Empirical life cycle models of labour supply and - Statistisk sentralbyrå

Social and Economic Studies 91 Empirical Life Cycle Models
3.6.1 Some arguments in favour of Hicks aggregation
Complete household expenditure data for Norway are collected by Statistics
Norway. The data for non-durables are based on accounts of expenditures over
two weeks, and expenditures for the whole year are found by multiplying these
data by 26. The measurement errors introduced by this procedure can be huge,
and we prefer to obtain the data from another data source.
This chapter suggests aggregating Ck and (Kk — using the Hicks
composite good theorem. In light of price reductions for housing over the last
years, the use of this theorem may be questioned. There are, however, some
arguments that favour this assumption. The first is that the consumer price
index, which we assume can be used to measure the price of non-durables32 ,
includes expenditures related to housing as well. According to Statistics
Norway (1991), the budget share of expenditures related to lighting and heating
is about 5 per cent. The second point to notice is that durables include many
variants, such as cars, private motorboats, furniture and kitchen and leisure
equipment, and price changes for these goods have been less dramatic than for
housing. The third point is that, as we have argued in section 3.3.2, it seems
reasonable to assume that the price path for durables is more or less similar to
the price path for non-durables in the long run. So even if it can be questioned
whether this approach is appropriate for the years included in this analysis, the
approach may well be more defendable in other periods.
3.6.2 Measurement error
The possibility of measurement errors in some of the endogenous variables in
the model makes the consequences of measurement errors of interest. The
estimates of the equations based on the marginal rate of substitution functions
are consistent only if the measurement error is of the classical errors in the
variables type. This means that the observed endogenous variable F in the
regression function is related to the true variable F0 according to F F0 +
where ro. is a randomly distributed error term that is distributed independently
of all instrument variables. Given the results presented in appendix D, the
measurement problems related to durables, and the fact that the cash flow
related to the purchases of durables and non-durables is observed indirectly
through the wealth constraint, this is a very strong assumption.
The same issues of measurement errors arise in the discussion of the
consequences of measurement errors in the estimation of the Euler equation
(134). If there are measurement errors in equation (132) and (133), the error
terms of these equations include measurement errors. This means that the
32 Unfortunately this index also includes prices of durables, and the observed price of
non-durables may then be biased.
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