pii: s0047-2727(98)00021-8darp.lse.ac.uk/papersdb/woittiez-kapteyn_(jpube_98).pdf · 1998. 11....

Journal of Public Economics 70 (1998) 185–205

Social interactions and habit formation in a model offemale labour supply

a , b*Isolde Woittiez , Arie KapteynaDepartment of Economics, Faculty of Law, University of Leiden, P.O. Box 9521, 2300 RA Leiden,

The NetherlandsbCenter for Economic Research, Tilburg University, P.O. Box 90153, 5000 LE Tilburg,

The Netherlands

Received 1 April 1993; received in revised form 1 November 1997; accepted 8 January 1998

Abstract

This paper investigates the influence of habit formation and preference interdependenceon labour supply behaviour of married females. A novelty of the paper is that weincorporate direct survey information on reference groups of individuals in a neoclassicallabour supply model. For that purpose we first estimate a latent variables model relating thedirect information to the ‘true’ but unobserved reference groups. One of the most interestingfeatures of the model is that the presence of young children becomes an insignificant factorin the hours equation while it remains a significant factor in the participation decision. Inaddition, the labour supply curve is much flatter in a model with habit formation andpreference interdependence than in a model without it. Both habit formation and preferenceinterdependence contribute significantly to the explanation of female labour supply. 1998 Elsevier Science S.A. All rights reserved.

Keywords: Household labour supply; Wages; Habit formation; Interdependent preferences;Latent variables; Factor analysis

JEL classification: H31; J22

1. Introduction

The main purpose of this paper is to incorporate preference interdependence and

*Corresponding author. Since 1 January 1998 working at the Social and Cultural Planning Bureau.Tel.: 131 70 3198700; e-mail: [email protected]

0047-2727/98/% – see front matter 1998 Elsevier Science S.A. All rights reserved.PI I : S0047-2727( 98 )00021-8

186 I. Woittiez, A. Kapteyn / Journal of Public Economics 70 (1998) 185 –205

habit formation into a neoclassical model of female labour supply. We allow forthe fact that individuals may get used to working a certain number of hours perweek (habit formation) and that the number of hours they prefer to work maydepend on the number of hours other people work (interdependence of prefer-ences). Habit formation and preference interdependence will be referred to jointly

1as preference formation. Labour supply behaviour of individuals is analyzedwithin a generalized Tobit framework. We allow for the possibility that the laboursupply function is discontinuous at zero hours. The data we use pertain to marriedfemales in Dutch households in 1985.

The notion that preferences may be endogenous has gained some foothold in theliterature on consumer demand equations (see e.g. Pollak, 1970, 1976; Phlips,1984; Gaertner, 1974; Blanciforti and Green, 1983; Darrough et al., 1983; Alessieand Kapteyn, 1991), but hardly any in the empirical labour supply literature. Inconsumer demand models, habit formation is usually the only component ofpreference formation that is taken into account in empirical analyses (habitformation may then be either rational or myopic, cf. Muellbauer, 1988). In a fewpapers, Alessie and Kapteyn (1991) and Kapteyn et al. (1997) have alsoincorporated preference interdependence into empirical models of consumptionfollowing theoretical notions developed by Gaertner (1974) and Pollak (1976). InKapteyn and Woittiez (1990) and ten Hacken et al. (1989) the frameworkdeveloped in the two former papers is extended to deal with household laboursupply.

In these papers parameters of individual (or household) utility functions aremade dependent on a weighted mean of consumption levels or hours worked byothers in society. The weights used in constructing such means are called‘reference weights’. This terminology refers to the notion of a social referencegroup, which can be defined roughly as the set of people whose behaviourinfluences the individual’s preferences. For the special case where everyone insociety has the same reference group and utility depends on average totalexpenditures, Oswald (1983) has investigated the implications for optimal non-linear taxation. In a somewhat related approach, Blomquist (1993) studies laboursupply in the case where preferences for leisure and consumption depend on themean number of hours worked in society and on mean consumption. Heinvestigates the effect of taxes on labour supply and compares the effect of a taxchange with and without accounting for the interdependence of preferences. Notsurprisingly, he finds that a neglect of interdependence may yield substantiallybiased predictions of the labour supply effects of a tax change.

There are of course much more general ways of relating individual preferencesto the behavior of others than just to some average. In particular the notion ofrelativity has been pursued by various authors. In Kapteyn (1977) the idea is put

1Rather than the terms habit formation and preference interdependence, Becker (1996) uses the termspersonal capital and social capital.

I. Woittiez, A. Kapteyn / Journal of Public Economics 70 (1998) 185 –205 187

forward that individual utility functions are identical to a perceived consumptiondistribution. Later work (e.g. Van de Stadt et al., 1985; Kapteyn and Wansbeek,1985) appears to corroborate this hypothesis quite strongly. Ok and Koçkesen(1996) provide a more general theory of the representation of interdependentpreferences, of which complete relativity is a special case. Cole et al. (1995)generate a concern for relativity in a very different manner. In their model, agentshave identical utility functions but different endowments. In particular, males areexogenously endowed with a certain amount of wealth, whereas females differ inproductivity in the labor market. The effort expended by a female determines withwhat male she can match, after which they consume their goods jointly. Thistournament for males induces a concern for relativity by the females whendeciding how much effort to expend. One should note that in this model,considerations of relativity do not stem from a structure of preferences, but ratherfrom the structure of the institutions in society.

Interdependence of preferences will most likely influence the equilibriumdistribution of wages. As an example, Frank (1984) considers a case whereworkers care about their relative income compared to their co-workers. It is foundthat an equilibrium distribution of wages within firms is less dispersed than if suchinterdependence does not exist. The reason for this finding is that workers with thelower marginal productivity need to be paid above their marginal product tocompensate for the disutility of working with others who make more money.Conversely, the workers with the higher marginal product receive part of theircompensation in kind, due to the fact that they can compare themselves with lowerpaid colleagues. Clark and Oswald (1996) provide evidence of the importance ofcomparison wage rates. They employ self-reported measures of job satisfactionand find that this measure is best explained by own wage (with has a positiveeffect) in combination with comparison earnings (obtained as predicted earningsfrom a conventional earnings equation). Comparison earnings have a negativeeffect on job satisfaction. If comparison earnings is omitted, own income has noappreciable effect on job satisfaction.

Neumark and Postlewaite (1995) introduce relativity concerns in a model offemale labour participation by assuming that families derive additional utility fromhaving a higher income than comparison families. They show that this inducessecondary effects of rising wages on female labour force participation. Theprimary effect is the usual effect of higher wages on labour force participation.However, if some females decide to start working in the labour market as a resultof higher wages, their family’s income will increase and thereby they may ‘jumpover’ the income of comparison families. This may induce the females in thesecomparison families to also start working, to restore the original ordering in familyincomes.

In the current paper we adopt the framework of Kapteyn and Woittiez (1990),where reference group means of female hours enter into the utility function of afemale. In the paper mentioned these reference group means are constructed bymaking specific assumptions about the unknown reference weights. The estimation


results showed an overwhelming influence of habit formation, relative to prefer-ence interdependence, but also preference interdependence proved to be asignificant factor in labour supply. Yet, the estimation results were not verysatisfactory. In many cases parameter estimates had to be constrained by an upper(one) or lower (zero) limit.

In the present paper a more sophisticated method is used for the construction ofthe social reference group variables. Here we make use of direct information onreference groups available in the data used, to construct a number of indicators forthe mean hours worked and the mean participation rate in an individual’s referencegroup. The observed indicators are next related to the latent ‘true’ reference groupmeans by means of a factor analytic model.

In Section 2 we briefly discuss how preference formation can be incorporatedinto a neoclassical labour supply model. In Section 3 we present the factor analyticmodel describing the relation of the indicators to the ‘true’ reference groupvariables. Section 4 shows the estimation results of the factor analytic model. InSection 5 we discuss how the estimation results of the factor analytic model can beexploited to analyze the role of reference groups in labour supply. In Section 6 theestimation results of the resulting labour supply model are given. Section 7concludes.

2. A labour supply model with preference formation

We consider females in households with at least two adults capable of workingin paid jobs. We shall refer to such individuals as married females. Our aim is tomodel the number of hours married females would like to work, i.e. their ‘desirednumber of hours’. Desired hours are elicited through a survey question. Thephrasing of the survey question (see Section 4 below) allows us to take the laboursupply of any person in the household other than the married female as exogenous.The labour supply of the married female is assumed to be consistent with thefollowing model

k 2h 5 b 1 b I 1 b w 1 b w 1 e , (1)d 0k 1 k 2 k 3 k hkkwhere h is the number of hours the female in household k would like to work perd

week; w is the after tax wage rate of the female in household k; I is the (weekly)k knon-labour income of the female in household k, including all incomes of otherhousehold members; b , b , b and b are parameters; e are i.i.d. error terms0k 1 2 3 hk

2with mean zero and variance s .hEq. (1) is a reparameterization of a modified version of the model introduced

by Hausman and Ruud (1984). Labour supply is made a quadratic function ofwages. The obvious advantage of a quadratic specification over a linear one (whichis used for instance by Hausman (1980), (1985) and Blomquist (1983)) is that it ismore flexible.


At this point we deviate from the standard Tobit model by allowing theparticipation decision to be different from the hours of work decision. We followMroz (1987) here, who finds that the Tobit model is rejected in favour of a modelwith an unrestricted specification for the participation decision (see also Blundell

det al. (1987)). We introduce a latent variable p that determines whether ankd dindividual wishes to participate ( p .0) or not ( p ,0). The participation equationk k

is defined consistently with the hours equation

d 2p 5 g 1 g I 1 g w 1 g w 1 e , (2)k 0k 1 k 2 k 3 k pk

2with e i.i.d. error term with zero mean and variance s .pk pThere are various reasons why the hours decision could be different from the

participation decision and our specification allows for this. In fact we allow thelabour supply function to be discontinuous at zero hours. We do not modelexplicitly the factors that may give rise to the discontinuity. Structural models inwhich these factors are taken into account are for example fixed cost models (cf.Cogan, 1981).

We model variation in preferences across agents by parameterizing thetranslation parameters b and g (cf. Pollak and Wales, 1981). The translation0 k 0 kparameters b and g are made dependent upon family size and the number of0 k 0 kchildren younger than six. We model preference interdependence and habitformation in the hours equation by making the parameter b also linearly0 kdependent upon actual hours worked by other working females in the referencegroup, lagged one period, and upon the actual number of hours worked by theindividual herself, lagged one period. Analogously, the parameter g in the0 kparticipation equation is made dependent upon the actual participation rate of otherfemales, lagged one period, and upon her own actual lagged participation. Thisresults in the following specifications

b 5 b 1 b f 1 b f 1 b a 1 b a 1 b a 1 b h (21)0k 01 02 1k 03 2k 04 2k 05 3k 06 4k 07 k

1 b j (21), (3)08 hk

g 5 g 1 g f 1 g f 1 g a 1 g a 1 g a 1 g p (21)0k 01 02 1k 03 2k 04 2k 05 3k 06 4k 07 k

1 g j (21), (4)08 pk

where h (21) is the lagged value of actual hours worked by the female inkhousehold k; p (21) is the lagged actual participation of the female in household kk(0 /1-variable); f is the (log of) family size of household k; f is the dummy for1k 2kthe presence of children younger than 6 in household k; a 51 if the female in2khousehold k is between 25 and 35 years old, 0 elsewhere; a 51 if the female in3khousehold k is between 35 and 45 years old, 0 elsewhere; a 51 if the female in4khousehold k is older than 45 years, 0 elsewhere; j (21) is the lagged value of thehkactual number of hours worked by females in the reference group of the female inhousehold k; j (21) is the lagged value of the actual participation rate of femalespk


in the reference group of the female in household k, and where b and g are01 01parameters.

The main empirical problem in this specification is to find a sensibleoperationalization of the reference group variables j and j .hk pk

3. Factor analytic model

Our data contain answers to a number of direct questions about reference groupsof individuals. The answers to the questions about reference groups are used toconstruct indicators of the female participation rate and number of hours worked inthe reference group of each respondent. These indicators are next used in a factoranalytic model to estimate the relation of the indicators to the ‘true’ participationrate and number of hours worked in the reference group. These ‘true’ variables canthen be proxied on the basis of the observed indicators. The proxies are used in thelabour supply model.

For ease of exposition we first present the questions that were asked in thesurvey about one’s reference groups.

1. ‘‘The following questions are about your social environment, that is peoplewhom you meet frequently, like friends, neighbours, acquaintances or possiblypeople you meet at work. Thinking of the people in your social environment, canyou indicate to which age class they belong primarily? Choose the answer which ismost in accordance with reality.’’

[01] under 16 [08] 46–50[02] 16–20 [09] 51–55[03] 21–25 [10] 56–60[04] 26–30 [11] 61–65[05] 31–35 [12] 65–70[06] 36–40 [13] 71 and over[07] 41–45

2. ‘‘What education level do most people in your social environment have?Check the number corresponding with the answer that comes closest to reality.’’

[1] primary education[2] lower vocational education[3] intermediate general education[4] high school[5] intermediate vocational education[6] higher vocational education B.A. or B.SC.[7] masters degree


The decision to include these questions in the questionnaire was made in thecontext of a research project on subjective poverty, where it was believed that theincomes and family composition of one’s reference group are important deter-minants of one’s subjective well-being. For the purpose of explaining householdlabour supply on the basis of preference interdependence the questions suffer fromone serious defect; no questions have been asked about the number of hoursworked or the participation rate in the reference group. Yet, we shall use theanswers to the aforementioned questions to construct indicators of the referencegroup means.

It seems reasonable to suppose that an individual will primarily assign positivereference weight to people whom she knows personally. Within the family wedistinguish two channels through which one can get to know other people. Thefirst one is that one meets someone directly. We assume that the people one meetsare primarily people of about the same age and education. The second channel isthat one meets someone through one’s partner. To formalise this idea we constructfour indicators of hours worked in a respondent’s reference group. The firstindicator is simply the mean number of hours worked by all working females inthe population who share the characteristics, education level and age bracket withthe respondent. The second indicator is the mean number of hours of all workingfemales in the sample who have the education level and age indicated by therespondent as typical for her reference group. The third indicator is the meannumber of hours worked by all working females in the population who share thecharacteristics, education level and age bracket with the husband of the respon-dent. The fourth indicator is the mean number of hours of all working females inthe sample who have the education level and age indicated by the husband of therespondent as typical for his reference group. For the participation rate in arespondent’s reference group the indicators are constructed analogously to thevariables for hours. For instance, the first indicator is the mean participation rate ofall females in the population who share the characteristics education level and agebracket with the respondent.

Having constructed the indicators, how can we use them to find reasonableoperationalizations of the ‘true’ reference group variables? Let x through x be1 4the indicators defined above of hours worked in the reference group of somerespondent and let x through x be the indicators defined above of the5 8participation rate. All indicators are taken as deviations from sample means.Furthermore, let j and j be the ‘true’ values in the reference group of theh pnumber of hours worked by all working females and of the female participationrate, respectively. Then we assume the following relationships between thesevariables

x 5 a j 1 n , (5)1 1 h 1

x 5 a j 1 n , (6)2 2 h 2


x 5 a j 1 n , (7)3 3 h 3

x 5 a j 1 n , (8)4 4 h 4

where n through n are error terms with mean zero and joint diagonal variance-1 4covariance matrix F , j is i.i.d. across individuals with mean zero and varianceh hv , n and j are assumed to be independent.h 1 h

Technically, (5)–(8) is a factor analysis model, where j is the factor, ah 1through a are the factor loadings, x through x are the specific indicators.4 1 4

For the participation rate a similar model is assumed

x 5 a j 1 n , (9)5 5 p 5

x 5 a j 1 n , (10)6 6 p 6

x 5 a j 1 n , (11)7 7 p 7

x 5 a j 1 n , (12)8 8 p 8

where the error terms n to n are error terms with mean zero and joint diagonal5 8variance-covariance matrix F and j is i.i.d. with mean zero and variance v , np p p 1and j are assumed to be independent.p

4. Data and estimation results of the factor analytic model

The data used come from the Socio-Economic Panel (SEP), run by StatisticsNetherlands. The SEP is a twice-a-year panel of households who are interviewedin April and October of each year. The panel started in 1984. For the estimation ofthe labour supply model only the wave of October 1985 has been used since thequestions used to construct reference groups have only been asked in that wave.The data set used contains 4225 households. In principle all persons in a householdof 16 years or older have been interviewed. The information collected pertainsprimarily to income, labour market status, subjective evaluation of income, andvarious background variables like household composition, education, etc. It turnsout that the information for many households is incomplete, so that a considerableamount of records had to be removed. One of the most interesting features of thesedata are the questions about reference groups, as described in Section 3. Anotherinteresting feature is that respondents are asked the number of hours they wouldlike to work, given their present after tax wage rate. It is this variable that is usedas a dependent variable in the labour supply model, the advantage being that thisvariable is a pure supply variable. Furthermore, the question for desired hours isframed in such a way that it implies a linear budget constraint. The respondentswere asked the following question: ‘‘Suppose that you can freely choose the


number of hours you work per week. How many hours would you like to work inyour present job, if you could choose them yourself and if you would earn onaverage the same amount of money per hour as you do now? If you choose fewerhours of work, you choose for less income. Assume that the number of hourschosen by other members of the household, if any, does not change’’. Thiswording implies that the respondent is offered a linear budget constraint and isasked which number of hours is optimal. Information on hours worked, wage ratesand other important variables in the sample is given in Table 1.

We have estimated the factor analytic models for hours and participation ratesseparately. Obviously, estimation of the two models for two-adult households withall the indicators included requires that all questions have been answered by bothspouses in the households. It turns out, unfortunately, that the routing in thequestionnaire has been such that the questions have only been asked to individualswho have their own independent source of income. As a result, the vast majorityof observations had to be discarded for this part of the analysis, including mosthouseholds with non-working housewives. For estimation only 272 householdsremain. In the next section we show how we can nevertheless use all observationsin the estimation of the labour supply model. In Table 2 the correlation matrices ofthe indicators are given.

Table 1Sample means

aVariable All Wanting to work

Desired hours per week 7.78 20.77Actual hours per week, lagged 1 year 7.66 19.22Participation rate 0.37 1.00Participation rate, lagged 1 year 0.33 0.81Reference group mean of hours worked 24.58Reference group mean of the participation rate 0.47 0.62Actual net wage rate 13.77Predicted net wage rate 12.57 11.57Level of education 1, lowest level 0.19 0.13Level of education 2 0.34 0.29Level of education 3 0.36 0.42Level of education 4, highest level 0.10 0.17Age category, younger than 25 0.06 0.09Age category, 25–35 0.41 0.43Age category, 35–45 0.29 0.34Age category, older than 45 0.24 0.15Non-labour income (guilders per week) 693.40 680.20Log of family size 1.20 1.10Dummy for presence of children younger than 6 years 0.57 0.35Number of individuals 977 366aThose who are employed and say they want to continue working and those not working who say theyare looking for a job.


Table 2Correlation matrices of indicators

Hoursx x x x1 2 3 4

x 1 0.58 0.82 0.601x 1 0.54 0.832x 1 0.583x 14

Participation ratex x x x5 6 7 8

x 1 0.40 0.75 0.455x 1 0.22 0.766x 1 0.387x 18

Table 3 presents the results of the factor analyses performed for hours andparticipation rates, respectively. The estimation method employed is maximum

¨likelihood, using the well-known LISREL program (Joreskog, 1973). Strictlyspeaking, this involves the assumption of multivariate normality of all variablesincluded. Especially, for the participation equation this can only be true as anapproximation. We have made the identifying assumptions that both factors haveunit variance (v 5v 51).h p

2The estimation results are satisfactory from a statistical viewpoint. The R ’s,iindicating the extent of the correlation between the ‘true’ reference group variables

2and the indicators x range from 0.16 to 0.82. The R ’s suggest that the indicatorsix , x , x and x , that have been based on the direct information about reference2 4 6 8groups available in our survey do better than the indicators x , x , x and x , that1 3 5 7

2could be constructed in any survey. The model R ’s of 0.90 and 0.83 indicate areasonable degree of fit for the two models. The signs of the a’s are all positive, asone would hope, whereas their magnitudes are comparable. The latter fact suggeststhat the informational content of the indicators about the true reference groupvariables is of similar magnitude, but of course not equal. (Otherwise, the

Table 3Estimation results for the factor analytic models

Hours Participation rate2 2Par. Est. S.E. R Par. Est. S.E. Ri i

a 3.89 (0.38) 0.34 a 0.07 (0.01) 0.251 5a 5.93 (0.34) 0.80 a 0.12 (0.01) 0.672 6a 2.91 (0.32) 0.29 a 0.05 (0.01) 0.163 7a 5.91 (0.33) 0.82 a 0.12 (0.01) 0.764 8

2 2R 0.90 R 0.83


indicators would have shown perfect correlation). The standard errors are small, sothat the a’s have been estimated with considerable accuracy.

5. Estimation of the labour supply model

The true reference group means defined in Section 3 cannot be observeddirectly. Hence, if one wants to use these variables in the labour supply model it isnecessary to replace the true variables by proxies. It is well-known however thatreplacing unobservable variables in a model by proxies may lead to inconsistentparameter estimates. Furthermore, the number of observations for which allindicators used in the factor analysis model are available is quite small. Basically,our solution amounts to the following. The proxies used for the unobservable truereference group variables are weighted means of the indicators. Given theestimates of the factor analysis model, one can construct these means optimally, inthe sense that a proxy gives the best unbiased prediction of the corresponding truevariable. Furthermore, the estimates of the variances of the n’s in the factoranalysis model can be used to compute the inconsistency that would arise inestimation if the proxies were used in estimation of the labour supply modelwithout further precautions. As a result it is also possible to introduce a correctionwhich guarantees consistent (and actually efficient) estimates of all parameters. Wewill now work this out in more detail.

Combining (1) with (3) and (2) with (4) leads to

dh 5 c 1 b j (21) 1 e (13)k k 08 hk hk

dp 5 d 1 g e (21) 1 e (14)k k 08 pk pk

where

c 5 b 1 b f 1 b f 1 b a 1 b a 1 b a 1 b h (21) 1 b Ik 01 02 1k 03 2k 04 2k 05 3k 06 4k 07 k 1 k2

1 b w 1 b w , (15)2 k 3 k

d 5 g 1 g f 1 g f 1 g a 1 g a 1 g a 1 g p (21) 1 g Ik 01 02 1k 03 2k 04 2k 05 3k 06 4k 07 k 1 k2

1 g w 1 g w , (16)2 k 3 k

x 5 A j 1 n , (17)hk h hk hk

x 5 A j 1 n . (18)pk p pk pk

Eq. (17) and Eq. (18) are the factor analysis model (5)–(12) written in matrixformat, A and A are column vectors of order 4, containing the a’s. The firsth ppoint to note is that the wages are not observed for non-workers. Both for workers


and for non-workers wages are derived from the wage equation presented inAppendix A (available from the authors upon request). Secondly the latentvariables j and j are not observable, so that we cannot use (13) and (14)hk pkdirectly. Instead of j and j we observe x and x . The way to get around thehk pk hk pkproblem of not observing j and j is to construct an expression of thehk pkexpectation of h and p conditional on x and x . In this expression normality ofk k hk pkall the variables involved is used heavily. The third point to note is that if we wantto use all observations in the estimation of (13)–(18) we will encounter manycases where not all elements of the vectors x are observed. We therefore constructproxies for the true variables that are optimal given the amount of informationavailable. Let z be the subvector of x which is observable for household k.hk hkThere holds

z 5 A j 1 n (19)hk hk hk hk

where A is the sub-vector of A corresponding with z and n corresponds withhk h hk hkz as well. The variance covariance matrix of the subvector of n is denoted byhk hkF , the appropriate submatrix of F .hk h

dWe can now write down the expectation and variance of h given c and z andk k hkdanalogously the expectation of p given d and z . We obtaink k pk

dE(h uc ,z ) 5 c 1 b E(j uc ,z )k k hk k 08 hk k hk219 95 c 1 b v A (A v A 1 F ) z (20)k 08 h hk hk h hk hk hk

d 2 219 9Var(h uc ,z ) 5 s 1 b (v 2 v A (A v A 1 F ) A v )b (21)k k hk h 08 h h hk hk h hk hk hk h 08

dE( p ud ,z ) 5 d 1 g E(j ud ,z )k k pk k 08 pk k pk219 95 d 1 g v A (A v A 1 F ) z (22)k 08 p pk pk p pk pk pk

d 2 219 9Var( p ud ,z ) 5 s 1 g (v 2 v A (A v A 1 F ) A v )g (23)k k pk p 08 p p pk pk p pk pk pk p 08

Notice that, after the factor analysis model has been estimated, most of thequantities appearing in (20)–(23) are known, except the parameters inherent in ckand d and b and g . The statistical model then becomes:k 08 08

d dh 5 E(h uc ,z ) 1 e if E(h uc ,z ) 1 e . 0k k k hk 1k k k hk 1kd (24)and E( p ud ,z ) 1 e . 0k k pk 2k

5 0 elsewheredp 5 1 if E( p ud ,z ) 1 e . 0k k k pk 2k

(25)d5 0 if E( p ud ,z ) 1 e # 0,k k pk 2k

where h is the observed number of hours an individual desires to work, p 51 ifk k


the individual wants to participate, 50 if the individual does not want toparticipate.

6. Estimation results for the labour supply model

Model (24)–(25) has been estimated by Maximum Likelihood on 977 observa-2tions of married females in the SEP-data.

For the sake of comparison we have also estimated a standard model withoutpreference formation. Table 4 presents the results. Let us first concentrate on the

Table 4Estimation results of the standard and extended model

Standard Extended

Estimate Standard error Estimate Standard error

Hours equationb (constant) 9.64 (23.78) 20.22 (16.42)01b (family size) 221.95 (3.11) 22.77 (2.07)02b (child ,6) 213.19 (2.42) 20.83 (1.49)03b (age 25–35) 27.06 (3.42) 23.84 (1.56)04b (age 35–45) 210.71 (3.65) 23.08 (2.11)05b (age .45) 222.08 (3.58) 24.43 (2.71)06b (habit form.) 0 (fixed) 0.60 (0.04)07b (pref. int.) 0 (fixed) 0.53 (0.65)08b (non-labour income) 20.0021 (0.0025) 20.0011 (0.0019)1b (wage) 3.91 (3.91) 0.002 (0.015)2b (wage-squared) 20.08 (0.15) 0.00 (fixed)3s 16.33 (0.71) 7.71 (0.21)h

Participation equationg (constant) 21.96 (1.60) 23.66 (4.53)01g (family size) 21.22 (0.18) 20.41 (0.30)02g (child ,6) 20.86 (0.13) 20.27 (0.22)03g (age 25–35) 20.08 (0.22) 20.29 (0.35)04g (age 35–45) 20.25 (0.24) 20.06 (0.44)05g (age .45) 20.99 (0.23) 20.51 (0.41)06g (habit form.) 0 (fixed) 2.74 (0.15)07g (pref. int.) 0 (fixed) 20.05 (0.09)08g (income) 20.0003 (0.0001) 20.0003 (0.0003)1g (wage) 0.47 (0.26) 0.43 (0.78)2g (wage-squared) 20.012 (0.010) 20.01 (0.03)3r (corr. coeff.) 0.98 (0.01) 0.68 (0.09)log lik. 21754.5 21374.1

2Conditional on wages, that is. Wages have been predicted on the basis of selection bias correctedwage equation. The results of the wage equation are given in an Appendix, which is available from theauthors upon request.


standard model of which the results are given in the first column of Table 4. Wesee that family size has a significant negative effect on both the degree ofparticipation of married females and the number of hours she would like to work.Also strong is the effect of the presence of children younger than 6 in bothequations. Females work fewer hours and participate less if they age. Non-labourincome is shown to have a negative effect on working hours and on theparticipation rate, implying leisure to be a normal good. The labour supply curve isforward bending for wages below 24 guilders per hour. For higher wages it isbackward bending. The higher the expected wage rate, the higher the participationrate for wages below 20 guilders per hour.

Next consider the extended model in which preference formation plays animportant role. In the flexible specification, the wage variable turned out to have anegative effect on labour supply and the squared wage a positive. As a result ofthis, in almost 60% of the observations, the Slutsky conditions were violated.Therefore, we have presented here the linear specification. The parameterestimates of the non-wage variables were roughly similar in both the linear and thequadratic specification. It is striking to see that especially the coefficients in thehours equation change a lot. The effects of family size and of the presence ofchildren younger than six become insignificant. Both the wage and the incomeeffects have decreased in size and are insignificant. The age effect has also becomemuch smaller, but is still significant. Habit formation has a very significantpositive effect on hours worked, and preference interdependence has a sizeablepositive, but insignificant, effect. In the participation equation the differencesbetween the standard and the extended model are less pronounced. Preferenceinterdependence apparently plays little role in the participation decision, whilehabit formation (or state dependence) has a strong effect.

These findings are corroborated by the results in Table 5, where we presentsome variants of the model. The estimation results of the model in which onlypreference interdependence is taken into account (see Table 5 first column) showus that it is habit formation and not preference interdependence that captures theeffect of family size on hours worked in the extended model. Preferenceinterdependence in this model has a strong positive and significant effect in thehours equation, but hardly any effect in the participation equation. This latter resultis remarkable in that it is at variance with the model put forward by Neumark andPostlewaite (1995). Column 2 of Table 5 (only habit formation) shows largepositive significant effects of habit formation in both the hours equation and theparticipation equation. Comparison of the log-likelihoods across the columns ofTables 4 and 5 shows that adding preference interdependence to the standardmodel provides a statistically significant improvement of the model (the log-likelihood rises from 21754.5 to 21744.0). The addition of habit formation ismuch more important however (the log-likelihood for the second column of Table5 is equal to 21398.8 as compared to 21754.5 for the standard model). Still, alsoafter allowing for habit formation, preference interdependence significantly


Table 5Estimation results of variants of the extended model

Only preference interdependence Only habit formation

Estimate Standard error Estimate Standard error

Hours equationb (constant) 252.95 (27.30) 21.09 (4.07)01b (family size) 219.68 (2.81) 22.86 (1.99)02b (child ,6) 211.87 (2.26) 20.32 (1.46)03b (age 25–35) 23.58 (3.17) 23.92 (1.56)04b (age 35–45) 25.74 (3.45) 23.11 (1.82)05b (age .45) 215.23 (3.74) 24.64 (2.37)06b (habit form.) 0 (fixed) 0.58 (0.04)07b (pref. int.) 3.00 (0.67) 0 (fixed)08b (non-labour income) 20.0021 (0.0025) 20.0012 (0.0018)1b (wage) 1.63 (3.68) 0.14 (0.37)2b (wage-squared) 20.04 (0.14) 0 (fixed)3s 14.76 (0.66) 7.63 (0.19)h

Participation equationg (constant) 21.93 (1.64) 22.48 (4.08)01g (family size) 21.15 (0.19) 20.38 (0.33)02g (child ,6) 20.85 (0.13) 20.37 (0.22)03g (age 25–35) 20.10 (0.23) 20.02 (0.33)04g (age 35–45) 20.25 (0.25) 0.41 (0.43)05g (age .45) 21.00 (0.24) 0.46 (0.37)06g (habit form.) 0 (fixed) 2.99 (0.14)07g (pref. int.) 20.006 (0.040) 0 (fixed)08g (income) 20.0003 (0.0002) 20.0005 (0.0002)1g (wage) 0.46 (0.27) 0.14 (0.70)2g (wage-squared) 20.012 (0.010) 20.0028 (0.03)3r (corr. coeff.) 0.57 (0.01) 0.53 (0.08)log lik. 21744.0 21398.8

improves the model (the log-likelihood for the second column of Table 4 is21374.1, whereas the log-likelihood for the second column of Table 5 equals21398.8, a difference of 24.7).

To give an idea of how well the extended model predicts labour supplybehaviour, we present graphs of observed and simulated hours distributions. InFig. 1 the observed (desired) hours distribution is confronted with the hoursdistribution, simulated by the standard model. Clearly, non-participation isoverestimated, and the frequencies of positive hours per week are underestimated.In Fig. 2 the simulated hours distribution derived from the extended model is

2shown. It fits the data much better. The x -statistic, calculated as squareddifference between the observed and simulated data, shows a reduction from 61.91in the standard model to 1.22 in the extended model.

Both in the standard and the extended model no observations violate the Slutsky


Fig. 1. Hours distribution simulated by the standard model.

Fig. 2. Hours distribution simulated by the extended model.


Fig. 3. Simulated labour supply curves.

conditions. The labour supply curves and participation rates derived by averagingover all individuals are shown in Figs. 3 and 4. Fig. 3 reveals a flatter laboursupply curve in the extended model than in the standard model. Analogous resultsare found for the participation rates. We believe that the wage effect is taken overby habit formation and preference interdependence. Just as is the case with theeffect of the presence of young children. One should note that these labour supplycurves are ‘short run’ curves in the sense that all right hand side variables, exceptthe wage, are kept constant. The models with habit formation and preferenceinterdependence are dynamic models, and hence it is also of interest to considerresponses to changing wage rates after more than one period.

To simulate the long-run effects of wage rate changes, we increase all wages by10% and simulate participation and hours worked after one period. Thesesimulated values are next fed into the right hand side of the hours and participationequations and we simulate hours and participation in the next period. We continuethis process until convergence. In the simulations it has been assumed that desiredhours and participation can be realized without delay (i.e. there is no involuntaryunemployment or other demand side restrictions). We summarize the aggregateeffects of the simulations by presenting the effects on average hours and

3participation in the form of elasticities.

3Given that we consider the effect of an across the board wage increase by 10% this means that wesimply divide the calculated percentage changes by 10.


Fig. 4. Simulated participation rates.

Table 6 gives the results. One should note that the elasticities of hours onlyrefer to mean hours for those who work. A negative sign for an elasticity maytherefore occur in cases where participation goes up quite a bit, but where the newentrants work few hours. This then depresses the mean.

In the extended model, the short term (ST) effects of a wage increase on hoursworked and participation are lower than the long term (LT) effects. But the longterm effects are still much lower than the wage effects in the standard model. Theshort term effects in the model with only preference interdependence resemble theeffects in the standard model: a strong positive effect on participation and a strongnegative effect on hours worked. But after only a few periods, preferenceinterdependence results in small positive effects on both hours worked andparticipation.

Table 6Elasticities of hours and participation with respect to wages

Standard Extended Only pref. int. Only habit form.

ST LT ST LT ST LT

Positive hours 21.97 0.08 0.61 21.99 0.11 0.15 0.18Participation 7.07 0.00 0.19 6.93 0.17 0.00 0.04


7. Conclusion

The modelling of preference formation has been the major point of emphasis inthis paper. To that end we have constructed reference group means of hoursworked and the participation rate on the basis of a factor analysis model. We haveemployed different pieces of information available in the data set to constructlatent variables which may be thought to be a more accurate reflection of thenotion of reference group means than the ones used in Kapteyn and Woittiez(1990). The factor analytic model, which relates these indicators to the ‘true’reference group means suggests that the indicators based on direct information bythe respondents about their reference groups perform better than indirect indicatorswhich we constructed ourselves. Unfortunately, due to a particular routing in thequestionnaire, the direct indicators of reference groups are only available for arelatively small part of the data. This has undoubtedly reduced the significance ofthe reference group variables in the labour supply and participation equations.

The estimation results indicate that the incorporation of preference formationleads to different conclusions than would otherwise obtain. One of the mostinteresting features of the model is that incorporating preference formation leads toa large decrease in the effects of the presence of young children on hours worked.Also, the wage effects on labour supply become smaller. The fit of the modelincreases significantly by incorporating preference formation.

At the same time, it becomes clear that despite our potentially betteroperationalization of reference group variables than in earlier work, most of theimprovement in model fit is caused by habit formation and a relatively small (butsignificant) part by preference interdependence. Although this may indicate a moreimportant role for state dependence in the explanation of labour supply, one canonly be sure about this, once better indicators of reference group variables areavailable.

Not only would one like to have direct measures for every respondent (ratherthan for a relatively small part of the sample), but also it would be important to askdirect questions about participation and hours worked in one’s social environment.In the current analyses these variables still had to be constructed in a somewhatroundabout manner.

Acknowledgements

We are grateful to Arthur van Soest for helpful comments. We thank StatisticsNetherlands for permission to use the data from the SEP.

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