Empirical life cycle models of labour supply and - Statistisk sentralbyrå

Social and Economic Studies 91 Empirical Life Cycle Models
As we would expect from the discussion of equation (26), Ao is a function of
preferences, initial wealth, and the lifetime price paths, here represented by the
(real) interest, r, and wage rate, wit . Since no data sets include all these
variables, estimation requires further assumptions. Boyer assumes that
Bcit = 1 — Bhit, that the time horizon is infinite, and that p = r, where r is not
observed. She also specifies the wage equation
(52) wit = 10i -F /lit -F
where ioi and /ii are "unspecified functions of time invariant determinants of
wages", and vit is an unobserved random variable.
The earnings function now becomes
bh r
(53)
witHit = bhwit Bhit[bhi0i + 1 + r itio — b]
where ioi and 1i1 are unbiased estimates of toi and hi obtained from a separate
estimation of the wage equation. Assuming further that Bhit can be related to
observable variables and a random error, Boyer uses this specification as basis
for estimating a linear earnings equation on wit , ioi , 11 , A 0 , individual
characteristics, and interactions of characteristics with ioi, Iii and Aio, by
minimizing a generalized instrumental variables criterion function. From this
estimation she obtains estimates of all the parameters of the utility function,
including the time preference rate p = r.
Regarding the properties of this approach, we notice that it is based on the
relevance of the Stone-Geary utility index. To find the reduced form expression
for Ao , one has to assume that there are no binding constraints in any market in
any period. Estimation requires observations of variables related to the actual
good, initial assets and demographic variables, but since most data sets do not
include observations of initial assets, estimation can be more complicated than
it may look like at first glance. Boyer also disregards income taxation, and this
decision simplifies estimation and reduces the data requirement.
An explicit solution of the optimization problem is also obtained in Biørn
(1981), where Biørn estimates a Stone-Geary utility index with the household's
aggregate consumption as the only argument in the utility index. By splitting
income at the beginning of the planning horizon into permanent and transitory
income, he relates consumption to permanent and transitory incomes.
In Bover (1991), Boyer modifies her Stone-Geary specification described above,
to allow for habits;
(54) E(1 + p)tk [Bhikin(bh+ Hik) Bk in (Cik — bc)} •
k=t
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