Empirical life cycle models of labour supply and - Statistisk sentralbyrå

Empirical Life Cycle Models Social and Economic Studies 91
can be rewritten as
(148) In c/4 — in Ao — (p -1- in rit + ( 4-1) In t - In tat > O.
Using the wage equation
(149)
the taste modifier equation
In wt Mt)3m E2t,
(150) rit exp(Nto + eu),
and the components of variance scheme
(151) Eit = 7/j yjt, j = 1,2,
for the disturbance vector (fit, €2t), this equation implies
(152) + in
> [— in Ao in cv/ -1-7/1 — 7/2 + NtO Mtfim ( 10 r)t]
since — 1) < O. Using the definition of f, VIA and Art from equation (48) and
(49), this equation can be written
(153) Vit > —f — Art -1- In T.
The first line of equation (146) can then be written
(154) In Lt in T if Vi > —f — Art + in
and this expression is equal to the first line of equation (47).
The second line of equation (146) says that the demand for leisure is
determined by the equation
(155)
Wi
rit41-1
Ao(i py
Wt
(1 -1- r) t.
Solving
(
this equation with respect to in Lt , and using the approximation
In -1-±-P-) p — r, yields
i+r
1
(156) ln Lt = [ln wt -1- in Ao (p — r)t — In co/ — in F 1 ].
—
Using the wage equation (149), the taste modifier equation (150), the
components of variance scheme (151), and the definitions of f, Vit and Art , the
second line of (47) can easily be found.
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