Social security and the choice between full-time work, part-time work and retirement

Journal

of Public Economics

14 (1980) 245-276.

4‘1 North-Holland

Publishing

Company

SOCIAL SECURITY AND THE CHOICE BETWEEN FULL-TIME WORK. PART-TIME WORK AND RETIREMENT A. ZABALZA,* London Schol

C. PISSARIDES

and

of Economics.

WCZA 2AE, UK.

Revised version

London

received

M. BARTON

April 1980

This paper investigates the determinants of retirement declslons in the UK. To deal with the endogeneity bias introduced by the piecemeal linear budget constraint generated by the social security system, it specifies a utility function in income+leisure space and assumes that individuals maximise it ober three discrete regimes: full-time work, part-time work. and retirement. Usmg maximum likelihood techniques, it estimates the utility function and quantifies the Influence of pensions. wages and personal characteristics (age, health, status, etc.) on the probability of partial and complete withdrawal from the labour market.

1. Introduction Social security is a tax-transfer system that affects individuals’ budget constraints and relative rewards from work and leisure, so its optimal design depends on individuals’ responses to its existence. Several studies have recently attempted a quantification of these responses by investigating the factors that influence the labour market choices of people near the end of their working life.’ A serious problem that besets cross-section studies of this type arises out of the discontinuous changes that take place in the rates of taxes and benefits associated with social security, as the person moves along his budget constraint. The ‘kinks’ introduced in this way render ordinary estimation of neoclassical labour supply functions least squares unsatisfactory, because they violate the assumptions required for efficient estimation.2 For this reason, most studies of retirement concentrate on the *Thrs work was carried out at the Centre for Labour Economics, London School of Economics, and an earlier version was presented to the NBER-SSRC Conference on Econometric Studies in Public Finance, held in Cambridge. 13-16 June 1979. We are grateful to J. Abowd. T. Barker, H. Davies. J. Gomulka, L. Hamill, H. Joshi, R. Layard. S. Nlckell, D. Piachaud, H. Wills and an anonymous referee for useful comments and suggestions. We would also like to thank the Department of Health and Social Security and the SSRC for support, and the Office of Population Censuses and Surveys who collected the data. ‘See Boskin (1977). Quinn (1977), Boskin and Hurd (1978) and Blinder and Gordon (1980) for the U.S.; and Zabalza, Pissarides and Piachaud (1979) for the U.K. ‘See Burtless and Hausman (1978), and Wales and Woodland (1979), for a discussion of this problem.

explanation of the two-state choice between being in and out of the labour force, ignoring the adjustments that people may make to their hours of work in response to the transfers associated with social security. In this paper we extend the cross-sectional analysis of participation and retirement by allowing individuals to choose between three states instead of the conventional two states discussed above. In particular, we consider choices between ‘full-time work’, ‘part-time work’ and ‘retirement’. As it will become evident below, this extension requires the specification and estimation of a utility function for each individual in the sample, and then the maximisation of this utility function over the three labour-market states, suitably defined for each individual. We specify and estimate a CES utility function by employing a maximum-likelihood estimation technique. The extension from two to three states is quite important for the study of the effects of social security on labour supply, since it introduces the possibility of ‘partial’ withdrawal from the labour market, by moving from the full-time to the part-time state. For most individuals the penalising implicit tax associated with the earnings rule will not be operative at parttime work, so the earnings rule may push those that would otherwise work full-time to part-time. It is still. of course, the case that our approach is more restrictive than a full-blown analysis of hours of work that takes into account all the possible kinks of the budget constraint. The latter utilises more information but it is considerably more complicated than the approach that we are proposing; whether it can add much to what we obtain below from the three-state choice framework will have to await its formal treatment. However, we believe that the severe restrictions that workers face in their choice of hours, where changing hours of work may often involve long and protracted searching for an alternative job with the required number of hours, increase the attractiveness of the type of model that we develop here. Indeed, this is to a large extent borne out by our sample, where hours actually worked are not bunched at or near the kinks of the budget constraint, as we would expect if continuous adjustments were possible.” Section 2 of the paper introduces our theoretical framework and defines the utility function and budget constraint. Section 3 describes briefly the data set. section 4 presents the results of the econometric analysis and section 5 concludes by summarising the main findings. 2. A model of retirement decisions Before defining precisely the three states to which we restrict choice, it is instructive to develop the conventional budget constraint in net income‘The reason that hours are not bunched at kinks may be due to the costs of changing one’s hours of work. Smce tax changes move the kinks around over time, if it is costly to change hours. e.g. If it requires searching for an alternative job, individuals may not aim to be at kinks at all times.

leisure space, faced by individuals around retirement age. This is done in fig. 1 where for simplicity income taxes and social security contributions have been assumed away. State retirement pensions become available to men aged 65 and over, and to women aged 60 and over provided that they do not have a husband under 65. The opportunities faced by the younger workers not entitled to a state pension are shown in fig. 1 by the line AFG, with FG indicating income from sources other than employment. For men in the age group 65-69 and women in the age group 60-64 without husbands under 65, the social security system consists of three elements. First a retirement pension, indicated by the distance FE. Second an implicit tax on this retirement pension if earnings exceed certain limits, termed the earnings rule. At the time of our sample, the earnings rule taxed earnings at 50 percent if they exceeded &35 per week, and at 100 percent if they exceeded &39 per week, until the pension was exhausted. These implicit

A Net income A

G

FIN. 1. The effecr of

social

security

on

the budget

Leisure

consttmnt.

tax rates are shown by the slopes of the segments CD and BC respectively. However, instead of claiming their pension, individuals in these age groups could defer for a higher pension in the future. Deferrers do not receive a pension, so their relevant budget line has the shape of AFG. By deferring these individuals could claim a higher pension in the future so their total net weekly income from work is adjusted upwards by the present value of the increments for that week’s deferment, that will be gained from whenever the pension is claimed until death. At the time of our sample the increase in the pension achieved by deferring for a year was 6.5 percent of the pension, and this, capitalised over the expected retirement period of individuals in this age group, increased weekly earnings during deferments by about 40 percent of

the pension.” (The effect of any past deferments that have already been credited to the individual is simply to increase the height of the pension entitlement FE). Finally, men aged 70 and over, and women aged 65 and over, could claim a retirement pension irrespective of their labour-market status. For these age groups the relevant budget constraint is A’EG. The presence of income taxes and social security contributions (not shown in fig. 1) introduces further kinks into the budget constraint. It is clear that estimation of the set of preferences of each individual by specifying fully the budget constraint and assuming that hours can be adjusted freely by workers will generally lead to very complex likelihood functions whose maximisation may not always be feasible.5 In addition, as we argued in the Introduction. such an approach may not be the most appealing one on a priori grounds. when there are costs or institutional constraints to workers changing their hours of work. In fact, most studies with samples divided between different work regimes find that the major avenue for supply responses is not along a continuous set of hours but between discrete regimes6 For these reasons we propose here a new method for the estimation of the utility function which relies on an approximation to the budget constraint based on the definition of only three states with fixed hours of work in each state. All labour-supply responses to changes in economic variables come from switches between the states, and not through marginal adjustments in hours of work. The three states are retirement (zero hours of work), parttime work and full-time work. The opportunity set under these circumstances is shown in fig. 2, with the three states shown by points il (retirement), B (part-time work) and C (full-time work). The first point involves an amount L, of leisure and an amount Y, of net income. The second involves L, of leisure (Lb < L,) and Y, of net income ( Yb> Y,). The third involves L, of ‘In calculatmg this return we assumed a 10 percent rate of drscount. Since we do not know the duration of deferment for everybody, the figure used is an average of a maxrmum present value obtained for a period of increased benefit of 12 years (that is. for a person who defers during his first year of eligibility and then retires), and a minimum present value obtatned for a period of increased benefit of 8 years (that IS. for a person who defers during hrs last year of eligibility and then retires). In both cases, the number of years of expected benefit were obtained from life expectancy tables. We aiso tried rates of discount of 5 percent (giving a gross average return of 43 percent of the pension) and of 2.5 percent (giving a gross average return of 49 percent of the pension), but these alternative assumptrons made practically no difference to the final results. Notice that, if the return to deferment was actuarially fair, the adjustment would be an mcrease in weekly earnings equal to the whole pension. In terms of fig. I, this would change the budget constraint to A’EG. ‘We experimented with likelihood functions that admitted unlimited substitution of hours but were unable to obtain convergence. ‘For the U.K.. see Layard, Barton and Zabalza (1980). In their study, they found that married women were subject to similar limitations in the adjustment of hours. The main supply response to changes in economic variables was found to come from the choice of whether to participate or not, rather than from the adjustment in hours worked. For a similar finding with U.S. data, see Schultz (1980) and Hausman (1980).

leisure (L, yb > Y,).’ A sufficient requirement for selecting all three points with positive probability is that the opportunity set be convex, in the sense that the part-time work point (B) be above the line that links the retirement and full-time work points (A and C). However, as will be seen below for a wide range of utility functions, the method of estimation would still work with mild nonconvexities in the opportunity set.

(net

income) yl

Fig. 2. The opportunity

set

Individuals choose the state which yields highest utility, where the marginal rate of substitution between income and leisure is assumed to depend on individual characteristics. For instance, we would expect people with personal characteristics that discourage work ~~ people of old age, with poor health, etc. to have, for any given combination of income and leisure, a higher marginal rate of substitution between these two variables than people with personal characteristics that encourage work. We assume that the marginal rate of substitution is derived from a utility function of the CES form? ‘This way of looking at the opportunity set should be taken as an approximation, manner as a continuous budget constraint is also an approximation of the actual opportunities open to individuals. An empirical base for our approximation is given that hours worked have a quite well defined btmodal distribution for elderly people, by the following table:

Hours

o-5

Men ( “j;) 40.2 Women ( yo) 51.0

in the same set of work by the fact as is shown

611

12p 17

18-m 23

24 29

3om 35

26m 41

42~ 47

48m 53

0.7 4.5

2.1 6.6

2.9 10.5

1.2 5.6

3.5 5.7

29.2 13.7

9.8 1.9

6.9 0.4

54 3.3

_

This table is based on the sample of weighted data described in section 3 below, and excludes unemployed and self-employed Individuals. “As will be seen below, this leads to a maxtmum likelihood function with cut-off points which are linear in all the parameters except p. This is not serious because p can be estimated by search of the maximum likelihood, whereas all other parameters are estimated directly.

250

A. Zahulzu

et ul., Social sccurit), und choice

ui=[C(iYi”+(l-,~,)L;P]-l.‘P, ‘%i=

(1)

l/( 1 + exp ( -fix,)),

(2)

where Xi is a vector of personal characteristics for individual i, fl and p are parameters, and exp denotes the exponential function e(‘). The marginal rate of substitution between income and leisure (MRS) is defined as

which, using (2), reduces to MRSi=exp(-fiXi)(~/Li)‘+P.

(3)

Thus, for a given income-leisure ratio, the MRS depends inversely on the vector of personal characteristics. A person with a lower PX (expected to be older, with poor health. etc.) will have a higher MRS between income and leisure (i.e. his indifference curves will be steeper) than will a person with a higher j?X (one that is younger, with better health, etc.). Thus, we should find that the person with steeper indifference curves will tend to prefer point A to points B and C, and vice versa for the person with flatter indifference curves. As is well known, the elasticity of substitution s is determined by the parameter p according to the expression .s=l/(l

+p).

The parameter p takes values from - 1 to z!. If p = - 1, then (1) reduces to a linear utility function, with linear indifference curves and, thus, with an infinite elasticity of substitution. If p = 0, the function tends, in the limit, to a Cobb-Douglas form, with unit elasticity of substitution. Values of p greater than zero will lower the elasticity of substitution of the function and, therefore. increase the degree of curvature of the indifference map. In the limit, if fiXi+ + ;(J, ~~41 and the utility function becomes

with horizontal indifference lines. Then fiXi-, - YJ, r,+O and the utility function

C is always is

preferred

to A or B. If

ui=L, with vertical

indifference

lines. Then the person

always prefers A to B and C.

A. Zubulzu

The behaviour

et ul., Socicrl security

of a given individual

(1) He will choose point

and choice

can be represented

A (retirement)

251

as follows:

if

u(Ki3La)>u(Y,i3Lb)9

(4)

where Y,, and Ybi are the potential levels of income of the ith individual if he were to choose points A and B respectively, and L, and L, are as defined previously. Note that if A is preferred to B, then due to the convexity assumed, A will also be preferred to C. (2) He will choose

point B (part-time

work) if

where Xi is his potential net income at full-time work and all other have already been defined. (3) Finally, he will choose point C qfull-time work) if

Again due to convexity,

symbols

if he prefers C to B he will also prefer C to A.

Changes in the parameters that define the opportunity set will alter the height of at least one of the three points considered. If we knew the parameters that define the utility function, we could investigate for each individual whether the change in question keeps him in his current position or makes him change to another. From this, we could then make statements on labour supply effects. The parameters of (1) can be estimated from observed behaviour, and this is discussed in the rest of this section. So far, we have assumed that in the utility function (l), for a given income-leisure ratio, the marginal rate of substitution will vary depending only on observable personal characteristics. However, two persons with the same opportunity set and with the same personal characteristics may choose differently between A, B and C if one is a harder worker than the other. The harder worker would tend, other things being equal, to choose C while the other would tend to choose A. We can incorporate this into our model by making the marginal rate of substitution between income and leisure dependent also on some unobservable random element, which may indicate attitudes to work. Call this random variable F: and assume that it is distributed according to some probability distribution across the population. Then we can re-specify the function xi in (1) as Xi =

l/(1 + exp [ - (pXi + $)I),

(7)

Then MR&=exp[-(~Xi+~i)](~/Li)l+P. The larger i: is (the more hard-working the person is), the lower the marginal rate of substitution (the flatter the indifference map), and the more likely he is to choose C in preference to B and A. From data on net earnings and hours. we can estimate (1) using the results (4) to (6). The probability that a given individual is observed at point A, P,(A). is equal to the probability that his utility at point A. Ulli, exceeds his utility at point B, U,i. That is.

(8)

Pi(A)=P(u,i>u,,).

Similarly. the probabilities that defined, using (5) and (6). as

he is observed

at points

B and

C can be

Pi(B)=P[(u,i>u,i) n (Ubi>U,i)]

(9)

and

P,(C)=P(Uci>U,;). Given the ordinal character by (1) can also be obtained by lirr”=riY;P+

of our utility

(10) function,

the ranking

obtained

(1 -q)L;“.

Then, in general, for any two points MIand II the individual will prefer nz to n if P(C';io< C,ip)for values of j)>O> and if P(U;p> Uzp) for values of p ~0. For /, >O, the probability that an individual is observed at point A, P,(A), can be written as

Pi(A)=P[r,Y,z;"+ (1 -sci)L,“
(1 -xi)&“]

=P[cq(Y,Q- Yn;")+(1 -:i)(L;P-L;Q)>O]. Since by definition L,> L,?LhP - Lip will b e positive. Then dividing sides of the inequality by zi(L;P -Lip), the left-hand side reads

Then. using (7), this reduces to

both

A. Zuhulzu

P

rt al., Social

security

yGp-ylp i L_p_Lnip > -eXP[-(PXi+Ei)] h

Y

ctnd choice

253

1

Multiplying both sides of the inequality by - 1 and taking logs, we obtain, after rearranging, the probability that the individual is observed at point 4:

(11)

It is easy to show, following the same procedure, that for p 0 and p < 0, that

P,(il) is also we find, for

and

P,(C)=P{E,> -lIl(z$s)--flxi). Then the likelihood

function

(13)

is

where

and

which has to be maximised with respect to the parameters where the sample is composed of I retired people, J people time and K people working full-time.

p and J and working part-

254

A. Ztrbalx

et al., So&l

security

and choice

To make the model operational we assume that the variable a is normally distributed with mean 0 and variance rr‘. That is, E_ N(0, a’). Then, in terms of the cumulative function F( . ) of the standardised normal variable s/a, the likelihood function is L= I’r F(Z,i) I-,

~

[F(Z,j)-F(Z,j)]

il I1 -F(Z,,)l,

(14)

!%=I

j=l

where

(15) and

(16) From the maximisation of (14) we then obtain estimates of t/o, p/a and p. As can be seen from (15) and (16) the expressions for Z are linear in all the parameters except p. The method that we follow below, in section 4, to obtain this parameter is to estimate the model over a grid of values for p, and then select that value for which the log likelihood of the function is the greatest. Expressions (14) to (16) specify the likelihood function when either p>O or p < 0. If /, = 0, the utility function (1) tends to

and the corresponding likelihood and Z,, defined as follows:

function

is as in (14) with the values

Z,,

and

It is clear from (15) and (16) that, under the present framework, income is an extra pound obtained from an not distinguished by its sources; occupational pension will have the same effect on supply as an extra pound obtained from the state retirement pension. Given previous results obtained in Zabalza, Pissarides and Piachaud (1979), this constraint imposed by the model may not be very serious.

Expressions (14) to (16) also show why convexity in the opportunity set is needed. For expression (14) to be adequately defined we need Z, >Z,, so that the probability measured by F(Z,)-F(Z,) is some positive number. But from (15) and (16), this requirement reduces to y,p_ L,P_L;P

y;P

y;p<

y,p

L,P_L,”

)

(17)

which states that, for the transformed variables, the slope between points A and B be greater than that between points B and C. The requirement imposed above on the opportunity set is s@cient because whenever this is true for the natural value of the variables (as it will be if points A, B and C are strictly convex), it will also be true for their transformed value; it is not necessary if indifference curves are convex to the origin (p > - 1). In the empirical analysis we checked whether there were observations for which this condition was not satisfied, but did not find any at the p that best fitted the data, so no individual was excluded on account of nonconvexities.

3. Data and definition of variables The data used in the estimation were collected by the Office of Population Censuses and Surveys in Great Britain in February and March 1977. The original sample consisted of 1,940 men aged 55-73, and 1,484 women aged 5@73, all of whom had a job after age 45. The sample used unequal sampling fractions to ensure adequate representation of certain groups. Thus, for example, people above statutory pensionable age, particularly those economically active, were oversampled relative to other groups. However, for estimation purposes, all data were weighted so that, for each subsample considered, the proportions agree with those of the corresponding population. Also, for each subsample considered, the weights are defined so that their mean is one. This implies that the number of weighted and unweighted observations are equal. This equivalence, however, is lost when observations are excluded from the original sample on which the weight is defined. Due to lack of data on hours worked, unemployed and selfemployed people were excluded from the analysis; this left a sample of 1,646 men and 1,363 women. Missing observations on other variables further reduced the samples to 1,417 men and 1,178 women. These correspond to weighted samples of 1,483 men and 1,207 women. In w‘hat follows, all the analysis refers to the weighted data. Full-time work is defined as work for pay for 30 hours or more per week, part-time work is correspondingly defined as work for pay for less than 30 hours per week, and retirement is defined as zero hours of work. Of the total number of men in the sample, about 54 percent were working full-time, 7

A. Zuhalx

256

et ul..

Sociul security und choice

percent were working part-time and 39 percent were retired. For women, the distribution was 22 percent in full-time work, 29 percent in part-time work and 49 percent retired. The most notable variation in the percentage distribution of the sample over these three states occurs at age 65 for men and age 60 for women, when both state and occupational pensions become available to most individuals entitled to them. Table 1 shows the percentage distributions for men and women in the age groups just before and just after age 65 and 60 years respectively.

Table Percentage

distribution

1

of men and women just below statutory pensionable age.

and just

above

Age group

Full-time

Part-time

Retirement

Men

60 64 65-69

19 9

3 16

18 15

Women

55 59 60- 64

39 12

40 26

21 62

the

We hope to be able to say whether this variation is due to social security, aging, health, or some other factor, in the empirical analysis of section 4. The variables used to estimate the parameters of the likelihood function (14) are defined as follows: Net income differential. The first variable in the likelihood function is the net income differential between the different regimes adjusted by the corresponding differential in leisure. We begin with the definition of the leisure components. (i) Leisure. The values for leisure are taken to be 65 hours per week minus the number of hours of work in each regime. Experiments with other origins yielded similar results. Thus, leisure of the retired (L,) is defined as 65 hours for both men and women. Leisure of part-time workers (L,) is defined as 65 hours minus 17 for men (the rounded average number of hours of work for men working part-time) and 65 hours minus 16 for women (their corresponding average). Finally, using also average hours, leisure for full-time workers (,!,,) is defined as 65 hours minus 38 for women and 65 hours minus 42 for men. (ii) Net income. Income in each of the three states is defined as the potentiul rzet income that the individual would have, should he decide to place himself in that state. Thus, retirement income (Yai) consists of unearned income, netted according to the allowances and tax rates applicable to unearned income. The following components make up unearned income: state retirement pensions, occupational pensions, income from savings, and

imputed rent from house ownership. In 1977 there were just two rates of state retirement pensions; E24.50 for all married couples with a husband 65 or over, and E15.30 for single men 65 or over and for single women 60 or over. Since our analysis is based on individuals and not on households, we followed the criterion of assigning to each individual the maximum amount of a pension that would be lost if he or she undertook paid work. This gives an idea of the different opportunity cost of working for different individuals. Thus, our state retirement pension takes the value E15.30 when the person is a married man 65 or over with a wife 60 or over; 224.50 when the person is a married man 65 or over with a wife under 60; E15.30 when the person is a single man 65 or over, a single woman 60 or over, or a widow under 60; and E9.20 (L24.50 minus E15.30) when the person is a married woman with a husband drawing a pension; otherwise, this variable takes the value zero.’ Since data about the amount of supplementary benefit received were not available, people receiving this benefit, or likely to receive it if they stopped work, were also given the pension corresponding to their sex and marital status. Occupational pensions were either as reported (if the person was in receipt) or predicted from an equation run on individuals reporting them. Persons entitled to an occupational pension but not receiving it were not asked how much they were expecting nor when they would become entitled to it. The equation used to predict the amount of their pension is reported in the Appendix (table A.l), and entitlement was assumed to start at age 60 for women and age 65 for men. Income from savings was calculated by applying a gross interest of 10 percent per annum to four very wide ranges of declared savings. Imputed rent for house ownership (excluded from the tax calculations) was calculated on the basis of the average rateable value of homes in 1977, and given the same value for all house owners, because no information was available on the value of a respondent’s house.” Income at the part-time and full-time work points (Ybi and Y,,) is made up of net earnings plus unearned income. Since loss of pension rights (e.g. because of the earnings rule) is treated as an implicit tax on earnings, the unearned income component in states B and C corresponds largely to that in state A. Gross weekly earnings are obtained by multiplying a predicted gross wage rate for each individual by the number of hours of work applying in each state. The equations used to predict wage rates were estimated on 91n addition, we mcreased the pension entitlement of a small number of retired men who had deferred claiming their pension, and of workmg men aged 65-69 who were not claiming their pension, and were therefore deferring (about 75 percent of full-time workers). For women no information on deferments was available, so no adjustments to their pensions were made. For every year of deferment, the pension was raised by 6.5 percent. “It should perhaps be noted that the last two variables, whtch are not very reliable, are a small component of incomes for most individuals.

258

A. ZuhUliu et al.. Sociul security und choice

participants and are conventional wage equations, run largely on individual characteristics. Since market opportunities are very likely to differ for people below and above the statutory pensionable age, the gross wages of all those under pensionable age was predicted from an equation run on workers under pensionable age, and the gross wages of all those over pensionable age was predicted from an equation run on workers over pensionable age (see Appendix, table A.2).’ ‘3’ 2 Gross weekly earnings are then netted according to the taxes, national insurance contributions, allowances, and earnings rule deductions applicable to each individual in each state. If, after application of the earnings rule, individuals were left worse off than they would have been had they deferred their pension, they were assumed to be deferrers. We added to their net weekly earnings 34 percent of their pension (the capitalised net returns from deferment) and deducted the pensions from their unearned income.’ 3 In terms of fig. 1, deferment is normally profitable if the individual is in the age group subject to the earnings rule and he is situated to the left of point B, or just to the right of it, nearer to B than to C. This makes deferment optimal for some full-time workers, but not for part-time workers who do not normally earn enough to suffer from the earnings rule. The vector X includes a constant term and the following variables: Poor health. This is entered as a (0,l) dummy and it is obtained from answers to the question ‘would you say in general your health is good, fair. or poor?’ - with 0 standing for ‘good, fair’. We are aware of the limitations of this ‘subjective’ measure of health, but the alternative measure we had, ‘number of weeks in bed through ill health during the last twelve months’, also suffers from deficiencies. Although the number of weeks in bed is in principle a more ‘objective’ measure, it is not necessarily better than the one used here. A person may have a health condition poor enough to prevent him or her from working, and yet not so bad as to require confinement to bed.14 It is interesting that ‘poor health’ was given as the main reason for retirement by 30 percent of the retired men and 34 percent of the retired women, so if the questionnaire evidence contained in our sample is taken at “The possibility that part-time jobs paid a different wage than full-ttme jobs was taken mto account m the wage equations by adding a dummy variable for individuals who worked less than 30 hours per week, but given its statisttcal mstgnificance it was subsequently deleted from the specifications used m the analysis. lZAs is well known, predicting wages using mformatton on participants only may introduce ‘selectivity bias’. Gtven the complexity involved in dealing with this problem within the context of our model, we have not attempted to measure the extent of this bias. although we think such problems should be tackled in future research. ,See Heckman (1974) for a discussion of this questton. r3The gross return to deferment calculated accordmg to footnote 4 is 39.48 percent of the retirement pension. For the average man of our sample, the extra money involved IS E4.8 per week of which, given the average level of unearned income, f0.67 would be paid in taxes. This implies that, on average, the net return would be equal to 34 percent of the retirement pension. 14This objecttve measure was tried in the participation equations reported in Zabalza, Pissarides and Ptachaud (1979) wtth no success whatsoevser.

face value it is consistent with the well-known finding of retirement surveys in the U.S., that poor health is one of the most important reasons for retirement.15 Age. The individual’s age is entered as one of the variables influencing his preferences for income and leisure. It is expected that the older the person the higher will be his valuation of leisure relative to income. This could reflect the effect of deteriorating health or of accumulated assets on preferences, but when included in conjunction with health and economic variables, it is more likely to reflect institutional or sociological factors which make older people more likely to retire. The other important influence of aging, via reduced earning capacity, is captured by the potential income variables, since age is also included in the equations used to predict wages. Statutory pensionuhle age. In addition to using actual age, we used an age 65 and over dummy for men and an age 60 and over dummy for women, both entered as (0,l) variables with 1 standing for the older groups. For men and most women, this variable coincides with eligibility for state retirement pensions, so if ages 6.5 and 60 are thought of by most individuals as statutory pensionable ages, preferences may change in favour of retirement. For most individuals mandatory retirement also takes place at these ages, so if the variable ‘involuntary loss of main job’, described below, does not include all those subject to mandatory retirement this variable may pick up some of the residue. In addition, this variable will capture any other influence on preferences (i.e. other than those already included in our vector of variables) that lead to the sharp drop in participation at these ages noted at the beginning of this section. Whiting bvfe. Women older than 60 whose husbands are not yet 65 (‘waiting wives’) do not become eligible for a state pension until their husbands reach eligibility age. To measure the effect of this institutional feature of the system on women, we include, in addition to the step age dummy described above, a dummy variable which takes the value 1 if the woman is a waiting wife, and 0 otherwise. Muritcrl stratus. A variable taking the value 1 if the person lives with a If husband’s and wife’s leisure are spouse, and zero otherwise. complementary. we expect the preferences of those living with spouse to shift in favour of leisure, but if the spouse imposes financial strains there may be a shift in favour of income. The latter is to some extent captured by the next variable. Spouse rtlorking. A (0,l) dummy, with value 1 given to persons who live with a spouse that is working for income. We have no information on the spouse’s earnings or hours of work. A (0, 1) dummy, taking the value 1 if the Incoluntary loss qf’ main job. ISThe other most important 19 percent

of women.

reason

given was mandatory

retirement,

34 percent

of men and

person gave as reason for leaving his or her mclin lifetime job one of the following: ‘was made redundant’. ‘had to retire’, ‘fired or sacked from job’, ‘business was sold/went bankrupt’, or ‘temporary/casual/part-time work ended’. Thus this variable is intended to capture the effects of mandatory retirement, and more generally ‘involuntary’ termination of the person’s main lifetime job, on the person’s preferences for work and leisure. Involuntary loss of job may induce earlier retirement because of protracted job search that may be necessary before finding a new job, or because of unwillingness to start in a new job late in life. 4. Econometric

results

Table 2 presents the parameters of the likelihood function estimated from the maximisation of expression (14) over the whole samples of men and women. In addition to the parameter p, it provides (in the order in which they appear in expressions 15 or 16) estimates of l/g and P/a. From expressions (14) to (16), it follows that variables which enter with a negative sign will increase the probability of retirement (i.e. the probability that point A is preferred to B or C), and vice versa for variables which enter with a positive sign. Equivalently, the larger a coefficient is, the smaller the marginal rate of substitution between net income and leisure and thus the greater the likelihood of work. The table also gives measures of the goodness of fit obtained. For comparison purposes, the ‘average likelihood’ measure (AL) is probably the most adequate, since it is standardised by number of observations. It gives the average likelihood of each observation and is obtained by dividing the log likelihood by the number of observations, and exponentiating the result. The parameter p that best fitted the data was 3.00 for men and -0.23 for women.lh We have thus estimated utility functions with shallower indifference curves for women than for men. Women’s indifference curves are less curved than those implied by the Cobb-Douglas specification, while men’s are more curved. Concerning specific results on elasticities of substitution there is, to our knowledge, only one other study which has estimated a labour supply model for older people based on an explicit utility function ~. that of Blinder and Gordon (1980). Their results for men (women are not analysed in their study) are very different from ours, with an implied elasticity of substitution of 12.5. In our case. we obtain an elasticity of substitution of 0.25 for men and 1.30 for women. This difference in the elasticity of substitution is also reflected in the estimated coefficients for the net income differential term. Although both are significant, the effect is much larger for women than for men, indicating that ‘“The values of p over which the search elahticlties of substitution would be separated

was done were defined by steps of 0.05.

so that

the corresponding

Table Parameters

of the

likelihood

2

function sample.”

estimated

from

the

whole

Variable

Men

Women

Net income differential

0.1 I (0.01) 8.12 (1.01) -0.11 (0.02) - I .44 (0.15)

0.95 (0.04) 4.89 (0.97) - 0.080 (0.013) -0.31 (0.16) 0.066 (0.153) - 2.40 (0.48) - 0.64 (0.12) 0.052 (0.118) -0.85 (0.14)

Constant Age Statutory Waitmg

penslonable

age

wife

Poor health Married Spouse working Involuntary

Parameter

loss of main job

p

Number of observations (IV) Log likelihood (L) ‘Average likehhood (AL) “Notes:

-2.13 (0.19) 0.15 (0.12) 0.38 (0.11) -0.58 (0.10) 3.00 1,483 - 654.33 0.64

-0.23 I.207 - 947.02 0.46

(1) Numbers in parentheses are asymptotic standard errors conditlonal on the value of the parameter p. (2) The parameter p is obtained by search of maximum likelihood. (3) The ‘average hkelihood is a measure of fit. and indicates the average likelihood of each obserxatloll. It is defined as AL=exp (L/N).

women are more responsive to economic incentives than are men. Evaluated at the mean values of the sample (this corresponds to an age of 63 for men and of60 for women), the wage elasticities implied by our estimates are - 0.020 for men and 0.37 for women. Thus, men’s labour supply curve presents the familiar backward bending shape with a very small elasticity, while women’s labour supply is upward sloping. The corresponding income elasticities are -0.023 and -0.38 respectively, again showing the higher responsiveness of women’s labour supply. The results for the variables depicting personal characteristics show in general that poor health and old age are important and very significant contributors to retirement, both for men and for women. Married men tend to value leisure relative to income less than single men, and therefore are more likely to work, while the opposite occurs with married women. Also, there is evidence of complementarity of the husband’s and wife’s leisure. If

the spouse works, the corresponding individual will tend to work, and vice versa. We have explicitly assumed that constraints that affect the individual’s choice of work, in addition to whatever effect they may have on earnings. will also have a direct effect on the individual’s taste for leisure and income. As expected. our results indicate that those individuals who have lost their main job involuntarily will have a stronger relative preference for leisure than those who have not. (Recall that we are talking of older people.) Age has a gradual effect on the MRS. The older people are, the more they prefer leisure relative to income. However, in addition to this effect there is a sudden jump at the statutory pensionable age (65 and 60). We have estimated our parameters from a likelihood function which already takes into account the effect on retirement of the increased net income that people can enjoy at zero hours of work when they become eligible for social security benefits. Thus, the effect picked up by the pensionable age dummy in table 2 must represent the discrete change in tastes that takes place at this age. Whether this change in tastes is a consequence of the fact that social security benefits become available at 60 for most women and 6.5 for men, or whether social security benefits become available at 60 for women and 65 for men because of this change in tastes. is something we cannot determine. Being a waiting wife may have an effect on women’s retirement because, although the person is above pensionable age, she is not entitled to a pension. However, statistically it does not seem to alter substantially the relative preferences of women between income and leisure. Among women who have reached statutory pensionable age, those who are waiting wives will tend to work more than those who are not, but the measured effect is small and insignificant. Using expressions (15) and (16), we can define for each individual three probabilities indicating the likelihood that he or she is found working fulltime, working part-time or retired. It is interesting, for illustration purposes, to see what the probabilities are for a ‘typical’ individual of each of our two samples. Let us define our ‘typical’ man with respect to the mean characteristics of our sample. He would be a married man, with no occupational pension, weekly income from savings of E2.5, a gross wage of C1.30, house owner, 63 years old, with good or fair health, whose spouse was not working and who did not leave his main job involuntarily. The ‘typical’ woman would be a married woman, with no occupational pension, no income from savings, a gross wage of E1.00, house owner, 60 years old, not a waiting wife, with good or fair health. whose spouse was not working and who did not leave her main job involuntarily. Fig. 3 shows the values of Z, and Z, for these two individuals and their respective probabilities of retirement. part-time work and full-time work.

The ‘typical’ man has the average salary, is healthy and relatively young and is not eligible for social security benefits. It is therefore not surprising that the probability of finding him retired is rather small. We might find him working part-time, although it is most likely (84 times out of 100) that we would find him employed full-time. The ‘typical’ woman is rather different. Although her personal characteristics are similar to those of the ‘typical’

A THE ‘TYPICAL’

MAN

Z, = -1.7026 z,= -1.0056

B THE ‘TYPICAL’

WOMAN

oz,

z2

Z, = 0.2187 z,- 1.3194

Note:

Fig.

3.

Probabilities

of

The density distribution is that of c/o, which is the standardised normal c/o”-N(O, I).

retirement.

part-time woman

work and full-tlme of our sample.

work

for the ‘typical’

man and

man, she is eligible for social security, and this has two effects. On the one hand, it makes her valuation of leisure relative to income larger than it was before (although not much) and, on the other, potential income at zero hours of work increases by the value of the corresponding pension. Both forces work in the same direction and explain the substantial probability of retirement. However, there is still a 32 percent chance that she is found working part-time and a 9 percent chance that she is found in full-time employment. The average likelihood for each observation gives an idea of the overall fit of the model to the data, and on this score the results prove to be very good,

if compared with other results obtained by likelihood methods.” However, we can be more precise than that. As discussed above, for each individual we have three probabilities. The aggregation of these probabilities, over all individuals in a given work regime, generates a predicted distribution across the three possible alternative choices, which indicates how many people in that regime have been successfully placed. and how many people have been predicted to choose an alternative different from that in which they are observed. Let PC be the probability that individual II observed in regime i is predicted to be in regime j (i, j= 1,2,3), and Ni be the number of people observed in regime i. Then the number of people of regime i who are predicted to be in regime j, Nij, can be defined as ,v

Njj=

I

c n=

Ptj,

(i,j=1,2,3).

I

This also generates a predicted aggregate across the three alternative choices:

Nj=

c

Nij,

distribution

of all the individuals

(j=l.2,3).

i=l

In table 3, we consider the predictive performance of the model on the sample of men. As can be seen from the overall predicted and actual distributions (bottom row and last column), the model predicts very well the number of people in all three categories. This overall result, however, is not a Table Actual and predicted

Actual distribution Full-time

(C)

Part-time

(B)

Predicted

distribution

Full-tlme

(CI

700 (87.8 “,) (Zi.5 ‘I,,)

Retirement

3 distribution

Part-time 55 (6.9 “,,)

(B)

of men

Retirement 43 (5.3”,,)

(JZ.3 ‘!“)

(& 48 (8.4”,,)

(& 442 (76.3”

813 (54.8 ‘:,)

114 (7.7U,,)

556 (37.5”,,)

(4)

0)

(A) 79x (53.8 Y”) 106 (7.1 ‘I,,) 579 (39.1 ‘:,,) 1.483 (100”“)

(1980) obtain for men an “In their study on retirement decisions, Blinder and Gordon average likelihood of 0.48. The average likelihood in our exercise is 0.64 for men and 0.46 for women.

A. Zahtrlzu

et trl.. Social

.srcurity

265

rrml choice

very strong test of the predictive performance of the model, because it is largely implied by its statistical structure (corresponding, by and large, to the property of OLS estimates passing through the mean of the sample). A stronger test can be devised by looking at the individual entries of the table. These should be read as follows. Taking the first row of the matrix, we see that out of the 798 men working full-time, the model predicts 700 working full-time, 55 working part-time and 43 retired. That is, it predicts correctly about 88 percent of the cases, and misplaces about 12 percent of the cases. The-results are also quite good with retired men (third row of the matrix). Out of 579 retired men, the model places correctly 442 (76 percent) and misplaces the rest. With part-time men, the number of correct placings is only about 10 percent. However, given the relatively small size of this category, this result does not distort the overall distribution to any great extent. In fact, looking at the sample as a whole, we see that the number of correct placings (the sum of the elements in the main diagonal of the matrix) is 1,153 ~ 78 percent of the total number of cases. The corresponding analysis for women is shown in table 4. The overall distribution shows again a very good fit. with all three predicted proportions

Table Actual

.4ctual distribution Full-time

(C)

Part-time

(B)

Retirement

(4)

and predicted

Predicted

distribution

Full-time

(C)

4

distribution

of women.

_____ Part-time

(B)

Retirement

114 (42.0’:“) 108 (31.0”,,) 64 (10.9”,,)

99 (36.4”,,) 122 (35.1 ‘50) 105 (17.9”“)

58 (21.6”,,) 118 (33.8”,,) 419 (71.2”.,)

286 (23.7 I’“)

326 (27.0”~)0

595 (49.3 ‘I”)

(A) 271 (22.5 ““) 348 (2X.8 “,,) 588 (48.7 ‘I,) 1207 (loo”,,)

very similar to their actual counterparts. The ordering is also the same: ‘retirement’, ‘part-time’ and ‘full-time’. Looking at the predictions, regime by regime, we find that the categories of work with the largest percentages of correctly predicted people are ‘retirement’, followed by ‘full-time’ and ‘parttime’. However, in general, the performance of the model for women is not as good as for men. The total number of correct predictions is 655, which amounts to about 54 percent of the total number of cases. Although the results obtained so far are very reasonable, the strong effect of the ‘statutory pensionable age’ dummy is somewhat worrying.

It is so powerfull that we investigated further whether there are substantial differences in behaviour depending on whether the individual is below or above statutory pensionable age. One way of testing for this would be to include this dummy interactively with all the other variables in the vector of personal characteristics. However, this would not allow us to detect differences in the individual’s response to the income variable, since the parameter p and the coefficient of the ‘net income differential’ variable would be common to both subsamples. Instead, we re-run the model separately for the two subsamples of people below and above statutory pensionable age. The results are given in table 5. Table Parameters

of the likehhood

5

function estimated from the samples statutory pensionable age.”

Men Variable

Age Waiting

0.016 (0.005) 10.98 (1.85) -0.16 (0.03)

65 or older

_ 2.14

Married Spouse workmg Involuntary loss of main job (I

Number of observations (Ri) Log ltkelihood (L) ‘Average’ Ilk&hood (AL)

and above

less than 60

60 or older

(1.13) - 0.037 (0.020)

1.12 (0.09) 4.26 (2.46) ~ 0.062 (0.025)

- 1.56 (0.36) 0.14 (0.13) 0.75 (0.14) - 0.58 (0.11)

- 2.84 (0.92) - 0.87 (0.28) 0.021 (0.252) - 1.20 (0.35)

0.9 I (0.06) 6.0 I (1.15) -0.10 (0.01) - 0.45 (0.16) - I .99 (0.51) - 0.39 (0.12) 0.50 (0.15) -0.72 (0.14)

-0.33

- 0.23

0.22

(0.021

1.20

wife

Poor health

Parameter

below

Women

less than 65

Net income differential Constant

of people

(0.27) 0.15 (0.25) 0.22 (0.19) -0.51 (0.22) 5.70

3.00

505 - 152.25

974 - 537.97

316 - 294.69

882 - 550.55

0.74

0.58

0.39

0.54

“R’ore.\: (I) Numbers in parentheses are asymptotic standard errors conditlonal on the value of the parameter p. (2) The parameter 0 1s obtamed by search of maxImum likehhood. (3) The ‘average likelihood’ is a measure of tit, and Indicates the average hkelihood of each observation. It is defined as .4L = exp (L/N ). (4) The sum of the two samples does not quite add up to the total number of observations, due to the weighting procedure used. ‘XPoor health 1s also an important Individuals in our samples.

variable.

but It affects only a very small

proportion

of

The separate estimation of the model over the subsamples of people under and above pensionable age results in some interesting differences.” First, the estimated indifference curves for men over pensionable age, although still quite curved, are much shallower than those for men under pensionable age (the implied elasticity of substitution of the former is 0.25 while that of the latter is only 0.15). This is also shown by the larger coefficient on the ‘net income differential’ variable, and indicates a much stronger response to economic incentives. A possible explanation is that being eligible for a state retirement pension makes the individual less dependent on his main job, and therefore much more flexible in his choice of work regime. The second important difference is the much weaker effect of age on labour supply. Before reaching 65, age has a marked negative influence on labour supply, but once eligibility has been reached the additional effect of age is very small and statistically insignificant. Finally, after eligibility, the effect of health is smaller and that of the working spouse larger than before eligibility for a pension. For women the differences are also quite noticeable. Contrary to what happens with men, the elasticity of substitution is larger before pensionable age than after (1.50 as compared with 1.30), and the effect of age is much weaker. The direction of the change in the effects of health and working spouse is the same as in the case of men and, additionally, some differences are observed in the marital status variable and in the dummy for involuntary loss of main job. But perhaps the most marked change is that of the ‘waiting wife’ dummy. When estimated on the whole sample of women, this effect was negligible and insignificant, while when estimated on the sample of women 60 or older it becomes negative and significant, thus indicating that among women who have reached pensionable age those who are waiting wives value leisure more highly than those who are not. With this exception, for both men and women, it is only the magnitude of the coefficients that changes; in all cases, the sign of the effects remains unchanged for the two subsamples. Using the results of table 5, we examine in tables 6 and 7 the quantitative effect on the probability of retirement resulting from changes in the set of opportunities and in the variables that determine the preferences between income and leisure. Naturally, we could measure these effects on any of the three probabilities that we have defined, but we will concentrate on retirement since this is the status on which researchers have turned most of their attention. As can be seen from the first row of table 6, the older the person the higher is his probability of retirement, the effect being much stronger before pensionable age than after. At age 65, this probability increases drastically “Althou& in the separate regressions the sample of people under pensionable age is much smaller thai that of people above pensionable age in the oxerall regression reported in table 2 the wught~ng pt-ocedure diwucsed abole makes the nt~mbct-\ 111each category about equal.

Table Retirement

6

probabilities

for men.”

58

61

64

65

68

71

1. Base case

0.025

0.069

0.159

0.776

0.807

0.836

2. 3. 4. 5. 6. 7.

0.571 0.015 0.034 0.073 0.025 0.025

0.746 0.045 0.090 0.166 0.069 0.069

0.873 0.112 0.195 0.312 0.159 0.159

0.990 0.503 0.742 0.910 0.810 0.766

0.992 0.547 0.177 0.926 0.839 0.798

0.994 0.590 0.X08 0.940 0.864 0.828

Poor health Spouse working Single Left main job involuntarily Increase in pension of &5 per week Increase in wage of 50 percent

“A’otrs: (I) The base case is a married man. with no occupational pension, income from savmgs of 62.5 per week, a gross wage of f1.30, house owner. with good or fair health, whose spouse is not working and who did not leave his matn job involuntarlly. (2) The probabilities up to age 64 are calculated from the estimates given m column 1 of table 5. Those for age 65 and above are calculated from the estimates given In column 2 of table 5.

from 16 to 78 percent due to both an increase in the individual’s MRS, and to an increase in potential income at point A relative to income in the other two points. This is consistent with the data (see table l).” Poor health is also a strong inducement to retire; for ages below 65, it is the only factor that increases the probability of retirement above the 50 percent level. If our ‘typical’ man were 65 and in poor health he almost certainly would be retired. It should be noticed that this variable represents poor health against good or fair health and must therefore be indicative of quite an anomalous condition; for our data only 7 percent of men were in this category. If the man is below 65, the fact that his wife is working almost halves his probability of retirement as compared with the case in which she is at home. After 65, however, this effect is relatively smaller. Being single rather than married increases the probability of retirement before 65 both on account of change in tastes and on account of lower return to work due to smaller tax allowances. However, after 6.5, the effect of a smaller (single person) pension predominates, and the probability of retirement decreases relative to married men. Line 5 in table 6 indicates that, if the individual has left his main job involuntarily, he will have, at any age, probably due to some discouragement effect, a much higher probability of being retired. The last two lines examine the partial effects of some changes in the economic variables that define the opportunity set. An increase of f5 in the pension will have a small effect on *‘This jump would also have been predicted if we had used the common set of estimates table 2. There. the main force behind this change would have been the eligbllity dummy.

from

the retirement probability when the man reaches eligible age. His probability will go up by 0.034 points. Retirement decisions are even less sensitive to wage changes, which would be expected from the very low elasticity of substitution estimated from our sample. An increase in the gross wage of 50 percent would leave practically unaltered the probability of retirement before 65, and would slightly decrease it after eligibility age (by about 0.010 points). Table Retirement

7

probabilities

for women.’

53

56

59

60

63

66

1. Base case

0.132

0.177

0.229

0.529

0.650

0.758

2. 3. 4. 5. 6. 7. 8.

0.132 0.958 0.128 0.023 0.535 0.132 0.092

0.177 0.972 0.171 0.036 0.608 0.177 0.127

0.229 0.982 0.223 0.053 0.678 0.229 0.170

0.504 0.990 0.336 0.497 0.785 0.628 0.441

0.627 0.991 0.456 0.620 0.865 0.739 0.566

0.738 0.996 0.581 0.732 0.921 0.830 0.684

Waiting wife Poor health Spouse working Single Left mam job involuntarily Increase in pension of E5 per week Increase in wage of 50 percent

“Notes: (1 ) The base case is a married woman, with no occupational

(2)

pension, no income from savings, a gross wage of f1.00, house owner, not a waiting wife, with good or fair health, whose spouse is not working and who did not leave her main job involuntarily. The probabilities up to age 59 are calculated from the estimates given in column 3 of table 5. Those for age 60 and above are calculated from the estimates given in column 4 of table 5.

Table 7 shows the figures of this comparative-statics exercise for our ‘typical’ woman. The distribution of the retirement probability across ages, although still showing a jump at 60 (the pensionable age), is much more evenly distributed than that of men. This, again, is consistent with the data. Now, contrary to what happens with men, the effect of age is stronger after pensionable age than before. Apart from the effect of the variable ‘waiting wife’, the influence of changes in personal characteristics (rows 2 to 6) are similar to those of men and do not deserve further comment, except those relating to marital status. As shown by the results in table 5, single women tend to have a flatter MRS, and therefore work more, than married women. This is reflected in the lower retirement probability for a single woman than for an otherwise similar married woman. The drop is quite substantial across all ages, but is particularly large before reaching statutory pensionable age. Women 60 or older who are waiting wives value leisure more than do women eligible for pensions. However, the fact that they cannot draw

pensions until their husbands reach pensionable age makes them more prone to work. As shown in table 7. the second of these two effects predominate, and the probability of retirement after eligibility age slightly decreases for women in this circumstance. Finally, the effects of pensions and wages both go in the same direction as happens in the case of men, but their magnitude is substantially larger. Tables 6 and 7 evaluate how changes in pensions and wages affect the probability of retirement. A more familiar way of measuring the labour supply effects is by means of the corresponding hours elasticities. We can do that by calculating the change in the expected hours of work of our typical man and woman that will result from increasing pensions and wages. This is done in table 8. The first thing to notice in this table, where the elasticities have been evaluated at the mean age values of each of the subsamples considered, is that individuals are more responsive to economic incentives after pensionable age than before. For men, the wage elasticity is very small and negative at

Table Hours Typical

8

elasticitm.”

man

Typical

woman

Elasticity with respect to

age = 59

age = 68

age=55

age = 66

Pension Wage

- 0.0078

- 0.74 0.012

0.26

- 0.48 0.47

“Note.

The typical

man and woman

are defined as m the footnotes

to tables 6 and 7

age 59. but increases to a positive value at age 68. The backward bending supply curve estimated above for the whole sample of men is seen now to be caused by the influence of men under pensionable age. When the two subsamples are separated, we find that men who have reached pensionable age display an upward sloping supply curve, although their wage elasticity is still very small. The wage elasticity of women, which is much larger than that of men, also increases after pensionable age, although in relative terms this increase is less than in the case of men. For both men and women, the elasticity of hours with respect to pensions has the expected negative sign and is higher than the elasticity with respect to wages. Overall, these elasticities accord with previous findings and, in particular, the low wage elasticities found for men are not very different from other results obtained with likelihood methods. Ashworth and Ulph (1977) find a wage elasticity of - 0.065 for U.K. prime-age male workers, and Burtless and Hausman (1978)

report a wage elasticity of -0.00003, using a sample of U.S. prime-age males who are heads of households. Finally, we present in tables 9 and 10 the labour supply effects that would result from abolishing the ‘earnings rule’. Table 9 shows the change in the probabilities of full-time work, part-time work and retirement of our typical man and woman that would follow from this policy change, together with the implied change in annual hours worked per person. Table 10 shows how the effect on annual hours worked per person varies with age. Although other modifications to the social security system could be considered, we concentrate on the earnings rule because of the special attention that researchers have paid to the potential disincentive effects of this feature of the system. According to our results, the abolition of the earnings rule would increase, although not by much, the labour supply of the typical individuals. Table The effect of abolishing TypIcal

Probabilities

of

Retirement Part-time work Full-time work

man (age = 68)

The typical

rule’.” Typical

woman

(age = 63)

With ‘earnings rule’

Wlthout ‘earnings rule’

With ‘earnings rule’

Without ‘earnings rule’

0.807 0.153 0.040

0.807 0.144 0.049

0.650 0.260 0.090

0.650 0.253 0.097

Implied increase in annual hours per capita “Note:

9 the ‘earnings

10.24 man and woman

are defined as in the footnotes

7.04 to tables 6 and 7.

It would leave untouched the probability of retirement and decrease slightly the probability of part-time work in favour of full-time work. For the typical man, the decrease in the probability of part-time work (and thus the increase in the probability of full-time work) is of 0.009 points, and for the typical woman 0.007 points. This implies an increase in annual hours worked of 10.24 for men (2 percent of the average number of hours worked by men. 65 or over), and 7.04 for women (1.6 percent of the average number of hours worked by women 60 or over). Table 10 shows that this effect is decreasing with age. The abolition of the earnings rule would have a greater impact the younger the person is. For men, the change in annual hours worked decreases from 12.27 if the man is 65 to 9.61 if the man is 69 - a decrease of 22 percent. This declining effect is even more pronounced for women, going from 10.13 annual hours at 60 to 6.10 annual hours at 64 - a decrease of 40

percent. To the extent that these typical individuals are representative of the population, we may conclude that the ‘earnings rule’ per se has a small disincentive effect on the labour supply of older people. A more detailed analysis, based on the simulation of this change on all the individuals of the sample, rather than on just two typical examples, is neeced before any firm conclusions on this issue can be reached. This task is beyond the scope of this paper, but we intend to carry it out, together with the analysis of other changes in the social security system, in future work.

Table Increase

in annual

10

hours per capita earnmgs rule.”

from

abolishing

the

Women

Men Age

Annual hours

A&e

Annual hours

65 66 67 68 69

12.27 11.57 10.90 IQ.24 9.61

60 61 62 63 64

10.13 9.07 8.04 7.04 6.10

“Note: These figures are calculated on the basis of our ‘typical man and woman. Apart from age. their characteristics are given m the footnotes to tables 6 and 7.

5. Summary and conclusions The objective of this paper has been to investigate the determinants of retirement decisions by men and women in Great Britain. The discontinuous changes in the rates of implicit taxes and benefits that characterise the social security system give rise to piecemeal linear budget constraints, and render ordinary least square methods of estimation inadequate. To deal with the endogeneity bias introduced by this type of budget constraint, we have proposed a method which requires the specification and estimation of an individual utility index, and the maximisation of this index over the budget constraint. The arguments of the utility function are net income and leisure, and the marginal rate of substitution is made to depend on individual characteristics. To estimate this function (by means of a maximum likelihood technique), we represent the budget constraint by only three points, which we characterise as ‘retirement’, ‘part-time work’ and ‘full-time work’, and we assume that each individual maximises his (or her) utility function subject to this budget constraint. Although this approach involves some loss of information, we believe that it leads to a relatively simple method of estimation of the utility

function. In addition, the severe restrictions faced by workers in their choice of hours lend some justification to our assumptions and may make our approach particularly relevant to many real world situations. The results obtained with this approach are very reasonable, from the point of view of theoretical expectations, and we doubt whether more complex (and expensive) methods can add much to them. We find that in general people respond to economic incentives, but that there are some important differences in behaviour between men and women, and also between individuals who are under pensionable age and those above. Women are, in general, more responsive to economic incentives than are men. Men’s supply elasticities are much lower before pensionable age than after. while for women the relative change is much less pronounced. It is particularly interesting that the usual backward bending labour supply curve for prime-age males disappears when pensionable age is reached and the wage elasticity becomes positive. For women, both before and after pensionable age the supply curve is upward sloping. Among the noneconomic variables, poor health is the most important variable and apparently the major inducement to retirement before pensionable age. Age has also a very significant effect, independently of the pensionable-age effect. For men the probability of retirement just before pensionable age is six times larger than that at age 58, but during the first six years after pensionable age it increases by only 8 percent. For women, the relative effect of age is also smaller after pensionable age, but the transition is smoother. Six years before 60, age increases the probability of retirement by 73 percent, and in the six years after 60 by 43 percent. The existence of mandatory retirement or other factors which lead to the involuntary separation of workers from their main job also affect retirement decisions to a very significant extent. Individuals who have left their main lifetime job involuntarily are much more likely to retire than are other workers. Finally, our results suggest that the disincentive effects of the ‘earnings rule’ are small, and that its abolition would increase the labour supply of those affected by the change by less than 2 percent. This increase would take the form of more workers taking up full-time jobs, rather than more retired people coming back to the labour force. The present exercise may help in improving the understanding of this complex problem, but we believe there are still some aspects that need further study before any firm conclusions can be reached. One such aspect is the strong increase in retirement at the point of eligibility, especially as far as men are concerned. The results of our analysis suggest that an abrupt change in tastes takes place when individuals reach eligibility age, but we feel that this conclusion should be accepted only provisionally, and that other lines of analysis should be explored. Maybe the sudden increase in retirement at age 65 is not due to a once and for all shift in tastes, but to the unwillingness of

employers to offer jobs to elderly people. If this is the case, what we have attributed to a change in tastes may be due to a lowering of points B and C in our model, through the reduced possibilities of getting a job. The same would apply to people who have lost their main job involuntarily. The chances of getting a job similar to the one they lost are probably very small, so for them points B and C may also be much lower than what their predicted wage would indicate. These are important questions which have to be answered, and which should figure prominently in our research agenda. We suspect, however, that before these questions can be tackled with success we will need much better information not only on personal characteristics of elderly people, but also on the set of opportunities open to them.

Appendix Table Occupational pensron equations pension (E per week); sample:

A.1

(dependent variable: Amount of occupatronal those receivmg any occupational pension).”

Constant Gross

weekly earnings

Over pension Number

age (dummy)

of different employers

Socioeconomtc Professional Other

in main occupation

m life

group (main job): and managerial

nonmanual

Skilled Semi-skilled

manual

Other

RI

Women

6.07 (4.45) 0.21 (0.02) -4.1 (1.5) - 0.69 (0.38)

0.15 (5.30) 0.23 (0.04) 2.0 (2.1) -0.81 (0.46)

16.7 (3.7) 12.1 (3.7) 4.1 (3.7) 5.4 (3.9) 3.3 (23.6)

6.2 (3.5) 4.2 (3.1)

0.56 271

IV “Note: Frgures

Men

m parentheses

are standard

errors

- 4.2 (3.4)

0.40 106

275 Table Wage equations

Age (Agef’ Health Education

completion

age

Trme in job Socioeconomic Professional Other

group (last Job): and managerial

nonmanual

Skilled manual Semi-skilled Other Constant

R2 N

manual

(dependent

A.2

variable:

log gross hourly

Men 65 and over

Women 60 and over

- 1.69 (0.72) 0.012 (0.005) -0.16 (0.06) 0.10 (0.03) 0.065 (0.016)

0.039 (0.256) - 0.0006 (0.0020) - 0.044 (0.058) 0.12 (0.02) 0.054 (0.015)

0.39 (0.10) 0.045 (0.071) - 0.029 (0.085) -0.12 (0.08) 0.053 (0.480) 58.71 (24.68)

0.41 (0.11) 0.061 (0.060) -0.091 (0.091) - 0.099 (0.059) - 1.23 (0.41) -0.66 (8.32)

0.23 379

0.30 356

wage).”

Men under 65 0.58 (0.29) - 0.0050 (0.0025) - 0.072 (0.036) 0.088 (0.019) 0.041 (0.012) 0.32 (0.08) 0.13 (0.08) 0.09 1 (0.072) 0.013 (0.077) 0.29 (0.32) - 16.71 (8.66) 0.30 312

Women under 60 0.33 (0.48) 0.003 1 (0.0044) - 0.083 (0.075) 0.11 (0.03) 0.041 (0.020) 0.40 (0.17) 0.052 (0.104) - 0.028 (0.161) - 0.045 (0.107)

8.36 (13.17) 0.21 175

Figures in parentheses are standard errors. ‘Working men and women over pensionable age were oversampled. In the estimation of the maximum likelihood functions the observations were weighted so that the sample proportions corresponded to the population proportions. No wetghtmg was used in the wage-prediction equattons, and this explains the larger number of observattons in columns 1 and 2 above, “N&r:

References Ashworth, J.A. and D.T. Ulph, 1977, Estimating labour supply with piecewise linear budget constraints, Umversity of Sterling, mimeo. Blinder, AS. and R.H. Gordon, 1980, Market wages, reservation wages and retirement decisions, Journal of Public Economics, this issue, 277-308. Boskin, M.J., 1977, Social security and retirement decisions, Economic Inquiry 15, l-25. Boskin, M.J. and D.H. Hurd, 1978, The effect of social security on early retirement, Journal of Public Economics 10, no. 3, 361- 378. Burtless, F. and J.A. Hausman, 1978, The effect of taxation on labour supply: Evaluating the Gary negative income tax experiment, Journal of Polittcal Economy 86, 1103-l 130. Hausman, J.A., 1980, The effect of wages, taxes and fixed costs on women’s labor force participation, Journal of Public Economics, this issue, 161-194. Heckman, J.J., 1974, Shadow prtces, market wages, and labour supply, Econometrica, 42, 679694.

Layard, R., M. Barton and A. Zabalza, 1980, Married women’s participation and hours, Economica 47, 51-72. Qumn, J.F.. 1977, Microeconomic determinants of early retirement: A cross-sectional view of white married men, Journal of Human Resources 12, 3299346. Schultz, T.P.. 1980, Estimating labor supply functions for married women, in: J.P. Smith. ed.. Female labour supply: Theory and estimation (Princeton University Press, Princeton). Wales, T.J. and A.D. Woodland, 1979. Labour supply and progressive taxes, The Review of Economtc Studies 46. 83 -95. Zabalza, A., C. Pissarides and D. Piachaud, 1979, Social security, life-cycle saving and retirement, Centre for Labour Economics, Discussion Paper No. 43, London School of Economics. (Forthcoming in: D. Collard and R. Lecomber, eds., The limits to redistribution).