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Pension Wealth and Household Saving

Evidence from Pension Reforms in the United Kingdom

By ORAZIO P ATTANASIO AND SUSANN ROHWEDDER

Using three major UK pension reforms as natural experiments we investigate therelationship between pension saving and discretionary private savings Unlike mostdifferences-in-differences approaches which rely on average differences betweencontrol and treatment group we use economic theory to model the response of eachindividual household The empirical analysis based on the Family ExpenditureSurvey uses both time-series and cross-sectional variation to identify the behav-ioral response The earnings-related tier of the pension scheme is found to have anegative impact on private savings with relatively high substitution elasticities theimpact of the at-rate tier is not signi cantly different from zero (JEL H55 H91)

The relationship between pension wealth andhousehold savings is crucial for important pol-icy issues such as establishing the effects ofchanges in pension legislation on saving behav-ior From a theoretical point of view the life-cycle framework suggests that the provision ofpublic bene ts after retirement constitutes anegative incentive to accumulate wealth duringonersquos working life Quantifying the resultingrelationship between pension wealth and sav-ing even within a simple theoretical frame-

work is dif cult however as the degree ofsubstitutability between pension and nonpen-sion wealth depends on a variety of factorsranging from the presence of liquidity con-straints that might be binding to the importanceof bequest motives to the size of discount fac-tors and rates of return to the possibility ofdistortionary effects of pension contributions onlabor supply behavior The complexity of thetheoretical relationship makes its empiricalquanti cation all the more important

Given the importance of the issues involvedthe empirical evidence on the relationship be-tween pension wealth and household saving isrelatively scarce Moreover the results are farfrom being conclusive Martin S Feldstein(1974) was among the rst to investigate therelationship between public pension wealth andhousehold saving empirically His study basedon the time-series behavior of aggregate savingrates and pension wealth indicates a large neg-ative effect of pension wealth on saving ratesSubsequently Mervin A King and Louis ADicks-Mireaux (1982) provided evidence frommicrodata analyzing the relationship betweenthe stock of pension wealth and saving ratesThey interpreted the coef cient of pensionwealth in a regression for nancial wealth as ameasure of the degree of substitutability be-tween the latter and the former They nd thatan increase of a dollar in social security wealthdecreases nancial wealth by 25 cents while anincrease in private pension wealth decreases

Attanasio Department of Economics University Col-lege London Gower Street London WC1E 6BT UnitedKingdom and Institute for Fiscal Studies 7 RidgmountStreet London WC1E 7AE United Kingdom (e-mailoattanasiouclacuk) Rohwedder RAND 1700 MainStreet Santa Monica CA 90407 and Department of Eco-nomics University College London (e-mail susannrrandorg) Both authors thank the TMR Network (Contract NoERBFMRXCT960016) on ldquoStructural Analysis of House-hold Savings and Wealth Positions over the Life-Cyclerdquo for nancial support Attanasio also acknowledges the fundingreceived from the Leverhulme Trust under the project ldquoTheChanging Distribution of Consumption Economic Re-sources and the Welfare of Householdsrdquo Material from theFamily Expenditure Survey made available by the Of ce forNational Statistics (ONS) through the ESRC data archivehas been used by permission of the controller of Her Maj-estyrsquos Stationers Of ce Moreover the authors wish tothank James Banks Richard Blundell Richard Disney CarlEmmerson Michael Hurd Paul Johnson Costas Meghirand seminar participants at UCL RAND and at the TMRconference in Deidesheim for helpful comments Any re-maining errors are of course our own

1499

nancial wealth by 10 or 18 cents depending onthe methodology

Peter A Diamond and Jerry A Hausman(1984) and R Glenn Hubbard (1986) usingUS data nd even smaller offsets than Kingand Dicks-Mireaux (1982) Agar Brugiavini(1987) and Tullio Jappelli (1995) have carriedout exercises similar to those of King andDicks-Mireaux (1982) on Italian data obtaininglarger estimates of the degree of substitutabilitybetween private wealth and public pensionprovisions

More recently the relationship between pen-sion wealth and savings has received renewedattention William G Gale (1998) uses USmicrodata from the Survey of Consumer Fi-nances to assess the extent to which changes inpension wealth are offset by changes in otherforms of savings Gale (1998) as we do belowstresses the importance of adjusting pensionwealth for the age of the individual He ndsthat for his favorite speci cation the offset issubstantial between 039 and 082 dependingon the estimator used Alan L Gustman andThomas L Steinmeier (1999) on the otherhand reach different conclusions using datafrom the Health and Retirement Study (HRS)They nd very small and insigni cant offsets ofpension wealth to total wealth1

The scarcity of empirical evidence on therelationship between pension wealth and savingbehavior is in part due to the severe data limi-tations that researchers face in this area Aggre-gate time-series information while it coverspotentially long time periods and thereforechanges in pension wealth is of limited usebecause of aggregation issues Data sets con-taining individual-level information on incomeand consumption (and therefore saving) are fewand far between Moreover data sets that con-tain this type of information very rarely containinformation on nancial wealth and even less onpension entitlements In addition to the limita-tions in available data sets pension wealth doesnot exhibit much exogenous variation espe-

cially because microdata sets typically coverrelatively short time periods Therefore differ-ences in pension wealth among individualscould re ect differences in tastes for saving

The approach we use in this paper differsfrom those used in the literature in two impor-tant dimensions First the data of our studyallow us to identify the parameter of interest ina much more robust way than in previous stud-ies Rather than using data on wealth we con-sider the implications of different levels ofpension wealth for saving rates We computethese from high-quality household data thatcontain detailed information on income andconsumption and go back to the early 1970rsquosBecause we have a long series of cross sectionswe can exploit not just cross-sectional variationbut also variation over time induced by severalimportant reforms to the UK public pensionsystem which affected different groups of indi-viduals differently Our period of study containsas many as three major reforms that inducedsubstantial exogenous variation in pensionwealth On the basis of these data we exploit thevariability in pension wealth induced by thereforms to identify the relationship betweenpension wealth and saving rates Second wecombine the differences-in-differences estima-tions with important implications from a simpletheoretical framework on how to relate stockand ow variables and on how to control fortiming effects of the reforms with respect to theage of the household and with respect to whenthe household is observed in the data As aresult we are able to derive an empirical specication in which the coef cients of interest canbe directly interpreted as the degree of substi-tutability between nancial and pension wealth

The conceptual framework we use is that of alife-cycle model in which individuals saveamong other reasons to nance their retire-ment In a simple version of the model pensionwealth is a perfect substitute of nancial wealthOur approach like the one in Gale (1998) rec-ognizes that the effect of a change in pensionwealth on saving behavior depends on the po-sition of an individual over her life cycle More-over consistently with the model the effect onobserved saving rates depends on when in thepast the individual experienced an (unexpected)pension reform As Gale we recognize thatseveral factors such as uncertainty and liquidity

1 The literature on the effectiveness of tax incentives onsaving such as IRAs and 401(k)s is also relevant towhether pension wealth constitutes a good substitute forother forms of wealth See for instance Eric M Engen et al(1996) James M Poterba et al (1996) and B DouglasBernheim (1997) and the references therein

1500 THE AMERICAN ECONOMIC REVIEW DECEMBER 2003

constraints might result in less than a full off-set However our empirical speci cation ismore exible than Galersquos in that we let thedegree of substitutability between pension andother forms of wealth vary with age recogniz-ing that the importance of these factors is likelyto be different for individuals at different stagesof their life cycle The paper most similar toours is Attanasio and Agar Brugiavini (2003)which has investigated the impact of the 1992reform of the Italian pension system Using twohousehold surveys collected before and after1992 they assess the effect that pension wealthhas on household saving In the Italian case asin our study the reform had different effects fordifferent groups of the population

The data we use are from the Family Expen-diture Survey (FES) covering a period in whichthree major pension reforms were implementedWe use the variation induced by these reformsand in particular the fact that they affect differ-ent groups of individuals differently to identifythe impact of changes in pension wealth onhousehold saving rates Our study goes beyonda simple differences-in-differences approachbecause we impose on the empirical analysis thestructure that we derive from economic theoryWe use the life-cycle framework to model thebehavioral response of every household If pen-sion reforms are not fully anticipated individ-ualsrsquo reactions will vary depending on when intheir life cycle they experience the reform forexample younger individuals will have moretime to absorb the changes entailed by the re-form In this context the life-cycle model givesus a framework in which we can specify aregression equation and in which we can inter-pret the estimated coef cients

While the relationship between pensionwealth and saving is relatively simple in a styl-ized model reality is likely to be much morecomplex In particular the presence of uncer-tainty (about income and rates of return) liquid-ity constraints the lack of liquidity of pensionwealth the interaction of saving for old agewith other savings motives and the interactionwith labor supply choices make the optimiza-tion problem of a typical agent very complexTrying to model all these features is extremelyhard and typically requires using numericalmethods in order to obtain a solution for theoptimization problem In this paper we use a

simpli ed theoretical setting to inform the spec-i cation of our regression equation and interpretthe results we obtain At the same time we keepour empirical speci cation exible to take intoaccount the fact that our simple model abstractsfrom very important features of reality

The paper is organized as follows In SectionI we give a brief overview of the UK pensionsystem and of the main reforms that havechanged its operation in the last 25 years InSection II we describe the data set we use andhow we construct for each individual householdin our sample an estimate of pension wealthWe do this by using information on the individ-ual household members and the pension legis-lation including its changes over the years InSection III we discuss the theoretical frameworkthat informs our econometric speci cation andpresent some preliminary evidence on the rela-tionship between pension wealth and savingSection IV deals with econometric issues andreports our main results Section V concludesthe paper

I The UK Pension System

Since the end of the last world war the publicpension system in the United Kingdom has beensubject to repeated changes Each decade hasseen at least one substantial pension reform Asa result entitlements to future bene ts exhibit afair amount of variation over time Moreovermany of these reforms have affected differentindividuals in different ways so that the in-duced changes in pension wealth (ie the ex-pected present value of future bene ts lessfuture contributions) also exhibit a considerableamount of cross-sectional variability In mostother industrialized countries pension reformshave only recently been included in the policyagenda so that the United Kingdom stands outin this respect as an interesting case to studyThe reform process has led to pension arrange-ments where both unfunded public and fundedprivate pensions are integral parts of the system

While the rules that govern the public com-ponent of the system are relatively straightfor-ward and homogeneous the private sector isvery heterogeneous People are enrolled in verydifferent schemes whose rules vary greatlyWithout knowing which pension plan someonebelongs to it is not possible even to approximate

1501VOL 93 NO 5 ATTANASIO AND ROHWEDDER PENSION WEALTH AND HOUSEHOLD SAVING

the personrsquos entitlements To our knowledgethere is no representative household survey inthe United Kingdom that would provide thisinformation forcing us to con ne our analysisto the impact of changes in public sectorschemes Nevertheless it is important to notethat this constraint does not interfere with the ndings of our study for two reasons Firstlyuntil 1987 participation in private pensionscould conceivably be assumed to be exogenouswith respect to saving choices as occupationalpensions were available only for those employ-ees whose employer provided such a schemeMoreover the introduction of SERPS (StateEarnings-Related Pension Scheme) in the1970rsquos did not change this and policy makerspaid particular attention in the design of SERPSnot to crowd out private pension provisions2

Coverage rates of occupational pensions werestable over that time overall it was between 49percent and 52 percent throughout our sampleperiod (Richard F Disney et al 1999) Cover-age increased gradually for women by about 6percent which goes along with women increas-ingly participating in the labor market In 1988the way public and private pensions wereintegrated changed making the assumptionof exogeneity less plausible3 Therefore welimit our analysis to the period before 1988Furthermore the heterogeneity among privatepension schemes which hindered their inclu-sion in the analysis in the rst place now be-comes a virtue Taken together with the fact thatthere have not been major regulatory changes inprivate pension arrangements between 1974 and1987 we argue that households observed in oursample do not experience any common shocksof considerable magnitudes in their private pen-sion wealth Hence as long as we control for

membership in private and public sector pen-sions our results should not suffer from theexclusion of a measure of private pensionwealth

In the remainder of this section we describethe evolution of the different components of thepublic pension scheme giving greater detailsfor the period we use in our study that is the1970rsquos to late 1980rsquos We start by describing thetwo main components of the UK public pen-sion system the at-rate Basic State Pension(BSP) and the so-called ldquoState Earnings-RelatedPension Schemerdquo (SERPS) We then explainthe possibility of opting out of the public sys-tem This is followed by a discussion of thevariations in pension wealth induced by thereforms that we use in our empirical analysis toidentify the effect of pension wealth on saving

A Basic State Pension (BSP)

The structure of the BSP was put in place in1948 It is a at-rate bene t scheme that iscompulsory for all workers and employees withearnings above a threshold the lower earn-ings limit When reaching state pension agemdashcurrently 60 for women and 65 for menmdashanindividual who has contributed at least nine-tenths of his or her working life is entitled to afull-rate pension that will be paid for the re-mainder of his or her life Virtually all menacquire entitlements to a full pension whereasuntil recently many women did not In that casetheir husbands can claim a dependantrsquos addi-tion which amounts to 60 percent of the fullrate4

Until the early 1970rsquos bene ts were up-ratedin a rather ad hoc way on average making upfor slightly more than average earnings growthFrom 1975 onwards they were increased

2 Andrew Dilnot et al (1994) state ldquoThe Social SecurityAct of 1975 introduced SERPS To avoid substituting forprivate sector provision occupational schemes were al-lowed to contract out of SERPSrdquo Contracting out wasallowed only if the private pension was at least as generousas SERPS In that case employers and employees weregranted a reduction in National Insurance Contributionswhich was designed to be comparable to the contributions toprivate pensions

3 We discuss this change and its implications in furtherdetail below when explaining the possibilities of opting outof public sector second-tier pensions A good discussion ofthe current UK pension system can be found in Disney etal (2001)

4 The reasons for fewer women acquiring their ownpension are twofold First until 1978 women had the pos-sibility to pay reduced National Insurance Contributions(the UK term for Social Security Contributions) in ex-change for forgoing bene ts to the Basic State Pensions intheir own right Furthermore many women have incompletecontribution records in a large part due to childbearing Thereform of 1978 dealt with this issue by explicitly recogniz-ing periods of ldquohome responsibilitiesrdquo as contribution yearsin the pension scheme It also introduced rules that wouldlead more divorced women to be able to claim their ownpension By 2002 all women will have had the chance totake full advantage of these changes


roughly in line with gross earnings In 1980ndash1981 the government decided to link them toprices onlymdasha step that would subsequentlyreduce considerably the growth of public pen-sions given that real earnings have exhibitedpositive growth on average As a result thevalue of the at-rate bene t which equaled 20percent of average earnings at its peak in thesecond half of the 1970rsquos has been erodedNow the value stands at just under 15 percent ofaverage earnings and is projected to fall furtherto be worth about 7 percent of average earningsby 20505

These indexation changes are the most im-portant reforms of the BSP contained in theperiod we study Note that this kind of reform isrelevant for everyone in the population and theeffects differ across households dependingmainly on the age of the head of household andin the case of married couples on the age of thespouse

B State Earnings-Related Pension Scheme(SERPS)

Legislation to introduce SERPS was passedin 1975 and the scheme was implemented in1978 It pays an additional pension that is linkedto earnings More precisely it pays 25 percentof those earnings that lie between the lower andthe upper earnings limitmdashtwo thresholds de- ned by the scheme Bene ts are calculated onthe basis of the best 20 years of earnings and arepayable together with the BSP6 The same re-tirement ages apply Until 1988 the only possi-bility to opt out of SERPS and to pay reducedNational Insurance Contributions (NIC) was ifthe employer provided an approved private pen-sion This was not at the discretion of the em-ployee but was decided by the employer a factthat is important in our empirical analysis and isdiscussed in further detail in the followingsubsection

C Opting Out

When SERPS was introduced the gov-ernment aimed to design an opting-outscheme to ensure that existing secondarypensions provided by the private sector wouldnot be crowded out by the new scheme Asa result membership in SERPS was com-pulsory only for those employees whose em-ployer did not offer an occupational pensionIt was not at the workerrsquos discretion whetherto participate in the new government schemeIn this setup which remained in place until1987 we argue that membership in SERPSwas not a choice variable for the employeebut an exogenous event This implicitly as-sumes that people with different attitudestowards saving do not systematically selectinto jobs that provide private pensionschemes7

From 1988 onwards this framework nolonger applied The new legislation ruled thatan employee could choose to opt out ofSERPS even if the employer did not offer aprivate occupational pension scheme In thiscase the employee could choose to join aso-called ldquoApproved Personal Pensionrdquo aform of individual retirement account thatmet the minimum criteria set out by the gov-ernment The new policy sought to increasefurther private pension coverage in the UnitedKingdom During the rst years the govern-ment offered an extra 2-percent incentive rebateon top of the reduced rate of National InsuranceContributions that a worker who opted outwould be entitled to8 An important implicationof this change especially in the context of thisstudy is that from 1988 onwards workers wereable to choose themselves whether to opt out ofSERPS Enrollment in SERPS could no longerbe considered an exogenous event for theworker after the date the new legislation wasimplemented For this reason we limit our anal-ysis to data before 1988

5 This projection assumes real earnings growth of 15percent per year and does not take into account the recentoff-the-rule increase of the Basic State Pension bene t inApril 2001

6 These are the rules applying to the period we studyThe 1986 reform announced changes to the computationsfor people retiring in April 1999 or thereafter

7 To our knowledge there is no rm evidence suggestingthat people systematically choose jobs with private pensionprovision

8 This incentive rebate was reduced to 1 percent inApril 1993 and only granted to those workers aged 30 andabove


D Variation in Pension Wealth and theDifferential Impact of the Pension Reforms

The UK pension system underwent manyreforms Our estimates of pension wealth re ectall the changes that were implemented duringthe period we consider However it is the vari-ation in the pension wealth variables caused bythe three most important and clear-cut reformsthat will mainly drive the identi cation of ourestimates in the empirical analysis These threemajor reforms include two indexation changesof the BSP in 1975 and in 1981 and the intro-duction of SERPS in 1978 While the index-ation changes decreased everybodyrsquos futureentitlements SERPS increased the public pen-sion wealth of those individuals who were notcovered by a private pension at the time andearned above the lower earnings limit

The indexation changes in the BSP affectedeverybody in the population since this part ofthe public pension scheme was universal Themagnitudes depended mainly on the age ofthe head of household and on the age of thespouse in the case of married couples Whilethe impact of this reform varied mostly acrossthe different date-of-birth cohorts it also var-ied within these groups due to differences inhousehold composition and age-pairs in thehouseholds

The introduction of SERPS affected cohortsborn after 1913 in the case of men (1918 forwomen) and targeted those workers who didnot yet have any private pension coverageSome people were not affected by this newscheme at all older cohorts who were retired bythe time the new scheme was implementedthose who already had a private pension andthose who have very low earnings Amongthose who could take advantage of SERPS theexpected entitlements were generally higher forlater cohorts This is because people who werealready close to retirement when SERPS cameinto being did not have many years remaining toaccumulate entitlements Furthermore later co-horts usually have higher earnings due to eco-nomic growth and therefore acquire higherentitlements on average Because SERPS isearnings-related there exists variation withincohorts due to differences in individual-levelearnings To exploit these differences we clas-sify our sample into four occupational groups

that differ in the shape of their lifetime earningpro les

In addition to the three important reforms inour period of study there are a number ofsmaller changes in pension wealth These weremostly due to minor updates in the informationavailable to the individuals when forming anidea about their expectations This concerns inparticular observing the actual up-rated bene tvalues for the BSP and revaluation factors forSERPS which were published every year andwhich individuals use to replace previously an-ticipated values with the actual realizationsEven though these are minor changes we incor-porate them in our calculation of pensionwealth

The expected pension wealth variables varymainly with age and occupation of the adultmembers of the households and their opting-out status with respect to the earnings-relatedscheme This is the variation we will use in ourempirical exercise to identify the effect of pen-sion wealth on savings

II Data Sources and Estimation of PensionWealth

Our main source of information is the UKFamily Expenditure Survey (FES) a time seriesof cross-sectional household surveys compris-ing roughly 7000 households per year As dis-cussed above we focus our analysis on the threemost important and clear-cut reforms of the1970rsquos and 1980rsquos ie the introduction ofSERPS and the two indexation changes of ben-e ts from the BSP We use observations span-ning the years from 1974 until 1987 focusingon people born between 1909 and 1968

We exclude from our sample householdsheaded by self-employed individuals whose in-come and consumption are often misreportedWe also exclude composite households that ishouseholds containing other adults than thehead of household and the spouse To reducethe in uence of a few outliers we trim thehouseholds that report income in the top andbottom 2 percent of the sample in each yearThis leaves us with a sample of about 4000households per year

In our data saving is measured as the residualbetween disposable household income and totalhousehold expenditure where the latter in-


cludes spending on durable goods The infor-mation on both income and expenditure is ofgood quality as documented in James Banksand Paul Johnson (1998) However our de ni-tion of saving is not ideal as for instance itexcludes capital gains on real estate and nan-cial assets

In addition to detailed information on expen-diture and family income which allows us tocompute saving the FES is also a rich sourcefor variables like earnings occupation and sev-eral demographic variables Combining thiswith our knowledge of the pension legislation inplace in each year we construct estimates of thepresent value of future pension bene ts net offuture contributions

A Pension Wealth

The FES data do not provide information onsubjective pension wealth expectations so thatthis variable has to be estimated We assumethat people have a reasonable understanding ofthe working of the scheme Given that everyoneis enrolled in the public pension system in someform general knowledge should be quite goodWe will compute the expected present value ofnet pension wealth where pension wealth isde ned as the sum of future bene ts assumingcontinued participation until retirement minusfuture contributions and use this measure as anestimate of perceived pension wealth

For each household observed during the cho-sen period we rst approximate the presentvalue of future bene ts both from the BSP andfrom SERPS For this purpose we use informa-tion on age sex and marital status of the adulthousehold members and the relevant legislationin the year of observation In a second step wecompute the present value of current and futurecontributions to public pensions schemes Wededuct these contributions from the values ob-tained in the rst step that is from the totalanticipated bene t receipts The result is whatwe refer to as pension wealth at the time ofobservation

There are many conceivable ways to computepension entitlements We refer the interestedreader to Appendix A where we discuss someconceptual issues involved in more detail Herewe shall only state the assumptions we makeand the main steps we use in our computations

We use the entitlements that people will haveacquired by the time they retire according tothe current legislation assuming they keepcontributing to the schemes they are enrolledin just as they do at the time they are observedin the data We take into account any reformsand future up-rating rules that have been leg-islated up to the time of observation Weassume that people expect the current legis-lation to persistWe net out current and future National Insur-ance Contributions (NICs)9

We express all values in constant prices andwe assume perfect foresight about in ationrates when computing future expectedbene tsWe assume that when forming their expec-tations people take their current characteris-tics such as marital status and their (non)participation in SERPS as given and xedWe account for uncertainty about longevityby applying survival probabilities to each pe-riod considered in the computations Themaximum attainable age denoted T is xedat 100We calculate lifetime earnings pro les thatare needed to compute entitlements forSERPS separately for groups de ned by co-hort occupation and sex using earnings in-formation from 32 years of cross sectionsfrom the FES and synthetic cohort tech-niques We describe the details of this proce-dure including the extrapolation over parts ofthe life cycle of each cohort not covered bythe survey in Appendix CWe assume that the age at which individualsexpect to retire is the of cial state pensionage of currently 65 and 60 for men andwomen respectively10

9 Note that NICs do not only pay for pension bene tsbut also provide the funds for other social security programsincluding unemployment statutory sick and maternity payincapacity bene t maternity allowance widowrsquos paymentwidowed motherrsquos allowance and widowrsquos pension No xed percentage is however assigned to these differentldquootherrdquo programs and compared to the payment of publicpension entitlements they are rather small

10 In face of the observation that on average individualsretire increasingly early it is worth noting that receipt ofpublic pension bene ts is conditional on reaching statutoryretirement age Hence early retirement trends affect publicpension wealth only in an indirect way early retirement will


We should stress that our computations re- ect only the knowledge of the period when theexpectation is formed That is for a householdwhose saving rate is observed at time t weestimate its pension wealth using informationon the current bene t rates earnings growthfactors in ation etc Changes in the rules willbe re ected in our calculation of pensionwealth

Given the assumptions above the formula forthe expected value of pension wealth at time tfor a single individual i Et(PWit) is de ned asthe present value of expected social securitybene ts reduced by the present value of currentand future social security contributions

(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t

R i21 w j z cj z stj

~1 1 r j

bitk denotes the annual level of bene ts ex-pressed in constant prices that will be receivedat time k according to the legislation at time tstk is the gender-speci c probability in period tof surviving until year k conditional on havingsurvived until period t Ri is the expected date of rst receipt of pension bene ts hence individ-ual irsquos retirement date r stands for the realinterest rate and T for the maximum attainableage Contributions in any one period are cal-culated by multiplying the expected level ofearnings at age j wj with the applicable con-tribution rate in place at the time cj taking intoaccount survival probabilities

The formula above applies to a single personFor married couples we take into account inher-itance rules that are relevant for pension enti-tlements This implies placing probabilities onthe events of joint survival as well as singlesurvival of the head of household and thespouse Hence the formula for married couplesbecomes

(2) Et~PW tc i

5 Ok 5 min~R1R2

Tbci tk z smtk z sftk 1 ~sftk 2 smtk z sftk

1 ~smtk 2 smtk z sftk z bsi tk

~1 1 rk 2 t

2 Oj5 t

Rm 2 1 w1j z ct z smtj

~1 1 r j 2 Ol 5 t

Rf 21 w2l z ct z sftl

~1 1 rl

where bcitkis the bene t rate for couple i in

period t to be paid in period k bsitk the bene trate that applies to a surviving single person i inperiod t and T the maximum attainable age Thebene t calculations run from the year when the rst member of the couple retires min(R1 R2)while the contribution summations span fromthe current period of observation until the end ofthe working life of each partner smtk is theprobability in period t for a man to survive untilyear k while sftk is the corresponding probabil-ity for a woman11 As in the case for singles theinformation on survival probabilities for menand women is taken from English Life TablesFor the probability of joint survival we use theproduct of the individual survival probabilitiesin that we do not have available any joint lifetables

These formulas are straightforward to applyonce the appropriate bene t rate is known Inthe case of the BSP the current bene t rate ispublished by the Department of Social Securityevery year For SERPS the bene t rates have tobe computed applying the contemporary set ofrules

B Cohort-Age Pro les of Pension Wealth

Having computed pension wealth for thehouseholds observed in the FES we now studyits variation over time and in the cross sectionThe pension reforms during our sample periodhave a differential impact on individuals de-pending on birth cohort and (for SERPS) occu-pation groups In this subsection we focusmainly on differences across cohorts and over

not reduce entitlements to the BSP as long as the individualhas contributed for the minimum number of years In thecase of SERPS bene t computations were originally basedon the best 20 years of earnings As long as a worker haspaid NICs for at least 20 years the impact of not workinguntil age 65 will be minor

11 All the relevant quantities such as the probabilities ofsurvival are adjusted for the actual age of the individuals inthe households considered No attempt is made however totake into account differential mortality by economic status


time The exact de nition of year-of-birth co-horts is given in Appendix B We should stressthat the variation in pension wealth we illustratehere is not the only one we use in our regressionanalysis To identify the parameters of interestwe also exploit the variation across occupationgroups within cohorts Groups were chosen tomaximize variation in both the level of pensionentitlements and in the effects of pension re-forms on these entitlements

We start by calculating cohort means for eachyear in the survey where a cohort is de ned bythe year of birth of the head of household Weplot the cohort-age pro les of these means inFigure 1 for BSP and in Figure 2 panels (a) and(b) for SERPS The expected value of pensionwealth (EPW) is set in real terms expressed in1996 prices and is discounted to the year inwhich the expectation is formed The numberscan be interpreted as the lump sum that has thesame present value as the personrsquos future ben-e ts net of future contributions Note that theway in which we compute pension wealth inthe absence of legislative changes EPW in-creases over the life cycle for three reasonsFirst older individuals need to discount overfewer periods so that the same entitlements areworth more in present value terms Second withevery extra year that an individual survivessome uncertainty about mortality is resolvedagain increasing the expected values Third ourpension wealth computations net out future con-tributions to the public pension scheme so thateach year fewer remaining contributions arededucted

Two important features emerge from Figures

1 and 2 First both pension wealth componentsvary a great deal as a consequence of the pen-sion reforms we are considering Second thisvariation is very different across cohorts

In Figure 1 the two marked downshifts in theBSP are due to the indexation changes rst in1974ndash1975 from an ad hoc regime to earningsindexation of bene ts and in 1981 a furtherchange towards price indexation Table 1 givesan idea of the magnitudes involved focusing onthe two large indexing changes and showing thelevel as well as the percentage changes in pen-sion wealth The rst indexation change of themid-1970rsquos led to an average decrease in EPWof 50 percent for all the cohorts considered hereHowever the effects differ greatly across co-horts The oldest cohort which was born be-tween 1909 and 1913 suffered a reduction inEPW of 25 percent while the youngest cohortslost around 80 percent of their expected wealthThe retirement period lies further in the futureand the slower growth rate of bene ts created amuch larger gap between previously expectedbene ts and adjusted expectations

Table 1 displays the impact of the indexationchange of the BSP in 1981 which linked bene tgrowth to prices It caused an overall reductionof wealth in the at-rate pension of 43 percentThe reductions range from 20 percent for thoseborn between 1909 and 1913 to as much as 81percent for the youngest cohort Both index-ation changes show as expected large varia-tions in pension wealth loss depending on whenin the life cycle the change happened

The same kind of graphs for SERPS is dis-played in Figure 2 where panel (a) refers tothose households where only one adult is part ofSERPS and panel (b) refers to couples whereboth adults participate in SERPS

In both panels we notice that the life-cycleexperiences of the cohorts differ tremendouslyThe oldest cohort had just a few years to buildup entitlements to the earnings-related schemeso their EPW from SERPS is small [see cohort(11) in particular] In addition later cohortshave higher earnings as a result of economicgrowth and also additional female earningsboth of which lead to higher entitlements perhousehold unit As shown in Table 2 the impor-tance of SERPS varied by cohort in 1975SERPS were only 04 percent of public pensionwealth for the cohort of 1909ndash1913 whereas for

FIGURE 1 COHORT-AGE PROFILES FOR PENSION WEALTH

FROM THE BSP 1974ndash1987


the cohort of 1954ndash1958 SERPS were 40 per-cent of total public pension wealth These g-ures show again the importance of the timing ofthe policy changes

While Figures 1 and 2 and Tables 1 and 2show differences across cohorts the data forEPW from both the BSP and from SERPS con-tain substantial variation within cohorts re ect-ing occupation opting-out status marital statusand different age matches among couples Togive an idea of the extent of this variation inTable 3 we display the fraction of total publicpension wealth that the earnings-related schemeaccounted for in 1975 but this time stratifyingnot only by cohort but also by occupation of thehead of household and opting-out status of thehousehold members We distinguish four occu-pation groups professional employees white

collar workers skilled workers and other occu-pations and unoccupied12

Table 3 shows large differences in the impor-tance of SERPS according to SERPS enroll-ment For example in the cohort of 1949ndash1953SERPS was about 59 percent of public pension

12 ldquoUnoccupiedrdquo means ldquonot workingrdquo This status isself-reported and could be permanent in the case of say ahousewife or temporary in the case of an unemployedperson For this group the question arises how to estimatetheir earnings pro les if we do not observe their wagesCertainly some of these people will have worked at somepoint in their life spans Nevertheless they are most likelyto belong to the low income groups in the population whomostly do not earn any entitlements to SERPS We thereforeset the EPW from SERPS to zero for individuals that belongto this group Note that the spouse of such an individual canstill be earning SERPS entitlements of any amount

TABLE 1mdashEXPECTED PENSION WEALTH FROM THE BSP(AMOUNTS IN 1996 BRITISH POUNDS)

Year

Cohort (year of birth)

9ndash13 14ndash18 19ndash23 24ndash28 29ndash33 34ndash38 39ndash43 44ndash48 49ndash53 54ndash58 All

1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160

Percent change na 220 219 224 232 239 248 258 271 281 243

Notes All summary statistics in this table are derived from the same sample that we also use in our nal estimation Detailswere provided at the beginning of the data description in Section II

a The number of observations in this cell is only 19 so that the numbers might give a distorted picture

(a) COUPLES WITH ONE ADULT OPTED OUT ONE IN (b) COUPLES BOTH IN SERPS SINGLES IN SERPS

FIGURE 2 COHORT-AGE PROFILES FOR PENSION WEALTH FROM SERPS 1974ndash1987


wealth among professionals when both spouseswere enrolled but just 25 percent of pensionwealth when only one spouse was enrolled Wealso see large variations in the importance ofSERPS across occupation categories

III A Theoretical Framework and Its EmpiricalImplications

A A Simple Model

The conceptual framework we use to inves-tigate the relationship between pension wealthand household savings is the life-cycle model Itguides our choice of the econometric speci ca-tion as well as the interpretation of the resultsIn this section we present the simplest versionof the model we can use to make the basicpoints about our econometric speci cation Wekeep the model simple in order to allow for aclosed-form solution and so we do not explic-itly consider uncertainty changes in rates ofreturn labor supply and many other importantelements

We analyze a four-period model so that wecan study how a pension reform affects peo-ple of different ages and how a pension re-form affects saving a number of years afterthe reform We assume that in the rst threeperiods of their life individuals work andreceive an exogenous income wi i 5 1 2 3In the last period they retire and receive pen-sion bene ts denoted by b During retirementin addition to their pension bene ts they canuse their savings that they might have accu-mulated during the rst three periods of theirlife These savings are assumed to appreciateover time at an exogenous and xed interestrate equal to r The individuals in our modelhave a log-utility function face no income orinterest rate uncertainty and have no bequestmotive Finally they do not face liquidity

constraints The optimization problem takesthe following form

(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3

where b is the factor by which future utility isdiscounted Note that the lifetime budget con-straint results from collapsing the budget con-straints of the four single periods

(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0

where At is the amount of assets held at the endof period t It is in the absence of liquidityconstraints that these four single constraints canbe collapsed into one

Solving the maximization problem yieldsthe optimal consumption levels for each pe-riod

(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

TABLE 2mdashEPW FROM SERPS BY COHORT PDV IN 1996 BRITISH POUNDS PERCENT OF TOTAL EPW IN 1975

Year



PDV in 1975 349 1787 4869 8828 11881 13315 12790 13594 14114 13669 10231Percent of total PW 04 22 64 124 175 221 247 299 363 401 168


51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r

Consumption in period 4 will equal the totalamount of remaining resources Notice that forc2 we present more than one expression The rst expression displays the solution as seenfrom period one The second expression showsthe solution as a function of current and futureresources as seen from the perspective of periodtwo Similarly c3 is written to depend on re-sources from the perspective of periods onetwo and three As long as no changes occurduring the four periods that were not anticipatedin period one the different expressions for c2and c3 are identical This can be veri ed bysubstituting the intertemporal budget constraintin (5) However should there be an unexpected

change in period t in some of the determinantsof the solution the equivalence breaks downsaving decisions taken before that date cannotbe changed and the individual has to reoptimizeover resources remaining from previous periods(At2 1) and future income To evaluate the ef-fect of an unexpected change in pension bene tsoccurring some time in period one on consump-tion (and saving) for an individual aged 2 onecan use the second expression for c2 whichtakes the asset level at the beginning of theperiod as given and determined by decisions inthe rst period For an individual aged 3 at thetime of reform we will use the third expressionfor c3

The simple point we want to make is thatwhile an increase in the exogenous level ofbene ts will decrease savings and saving ratesduring working life the effect will be differentfor individuals at different stages of their lifecycle The impact depends on when during theindividualrsquos lifetime the household learnedabout the change because it matters over howmany remaining periods the individual can dis-tribute the readjustment This corresponds to theadjustment discussed in Gale (1998) Further-more the magnitude of the effect we observedepends on how long the reform occurred be-fore the period of observation The combinationof these two factors determines the impact of achange in pension wealth on an individualsrsquoconsumption and savings choices in any oneperiod

TABLE 3mdashEPW FROM SERPS EXPRESSED AS A PERCENTAGE OF TOTAL PUBLIC PENSION WEALTH BY COHORT AND

OCCUPATION IN THE YEAR OF LEGISLATION 1975

Occupation


9ndash13 14ndash18 19ndash23 24ndash28 29ndash33

SERPS enrollment

Couplesone inone out

Couplesboth insingle

in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295

Skilled amp other 08 02 09 29 21 86 39 144 65 215

Unoccupied etc 00 01 00 02 00 05 00 03 na 44

All 07 03 10 32 26 103 58 190 83 273


B Empirical Specication

Rather than basing our empirical analysis onconsumption as in equation (5) we will base iton saving rates as this formulation is likely tolead to a better error structure From equation(5) one can derive an expression for saving ratesas a function of pension wealth For examplethe saving rate in period 2 is

(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r

where is a function of b given by one of thetwo expressions on the right-hand side of equa-tion (5) depending on when we observe thehousehold in the survey For example if an age2 household is observed in a reform year wewould use the second expression for c2 in equa-tion (5) while if it is observed the year after areform we would use the rst expression Givenb r and future pension entitlements b one cancalculate and z (b((1 1 r)2y2)) It is thelatter expression generalized to an N-periodproblem that we enter as a regressor in ourempirical speci cation for saving rates

The empirical speci cation generalized to amultiperiod framework is

(7) SRit 5 X it u 1 gX ~ti tri zEPWit

yitD 1 laquoit

where SRit is the saving rate of household iobserved at time t EPWit is the present value of(earned) expected pension wealth (whose com-putation was described in Section III) and yit iscurrent income (ti tri) is the normalizationfactor equivalent to in equation (6) by whichwe multiply each householdrsquos expected pensionwealth In a multiperiod model with log-utility

(ti tri) is given by the expression13

(8) ~ti tri 51 2 b

1 2 bE~T 2 triz b ti 2 tri 2 1

where ti denotes the t-th period in household irsquoslife cycle and tri the number of the life-cycleperiod in which the last reform experienced byhousehold i occurred t runs from 1 when thehousehold begins working life until E(T) (set to56 in our case) the number of the last periodthat households expect to reach on average Thevector X in equation (7) represents a number ofcontrol variables including group and timeeffects that are meant to capture various

13 The derivation of (ti tri) for a multiperiod modelwhich is clearly related to the adjustment factor in Gale(1998) is included in Appendix D

TABLE 3mdashContinued


34ndash38 39ndash43 44ndash48 49ndash53 54ndash58 All

SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242

Note namdashno observations in that cell


determinants of saving other than pensionwealth The groups are de ned by year of birthoccupation and SERPS enrollment

Given the structure of the model it would bedesirable to include a measure of householdwealth but our data do not contain informationon this variable We can proxy householdwealth by a exible (group-speci c) function ofage As our groups are de ned (among otherthings) by year-of-birth cohort including indi-cator variables for group and time is equivalentto considering a categorical variable in age Asimilar argument applies to including thepresent discounted value of future earnings inthe regression which also appears in the equa-tion for saving derived from the structuralmodel In some of the speci cations we triedwe included estimates of future earnings in Xand applied the same adjustment as to pensionwealth variables

A literal interpretation of our model in whichpension wealth is a perfect substitute of nan-cial wealth would imply that the coef cient gin equation (7) is 210 In what follows weestimate g and interpret it as a measure of thesubstitutability between nancial and pensionwealth Our coef cient g is therefore equivalentto the coef cient that Feldstein (1974) Kingand Dicks-Mireaux (1982) and many other au-thors have tried to estimate on micro- and ma-crodata14 To allow for more exibility in ourspeci cation we let the coef cient g varywith age re ecting the fact that the degree ofsubstitutability between nancial and pensionwealth might be different for individuals atdifferent points of their life cycle After ex-perimenting with various polynomial speci -cations we decided to let the coef cient be astep function of age The results using poly-nomials were similar and are available uponrequest

As we described in Section I the public pen-sion system in the United Kingdom consists oftwo different tiers the BSP and SERPS Thesetwo components vary substantially in theirstructure Therefore we let g take different val-

ues for each of these components and estimatethe following relationship

(9) SRit 5 X it u

1 g1X ~ti triSERPS z

EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit

C Preliminary Evidence on the RelationshipBetween Pension Wealth and Saving

Before taking equation (9) to the data orconsidering slightly more complicated modelsthat allow for different degrees of substitutabil-ity between nancial and pension wealth fordifferent ages we investigate whether we can nd any evidence in the raw data of a relation-ship between EPW and saving rates andwhether such evidence is consistent with ourtheoretical approach We focus on the twoepisodes that induced the largest changes inEPW the introduction of SERPS which coin-cided with the rst change in the indexationof the Basic State Pension in 1975 and thenext indexation change of the Basic StatePension in 1981

In order to control in the simplest possibleway for aggregate shocks and group differenceswithout imposing any further structure we re-gress saving rates on pension wealth adding ascontrols group and time dummies We de negroups in the same way as in Section II that ison the basis of cohort occupation and enroll-ment in SERPS Notice that as we condition onyear-of-birth cohort and time we also implicitlycontrol for age

The results we obtain are promising the re-gression of individual saving rates on the PV ofEPW as well as group and year dummies yieldsa negative relationship that is signi cant at the1-percent level Carrying out the same exercisefor the level of consumption the choice variableof our theoretical model leads to equivalentconclusions it provides evidence of a positiverelationship between consumption and EPWwhich is also signi cant at the 1-percent levelWe report the estimated coef cients on EPW inTable 4

14 Feldstein studied the time-series relationship betweenaggregate saving rates and pension wealth Dicks-Mireauxstudied the relationship between the stock of nancialwealth and pension wealth in microdata


The coef cients in Table 4 give the popula-tion average of the observed response to thechanges in EPW conditioning on time andgroup effects On average an increase in EPWof pound1000 leads to an increase in annual con-sumption spending of 80 pounds or an averageincrease of 008 percentage points in house-holdsrsquo saving rates

Having checked the existence of a simplerelationship between saving (or consumption)and pension wealth we move on to estimatingmore structural models based on equation (9)This analysis will allow us to estimate the de-gree of substitutability between nancial andpension wealth which cannot be inferred fromthe numbers in Table 4

IV Results

A Identi cation Using the DifferentialEffects of the Pension Reforms

There are several reasons why ordinary least-squares (OLS) estimation of equation (9) onhousehold data would yield biased and incon-sistent estimates First the subjective expectedvalue of pension wealth is unlikely to be equalto actual pension wealth furthermore we onlyhave an approximation to pension wealthTherefore we need to allow for the presence ofmeasurement error Moreover it is possible thatunobserved heterogeneity in the taste for sav-ings is related to the individual stock of (pen-sion) wealth For these reasons we take aninstrumental variable approach and use the pen-sion reforms to identify a number of instru-ments As the effects of these reforms weredifferent for different groups we use the inter-action of group dummies and year dummies as

instruments for our measure of pension wealthThe group indicators distinguish between co-horts occupations and enrollment in SERPSThe use of such a differences-in-differencesestimation strategy is legitimate if two condi-tions are satis ed once we control for groupand year dummies their interaction does notenter the equation for saving in its ownrightand pension wealth has variation overand above that captured by group and yeardummies

The rst assumption is an identi cation as-sumption and therefore is not testable We cantest the second by nding whether pensionreforms affect different groups in differentways The analysis presented in Section III sug-gests that this is the case and an F-test for thesigni cance of the interactions between yearand group dummies shows this formally That iswe reject at any sensible level of signi cancethe hypothesis that the variation in pensionwealth is fully explained by time and groupeffects Detailed results are available uponrequest

B Empirical Specications and Results

The empirical speci cation we use is slightlydifferent from the one in equation (9) in that weallow g1 and g2 to vary with age The rationalefor this is that our model omits aspects of realitythat are bound to have an impact on the substi-tutability between pension wealth and other as-sets While these simpli cations kept ourtheoretical framework analytically tractablethere are reasons to believe that the direct im-plementation of equation (9) would be too re-strictive For example we do not model liquidityconstraints which are likely to be more impor-tant among the younger population and arebound to affect the elasticity we are trying toestimate Therefore the speci cation we useallows the coef cients on (adjusted) pensionwealth to vary with age

Equation (9) includes in addition to futurepension wealth future earnings There are twopossible approaches to deal with this variableThe rst is to estimate it using a methodologysimilar to the one used for EPW Alternativelyas the present discounted value of future earn-ings is a function of age cohort and occupa-tion we can control for such a variable using

TABLE 4mdashREGRESSION OF SAVING RATES AND

CONSUMPTION ON EPW CONDITIONING ON GROUP AND

TIME EFFECTS CONSUMPTION AND EPW IN THOUSAND

POUNDS

Variable Coef cient on EPW p-value

Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)

Note Standard errors are in parentheses


group and age effects15 We have imple-mented both strategies and found that theresults for the effect of pension wealth are notaffected by this choice However we preferthe second strategy because in contrast to theEPW variable we have no exogenous varia-tion that we could use to instrument futureearnings in order to deal with measure-ment error and correlation with unobservedheterogeneity

In the pension wealth calculations and in thecomputation of we need to make an assump-tion about the discount factor b and the interestrate r We tried several combinations of valuesThose we report are for r 5 003 and b 5 098The results did not change substantially withdifferent values of the discount factor andthe interest rate We use annual data from1974ndash198716

In Table 5 we report the results from estimat-ing equation (9) While our regressions includetime and group dummies and some demo-graphic variables we only report the coef -cients on pension wealth from SERPS and fromthe BSP for different age groups These coef -cients are estimates of the degree of substi-tutability between the two types of pensionwealth and other wealth holdings As suchthey answer the question of the followingunderlying thought experiment If pensionwealth from SERPS (BSP) were increased by

1 pound what fraction of this amount wouldresult in a reduction in other wealth andeventually show up as (appropriately dis-counted) consumption We plot these coef -cients in Figure 3

For SERPS we see that for individuals abovethe age of 31 pension wealth is a good substi-tute for nancial savings Indeed for the indi-viduals in the top age group the coef cient is ashigh as 2075 implying that for an increase inSERPS pension wealth of 100 pounds theywould decrease nonpension wealth by 75pounds For the youngest individuals the esti-mated coef cient is not signi cantly differentfrom zero indicating no substitutability be-tween future pension bene ts and nancialsavings This result might be explained bybinding liquidity constraints for the youngestindividuals

For BSP we only nd a signi cant effect forthe youngest group and even for this group theeffect is relatively small (203) For all theother age groups the effect is not signi cantlydifferent from zero

These results are quite robust we have trieda number of different speci cations changingthe controls in the regression and the sampleover which we estimate it In particular wehave added estimates of future earnings agepolynomials to capture differences in the ageeffect within cohorts and demographic vari-ables All these experiments whose detailedresults are available on request con rmed thebasic pattern of age-speci c coef cients re-ported in Table 5

15 As noted earlier by controlling for group and timeeffects we are implicitly controlling for age because onedimension of the group de nitions is date-of-birth cohort

16 When we introduce future earnings we use the samediscount rate as for future pension bene ts that is a realrate of 3 percent

TABLE 5mdashESTIMATES OF THE SUBSTITUTABILITY OF

PRIVATE SAVING FOR EPW FROM SERPS AND BSP

Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)

Note Standard errors are in parenthesesFIGURE 3 ESTIMATED AGE PROFILES FOR THE EFFECTS OF

SERPS AND BSP


C Interpretation of the Regression Results

Our empirical results indicate that SERPSand nancial wealth are good substitutes for allbut the youngest individuals This nding isconsistent with the life-cycle model The ab-sence of an effect for individuals younger than32 may be an indication of binding liquidityconstraints for this group

Our estimates are substantially higher thanthose found in various empirical studies such asKing and Dicks-Mireaux (1982) Brugiavini(1987) Jappelli (1995) or Gustman and Stein-meier (1999) and they are more in line with theevidence presented in Gale (1998) This resultmight be an indication of the fact that the last setof authors failed to correct for the differentialeffects of pension wealth by age andor of theimportance of measurement error and simulta-neity biases Our methodology addresses bothof these issues Furthermore we exploit exog-enous variation induced by policy reforms Dis-ney et al (2001) discuss the likely effects of thepension reforms of the late 1980rsquos and 1990rsquoson saving behavior in the United KingdomWhile they do not use a formal econometricanalysis they argue for the degree of substitut-ability between (private) pension wealth and nancial wealth to be close to the one weestimate

The evidence on BSP is quite different as wedo not nd any signi cant effect of changes inthis component of pension wealth on savingrates except for the youngest individuals Onepossible explanation is that the variation we useto identify the coef cient of interest is exclu-sively induced by changes in the indexationrules Even though the effects proved quite sub-stantial as shown in Section III maybe peopledid not fully understand the implications at thetime the reform was implemented While theSERPS legislation was the outcome of a publicdebate that lasted many years the indexationchanges to the BSP were quite different in na-ture in 1975 explicit up-rating rules took theplace of implicit ones and in 1981 price index-ation was discussed to be a temporary measureat rst but was then turned into a permanentone

Another possible explanation for the differ-ence between the effect of changes in SERPSand BSP might be due to the fact that the poorer

part of the population does not earn pensionwealth from SERPS while still being entitled tothe BSP SERPS have a bottom threshold forearning bene ts but BSP does not17 Substitu-tion of pension wealth for private wealth in thepoorer part of the population is likely to besmall due to liquidity constraints Differentialenrollment combined with a lack of substitutionwould lead qualitatively to our results

V Conclusions

In this paper we use an estimate of pensionwealth from the public pension scheme to in-vestigate its impact on household saving behav-ior We focused on the time period thatencompassed three major reforms the introduc-tion of SERPS in 1978 which was legislated in1975 and the two indexation changes of theBSP in 1975 and 1981 The pension wealthpro les show substantial differences across andwithin cohorts and occupation groups The vari-ation induced by these reforms combined withimplications from economic theory allowedus to analyze the link between pension wealthand household savings rates in a way that goesbeyond a simple differences-in-differencesstrategy

The results we obtain indicate a considerabledegree of substitutabilityof SERPS for nancialwealth for example among 43ndash53-year-oldswe estimate an elasticity of substitution of about2065 and 2075 for the 54ndash64-year-oldsHowever we estimate little if any substitutabil-ity between the BSP and private wealth

Our results have important implicationsThey con rm qualitatively Feldsteinrsquos (1974) ndings which were based on time-series dataWe nd that once we allow the effect of pen-sion wealth to be age dependent for large frac-tions of the population the substitutabilitybetween pension and nancial wealth is rela-tively high This result is in accordance with thebasic prediction of the life-cycle model How-ever it does not hold for the youngest consum-ers who are likely to be affected by liquidityconstraints and for the Basic State Pension

17 As discussed in Dilnot et al (1994) the poorer part ofthe population tends not to have either SERPS or a privatepension and relies exclusively on the BSP for retirementincome


The implications of our results are also im-portant for the debate on pension reform and onthe adequacy of individual savings should pub-lic pensions be reduced households will in-crease their savings to make up for a large partof the loss There is however one importantmodi cation to these conclusions the resultsmight not extend to the poorer part of thepopulation since they were derived from theearnings-related tier of the public pensionscheme Poor households generally do not earnany entitlements from SERPS so for them therelationship between pension wealth and sav-ings might look different In this sense ourresults are in accordance with the studies thathave expressed concern that the reforms to theUK pension system during the 1980rsquos and1990rsquos have left some (relatively small) sectorsof the population without suf cient provisionsfor old age

APPENDIX A CONSTRUCTION OF THE VARIABLE

ldquoEXPECTED PENSION WEALTHrdquo (EPW)

In the absence of survey data for expectationsof PW we will use an estimate of actual antic-ipated entitlements

A Discussion of Some Conceptual Issues

There exist many conceivable ways of mea-suring expected pension wealth Obviously inorder to determine how to proceed a number ofchoices have to be made each of which hasimportant implications for the nal results Nat-urally the choices we make will be driven ei-ther by considerations of feasibility or bycoherence with the ultimate purpose of thisstudy What this means in detail should becomeclear in the course of the discussion

In face of the ultimate purpose of our com-putations that is to investigate the impact ofpension wealth on peoplersquos saving decisionsone would ideally want to enter subjective ex-pectations of pension wealth into the analysisThese perceived pension rights are likely todiffer from the true values The 1989 Retire-ment Survey has collected this informationHowever it only covers very few cohorts andwith only one observation we are not in theposition to follow individuals over time to iden-tify our parameter of interest Hence we need

to nd a concept that is likely to come closeto these subjective expectations but can besystematically computed from individualcharacteristics

Anticipated Versus Acquired RightsmdashIn thecase of anticipated rights individuals form ex-pectations about the bene ts that they shouldreceive during retirement if they continue tocontribute to the pension schemes as they cur-rently do The discounted values of these ex-pected bene t ows constitute the anticipatedrights that might in uencemdashamong otherthingsmdashindividual saving behavior Anotherpossibility would be that individuals rather con-sider those pension rights as important that theyalready have acquired instead of basing theirsaving decisions on some expectation about theusually distant future It is worth laying outwhat this roughly means in the case of the UKpublic pension scheme For the case of the at-rate part of the public pension scheme aslong as contribution records are not completedreduced rates apply Given that almost all maleworkers end up receiving the full rate it isunlikely that they would work out their cur-rently accrued rights The portion of womenentitled to a full pension in their own rights hasincreased over the past two decades especiallysince the recognition of ldquoHome ResponsibilityPeriodsrdquo was introduced18 Nevertheless alsofor them working out reduced rates seems anunlikely approach People will hence ratherhave these full amounts on mind instead ofworking out the fraction that they are so farentitled to in some period before retirement

For the earnings-related tier of the publicpension scheme (SERPS) the arguments looksimilar Especially if we believe that peoplehave at least a rough idea about their needs inretirement then in order to determine how muchextra saving they should involve in apart fromthe compulsory amounts they have to havesome expectations of what they will get fromthe public pension schemes in total

Therefore we base our computations on thenotion of anticipated rights

18 Home Responsibility Periods (HRP) were introducedin 1978 This change is also taken into account in ourcomputations of EPW


To predict future bene t ows people alsoneed to make assumptions about the future pathof a number of factors involved in the conceptof expected pension wealth

Pension ReformsmdashOne central issue is theevolution of the pension scheme itself and towhat extent people anticipate changes to thesystem Static expectations where individualstake the pension scheme ldquoas isrdquo ignoring thepossibility of reforms seems extremely rigid at rst sight particularly when considering theldquotraditionrdquo of pension reform in the UnitedKingdom over the past decades Neverthelessthe look at the systemrsquos history reveals at thesame time that the outcome of reforms stronglydepends on which part is in government in away that even anticipating the qualitative direc-tion of the system in the long run might bedif cult if not impossible That is why anyparticular assumption about the future evolutionof the system would be arbitrary therefore thestatic assumption may be simplistic but a pru-dent one

Concerning reforms that have been passedinto law but have not been implemented yet weassume that people integrate these changes intheir expectations This seems a reasonable as-sumption since this type of legislation is pre-ceded by a fair amount of public debate

Demographics and other Individual Informa-tionmdashSome individual characteristics that mat-ter for the calculation of pension bene ts mightchange over time Consider the example of asingle male worker in his mid-30rsquos The mag-nitude of his pension bene ts depends on theoutcomes of a number of variables

potential spells of unemployment and the en-tailed interruption NIC paymentspossible change in expected earnings due tojob changechange in marital statuslife expectancy

A way of dealing with these uncertaintieswould be to place probabilities on the variouspossible outcomes ideally cohort- and occupa-tion-speci c probabilities but this is beyondwhat we are doing in this study For marital

status we assume that people form their expec-tations on the basis of their current marital sta-tus ignoring the possibility that it might changeie we use the information recorded in the FESat the time of observation We adopt the samestrategy also for employment status andoccupation

B The Actual Pension Scheme A FeasibleSet of Simpli ed Rules19

Computationof Entitlements to the BSPmdashGiventhat the BSP is a at-rate scheme there are notmany different possible outcomes that need tobe considered either an individual meets therequirements to claim a full-rate pension ormdashifher contribution records are incompletemdasha re-duced rate applies Should a woman not qualifyfor a pension in her own right then her husbandcan claim a dependantrsquos addition for her on hiscontribution records

It is hard to know who is likely to be able toapply for a full pension at retirement age on asingle observation basis as one would need con-tribution histories It will therefore be necessaryto base the computations on simplifyingassumptions

The simpli cations listed below yield a rea-sonable approximation of the actual portions offull rates and married couplesrsquo rates that arepaid out in reality

Men always expect to complete their contri-bution records and to receive the full-rateBSPSingle women tend to have a similar workinglife as single men and therefore we assumethat they also acquire the entitlements for afull-rate BSPMarried women who retired before 1978never acquired entitlements to a full-rate pen-sionmdashmainly due to breaks in their workinglives for childbearing or because they choseto pay reduced National Insurance Contribu-tions and to forgo pension entitlements intheir own rights They therefore usually hadto rely on the dependantsrsquo rate which they

19 Tolleyrsquos Social Security amp State Bene ts Handbook(various years) describes the rules governing the UK pub-lic pension scheme in great detail


could claim on their husbandrsquos contributionsthat is the rate I apply in this caseWomen who retire in 2018 or later will all beentitled to a full-rate pension on their ownrights due to the recognition of home respon-sibility periods (HRP) as contribution yearsNote that by 2018 the 1978 HRP rules willapply to the entire working life of all women

Women retiring between the above bounds(ie between 1978 and 2018) increasingly pro tfrom the HRP rules To what extent this is the casefor each single woman is however impossible toknow We therefore suggest the following approx-imation the dependantsrsquo rate amounts to 60 per-cent of the full-rate BSP The transition period

lasts at most 40 years hence add 1 percent of thefull rate to the dependantsrsquo rate each year to takeaccount of the increasing recognition of HRPs

Based on these simpli cations a rather simplesituation for the BSPs emerges that is illustratedin Figure A1

We addressed the dif culty of dealing withreduced rates earlier ie that there is no way ofknowing for how many years an individual hasactually contributed to the scheme and withoutthat information we are unable to calculate theappropriate reduced rate Furthermore the FESdoes not distinguish singles from divorced peo-ple until 1978 As a consequence we are leftwith only two outcomes that is the full rate andthe married couplersquos rate not counting extra the

FIGURE A1 ENTITLEMENTS TO THE BSP A SIMPLIFIED SCHEME


transitional outcomes for married couples be-tween 1979 and 2018

Computation of SERPS EntitlementsmdashTowork out the bene t formula for SERPS belowlifetime earnings pro les are required Theirestimation is explained in Appendix C

The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt

and Wt 5 UELt if Wt UELt

Wtmdashweekly gross earnings at time t

LELmdashLower Earnings Limit

UELmdashUpper Earnings Limit

Rmdashretirement age

xRtmdashaccrual factor

To calculate the weekly SERPS entitlementsfor each relevant tax year the individual weeklyearnings are revalued to the year prior to retire-ment age The Department of Social Securitypublishes these revaluation factors every yearwhich are captured by YR2 1Yt above These aresupposed to preserve the value of ldquopastrdquoamounts along with average earnings growthFrom the resulting amount the lower earningslimit of that very preretirement year is deducted toobtain the so-called ldquoexcess earningsrdquo These aremultiplied with the accrual factor as xRt that wasoriginally xed at 180 for each year of serviceSumming up the calculated amounts for the 20best years of earnings during which the individualpaid National Insurance Contributions will yieldthe weekly bene t that an individualearned in thisscheme The accrual factor as well as the calcula-tion of excess earnings was changed in subsequentreforms reducing the generosity of the scheme

APPENDIX B DATA DETAILS AND COHORT

DEFINITIONS

We use a sequence of cross sections from theFamily Expenditure Survey spanning the period1974 to 1987 (see Table B1) Given the purpose

of our study we exclude households whosemain earner is self-employed or reported to beretired at the date of observation We furtherexclude composite households

This leaves us with roughly 4000 householdobservations per sample year

APPENDIX C EARNINGS PROFILES

The lifetimeearningspro les are required to workoutSERPS entitlements We construct these for eachsex and occupation group of different cohorts

Basic Strategy

Use the 32 years of FES data to computeaverage cohort earnings for the years whereeach sexoccupationcohort group is ob-served We distinguish four different occupa-tion groups ldquoprofessionalrdquo ldquowhite collarrdquoldquoskilled and other occupationsrdquo ldquorestrdquo (mainlythe unoccupied)20

Despite the length of the time series of FESsurveys each of these groups still exhibit

20 Note that the last group mainly consists of zero- orclose to zero-earners Being unoccupied is usually a transi-tory state for heads of households and hence also not arepresentative state in the life cycle of a head of householdMost people included in this last group are individuals onvery low incomes who mostly do not earn any or only verysmall entitlements to SERPS Hence we do not estimate anyearnings pro les for this group and set their SERPS entitle-ments to zero

TABLE B1mdashCOHORT DEFINITION

Cohortnumbera Date of birth

Years observedin the sample

11 1909ndash1913 1974ndash197716 1914ndash1918 1974ndash198221 1919ndash1923 1974ndash198726 1924ndash1928 1974ndash198731 1929ndash1933 1974ndash198736 1934ndash1938 1974ndash198741 1939ndash1943 1974ndash198746 1944ndash1948 1974ndash198751 1949ndash1953 1974ndash198756 1954ndash1958 1974ndash198761 1959ndash1963 1979ndash198766 1964ndash1968 1984ndash1987

a Cohort numbers re ect the midpoint of the ve-yearinterval spanned by each cohort group


some missing values in its lifetime pro leThese are extrapolated using the approachsuggested in Attanasio and Banks (1998)where they construct lifetime pro les of var-ious variables by using the information ofadjacent cohorts that are observed at ageswhere another cohort in question is not Themissing parts in a pro le are hence extrapo-lated by applying a weighted average of thedifferences observed for other cohorts Theresulting pro les are smoothed using a Ker-nel estimator

Sample for Estimating Earnings ProlesmdashTheearnings pro les will be used to compute theSERPS entitlements of individuals Hence thequestion arises whether the earnings pro lesshould only be estimated on the sample of thoseto whom these earnings will actually be as-signed in the pension wealth computations (iepeople contracted-in to the second tier of thepublic pension scheme) or should we rather usethe entire population

We decide to use the entire population fortwo main reasons First we are interested inlifetime pro les ie we also have to work outearnings observations for the years before 1978when SERPS did not exist and opting out didnot exist We could of course use private pen-sion contributions as a proxy This strategywould however lead to considerably reducedcell sizes

Another detail is related to employment sta-tus and how to deal with unemployed individ-uals Some of these may be unoccupiedthroughout their lives while others might beunemployed only in the period we observethem but are participating in the labor forceotherwise We include all zero-income individ-uals in the sample on which we estimate theaverage earnings pro les so that the portion ofzero earners is well taken into account Ourapproach is guided by the desire to obtain thecorrect cohort average of lifetime earnings

APPENDIX D DERIVATION OF (ti tri)

In the derivation we will use the following

(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r

The starting point is equation (5) In the caseof no reforms the generalized term for at timet follows from considering the factor in front ofthe parenthesis in the rst expressions for eachtime period in equation (5)

(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1

Using (D1) this can be rewritten as

(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1

To generalize further to accommodate theoccurrence of a reform at time tr let us assumethat in the four-period model a reform tookplace at the end of period one The consumerneeds to reoptimize her choices over the re-maining periods two to four In equation (5) thesecond expressions for periods two and threeapply The following pattern for the factor infront of the parenthesis emerges for any timeperiod t after the reform in tr

(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1

Replacing T the maximum attainable pe-riod in a personrsquos life cycle with the expec-tation and indexing the time periods to re ectthat individuals experience a reform in agiven year at different stages of their lifecycle yields the generalized form of the ad-justment factor (ti tri) stated in equation(8) and that we use in our analysis Note thatin the case of multiple reforms over time thevalue of tr in the expressions for the adjust-


ment factor is determined by the timing of themost recent reform

REFERENCES

Attanasio Orazio P and Banks James ldquoTrendsin Household Saving A Tale of Two Coun-triesrdquo Working Paper No 9815 Institute forFiscal Studies 1998

Attanasio Orazio P and Brugiavini Agar ldquoSo-cial Security and Householdsrsquo SavingrdquoQuarterly Journal of Economics 2003(forthcoming)

Banks James and Johnson Paul eds How reli-able is the family expenditure survey Trendsin incomes and expenditure over time Lon-don Institute for Fiscal Studies 1998

Bernheim B Douglas ldquoRethinking Saving Incen-tivesrdquo in A A Auerbach ed Fiscal policyLessons from economic research CambridgeMA MIT Press 1997 pp 259ndash313

Brugiavini Agar ldquoEmpirical Evidence onWealth Accumulation and the Effects of Pen-sion Wealth An Application to Italian CrossSection Datardquo Financial Markets GroupDP 20 LSE London 1987

Diamond Peter A and Hausman Jerry A ldquoIndi-vidual Retirement and Savings BehaviorrdquoJournal of Public Economics FebruaryMarch 1984 23(1ndash2) pp 81ndash114

Dilnot Andrew Disney Richard Johnson Pauland Whitehouse Edward Pension policy inthe UK An economic analysis London In-stitute for Fiscal Studies May 1994

Disney Richard F Emmerson Carl G and Tan-ner Sarah ldquoPartnership in Pensions An As-sessmentrdquo London Institute for FiscalStudies Commentary No 78 1999

Disney Richard F Emmerson Carl G andWake eld Matthew ldquoPension Reform andSaving in Britainrdquo Oxford Review of Eco-nomic Policy Spring 2001 17(1) pp 70ndash94

Engen Eric M Gale William G and Scholz

John Karl ldquoThe Illusory Effect of SavingIncentives on Savingrdquo Journal of EconomicPerspectives Fall 1996 10(4) pp 113ndash38

English Life Tables Government Actuaryrsquos De-partment various issues

Family Expenditure Survey Waves spanning theyears 1974ndash1987 made available by the Of- ce for National Statistics (ONS) through theESRC data archive

Feldstein Martin S ldquoSocial Security InducedRetirement and Aggregate Capital Accu-mulationrdquo Journal of Political EconomySeptemberOctober 1974 82(5) pp 905ndash26

Gale William G ldquoThe Effects of Pensions onHousehold Wealth A Reevaluation of The-ory and Evidencerdquo Journal of PoliticalEconomy August 1998 106(4) pp 706ndash23

Gustman Alan L and Steinmeier Thomas LldquoEffects of Pensions on Savings Analysiswith Data from the Health and RetirementStudyrdquo Carnegie-Rochester Conference Se-ries on Public Policy June 1999 50(99) pp271ndash324

Hubbard R Glenn ldquoPension Wealth and Indi-vidual Saving Some New Evidencerdquo Jour-nal of Money Credit and Banking May1986 18(2) pp 167ndash78

Jappelli Tullio ldquoDoes Social Security Reducethe Accumulation of Private Wealth Evi-dence from Italian Survey Datardquo RicercheEconomiche March 1995 49(1) pp 1ndash31

King Mervin A and Dicks-Mireaux Louis AldquoAsset Holdings and the Life-Cyclerdquo Eco-nomic Journal June 1982 92(366) pp 247ndash67

Poterba James M Venti Steven F and WiseDavid A ldquoHow Retirement Saving ProgramsIncrease Savingrdquo Journal of Economic Per-spectives Fall 1996 10(4) pp 91ndash112

Tolleyrsquos Social Security amp State Bene ts HandbookLondon Tolley Publishing Company Ltdvarious years


nancial wealth by 10 or 18 cents depending onthe methodology

Peter A Diamond and Jerry A Hausman(1984) and R Glenn Hubbard (1986) usingUS data nd even smaller offsets than Kingand Dicks-Mireaux (1982) Agar Brugiavini(1987) and Tullio Jappelli (1995) have carriedout exercises similar to those of King andDicks-Mireaux (1982) on Italian data obtaininglarger estimates of the degree of substitutabilitybetween private wealth and public pensionprovisions

More recently the relationship between pen-sion wealth and savings has received renewedattention William G Gale (1998) uses USmicrodata from the Survey of Consumer Fi-nances to assess the extent to which changes inpension wealth are offset by changes in otherforms of savings Gale (1998) as we do belowstresses the importance of adjusting pensionwealth for the age of the individual He ndsthat for his favorite speci cation the offset issubstantial between 039 and 082 dependingon the estimator used Alan L Gustman andThomas L Steinmeier (1999) on the otherhand reach different conclusions using datafrom the Health and Retirement Study (HRS)They nd very small and insigni cant offsets ofpension wealth to total wealth1

The scarcity of empirical evidence on therelationship between pension wealth and savingbehavior is in part due to the severe data limi-tations that researchers face in this area Aggre-gate time-series information while it coverspotentially long time periods and thereforechanges in pension wealth is of limited usebecause of aggregation issues Data sets con-taining individual-level information on incomeand consumption (and therefore saving) are fewand far between Moreover data sets that con-tain this type of information very rarely containinformation on nancial wealth and even less onpension entitlements In addition to the limita-tions in available data sets pension wealth doesnot exhibit much exogenous variation espe-

cially because microdata sets typically coverrelatively short time periods Therefore differ-ences in pension wealth among individualscould re ect differences in tastes for saving

The approach we use in this paper differsfrom those used in the literature in two impor-tant dimensions First the data of our studyallow us to identify the parameter of interest ina much more robust way than in previous stud-ies Rather than using data on wealth we con-sider the implications of different levels ofpension wealth for saving rates We computethese from high-quality household data thatcontain detailed information on income andconsumption and go back to the early 1970rsquosBecause we have a long series of cross sectionswe can exploit not just cross-sectional variationbut also variation over time induced by severalimportant reforms to the UK public pensionsystem which affected different groups of indi-viduals differently Our period of study containsas many as three major reforms that inducedsubstantial exogenous variation in pensionwealth On the basis of these data we exploit thevariability in pension wealth induced by thereforms to identify the relationship betweenpension wealth and saving rates Second wecombine the differences-in-differences estima-tions with important implications from a simpletheoretical framework on how to relate stockand ow variables and on how to control fortiming effects of the reforms with respect to theage of the household and with respect to whenthe household is observed in the data As aresult we are able to derive an empirical specication in which the coef cients of interest canbe directly interpreted as the degree of substi-tutability between nancial and pension wealth

The conceptual framework we use is that of alife-cycle model in which individuals saveamong other reasons to nance their retire-ment In a simple version of the model pensionwealth is a perfect substitute of nancial wealthOur approach like the one in Gale (1998) rec-ognizes that the effect of a change in pensionwealth on saving behavior depends on the po-sition of an individual over her life cycle More-over consistently with the model the effect onobserved saving rates depends on when in thepast the individual experienced an (unexpected)pension reform As Gale we recognize thatseveral factors such as uncertainty and liquidity

1 The literature on the effectiveness of tax incentives onsaving such as IRAs and 401(k)s is also relevant towhether pension wealth constitutes a good substitute forother forms of wealth See for instance Eric M Engen et al(1996) James M Poterba et al (1996) and B DouglasBernheim (1997) and the references therein


























C Opting Out






















A Pension Wealth











(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t


~1 1 r j



(2) Et~PW tc i

5 Ok 5 min~R1R2



~1 1 rk 2 t

2 Oj5 t


~1 1 r j 2 Ol 5 t


~1 1 rl


























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES















































C Opting Out






















A Pension Wealth











(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t


~1 1 r j



(2) Et~PW tc i

5 Ok 5 min~R1R2



~1 1 rk 2 t

2 Oj5 t


~1 1 r j 2 Ol 5 t


~1 1 rl


























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES






































C Opting Out






















A Pension Wealth











(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t


~1 1 r j



(2) Et~PW tc i

5 Ok 5 min~R1R2



~1 1 rk 2 t

2 Oj5 t


~1 1 r j 2 Ol 5 t


~1 1 rl


























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES



























C Opting Out






















A Pension Wealth











(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t


~1 1 r j



(2) Et~PW tc i

5 Ok 5 min~R1R2



~1 1 rk 2 t

2 Oj5 t


~1 1 r j 2 Ol 5 t


~1 1 rl


























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES





































A Pension Wealth











(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t


~1 1 r j



(2) Et~PW tc i

5 Ok 5 min~R1R2



~1 1 rk 2 t

2 Oj5 t


~1 1 r j 2 Ol 5 t


~1 1 rl


























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES

























A Pension Wealth











(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t


~1 1 r j



(2) Et~PW tc i

5 Ok 5 min~R1R2



~1 1 rk 2 t

2 Oj5 t


~1 1 r j 2 Ol 5 t


~1 1 rl


























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES

























(1) Et ~PW it

5 Ok 5 R i

T b itk z stk

~1 1 rk 2 t 2 Oj 5 t


~1 1 r j



(2) Et~PW tc i

5 Ok 5 min~R1R2



~1 1 rk 2 t

2 Oj5 t


~1 1 r j 2 Ol 5 t


~1 1 rl


























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES








































Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES





























Year



1974 106723 111578 108864 107442 105580 102823 99514 91497 87146 83200 1019271975 79819 78536 71522 62249 55826 46834 39068 31914 24719 20420a 50492

Percent change 225 230 234 242 247 254 261 265 272 275a 250

1980 na 85576 87738 78483 70302 62940 54746 46806 39247 32257 584611981 na 68624 71110 59348 47837 38494 28644 19643 11508 6214 33160









A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES

























A A Simple Model




(3)

max$ct t 5 14

Ot 5 1

4

bt2 1log~ct

stOt 5 1

4 ct

~1 1 rt2 1 O

t5 1

3 X wt

~1 1 rt2 1D 1b

~1 1 r3


(4) At 5 At 2 1~1 1 r 1 wt 2 ct t 5 1 2 3

A0 5 A4 5 0



(5)

c1 51

1 1 b 1 b2 1 b3

3 w1 1w2

1 1 r1

w3

~1 1 r2 1b

~1 1 r3

c2 5b

1 1 b 1 b2 1 b3

3 w1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2


Year





51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES























51

1 1 b 1 b2

3 A1 ~1 1 r 1 w2 1w3

~1 1 r1

b

~1 1 r2

c3 5b2

1 1 b 1 b2 1 b3

3 w1 ~1 1 r2 1 w2~1 1 r 1 w3 1b

~1 1 r

5b

1 1 b 1 b2

3 A1 ~1 1 r2 1 w2 ~1 1 r 1 w3 1b

~1 1 r






Occupation



SERPS enrollment



in



in



in



in



in

Professional na 07 12 65 32 190 89 280 100 404

White collar 08 05 10 49 27 141 61 229 89 295



All 07 03 10 32 26 103 58 190 83 273




(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES

























(6)y2 2 c2

y25 1 2 z

b

~1 1 r2y2

2 z1y2

w1 ~1 1 r 1 w2 1w3

1 1 r




yitD 1 laquoit



(8) ~ti tri 51 2 b







SERPS enrollment



in



in



in



in



in



in

120 471 142 481 164 527 249 586 na 684 115 384

106 364 86 396 139 427 250 490 232 534 76 305

106 255 88 279 156 338 151 324 151 374 61 179

00 15 00 34 00 467 00 17 00 00 00 10

108 322 97 355 147 398 230 418 200 448 77 242








(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES




























(9) SRit 5 X it u


EPWitSERPS

yitD

1 g2X ~ti triBSP z

EPWitBSP

yitD 1 laquoit









IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES

























IV Results











POUNDS


Saving rate 2000087 0000(000017)

Consumption 008347 0000(000234)














Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES


































Age group SERPS BSP

20ndash31 00135 203061(0334) (0133)

32ndash42 205472 00060(0277) (0139)

43ndash53 206511 00432(0269) (0087)

54ndash64 207487 00351(0243) (0040)


SERPS AND BSP








V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES





























V Conclusions










































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES



























































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES














































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES
































The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES

























The SERPS formula

(A1) bSERPS 5 Ot 5 1978

R XWt

YR 2 1

Yt2 LELR 2 1DxRt

if LELt Wt









DEFINITIONS






Basic Strategy
















(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES





























(D1) Oj 5 0

n 2 1

rj 51 2 rn

1 2 r


(D2) ~t tr 5 0

51

1 1 b 1 b2 1 1 bT 2 1 z b t 2 1


(D3) ~t tr 5 0 51 2 b

1 2 bT z b t 2 1


(D4) ~t tr

51

1 1 b 1 b2 1 1 bT 2 tr 2 1 z b t 2 tr 2 1

for t tr


(D5) ~t tr 51 2 b

1 2 bT 2 tr z b t 2 tr 2 1




REFERENCES
























REFERENCES























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