Empirical life cycle models of labour supply and - Statistisk sentralbyrå

Empirical Life Cycle Models Social and Economic Studies 91
The first order conditions corresponding to this optimization problem implicitly
define the demand for goods and leisure as functions of wt, Pt, Yt and rtAt-i,
and the parameters of the tax function and the preferences. In order to simplify
the exposition further, ignore income taxation and assume that these demand
functions can be given closed form solutions. If _C_t f (Ce , Lt) is the vector of
consumption goods with corresponding price vector pt = (tvt , Pt), the
within-period demands can be written as
(60) = (Pt , Yt)
where Lt is the vector of demand functions.
These demand functions are called y-conditional demands since consumption is
chosen conditional on full income. They are homogenous of degree zero in prices,
pt , and full income, Y, and the functional form varies across goods. According
-to Blundell and Walker (1986), the demand functions for all goods generally
change if there are binding constraints in any market in period t. In contrast
binding constraints in the future only change the value of Y. The assumption of
intertemporal additive separability then allows for decentralization over time.
Although we are assuming perfect certainty, we notice that the introduction of
uncertainty about future prices and preferences leaves the two-stage budgeting
model almost unchanged, since all uncertainty is captured through the
distribution of full income across the life cycle, cf. Blundell and Walker (1986).
From the discussion of the determination of full income it is evident that the
full income variable in the y-conditional demands summarises the effects of past
decisions and future prices and preferences, on current decisions. In that respect
full income serves the same purpose in the y-conditions demands as the
marginal utility of wealth does in the Frisch demand functions.
Compared with the Frisch demands, the y-conditional demands, however, only
include variables that can be observed, and they can be observed within the
current period. Estimation of the demand function for a particular good
requires observations of the demand for the good, the price vector pt and full
income. If we take account of income taxation, rtAt_i must also be observed in
addition to the parameters of the tax system. Since many surveys are either
income or expenditure surveys, it can be hard to find data sets that include all
these variables.
Blundell (1987) points at that empirical specifications based on parametrization
of direct utility, can often be shown to be unnecessarily restrictive compared to
dual representations. In that respect the following results are important:
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1. If preferences are intertemporally separable, within-period allocation of