears, althoughboth equationstrack this periodquite well. The root mean-square percentageerror of the forecastmodel is 3.85 percent,while that for the Houthakker-Taylormodel is 4.65 percent. The largedecline in the savingrate in recentquarters is well explainedby the forecastmodel. From 1970:3to 1972:3,the rate declinedby 1.73 percentagepoints. Of this decline,0.70 point is explainedby the unemployment variables,0.62 by the pricevariables, and 0.17 by the income ratios; the rest is unexplained.

Estimatesof FutureSaving Rates

Futuresaving rates, according to ourmodel, will dependon threethings: (a) the differencebetween changes in personaltaxes and transfers,which have tendedto have offsettingeffects on income secularlybut reinforcing effectscyclically; (b) the path of unemploymentrates; and (c) the difference betweenactual and expectedrates of price inflation. We assumethat changesin taxes and transferswill tend to offset each otherover the next year,and that unemploymentrates will go down somewhat. In the model, a 0.1 percentagepoint drop in the level of unemployment will be just offset by a 0.33 percentagepoint decline in the four- quarterchange in unemployment.On balance, decliningunemployment will generallylead to a highersaving rate. The probableeffects of inflation rates are riskierto assess. At this writing,actual inflation exceeds the ex- pectedrate of inflationby 0.4 percentagepoint. If actual inflationspeeds up, past historysuggests that expectationswill lag, leadingto a 0.26 percentagepoint rise in the savingrate for everyone percentagepoint of unanticipatedinflation. But past history may be a poor guide in this case, sinceexpectations appear to have quitelong lags and are still basedheavily on the inflationrates of 1970 and 1971. Prospectivedeclines in unemploymentduring 1973 will tend to increase savingrates, all other thingsheld constant.If the unemploymentrate de- clinesto 4.8 percentby 1973:4so that the averagerate for 1973is 5 percent, the savingrate will increaseby 0.4 percentagepoint from 1972:4to 1973:4. If the unemploymentrate declinesless rapidly,to 5.0 percentat year-end 778 BrookingsPapers on EconomicActivity, 3:1972 with an averagerate of 5.15 percentin 1973, the savingrate will still increase,but by less than 0.3 percentagepoint. Whilethe likelycourse of pricesin 1973is unclear,some reasonablepos- sibilitiescan be suggested.If inflationlevels off at a fully anticipatedrate of 3 percent,the savingrate will decreaseby 0.1 percentagepoint. If, on the otherhand, the inflationrate shouldrise by 2 percentagepoints morethan expected,the savingrate will rise by 0.4 percentagepoint. A final changethat is expectedto increasesaving rates is the declinein the ratio of personaltax to personalincome because of the unusuallylarge refundsdue in 1973 from overwithheldincome taxes during 1972. The declinein the ratio may be about 1 percentagepoint in 1973:1 and 1.5 percentagepoints in 1973:2, with a returnto normal levels thereafter.The effect would be an increasein the saving rate of 0.8 percentagepoint in 1973:1 and of 1.3 percentagepoints in 1973:2,followed by a declineto the 1972:4level. The analysisclearly suggests that the savingrate will tend to rise during 1973. The only influencein our model that might act to reducethe rate wouldbe a declinein the actualrate of inflation,but it is difficultto visualize a reductionin priceinflation of sufficientmagnitude to preventthe saving rate from rising.