We study a model of domestic transfers based on exchange in which children can either work or provide services to their parents to earn some money. Using a French survey, we show that there exist attention-payment mechanisms to the young children from the parents, but these exchanges disappear when children can enter the labor market.

Barnet-Verzat Christine

Wolff François-Charles

English

Research Papers in Economics

Labor opportunities against family intergenerational
exchange 
Barnet−Verzat Christine Wolff François−Charles
LEN−CEBS Université de Nantes, France and INED LEN−CEBS Université de Nantes, France; CNAV and
INED
Abstract
We study a model of domestic transfers based on exchange in which children can either work
or provide services to their parents to earn some money. Using a French survey, we show that
there exist attention−payment mechanisms to the young children from the parents, but these
exchanges disappear when children can enter the labor market.
Citation: Christine, Barnet−Verzat and Wolff François−Charles, (2003) "Labor opportunities against family intergenerational
exchange." Economics Bulletin, Vol. 10, No. 1 pp. 1−7
Submitted: February 3, 2003.  Accepted: February 10, 2003.
URL: http://www.economicsbulletin.com/2003/volume10/EB−03J00001A.pdf1. Introduction 
When they attempt to understand the motives underlying intergenerational family 
transfers, economists usually define two types of behavior. According to the altruistic 
hypothesis, caring parents give out some of their resources to their children in order to 
compensate differences in standards of living (Becker, 1991). According to the exchange 
model, money given by parents fits in a reciprocity structure and is the counterpart of a 
transfer done by the children. Payment for children's attention is one of the most frequent 
kinds of exchange (Cox, 1987, Cox and Rank, 1992).  
However, empirical studies are rather incompatible with the hypothesis that exchanges 
occur between generations (see Laferrère and Wolff, 2003). Why do we observe so little 
exchange between generations? Two main difficulties have been previously suggested in the 
previous literature. First, the sign of the recipient's income on the amount of money received 
(which is used to provide a test to tell various motivations apart) cannot provide any reliable 
information (Altonji et alii, 1997). Second, cross-sectional data does not allow taking into 
account any possible delayed reciprocity. Parents can all at once give some money to reward 
services which have been given over a long period of time.  
In this paper, we put forward another reason to explain the absence of exchange 
observed in the data. Parents offer their children a certain payment for their services, but 
children have the choice between two activities. They can earn money either by helping their 
parents or by turning to the labor market. Thus, participation in domestic exchanges depends 
on the relative payment for these two activities.  
To study the influence of outside opportunities on money-services exchanges, we use 
a survey completed in France in 1992 on parental investments in children's education and 
focus on pocket money given by parents to schoolchildren
1. In France, holding a job before 
the age of 16 is illegal. But moonlighting work exists and children can find job opportunities 
like baby-sitting for example before this age. Yet, the easiest way to earn money before 16 is 
still to work inside the family. After this age, children can either carry on helping at home or 
find a paid job. The data shows that family reciprocities disappear as soon as the children 
have the possibility of obtaining an outside income by working on their own.  
The remainder of the paper is organized as follows. In section 2, we display a model of 
transfers based on exchange in which children share their time out of school between market 
work and paid home services. In section 3, we describe the occurrence of family exchanges. 
An econometric analysis is performed in section 4. Section 5 concludes. 
 
2.  An exchange model of transfers 
Let us consider a family consisting of one parent and one child, respectively indicated by 
p and k. Following Cox (1987) and Cox and Rank (1992), the exchange mechanism is as 
follows. The parent gives a certain amount of money T to his child and he receives a volume 
of services S in return. The parent derives satisfaction from his own consumption Cp and from 
the services he receives from his child. Furthermore, he is altruistic and derives utility from 
the child's satisfaction. The child is selfish. He draws utility from his own consumption Ck, 
                                                 
1 Up to now, economists have neglected this type of intrafamily transfers, with a few exceptions (Barnet-Verzat 
and Wolff, 2002, Dustmann and Micklewright, 2001, Furnham, 1999, 2001).   1
but he suffers a loss of well-being when helping the parent. Let U and V be the utility 
functions of the parent and child respectively; they can be expressed as U(Cp,S,V(Ck,S)) and 
V(Ck,S), with Uc>0, Us>0, Uv>0, Vc>0 and Vs<0. We assume that U and V are continuous, 
twice differentiable and concave. 
The resources constraints are as follows. The parent gets an exogenous income Yp that he 
devotes to his consumption Cp and to a transfer T to the child, so that Cp=Yp-T. The child's 
resources are of two types, wage and transfer. He can either work at a wage rate w or provide 
services to his parent. We admit that the total time of the child is equal to 1, 1-S being the 
time devoted to the labor market. Hence, the child's budget constraint is Ck=w(1-S)+T. Let 
U
0=U(Yp,0,V(w,0))  and V
0=V(w,0) be respectively the parent's and the child's reservation 
utilities. They fit a situation characterized by an absence of time and money transfers. The 
optimal choices for T and S are determined under the hypothesis of a dominant parent
2. In 
case of money-service exchange, the child's level of satisfaction is given by his threat point 
utility level V
0=V(w,0). For a utility function U such that U(Cp,S)+β pV(Ck,S)) with β p the 
parental degree of altruism, the maximization program under exchange is
3: 
max U(Yp-T,S)+ β pV(w(1-S)+T,S) s.t. V(w(1-S)+T ,S))=V
0(w,0)   (1) 
In this model, exchange occurs when the marginal rate of substitution of the financial help 
with regard to the services to the parent MRSp
0 is higher than the marginal rate of substitution 
of the transfer with regard to the services for the child MRSk
0, these marginal rates being 
estimated for S=0 (Cox, 1987). If one admits the absence of crossed effects (Ucs=0, Vcs=0), 
we have: 
MRSp
0=Us
0/Uc
0 
      (2) 
MRSk
0=w-Vs
0/Vc
0        (3) 
Thus, from (3), we observe that the market wage competes with the realization of exchanges 
within the family. When outside opportunities are profitable, the child has no interest to take 
part in transfers except when the parent agrees to pay a high price for his help. Let us examine 
the effect of an increase in w on the child supply price for the first unit of services. The 
derivative ∂ MRSk
0/∂  w is: 
∂ MRSk
0/∂  w=1+wVs
0Vcc
0/(Vc
0)
2>0
       (4) 
The sign of this derivative is strictly positive since Vs
0<0 and Vcc
0<0. The probability of 
observing an interior solution in case of exchange decreases with the level of market wage. 
Clearly, when w is sufficiently high, the child prefers a wage-earning work because the parent 
is unable to offer a sufficient price of attention. 
 
3.  Data and descriptive statistics 
Our empirical investigation relies on a survey completed in France in 1992 by Insee and 
Ined on parental investments in children's education. This data set turns on a representative 
sample of 5300 households, including at least one schoolchild from 2 to 25. The data provides 
                                                 
2 We could also consider a Nash bargaining model where both generations maximize (U-U
0)(V-V
0), but this does 
not affect our theoretical results (see the discussion in Cox, 1987, Cox and Rank, 1992). 
3 Let λ  be the corresponding Lagrange multiplier. Given the existence of exchange, one has λ >0 and the first-
order conditions are -Uc+β pVc+λ Vc=0 and Us-β pwVc+β pVs-λ wVc+λ Vs =0.   2
information on the parental economic position and the children's personal resources. For 
them, we know whether they have their own source of income and whether they get pocket 
money, regularly or not, and how much. The survey provides some information on the 
circumstances under which irregular allowances are given: in return for services or jobs done 
by children, as rewards for school results. 
The data are original in the following ways. First, by considering the case of 
schoolchildren, we can study how opportunities resulting from labor market income gradually 
influence individual decisions of upstream services. To date, previous studies have mainly 
been interested in transfers between generations not living together. Yet, the amounts of 
money that circulate between young children and parents are of considerable importance (see 
Barnet-Verzat and Wolff, 2002, Furnham, 1999). Second, the questionnaire allows us to 
directly identify the payment of services and domestic tasks realized by the children. Clearly, 
this type of intergenerational exchange matches the mechanism of attention payment initially 
described by Cox (1987).  
After deleting missing values, the sample includes 6050 parent-child pairs. According 
to the data, 74 % of the children receive some money from their parents for an average 
amount of about 460 euros per recipient. 44.7% receive some money regularly, while 36.0% 
receive irregular payments. Besides, among the recipients, 25.1% of children get both forms 
of help. For unsteady transfers, 10% of the children receive some money for the services and 
9.8% are rewarded for their good results at school. 
The fact that a high proportion of children benefit from regular payments comes rather 
against an altruistic motive, since altruistic parents should fit their financial effort to the needs 
of their offspring. The data rather points out that there are forms of money-services exchange 
such as those described by Cox (1987). However, households' behaviors are heterogeneous. 
The population includes at the same time cases of altruism (punctual sums are given to meet 
the children's need) and situations more in agreement with the exchange hypothesis. 
Reciprocity may occur either through the use of regular gifts being paid off latter on in the 
future or through the payment of non-market services. 
 
4. Econometric  analysis 
We explore the relationship between exchange-motivated transfers and the characteristics 
of the donor and the recipient through an econometric analysis. We estimate a Probit model 
with the dependent variable equal to one if the child receives some money against services 
and zero otherwise, then a Tobit model for the gift value
4.  
According to Table 1, children with young parents tend to be more often concerned with 
that kind of exchange. The payment of services is more likely to appear when the child has 
got siblings and is a boy, and the amount of money offered is more substantial. Our main 
result is that the child's age is of considerable importance to explain the existence of 
exchange. Both for the probability and the amount of gift, the age profile is characterized by 
an U-inverted form. The occurrence of a services payment begins to increase with the age, 
with a maximum around 14, and falls down afterwards. After 20, the probability of money-
services reciprocity is very low. Our results suggest that the exchange motive of family 
                                                 
4 In the regression, the child's education is not introduced given its very high correlation with age.   3
transfer is relevant, but mainly applies to young children. For families with two children, we 
have also controlled for unobserved heterogeneity using Probit and Tobit random-effect 
models, and the U-shaped age profile still holds (see Table 1). 
Our interest is now to give an explanation for the decline of exchange transfers with the 
age. We argue that money-services exchanges compete with labor work as the child grows up. 
For this purpose, we examine the child's age profile for different types of transfers: payment 
of services, school rewards, irregular pocket money, regular. Given these four specific forms 
of help (payment of services, school reward, irregular pocket money, regular allowances), we 
estimate a quadrivariate Probit model using the GHK simulator, and then use these estimates 
to compute the age profile for each type of transfer. According to the data, the age profile of 
the probability of exchange is U-shaped, but it is significantly different from that observed for 
regular or irregular payments which increase steadily (Figure 1). In these cases, parents try to 
meet children's needs, which get regularly higher as they grow up. 
Pocket money given to buy services fits in a different logic. The payments are only linked 
to the amount of work done, and it is obvious that children do not increase their domestic 
work supply as they age. One reason can be found in the existence of opportunities to earn 
more money elsewhere, particularly in the labor market. Teenagers can for example baby sit, 
and be better paid than by setting the table or washing their parent's car. As they grow up, the 
range of accessible jobs widens and the potential wage increases. Thus, the choice between 
home services and outside opportunities is done at the detriment of the former, so that 
exchange-motivated transfers within the family tend to lessen at an older age. In Figure 1, we 
also report the estimated probability that a child earns money by working. The data shows that 
this probability is very low till the age of 14, less than 10%, but there is a steep increase after 
this threshold level. Remarkably, the participation in job market activities coincides with the 
decline of payment-services family exchange, while regular allowances and irregular pocket 
money are not affected by the rise of child's labor
5. 
 
5. Conclusion 
In this paper, we explain why previous studies on family transfer motives have widely 
rejected the exchange model in which parents buy their children's services (Cox, 1987). Using 
data on pocket money in France, we show that there exist mechanisms of purchase of 
attention from the youngest age within the family, but these exchanges tend to disappear 
when children can make more money outside of it. Our analysis suggests that it would be 
constructive to consider the possibility that the altruism and exchange models may be more 
appropriate to characterize the behaviors of particular subgroups of population. 
 
 
                                                 
5 We have also attempted to estimate the effect of child's labor participation on the probability of receiving an 
exchange transfer from the parent. The decision of child's labor is instrumented using child's characteristics, sex 
and age (quadratic), and parent's characteristics (education and income). The estimated probability of child's 
labor as a regressor is negatively related to the receipt of an attention payment. The effect is significant at the 5 
percent level when the child's age is excluded from the exchange transfer equation.   4
References 
 
Altonji J.G., Hayashi F., Kotlikoff L.J., (1997), “Parental altruism and inter vivos transfers: 
Theory and evidence”, Journal of Political Economy, vol. 105, pp. 1121-1166. 
Barnet-Verzat and Wolff, (2002), “Motives for pocket money allowance and family 
incentives”, Journal of Economic Psychology, vol. 23, pp. 339-366. 
Becker G.S., (1991), A Treatise on the Family, Enlarged Edition, Harvard University Press, 
Cambridge. 
Cox D., (1987), “Motives for private income transfers”, Journal of Political Economy, vol. 
95, pp. 508-546. 
Cox D., Rank M.R., (1992), “Inter vivos transfers and intergenerational exchange”, Review of 
Economics and Statistics, vol. 74, pp. 305-314. 
Dustmann C., Micklewright J., (2001), “Intra-household transfers and the part-time work of 
children”, CEPR Discussion Paper, n° 2796. 
Furnham A., (1999), ‘The saving and spending habits of young people’, Journal of Economic 
Psychology, vol. 20, pp. 677-697.  
Furnham A., (2001), ‘Parental attitudes to pocket money/allowances for children’, Journal of 
Economic Psychology, vol. 22, pp. 397-422.  
Lafferrère A., Wolff F.C., (2003), ‘Microeconomic models of family transfers’, in S.C. Kolm, 
J. Mercier Ythier, Handbook on the economics of giving, reciprocity and altruism, North-
Holland, Elsevier, forthcoming. 
 
   5
 
Table 1. Determinants of exchange-motivated pocket money 
Variables  Probit  Random effect Probit Tobit  Random effect Tobit 
  coef t-test coef t-test coef t-test coef t-test 
Constant  0.214 0.35 2.174 1.00  35.452  0.08  -510.618  -0.84 
Characteristics  of  the  child          
Female  -0.060  -1.35  -0.281  -2.17 -59.349 -1.76 -66.917 -2.18 
A g e           
Less than 9 years   -0.406  -4.95  -1.505  -5.87  -329.259  -5.22  -302.900  -5.18 
10-11  years  -0.059 -0.75 -0.500 -2.14  -90.200  -1.49  -143.677  -2.71 
12-13  years  -0.061  -0.76  -0.346  -1.54 -71.501 -1.18 -99.189 -1.84 
14-15  years  ref  ref  ref  ref  
16-17  years  0.050  0.61 -0.052 -0.23 95.013 1.56 83.802 1.51 
18-19  years  -0.226 -2.47 -0.523 -2.13  -101.208  -1.49  -16.633  -0.26 
20  years  and  more  -0.369  -3.77  -0.999  -3.82 -154.316 -2.15 -111.483 -1.61 
Characteristics  of  parents          
Age  -0.048  -1.74  -0.224  -2.19 -33.341 -1.60 -18.158 -0.68 
Age squared (10
e-2)  0.028 0.91 0.147 1.34  18.350  0.79 2.261 0.08 
Married  -0.066  -1.06  -0.150  -0.64 -20.070 -0.43 -30.067 -0.56 
Number  of  children          
One  ref  ref  ref  ref  
Two  0.297 3.53 1.045 3.53  207.600  3.26  224.677  3.22 
Three  0.314 3.53 1.190 3.65  230.659  3.43  229.178  3.02 
At  least  four  0.314 3.17 1.253 3.51  217.561  2.90  233.371  2.79 
Education  -0.027  -1.37  -0.119  -1.65 -20.386 -1.40 -15.353 -0.98 
Level of income (10
e-6)  0.440 1.90 1.511 1.84  250.500  1.44  117.707  0.61 
Number  of  observations  6050 6050 6050 6050 
Number  of  recipients  602 602 602 602 
Log  likelihood  -1896.2 -1640.5 -6004.8 -5819.0 
Source : Survey Education Insee-Ined 1992. 
 
 
 
Figure 1. The effect of child's age on the receipt of parental transfers 
0
0,2
0,4
0,6
0,8
8 1 21 62 02 4 Child's age
 Probability
payment of services
regular allowances
irregular pocket money
school rewards
labor work
 
    Source : Survey Education Insee-Ined 1992. 
 
  

Labor opportunities against family intergenerational exchange

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