Empirical life cycle models of labour supply and - Statistisk sentralbyrå

Social and Economic Studies 91 Empirical Life Cycle Models
where
qt qt
— f
1 4-- Rt+i qt+i
is the user price of durables. Since Rt+i depends on the marginal taxation of
interest incomes, the user price is endogenous.
At this moment we notice that if preferences are non-separable both between
and within period's, all the marginal utilities depend on the consumption of all
goods in all periods, and estimation of a particular first order condition is very
data demanding even if we could observe A. If preferences are additively
separable between, but not within periods (and the monotonic transformation
of lifetime preferences is the identity transformation), the marginal utilities for
a particular period all depend on the consumption of all goods in that period,
and estimation of a particular first order condition requires less data. If,
however, preferences are both intra- and intertemporal additively separable, and
the monotonic transformations of both intra- and intertemporal preferences are
the identity transformation, the marginal utilities only depend on the
consumption of the actual good, and estimation is considerably simplified.
In the case of no binding credit market constraints in any historic period as well
as no binding constraints in the labour and credit market in the current period,
yt , -7, 1 and at equal zero. If we also assume additive within-period utility and
that the monotonic transformation (1) t of within period preferences is the
identity transformation, the Frisch demand functions become
(23) Ct Ct [(I -I- P) t AoDtPt] t --= 0, 1, • .•,T,
(24) _Kt Kt [(I -I- P) t Àoptqut] t = 0, 1, . . . ,T ,
and
(25) lit lit [(1 P) tAoptrnt] , t = 0, 1, . ,T ,
where the Ce-, Kt- and lit-functions are the inverse of the functions for the
subutilities of C, K and H respectively.
This specification illustrates the advantage of what MaCurdy (1981) labels the
A-constant demand functions. In the case of no binding constraints in any
historic period in the credit market, no current binding constraints in the credit
and labour markets, and inter- and intraperiod additive separable preferences
with 4:1)t equal to the identity transformation, the arguments of the demand
functions, apart from the discounting rate, are reduced to prices observable
within the current period and the (latent) life cycle component Ao. This means
that with the exception of the information that is included in Dt , mt and qut , Äo
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