2. The model
Individuals are constrained in their choice of labour by the availability of job offers. The number of job offers, n, follows a Poisson distribution with parameter
l. An advantage of this Poisson specification, as opposed to the binomial Ž
. Ž
. specification of Tummers and Woitiez 1991 and Van Soest et al. 1990 , is that it
can easily be made dependent on individual characteristics. In these studies, the effect of individual characteristics has typically been ignored. Moreover, the
binomial distribution requires the choice of a fixed maximum number of offers. A job offer has two determinants, the wage w and a weekly number of working
hours h. A job offer is modelled as a simultaneous draw of a wage rate w and a weekly number of working hours h from a joint wage–hours offer distribution
Ž .
1
f w,h . Hours are assumed to be distributed according to a discrete distribution: P h
s h s p ,
l s 1, . . . , m
1
Ž .
Ž .
l l
in which m is the number of categories of hours, and h , l s 1, . . . ,m, are the
l
different values that the hours offer can take. The advantage of this approach is that no heavy restrictions, like single peakedness or symmetry, are placed on the
shape of the distribution. The wage offer distribution is assumed to be log-normal:
lnw s x
X
h q Õ,Õ ; N 0,s
2
2
Ž .
Ž .
l Õ
The wage depends on individual characteristics x . The subscript l indicates
l
Ž .
possible dependence on the hours offer. Tummers and Woitiez 1991 specified a normal wage distribution, thereby not restricting the range of possible wages to
positive values. The equation is formulated in terms of the net wage rate. Ž
. Individuals have a utility function u h, y , defined over labour supply h and
Ž .
income y. The utility function is specified according to Hausman 1980 . The Ž
. Hausman 1980 utility function yields a linear labour supply function when
maximized subject to a linear budget constraint.
b h y Xd y e y b y
Ž .
u h, y s yln g y b h y
3
Ž .
Ž .
Ž .
g y b h where
Ø b, g , d are parameters, b - 0, g 0
Ø y is disposable income
Ø h is the number of working hours
Ž
2
. Ø
e is an unobserved random taste variable, e ; N 0,s
e
Ø
X is a vector of individual characteristics
1
Ž .
A discrete hours distribution was introduced by Dickens and Lundberg 1985 .
For any given number of working hours the budget constraint is
2
y s wh q m
4
Ž .
where m is non-labour income. Ž
. At a given point in time, an individual receives n possibly zero job offers,
each of them consisting of a wage w, 0 - w - ` and a number of working hours 4
h g h , . . . ,h . Furthermore, an individual can always choose not to work. The
1 m
alternative which yields the highest level of utility will be chosen. An individual will be observed to be non-working if the utility level of not working exceeds the
utility level of all of the n job offers.
3. Maximum likelihood estimation
Kategori