Optiom md conclusionsexprwsti in &k dommcnta tiose of tie atior(s)

md donotn=~stily reprcsmtm officialpositionoftic Bureauof Ltir SIfiIkti~

ortie U.S.Dep~ent ofL&oI.

.

,.,

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.-
Retirementin a Family Context:

A StructuralModelfor Husbands and Wves

Man L. GUS=

Dartmoufi College md National B~eau of Economic Resemch

Thomas L. Steinmeier

Texas Tech Univmsity

January 1994

~is papr W= fundsd by the U.S. Depwent of hbor, B-n of hbor Smdstics, under tiant Numkr

E-9-J-l-W&: Opinions stated in WISpaper do not nwessarily re~esent the offIciafposition or policy of

tie U.S. Depment of bbor. Resmrch sup~t was dso povidd by the National Institute on Aging.

Any opinions expres~ti afso do not repm=nt tie opinions of the W or the NB~. This paper is part of

the NB~ progrmns in hbor Studies snd Aging. The authms wish D thank Andrew Samwick, Olivia

Mkhell, snd ptici~ts in seminms held at the Bureau of ~bor Statistics and the ~~ Summer

Institute fm providing helpful comments.
NLS

Discussion

- Papers
I. Introduction.

This paper specKzes and estimates a structural model of the retirement decisions of

husbands md wives. The feature of the data that is of centraJ interest to us”is the tendency of

husbmds artd wives to retire together. An econometric approach is developed for estimating

preferences of both spouses jointly and is implemented using data from the National

Longitudind Survey of Mature Women (NLS), a sumey that provides the most recent data

avtilable for a joint retirement study. Alternative specifications of joint decision mtig =e

tested, md the imponmce of vtious sources of interdependence in decision making me

investigated.

The present mdysis joins together two brmches of the retirement literature. In one,

stmcturaJ retirement models ~e estimated from data on individuds, usually men, while

ignoring the retirement deckio”ns md retirement status of their spouse.’ fn the other,

retirement decisions of husbmds and wives, md the tendency of their retirement dates to

cluster, aze artdyzed in the context of a reduced fom model.?

To join these stmrrds of the literature, this paper extends stmcturrd retirement modeling

to inco~orate the joint detemrination of retirement decisions of husbands md wives.3 In

1. See, for example, Bufiless azrd Moffitt (1984), Fields and Mitchell ( 1984), Gustman and

Steinmeier (1986a fid b), Stock and Wise (1990a and b), Berkovec md Stem (1991) md

Lumsdairre, Stock and Wise (1990, 1992a and b).

1

2. Estimates of systems of reduced fom retirement equations, such as those in Clink md

Johnson (1980) attd Hurd (1990), suggest the imponarrce of the spouse’s retirement status, and

of the joint determination of the retirement decisions of husbmds and wives.

3. One paper which comes closest to bridging these two strands of the. literature is Pozzebon

md Mitchell (1989). That study fits a version of the Fields aud Mitchell stmcturd model of

retirement to data for retied women using the obsewations for worting wives that ~e

available in the Retirement Histo~ Study. It assumes that the retirement decision of the
particular, the model is designed to recognim a number of potential sources of

interdependence in the retirement decisions of both spouses. In the opportunity set, jobs may

be selected with peaks in pension accrual profiles that encourage joint retirement. On the

preference side, each spouse’s utihty may depend on the retirement status of the” other spouse:

the preferences of each spouse may be correlated; and each spouse may not make a retirement

decision independently, but may collude to insure that the retirement decision of each is

jointly optimal.

In a world where both the husband and wife are more and more likely to be working

untfl the retirement years, this kind of a model will be increasingly necessa~ to assess how

pension, social security and other retirement related policies affect retirement outcomes,

including the question of whether pohcy measures which affect the retirement decision of one

family member cart irldtiectly influence the retirement of the remaining spouse.

A second purpose of this paper is to provide a structural retirement analysis using much

more recent data for a nationally repr~entative panel study than has been used in the past.q

The women in the National Longitudinal Survey of Mature Women (NLS) were born between

1923 and 1937. In the last year for which the survey is available: 1989, they were 52 to 66

husband is predetermined from the perspective of the wife’s decision.

4. Most structural analyses which are based on natiorrafly representative panel data sets, even

recently completed studies, have made use of the Retirement Histo~ Study (RHS), a

[ongitudind survey with cohorts born between 1906 and “1911. Only very limited information

was provided in the RHS on the labor market activities of wives. In addition, even if

sufficient information had been provided in the RHS for a family labor market study, the

cohorts in the RHS would be outdated because the participation patterns of wives have

changed so drastically over the past two decades. Studies which use data from the past five

or ten years have not employed data which is nationaRy representative. See, for example,

Lumsdaine, Stock and Wise ( 1990, 1992a and b).

2
years old, about as young as feasible for a retirement study.

+ X,.*

The paper dso addresses a number of econometric and behavioral issues. One issu& is

selection bias. In art old panel such as the RHS, afl couples have retired, so there is complete

information on retirement dates md on the characteristics of dl individuals included in the

sample. In a more recent panel such as the Natiortaf Longitudind Survey of Mature Women,

many of the couples are too young for both to have retired. Accordingly, in the proc~s of the

analysis, we deaf explicitly with truncation of continuing employment spells. A related

selection problem occurs in data sets which are restricted to retirees, such as the Survey of

Newly Retired Beneficiaries an~y=d by Hurd (1990).

k the course of specifying and estimating the retirement model for couples, we will

address the following specific questions How does the retirement behavior of each spouse

compare to that of the other? To what extent is the wife’s retirement decision influenced by

the husbands, the husbands decision influenced by the wife’s, and to what extent are their

unmeasured tastes correlated? How does interdependence in the opportunity set and in

preferences affect the coordination of retirement by the spouses? What are the effects on

model parameters of entirely ignoring interactions ii preferences? What are the effects of

treating each spouse’s retirement decision as exogenous in estimating the retirement behavior

of the other?

The next section will present evidence from the NLS that in fact, in the raw data, there

is a noticeable tendency among couples who have both retired to retire together. A family

labor supply model is developed in Section 111. Section IV details the data preparation and

presents aftemative estimates of the model. Section V presents some simulations based upon

3
the =timated model, concentrating mainly on the extent to which the husbands and wife’s

retirement deci~ons me coordtiated, A finaf section presents some concluding thoughts. —

IL Evidence of Joint Retirement.

There is not much point in investigating the cause of couples tending to retire together

~ the phenomenon is not evident empiric~ly. The purpose of this section is to verify that the

phenomenon does exist in the NLS older women’s data, and to document the sample which k

used in this section and in the remainder of the project.

Table 1

Sample Inclusion Criteria For The NLS Data Used h This Study

Selection Criteria

Number of women in the 1967 NLS sumey

With obser, atl!-,rrsIn dl NLS surveys

With the same husband in atl suweys

Who worked fu~-time at age 50

With husband who worked full time at age 50

With at least one full-time wage obsemation for the wife

With ~ least one fu~-time wage obsemation for the husband

5083

2715

1520

654

594

578

564

Note: The numbers for each line represent the number of respondents in the previous

line with the additiond characteristic

The sample we use from the National Longitudinal Survey of Mature Women (NLS) is

restricted in several ways in order to meet the objectives of this paper. Table I indicates the

effects on the number of obwmations applying various screens for inclusion in the sample.”

4
First, the sample is restricted to women who remained in the survey? Second, since the

project focuses on the joint retirement decitions of husbmds and wives, the sample is

restricted to women who were married to the same mart in each yea. of the sample, and to

those couples both of whose members survived. 6 Third, the sample is restricted to couples for

whom the idea of retirement is a meaningful concept. Specifically, it excludes any couple if

either the husband or wife quit full-time work for good prior to age 50.7 Additiontiy, it

excludes any couple if the wife did not have at least three consecutive surveys of fu~-time

work after age 40, or if the husband worked full-time for less than two-thirds of the sample

years before he left full-time work for good.* Thus the sample does not include women who

tried working for a year or two and then dropped out of the labor force. For these women, it

would be stretching things to construe the fact that they dropped out of the labor force as

5. Most of the women who do not meet this criterion were women who attritted permmtently

from the survey. Typic~ly, they were interviewed in the early years and then dropped out

Cases where one or two interviews are missing in the middle of the survey are relatively rare.

Since the initi~ age is 30 to M in 1967, most of the women who dropped out in the early

years did so before reaching retirement age,, md hence these women would not shed much

light on a retirement artrdysis in any case.

6. The survey do=. not directly ask the question “Are you married to the same man as you

were during the previous survey”, but we do make sure that the woman is never obsemed to

be separated or divorced, and that the answers to questions in 1977 indicate that the marriage

to her husband was before 1967.

7. For wiv=, fu~-time m-s at least 25 hours per week at the time of the survey. For

husbands, for whom usual wee~y hours is not always available, it means at least 1250 hours

in the past year, with one exception. If, on the last instance in which the annual hours

exceeded 1250, the weeks worked were less than 48, and the weeks worked on the following

survey were =ro, we conclude that the husband retired before the survey date.

8. The women in the NLS have been sumeyed periodicdly, sometimes at yearly intervals,

but mostly at two-year intervals.

5
retirement. Mtly, to be included in the sample, at le=t one full-time wage obsemation must

have been collected both for the husband rmd for the wife.

In this study retirement is defined as no longer working full-time? Some wives work

full-time up to a given survey date, and after that date she does not work full-time (she may

report she is retired, or that she is a housewife). 10 A sm~ler number of wives have a period

where they work full-time continuoudy for a period of time, and then have a period of time

where they work full-time some years but not others. In this section, the retirement date is

taken to be the year following the last year of full-time work, unless the l= yea is 1989 (the

last yew of the sumey). If they are st~ working fuu-time in 1989, they are treated as retiring

sometime after the suwey ends, with the date being left unspectled. Retirement of the

husbands is defined in a similar manner.

Table 2 shows ,,ie distribution of retirement ages of wives tid husbands. Those wit!~ a

recorded retirement age are a minority of the sample, since most of the couples had one or

both partners not retiring by 1989. ~1 The diagond dotted path indicates retirement at tie

9. The analysis does ilot distinguish between full-retirement and partial retirement, counting

the p~idly retired and the retired in a single category. For d~cussions of partial retirement,

se,e Gustman and Steinmeier (1983, 1984, 1985a, 1986a).

10. The number of retired wives is greater than the number of wives who explicitly said that

they were retired in 1989, since many wives report themselves as housewives rather than as

retired once they stop working.

11. The number of couples included in Table 2 in the catego~ where both spouses have

retired includes a lager number of early joint retirees thti will be observed for the whole

sample. Bias from this source will cause the gap in retirement ages to be understated in that

table. From the last column and bottom row of that table it can be determined that those in

the sampie who have yet to both retire, 228 couples have both husbands and wives still

working full-time, 61 have only the husband working full-time, and 115..have only the wife

working fuU-time.

6
Table 2

Retirement Ages

Retirement Age of Husband

51 52 53 54 55 56 .57 58 59 60 61 62 63 64 65 >65 nr

51 . 21 21 113 11

521.1 12 1 1 1 1 5

53 0 11 1 1 1 5

54 . 1 12 43 2117

55 I 2. 1.2 12 11 4

56 113 22 2 19

ctircmcnt 57 5.2 22”41 1 3

Age of 58 1 1 1221 23 1

Wife 59 121112 2332145

60 11 22 121 2

61 1323”1 5

62 1 1 1111111 3

63 1 2 21.1 2

64 1 0 1 2

65 1 1 1.

nr 43567698 6 11101213654 228

same age for both partners. The fact that the midpoint of the data is above the dotted line

suggests that, on average, husban~retire at ages that are two or three yews later than the

ages their wives retire, on average.

Table 3 rearranges the data on the basis of retirement dates, artd addresses the central

7
Table 3

Distributions of Retirement Dates for Couples

With Both Husband and Wife Retired

Difference in Retirement Dates

(Husband - Wife)

-7 -6-5-4-3-2-1012 345678

-5 1

4

-3

-2 1 1

-1 11 1

0 31 1351 2 3

Age 1 21 4 3221 1 1

Difference 2 21”12 9 44 2112

3 1121 4132 2

(Husbartd 4 2172 2 222

- Wife) 5 421 1

6 3 12 1

7 12 1

81 3 1

9 1 1

10 1 1 2

Column 2 21041414538713 13210122

Total

Note Retirement datm are calculated as the year immediately following the last

observation of full-time work

concern of this paper, the coordhration of retirement dates by husbands and wives.’~ Down

12. The reader should remember that these data refer only to those couples who have both

retired at the time of the 1989 sumey. This means that for wives of a given age, a larger

proportion of couples with a husband who is much older than his wife will be retired, and

thus included in the table. In addition, those individuals who have a stronger preference for

leisure are disproportionately more likely to be reported among those couples who have both

retired. The later estimation will t&e account of this selection problem.

8
the left side are the age differences between the husbands and wives. A value of 7, for

instance, indicates that the husband is seven years older than the wife. Most of the entries are

in the part of the table lower than the line corresponding to an age difference of =ro,

indicating that in most cases the husbands are somewhat older than the wives. Across the top

are the difference in retire-merit dates between the husband and wife. A vafue of 5 indicates

that the husband retired five years after the wife.

One might expect a negative relationship in these data, because if the husband is

considerably older thm the wife, it is not unreasonable to expect him to retire earlier relative

to the wife’s retirement. There does not appear to be a dominating relationship, though.

The interesting feature of this table is the distinct concentration of retirement when the

husband and wife retire simultaneously. Given the way the retirement dates were constructed,

what this redly means is a concentration of couples reporting the last date of full-time work

in the same survey ytar. Because the surveys were frequently conducted at two-year

intervals, the actuaf retirements could have ttien place a year apart one way or the other.

Even so, the concentration of retirements at. dates so close to one another suggests that

couples do tend to retire at about the same time, and that this phenomenon is evident in the

data to be used in this study,

III. A Model of Family Labor Supply and Retirement.

In this section we will develop a model of family labor supply and retirement. In the

course of investigating the characteristics of this model, we will also find an approach to

estimating the model empirically.

A. Relation Of The Present Analysis To The Retirement Literature.

9
Before engaging in an effort to bridge the structural retirement literature and studies of

family retirement, it is appropriate to comment on the state of the structural retirement

literature, and where the approach taken in this paper fits into that literature. There me a

number of elements which should be included in a fully dynamic specification of a structural

retirement model. No single structural retirement model incorporates W of these elements,

and they are not dl incorporated here either.

To be more specific, Larear and Moore (1988), Stock and Wise (1990a and b) &d

Lumsdtine, Stock and Wise (1990, 1992a and b), have emphasimd the importance of

including the option vrdue of the pension in the opportunity set. Gustmarr and Steinmeier

(1983, 1984, 1985a, 1986a and b) have emphasi=d the impo~ce of mode~ng hours

constraints on the main job, and the availability of p~iti retirement only at a lower wage.

Berkovec and Stem (1991) and Rust ( 1990) have emph~imd the role of reverse flows in ~

dynamic model. There is no model, which incorporat~ atl of these features. Analyses of

retirement which take account of the pension and the option value of the pension focus on the

decision to leave the main job, but do not model either the decision to engage in part-time

work, or the dynamic of flows among retirement states. Models which take account of ffo~vs

among retirement states, including reverse flows, ignore the existence of the pension, let done

the option value of the pension.13

13. Lack of detied information on the pension has presented problems for these studies.

Gustman and Steinmeier use self reported pension infotiation to fashion the oppofiunity set.

A few studies do have matched, employet provided information on the details of the pension.

Fields and Mitchell (1984) use a Iongitudlrraf sample of retirem from fourteen firrrs, while

Stock and Wise ( 1990a and b) md Lumsdaine Stock and Wise ( 1990, 1992a and b) use one

or two firms. Because the data sets used in the studies based on a few firms are not

repmentative of the entire universe of pension-covered workers, empiricaf findings cannot be

10
The model used in the present study both extends a stmcturd anafysis to incorporate the

retirement decidom” of households with two full-time earners, and aLso specifies md ~tima[a

the model to incorporate the incentives from the option value of the pension. However, the

model focuses only on the decision to reduce work effort below full time. It does not aztdyze

the decision to partially retire, nor does it analyze reverse flows among retirement states.

Accordingly, the work presented in this paper falls short of an ided structural retirement

anafysis in a family setting. This ided has yet to be reached in my structural retirement

analysis, despite students of the subject having confined such studies to the analysis of

behavior of individuals considered in isolation.

B. Model Specification And Estimation Strategy.

The model begins with a fairly standard utility function for the wife”%hich depends on

hfetime consumption “ind iabor supply:

In this utility function, C is consumpcioti and L. is a \,ariable which indicates whether the

generafimd. More importmtly, the data sets which use detailed employer provided

information on the pension do not have information on the opportunities or activities of the

individud after leaving the firm offering the pension. Other structural analyses using more

sophisticated dynamic specifications have.ignored the pension (Berkovec and Stem, 1991), or

have eliminated pension-covered workers from the sample (Rust, 1990). The present paper

utilizes a nationally representative sample, but approximates the incentives from the pension

by using worker reported information on the plan.

11
wife has retired from fuu-tirne work.14 The term exb+’ determines the relative value of

retirement to the wife. The variables in ~ include, among. other things, age and heahh. As

the wife becomes older, exp+c increases because of the effect of age. Eventutiy the value of

retirement outweighs the vafue of the wages from working, and the individud retires. The

value of E is an indlviduaf effect which determines the relative vahte of retirement for

different women. The higher the value of E, the more the wife vafues retirement, and the sooner

she will retire, dl other things constant,

There are three ways in which this utifity function can be construed to be part of a family

labor supply model.’s First, the consumption in this function is not the consumption from the

wife’s own e~ings, but the family consumption financed by the earnings of both husband

~d wfie.lg Second, one of the vtiables in XW is ~, the retirement status of the husb~d.

.

If the, coefficient of L~ is positive, the wife will value her leisure more highly if the husband

is already retired. Flnafly, the value of &Wmay be correlated with the corresponding value

&h for the husband. ThN is the means by which the retirement preferences of the husband

and wife may be correlated.

The utility function for the husband is symmetric:

14. A time preference term of the form e“v’ could dso be included in the utility function.

However, since no data on consumption (which is poorly measured in datasets such as the

NLS) is used in the mimation, the vafue of @ and the value of the Constmt tem in the Iinea

expression ~X are not separately identified. As a result, the value of Q will be subsumed in

the value of the constant term in ~X.

15. The specification we employ is a version of what Klllingsworth ( 1983, p. 34) calls the

indlviduaf utifity, farnfiy budget constraint model of labor supply of family members.

16. If one prefers to think of the wife consuming a fixed percentage of the totat family

budget, it would be a simple matter to insert that percentage in front of the family

consumption in the utility function. The nature of the model would not change matendly.

12
The terms in this function are analogous to the terms in the wife’s func~ion, with the term X~

in the husbands function containing “avtiable L. indicating the wife’s”””ietkement status.

Both husband and .w.ife maximi~ their respective utifity functions subject to the constraint

that lifetime family consumption cannot exceed family income

t-T z-r

~ e-mCt = ~ e-nWw(l-L# + ~ e-nWk(l-L~

M C*

In this budget constraint, both consumption and wages are expressed in red terms, and r is a

resd interest rate. 17

It is perhaps easier to anafyre the model if we start with a simplified version. This

simplified version in~iudw only the wife’s age in the vector X. We initisdly concentrate on

the wif<s retirement del-ision. In the simplified model, her uttiity function is given by:

The first problem is to calculate the range of vdtres of E which will induce her to retire at

some given age R.

To begin the analysis, we first calculate the marginal utility of income in the model.

17. Some forms of ahruism cart dso be accommodated within this model. For..inst~ce, if

the husband values the wife’s leisure time, and the wife w~ts to t~e ttil.s into. account in

choosing her retirement date, the vafues of ~. can be interpreted as including both her ~d

her husbands value of her leisure. However, if the husb~d values the wife’s IekuIe !irne

only if he is retired himself, the wife cmnot t~e this into account in the present model, and

a more complicated model is required.

13
Given her husbands income stream ~–d retirement date R~, and given that the wife is to

retire at %, the totsd farnfly discounted income can be denoted w

This income is to be divided up among consumption at various points in time so as to

mtimim tiC~. The Lagrarrgian for the consumption decision is:

Note that h in this problem is the margirraf utility of income.

Taking the first-order condition for C, yields

C;-1 - ~e-m = o

Solving the first order {orrdition for C, md summing over dl the periods gives

Solving for L imphex

where k is defined as the denominator of the middle term.

In arty given year, the wife would want to work if the value of the wages exceeds the

value of the leisure foregone, and otherwise she would want to retire. In terms of the values

14
we have derived, she would want to work if

[r

-1

ke ‘%w = Z e ‘~~ > e SO+BA+K

k

and othewise she would want to retire. %, in this equation is the “age of the wife at time’”

t. Taking the log of both tides of the above inequality and raanging implies that the wife

would like to continue working as long w

+1

e < bg(e ‘Nw) + (a -1) ~-~ Po-P#w

Another way of looting at this equation is that the right-hand side defines the vafue of E

which makes the wife just indifferent between working and retiring at age R.

Consider a series of potential retirement ages between 60 and 64, and for the time being

let discounted wages be constant (i.e., wages grow by the discount factor each year). X1 age

60, the right-hind slds of the equation above will yield some value of E which will makf

the wife just indifferent between workng and retiring: Denote this value of E as ESO. At

age 61, the right-hrmd side of the equation will yield another, presumably lower, value of E

which will make the wife just indifferent between working and retiring during that year.

Denote this vafue as EC,. How much lower is Eb, than EbO? If wages are growing at

approximately the rest interest rate, the term log(e”Ww,) is approximately constant. Since

the intervening year’s wages fom only a small fraction of the lifetime family income, the

term log(yk) should dso be approximately the same. If wages are growing at

approximately the reaf interest rate, the main difference between ECOand E61 arises from the

te~ -~,~c Since ~, increases by one between age 60 and 61, Es, ..should be lower that

15
RO by an amount about equal to ~,.

Figure 1

Relationship Between the Error Term md Retirement

1 I 1 ! I

I e

~,. ~63 ~6, ~., e,,

(a) Steady Wage Growth Over Time

1 I I I

G

~,, G,, ~,. ~,,

(b) Decline in Wages at Age 65

The same arguments ako apply to &,,, E63, and E6,. If wages are growing at

approximately the rral interest rate, each of these E’S should be lower than the previous one

by about ~,. The situation is depicted in the top panel of Figure 1. Each of the E’s in this

figure depicts the vduc of & for which the wife is just indifferent between working another

year and retiring. The wife’s actual behavior depends on the value of E she actually has,

that is, On how strong k,er preferences are for leisure over consumption. If, for instsrtce, the

wife has a v~ue of e between E~z and Eb~, she will find it advmtageous to work at age

62 but not at age 63. That is, she wi~ retire at age 63. Note that the higher the vatue of s

is for the wife, the ear~er she will retire.

What if wages do not grow over time at the reaf interest rate? The lower panel in

Figure 1 illustrates the case where compensation drops at age 65 because the delayed

retirement credit in the soci~ secufity program is not actuarially fair. The differences

16
between E63 and E64 and between Edj and Ec~ are approximately equal to ~1, for the

reasons indicated in the previous paragraph. Between E6; and EdS, however; there is

another factor at work. l~ot only is ~~ lower.than G4 because t in the term -~lA,,, is

incremented by one unit, but also because the term Iog(e””Ww,) is lower at age 65 than at age

64. This means that the gap between E64 and eb~ is larger than is the gap between the s’s

in other pairs of years, as is shown in the lower panel of Figure 1. If thq values of E for

different individuals are”coming from a relatively smooth distribution, this means that the

probability that E will fall between Es, and E65 will be enhanced relative to other pairs of

&. This in turn implies that the individud has a higher probability of retiring at age 65 than

at other nearby ages; -

The same general line of reasoning applies to the husband, For each potential

retirement age, ther~ is a critical value of & for which the”husband will be indifferent

between retiring and \yorting another year.

Combining the results for husbands and wives ieads to a diagram along the lines oi

Figure” 2. In this figure, potential values of EW are measured along the horizontal axis. The

verticaf lines in the diagram denote the values of E. for which the wives are just indifferent

between worting and retiring at the indicated age, much as in Figure 1. Potential values of

Eh are measured along the vertical =is, and the horizontal lines in the diagram are the values

of Eh for which the husbands are indifferent between worting and retiring at the indicated

age. The cells in the figure are ,combinations of EW and E~ for which the wife will retire at

17
Figure 2

Relationship Between Error Term Vahses and Retirement

When Utility of Leisure Is Not Affected by the Retirement of the Spouse

63 62 61 60

60 60 60 60

63 62 61 60

61 61 61 61

63 62 61 60

62 62 62 62

63 62 61 60

63 63 63 63

~,, ~$, ~,: ~,, ~,,

Upper number in each box represents the retirement age of the wife;

lower number represents the retirement age of the husband.

the upper age indicated in the cell and the husband will retire at the lower age.’s For

18. The dividing lines in the figure are in fact not quite” horimntd and venicd, as they are

drawn. The reason is that as you move up one of the vertical lines, the husbands retirement

age is decreasing, and this causes .a small percentage decline in the Iifetime fmily income.

This will cause a small decrease in the term log(yk) in the equation defining the cnticd

value of R along that vertical line. This means that m you go up the line, the values of EW

la
instance, if the \,dues of &w and ES are in the upper left cell pictured in the table, the wife

will retire at age 63, and the husband will retire at age 60.

In the figure, note that the wife’s retirement age decreases as you go to the right in the

diagram, reflecting the fact that (he higher c. is, the more the wife values leisure, and the

earlier her retirement is likely to be. Similarly, the husbands retirement age decreases as you

move up the diagram, for similar reasons. Only a small fraction of thk cells are actuafly

plorted in the figure, but the other cells are located in a similar manner.. =Note afso that values

of Ew and s~ can be negative as well as positive, so that the cells may be located in the

non-positive quadrants of the figure.

Now let us reintroduce the variables reflecting spouse retirement ‘into thS model.” For

the wife, this means that the critic~ value of E which makes her indifferent between

worting and retiiirig at age A.,, is given in the following equation:

Note that in addition to the terms previously discussed. there is now the term -~lL~, which

reflects the retirement status of the husband. If the husband is retired at time t, the criticaf

value of E will be lower. In other words, if the husband is retired at time t, the wife is

more likely to want also to be retired at time t. A symmetric relationship also exists for the

husband.

increase slightly (recall that a-1 is negative), implying that the line shifts slightly to the right

as you go up it. Similar arguments imply that as you go to the right along any of the

horizont~ lines, the lines tilt slightly upward. However, the effecu should not be large M

long as the vd,ue of et is not excessi~,ely negative.

19
Figure 3

Relationship Between Error Term Values and Retirement

When Utifity of Leisure Is Affected by the Retirement of the Spouse

S;. ~:,

.

62 61 .60. . 59 L

60 60 ..6o. 60 57

59

62 61 .60. .

61 61 ..61. 58

60

62 61 ....

62 62 ..... 59 58

.. 61 61

62 .. . E;,

63 .60 ...... ..... 59 58

62 .......... 62 62

~:,

61 .60. . 59

58 ..-

63 ..&3. 63 63

62 61 .60. . 59 58

64 64 ..64. 64 64

. ..

Upper number in each box represents the retirement age of the wife;

lower number represents the retirement age of the husbmd.

The implications of this cm be illustrated with Figure 3. This figure shows, for a

couple where the wife is two years younger than the husband, the retirement ages associated

with various values of &“ and E~. As with the previous diagram, the upper number in each

20
cell gives the wife’s retirement zg?, and the lower number giv~s the husb~~s re!i!ement. .?ge.

Let us concentrate i.nitiafly on the cells marked w’ith the dots. These are all cells for

which the wife retires at age 60. Among these ceW, Lhe lower two correspond to the husband

re~ring at age 63 or 64; that is, these cells correspond to the husb~d .cetiring. after the wife.

If this is the case, the wife will want to retire if her value of EW frdls between &~Oand Ef9,

as calculated in the formula above and illustrated in the figure. The upper two cells in this

group correspond to the husband retiring at age 60 or 61, that is, before the wife retires. If

the husband retir~ at age 61 or earfier, then the wife will want to retire if her value of s

falls between &~Oand E~g. Note that the critical values E,, and Es~ will be greater thv

E~Oand E:~ by an amount approximately equal to ~z. That is, if the husb~d retires at age

61 or before, the wife is willing to retire at age 60 with a lower vafue of. Ev thm if the

h~sb~d retires al i.:,: ,;3 or .Iater. .Recall that .a lower value of &Windicates that the wit’c.

placa a lower val,.[c CJLleisure and retirement than if Ew is high.

Under what circumstances will the wife want to retire at age ’60 and the husband at ~ge

62? If the husbmd I:!ires at age 62, the critical values for the wife are Es~ (because the

husband is not retired when the wife is age 59) and E~O(because the husband is retired

when the wife is age 60). That is, if the husband retires at age 62, the wife would wish to

retire at age 60 ff her value of EW fafls between ~0 and &s~. S~.milarly,if. the wife were to

retire at age 60, the husbmd would want to retire at. age 62 if his value of .Eh fafls between

%2 and E~,, as indicated’ on the horimntd lines in the figure. Thus, it might appear that the

wife would want to retire at age 60 and the husband. at age 62 if her v~ue. of EW falls

between E&Oand E~g and his ~,alue of s~ falls between E:? and %,, which would b! a

21
rectangle in the ~, &~ space.

However, the diagram indicates that the wife will retire age 60 and the husband at age

62 only in an L-shaped area, not the complete rectangle. What about the remainder of the

rectangle? K the values of ~ and E~ fdl within the bounds fisted above, then it is true

that the husband will want to retire at age 62 if the wife retires at age 60, and the wife wi~

want to retire at age 60 if the husband retires at age 62. On the other hand, if within this

rectmgle, the vdrre of &w is above @g and the value of &~ is above %1, the combination

will dso fafl within the rectangle for the wife retiring at age 59 and the husband at age 61.

For points falling within both rectangles, utility is higher for both husband and wife if they

retire at the earlier ages. Thus, for such points, sdthough it is true that the wife would retire

at age 60 if the husband retires at age 62, and the husband would retire at age 62 if the wife

retir~ at age 60, they- .vould both be better off if they agreed “to retire at 59 and 61,

respectively. This means that where the rectangles for two retirement age combinations

overlap, the rectangle for the younger retirement age combination dominates. The r=ult is

the L-shaped areas when both the husband and wife retire at the same time.

This analysis dso provides the key to estimating a model of family labor supply and

retirement. Given the observed retirement ages for a husband and wife, the preceding

anafy+s shows how to construct the area in the Ew-&~plane which would result in retirement

at those ages. U we assume that values of &w and &h over the population come from a

parameterimd distribution, then integrating the probability density over that area gives the

probability that a family with obse”med characteristics would retire at those ages. This

probability, in turn, can form the basis of a likelihood function.

22
To be more specific, the available parameters in the model are a, the ~W \,cctor for

the wife; and the ~ vector for the husband. For specific values of these parameters, and

using the obser~,ed compensation stream of the two partners and their retirement ages, the

apprOPdate cell boundaries in the &.-E~ plane can be calculated, Ew and &~ may be

regarded as random variables coming from a bivariate normal distribution with rero mems,

variances given by s: and ~, and a correlation given by p. Given these parameters of

the distribution, the probability of retirement at R. and R~ ages can be calculated as

These probabilities can be calculated feasibly from a bivariate norrnrd distribution function.

The log-likehhood function is constructed from these probabilities m:

1-N

~ = ~ ~~~~~la,p~pk,aiai,p)

l-l

where the i subscrip~ indicates individual couples in the sample. The likelihood function

can then be maximized by any standard function maximizer, and the resulting vahtes of the

parameters will be mmimum likelihood estimates. Standard errors for these estimates cm he

calculated by the Bemdt-Hdl-Hall-Hausmrm method.

In the NLS data, it i: often not possible to tell exact dates of retirement by lookhrg at

the activity on the srrmey dates, since in most instances the sur~,eys were t~en two years

apart. For exm~e, it may be possible to tell that the wife was workln~ at age j7 in l~s~ ., .

and was retired at age 59 in 1984, and that the husband was working at age 60 in 1986 Wd

retired at age 61 in..l987. In this instance, the probability used in the hkelihood function is

the sum of two of the areas in Figure 3: one area for the wife’s retirement at ~ge j8 and the

23
husbands retirement at age 61, and another area for the wife’s retirement at age 59 and the

husbmds retirement at age 61. This approach is dso used if both retirement dates occur after

a two-year interview interval; in that case, the probability would be calculated over four of

the areas in Figure 3.

To implement the estimation scheme, it is necessary to adjust the estimation procedure

to include the information on incomplete employment spelfs for those who have not yet

retired. Dropping the many couples with one or both partners still worting at the end of the

observation period would subject the estimates to right censoring, so the following method is

applied. Suppose that the wife of the couple was observed to retire at age 54, but the

husband was stiff wortig at the end of the observed period, when he was 63. This implies

that the vdrres of ~ and &~ must lie somewhere in the ce~s defined by the wife’s

retirement age of 54 and the husbands retirement age of more than 64. In terms of Figure 3,

three ceW would for>?: a column starting at, the cell (54, ~) and extending downward. Nt-te

that the starting cell must lie below the L-shaped cells, since the wife is observed to retire

before the husband. IL is possible to cdcrrlate a probability over this area, and it is this

probability which is included in the lkelihood function.

Similarly, it is possible that at the end of the sample, neither spouse has retired.

Suppose that at the end of the sample, the wife was 57 and the husband 63, and that both

were sti~ wortig. This must mean that the wife retired at age 58 or later, and the husband

retired at age @ or later. For such a family, EW.and &~ must he somewhere on or to the

southwest of the L-shaped cell (58, 64). This cell is L“-shaped because if both retired the year

after the survey ended, they would have retired together. Again, the probability of this area

24
can be calculated, and that probability can be included in the likelihoo~ function.

One last estimation issue arises due to spikes in ~ension accruals. Sometimes “m

individual will retire just after becoming eligible for a more favorable pension. Such

occurrences have become hewn as pension “spkes,” and they may arise because the pension

formula becomes more favorable if the individual waits until at least the early retirement age

to leave the firm.

retirm, the critical

preferences.

If a person works the year she becomes eligible for a spike and then

v~ue of & as calculated above may overstate the indlvidu~s actual

For instance, consider art individual whose wages are $20,000 and who gains a pension

spike worth mother $20,000 if she works her 54th year (this might occur if the early

retirement age were 55)”. The critical value of E calculated from the fomula above wodd

be fairly high at xgc 54, since log(e’r’w) would be high. In other words, looking only .~,t

age 54, the individw~l would want to work unless the value of leisure were fairly high, Rui

consider ages 53 and 54. combined. The individud would want to retire at age 53 if

k~-S3rw53 + e-s~ wsi] < e

%3P+~+ e%$+e

that is, if the sum of thevafue of wages stages j3 and j4 is iess than the sum of the value of

retirement during those same two years. Substituting in for k and factoring s out of the

right-hind expression, the individual will want to retire at age 53 if

+1

E > k*-s*w5, +e”’*ws4]+(a-l)b ~ -lo~e%p+ e%’]

If Wjj is $20,000 and W$, is $40,000, the value of E csdculated from this expression

may well be lower than the value ctilculated from w~, and X~4 alone. In such a case. the

25
19. Ifaindividuaf isobserved to retire just before aspike”(e.g.,just before she becomes

eligible fora more advantageous pension formula), the area in Flgtire 3 may become mro

unless the coefficient of the age variable in X~ is large enough. If such observations are

taken at face value, they dominate the model by forcing the estimated coefficient of the age

variable to be quite large. However, such observations may well be the result of inaccuracies

in reporting the date of the pension spike or of some other factor which is not considered in

the model. We tried to accommodate this by including a trivariate observation error term, but

the resulting model failed to converge, .Therefore, in order to avoid having these anomalous

cases unduly influence the intimated coefficients, the pension spkes are omitted for 8 wives

and 5 husbands who retire just before they are eligible to receive them.

26

criticaf value of E for retirement at 54 is the vafue c~culated for the two-year combination

of 53 and 54, rather than the vatue calculated for age 54 done. The same procedure catr be

extended for three-ye~ periods, or further if these yield still lower values of E. Thus, for

individuals who retire just after they become eligible for a pension spike, the critical values of

E are cafcrdated by using a Iongerpenod, if necessa~.’9

A,

IV. Estimation of the Model.

Data Preparation.

The model isestimatedting data from the Nationaf Longitudirrd Survey of Mature

Women, 1968-1989. Section H outlined the sample inclusion restrictions.

The data requirements forestimating the model fdlinto three categories. First, the

dependent variable (retirement) must remeasured. Determining the last survey of full-time

work is described in Section II, and in the estimation, the first date of retirement is taken to

bethedateof the next survey. Forinstrmce, if the wife is last working full-time at age 59 in

1982 arrd is not wortixg full-timeat age61 in 19840rrmy succtisive survey, she is

considered to have retired at either age 60 or age 61 -- it makes no difference to the

estimation procedure since the dates are bracketed. The same procedure is used for the
.

husbands.

.-

Theother data requiremerrts are the elements of the X vector in the utility function for

the husband ~d wife. year by year, and the compensation oppoflunities available for the

husband md wife for each year of potential work. The X vectors cont~n four elements

(besides a”constant) for both thehusband and wife. These are: age,. spouse retirement, health,

and vintage. The age variable is the individua~s reported age in 1967. incremented by 1,fOr .

each year. Vintage is simply 1967 minus the ageirt 1967, and spouse retirement in a given

year is whether the spouse isretirid at the time. Forthebin~ vantile foraheafth problem,

we examined in each year answers to questions about whether health prevented the individual

from working orwhether hedthlimited themount ortindof work that could be done. .If

health wasreporred as a problem in the first two surveys, weusequestions about the length

of the heafth problem :0 ascertain .when the problem began. Othemise, we look for thl? fir!~~

instance in which h>,~itl was reported as a problem in two consecutive surveys, and the hcaith

variable is set to one in afl years on or after these two sur~’eys,. The idea is to record longterrn heatth problems, and the two-survey requirement is imposed to screen out instances in

which there is an isolated survey with reported health problems (a fairly common occurrence

in the data). If the proble.rn lasts for two surveys, it is usuafly apparent in most of the

subsequent surveys as well.

The major diffictilty in preparing the data set for estimation is to impute compensation

streams. The compensation streams consist of three components wages, pensions, and social

security. Details of the construction of the wage offer Wd pension in the oppoaunity set are

presented inan appendix which is available from the authorson request. Key highlights of

27
theestirnation of the opportunity set are as follows.

Wages

Fordl thesrrrvey years except 1968, the survey asks about armuaf income from wages

and salties, as well as enough information to construct an hourly wage rate. For those years

in which the wife is worting full-time at the time of the survey and for which usable annrtd

wage and salary information is avtilable, the artnud wage and sal~ information is used. For

other y~s, mnud wages must be imputed. The imputation process uses the tenure,

experience, and heaftb coefficients from m hourly wage regression. Hourly wage regressions,

computed with and without fixed individud effects, are reported in the appendix. Those with

fixed individud effects are used.

Pensions

The next elemc~t of compensation is the pention profile. Information on pensions

comes mainly from qut:stiom that were Wed in 1982, 1986, and 1989. h the first two (!f

these years, thesumey Aed about whether the respondent was eligible forapetrtion from

the current or past job. Hthe individud was eligible for a pension from either tbe current or

patjob, thesumey inquired about theyems ofsewicein that job. Ifthe pension was for the

current job, the survey dso asked about the age of initial eligibility for benefits. The 1989”

survey expanded the questions so that they include the early and normal retirement ages on

the present job, the early and normal retirement ages for pensions on previous jobs, and the

amounts that the individrrd would be eligible to receive on those dates. Inaddltion, the

survey a~ed about the actual amount of benefits received if the respondent reported that

benefits were currerttly being received.

28
The full pension is assumed to be determined by the formula P = g w T, where P is

the annusd pension benefit, W is the find wage, T is years of sewice, tid g is a

generosity factor.~” For individuals who retire after the early retirement date but before the

norm~ retirement date, the full pension is reduced by 4.9% per year. This is the average

weighted reduction rate in Hatch et al., Table 4-8. For individuals who retire before the early

retirement date, the reductions are actuariaf. This arrangement, which is the basis of the early

retirement spike dticribed by Lumsdaine, Stock, and Wise, also appears to be fairly common

in the plans in the 1983 Survey of Consumer Flnuces. The generosity figure is calculated on

the basis of the individuals expected or actual pension benefiw, if no figure is given, we use

1.6Y0, which is the median figure of plans for which we do have enough information to

calculate it. We assume that, once begun, firms increase the v~ue of the pensions by 37.970

of the inflation rd!r:, .“e figure found in Allen, Clark, and Sumner (1986)?]

Pension com.pc’r?~ation (pension accrual) is the amount by which an additiond yem’s

work increases ~he expected present value of the pension. Several factors come into play 1,1

determining the change in present value from an additiond year’s work. An. additiond yefir’s

20. Given the incidence of severe reporting error in self reported plan type which we found

in Gustman and Steinmeier (1989), we have not attempted to distingul.sh those with PrimarY

defined benefit plans from those with primary defined contribution plans. Instead, we have

treated dl workers as if they were covered by a primary defined benefit plm.

21. An dtemative procedure to impute pensions would be to match each observation in the

NLS to pensions from the Sur\rey of “Consumer Finance pension file on the basis of

occupation and industry. The problem with this approach is that it dom not insure that the

early retirement dates would be correctly aligned with the date the respondents ga~,e. This is

a serious drawback, since the early retirement age is probably the most important date in a

pension profile, marking as it does a sharp drop in the accumulation rate of pension benefits.

Another idea would be to match with the SCF on the basis of occupation, industry, and early

retirement dates, but the SCF is too thin for this detailed a match.

29
tenure wi~ increase the mnuaf pension through the benefit formula. If the nominal wage

increases during the course of the year, the annuti pention amount increases proportionately.

If the work is before the normal retirement date, the reduction for early retirement will be

less. The present vafue of these increases is obtained by multiplying the pension amounts

times the appropriate srsrvivd probabilities in future years and discounting back to the

present.22 Offsetting thm factors is the fact that art individud who is afready eligible for the

pension will lose the current year’s benefits because pensions are rarely paid to continuing

employees. The net effect is to cause pension accruafs to change relatively smoothly except

at the early and norrnd retirement dates, when the amount of the accrufi drops sharply.

Further details of the pension calculation are presented in the appendix. Nthough the

imputations are necessarily approximate, they do capture the main effects of pensions on

compensation, which :>~.ethe declines at the early and normrd retirement ages. Especially

important are the declines at the early retirement age. We do know, for most indlviduds,

when the early retirement age is, and these calculations do capture, however approximately.

the decline in compensation that usrsafly occurs at that age.23

Sociaf Security

22. The red discount rate is taken to be equat to the red growth rate of adjusted hourly

earnings. Both this and the expected inflation rate are the average vdtses obsefi~d over the

ten years previous to the year in question. The growth rate of adjusted hourly earnings is less

than the interest that could be obtained with 10-year tre~ury bonds over the post-war period,

but is about equrd to the interest on 3-month treasu~ bills and probably exceeds what most

households could obtain with banks or money market funds, especially if after-tax interest is

considered.

23. For discussion of misreporting of early and norrnaf retirement dates in the SCF, see

Gustman and Steinmeier ( 1989).

30
The derivation of sociaf security accrurds is less subject to error tha are pension

accruals, primdy because dl elements of the socifl security formula are fmown and apply

to everyone. The computations do t~e into account the increases in the nornraf retirement

age and in the delayed retirement credh scheduled to t~e effect, ss specified in the 1983

Social Security Amendments. For the husbm~, the computations t~e into account the effect

of his retirement age on the eventrrd widow’s benefits.

The present vafue calculations ae similu to those for the pensions. Worting another

year can charrge the present vahse of social security benefits for three reasons. Fust, higher

reaf wagm during prime worting years are lkely to displace earlier wages from the average

earnings calculations, incre~irr~ benefits. This effect is enhanced for those over sixty years of

age because under the calculation of average indexed monthly earning (A~E), the basis for

calculating monthly ~,r.“?efits, wages are indexed only to age 60. Second, if the inrfivid~sl ;?

over the early retirement age, worfring another year will reduce the early retirement reducli.?~

factor or increase the delayed retirement credit. Finally, if the individusf is over the ear~y

retirement age, wortin~ another year may cause benefits to be lost to the earnings test. In

general, the effects of the social security ~stem are to cause reductions in compensation

primarily at the norrnd retirement age, since the delayed retirement credit is not sufficient to

offset the loss of benefits from continuing workrrg.24

The overall compensation paths for the wife and the husbmd are calculated by adding

to the wage the accruals for social security and, if appropriate, the pension. These are then

24. For further discussion of the sociaf security rules and estimates of the incentives they

create, see Gustman and Steinmeier ( 1985b, 1991).

31
combined with the retirement ages of both spouses and the values of the X vectors to

provide the data set for estimation. The find data set has 5@ observations “of couples who

satis~led all of the inclusion criteria and who had at least one wage and salary figure on which

to base the compensation paths.

B. Estimation.

The estimates for various forms of the model are given in Tables 4 and 5. Table 4

reports on results when the spouse’s retirement is ignored or is treated as exogenous. Table 5

repotis on estimation of the model on the assumption that retirement is jointly determined,

applying the estimation procedure outlined in Section 111above. The esdrnated parameters in

these tables include the exponent of the consumption term in the utifity function (a), the

coefficients of the linear forms for both the wife and the husband (the @s), the variances in

retirement tastes for b(:th the wife and the husband (the 6s), and when retirement is trcate<! as

jointly determined, the comelation of these tastes (p). The P vectors for both the wife ~.d

the husband include a constant, age, whether or not the spouse is retired at the time, whether

or not there is a health problem at the time, and the vintage of the individud.

The fiist two columns of Table 4 conttin estimates for the wife and the husband

separately, saris any v~ables which might !i* the two retirement dates. In both cases, the

earnings of the remaining spouse are tien as exogenous. AU of the variables are significant

at conventional levels. The coefficients on the consumption terms indicate, for both partners,

a moderate desire to smooth consumption over time. For this parameter, a value of unity

would indicate no desire to smooth consumption over time, while a large negative value

would indicate a great desire to smooth consumption. Since the difference between the wife’s

32
a Consumption”

fio constant

p, Spouse Retired

~ Std. Dev. of r

Smple Size

Log Llklihood —

Table 4

Model EstimatesTreating Spouw RetirementasExogenous

No Intertipendeoce

Wife’s Husbands

Equation Equation

(1) (2)

-1,549 -1.355

(-3.13) (-2.35F

-19.042 -18.350

(-21,83) (-11,32)

0.578 0.65

(4,52) 0.24)

I .050

(2.82)

0.101

(2,20)

2.878

(4.79)

564

-668.2

1.974

(3.04)

0.127

(2.28)

3.427

(3.72)

564

-743.4

Wife’s

Equation

(3)

-.1.563

(-3.15)

-19.401

(-20.82)

0.528

(4.40)

0:953

(3.05)

1.036

(2.79)

0.094

(2.08)

2.864

(4.73)

564

-658.67

Husbands

Equation

(4)

-1,2.56

(-2.27)

-17.489

(-10.83)

0,599

(3.25)

1.302.

(2,71)

2.005

(3.09)

0.108..

(2.08)

“!3

..

,,..,.,,

564

.? ;27 .

- —

Totes:

(a) Figures in paenthes.:sae qmptotic t-statistics.

[b)For age and vintage,tieactualvaiables we (age-55)and (vintage-30),

p=meter and the husbmd’s pmmeter islessthm their stmdwdemors, it appews unlkelya

priori whether these twovdues mesignificautly different.

For the wife, the coefficient of theagetem is O.578. This indicates that the utility of

retkment is rising by about over 78% (e0”578-1)peryew during theperiod ofmtirement. The

procedure estimates this effect primtilyby looting at how much retirements concentratedin

yeas where compensation fafls considerably. Intemsof Flgure3, ifthe coefficient ofageis

33
smaller, then the areas in the figure will be generally smaller, except where there”me large

declinesi ncompensation. This memsthat yeas having lmgerdeclines in compensation will

have a relatively l~ger~ea in the figure, arrd more individuals should beretinng in those

years. Ifthecoefficiefit ofageislarg.er, then the tieas in Figrrre3 are much-larger, anda

decline in compensation, though incretiing the area by thesame absolute smount, wi~ not

result in nearly as large a proportionate increase in area. The result is that if this is the case,

a dectie in compensation should increase retirement more moderately.

Among the other parameters, having a health problem has thesarne effect on retirement

as being a not quite two years older, and the effect of vintage is m“odest. The standard error

of the retirement taste term & is 2.878, which amounts to over five times the coefficient of

the age term. It is fairly clear that the taste term plays,ave~ large role in accounting for the

large range of ages at which various individuals retire.

For the husband. the value of the health coefficient amounts to a little over three times

the magnitude of tile (coefficient of the age term, and the standard deviation in tastes for

retirement are a little over five times the sim of the coefficient of the age term. The age tc:m

itself is somewhat larger than it is for the wives. This may reflect two possibilities. First, lhe

husbands may be less sentitiveto monet~ incentives to retire. From the discussion above, a

higher coefficient ontheageterrn impliwthat the husbands are more l~elyto retire at ages

determined bytheirvduesof c, regardless ofchanges in compensation incentives.

Alternatively, the high coefficient may arise iftheaga of compensation decreases are

mismeasured, which would reduce the correlation between retirement and compensation

decremes. It is plausible that such mismeasurement maybe more severe for husbands than

34
for wives, since the wives and not the husbands were the prim~ respondents in this data set.

The last two columns of Table 4 continue to treat thespouse’s retirement behavioral

exogenously determined, but for each spouse allow the preference” for leisure to depend on the

retirement status of the other. The husbands retirement status has a significant effect on the

vrdrration of leisure by the wife, with the effect of the husband being retired increasing the

value of leisure by an amount equivalent to aging two years”. There is only a small effect of

includlrrg husbands retirement status on the other parameters. With regard to the estimate of

the utility function of the husband, the effect of wife being retiredjs dso significmt, and

equ~ to the effect of an additional two years of age. As in the wife’s equation, there is only

a modest effect on including spouse retirement status on the coefficients of other variables.

Given that each spouse’s retirement decision is influenced by the retirement status of the

other, it becomes impomt to recogni~ in the estimation the joint determination of

retirement, and not to 3ssume that the retirement status of one spouse is an exogenous

determinmrt of theretirement status of the other. Forif the decisions are truly joint, then

treating the decisions as exogenous to one another will lead to an overstatement of the effect

of the retirement status of one spouse on the retirement decision of the other. “F”orinstance,

the wife may tell the husband “If you retire early, I will too, and we can enjoy our retirement

years together: Thehusbmd, me=while, may bethiting thesamet hing,andbothhusbmd

and wife of this couple will retire early. To the researcher studying only the wife andttirrg

the husbands retirement as exogenous, it will appear that an early retirement by the husband

is associated with art early retirement by the wife. In fact, the emly retirement of the husband

is partly the result of the wife’s own preferences, which will be mist~enly attributed to the

35
husbands retirement?5

Moreover, the preferences of thetwospouses may he correlated. Kindividuds who

have high preferences forearly retirement tend tomsrry onesnother, then theretkement age

of the spouse WU be correlated with the individutis own preferences. Again, the investigator

who is ttig the husbands retirement as exogenous wi~ observe that if the husband retires

early, the wife is ~ely *O to retire early. Thus it may m=erdy be concluded that the

husband’s retirement has a large Muence on the retirement date of tie wtie, when in fact it is

the correlation’ in retirement preferences that k driving both retirements.

The ewirnates in Table 5 are deQgned to ded with these issues. The f~ column of

Table 5 provides a basis for compfion with equations reported in columns 2 through 5. It

imposes the restriction that the consumption parameter is the same betw~n husbads and

wives, but as in columns 1 and 2 of Table 4, excludes the indicator of whether the spouse is

retired. This is nec=%ary if tie couple is to share a common consumption stream. The

resulting coefficient of et is about htiway between the estimates for wives and husbands in

columns 1 and 2 of 7 able 4. The values of the I&elihood statistics indicate that the

25, Notice dso that the results of the retirement decisions made by each spouse, as @imated

in columns 3 and 4 of Table 4, should not be tkn as additive. For if the preferences are

interdependent, each ystem of equations wiD be mirnated to expltin whatever joint pe~

there is in the retirement outcomes of both spows. Together, the estimates are I&ely to

“overexplain” any joint retirement behavior.

36
Table5

Model&ttites WithRetkementJointly~!eti”ed

:onsmption il) (~) (3) (4)

a .1.465 -1,427 -1.612 -1,5M

(-4.13) [-4.m) (-439) (-4.M)

VifesPmmetem:

~, COnstmt -18.151 -17.762 -19.410

(-~3.63)

-18,615

(-23,42) (-32.75) (-26.78)

~, Age 0566 ..0.555 _o.542 0531

(4.91) (4.89) [5.94) (5.19)

~, Husbmd ktied 0.092 0.095

(0.27) (0.27)

~, HealthRobIem 1.019 Lm3 .1.005 0981

(2.96) (2.96) (3.30) (3.06)

~, W“tage 0.099 0.096 0.088 0.0.%

(2.22) (2.16) (2.21) (2.01)

~ Std.~V. of% 2.821 2.787 2.761 2.713

(5.33) (5.40) (6.16) (5.78)

Iusbmds Par~ters:

~, Constmt -19.5@ -19.383 -20.744 -20.031

(-13.41] (-12.71) (-17.m) (-15.67)

~, Age 0.670 0.633 0.632 0.613

(3.67) (3,63) (4.32)“– (4.07)

~? Wife Wtied 1,256 0.582

(2.15) (1.12)

~, Hedti Roblem 2.043 2119 2,017 2.046

(3.41) (3,38) ““””-(3.91) (3.-1)

p, V,”tage 0.130 0,114 0.126

(2.43)

0.109

(2.19) (2.69) (2.29)

d Std.WV. ofc, 3.530 3.572 3.411 3.394

(4.25) [4.21) (j.06) (4,76)

:omelation

P 0.312 0.236

6.46 4.13

;mpIe Size 5m “.. “-”564 564 5@

.ogLkelihood -1411,80 -1401.11 -1397.43 -1394.47

~otestoTable5 (a)F,gwesinpuenthesesme wymptotict.statistics. (b)Forageandvintage.th.mtuai.tiab[eswe

(age-j5)md (vintage-30).

37
imposition of this constraint is not statistically significant .26

Column 2 .of Table 5 look again at the possibility that spouses might find retirement

..—

more attractive if the other spouse is retired by including spouse retirement variables in the ~

vectors. The difference between these resrdts, and those in columns 3 and 4 of Table 4, is

that the estimation treats spouse’s retirement status as endogenously detemirred.

In Table 4, with spouse retirement t~en as exogenous, the spouse retirement

coefficients depend on the degree to which the indlvidud retires on the same date as his or

her spouse. k Table 5, the spouse retirement coefficients depend on whether, when one

spouse retires at a date when compensation drops substantially, the other spouse retires also.

Comparing spouse coefficients for the husband mtd wife, the coefficients suggest that when

wives retire on their early retirement dates, the husbands are. a lot more ~ely to retire at that

time dso than if the situtiion is reversed.

When the spouse’s retirement status is treated as endogenously determtied, the

coefficient of the husbands retirement status affecting the wife’s retirement becomes smafl

and insignificant. The coefficient for the wife’s retirement status in explaining the husbands

retirement, however, is of the proper sign and has an estimated t-statistic of over two. This

coefficient indicates that, for husbands, having a wife that is retired has the same effect on the

desirability of retirement as does being about two years older. These estimates suggest that

the husbands retirement does not affect the retirement preferences of the wife, but the wife’s

26. The Iog-Wefihood when this constraint is not imposed (-1411 ,60, which is the sum of

-668.20.. and -743.40) is ordy 0.20 above the Iog-lkelihood of the constrained ~quation. This

impfies that the fiielihood ratio test statistic is 0.40, considerably less than the Xz(1) cnfic”~

vafue of 3.84 at a 570 significmce level. Hence, the test does not reject the hypothesis that

the vdrre of a is the same between wives and husbands.

38
,

retirement has a notable effect on the retirement preferences of the husband. An expos~e

rationale for this result is that some husbands do not wish to find themselves with more time

to take cme of the household while the wife is stiu devoting a substantial part of her time to

market work. But stronger confirmation of this result and investigation. of further implications

would be required before any conclusion is drawn.

Column 3 looks at an dterrrative explanation for couples retiring at around the same

time. H men and women who prefer to retire early tend to marry one other, and men and

women who prefer to retire later (and consume more over their lifetimes) tend to marry each

other, the values of Ew and &~ in the model will be correlated with each other. This

column introduces the correlation term p into the estimation (and omits the ~z’s). As can

be seen” from the table, the estimated value of p is about 0.3, md it is highly significmt.

Finally, Column 4 in Table 5 allows these two competing explanations to be includ?d in

the same equation. Compared to Column 3, the value of p is now only about three-quarttrs

as large, but it is still highly significmt. The spouse retired coefficients now both have the

proper sign, but neither one has a t-statistic above 1.2. However, the combined effect of the

two of them is marginally significant, as can be seen by comparing the log-l~”elihood of

Columns 3 and 4. Adding these two vtiables to a specification which rdready includes p

increases the log-likelihood by 2.97. This implies a likelihood ratio test statistic of”5.94,

which is approximately equal to the XZ(2) criticaf value of 5,99. at a 570 cotildence level,

Although the estimation procedure is unable to separate out the sponse retirement coefficients,

they are jointly significant. Moreover, the point estimate of the coefficient on the spouse

retirement variable is over six times as large for the husband than it is for the. wife. Because

39
the relative effects of the ~2’s and P cannot’ be inferred simply by comparing the relative

si~ of the par~eters, that issue will be investigated by si,mulation.z’

Before that, we should comment on the magnitudes of ~he other parameters in this find

specification. The magnitude of a in this specification is slightly greater (in absolute vafue)

than in the specification Without the correlation of the spouse retirement variables (-1.53 vs -

1.46). The coefficients in the ~ vector for the wife look very similar to the coefficients for

the specification with no spouse interactions included (Column 1 of Table 5). The same is

true for the coefficients ti the ~ vector for the husband.

V. Simulations Of The Effects Of Husband Wife Retirement Interactions.

The model paarneters do not indicate the relative importance of the interdependence of

retirement decisions and correlation of tastes in shaping’ retirement outcomes. The figures in

this section, which are based on simulations for the sample, will shed more Hght on this issue.

The simulations = performed as follows. First, the paths of the X vectors and the

compensation stream for both husband and wife are calculated as indicated in the first part of

the preceding section. The model parameters are taken from the last column of Table 5, that

is, from the full model. Given the estimated variances of ihe error terms and the correlation

27. Identification of these effects comes by examining the peak of joint retirement. To the

extent that the cause of the peak is the spouse retirement variables, there should be a pe~ of

couples retiring at exacdy the same date (See Figure 3). To the extent that the cause is a

correlation of preferences, there should be a broad peak of couples who retire within a few

years of each other, but not necessarily at exactly the same time. Separate identification of

the two spouse retirement variables comes by examining when the joint retirement tends to

occur. If joint retirement occurs ‘at the time the wife (but not the husband) has strong

financial incentives to retire, this would indicate that it is the husband who vafues having the

wife at home. If it occurs when the husband has incentivti to retire; the reverse would be

true.

40
between them, a random draw is made to obtain ~ and E~. These values of the x

vectors, the compensation streams, a, the ~ vectors, and the two E’s then imply specific

retirement ages for the wtie and the hWband.

The solution method cm be visuafimd easily with the aid of Figure 3, We begin by

setting the potentiaf retirement age of the husband at 75 and the potential retirement age of

the wife at 73. This correspond to an L-shaped area far down and to the left in Figure 3. We

then calculate whether the values of ~ and Eb are sufficiently high to move to the Lshaped area immediately up and to the right, If they are, we then repeat the process until we

reach an L-shaped area for which either ~ or E~ (or both) is insufficiently high to move to

the next L-shaped area. If both are too low, this L-shaped area is the solution. If &~ is too

low but &Wis not, we see whether &Wis sufficiently high to move to the rectangular area

immediately to the right of the L-shaped block, and we continue this process until &Wis no

longer high enough to move my further to the right. At that point, we check to see whether

Eh is in the proper range for that rectasrgle, and if not we move up or down and repeat the

process. A symmetrical process is done if EW is too low to move to the next L-shaped box,

but &b is not. The objective of this procedure is to rmch that area which corresponds to the

rarrdom draw for ~ md Eh. The ages for that area are the solutions for the simulation,

given the obsewed opportunity set and the draw for Q and s,. In the results reported

below, there are 1000 simulations per indiiidud.

Figure 4a presents the distribution of retirement ages among wives from the base

simulation, and Figure 4b presents the coksponding distribution for husbands. For

41
Hgure 4a

Retirement Among Wives

12%-

lo%-

m

.5

.$ a%-

%

m

% 6%-

2

:

: 4z2

2%-

0%

51 53 55 57 59 61 63 65 67 69

Age

+ Smulated + Observed

comparison, the distributions of observed rates are afso plotted in these figures:?* Note from

Flgrrre I that if tastes for leisure (the &’s) are distributed normally, then the distribution of

retirement ages should be approximately normal dso. The obsewed distributions have Imge

humps in the 61-63 age rmge for wives and in the 62-64 age range for husbwds. However,

there is no noticeable spke at age 62, which is the Social Security early retirement age and is

also a common retirement age in many pension plans. As a result, the model overpredicts

28. The observed rates are calculated by tting percentages of the sample who were retired

at different ages and first differencing the results. .While the rates in the ewly 50’s are based

on sample sires of over 500, the sample si~s decfine in the late 50s and 60s until they reach

54 at age 65 for wives md 164 at the same age for husbands.

42
F;gure 4b

Retirement Among Husbands

12%

lo%-

m

.2

.= 8%-

%K

~ 6Z -

~

c

:

4% -

k

L

2%-

0%

51 53 55 57” 5g 61 63 65 6> “69

Age

+ Smulated - Observed

retirement in the late 50s and underpredic~ it in the 60s. The model predicts ftint peaks at

ages 62 and 65, reflecting the role of pensions and the downturn in the sociaf security

actuarial adjustment rates at age 65, but the lack of distinct and large peaks simply mirrors

the lack of distinct peaks in theobserved data at those ages.~9 Ftitiy, both the simulated and

actrsd distributions are shifted to the left for wives, reflecting the fact that wives in general

retire at an earfier agethm their husbands. (Gustman and Steinmeier, 1986a and b).

29. Note that the peaks in the hazard rate would be sharper at the relevant ages associated

with a particular pension profile, but the results in Figure 4 are averag~ among people

covered by pension plans with different requirements for””etily and norrnfl ie[irernent”and with

different employment histories.

43
Figure 5

Simulated Hazard Rates

‘“4~

0.35

0.3

: 0.25

K

; 0.2

g 0.15

0.1

0.05

0

Age

* Wves ~ Husbands

Figure 5 presents the simulated hazard rates for both husbands and wives. Because the

retirements in Figure 4 are from a smaller base at older ages, the hazard rates are generally

increasing. The rates are higher for women throughout the entire age range displayed. The

sm~ pe~s at age 62 and 65 are upward bumps on the gener~ trend.

Hgure 6 tivestigates a central concern of this paper, the coordination of retirement by

husbands and wives. The figure indica~ the differences in retirement dates between the

husband and wife under dtemative specifications for the model. A can be seen, when the

full model is estimated, there is a sharp pe~ at mro difference in retirement dates, with over

11 percent of the couples retiring at the same time, whereas for other age differences, the
Figure 6

Effects of Joint Retirement Variables

Z%”i I

0% 1

-6 -4 -2 ‘ o 2 4 6

Differencein RetirementOates (H - W)

~ Base + W/O rho + w/o sp ret * w/o either

probability ranges around 4 to 5 percent.

It is clear from Figure 6 that the source of interdependence in retirement is in the

coordination of preferences among spouses and is not due to the correlation of incentives

between the opportunity sets facing husbands and wives. This result can be seen by

comparing the probability of joint retirement under the full “base” model, where al sources of

retirement are included, with the probability of joint retirement when all sources of

interdependence in the utility function are suppressed (but the opponunity sets remtin

unchanged).

Investigating the source of the interdependence within the utility function, it can be “seen

45
that the peak in the probability of retiring at the same age remtis when p (the correlation

between q and q) is set equa to mro, falling by only about one percentage point. In

addition, setting p = O has virtually no effect of the distribution of retirement ages among

either husbands or wives (result not shown). The conclusion is that the modest estimated

correlation between E, and E~ produces at most a modest increase in the tendency of

couples to retire around the same time.

The remaining two lines in Figure 6 indicate that joint retirement is due ahnost entirely

to the presence of spouse retirement status in the utility function?” The tendency for COUPI=

to retire together is reduced from tiout 1170 to about 590 in the simulations where the LS

are set equal to mro, whether or not the correlation in the E’s is included. In these

simulations, retirement at exactly the same year is only a little above retirement at dates

which are a year or two apart, in marked contrast to the situation in the previous two

simulations. Moveover, retirement at dates which are a year or two apti (but not the same)

is fittle affected as compared to the simulations in which the PZ’Sare included.

In sum, from the simulations it is clear that most of the spike at ~ro years

difference in retirement dates is due to the spouse retirement variables. Dropping p

~inishes this pe~ only slightly, but dropping the ~;s timost eliminates it. The reverse

seems to be true for dtiferences in retirement dates of one yew or more: in th~ case, the

30. Simultaneously, the constants in the linear forms X~ are increased to offset the

omission of the spouse retirement variables. Otherwise, omitting the spouse retirement

variables will reduce X9 generrdly and will lead to an increase in the average retirement age.

Since the spouse retirement variables average one hdf around the years of the retirement

decision, the constant terms in the linear forms X~ are increased by one hdf of the

corrmponding ~ parameters.

46
difference in retirement dates seems to be due mostly to the correlation between R and &h.

Dropping the ~;s has very little effect on those differences, but dropping p lowers them to

about the level found in the model @ which atl interdependence is suppressed.

Figure 7

Effect of Spouse Retirement on Husbands

40%

~

: 35%-

.

~

K 30%-

m

c

‘~25Z2

0 20%- U

8

; 15%-

?.

~lo% - \

\

z

: 5%-

$“OZL-T. ,,, !,I,

51 53 55 57 59 61 63 65

~; ‘..69

Retirement Age in Base Smulation

Figure 7 investigates. the magnitude of the impact of the spouse retirement variables.

Since the husbmd~s coefficient is considerably larger than the wife’s coefficient, the effect of

that coefficient R “presented. In the simulation, the wife’s retirement age ii. held to be exactly

the same as in the base simulation. The coefficient of the spouse retirement variable in the

husbands utility function is. then set equal to mro, and the husbands optimal retirement age is

calculated. If the wife Is still working, this will have no effect, but if the wife is already

47
retired, the husbmd may be induced to work a while longer.

The vertical MS on this figure me~”ures the percentage of irtdividuds retiring at that

date who are induced to delay retirement by a year. For example, 8 percent of the husbands

retire at age 60 in the base” simulation. If the effect of spouse retirement is suppressed, 1.7

percent of the husbands work another year rather than retiring at age 60. The ratio of the

two, which amounts to around 21 percent, is what is plotted in the figure.

After a modest decline in the early 50s, the chart turns up for the remtider of the age

rartge. This means that as the age increases, the percentage who would want to work another

year increases. One reason is that as the husband; retirement age increases, it is more

probable that his wife h= already retired, in which case setting the spouse retirement

coefficient to =ro WIII make a difference. The dips at age 62 and 65 occur because at these

ages pensions and social security are larger factors in the husband’s retirement decisions. ar,d

whether or not the spouse has retired is less of a factor.

The average over dl ages is about 24 percent. In the base simulation, the fraction of

cases where the wife is tieady retired when the husband retires is about 57 percent. This

means that in cases where the wife retires first, the about 42 percent of the husbmrds would

delay retirement by another year if the spouse retirement effect were inoperative. For the

affected group, this trsnsfates into an increase in the average retirement age of about 5

months. Whfie this is not an overwhelming effect, it is in the same order of magnitude as the

average effects which have been reported in the literature for pensions and social security.

VI. Summary and Conclusions

This paper has spec~led and estimated a structural retirement model in which retirement

48
decisions by husbmds nnd wives are join!ly dete~ined. The P~~eters estim~ed for the

model generate behavior that brings the retirement dates of husbands and wives closer

together thw would otherwise be the case, with the probability of retirement at the same time

being about 11 percent of couples.

Although the estimation procedure is unable to separate out the spouse retirement

coefficients, they are jo”intly significmt. Thus, both of the competing explanations (the spouse

retirement explanation and the preference comelation explanation) are significant in the data.

Simulation indicates the relative importmce of each of these sources of interdependence in

increasing coordination of the retirement outcomes of spouses. In contrast to the support

found for the hypothesis that coordination of retirement outcomes is “due to interdependence

in preferenc~, support is not found for the hypothesis that coordination in retirement of

spouses results from coordination in the incentives created by the spouse’s opportunity sets.

There is some suggestion in the data that the wife’s retirement decision is not strongly

influenced by the husbands, but the husbands decifioi is more strongly influenced by the

wife’s. Although such a result is consistent with art interpretation that the husband would

rather not face the house and related work load afone, this result is a prehminary suggestion

that requires fufiher support.

Finally, because the National Longitudirrd Survey of Mature Women provides the most

recent, nation~y representative iongitudirraf sample available for a study of retiremerit

behavior, the results reported in this study reflect the labor market trends shaping the

retirement behavior of women. Although many members of the cohorts included in the NLS

have not yet retired, the estimating technique has explicitly accounted for incomplete

49
employment spells.

50 .—
References

Allen, Steven G: Clark, Robefi L. md Sumner, Dmiel. “Post Retirement Adjustments of

Pensions”, Journal of Human Resources, Winter 1986, 21(1), pp. 118-137.

Berkovec, James C. and Stem, Steven. “Job Exit Behavior of Older Men”, Ecorrometriib,

January 1991, 59 (l),” pp. 189-210.

Burtless,-Gq and Moffitt, Robert A. “The Effect Of Social Security Benefits On The Labor

Supply Of The Aged”, in Henry Aaron and Gary Burtless, Editors, Retirement And Economic

Behavior, Washington, D.C., Brookings Institution, 1984, pp. 135-74.

Clark, Robert. “Labor Market .Responses of Divorced And Widowed Women”, Report To

The Nationsd Commission On Employment Policy, March 1984.

Clark, Robert and Johnson, Thomss. “Retirement In The Dud Career Famfly”, Find Report

To The Sociaf Security Administration, June 1980.

Fields, Gary S. and Mitchell, Olivia S. Retirement, Pensions and Social Security.

Cambridge: MIT Press, 1984.

Gustmrm, Alan. L. and Steinmeier, Thomas L., “ Minimum Hours Constraints And

Retirement Behavior”, in Corrtempora”~ Policy Issues. a Supplement to Economic [nqai~,

1983, pp. 77-gl

“Partial Retirement And The Analysis of Retirement Behavior”, Industrial

And Labor Relations Review, April 1984, 37(3), pp. 403-415.

“The Effects of Psrtid Retirement on Wage Profiles of Older Workers”,

Industrial Relations, Spring, 1985a, 24(2), pp. 257-265.

, “The 1983 SociA Security Reforms and Labor Supply Adjustments of

Older Individuds in the Long Run; Journal of Labor Econonzics, Vol. 3, 1985b, pp. 237-253

“A Structural Retirement Model; Econorrretrica. May, 1986a, 54(3), pp,

555-584.

“A Disaggregate Structural Analysis of Retirement By Race, Difficulty

of Work and Heaf~h; Review of Economics And Statistics, 67(3), August, 1986b,. pp. 509-513.

“An Anafysis of Pension Benefit Formulas, Pension Weakh and

Incentives From Pensions,” in Researcft In Labor Economics, 10. Edited by Ronald

Ehrenberg. Greenwich, Ct: JAI Press, 1989. pp. 33-106.

51
“Chartgirrg Social Security Rules For Workers Over 65: Proposed Policies

And Their Effects”, Indusm’al And Labor Relations Review, July 1991, Vol. 44, No. 4, pp.

733-745.

Hatch, S.P., et af. “Flnancid Retirement Incentives fn Private Pension Plm”, Find Repon

by the Urban Institute to The Department of Labor, 1981.

Hurd, Michael D. “The Joint Retirement Decision Of Husbands And Wives”, in Issues In Tlze

Economics of Aging. M. David A.Wise. Chicago: Universi~ of Chicago Press, 1990, pp.

231-254.

Klllingsworth, Mark R. Labor Supply, Cambridge Cambridge Urrivertity Press, 1983.

Lazear, Edward P. and Moore, Robert L. “Pensions and Mobility; in Pensions In The U.S.

Economy. Mted by Zvi Bodie, John Shoven md David Wise. National Bureau of

Economic Research. Chicago: The University Of Chicago Press, 1988, pp. 163-188

Lumsdaine, Robin; Stock, James and Wise, David. “Efficient Windows And Labor Force

Reduction”, Journal of Public Economics 43, 1990, pp. 131-159.

“Three Models of Retirement: Cornputatiortd Complexity versus

Predictive vdldity”, in David Wise, editor, Topics In The Economics of Aging, Chicago:

University of Chicago Press, 1992a, pp. 19-57.

“}:’errsionPlm Provisions And Retirement: Men & Women, Medicare,

And Models”, Ctibrklge, Mimeo, June, 1992b.

Pozzebon, Stivana and Mitchell, Olivia S. “Married Women’s Retirement Behavior: Journal

of Population Economics, 2(1), 1989. pp. 301-53.

Rust, John. “Behavior of Mde Workers At The End Of The Life-Cycle: An Ernpincaf

AnWysis Of States And ControW, in David A Wise. Editor, Issues In The Economics of

Aging, Chicago: University of Chicago Press, 1990, pp. 317-379.

Stock, James H. and Wise, David A., “The Pension Inducement to Retire: An Option Value

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September, 1990b: 58(5), pp. 1151-1180.

52
Appendix

Constmction of The Opportunity Set

The Wage.

To construct the wage profile, we begin at the last obsemation of full-time arrnud

wages mtd sdties. This figure is projected forward on the basis of the tenure, experience,

and if appropriate; heafth coefficients in the fixed effecb” wage regression. It is atso projected

backward on the basis of these coefficients untfl the next obsewation of full-time wages and

salaries is encountered. That obsemation is used, and is projected backward urrti the next

obsemation is encountered. This process is repeated for each successive annual wage and

salary obsewation. For years before the beginning of the sumey, there may be a time before

the start of the job held at the beginning of the sumey when we do not obseme the sequence

o.fjobs, and hence do not know the tenure levels. In this case, we assume that such years

formed a single job.:’. If the experience levels at the beginning of the sumey indicate

insufficient experience to fill in the wage profile back to age 25, the wife is asstsmed to have

been out of the labor force in the remaining years.

Construction of the wage profile for husbands follows a similti strategy as for the

wives, except that it is the age coefficients that are used to project wages between acturd

observations of annuaf wages and salaries. For the years before the beginning of the survey,

the wages were projected backward until age 25, the beginning year of the period used in

31. This assumption probably does not matter a great ded, since it has only a minor effect

on the toti lifetime earnings (y) and no effect on annuaf compensation (w) in any year used

in crdculating the retirement values of E.

53
both the estimation and simulations.3z

The hourly wage regression is estimated based ofi usable hourly wage observations in

non-self-employed jobs. For each observation, variables are created for education, health

status, residence (centraf city, suburban, rural, and south or non-south), industry (9 categories),

and occupation (3 categories). These variables are measured at the time of the survey. h

addition, i-reputed tenure and experience variables are used. For tenure, the NLS lists a

unique employer number for each job, so that it is possible to see whether the wife worked

with the same employer in previous years. The beginning date of the job is the survey date

the wife first worked for that employer, unless the wife worked for that employer in the first

survey (in which case the beginning date is calculated from a question in the first survey

about the length of time the wife had been with that employer). Once the beginning of the

job is @ablished, te]~tire is cafcula~ed as the time from the beginning of the job to the sur~,ey

in question.33 A simi !ar approach is taken to construct the experience variable. k the first

survey, the wife was ~sked how matty years of full-time work she had engaged in before that

32. There would be a problem with this strategy for calculating the wage profile if either

the husband or the wife dld not have any vafid observations for full-time annual wages “=d

salaries. This does not often happen if the couple met the other selection criteria, but in the

relatively few cases where it does, the couple is excluded from the sample. It might have

been possible to project the wages from the wage equations, but the estimated Rz of the wage

equations leaves plen~ of room for large errors in such an imputation process. Basicafly, if

there are no observations to pin down whether we are t~ng about a high-wage or low-wage

worker, the entire profile may be very poorly located, and in such cases we deemed it

advisable to omit the couple from the sample.

33. This method of calculating tenure will produce consistent numbers across different

surveys. This eliminates inconsistencies where, for instance, the individud reports that he has

worked for the employer 10 years in one survey and, when asked the same question two years

later, responds that he has worked 9 years in the later survey.

54
survey. The experience variable simply increments this v~ue by one or two (depending on

the length of time between surveys) if the wife reported workng full-time at the time of the

survey.

The resulting (log) hourly wage regression for the wives is presented in Table A.1.

Marty of the variables are significant, “and most have the expected sign. The second order

terms of experience ‘~d tenure indicate that both have the expected concave shape. The

effect of experience pe~ after only 28 years, but this is counteracted to some extent by

tenure petig after 54 years. The R* of this regression is 50%, which is certtinly

respectable for a wage regression.

Since severaf observations for each individud are included in the regression, it is lkely

that the regression contains a fixed effect, meaning that some individuals consistently earn

more due to facmrs not included in the wage regression, and others less. Such a fixed eifcct

may cause the standmd errors in the regression to be understated, and if it is correlated with

other explanato~ v~ables, it may lead to biased estimates as well. Table A.2 presents

estimates which mow for the fixed effects among individuds. This regression drops out

education, since any variable which is constant for a particular indlvidud cannot be

distinguished from the fixed effect. The results for the health, residence, industw, and

occupation variables show widespread reductions from the values found in the previous

regression. The linear term in experience is unchanged, but the second order term now

suggests that the effect of experience pe~ at around 40 years. Both the linear and second

order tenure terms are reduced by about a third, but they still indicate a pe~ in the effect of

tenure at a little over 50 yews.

55
For the husbands, a similar strategy is followed, except that there is not as much

information for the husb~d in the survey. In evev survey yea” except 1968, the survey MS

about the wage ad salary income of the husb~m over the previous 12 months (or sometimes

the previous calendar year). This information is much the same as was collected from the

wives. Mso, the section on other household members collected information about the

husbands occupation, if he was worting. The surveys dld not co~ect regulw information

about the industry of the husbands employer. Also, they did not regularly W about the

length of the husbantYs stay with an employer, nor were we able to teU whether the husband

had been with the same employer as in the previous survey. This mems that it is not

generally possible to construct a tenure variable.

As a result, the wage regression for husbands omits experience, tenure, and indust~ and

54 Tbe results Me pr~ented in Table A.3. Agtin maY of the v~ables ‘e adds age instead. .

significant and of the expected sign. The relative magnitudes of the linear arrd second-order

age terms indicate that the effect of age pas at around 50. The resulE of the fixed effects

regression are presented in Table A.4. This regression sharply reduces the effects of heaftil

md occupation, but not of centraf city or suburban location. The age coefficients are about

10-20% lower, but they still indicate that the pe~ effect of age occurs at around 50 years old.

Pensions

We are particulmly concerned with pensions on the last job before retirement, since

these pentions contain incentiv~ relevant for the retirement decision. We are in relatively

34. We could have used an experience vtiable rather than age, but if experience is defined

as (age - education - 5), the two variables are pitting up the same effect, given that education

is also in the regression.

56

—
good shape if the individusd worked until at least 1982. h that case, we can tell reasonably

weU whether the irtdividuaf retired under a pension. The years of service in the job is

avtiable h most instances. b many cases we can tell the age they were first ehgible for a

pension, and we can get at least one figure as to the amount of the expected pension.

However, the information on the norrnd retirement age appeas in generaf to be either missing

or unreasonable, and very few indlviduafs provided enough information to be able to infer

how much pentions are reduced for wly retirement.

Faced with this situation, we proceed as follows. For individuals who were covered on

their last jobs before retirement, we use the last figure they reported as the emly retirement

35 [f the individu~ reported that be or she w~ age. ff no figures ae reported, we use age 55..

receiving benefits after the last year of full-time work but before the repofied early retirement

age, the early retirement age was adjusted downward to be consistent with the reported

benefits. The norrnd retirement age, about which we have relatively little information, is

taken, to be 62 except if the indlvidud retired around age 65, in which case the norrnaf

retirement age is taken to be 65. For women, the tenure is the tenure calculated for the wage

profiles, md for men, if no tenure is given in the pension section, tenure is measured from

age 25..

For incfividuds who retired before 1982, we hake much the same information about the

.. .

35. Age 55 is the mow..common early retirement age among those who do report an early

retirement age. The d~ribution of cases is as follows

TotA pedons--wiv~ 399

Of which early retirement date imputed 48

Total penions--husbands: 319

Of which early retirement date imputed: 133

57
pention, but the data do not indicate which job is associated with the pension. For women

who retire before 1982 and repofi that they had a pension, the pension is considered to have

come from the latest job if that job lasted for longer than five years.3b For the husb~ds, we

have Iitde choice but to assume that if they retired before 1982 md had a pension, the

pension came from the last full-time job. If it appears that the pension did come from the last

job, the calculations of the value of accruals proceed in the same manner as outhned above.

If the pention is from a job previous to the last job, the incentives from the pension do

not affect the retirement decision directly. The only effect of these pensions on retirement is

through a wealth effect. The wealth effect can be cafcrrlated from the sifi of the pefion and

the length of time the indlviduaf has been collecting it, which we bow for most such

individuals. In cases of missing information, the pension amounts andor the period of

coUection are constructed along the lines outlined for individuals who receive pensions on

their last job.

36. The numbers for each of these cases are as follows

Pentiom before 1982

fmputed to last full time job >5 years 22

Imputed to previous job on basis of years of service: 10.

Imputed to longest previous job: 3

Note that the pension is considered to come from the latest job if that job lasted longer

than five years. M the latest job lasted less than five years, previous jobs are searched for the

one whose tenure came closest to matching the tenure given in the pension questions. If no

tenure was given in the pension questions, the pension is tken to come from the longest

previous job.

58
Table A.1

Wage Regression For. Wives

Dependent Vari~le: Log of Hourly Wage

Mean 1.390

S-ndard Deviation .444

Coefficient

COr.stant .476

Education

Years of Education .043

High School Graduate -.007

Years 0 f Co 1lege -.010

CO1 lege Graduate .057

Health Probla -.082

Residence

Central City SMSA

suburb- SMSA

.152

.158

South

Years of

s~are

Years of

Square

Industry

-.126

E~eri enc.e .015

of Experience / LOO -.027

Tenure 013

of Tenure / 100 -:012

Agriculture, F(>r+stry & Fishing -.233

Mining .212

Construction .036

Transport & Communication .146

Wholesale & Retail Trade -.230

Finance, Insurance & Real Estate -.061

Services -.132

Public Administration .074

Occupation

Management & Professional ..384

White Colla ..173

t

Statistic

1.1.84

11.14

-0.50

-1.41

2.13

-7.73

16.31

17.25

-15..7”0

8..61

-6.93

8.24

-2.36

-5.17

3.06

0,89

6.80

-17.87

-3..59

‘12.61

4.2S

29.93

16.22

11.8

.694

.755

.133

.139

.327

.347

.411

20.5

505

.9.9

159

.. 007

.003

.009

.036

.146

.070

.439

““:06s

.273

.379

Nwber of Observations = 7317

R Sqare = 0.5036

Standard Error of Estimate = .313

59
Table A-2

Fix4 Effects Wage Regression For Wives*

Dependent !lariable:. .Log of Hourly Wage

Mean 1.390

Standard Deviation “ .444

Health Problem

Residence

Central City SMSA

Suburban SMSA

South

Years of EWeri Sice

Square of E~erience / 100

Years of Tenure

Square of Tenure “7 100

In”dustry

Agriculture, Forestry & Fishing

Mining

Construct ion

Transport G Co-unication

Wholesale &. Retail Trade

Finance, Insurance .& Real Estate

Services

Public Atiirl~: ,..:l,t ion

Occupat ion

Management & Pr: i:essional

White Collar

Coefficient

-.030

.019

.043

-.073

.015

-.018

009

-:008

-.123

..032

-.039 ‘“

-.018

-.131

-.042

-.119

-.04a

.061

.004

t

Statistic

-3.58

t<ean

.139

0.79

1.88

-2.22

10.51

-5.88

6.88

:. -2.01

-2.87

0.40

-1.13

-0”.65

-8.47

-1.77

-8.27

-2.31

4.73

0.3.1

.327

.347

.411

20.5

505

9 .,9

159

.007

.003

.009

.,036

.146

- ~., .,

.433

q:,

.s

,3.7.>

Number of Obser.>ations = 7317

R Square = 0.8265

Standard Error of Estimate = .185

* Regression incluties dumy variables for rep=ted observations on each

individual.

60
Table A.3

Lrage Regress ion for Husbands

Dependent Variable: Log of Hourly Wage

Mean 1.809

standard Deviation .498

Const=t

Education

Years o f Educat ion

High School Graduate

Years of College

CO1 lege Graduate

Health Problem

Residence

Central City SMSA

Suburban SMSA

South

Age

Square of Age / 100

Occupat ion

Management & Professional

White Collar

Coefficient

.021”

.049

.048

-.016

-.028

-.113

.184

.209

-.168

047

-:051

.211

.073

t

Statistic

0.10

9.50

2.02

-1.55

-0.71

_~:TT..

11.42

14.49

-~j.~g

5.82

-6.09

12.44

3.61

Number of Observations = 4s75

R Square = 0.3120

Standard Error of Estimate = .413 .“””-”””-

61

Mean

11.8

.656

1.04

.178

.104

.257

.407

.370

49.2

2483

.325

.124
Table A.4

Fixed Effects Wage Regression for HusbandsDependent Variable: Lcg of Hourly Wage

Mean 1.809

Standard Deviation .498

Coefficient

Health Problem -.054

Residence

Central City SMSA .220

Suburban SMSA .221

South -.120

Age 042

Square of Age f 100 -:042

Occupation

Management G Professional 004

White Collar -:022

t

Statistic

-3.18

6.31

7.00

-2.89

7.33

-7.07

.26

-1.07

.104

..257

.407

.370

49.2

.2483

.325

.124

blumber of Observations = 4575

R Square = O .7224 ‘

Standard Error of Estimate = .2622

* Regression includes dummy vtiables for repeated observations on each individud.

62
Retirement In A Family Context: A Structural Model For Husbands and Wives

Alan L. Gustman

, Dartmouth College and National Bureau of Economic Research

and

Thomas L. Steinmeier

Texas Tech University

Executive Summary

L Introduction.

This paper specifies and estimates a stmcturd model of the retkement decisions of

husbads and wives. The feature of the data that is the focus of this paper is the tendency of

husbads md wives to retire together. An econometric approach is developed for estfiating

preferences of both spouses jointly md is implemented using data from the Nationaf

Longitudmd Suvey or Mature Women (NLS), a sumey that provides the most recent data

avtilable for a joint retirement study. Alternative specifications of j oint” decision m~ng are

tested, md the impo~ce of vtious sources of interdependence in decision m~ng are

tivestigated.

In the course of specifying md intimating the retirement model for couples, we address

the following spectilc questions How does the retirement behavior of each spouse compme

to that of the other? To what extent is the wife’s retirement decision influenced by the

husbartds, the husbmds decision influenced by the wife’s, acrd ‘to what extent me their

unmeasured tastes comlated? How does interdependence in the opportunity set md in

preferences affect the coordination of retirement by the spouses? What are the effeets on

i
model parameters of entirely ignoring interactions in preferences? What are the’ effects of

using an inappropriate estimating technique, one which treats each spouse’s retirement

decision as exogenous, ~d therefore does not recogni~ the dependence of each spouse’s

retirement decision on the other’s?

Although wives are younger, and women retire at younger ages, we find that husbands

and wives coordinate their retirement. One reason is a coincidence of tastes for leisure.

More importantly, each spouse, and perhaps husbands in particular, find leisure in retirement

to be more vrdrrable once their spouse has retired. Holding jobs with similar incentives is not

the reason husbands and wives coordinate retirement dates.

The present anafysis joins together two branches of the retirement literature. In one,

structural retirement models, that is modek that separate the roles of market opportunities and

individud preferences, are estimated from data on individuals, usually men, while ignoring

the behavior of their spouse. In the other, retirement decisions of husbands and wives, md

the tendency of their retirement dates to cluster, are andymd in the context of equations in

which retirement outcomes for each spouse are related to a set of explanatory variables, but

the itiuences of preferences and tastes are not sep~ately arrdy~d.

In a world where both the husband and wife are more and more likely to be working

until the retirement years, this kind of a model will be increasingly necesa~ to assess how

pention, social security and other retirement related policies affect retirement outcomes,

including the question of whether policy measures which affect the retirement decision of one

family member ca indirectly influence the retirement of the remaining spouse.

A second purpose of this paper is to provide a structural retirement analysis using much 

--

ii
more recent data for a nationally representative panel study than has been used in the past.

The women in the National Longitudlrtd Survey of Mature Women (NLS) were born between

1923 smd 1937. They have been surveyed since 1967. In the last y= for which the survey

is available, 1989, they were 52 to 66 years old, about as young as feasible for a retirement

study.

The paper dso addrewes a number of econometric and behavioral issu~. One issue is

selection bias. h an old panel data set, ~1 couples have retired, so there is complete

information on retirement dates and on the characteristics of al individuals included in the

sample. In a more recent panel such as the National Longitudind Survey of Mature Women,

many of the couples are too young for both to have retired. Accordingly, in the process of the

anrdysis, we ded explicitly with truncation of continuing employment spells, that is, the fact

that we do not observe the ultimate retirement date for one or both members of the couple.

Section II of the paper presents evidence from the NLS that in fact, in the raw data,

there is a noticeable tendency among couples who have both retired to retire together. A

fmily labor supply model is developed in Section III. Section IV details the data preparation

and presents dtemative estimatm of the model. Section V presents some simulations based

upon the estimated model, concentrating mainly on the extent to which the husbands and

wifds retirement decitions * coordinated. A finat section presents some concluding

thoughts.

II. Evidence of Joint Retirement.

There is not much point in invmigating the cause of couples tending to retire together

if the phenomenon is not evident empirically. Section II presents data that verifies that the

.

111
phenomenon does exists in the NLS older women’s data, and documents the sample which is

used is this section and in the remainder of the project.

In this study retirement is defined as no. longer working full-time. The sample we use

from the Nation~ Longitudind Survey of Mature Women (NLS) is restricted in several ways

in order to meet the objectives of this paper. First, the sample is restricted to women who

remained in the survey. Second, since the project focuses on the joint retirement decisions of

husbands and wives, the sample is restricted to women who were married to the same mmr in

each year of the sample, and to those couples both of whose members survived. Third, the

sample is restricted to women for whom the idea of retirement is a “meaningful concept

because they have spent a prolonged period as a full-time member of the labor force.

Specifically, to be included in the sample, the woman must have been wortig full-time (at

least 25 hours per week) for at least three consecutive surveys after the age of 50.

Data on retirement date differences between husbtids and wives is found to exhibit a

distinct concentration of retirement when the husband and wife retire simultaneously. Given

the way the retirement dates were constructed, what this reafly means that there is a

concentration of couplas reporting the last date of full-time work in the sam~ survey year.

The concentration of retirements at dates so close to one another suggests that couples do

tend to retire at about the same time, rmd that this phenomenon is evident in the data to be

used in this study.

111. A Model of Family Labor Supply and Retirement.

Section ~ develops a model of family labor supply and retirement, and finds an

approach to estimating the model empirically. The model begins with a fairly standard

iv
preference funcfion in which utility depends on lifetime consumption of the family together

and the labor supply (leisure) of the husband and wife indlvidutiy. Uttity is gained from

●

consumption and leisure at each moment in time, and is *O influenced, among other fhings,

by age and health. As each spouse becomes older, eventually the value of retirement

outweighs fhe value of the wages from working, and the individud retires.

There are three ways in which this is a family labor supply model. first, the

consumption in this utifity function is not the consumption from the wife’s or husbands own

e-gs, but tie family consumption financed by the earnings of both husband md wife.

Second, the value the wife places on leisure is itiuenced by the retirement status of the

husband, in that she enjoys her retirement more when he is home. Simflarly, the value the

husband places on leisure is specified to be influenced by the retirement status of the wife.

Finally, the retirement preferences of the husband and wife may be correlated because people

who share the same tastes Me “more likely to marry.

Both husbad and wife choose a path of consumption and work md ultimately

retirement, consistent with their preferences, but subject to the constraint that lifetime family

consumption cannot exceed family income. In this budget constraint, the value of

consumption over the lifetime cannot exceed the value of wages, pensions and social security.

In any given year, the wife would want to work if the value of the wages exceeds the

value of the leisure foregone, and otherwise she would want to retire, and the same is true for

the husband. A methodology is developed for determining the range of values placed on

leisure which would lead each individud in the sample to decide to retire, given the labor

market opportunities they faced. The estimating routine searches for vdu= to place on

v
parameters representing each individuals vafuation of leisure, searching for parameter values

that would mtimi~ the l~elihood of the individud retiring when he or she does given those

Opportunities. That iS, in light of the opportunities avtilable to each husband ~d wife, and in

view of the retirement behavior they exhibited, the estimating routine XS what parameters

of their preferences are most lkely to account for the behavior that is seen in the sample?

The methodology is detigned to allow the preferences of the husband and wife to

interact on a number of dimensions, and incorporates the fact that the value placed on leisure

by one spouse is lkely to be kfluenced by the retirement status of the other. To implement

the estimation scheme, it is necessary to adjust the estimation procedure to include the

information on incomplete employment spells for those who have not yet retired. Dropping

the many couples with one or both pmrters still worfdng at the end of the observation period

would subject the estimates to censoring. Accordingly, the methodology is adjusted to

incorporate the information on retirement behavior for dl of those couples in which o~y the

husband, or only the wife has retired, or indeed if neither has retired.

IV. Estimation of the Model.

The data requiremenfi for estimating the model fall into three categories. First, the

dependent variable (retirement) must be measured. The other data requirements are for

measures of the elements which affect the vrdue the individud places on leisure. These are

age, spouse retirement, heafth, and vintage. The age variable is the indlvidutis reported age

in 1967, incremented by 1 for each year. Vintage is simply 1967 minus the age in 1967, and

spouse retirement in a given year is whether the spouse is retired at the time. For the health

variable, we examine in each year the answers to questions about whether health prevented

vi
.

the individud from working or whether herdth limited the amount or kbrd of work that could

..

be done.

The major difficulty in preparing the data set for estimation k to calculate compensation

streams. The compensation streams consist of three componens wages, pefions, and social

security.

For dl the survey years except 1968, the survey asks about annrrd income from wages

md salaries, as wefl as enough information to constmct rm hourly wage rate. For tiose years

in which the wife is working full-time at the time of the survey and for which usable annual

wage and sal~ information is available, the armu~ wage and sal~ information is used. For

other years, annual wages must be imputed. The imputation process uses the tenure,

experience, mrd health coefficients from an hourly wage regression with fried individual

effects.

The next element of compensation is the pension profile. information on pensions

comes mairdy from questions that were asked in 1982, 1986, and 1989. In the fiist two of

these YWS, the survey asked about whether, the respondent W= eligible for a pen~on from

the current or past job. If the tidividrr~ was eligible for a pention from either the current or

past job, the sumey inquired about the years of service in that job. If the pension was for the

current job, the survey afso asked about the age of initial eligibility for benefits. The 1989

survey expanded the questions so that they include the early and norrnat retirement ages on

the present job, the ealy and normal retirement ages for pensions on previous jobs, and the

amounts that the individud would be eligible to receive on those dates. h addition, the

survey asked about the actual amount of benefits received K the respondent reported that

vii
benefits were currently being received. The pension is calculated on the basis of this

information assuming that the individud faces a defined benefit pension plan.

The present value calculations for social security are similar to those fot the pensions.

WorMng another yem can change the present value of social security benefits for three

reasons. First, higher rd wages during prime wortirrg years are Ifiely to displace earfier

wages from the average earnings calculations, increasing benefits. This effect is enhanced for

those over sixty years of age beca~ under the calculation of average indexed monthly

earning (AmE), the basis for calculating monthly benefits, wages are indexed ody to age 60.

Second, if the individud is over the early retirement age, worbng mother year wiU reduce

the early retirement reduction factor or increase the delayed retirement credit. FlrtMy, if the

irrdividu~ is over the early retirement age, wortig another ya may cause benefits to be lost

to the earnings test. In general, the effects of the social security system are to cause

reductions in compensation primarily at the norrnat retirement age, since the delayed

retirement credit is lIut sufficient to offset the loss of benefits from conttiuing wortig.

The overti compensation paths for the wife and the husband are calculated by adding

to the wage the accruals for social security and, if appropriate, the perrtion. These are then

combined with the retirement ages of both spouses and the values of the variables reflecting

age, vintage, spouse retirement status and herdth, to provide the data set for estimation. The

find data set has 564 observations of couples who satisfied dl of the inclusion criteria and

who had at least one wage and salary figure on which to base the compensation paths.

The estimation begins with a simple model in which =cb spouse is assumed to retire

independently. The estimates indlcare that having a hdth problem has the same effect on

...

Vul
retirement as being not quite two years older, and the effect of vintage is ve~ srn~. The

standard deviation of the retirement me term amounts to over five times the coefficient of

the age term. It is ffily cleu that the taste term plays a very large role in accounting for the

large range of ages at which various individu~ retire.

For the husband, the vahre of the health coefficient dso antounm to a fittle over three

times the magtitude of the coefficient of the age temr, and the standard deviation in tses for

retirement are a fittfe over five times the sire of the coefficient of the age term. The age term

itseff is somewhat larger than it is for the wives.

When interdependence in retirement is exmined, but not in the context of a fuUy

integrated model for both the husband and wife, there is some suggestion that the husbmds

retirement does not affect the retirement preferences of We wife, but the wtie’s retirement hm

a notable effect on the retirement preferences of the husband. One possible rationale for this

result is that some husbands do not wish to fiid themselves with more time to take care of

the household wtie the wife is sti~ devoting a substarrtid pm of her time to market work.

But stronger confiiarion of this result and investigation of further impficarions would be

required before any conclusion is drawn.

& dtemative explmation for couples retiring at mound the same time is examined. U

men and women who prefer to redre early tend to marry one other, and men and women who

prefer to retire later (and consume more over their lifetimes) tend to marry each other, the

tastes for leisure of husbands and wives will be correlated with each other. When this

explanation is examined in iso Iation, the estimates indicate that the correlation in preferences

. is bigtiy Sigtilcant.

ix
Given that each spouses retirement decision k“ influenced by the retirement status of the

other, it becomes impoflant to rwogni~ in the estimation the joint determination of

retirement, and not to assume that the retirement status of one spouse is an exogenous

determinant of the retirement status of the other. Moreover, the model should be specified to

incorporate W influences affecting the decisions of the husband and wife.

When th~e two competing explanations are included in the same equation, the

correlation in preferences is only about two-thirds as large, but it is sti~ higMy significant.

The spouse retired coefficients now both have the proper sign, but neither one done is

Significmt. However, the combined effect of the two of them is margirrtiy significWt.

Because the relative effects of these different dimensions of preferences cannot be inferred

simply by comparing the relative sim of the parameters, the issue is investigated by

simulation.

V. Simulations Of The Effects Of Husband Wife Retirement Interactions.

The simulated r~.irement outcomes track the retirement outcomes in the data fairly well.

The model dso does a good job of simulating the coincidence of retirement dates among

couples. When the full model is estimated, there is a sharp pe~ at ~ro difference in

retirement dates, with over eleven percent of the couples retiring at the same time, whereas

I

for other age differencei,-the probability ranges around 4 or j percent.

It is clem that the source of interdependence in retirement is in the coordination of

‘preferences among spou=s and is not due to the correlation of incentives between the

oppofiunity Sets factig husbmds and wives. This result is seen by comparing the probability

of joint retirement” under th: full model, where rdl sources of retirement are included, with the

x
probabili~ of joint retirement when M sources of interdependence in the utfity function are

suppressed, but tie .opporturdty sets remain unchanged.

hvestigating the source of the interdependence within the u~ty function, the

conclusion is that joint retirement is due tiost entirely to the presence of spouse retirement

status in the utfity function. It appws th~ conaidefing the SPOU*’S retirement irnphes that

couples have a considerably greater probabfity of retiring together. The modest estimated

correlation between the preferences of husbands and wives produces a modest incr~ in the

tendency of couples to retire around the same time.

k sum, from the Simuhtions it is clear that most of the coincidence in retirement

dates at ~ro years difference in retirement dates is due to the spouse retirement variables.

Dropping the timple correlation between the error terms d~es this pek ordy dightly,

but dropping the retirement status of one spouse in the leisure valuation of the other host

etiinates it.

A fmaf simulation shows that in cases where the wife reb first, about 42 percent of

the husbrmds would delay retirement by another year if the spouse retirement effect were

inoperative. For the affected group, this trandates into an increase in the average retirement

age of about 5 months. Wtie this is not an overwhelming effect, it is in”the same order of

magtitude as the average effects which have been reported in the literature for pefions and

social security.

VI. Summary and Conclusions

——

This paper specfles and estimates a structured retirement model h which retirement

* decisions by husbands and wives are jotitly determined. The estimated model genera-
behavior that brings the retirement dates of husbands and wives closer than their” age

differences, with the probability of retirement peaking ‘at the same time for over eleven

percent of husbands and wives.

Although the estimation procedure is unable to separate out the spouse retirement

coefficients,” both of the competing explanations (the spouse retirement explanation and the

preference correlation explanation) are significant in the data. Simulation indicates the

relative impommce of each of these sources of interdependence in incting coordination of

the retirement outcomes of spouses. In contrast, there is no evidence that the coordination in

retirement outcomes results from couples selecting jobs with pensions offering compatible

incentives. Accordingly, in contrast to the support found for the hypothe~s that coordination

of retirement outcomes is due to interdependence in preferences, support is not found for the

hypothesis that coordination in retirement of spouses results from coordination in the

incentives created by the spouse’s opportunity sets.

Moreover, the evidence suggests that ignoring the statistically signtilcant effec~ of orie

spouse’s retirement behavior on that of the other, by treating retirement outcom= of one

spouse as an exogeno,.ls determinant of the other’s, does affect the estimates of other key

parameters in the model.

There is some suggestion in the data that the wife’s retirement decision is not strongly

influenced by the husbands, but the husbands decision is more strongly influenced by the

wife’s. Although such a result is consistent with an interpretation that the husband would

rather not face the house and related work load done, this result is a preliminary suggestion

that requires further support.

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Finally, because the Nationaf Longitudin~ Survey of Mature Women provides the most

recent, nationtiy representative longitudirrd sample available for a study of retirement

behavior, the results reported in this study take account of the labor market trends shaping the

retirement behavior of women, at least to the extent that these trends have influenced the

experience md behavior of the youngest generations of women yet to enter retirement.

Although some members of the cohorts included in the NLS have not yet retired, there is

~ily to be only a smafl effect on key parameter estimates.

explicitly accounted for incomplete employment spells.

The estimating technique has

*

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