Hymans

E. PHILIP HOWREY University of Michigan

SAUL H. HYMANS University of Michigan

The

Measurement and

Determination of

Loanable-Funds Saving Saving is taken to be the source of the resourcesneeded to producecapital.It representsnew materialsand labor which could have been used for current consumptionbut which, instead, are held back (saved) in order to make possible the productionof largeroutputs in the future. Thus savingsare the supply side of the supplyand demandfor new capital.-William J. Baumoll

WHILEthere may be many reasons to be concernedabout what determinesthe flow of savingin the U.S. economy,it is the role of savingas the supplyside in the processof capitalaccumulationthatseemsto lie at the heartof the renewedinterestin savingbehaviorin recentliterature.That sameview of savingis the focus of our attentionandguidesthe choiceswe make in the empiricalanalysispresentedhere. Our majorobjectiveis to investigatethe propositionthat saving-in the sense of the flow of resources availablefor capital formation,or "loanablefunds"-is determinedin partby the rateof interest.

Note: We thank David M. Garman for his exceptionally competent research assistance. Our colleague, Theodore C. Bergstrom, and members of the Brookings panel made many helpful suggestionson earlier versions of this article.

1. William J. Baumol, Economic Theory and OperationsAnalysis, 4th ed. (Prentice-Hall, 1977), pp. 650-51.

EBrookingslutftuoton 0007-230317810003-0655$00.25/0

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A criticallyimportantpolicy problem is at issue here. Suppose, as Feldsteinhas claimed,thatthe UnitedStatessavestoo little andtherefore forgoesthe benefitsof unrealizedadditionsto productivecapacity.2Suppose furtherthat, as a numberof writershave recentlysuggested,partof the reasonthatthe UnitedStatesdoes not save a sufficientlylargefraction of its incomeis thatthe tax structuredrivesa wedgebetweenthe marginal rate of returnto privatecapitalformationand the after-taxrateof return to private saving, and thus the latter is low relativeto the former.3In that case, a changein the tax laws could be expectedto changethe ratio of savingto income.Specifically,if savingis positivelyrelatedto the aftertax rate of returnto saving,a reductionin the marginaltax rate on earnings from savingwould raisesavingat any givenlevel of income;in other words,the reductionwould raisethe savingrate.For such a prescription to be usefulto policymakers,two findingsmustemergefromthe empirical analysis.First,it mustbe demonstratedthat a positive,reliablymeasured partialderivativeexists connectingloanable-fundssavingand the appropriateinterestrate. And if this can be shown, the second requirementis that the positiverelationshipmust be "important"as well as significant.

Thatis, policymakerscannothavemuchinterestif the estimatedresponse of the savingrateto a unit changein the rateof returnto savingis 0.0001, regardlessof how smallthe standarderroron that 0.0001 mightbe.4 2. See Martin Feldstein, "Does the United States Save Too Little?" American Economic Review, vol. 67 (February 1977), pp. 116-21. Feldstein argues that realizing those additional benefits would increase economic welfare so that existing saving is inefficientlysmall.

3. See the excellent survey article on this and related topics: George M. von Furstenbergand Burton G. Malkiel, 'The Government and Capital Formation: A Survey of Recent Issues," Journal of Economic Literature, vol. 15 (September 1977), pp. 835-78. Also see Michael J. Boskin, "On Some Recent Econometric Research in Public Finance," American Economic Review, vol. 66 (May 1976), pp.

102-09; Michael J. Boskin, "Taxation,Saving, and the Rate of Interest,"Journal of Political Economy, vol. 86 (April 1978, pt. 2), pp. S3-S27; and Feldstein, "Does the United States Save Too Little?"

4. Presumably the fiscal issue here is not a net tax cut, but a tax reform that lowers the tax rate on interest income and then raises other tax rates (say, taxes on wage and salary income) to maintain fixed total tax revenue. We would then want to measure the responsivenessof saving to a change in the after-tax rate of return to saving, given the level of total tax revenue. This means that the fiscal authorities would have to raise the tax rate on wage and salary income by enough to offset the tax revenue lost on interest income from the entire stock of consumer saving, not just from the flow of saving from current income. Our final empirical results below

E. Philip Howrey and Saul H. Hymans

657

It is by no meanstrue that all writerson this topic claimthe existence of a positiverelationbetweensavingandthe interestrate.In the Fisherian gospel thatformsthe theoreticalbasisfor the analysisof savingbehavior, it is well recognizedthat the responseof an individualwho is a net saver at interestrateR0 to a changein the rate to R0 + AR is, in general,indeterminatebecausethe substitutionandincomeeffectsareof oppositesigns.

Indeed the recent attackon neoclassicalcapitaltheoryfrom Cambridge (England) includesthe view thatthe effectof the interestrateon savingis likely to be negligible,and focuses on businessdecisionsand the division of nationalincome betweenworkersand entrepreneursas the majordeterminantsof saving.5 To shed light on the role of the interestrate in determiningloanablefunds saving,it is importantthat we know what interestrate to consider and that we are able to observe an empiricalcounterpartof loanablefunds saving.There is fair agreement,at least in principle,that the relevant rate of returnto savingshouldbe an expected,after-tax,real rate of return.Thereis less agreementon preciselyhow to measurethe expected after-taxreal rate., As we indicatein the next section,the resultscan be quite sensitiveto the choice of data on interestand inflationrates.

And what is loanable-fundssaving?Observationsof two savingflows are publishedregularly:saving in the nationalincome and productaccounts (hereafterNIPA) and savingin the flow-of-fundsaccounts(hereafterFF). We claim that neitherof these is the appropriatemeasureof measure such an effect by treating the after-tax rate of return and personal tax payments as separate independentvariables in a multiple regression explaining saving. This procedure is not the same as the one implied in the usual conceptual experiment of isolating the income and substitutioneffects of a change in the after-tax interestrate.

5. A concise and insightful discussion of the capital theory controversy may be found in Baumol, Economic Theory and OperationsAnalysis, pp. 653-70. Baumol concludes that "a priori surmise"cannot tell us what determinesthe flow of saving; "It is a matter for empirical investigation, and the issue is still far from being settled" (p. 657).

6. In the presence of uncertainty, is it only the expectation of a probability distribution that matters? If the interest rate, tax rate, and inflation rate are perceived to be random variables, is it appropriatesimply to combine them into a single random variable (the after-tax real rate of return), or is the saving decision a more complex function of all three variables? Is a single interest rate all that matters, or is there an array of interest rates on alternative assets that affects the saving decision? In this paper we cannot treat all these issues, but we look at some of them.

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savingfor the propositionunderconsideration.No firminterestedin borrowing(throughthe bond or equitymarketsor fromthe bankingsystem) to finance capital formationcan borrow either NIPA personal or FF personal saving. The former includes expenditureon owner-occupied dwellingsand a numberof imputations;the latter,expenditureon owneroccupieddwellingsand all otherconsumerdurables,and severalimputations.Whatindividualscontributedirectlyto the loanablefundsavailable for businesscapitalformation-and the quantitythat mightbe affected by tax changesthat alterthe rateof returnto saving-is theircashsaving.

This savingis the differencebetweentotalcashreceiptsandtotal cash expenditureson anythingexcept those financialassetsprovidingfunds for capital expenditureseither directly (such as corporatebonds) or indirectly (such as time deposits). Individualsspend money to purchase claims to retirementincome, say, by participationin a privatepension plan, and some or all of thatmaywell be regardedby theseindividualsas a part of theirpersonalsaving.But is it part of personalloanable-funds saving?To the extentthatthe pensionfundsaccumulatecashin excess of theiroperatingexpenditure(includingthe paymentof pensionbenefits), those fundsmay become availablefor capitalformation;if they do, they shouldbe viewed as a componentof the net cash flow in the businessor nonpersonalsector of the economy.7How pensionfunds hold their net cash flow is a separateissue from whetherthe interestrate is a determinantof personalcash saving.8In whatfollowswe use the terms"personal cash saving"and "personalloanable-fundssaving"interchangeably.Our empiricalanalysismakesuse of NIPA, FF, andcash saving,but our main focus is on cash saving.

Table 1 providesa detaileddescriptionof personalcash saving as it relatesto NIPA personalsavingand our conceptof FP personalsaving, 7. We do not deny that the purchase of pension rights may affect personal cash saving or that business cash flow may affect personal cash saving. Rather, we assert that the expenditureon such claims is not itself a component of personal loanablefunds saving. The behavioral relationship between business saving and personal saving has been treated in Paul A. David and John L. Scadding, "PrivateSavings: Ultrarationality,Aggregation and 'Denison's Law,"' Journal of Political Economy, vol. 82 (March-April 1974, pt. 1), pp. 225-49, and we addressthis in our empirical work below.

8. It is possible that changes in the interest rate may lead individualsto vary the amount saved in cash and through private pension funds. We treat such behavior at least indirectlyby allowing for the possibility of substitutionbetween these forms of saving.

E. PhilipHowrey and Saul H. Hymans

659

Table 1. Derivationof AlternativeConceptsof PersonalSaving,1975 Billions of dollars Itene

Amount

NIPA personalsaving Minus: Gross investmentin owner-occupied buildings Marginon owner-builthouses Plus: Capitalconsumptionallowanceswith adjustmenton owner-occupiedbuildings

80.2

SCB, table 2.1

43.6 0.7

SCB, table8.3 (80 + 81) SCB, table 8.3 (87)

28.0

SCB, table 8.3 (64 + 70 + 76)

Sourceb

Equals:NIPA personalsaving,excludingimputations 63.8

SCB, table 8.3 (60)

Minus: Changein reservesof privatepensionand insuranceplans

27.8

FF(13 + 14 + 15)

Equals:Personalcash saving

36.0

Plus:

Gross investmentin owner-occupied buildings Minus: Capitalconsumptionallowanceswith adjustmenton owner-occupiedbuildings

43.6

SCB, table8.3 (80 + 81)

28.0

Plus:

22.7

SCB, table 8.3 (64 + 70 + 76) FF (41)

Net investmentin consumerdurables

Equals:FF personalsavingo

74.3

a. NIPA refers to items from the national income and product accounts; FF, to items from the flow-offunds accounts of the Federal Reserve System. b. SCB is Survey of CurrentBusiness, vol. 57 (July 1977), and FF is Flow of FundsAccounts,4th Quarter 1977 (Board of Governors of the Federal Reserve System, February 1978), p. 53. The numbers in parentheses refer to line numbers in the source table. Figures are rounded. c. This item does not equal the category "personal saving, F/F basis" in the flow-of-funds accounts. which was $104.9 billion in 1975.

using 1975 data.9Briefly,the majordifferencebetweenNIPA personal saving and our definitionof personalcash savingis that the net investment in owner-occupiedbuildings and the net contributionto private pensionandinsuranceplansareincludedin NIPA personalsavingbut excludedfrompersonalcash saving.10OurFF personalsavingaddsnet purchasesof consumerdurablesandnet investmentin owner-occupiedbuild9. The FF saving as definedhere is conceptuallythe same as that in the published data of the Federal Reserve Board, but we have not reconciled it exactly with the published series.

10. Our treatmentof private pension and insurance plans is thus consistent with the NIPA treatmentof social insurancefunds.

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660

of GrossPrivateSaving,1975 Table2. Derivatdonof AltenativeConcepts Billionsof dollars Item

Amount

Changein reservesof privatepensionand 27.8 insurance plans corporateprofitswithinPlus: Undistributed ventoryvaluationandcapitalconsump16.7 tionadjustments 0.0 Wageaccrualslessdisbursements allowances capitalconsumption Corporate 101.7 withadjustment allowcapitalconsumption Noncorporate 60.8 anceswithadjustment with allowances Minus:Capitalconsumption buildings 28.0 on owner-occupied adjustment

Source

FF(13 + 14 + 15)

SCB,table5.1 SCB,table5.1 SCB,table5.1 SCB,table5.1 SCB,table8.3 (64+70+76)

privatecashsaving 179.0 (business) Equals:Nonpersonal Plus: Personalcashsaving Equals:Grossprivatecashsaving in owner-occupied Plus: Grossinvestment buildings houses Marginon owner-built Equals:NIPAgrossprivatesavingb

36.0

Authors'calculations fromtable1

215.0 43.6 0.7 259.4

SCB,table8.3(80+ 81) SCB,table8.3(87) SCB,table5.1

a. See table 1, note b. b. NIPA refers to items from the national income and product accounts.

ings to personalcash saving.In this way we treatpurchasesof consumer durablesand housingconsistently.Table 2 makesthe transitionto gross privatecash savingandNIPA grossprivatesaving;the formeris obtained by adding personal cash saving and the nonpersonal(business) gross cash saving.Table3 outlinespersonalcashreceiptsandNIPA disposable personalincome;table4, privatecashreceiptsandNIPA privatereceipts.

All calculationsareillustratedfor calendaryear 1975, basedon published dataas indicated.Variablessuchas personalcash savingor personalcash receiptsare availableonly on an annualbasis, and we calculatedannual observationson all the relevantvariablesin tables 1 through4 for the period 1951-74 for purposesof the empiricalanalysis.The last year we

E. Philip Howreyand Saul H. Hymans

661

Table3. Relationof NIPAPersonalIncometo PersonalCashReceiptsbeforean afterTaxandCashFlowsPlusNoncashReceiptsafterTax, 1975a Billionsof dollars Item

Amount

Personalincomewithoutimputationso Minus:Investment incomeof privatepension andinsurance funds

1,217.0 20.6

for privatepenEmployer contributions 56.8 sionandinsurance funds Plus: Personal contributions forsocialinsurance 50.4 Benefitspaidfromprivatepensionand 45.2 insurance funds Equals:Personalcashreceiptsd 1,235.2 Minus:Personaltaxandnontaxpayments Equals:Personalcashreceiptsaftertax Plus: Imputationse

169.0 1,066.2 36.2

forsocialinEmployer contributions 116.6 suranceandprivatepensionand funds insurance Equals:Personalcasbandnoncash receiptsafter 1,219.0 tax incomeof privatepension 20.6 Plus: Investment andinsurance funds Minus:Employer contributions forsocialinsurance 59.8 Benefitspaidfromprivatepensionand 45.2 insurance funds Personal contributions forsocialinsurance 50.4 Equals:NIPAdisposable personal income 1,084.4

Sourceb SCB, table8.3(42) SCB, table8.2(43)

minustable8.3 (35 + 38 + 56) SCB,table6.13 SCB,table2.1 SCB,table6.13

SCB,table2.1 SCB,table8.3 (68 - 66 + 79 + 82 + 84 + 85 + 86 + 87) SCB, tables1.13 and6.13

SCB,table8.2 (43) minustable8.3 (35 + 38 + 56) SCB, table1.13 SCB,table6.13 SCB,table2.1 SCB,table2.1

a. NIPA refers to items from the national income and product accounts. b. SCB is Survey of CurrentBusiness, vol. 57 (July 1977). The numbers in parenthesesrefer to line numbers in the source table. Figures are rounded. c. Personal income without imputations, as published, does not correspond to personal cash receipts because of the attribution of investment income of private pension and insurance funds to individuals (not regardedas an imputation by national income accountants), the inclusion of employer contributions to private pension and insurance funds, and the exclusion of personal contributions for social insurance (but not personal contributions for private pension and insurance) and benefits paid from private pension and insurance funds. We have simply reversed these items so that private pension and insurance contributions are treated exactly the same as social insurance contributions, and private "transfer payments" to Individualsare treated exactly the same as government transferpayments. d. Includes personal contributions for social and private pension and insurance funds. e. Includes net imputed profit-type income on owner-occupied buildings, income in kInd, and services furnished without payment by financial intermediariesexcept life insuranos carriers

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Table 4. Relationof NIPA PrivateReceiptsto PrivateCash and Nocas Receiptsafter Tax, 19758 Billions of dollars

Item

Amount

Sourceb

179.0

Authors'calculations

Nonpersonal privatecashsaving Plus:

Personalcash receiptsafter tax

Equals:Privatecash receiptsafter tax Plus:

1,066.2 1,245.2

Imputations

36.2

Employercontributionsfor social insuranceand privatepensionand insurancefunds Capitalconsumptionallowanceswith adjustmenton owner-occupiedbuildings Equals: Privatecashandnoncashreceiptsaftertax Plus:

116.6 28.0

SCB,table 8.3 (68 - 66 + 79 + 82 + 84 + 85 + 86 + 87) SCB,tables 1.13 and 6.13

SCB,table 8.3 (64 + 70 + 76)

1,426.0

Investmentincome of privatepension and insurancefunds

Minus: Employercontributionsfor social insurance Benefitspaid from privatepensionand insurancefunds Personalcontributionsfor social insurance Interestpaid by consumersto business Personaltransferpaymentsto foreigners Changein reservesof privatepension and insuranceplans Equals:NIPA grossreceiptsof individualsand business

from table 2 Authors'calculations from table 3

20.6

SCB,table 8.2 (43)

59.8 45.2

minus table 8.3 (35 + 38 + 56) SCB,table 1.13 SCB,table 6.13

50.4 22.9 0.9 27.8

SCB, table2.1 SCB, table 2.1 SCB, table 2.1 FF(13 + 14 + 15)

1,239.8

SCB, table 8.1

a. NIPA refers to items from the national income and product accounts. b. SCB is Surveyof CurrentBusiness,vol. 57 (July 1977), and FF is Flow of FundsAcccounts,4th Quarter 1977, p. 53. The numbers in parentheses refer to line numbers in the source table. Figures are rounded.

includedwas 1974 becausethatwas the most recentyear (as of the start of this research)for whichthe datawouldno longerbe subjectto regular annualrevision.Becausethe KoreanWarperiodmayhavebeen"special," we used 1955-74 as a separatesubperiodin some cases."1 11. This argumentseemsless compellingthanit once did in viewof the extraordinaryeconomiceventsthathaveoccurredsincethe latterpartof the 1960s.

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663

Reviewof PreviousStudies As a basisfor ourempiricalwork,we beginwitha reviewof recentcontributionsto the empiricalstudy of the role of interestratesin aggregate consumptionand savingbehavior.We compareand integratethree general approachesthat appearin the literature.The first concentrateson aggregateconsumptionexpenditureandintroducesthe interestratein the consumptionfunction.This approachis used by Boskinand others.'2The second approachis based on the Houthakker-Taylorsavingfunctionin which aggregateor per capita saving is the dependentvariable.'3This work has led to the use of disaggregatedincome flows as separateindependent variablesin the saving function.'4 The third approachis concerned, at least implicitly,with a disaggregationof savinginto personal and nonpersonalcomponents.The workof Denisonand Davidand Scaddingis illustrativeof this approach.15 These three approachesreach widely differentconclusionsabout the interestelasticityof saving.It is thereforenecessaryto analyzeeach and, if possible, consolidatethe approachesor at least understandhow they differ.

AGGREGATE

CONSUMPTION

FUNCTIONS

In his recent paper, Boskin reportsa positive and significantinterest elasticity of saving.'"This conclusionis based on an aggregateannual consumptionfunctionof the form (1)

In C = ao + a,lIn YD + a2 ln YD-1 + a3 In W, + a4 In U + a5(R -7r) + a6r,

12. Boskin, 'Taxation." The studies by Martin Feldstein, "Social Security, Induced Retirement,and Aggregate Capital Accumulation,"Journal of Political Economy, vol. 82 (September-October1974), pp. 905-26, and Robert J. Barro, The Impact of Social Security on Private Saving: Evidence from the U.S. Time Series (American EnterpriseInstitute, 1978), also employ this general approach.Neither of these last studies is specificallyconcernedwith the effects of the interestrate,however.

13. H. S. Houthakker and Lester D. Taylor, Consumer Demand in the United States: Analysis and Projections, 2d ed. (Harvard University Press, 1970), pp. 287303.

14. See, for example, Lester D. Taylor, "Saving out of Different Types of Income," BPEA, 2:1971, pp. 383-407.

-15. Edward F. Denison, "A Note on Private Saving,"Review of Economics and Statistics, vol. 40 (August 1958), pp. 261-67, and David and Scadding, "Private Savings."

16. Boskin, "Taxation."

Brookings Paperson EconomicActivity,3:1978

664 where

C = realper capitaprivateconsumption YD = realper capitadisposableprivateincome W = end-of-yearreal per capitawealth U

R-

=

unemployment rate

the expectedreal after-taxreturnon capital = expectedrate of inflation.

=

Fitting the equationto annual data for the period 1934-69 (excluding 1941-46), Boskin reports the estimatedequation (after correctionfor first-orderserialcorrelationof the residuals)as (2) ln C = -0.456 + 0.569 In YD + 0. 1801n YD. +0.+265 In W-1 (-0.34) (4.75) (2.25) (3.71) -0.002 In U- 1.066 (R - r)- 0.029 , (-0.27) (-3.24) (-0.47) with estimatedt-statisticsshownin parentheses(here andthroughoutthe paper).17Boskinreportsthat virtuallythe sameresultswereobtainedusing differentinterestrates,sampleperiods,andestimationtechniques.18 The importantfeatureof this equationfor our purposesis the statistically significant,negativecoefficientof the realrateof return.This implies a positivesavingelasticityand hence an increasein the savingratein responseto an increasein the realinterestrate.By definingsavingimplicitly as S = Y-C, it followsthat (3)

In (I - S)

lnC)

;

hencefor fixed Y, (4)

_ yS)(

C

An upper bound on the sensitivityof the saving rate to changesin the interestrate is thus -a In C/9R when this quantityis positive.Because 17. The results shown here correct typographicalerrors in the coefficientsfor the inflation rate and the unemployment rate appearingin Boskin, 'Taxation," p. S13.

Here and in the remainderof this discussion, the interest and inflation rates are expressedas proportionalratherthan as percentagerates.

18. Ibid., p. S16.

E. Philip Howrey and Saul H. Hymans

665

equation2 yields the estimate-0 In C/OR _ 1.066, Boskin'sworkimplies that a 1 percentagepoint increasein the real rate of return (say, from 4 to 5 percent) would be expected to lead to (at most) a 1 percentagepoint increasein the savingrate (say, from6 to 7 percent). Thus this estimateof the interest-rateeffect is both statisticallysignificantand sufficientlylargeto be meaningfulfor policy purposes.

An equationlike the one employedby Boskinrequiresthatsaving,and hence the saving rate, be definedimplicitlyby the specificconsumption and income data that are used. Boskin'sconsumptiondata exclude expenditureson all consumerdurablesandincludethe flowof servicesfrom durables,includingowner-occupiedbuildings.The saving implicitlydefined therebycomes closest to an FF savingconcept,ratherthan a loanable-fundssavingconcept.It is not obviousto us why such savingshould respondpositivelyto the interestrate. In particular,FF savingincludes net investmentin consumerdurablesand housing.It is generallythought that purchasesof consumerdurables and housing would, if anything, vary inverselywith the interestrate. ViewingFF savingessentiallyas an aggregateof cash saving and net investmentin housing and other durables, one would expect the coefficientof the interestrate to be an average of the negative value derivingfrom the net investmentcomponent and a possibly positive value taken from the cash-savingcomponentof FF saving.Boskin'sfindingof a largepositivecoefficientrelatingthe rate of interestand FF saving is thereforea novel and intriguingresult that calls for replicationandfurtherscrutiny.

Boskin providedus with the data used in his analysis.Most of these data derivedirectlyfromthe calculationsof ChristensenandJorgenson."9 However,Boskincontributeda calculationthatis of criticalimportancefor the problem at hand. The real after-tax rate of return (R -7r),

which ap-

pears in 2, resultsfrom Boskin'sprocessingof the rate of returnand the price data appearingin the work of Christensenand Jorgenson.Boskin applied a process of smoothingand forwardprojectionto produce an (R -7r) thathe regardedas an appropriatemeasureof the expectedaftertax real rate of return.We were struckby two facts in our visual inspection of the (R -7r) series. The first was that the observationfor 1934 seemed to be uniquelydifferentfrom nearbyobservations;we therefore 19. See LauritsR. Christensenand Dale W. Jorgenson,"U.S.Income,Saving, and Wealth, 1929-1969,"Review of Income and Wealth, series 19 (December 1973), pp. 329-62.

BrookingsPaperson EconomicActivity,3:1978

666

droppedit from the sampleto determinewhetherit was exertinga peculiarly strongleverageon the regression.This experimentproduceda coefficient of -0.877

on (R

-

7r), rather than the -1.066

reported by

Boskin, with an estimatedt-statisticof-1.62, which clearly calls into question the statistical significance of (R

-7r)

.20

The secondpointwe noticedwas thatthe (R -7r) seriesresembledthe invertedunemploymentratelaggedtwo years.To test whetherthe interest rate played a purelycyclical role in the equation,we enteredthe unemploymentrate lagged two years ratherthan the (insignificant)current unemploymentrate;the resultfor the period1936-40, 1949-69 is (5) In C= -3.547 + 0.675 In YD -0.0441n (-0.26) (-4.05) (4.73)

YDL1+ 0.6801InW-i (27.19)

-0.042 In U2 - 0.120 (R -7r) + 0.0597r.

(0.39) (-4.62) (-0.17) = 1.70;standarderrorof estimate= 0.013;p = 0.250.

Durbin-Watson

The laggedunemploymentratehas a significantnegativecoefficient,while the real interestrate is no longerstatisticallysignificant.A similarresult holds for the postwarperiod;when ln U-2 ratherthan In U is used in the equation,the t-statisticfor the coefficienton the interestrate is -0.90, whichmakesits significancequestionable.

As a finalcheckon the sensitivityof the Boskinresult,we used several alternativeinterestrates in place of Boskin's interestrate. These rates were of the form (R -7r), where 7ris Boskin's expected rate of inflation,

and R is the Aaa, Baa, or municipalrate. Averagedand exponentially smoothed (R -7r) rates were also used. We were never able to reproduce

Boskin'sresultusing any otherinterestrateswith or withoutaveragingor exponentialsmoothing.Indeed, when we restrictedthe consumptionregressionsto postwardata (1947-69), the coefficientsfor the interestrate wereinvariablypositive,andin most casesexceededtheirstandarderrors by a factorof two or more.

Perhapsno regressionequationwouldwithstandall the sensitivitytests that we performed.In this case, however,we found that the positiveand significantsaving elasticityreportedby Boskin is extremelysensitiveto the sampleperiodhe used, the timingof variablesin the equation,and, finally, to the way in which the interest-rateseries was processed. In 20. The remainderof the equationwas quiterobustwhenwe dropped1934.

E. Philip Howrey and Saul H. Hymans

667

view of this sensitivity,it is difficultto have much confidencein the reportedresultfor the interestrate.Moreover,as indicatedearlier,the saving conceptto which this resultis appropriateis not the personalor private loanable-fundsconceptin which we are interested.

AGGREGATE

SAVING

FUNCTIONS

In contrastto Boskin, Tayloruses savingratherthan consumptionas the dependentvariablein his work.2'His basic model drawsupon the theory of saving developed by Houthakkerand Taylor.22In brief, the mainpremiseof this theoryis that desiredwealthis a functionof income and the interestrate, (6)

W*=btY+bbR.

Savingis then assumedto be proportionalto the differencebetweendesiredandactualwealthso that S = X(W*-W1).

(7)

Differencing7 and substituting6 for desired wealth yields the saving equation, (8)

S = b1S_1+ b2AR+ b3AY,

whichformsthe basisfor empiricalwork.

The majorrecentinnovationby Tayloris the disaggregationof income by type,basedon the NIPA identity, YD = L + P + TR-SI-TX,

(9)

where YD = L= P= TR = SI = TX =

NIPA disposablepersonalincome laborincome propertyincome governmenttransferpaymentsto individuals personalcontributionsfor social insurance personaltax and nontaxpayments.

21. Taylor, "Savingout of DifferentTypes of Income."

22. Houthakker and Taylor, Consumer Demand in the United States. See also Lester D. Taylor, "Price Expectations and Households' Demand for Financial Assets," Explorations in Economic Research, vol. 1 (Fall 1974), pp. 258-339, where income and the interestrate are treatedin a parallelmanner.

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668

Thisdecompositionleadsto the extendedmodel, (10) S = b1S_j + b2AR+ b3AL+ b4AP+ b6ATR+ b6ASI+ b7ATX.

In his empiricalwork, Taylor found that the coefficientson labor and propertyincome did not differgreatly,and most of his work combined thesetwo sourcesof income (designatedas LP).

The originalresult reportedby Taylorfor aggregatepersonalsaving, in constant1958 dollars,is (11)

S = 0.953 S-1 + 0.418 ALP + 0.890 ATR - 2.194 ASI

(45.27)

(5.11)

(2.87)

(-4.92)

-0.884 ATX+ 4.011 ABaa. (2.50) (-4.92) Two importantconclusionsemergefrom Taylor'sanalysis.First,the coefficientson differenttypes of income are substantiallydifferent.Second, the significanceof the interestrate is higherusing disaggregatedincome The variable thanwhendisposableincomeis used alonein the equation.23 Baa used by Tayloris the nominalyield on Baa corporatebonds.As we mentionedabove, it is generallyagreedthat the interestrate appropriate in a savingfunctionis the expectedreal rate. If so, the Taylorequation may be specifiedincorrectlybecause it uses a nominalinterestrate but no expectedrateof inflation.

Juster and Wachtel have extended the Houthakker-Taylorsaving model to include considerationof inflationaryexpectationsand uncerFor this purpose,inflationaryexpectataintyaboutthe rate of inflation.24 tions are measuredby the meanexpectedpricechangeobtainedfromsurvey data collected by the SurveyResearchCenterat the Universityof Michigan.Uncertaintyaboutinflationhas been measuredby the standard deviationof the observeddistributionof expectedpricechanges.25Juster and Wachtelhave found thatuncertaintyaboutinflationhas a significant 23. This last conclusion follows from an examination of the alternative regressions shown in table 1 of Taylor, "Savingout of Different Types of Income,"p. 391.

24. See, for example, F. Thomas Juster, "A Note on Prospective 1977 TaxCuts and Consumer Spending" (University of Michigan, Institute for Social Research, January 1977); and Paul Wachtel, "Inflation,Uncertainty, and Saving Behavior since the Mid-1950s,"Explorationsin Economic Research,vol. 4 (Fall 1977), pp. 558-78.

25. The details of the methods used to constructthese series as well as the series themselves are given in F. Thomas Juster and Robert Comment, "A Note on the Measurement of Price Expectations" (University of Michigan, Survey Research Center, n.d.).

669

E. Philip Howrey and Saul H. Hymans

impact on consumersaving,with growinguncertaintyleading to an increasein saving.But little is said about the effectsof the interestrate in theirwork and, as in the case of Taylor'sresearch,the focus is on NIPA or FF savingratherthanpersonalcashsaving.

DISAGGREGATED

SAVING

FUNCTIONS

In a recentreexaminationof Denison'slaw, David and ScaddingconfirmDenison'soriginalfindingthat the privatesavingrate, adjustedfor the businesscycle, hasremainedremarkablystableovertime.28The model thatformsthe basisfor theirempiricalinvestigationis (12)

S = ciGNP + c2AGNP*,

where S = NIPA grossprivatesaving GNP = grossnationalproduct year GNP AGNP*= differencebetween the last "high-employment" and currentGNP.

For the period 1921-64 (excluding1941-47), they report the following result: (13)

S = 0.1552 GNP - 0.1376 iAGNP*.

(161.52)

(-7.407)

The ratio of the standarderrorof the regressionto the meanvalueof S is 0.049. This relativelysmall standarderror,togetherwith the stabilityof the estimatedequationover varioussubperiods,is taken as supportfor Denison'slaw-namely, that year-to-yearchangesin the savingrate are small and that thereis no long-runtrendin the savingrate.

One explanationofferedfor the stabilityof the savingratethus defined personalsavingdecisionsare conis that householdsare "ultrarational": ditional on the amountof nonpersonal(that is, corporate) saving.Suppose the basicsavingequationis rewrittenas (14)

Sp = c1GNP+ caAGNP*+ csS.,

whereSpand S,, are personaland nonpersonalsaving,respectively.Then the ultrarationalityhypothesis is tantamount to the restriction that c = -1. Statisticalanalysisof this last relationshipwould providethe basis for a moredirecttest of the rationalityconjecture.

26. David and Scadding, "Private Savings," and Denison, "A Note on Private Saving."

670

BrookingsPaperson EconomicActivity,3:1978

The relativeconstancyof the privatesavingrateis sometimestakenas evidencethatprivatesavingis insensitiveto interestandtax ratechanges.

As Boskin has argued,such a conclusionis not warrantedfor a number of reasons.27In any event, a directtest of the hypothesisof interest-rate insensitivityis clearlydesirable.To do this, in the context of the David and Scaddingmodel, it would be necessaryto modify the personalsaving functionaboveto includethe effectof therealinterestrate, (15)

SP,= c1GNP+ c2AGNP*+ c3Sn + c4(R- ir).

A directtest of the hypothesisc4 = 0 is possibleusingthis model.

None of the empiricalworkthat we reviewedprovidesa directtest of the interestsensitivityof savingdecisionswithinthe context of a model that allows for the ultrarationalityof David and Scadding.Boskin includes corporatesavingas part of incomebut not as a separatevariable.

This procedurerestrictsthe corporatesavingcoefficientto beingthe same as the income coefficient(presumablypositive) and hence does not, in general,allow for rationalityof the David and Scaddingvariety.Taylor uses NIPA personal saving as his dependentvariable,which does not have a directloanable-fundsinterpretation.Moreover,corporatesaving is not includedas one of the determinantsof personalsaving.David and Scaddingdo not directlyinvestigatethe potentialeffectof the interestrate on savingbut ratherargueindirectlythatthe effectmustbe small.Hence previousworkis not adequate,in our opinion,to drawany definitiveconclusionsaboutthe interestelasticityof personalsavingdecisions.Because the theoreticalargumentsfor the effect of the interestrate are generally given in termsof personaldecisionsabout loanable-fundssaving,an investigationof this conceptof savingis needed.

A FirstLook at Loanable-FundsSaving In this section we take anotherlook at the saving decision in what might be called the new public finance frameworkthat Boskin uses.28 27. Boskin, 'Taxation."

28. A similar econometric approach is found not only in Boskin's work but in that of Feldstein, Barro, and others who have advanced quite dramatically the application of econometrics to crucially important questions in the field of public finance. Interestingly, as far as consumption behavior is concerned and despite the acceptance of a high level of aggregation,these researchershave taken a direction quite differentfrom the familiar one in the long history of work associated with the major macroeconometricmodels of the U.S. economy.

E. PhilipHowrey and SaulH. Hymans

671

We have already alluded to two importantdifficultieswith Boskin's work-namely, savingis definedonly implicitlyand the dataused appear to be most relevantto the analysisof FF savingratherthan to loanablefunds saving.In our effortsto overcomethese difficulties,we firsttranslate the logarithmicconsumptionfunctioninto a savingfunctionandthen applythe latterto severalalternativesavingconcepts.

We beginwith the logarithmicconsumptionfunctionof equation1 and subtractIn Y from both sides. Using the implicit definitionof saving, S = Y - C, it followsthat (16) In (1

)

-

= ao + (a, - l)In Y + a2ln Y_1+ a, In W.1 + a4 In U + a5(R - r) + a6wr.

For smallS/Y, the left-handside of this equationis closelyapproximated by -S/Y itself, whichimplies (17)

--ao -a4

+ (

In U

-

-

a,) In a5(R-

Y7r)-

In Y.1

a2

-

as In W.1

a6r.

Thus the logarithmicconsumptionfunctionimplies an equationfor the savingratewiththe sameindependentvariables.

We applied17 to threebasicsavingratesderivablefromthe definitions containedin tables 1 through4: NIPA personalsavingrate = NIPA personalsavingdividedby NIPA disposablepersonalincome personalcash savingrate = personalcashsavingdividedby personalcash and noncash receiptsaftertax FF personalsavingrate = FF personalsavingdividedby personalcash and noncash receiptsaftertax.29 29. The basic summary statistics for these three saving rates for 1951-74 are as follows.

Savingrate

Mean

Standarddeviation

NIPA personal saving rate Personal cash saving rate FF personal saving rate

0.0636 0.0022 0.0559

0.0086 0.0142 0.0149

The regression results in table 5 are rather insensitive to whether the FF personal saving rate is defined with personal cash and noncash receipts after tax or with NIPA disposablepersonal income in the denominator.

(1 are and U.S. 5-9 5-8 5-7 5-6 5-5 54 5-3 5-2 5-1 rate. sonalsonal is of t) U. from provided The is Equation cash Sources: F. from byBaa, FF FF FF income and from NIPANIPANIPAsaving and The Department numbers whero Personal Personal Personal the Joseph Robert Thomas of rate in J. conceptNIPA A. personal personal noncash personal Baa U.S. cash cash cash concept is Juster that personal personal personal Barro, theand personal BureauCommerce receipts Pechman parentheses appears (2.23) of The (0.25) (3.26) (0.24) (3.28) (3.97) (0.38) (2.16) (4.09) 1.131 of 1.162 1.573 0.962 0.219 0.114 0.106 1.574 1.002 are Constant in and after saving the Robert corporate Impact Labor the tax in as rate of is bond Y t-statistics. the (2.14)(2.35)(2.69)(-1.02)(-1.12)(-1.41)(0.96)(1.11)(0.90) Brookings Comment, flow-of-funds0.200 0.238 0.237 -0.123-0.130-0.1420.090 0.102 0.073 Social rate Statistics.

NIPA "Aw, denominator and In is the of NoteSecurity Institution. theaccounts personal denominator. onmean on (1.26) (1.78) (0.26) (0.82) (0.26) (1.22) (-0.37) (-0.25) (-0.31) from 0.029 0.178 0.180 0.075Y1i -0.037 -0.038 0.030 -0.029 0.200 data the of These saving Private In Moodys the expected series W corresponding divided (-0.29) (-0.29) (-3.07) (-0.40) (-3.07) (-2.23) (-3.93) (-2.07) (-3.82) -0.028 -0.016 -0.183 -0.132 -0.183 -0.110 -0.015 -0.130 -0.119 price Saving: are Board Measurement by Investors of saving of a.

Table 5.

Saving Rate

Equations,

1951-740

Independent

In change, defined NIPA Price rate,in U Service. and (-1.85) (-2.13) (-1.73) (-0.94) (-4.26) (-1.24) (-3.97) (-1.05) (-3.60) -0.015 -0.007 -0.008 -0.028 -0.015 -0.006 -0.016 -0.026-0.026 Evidencefrom Governors variable Inc., SD. tables the of 1 disposable the expressed in the while (0.58) (0.84)(0.64)(0.60) (0.35)(0.81) (0.49) (0.36)(0.57) 0.003 Expectations U.S. 0.003 0.00150.004 0.004 0.004 0.00150.002 0.002Baatax :, real through personal the standard TimeFederal 4 per and (University T Series income; .. ...

(0.02) ... capita are (-1.75) of deviation (0.24) marginal (0.71) Reserve (-0.24) 0.001 -0.001 0.002 -0.0050.0000 (0.38) 0.0005 the of from terms. the(American federal System.

W ta Michigan, personal is The national ... SD ... (0.75) ... ... (-0.30) ...

(2.13) ... the -0.001 rate observed cash 0.007 0.0025 Survey Enterprise real and income income per FF applicable Research and Institute, to distribution 1.87 2.01 2.01 2.32 2.26 2.29 2.13 2.24 2.29 capita Watson Durbinvariables, of personal Y product net Center, 1978). income and A2 Summary The n.d.). worth saving 0.801 0.760 0.773 0.634 0.654 0.672 0.370 0.386 0.403 expected from Y-s, of accounts price are rates data Baatax statistic error theof use capital, households changes, unemployment perwas equals theper-

0.00670.00730.00710.00860.00840.00810.00690.00680.0067 estimate of Standard

673

E. Philip Howrey andSaul H. Hymans

The income variable,Y, used on the right-handside is the personalincome conceptthat appearsin the denominatorof the correspondingsaving rate, adjustedto be measuredin real per capitaterms;W is real per capitanet worthof householdsat the beginningof the year;30and U is the unemploymentrate. The resultsof estimating17 for varioussavingrates aregivenin table5.

We experimentedwith interestrate data that includedthe municipal bond rate (whichshouldalreadybe an after-taxrate), the corporateAaa rate, and the corporateBaa ratemeasuredin percent.The best results(in the sense of the strongesteffectsof the interestrate on saving) were obtainedusingan after-taxBaa ratedefinedas Baatax = (1

-

t)Baa,

wherethe tax rate, t, is the marginalfederaltax rate applicableto income fromcapital.31We employedthe meanexpectedprice changevariable,r, derivedfromSurveyResearchCenterdatacited in the precedingsection, as a separatevariableto allow for both the effect of a real rate of return on saving and a separateinflationeffect. To measureuncertaintyabout inflationwe used the standarddeviation,SD, of the expected inflation variabledefinedabove. The equationswere estimatedusing annualdata for the period 1951-74 as well as for the subperiod1955-74. The same basic story is told in both cases, and the results are shown only for 1951-74.

Table 5 shows that the form of the equationunderconsiderationexplains little of the variationin the NIPA saving rate. Only the wealth variablemakes any significantcontribution.Personalcash savingis not explainedwell either. Only the FF personalsavingrate-and that is the one closest to the saving rate implicit in Boskin'swork-seems to be explainedby this form of equation.Allowingfor the parametertransformationsimplicitin the use of SIY ratherthanln C as the dependentvariable, the coefficientson currentincome and wealthin the regressionsfor the FP personalsavingratearegenerallysimilarto thosereportedby Boskin. The effectof the unemploymentrateon FE savingis negativeandsig30. The data correspond to that used in the Fed-MIT-Penn model and were taken from Barro, The Impact of Social Security on Private Saving.

31. The original data for this tax rate appear in Colin Wright, "Savingand the Rate of Interest,"in Arnold C. Harbergerand Martin J. Bailey, eds., The Taxation of Income from Capital (Brookings Institution, 1969), p. 300. Joseph A. Pechman of the Brookings Institutionprovided us with an updated series.

674

BrookingsPaperson EconomicActivity,3:1978

nificant,ratherthaninsignificantly positiveas reportedby Boskin.The coefficienton the interestrate is alwayspositive,whetheror not inflation variablesare included,but it neverbecomesstatisticallysignificant.Inflation is a significantdeterminantof the FF personalsavingrate if both 7r andSD areincluded(makingthe coefficienton the interestratezero). In that event, it appearsthat higherexpectedinflationreducesFF saving, while greateruncertaintyaboutinflationincreasesit.

If a negativerelationexistsbetweenthe interestrate and expenditures on durablegoods, one would expect that to be evidentin the FF saving rate equationsbecause FF savingincludesnet expenditureson all consumerdurables,includinghousing.One wouldalso expect,however,that the cash savingrate, which containsno expenditureson durablegoods, wouldbe the most likelyto show a positiverelationwiththe interestrate.

It mightbe possibleto find a hint of such an outcomein equations5-3, 5-6, and 5-9. Judgingby the coefficientvaluesalone, a 1 percentagepoint increasein the after-taxinterestrate increasesthe FF and NIPA saving rates by 0.15 percentagepoint (say, from 6 percentto 6.15 percent), whilethe correspondingincreasefor the cashsavingrateis 0.4 percentage point. These are small comparedwith Boskin'spoint-for-pointoutcome; none of them is anywherenear statisticalsignificance.In fact, no coefficient on the interest-ratevariablein table 5 has a t-statisticgreaterthan 0.84. Fromthe tableit seemsthatno personalsavingrate-whether cash or some other form-responds to variationsin the real after-taxrate of return.

In the followingsectionwe investigatethe determinationof cashsaving in more detail by bringingtogetherthe most promisingaspects of the researchreviewedabove.

A CloserLook at Loanable-FundsSaving One frameworkthat has been used successfullyfor the analysisof savmodel as expandedby the workof Juster, ing is the Houthakker-Taylor Wachtel,and othersto includeconsiderationof the effectsof inflationan issuelong discussedin the workof Katona.82 We applya similarframe32. Some of the relevant work of Juster and Wachtel has already been cited.

See also George Katona, The Powerful Consumer: Psychological Studies of the American Economy (McGraw-Hill, 1960).

675

E. PhilipHowrey and SaulH. Hymans

work,with furthermodification,to the analysisof cash or loanable-funds saving.The theoryunderlyingthe Houthakker-Taylor analysisimpliesan estimatingequationof the form (includingthe stochasticerrorterm, u) (18)

S = aiS_i + a2AY+ a3AR+ u

if the level of income, Y, and the interestrate, R, determinethe desired or equilibriumlevel of personalwealth. To this basic model we add the disaggregationof income (from the work of Taylor), expectationsabout inflationand uncertaintyregardinginflation (from Katona,Juster, and others), the interrelationsof personaland nonpersonalsaving (the ultrarationalityhypothesisfrom David and Scadding), and our own views on the most appropriatedefinitionsof the savingand incomeflows.

To cover all these issues we must rely on annualdata for the calculation of cash or loanable-fundssavingand the correspondingcash income flows. Earlier successes with the Houthakker-Taylorsaving model, by Taylor himself and by Justerin the incorporationof inflationvariables into the analysis,have been achievedwithinthe frameworkof quarterly data. If a calendarquarteris the appropriatetime framefrom the viewpoint of the underlyingeconomicbehavior,the use of calendar-yeardata as thoughthey were quarterlydata involves a time-aggregationerrorof specificationthat is potentiallyserious.If we begin with 18 for the basic equation with quarterlydata and averagethe four successive quarters referringto a given year, say 1970, we obtain (19)

1 + a2 (Y70:4370 = alS69.470o3

I

+ a3 (R70:4-R69:4) +

Y69:4) u70.

The dependentvariable,S, is saving for calendaryear 1970 as usually measured(assumingthe quarterlyflow data are seasonallyadjustedat annualrates). But the laggeddependentvariableis now a calendaryear of savingdefinedover the four quartersfrom 1969:4 to 1970:3, and the quarterlychange variables (AY and AR in the original equation) are transformedinto changes measuredfrom 1969:4 to 1970:4.383Plainly, this is not the same set of independentvariablesthat would resultfrom 33. If the quarterlyerrorterm,u, is homoscedastic andseriallyindependent, so is the averagecalendar-year errorterm,a. If u is first-order seriallycorrelated,the serialpropertiesof fi are considerablymore complicated.

PapersonEconomicActivity,3:1978 Brookings the use of calendar-yeardata on all variables,and we know of no way to derive an equationusing calendar-yearsavingas the dependentvariable that does not also requireobservationson within-yeardata (assuming that the quarterlyspecificationis appropriate).In orderto use the saving and income concepts definedin tables 1 through4, we are limited to calendar-yeardata.The sameis not trueof dataon the interestrate (and inflation). Changesin the interestrate are readilyavailable,as shownin the aggregatedequation 19 above. We experimentedwith annualequationsof the followingtwo types: 676

S70 = aS*369+ a2*(Y7o-

(20-A)

Y69)

- Rs9)+ a (ir7u+ ac*(R70

(20-B)

570 =

r6@)

al*S69+ a**(Y7o - Ye9) -

+ a3**(R70:4R9:4) + a4*(ro70:4-

169:4)

Almost uniformly,the typeB formsthatemploy"properaggregation"for interestrate and inflationvariablesoutperformthe type A forms when judgedon the basis of overallfit and the significanceof the interestrate and inflation variables as a set. In addition-and of greatest importance-the conclusionsthat would be drawn about the significanceof the interestrate are not sensitiveto whethertype A or type B equations are estimated.The measurementof the effectsof the interestrateis sensiissuesbut not to whetherchanges tive to the inflationand ultrarationality in the interestrate are measuredon the basis of a calendaryear or from The resultsgivenbelow correspondto fourthquarterto fourthquarter.84 the typeB formof the equation.

The income decompositionused by Taylorfollows the NIPA breakdownshownin 9. Webegininsteadwiththe definitions (21)

(22)

YCASH = LPCASH + TRCASH + SI

-

TX

YCNC= YCASH+ IMP + FRINGE,

34. The time aggregationmay even have some advantages.Supposethe quarterly frameworkis correct, but that the interest rate enters as AR., rather than AR. The use of AR could produce serious errors in the parameterestimates of the incorrectly specified quarterlyequation. In contrast, the use of (R70:4 - R69:4) rather than the appropriate (R70:3 - Re9:3) in the type B annual equation may involve a minor specification error compared to the correspondingerror in the quarterly equation.

E. PhilipHowreyandSauilH. Hymans

677

where YCASH= personalcash receiptsaftertax (table3) LPCASH = labor and property cash income (defined implicitly in 21 above) TRCASH= cash transfersto individuals(the sum of government transfers and benefits paid from private pension and insurancefunds(the lattershownin table3) SI, TX = as in 9 YCNC = personalcash and noncashreceiptsaftertax (table3) IMP - imputations(table3) FRINGE= employercontributionsfor social insuranceand private pensionand insurancefunds(table3).

We thencombine21 and22 to obtain

(23) YCNC= LPCASH+ TRCASH+ (SI + FRINGE)+ IMP - TX as our basicincomedecomposition.A numberof fundamentaldifferences between our components and the NIPA components are of interest.

LPCASH excludes imputations,personalcontributionsfor social insurance, and the changein reservesof privatepensionand insurancefunds; LP includes all three.835 TRCASHincludessocial insurancebenefitpayments (as does TR) and privatepensionand insurancebenefitpayments that are logically similar. The variable (SI + FRINGE) includespayments to privateand social pensionand insurancefundsmade on behalf of individuals,as well as the social insurancepaymentsmade by the individuals.

To addressthe issue of ultrarationality,we modify the HouthakkerTaylor savingmodel in the followingway. We firstdefineaggregatepersonalincome,YT,as (24)

YT =

YCNC+ OiBCS+ 02GCS,

where BCS = businesscash saving GCS = governmentcash saving.

This formulationallows for the possibility that individualsimpute to themselvesthe fraction6l of businesscash savingand the fraction62 of 35. LPCASH(and LP) includespersonalcontributionfor privatepensionand insuranceplansthatwe wereunableto separate.

PapersonEconomicActivity,3:1978 Brookings governmentcash saving as income. Similarly,aggregatepersonalsaving is definedas 678

ST = S + y1BCS+ A2GCS,

(25)

where S is personal cash saving. Again, the coefficientst,a and A2 are presumablynonnegative,but their values are not prescribeda priori.If householdsperceivethat some fractionof the savingof businessand governmentultimately accrues to them as individuals,that would imply O < jl

landO<u2<

1.

We thenassumethatthe savingdecisionis describedby (26)

ST =

diYT +

d2(W*-W1),

where W = personalcash wealth W* = desiredpersonalcash wealth.

Thuswe postulatetwo majordeterminantsof saving:the level of income, broadlydefined,andthe discrepancybetweendesiredand actualpersonal cash wealth.Finally,followingHouthakkerand Taylor,desiredwealthis specifiedas W* = R Yr + b*R. When24 through27 are combinedand differencedto eliminatethe stock of personalcash wealth, the savingequationthat forms the basis of our empiricalworkis obtained:

(27)

(28) S =

+ (1 -d2)S_ + + (di d2b*)AYCNC d2b2AR + [02(d1+ d2b*)- A2]AGCS. + [01(d1+ d2b*)- .&JkBCS

The equationfor personalcash savingthatwe proposeto estimatecan now be writtenas + a3A(TRCASH) (29) S = ao + a,S_. + a2A(LPCASH) + a4A(SI+ FRINGE)+ a5A(IMP)+ a6A(TX) + a7A(BCS)+ a8A(GCS)+ agA(Baatax-r) + a,oA(7r) + alln(SD)

+ u.

The dependentvariable,S, is calendar-yearpersonal cash saving measuredin 1967 dollarsper capita;the income componentsare changesin calendar-yearvaluesmeasuredin 1967 dollarsper capita;andthe interest

E. Philip Howrey and Saul H. Hymans

679

rate and inflationare measuredas changesfrom fourthquarterto fourth quarteras in 20-B. The variableBCS is businesscash saving as defined in table 2 above, and GCS is cash savingof the federalgovernment,defined as the governmentsurplus (NIPA basis) minus the surplusin the social insuranceaccount.Both BCS and GCSare measuredin 1967 dollars per capita.

The variableBCS is directlyrelevantto the ultrarationalityargument of David and Scadding.This hypothesismaintainsthat businesssavingis viewed by the rationalconsumeras a componentof income and saving, with 81 and a1 both equal to unity. Thus we should find that a2 = a7 - 1,

provided that the coefficientof labor and propertycash income is also appropriatefor the businesscash saving componentof income.36David and Scaddingdo not considergovernmentcash savingto be a substitute for personalcash saving;rather,theyproposethatgovernmentsavingand privateinvestmentare substitutes.We take an agnosticposition on this issue and includegovernmentcash savingin the savingfunction.

The variable(SI + FRINGE) is relevantto the controversybetween Feldstein and Barro about whether social security depressespersonal saving.37Thisvariablecombinesthe correspondingsocialandprivatecontributionsbecause it seems unlikely that individualsare more awareof their social securityrightsthan they are of theirprivatepensionrights.

The resultof estimatingthe personalcash savingequationas specified in 29 is shownin table 6. The estimateshownin 6-1 was obtainedusing annualdatafor the period 1951-74. Severalvariationsof the basic equation werealso examined.Equation6-2 givesthe resultswhenthe variables for inflationand uncertaintyare omitted.Whenthe cash savingvariables for businessand governmentare deleted,the resultsshownin 6-3 are obtained.Finally, 6-4 indicateswhat happenswhen the sampleis limitedto the 1955-74 period.

The overall impressionthat emergesfrom these parameterestimates can be characterizedas follows. The coefficientsof the income components arebroadlyconsistentwithpreviousresultsbutnot all areestimated with sufficientprecisionto warrantsharpdistinctions.Businessand gov36. This follows directly from 28 in which as is identified as d1 + dbj and =pI = 1.

- 1if1 37. This may be viewed as another part of the ultrarationalityargument. See Feldstein, "Social Security, Induced Retirement, and Aggregate Capital Accumulation," and Barro, The Impact of Social Security on Private Saving. Feldstein claims that social security depresses personal saving; Barro says the claim is unwarranted.

a7 di+d2b

Brookings PapersonEconomicActivity,3:1978

680

1951-74 IncomeDecomposItion, BasedonAuthors' Table6. PersonalSavingEquations IAdependent Equation,sampleperiod, and concept of saving

Constant

6-1 Personalcash 1951-74 6-2 Personalcash 1951-74 6-3 Personalcash 1951-74 6-4 Personalcash 1955-74

-4.657 (-0.61) -3.068 (-0.31) -7.403 (-0.61) -8.274 (-0.92)

6-5 NIPA personal 27.547 (1.60) 1951-74 2.391 6-6 FF personal

1951-74

A A A (SI + S-i (LPCASH) (TRCASH) FRINGE)

A (IAMP)

A (TX)

0.550 (4.05) 0.649 (3.63) 0.355 (1.79) 0.609 (5.23)

0.278 (2.75) 0.369 (2.80) 0.095 (0.78) 0.387 (4.35)

0.682 (1.73) 0.082 (0.17) 1.390 (2.54) 0.893 (2.34)

-0.842 (-1.73) 0.327 (0.43) -1.573 (-2.26) -0.848 (-2.16)

-0.693 (-0.60) -0.550 (-0.35) 0.634 (0.41) 1.444 (1.32)

-0.121 (-0.49) -0.562 (-2.12) 0.233 (0.79) -0.475 (-2.28)

0.771 (5.46) 0.894

0.344 (3.38) 0.521

0.573 (1.59) 0.810

-0.671 (-1.42) -0.643

-0.819 (-0.72) -2.037

-0.363 (-1.33) -0.387

(0.27) (12.88) (6.15) (3.03) (-1.50)

(-1.97)

(-1.72)

Sources:Derivedfrom datain the nationalIncomeand productaccounts(NIPA)of the U.S. Depart. accounts(FF) of the Boardof Govmentof Commerce.In addition,S usesdatafromthe flow-of-funds ernorsof the FederalReserveSystem.For definitionsand sourcesof Baatax,v, and SD. see table5. for socialinsurance;and TX to SI is contributions is cash TRCASH tranfers individuals; personal a. is personaltax and nontaxpayments.LPCASHis laborand propertyincomeand equalspersonalcash receiptsafter tax (definedin table 3) minusTRCASHand SI. FRINGEis employercontributionsfor socialinsuranceandprivatepensionandinsurancefunds;IMP is the NIPAimputationsincludedin table

emnmentcash savings are significantdeterminantsof personalcash saving. Neitherthe real interestratenor the rate of inflationis an important determinantof personalcash saving,but the uncertaintywithwhichinflationaryexpectationsareheldis in itselfa significantdeterminantof saving.

Whenwe compared6-1 and 6-4 for instancesof coefficientinstability between 1951-74 and 1955-74, we found the following.The variables S 1, (SI + FRINGE), andSD are highlysignificantand theircoefficients are robustwith respectto sampleperiod.LPCASHis highly significant, and althoughits coefficientincreasesfrom about 0.3 to about 0.4 when the early years are droppedfrom the sample,the changeis clearlynot statisticallysignificant.The coefficientof the imputationsvariable,IMP, is particularlyunstable,but the variableis insignificant.The tax variable, TX, is insignificantin the full sampleperiod (6-1 ) but is quitesignificant in the 1955-74 period (6-4) when its absolutevalue differslittle from the coefficientof labor and propertycash income, LPCASH. It is also clearthat the size of the coefficienton tax paymentsis heavilydependent on whetheror not the inflationvariablesare included,indicatingan obviouscorrelationbetweenrealtaxesandinflation.

The variablemeasuringcash receiptsfromsocial and privatepensions andinsurance,TRCASH,has a marginallysignificantcoefficientof about

682

BrookingsPaperson EconomicActivity,3:1978

shortersample period yields a correspondingeffect of 19 cents. These resultsindicatethatthereis less thancompletesubstitutionof government savingfor personalsaving.

The evidenceon social plus privatepensionsand insuranceseems to favor the view that there is substitutionbetween (SI + FRINGE) and personalcash saving.However,the estimateof this effectis quitesensitive to whetherthe inflationvariablesappearin the equation.

Finally, we turn to the majorquestionof whetherthere exists an interest rate effect. By this time we think it is unlikely.In the presenceof our income decompositionand the variablesmeasuringcash saving by business and government,inflation,and uncertainty,the interestrate is clearlyinsignificant.Indeed,the real after-taxinterestrateis insignificant even if we drop the expectedinflationand uncertaintyvariables(7r,SD) or the variablesfor businessand governmentsaving (BCS, GCS). It is possible that equationsindicatinga strong effect of the interestrate on savinggive inadequateattentionto nonpersonalsavingand inflation.An obviousnegativecorrelationexistsbetweenBCS and the interestratebecause higherinterestchargesreduceprofits;and thereis a positivecorrelation between the interestrate and the inflationrate. This implies the potentialfor spuriouscorrelationwith a vengeance.

For the sake of completeness,we reviewthe last two equationsin table 6. Equation6-5 presentsthe resultsobtainedusingNIPA personalsaving as the dependentvariable,and 6-6 showsthe resultsfor FF personalsaving. We have arguedthat neitherof these savingconceptsis relevantfor an analysisof the supplyof loanablefunds.In any event, these equations show that our result for the interestelasticityof savingis not uniqueto our use of personal cash saving. Neither NIPA saving nor FF saving shows a significanteffect of the interestrate. Indeed, as we anticipated earlier when we discussed the effect of including durable goods and purchasesof homesin these savingconcepts,the coefficientson the interest rate in these equationsare both negative,with FF saving having a particularlyhigh value.

PrincipalFindings In this articlewe addressthe interestsensitivityof the resourcesthat individualsmake availablefor financingbusinesscapitalformation.We arguethat neitherof the traditionalmeasuresof saving,NIPA personal

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681

andSubpiod Summarystatistkc

wariable

A (BCS)

A (GCS)

-0.484 (-2.10)

-0.336 (-4.04)

-1.014

-0.394

(-4.25)

(-3.61)

A (Baatax-w)

7.079 (0.69) -3.344

-0.701 (-3.66)

-0.191 (-2.18)

(-0.76) 14.853 (0.92) 8.469 (0.96)

-0.169 (-0.78) -0.095 (-0.50)

-0.288 (-3.56) -0.085 (-1.15)

-1.455 (-0.14) -11.286 (-1.22)

A (x)

A (SD)

-0.724 (-0.07)

29.966 (3.12)

...

...

-2.469 (-0.16) 0.348 (0.04)

51.547 (4.08) 26.247 (3.24)

-7.228 (-0.72) -22.177 (-2.45)

23.549 (2.42) 20.681 (2.29)

DurbinWatson

52

Standard error of estimateb

2.00

0.908

12.45

2.36

0.833

16.75

1.76

0.766

19.82

2.01

0.955

9.15

1.99

0.919

12.15

2.25

0.974

11.00

3; BCS is business cash saving as defined in table 2; and GCS is the NIPA governent surplus less the surplus on the social insurance account. S is either personal cash, FF personal, or NIPA personal saving, as defined in table 1. All the above variables are expressed in real (1967 dollars), per capita terms.

A(LPCASH), A(TRCASH), A(SI + FRINGE), A(IMP), A(TX), A(BCS3, and A(GCS) are first differences of calendar-year data. A(Baatax-.), A(T), and A(SD) are measured as changes from fourth quarter to fourth quarter. The numbers in parentheses are t-statistics. b. In 1967 dollars per capita.

0.7 in the full sample,but a clearlysignificantcoefficientof about0.9 for 1955-74. This may not be muchof a mysterybecausethe coefficientsare insignificantlydifferentfromunityin each of the periods;if 1.0 is the true value, in the short run every dollar reductionin pension and insurance benefitsresultsin a dollarreductionin cashsaving.

Table 6 containssome importantresults for the ultrarationalityhypothesis.For the full sample (6-1) the point estimateimpliesthat a one dollar increasein businesscash saving reducespersonalcash savingby about 48 cents. The correspondingresult for the 1955-74 period indicates a substitutionof about 70 cents. In eithercase it is not possibleto rejectthe hypothesisthat businesscash savingis regardedas both "personal"incomeand "personal"savingin the sense of David andScadding.

A formalstatementof this rationalityhypothesisis a2 -a7 = 1 in equation 29, on the assumptionthatbusinesscash savingis viewedas an addition to laborand propertyincome.The datado not rejectthis hypothesis for either sampleperiod. Govenment cash saving also has a significant negative impact on personal cash saving, althoughit is somewhatless pronouncedthan the businesssavingeffect.The point estimatein equation 6-1 implies a reductionof 34 cents in personal cash saving per dollar increase in governmentsaving in the full sample period. The

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savingor FF personalsaving,is the appropriateempiricalcounterpartfor personalloanable-fundssaving.We believethatthe appropriateloanablefunds conceptis personalcash saving,which, unlikeNIPA and FF saving, excludes expenditureson both owner-occupiedbuildingsand consumerdurables.

If this view is correct,the empiricalevidenceof previousstudiesis not Virdirectlyrelevantto the majorquestionregardinginterest-sensitivity. tually all the studiesof whichwe are awareare concernedwith the more traditionalsavingconcepts.Our reviewof previousresearchproducesa numberof reasons to questionthe conclusionthat there is a significant positive relationshipbetweenpersonalsaving,howeverdefined,and the rate of interest.The sensitivityof these empiricalresultsto small variations in the sampleperiod,to the definitionsof variables,and to the dynamic specificationof the savingequationweakensubstantiallyour confidence in such results. Moreover, none of the previous studies we reviewedhas dealt adequatelywith the ultrarationalityhypothesisdiscussedby David and Scadding.

Based on this reviewand our empiricalwork we concludethat David and Scaddingwere correctin claimingthatthe currentdataupholdDenison's law. Stated more conservatively,the data we examinedare consistentwith the followingformulationof the equilibriumfunctionfor personal loanable-fundssaving: (30)

S _ d1(YCNC + O1BCS+ 02GCS) -,p1BCS

-

M2GCS.

Our empiricalresults are consistent with 01 = tu, = 1, but not with 02 = 1, = 1; rather,they suggestthat 02 and I2 are less thanunitybut not zero. Thusthe resultsarenot in conflictwiththe propositionthatbusiness savingis a nearlyperfectsubstitutefor personalsaving.Governmentsaving is also apparentlyviewed as a substitutefor personalsaving,though not to the same extent as is business saving. In general,the parameter estimatesare sensitive both to the sample period used and to the way inflationand uncertaintyare treated,but the followingapproximationappearsto tell the essenceof the story.With/uq_ 1 and 01 - 1, equation30 canbe rewrittenas (31)

-YCNC S+BCS + BCS

d1 +

d (dY22-12)

GCS + GCS YCNC

This impliesthat the gross privateloanable-fundssavingrate is approx-

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imately constantin the long run. Approximateconstancyfollows both because (d62 - /L2) is estimatedto be small and becauseGCS is negligible in comparisonwith (S + BCS). Overthe 1951-74 period, for example,GCSaveragedonly 8 percentof the averagevalueof grossprivate loanable-fundssaving.Equations30 and 31 neglectshort-runvariability arisingfrom variabilityin the relativesharesof the componentsof total As for the major income and in changesin uncertaintyaboutinflation.88 question,there simply is no strongevidence that loanable-fundssaving can be manipulatedby policy aimed at changingthe after-taxrate of returnto saving.

Our nonresult-that we have been unable to isolate a significantinterest rate effect-is not surprising.There are good reasonsto find the nonresultbelievable.The microeconomictheory of saving permits any effectfrominterestrates (positive,negative,or none) for a net saver,and the net cash saverssurelyoutweighthe net cash dissavers.Two factorsin our analysiscancelthe positiveeffectof the interestratethat othershave found. The firstis the effect of inflationon saving.Takingadvantageof the recentlydevelopedoptionof measuringboth expectationsanduncertaintyaboutinflation,we findevidencein supportof the propositionlong espousedby Katona,Juster,andothers.The incentiveto "savefor a rainy day"has a strongeffectwhen uncertainty(SD) increases.And it is easy to see how the interestrate could enter the picture as a proxy for the direct influenceof uncertaintyeffects in saving equations.The second the apparentsubstitutability betweendirectperfactoris ultrarationality: sonal savingand savingdone "on an individual'sbehalf"by the business sector.One could argue,we suppose,thatthe significanceof businesscash saving derives from sources unrelatedto ultrarationality;for example, times are bad or are gettingbad when BCS declines,so individualssave more.BecauseBCShas a greaternegativeimpacton savingin the absence of SD than when SD is presentin the savingfunction(table 6), the possibilityexiststhatthe BCSvariablerepresentsthe reactionto uncertainty.

But SD shouldand apparentlydoes pick thatup andstill leavesBCSwith a statisticallysignificanteffect.And even if the BCS effectdoes not meabut rathera differentaspectof uncertaintythanthat sureultrarationality, containedin SD, it is clearlydoing so better than the interestrate with 38. Variation in income components relative to total income and in the inflation variables are obviously more detailed, and perhapsbehavioral,alternativesto adjusting for the business cycle by means of the unemploymentrate or the GNP gap.

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whichit is correlated.It is difficultto turnthe argumentaroundandclaim that there is an importanteffect of the rate of returnthat is bettermeasuredby BCS thanby the rate of returnitself.

There are manygood reasonsfor tax reform,but thereis no good evidence to supportthe view that a positive interestelasticityof loanablefundssavingis one of them.

Commentsand Discussion MartinFeldstein: The paperby HowreyandHymansrepresentsa serious effortto approachan importantissue in a new way. The low savingrate of the United States in comparisonto most other industrialnations is notorious.It is not surprising,therefore,that a growingnumberof economists and others who are concerned about this problem are asking whetherwe shouldfollow the lead of the Europeancountriesin placing less emphasison the taxationof investmentincome (relativeto consumption and payrolls) and in devisingspecialschemesto exempta substantial fractionof personalinterestincome from the individualincome tax.

The Howrey-Hymanspaperseeksto contributeto the analysisof thattax policy questionby measuringthe effectof the real net-of-taxinterestrate on whatthe authorscall personalcash saving.

The authorsare certainlycorrectthat theoryalone cannotpredictthe effecton the savingrateof a changein the net-of-taxinterestrate.Indeed, the ambiguityis even greaterthanthey appearto realizewhen they refer to the countervailingincomeand substitutioneffects.Even if we consider a compensatedchange, such as increasingthe payroll tax and reducing the rate of tax on interestincome, theorycannotpredictthe sign of the personalsavingresponse.'All that we knowfrommicroeconomictheory is that a compensatedincreasein the interestrate (that is, a compensated fall in the priceof futureconsumption)causesan increasein the quantity of futureconsumption.But currentsavingis equivalentto expenditureon futureconsumption.The expenditureon futureconsumptiononly risesin responseto a compensatedfall in its price if the compensateddemand 1. This paragraphand the next are discussedmore fully in MartinFeldstein, "The Rate of Return, Taxation and Personal Savings,"Economic Journal, vol. 88 (September 1978), pp. 482-87.

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elasticityexceeds one. The substitutionof a payroll tax for an interest income tax may thereforereducecurrentpersonalsaving.

Despite this ambiguityabout personal saving, traditionaltheory has an unambiguousimplicationabout the effect on total nationalsaving.A compensatedtax changethat raisesthe realnet returnon personalsaving unambiguouslyreduces present personal consumption.If government consumptionremainsunchanged,total nationalconsumptionmust fall.

Thus total nationalsaving (government,private,or both) mustincrease.

It is neverthelessinterestingto considerempiricallythe magnitudeof the savingeffect of uncompensatedchangesin the real net yield. Unfortunately,such an analysisis difficultto do in a convincingway. The basic problemis thatthe expectedrealnet yield availableto individualsaversis not observableand is hard to measure.What asset or combinationof assetsshouldone look at to measurethe yield?Savingsaccounts?SeriesE savingsbonds? Corporatebonds?Corporateequities?Mortgageinterest rates? Consumercredit rates?The yields on these assets have behaved differentlyand there is no obvious choice amongthem. The problemis exacerbatedbecausethe mix of assets and liabilitiesdiffersamongindividualsaccordingto theirtax situation,wealth,and othercircumstances.

And what about expected inflation?The MichiganSurveyResearch Centerresponsesdeal with very short-runinflationexpectations,not the horizonof fifteenor twentyyears needed for calculatingreal returnson the long-termbonds that the authorsuse to measurethe interestrate appropriateto life-cyclesavingdecisions.The autoregressiveextrapolations used by MichaelBoskinmay be better,but they clearlyintroducea furthersourceof noise.

If we limit attentionto a bond interestrate, the real pretaxyield has remainedapproximatelyconstant.All the variationsin the net yield therefore reflect changes in the effective tax rate. But what is the relevant effectivetax rate for this aggregateequation?It is a weightedaverageof marginaltax rates,but with what weights?Certainlythe weightsare not income or ex post saving.This crucialvariableis hardto definecorrectly and harderto measurein practice.

In summary,the key variablein the analysis-the real net yield-is subjectto substantialmeasurementerror.Even if this erroris purelyrananalysisimpliesthatits coefficient dom, the traditionalerrors-in-variables will be biasedtowardzero. But thereis no reasonto believethatthis error is random;the systematicrelationthat would resultif the errorcontains

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a trendor if the erroris correlatedwith any of the other variablescould bias the interestcoefficientin any direction.

The problemis exacerbated(and the fruitfuluse of instrumentalvariable estimationprecluded) by the small effectivesamplesize: no more thantwenty-threeannualobservationsandas manyas elevenexplanatory variablesin a single equation.With possibly little variationin the expected real net yield (or its certaintyequivalent),substantialnoise in its measurement,and a relativelysmall samplesize, thereis insufficientinformationin the data to provide useful parameterestimates.While I recognizethe dangers,I am moresympatheticto Boskin'sdecisionto use a longersampleperiodin whichtherewas greatervariationin the relevant variable,therebyboth reducingthe likely ratio of noise to signal and increasingthe samplesize.

Let me now tum to the principalinnovationin the paper,the focus on personalcash saving.I thinkthat specificationof savingbehaviorin this way is basically a mistake.A reasonabletheory of individuallong-run decisionmakingshould focus on a much broaderconceptof saving that more closely resemblesthe increasein the individual'snet worth. The authorsrecognizethis to some extent by includingsome proxies for a numberof other forms of wealth accumulationamong the explanatory variables,implicitlytreatingpersonalcash saving as conditionalon the otherformsof saving.Unfortunately,theseothersavingmeasuresarenot definedin a satisfactoryway.Whyis grossbusinesssavingincludedrather than net saving?Why are employerand personalcontributionsto social securityusedinsteadof "socialsecuritywealth"or someothermeasureof expectedbenefits?The governmentsurplusis includedeven thoughit is an endogenousvariable: a disturbancethat increases consumptionis likely to raisetax revenuesand increasethe governmentsurplus,a correlation that may accountfor the negativesign on that variablein the saving equation.Moreover,the theoreticalcase for includingthe government surplusamongthe explanatoryvariablesimpliesthatthe correctvariable is the changein realgovernmentdebt;obviously,recentdeficitshavebeen offsetto a considerableextentby the effectof inflationon the real value of such debt.

Then there is the issue of tax policy. Whatwould be the appropriate policy implicationif the authors'conclusionthat the uncompensatedinterest elasticity of saving is zero were accepted?Contraryto the final paragraphof the paper,if the uncompensatedsupplyelasticitiesof saving

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and work effortwere both zero, a substantialwelfaregain would result from reducingthe tax on interestand increasingthe tax on wage income.

The intuitivereasons for this statement,which I have proven formally elsewhere,2are that welfare gains depend on compensatedsupply elasticities,and the relevantpriceelasticityfor intertemporaldistortionis the quantityelasticity(futureconsumption)ratherthanthe smallerexpenditure elasticity (saving).

More generally,what policy implicationfollows if one believes that a higher saving rate would be desirablebut accepts the view implied by this paperthat our methodsof statisticalmeasurementare not powerful enoughto assess the effect of the interestrate on the basis of the experience of the recent decades?Howrey and Hymansstate that the tax on interest income should be lowered only if there were a "reliablymeasured"and "important" effecton behavior.Why?Becausea compensated reductionin the tax can be predictedto increasenational saving. The worst that can happen is that the increasemay be small. There seems nothingto lose andeverythingto gainby trying.

Some participantsat this meetingwill object on the groundsthat any move awayfrom taxing all income at the same rate is somehowunfair.I rejectthis point of view for two reasons.First, I believe the currenttax laws are unfairto those who cannotbenefitfrom the many specialrules that allow some forms of savingto go untaxed (accruedgains, pension contributions,IRAs, Keoghs,homeownerreinvestmentrollovers,and so forth). Second, and more fundamentally,I believe that a fair tax system allocatesthe tax burdenon the basis of consumptionratherthanincome.

As is well known, a progressivetax on consumptionis equivalentto an incometax thatexemptsall investmentincome.3 Finally, it is interestingto ask why other countrieslike France have tax policiesthat aremuchmorefavorableto capitalaccumulationin general and to savingby low- and middle-incomefamiliesin particular.It is certainlynot that they are less egalitarianor more committedto private enterprisecapitalism.Perhapsthey know somethingthatwe do not. Perhaps the answerlies in the differencesin our historicalexperienceand intellectualtradition:the currentEuropeantax policies may reflect an 2. See Martin Feldstein, 'The Welfare Cost of Capital Income Taxation," Journal of Political Economy, vol. 86 (April 1978, pt. 2), pp. S29-S51.

3. Exceptions occur when there are differencesin progressivitythat reflect timing differences.

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BrookingsPaperson EconomicActivity,3:1978

earlierdesire to rebuildcapitalstock after the war while tax policies in the United States are conditionedby the vestigesof a Keynesianfear of oversavingthat was neververy influentialon the Continentbut that still, remarkably,influenceseconomistsin the UnitedStatesand Britain.

John B. Shoven: This is an importantpaperon a topic that has received increasingattentionand deserves more. The authors, as well as those whose previouswork is examinedin this article,are to be congratulated for theirwork on such a key issue. In all growthand macromodelstwo importantvariablesare the averageand marginalpropensitiesto save.

In all evaluationsof the generalefficiencyof the economy,the consumption-savingmargin-that is, the intertemporalallocation of consumption-is secondin importanceonly to the labor-leisurechoice.In political discussionsregardingthe competitivenessof the U.S. economy in the worldmarket,the analysisof savingbehavioris often looked upon as the major problem. And, most relevant to the paper, the debate on how heavilycapitalincomeshouldbe taxeddependscruciallyon the elasticity of substitutionbetweenpresentand futureconsumption,whichin turnis a functionof the uncompensatedelasticityof savingwith respectto the real after-taxrateof returnestimatedhere.The authorsshould,however, explicitlyrecognizethat it is the substitutionelasticitythat is the variable of finalinterestwhenconsideringefficiency,andthata zero elasticitywith respectto the real rate of returnimpliesa unityratherthan a zero substitutionelasticity.One finalwordregardingthe efficiencyconsequencesof all this: it is importantto bear in mindthat this is a "second-best"problem. Eliminatingthe taxationof savingcertainlywill improveefficiency by itself. However,the lost revenuemust be made up in some manner, presumablyone imposinginefficienciesupon the economy.The replacement tax must be consideredin orderto completethe analysis.

The paperbeginswith definitionsof types of savingand theirrelative magnitudes.The first strikingfact is that personalcash saving (the net accumulationof demandplus savingsaccounts,bonds, new equities,and so on) amountsto only a small fractionof gross privatesaving.Table 2 indicatesthat personalcash savingwas only 14 percentof NIPA gross privatesavingin 1975 and only 20 percentof businesscash saving.Personal cash saving accountsfor approximately35 percentof net private saving,and the averagepropensityto save in the form of personalcash

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savingis shownto be only 0.22 percentfor the period1951-74. Certainly the direct effect of this form of savingis relativelysmall in determining economicgrowth.Unless HowreyandHymansimputebusinesscash saving to consumersand unless it is total privatesavingthat is interest-rate sensitive,their measureof interestelasticitymay be misleadingin terms of policy implicationsbecauseit appliesto such an unimportantcomponent of the entirepicture.

Howreyand Hymansalso discussthe inclusionof the accumulationof consumerdurables,net mortgagerepayment,and imputationsin FF saving and (with the exceptionof consumerdurables)in NIPA saving.They argue,correctlyI think,that these forms of savingare not what persons concernedwith capitalformationhave in mind.However,in a complete portfoliomodel of consumerbehavior,the stocks and accumulationsof these itemswill affectloanable-fundssaving.

A majorportionof this paperis devotedto a reexaminationof three alternativeapproachesto the examinationof savingbehavior.

First, and most controversiallyI suppose, they look at the aggregate consumption-functionapproach associated with Michael Boskin. The techniqueis to add the real after-taxrate of returnand inflationas explanatoryvariablesto a relativelysimple aggregateconsumptionfunction. Savingbehavioris inferredimplicitly.The centralBoskin resultis that the uncompensatedelasticityis +0.4, whichis derivedfrom the examinationof eight differentspecificationsand econometricapproachesto the basicequationreportedin thispaper.

Howreyand Hymansalso challengethe robustnessof Boskin'sresults.

Each permutationof the data set or econometricsthey make (including the deletionof 1934, the depression,substitutingU2 for U, andmost importantly,using actualinterestrates ratherthan expectedrates) reduces the saving elasticity and frequentlyreduces it so that it is no longer statisticallysignificantlydifferentfromzero.

I have severalcommentsthat applyboth to Boskin'swork and to this paperby HowreyandHymans.

To begin, these are extremelysimple aggregateequations.What interestrate shouldbe used with them?Saverspresumablylook at an entire set of interestrates of differentmaturityand risk classes, borrowingas well as lendingrates,expectedfutureinterestrates,and so forth,in allocatingconsumptionover time. Choosingone interestrate is both difficult

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BrookingsPaperson EconomicActivity,3:1978

and simplistic.A paperby Backus and Purvis,"outlinesan approachto estimatedisaggregatedportfolioholdingsas a functionof an entirearray of ratesof return.This approachseemsmore appropriateto the question at hand.

The strongestresultin the Howrey-Hymanspaperis that when actual long-runinterestrates are used in the regressionsin place of Boskin's expectedinterestrates,the sign of the savingelasticitybecomesnegative and significant.Shouldactualor expectedinterestratesbe used?The answer dependson the planninghorizonof the savers.If the householdis savingfor an acquisitionto take place twentyyearslater, the actualrate offeredon twenty-yearbonds (preferablypurediscountbonds) is appropriate.However,if the householdis waitingfor a periodshorterthan the maturityof the bond (say, the savingperiodis threeyears,usingtwentyyear bonds), then it wouldbe correctto use boththe currentrateandthe expectedrateat the timeof liquidation.

An entire literatureexists on how demographicsand life cycle considerationscan largelyaccountfor aggregatesaving.These issues are ignored here. In lengthytime-seriesanalysissuch as this, ignoringdemographicsseems untenable.Considerationsof life cycle would also imply that savers(and dissavers)look at the entirespectrumof futureexpected short-runrates, perhapsderivedfrom the existingterm structure,in determiningoptimalbehavior.

The time-seriesapproachmay not be the way to determinethe real storyhere. Gleaningthe effectof the real rate of returnon savingseems nearlyhopeless,particularlywhen businesscycle effectsare modeledby the unemploymentratealone.This maybe why the inclusionor exclusion of the depressionyearsis shownto be crucialto the results.

It should be noted that Boskin has done a considerableamount of work on this questionsince his articlereferredto above was completed, and he has producedsome instrumentalvariableregressionsthat imply even highersavingelasticitiesthan I have mentionedabove.In his commenthe describesthis additionalworkand its implicationsand relevance for the currentdebate.

On the basis of the Howreyand Hymanspaper,one mustsay that the weightof the evidencesupportingthe positionthat the real after-taxrate 1. David Backus and Douglas Purvis, "An IntegratedModel of Household Flowof-Funds Allocations," Cowles Foundation discussion paper 493, Cowles Foundation-StanfordResearch Institute, flow-of-funds project (CF, July 1978).

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693

of returnto saversis not a primedeterminantof savingis increased.However, becauseof the qualificationsI have mentionedaboutboth studies, I would still finda wide rangeof values (on both sides of zero) plausible for this key elasticity.

I have some briefercommentson the other approachesto estimating savingbehaviorin the paper.

The authorsfind a more robustpositive savingelasticityin the equation representingthe Houthakker-Taylorapproach.However,the inclusion of inflationand the uncertaintyregardingfutureinflationdo weaken the rate-of-returnvariableto the point that it is statisticallyinsignificant.

They also observethat the propensityto save fromdifferentformsof income is substantiallydifferent,supportingto some extentthe Cambridge theory,which states that the functionaldistributionof incomeis the primarydeterminantof saving.

When, in table 5, Howrey and Hymansestimatesavingfunctionsdirectly (for different definitions of saving) rather than consumption functions,they never obtaina significantcoefficienton the real after-tax interestrate. Importantly,they use the actual Baa rate ratherthan the expectedratein this section.They also showthatinflationreducessaving, whereasuncertaintyabout inflationincreasesit. Here, too, however,the coefficientsare hoveringnear statisticalinsignificance.

The last sectionof the paper,in whichfunctionsare estimatedfor the small fractionof savingclassifiedas personalcash saving,is a step backward in my opinion. One constantlymust keep in mind how small the fractionof loanable-fundssavingis that is referredto in interpretingthe resultsof table 6. The authorsexaminethe degreeof rationalityof savers with respectto businesscash savingand governmentcash saving.Here, the single-equationapproachis most offensive.The directionof causality implied by the equation (business cash saving "determining"personal cash saving) clasheswith my belief that these variablesare, at least to an extent, simultaneouslydetermined.The single-equationapproach severely distortsthe results and does not provide meaningfultests of the hypothesesunderconsideration.

My final observationis that this paperdoes blunt the impressionthat empmcaleconomistsare finallycomingcloserto pinpointingthe valueof key variablesin their models. That bluntingmay be valuablegiven the severe shortcomingsof the studies undertakenthus far (including this one by Howrey and Hymans), but it should not discourageeconomists

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from continuingto tackle issues such as this, which the professionhas avoidedfor so long.

MichaelJ. Boskin:I am pleasedto have the opportunityto presentcomments on the Howrey-Hymanspaper.Let me divide my commentsinto threeparts: commentson their critiqueof my study;commentson their estimatesof savingequationsandon Denison'slaw;anddiscussionsabout the relationshipof the interestelasticityof saving to the desirabilityof incomeor consumptiontaxation.

My originalreactionto seeing eminentauthorssuch as Howrey and Hymansdevoteso much attentionto my earlyworkon the consumptionsaving choice was that I was flattered.Unfortunately,as I continued studyingtheirpaper,I notedthattheydid not coverin anydetailthe most importantparts of my work. Thereforemy first commentis they have totally ignored-to the extent of not even discussing-the most important resultsfrom my Journalof Political Economypaper or any of the results from my Treasurycompendiumpaper with LawrenceLau.' In each of these-the latterhalf of my JPE paper and the entire compendiumpaper-I estimatedinterestelasticitiesmuchlargerthanthose containedin the equationHowreyand Hymanssoughtto reestimate.One of the major points of my JPE paper was that it was not reasonableto estimate consumptionfunctionsby single-equationmethods;indeed, it was necessaryto use an instrumentalvariablestechnique.In the second half of that paperI did so using as instrumentsprincipalcomponentsof a variety of exogenous variables from the major macroeconometric models. This resultedin a doublingof the estimatedinterestelasticity fromaround0.2 to 0.4, withone estimateas high as 0.6. In my paperwith choice in a full model allowLau, we embeddedthe consumption-saving ing also for a labor-leisurechoice; this also resultedin preciseestimates of an interestelasticityof saving on the order of 0.4. Once again, the instrumentsused were principalcomponentsof exogenousvariablesof macroeconomicmodels. This procedurenot only accountsfor cyclical fluctuations,but in principledistinguishesour saving (or consumption) 1. Michael J. Boskin, 'Taxation, Saving, and the Rate of Interest,"Journal of Political Economy, vol. 86 (April 1978, pt. 2), pp. S3-S27; Michael J. Boskin and Lawrence J. Lau, "Taxationand Aggregate Factor Supply: PreliminaryEstimates," in Department of the Treasury, Office of Tax Analysis, 1978 Compendium of Tax Research (GPO, 1978), pp. 1-15.

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functionfrominvestmentbehavior.Hence, I am in the somewhatembarrassingpositionof critiquinga critiqueof my studythatfocuseson the issue of the interestelasticityof savinganduses my equationswith the lowest estimatedinterestelasticity-equations thatI personally,for economic and statisticalreasonsdiscussedin the papersmentionedabove, do not claimto be my best results.In briefsummary,the authorshavebeen very selectivein the part of my work they have chosen to critique,and under no circumstanceswould I considertheirresultsand reestimationsat all a satisfactorydiscussionof my previouswork.

I do not even believe that the authors'interpretationof theirreestimation of my equationscasts seriousdoubton the basic estimates.Any battery of reestimatesof any time-seriesequation is likely to change the results. For example, in runs where the t-statisticsare reduced to only marginalsignificance,HowreyandHymansmakemuchmoreof this than is reasonable.Reducingthe t-statisticso thatthe estimatedelasticityof approximately0.2 is only marginallysignificantis not the same as demonstratingthatit is remarkablysmallandeconomicallyinsignificant.Indeed, most of the estimatesconfirmmy previousresults;for example,takinga Koyck lag resultsin estimatesthat are similarto my originalequations.

Droppingobservations,laggingobservations,changingthe sampleperiod, and so forth sometimesreducethe estimatedcoefficientto statisticalinsignificance(usuallybecause the numberof observationshas decreased or becausethe variabilityof the right-handvariableis so reducedthat a precise estimateof the coefficientcould not be obtained). There are a variety of suggestionsgiven as to why the authorshave chosen to lag unemploymentandso on, but againI mustpointout thatthe instrumental variablestechniqueused in the second half of my JPE paperessentially accounts for the cyclical pattern of the economy, its growth, and the interactionof savingand investment.Hence I must concludethat even if the workthey reviewwas all I had presented,the Howrey-Hymanspaper would not alter my conclusionsvery much. Indeed, their resultsreflect exactlywhatI wouldhaveexpectedwouldhappenfroma varietyof transformations,droppingobservations,changingsampleperiods,andthe like.

But again,more importantly,the selectivenatureof theircritiqueignores the most importantsets of estimateswhich,coincidentally,are those with the largestestimatedelasticities.This renderstheircritiquesomewhatless relevantthanit mightappear.

Next let me turnto Denison'slaw. It was pointedout to me by my col-

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league, Victor Fuchs, that the female-malewage ratio in both 1960 and 1970, holding other things constant,was approximately0.6 and that if one looked at the Bible, in particularLeviticus,one would note that female slaves sold for 30 shekelsof silverwhile male slaves sold for 50. I would attach no more structuralinterpretationto Denison's law, the alleged constancyof the gross private saving rate, and the inabilityof any economicpolicies to affectit than to the much longer apparentconstancyof the female-malewage ratio.One of the two majorpointsof my JPE paperwas to pointout how foolishit was to try to drawstrongstructuralinferencesaboutsavingbehaviorfromthe apparentconstancyof the grossprivatesavingrate.

I do not see how anyonecould disagreewith this point. I am glad to see that Howreyand Hymansseem to agreewith it, althoughit deserves morethantheircasualmention.

And what problemsexist in the structuralinterpretationof Denison's law?First,neitherthe numeratornor the denominator,grossprivatesaving or gross nationalproduct,measurethe economicallyrelevantconcepts. Human capital is omitted from the analysis even though John Kendrick,Jacob Mincer, and others have indicatedthat much saving, especiallyearlyin life, is in the formof humancapital.Also missingis the net savingof U.S. citizensoverseas,which has increasedsubstantiallyin recentyears.Savingtheoryrelatesto net incomeandnet saving,and again thesevarymarkedly.Indeed,an interestin grosssavingwouldonly occur in the United States if we were strong believersin embodiedtechnical changeand caredaboutthe rate of turnoverof the capitalstock.My own estimatesuggeststhat the coefficientof variationof net savingis a large multipleof the coefficientof variationof gross saving for the postwar period.Further,this coefficientof variationwould increasesubstantially if savingwere adjustedto reflectreplacementratherthan historicalcost depreciation.I take this to be a strongindictmentof the simpleststructuralinterpretation of Denison'slaw.

It is also worth noting that a constancyhas never been noted in the privatesaving rate in any other countryfor a sustainedperiod of time.

MichaelEdelsteinhas noted a substantialinterestelasticityof savingin the United Kingdom,and Paul David has done so for the United States in the nineteenthcentury.Even if the view were taken that public and privateconsumptionwere perfectsubstitutes,so the share of total consumption,public and private, out of income was a constant share of

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wealth, as David and Scaddinghave argued,the fractionof wealthconsumedwould still be a functionof the net rateof interestwhereasincome would be a flow from wealth at the gross rate of interest.As a consequence,policies that affectedthe ratio of the net to the gross rate of interestwould affectthe consumption-saving choice.

It is also worth noting some of the enormouschangesthat have occurredin the U.S. economy in the last few decades. The changingage structureof the populationhas been marked.The ratio of retireesto workerswill go up 75 percentshortlyafterthe tum of the centurydue to the combinationof the post-WorldWar II "babyboom" and the recent "babybust."Since WorldWar II, the life expectancyat age 60 has increasedabout a year and a half for men and threeyearsfor women, and the averageretirementage has gone down substantially.For example,in 1948 one-half of men over the age of 65 were in the labor force. That numberis now about one in five. This implies perhapsa 30 percentincrease in the averageretirementperiod. A large increasein the female laborforceparticipationratehas occurred.The hugegrowthin the public sectorincludesa largerise in both averageand marginaltax ratesand an enormousgrowthin social insuranceprogramssuch as those for social securityandunemployment,whichmay substitutefor privatesaving.The increasein inflationin the last ten years affectssaving decisions.There has been a sizable decreasein the averageworkweek,about 22 percent since 1929. This alone rendersGNP suspectas an incomemeasure.The savingrateout of "fullincome"has fallen substantially.And tremendous changeshave occurredin typicalfamilypatterns.All these factors,if they had occurredalone,wouldhave resultedin substantialchangesin saving.

The fact that they have balancedout each otheris what leads to the apparentconstancyin the gross privatesavingrate, and I see no reasonto give a structuralinterpretationto that fact.

Effortsought to be devotedto disentanglingthese effectsratherthan to giving strongstructuralinterpretationsto the reduced-formoutcome.

My own currentresearchis specificallydesignedto disentanglesuch age and household effects from interest rate, income, and other effects on saving.

Let me now discuss the second half of the Howrey-Hymanspaper in which the authorsdiscuss their estimatesof saving equations.They look at only a small fraction of saving. While this does account for a substantialfraction of the total variance, they essentiallyregress one

Paperson EconomicActivity,3:1978 Brookings componentof savingon othercomponentsof saving,or the sum of other componentsof saving.This is the same as regressingthe consumptionof automobileson the consumptionof cigarettes,the consumptionof food, and so forth.Thatis, it resultsin the usualkindsof specificationbias and correlationbetweenright-handvariablesand the errortermsin suchestimated equations.Hence the estimatedcoefficientsare biased, and I can give no statisticalinterpretationto theirresults.Ideallywhat oughtto be done, and I think Howrey and Hymanswould agreewith me, is to disaggregatesavinginto its numerouscomponents,includethe ratesof return of all types of savingin the economy and their covariancesas well as a varietyof other determinantsof aggregatesaving,and estimatea system of such equations.Unfortunately,this places extremedata demandson the researcher,demandswhichare well beyondcurrentcapabilities.That is why I focusedon aggregateconsumptionfunctionsin the firstplace.

The Howrey-Hymansinterest-ratevariablesuffersfrom a majorconceptualerror.They subtracteda one-yearexpectedinflationrate from a long-termbond rate. Obviously,an expectedinflationrate over the time horizonof the bond is necessary.In my JPE paper, I contributedsuch estimatesof long-termexpected inflationrates. I also constructedestimates of the long-termexpected returnto capital from the JorgensonChristensendata on actualreturnsto capital.I used alternativemeasures of the long-runexpectedreal net rate of returnbased on Moody'sbond rates,high-grademunicipalbond rates and the expectedlong-runreturn to capital.Whilethe resultsdifferedslightly,each estimateof the long-run expectednet-of-taxrate of returnto savingproduceda modest positive estimatedinterestelasticityof privatesaving.In view of the inconsistency in the generationof the Howrey-Hymansinterestrate seriesand the likelihood that measurementerrorbiasesthe estimatedcoefficients(in addition to the biasesnoted above), I do not believe muchweightshouldbe given to the equationsthey report with their own generatedrates of return.

A varietyof other issues relate to the interestelasticityof saving.To begin, it is simplynot the case that a positiveinterestelasticityof saving implies that a consumptiontax is preferableto an income tax and that a negative interest elasticity or a zero interest elasticity implies that an income tax is preferable.It could be that a consumptiontax, or even an interest income subsidy, is desirablewith a negative interest elasticityof saving;and a savingtax or a high interesttax-perhaps one 698

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even heavierthan that at present-could be desirablewith a positiveinterestelasticityof saving.As pointedout in papersby JosephStiglitzand me, by MartinFeldstein,andby A. B. AtkinsonandStiglitz,2 for example, this choice dependsupon the relativesubstitutabilityand complementarity with leisure of consumptionearly in workinglife and consumption duringretirement.The full set of suchcompensatedcrosspriceelasticities must be known to reach a conclusion about the desirable,or efficient, degree of taxationof capitalincome. Lightertaxation,or subsidization, of capital income increases with the interest elasticity of saving only ceterisparibus.

Next, general equilibriumgrowtheffects imply that the interestelasticity of saving in the overall economy is likely to be larger than that embedded in single-equationconsumptionestimates such as mine, or estimatesof the elasticityof substitutionin utilityfunctionsbetweenconsumptionnow and consumptionin the future.The growthof the population and the likely growthof incomedue to technicalchangeimpliesthat, to obtain the total derivativeof saving with respectto the interestrate, researcherswould have to take accountof the fact that a largefractionof total saving is being done by the young and it has to be comparedwith the dissavingbeingdoneby the elderly.Evidenceof an enormousamount of dissavingdone by young workerswould be a strongindictmentof a large estimatedinterestelasticity.Actuallyit appearsthat thereis a substantialamountof saving done by young workers,althoughit is mostly in the form of investmentin humancapital.

I shouldalso note thattherearetwo issuesin savingefficiency.The first is the "goldenrule" rate in which the marginalproductof capital will equal the rate of growthof the effectivelaborforce, or the profitsharein the economy will equal the net saving rate. If saving were below this golden rule rate, as ArthurOkunand othershave mentioned,a varietyof policy instrumentscould be used to deal with this: for example, by changesin governmentfiscal policy such as runninga surplus,changing social securityfinancing,and the like. There is still the issue of the mis2. Joseph E. Stiglitz and Michael J. Boskin, "Impact of Recent Developments in Public Finance Theory on Public Policy Decisions: Some Lessons from the New Public Finance," American Economic Review, vol. 67 (February 1977), pp. 295301; Martin Feldstein, "The Welfare Cost of Capital Income Taxation,"Journal of Political Economy, vol. 86 (April 1978, pt. 2), pp. S29-S51; A. B. Atkinson and J. E. Stiglitz, "The Design of Tax Structure: Direct versus Indirect Taxation," Journal of Public Economics, vol. 6 (July-August 1976), pp. 55-75.

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allocation of consumptionduringindividuals'lifetimesif their lifetime consumption-savingchoices are distortedby heavy taxationof interest income.The second-bestproblem,as pointedout repeatedlyby Feldstein, Atkinson, Stiglitz,Diamond,myself, and others, also needs to account for misallocationsin the labor market.These misallocationsare purely a functionof the compensatedelasticities,not the uncompensatedones, and even if the total interestelasticitywere zero, the compensatedelasticity mightbe positive;if the total elasticitywere negative,the compensatedforward-priceelasticityof the demandfor futureconsumptioncould still be substantiallynegative.In either of these cases a situationwould result in which a consumptiontax or a lightertaxationof interestthan laborincomemightbe desirable.

If throughdynasticfamilies or any other means, householdstook a muchlongerrunview and,for example,maximizedthe sumof discounted utilitya la Ramsey,all the problemsunderconsiderationwouldbe transitory,andthe economywouldconvergeto a new steadystatewiththe same realnet rateof return.

Let me make one final statementabout the Howrey-Hymanspaper and one plea for more research.Howreyand Hymansdo point out that my work on consumptionfunctions-as all other work on consumption functions, with few exceptions-does not explicitly build a dynamic model of savingbehavior.I concurwith this observation,andI am working on this problemnow. I only reportthat my originalresultsdid not do so becauseI was hopingto comparethemwith the traditionalconsumption functionestimates.And thereare few parametersof moreinterestin the economythan the interestelasticityof saving.This parameteraffects our notionsaboutthe long-runefficacyof fiscaland monetarypolicy, the effectof inflationon the real economy,the incidenceof varioustaxes, the desirabilityof consumptionversus income taxes, and the social rate of discountor the social opportunitycost of publicfunds.Furtherwork on this subjectis desperatelyneeded, and I look forwardto addingHowrey and Hymansto the list of people who are workinghard to improveour knowledgeon the subject.

E. Philip Howrey and Saul H. Hymans: The discussantsof our paper have raisedseveralgeneralquestionsthat are best handledby a common response,afterwhichwe shall turnto some of the specificmattersraised by individualdiscussants.

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We acknowledgethe need to considermorecarefullyyieldson alternative typesof savingassets.We also acceptas validthosecriticismsregarding possible simultaneitybias in our estimates.However,the concernof severaldiscussantswith potentialsimultaneitybias in our estimateof the effect of governmentsaving (GCS) on personal saving is surely misplaced. It is arguedthat a disturbancethat lowers saving (the dependent variable) is likely to increase tax revenuesand hence the government surplus(an independentvariable) and thus producethe estimatednegative coefficientthat relates GCS to personalsavingin our equation.But the presenceof personaltax payments(TX) in our equationeffectively rules out this kind of spuriousresult. Simultaneitybias may be present, but if it is, it has a moresubtleoriginthanis suggestedby the discussants.

A resolutionof the simultaneityissue as well as the questionof which of severalinterestratesshouldbe includedin the analysisrequiresa richer data base than is currentlyavailable.The aggregatetime-seriesapproach is subjectto severelimitationsthat cannot,in our opinion,be adequately overcome by increasingthe data base to include observationsfor the period between the two world wars or by using quarterlydata for the postwarperiod. We firmlybelieve that any chance of substantialrefinement of the estimationof interestrate effectson savingawaitsthe ability to conductthe analysisas a panel studybased on a time seriesof crosssectional observationson household decisions. Within that context it would be possible to disaggregateaccordingto wealthlevels, to observe units that may react to differentrates of returnand that are subjectto differentmarginaltax rates, and so on. At an aggregativelevel, there is little choice but to try to identifya best representativeinterestrate, as we did; the data are basicallyunable to distinguishindependenteffects of alternativeinterestrates at a high level of aggregation.

Tlhespecificissues raised by variousdiscussantsare much less compellingcriticismsthanthe generalissuesjust discussed.MichaelBoskin's criticismof our workis based largelyon a contentionthatwe have failed to review all of his work on the estimationof the interestelasticityof saving. Virtuallyall Boskin's results are based on an interestrate processed accordingto some "magic"formula,which seems to have produced some anomalous results. For example, Boskin's expected real interestrate and expectedrate of priceinflationimplyan expectednominal interestrateof -3.7 percentin 1934. We suggestthatBoskin'sresults should not be taken seriouslyuntil the constructionof his interest-rate

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series is explainedand justified.It may be the uniquelycorrectmeasure of the rate of returnto saving,but at this point it is merelythe productof a black-boxtransformation.

John Shovenarguesthat our analysisis unimportantbecausepersonal cash saving is a small proportionof aggregatenational saving. Surely this misses the point. Personal cash saving is small on average,but it accountsfor a good deal of the variationin total saving,and that is what countsfor stabilityof the aggregatesourceof fundsfor capitalformation.

Shoven also argues that the interestelasticityof saving is not the key parameterfor the question of microeconomicwelfare efficiency.That may be so, but it is the key parameterwith respectto the availabilityof loanablefundsthat is the issue we attemptedto study.

MartinFeldsteinarguesthat the substitutionof a payrolltax for a tax on interestincome may reduce currentpersonalsaving,but that it cannot reducetotal nationalsaving.But supposethat our interestelasticity result is correctand that a tax substitution(a compensatedtax change, in Feldstein'sterms) leaves personalsavingunchanged.By definition,a compensatedtax change leaves currenttax receiptsunchangedso that governmentsavingis also unchanged,and aggregatesavingis constantas well. The only possibilityfor increasedsavingas a resultof the tax substitutionmust thereforearisefrom its being accompaniedby a changein the level or distributionof income.It wouldthenbe necessaryto uncover andanalyzethe processby whichthe tax substitutionwouldproducesuch a changein incomeand establishits effecton saving.

Feldsteinand Boskinboth arguethat our estimatedinterest-rateeffect is likely to be biased towardzero because of measurementerrorin the rate of returnenteredin our equation.As is well known,the implication that measurementerrorbiases coefficientestimatestowardzero derives from the elementarysituationin which a single independentvariableis measuredwitherror.We wouldnot wantto claim-even if Feldsteinand Boskinbelieve it-that the only possibleviolationof the classicalregression assumptionsthat pertainsto our equationis measurementerrorin the rate of return.We doubtthat it is possibleto point to a particulardirection of bias in our interest-ratecoefficientwith any degree of confidence. Indeed, we believe that our discussionof how the interestrate should affectsavingaccordingto what is includedin differentmeasures of savingis far moreimportantand to the pointthanis the statementof a highlyrestrictiveresultconcerningerrorsin variables.

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Boskin and Feldstein argue more specificallythat our interest rate series is conceptuallyincorrectbecause we have subtracteda short-run expected rate of inflationfrom a long-runnominalimterestrate. Three pointsshouldbe noted in this connection.First, a distributedlag involving past ratesof inflationin place of the SurveyResearchCenterexpectations variable yields similar results in our saving equations. Second, observationson an expectedlong-runrate of price inflationare simply not available,exceptas maybe measuredby a weightedaverageof recent price changes.Third, we see no reason to believe that any mechanical procedurefor derivinglong-runexpectationsof inflationfrom past price changesis a bettermeasureof inflationaryexpectationsthan the Survey measurewe used. The SurveyResearchCentervariableindicateswhat respondentsthink about inflation,and its interpretationcan hardly be limitedto the exact time frameof the surveyquestion.

Finally, Feldstein-like Shoven-misses an importantpoint by discussinga problemin whichhe is interested,ratherthanthe problemthat we addressed.We stated that a policymakerinterestedin increasingthe funds availablefor capital formationwould be unlikely to manipulate the tax rate on interestincomeunlessthe after-taxrateof returncould be shown to have a substantialand reliablymeasuredeffect on saving.Our analysiscasts seriousdoubton the propositionthatloanable-fundssaving respondsto the rate of returnto saving,and that justifiesour concluding paragraph.If Feldsteinwishesto arguethatothergoals (such as increased welfare or economic efficiency) justify tax substitution,he is certainly free to do so. Whatwe claimis thatthe argumentfor tax substitutioncannot be justifiedby the propositionthat it will changethe supplyof funds availablefor capitalformation.

GeneralDiscussion Severalparticipantscontinuedthe discussionof the interestrate that was used by the authorsand by earlierresearchers.ArthurOkun questioned the use of the Baa bond rate becausethe greatmajorityof savers do not hold such bonds. He was also doubtfulof using financialassets with large liquidity premiums,such as money or time deposits, even thoughthey are widely held and suggestedthat the rate individualspay to borrowmoney was a muchbetterindicatorof theirrate of time pref-

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erence and was also a rate that applied to a great numberof people.

FredericMishkinnoted that the Baa rate is sensitiveto changesin the degree of uncertaintyand conjecturedthat its success in the equations might reflectthe responseof saving to uncertainty.Thomas Justerand othersremainedpuzzledby how MichaelBoskin'sinterestrate variable was constructedand were troubledthat the estimatedresponseof saving to interestrateswas apparentlyso sensitiveto this construction.William Brainardnoted that includingboth wealth and interestrates in Boskin's equation might confuse the relation between interest rates and saving becauseinterestrates and wealthwere themselvesrelated.He also suggestedexaminingthe responseof net saversand net dissaversseparately to determinehow mucheach groupcontributedto variationsin total saving andto whatthe net savingof each groupresponded.

ChristopherSimsdid not believethe estimatedequationscouldbe used to inferthe responseof savingto a changein the taxationof saving.The historicaldynamicrelationof the after-taxreal interestrate to savingis probablynot reliableif used to predictthe effect of permanent,policygeneratedchangesin after-taxreal interestrates.Expectationsare important in saving and investmentdecisions, and policy-generatedchanges would probablybe expectedto be morepersistentthannormalhistorical changes in interestrates. He suggestedthat internationalcross-section analysismight be more useful for identifyingthe responseof saving to alternativetax treatments.

Participantsdiscussedthe other explanatoryvariablesin the authors' preferredsaving equations.LarryDildine observedthat the calculation of imputedincomesoften utilizesinterestrates,which mightexplainthe largecoefficienton this variable.He also notedthe ironythatthe authors' incomedecompositionimpliedthat savingwould be increasedby raising taxes in orderto increasetransferpayments.Mishkinreasonedthat one would have to distinguishbetweenchangesin permanentand transitory componentsof the differentincome measuresto derivelong-runconclusions aboutthe propensityto save out of differentcomponentsof income.

Justersuggestedthat the Denison'slaw resultsmightreflecta rise in pessimismthat correlateswith a decline in corporatesaving.He suggested that a direct measureof optimismbe used to explorethis possibility.

The panel also consideredthe paper'spolicy implications.Sims observed that wheneverthe high U.S. tax rates on capitalincome are discussed, economistscan offer only vague theoreticaldiscussionsand un-

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certainempiricalevidenceregardingthe effectof taxationon saving.The argument invariably turns to distributionaleffects of proposed tax changes,and Sims asked how much is known about that. Okunpointed out that,evenif the evidenceon the responseof personalsavingto interest rates were more robust,it would tell us little about whetherinvestment should be increased.And if more nationalinvestmentis desirable,there maybe betterwaysto pursueit thanby reducingtaxeson personalsaving.

Nationalinvestmentand savingcan be encouragedby alteringthe fiscalmonetarymix of policy or by changingfiscal instrumentssuch as the investmentcredit or other business taxes. The distributionaleffects of these policies are less tendentious.And their effects on investmentare more predictable.