creating a variable that is a function of real per-capita gross domestic product at
the time individuals entered the labor force. This way they can be fully flexible in
their specification of age and time effects.
An extreme assumption on cohort effects is made in Paxson’s (1996) analysis of
the saving rate: they are set to zero. This is equivalent to assuming that consumption
and income cohort effects exactly cancel out.
9
2.4 DATA REQUIREMENTS
Equations (2.6) and (2.3) show that there are three different ways of measuring
saving (defined in the traditional way, that does not include changes in social
security wealth):
. first, by comparing asset holdings at the beginning and at the end of a period:
A
tþ1
A
t
. secondly, by adding inflows and outflows of wealth accounts during 1 year:
P
j
ðr
jt
A
jt
þ D
jt
Þ
. thirdly, by taking the residual of income minus consumption expenditures:
y
t
þ r
t
A
t
þ b
t
t
C
t
.
Equality of these measurement concepts is only achieved when the variables
involved stock of wealth, flows into and out of accounts, income and expendi-
tures are consistently defined. Ideally, one would like to report all three measures
in order to learn how reliable actual measurements of all variables involved are.
As noted above, household saving is the sum of discretionary and mandatory
saving. Discretionary saving (active and passive) is completely under the control of
the household. Households choose its absolute value as well as its portfolio
composition, given their budget constraints and applicable incentives such as tax
relief and mandatory contributions to funded and unfunded pension schemes.
Instead, mandatory saving is beyond the control of the household.
So far, we have taken social security contributions as the only type of
mandatory saving. However, other forms of retirement saving are sometimes seen
as part of mandatory saving. For instance, according to Bo
¨
rsch-Supan (2001a):
the most important example are mandatory contributions to funded occupational
pension plans. Here, the contributions are prescribed (e.g., a fixed absolute sum or
a fixed percentage of gross income) and frequently even the portfolio composition is
outside the control of the household (e.g., the employer provides a single pension plan).
9
Kapteyn et al. (1996) derive sufficient conditions for Paxson’s assumption to hold. They show that
in a model with quadratic preferences, time preference equal to the interest rate and productivity growth
that has only a one-off proportional impact on income, cohort effects are the same on wealth,
consumption, and income.
50 Chapter 2 Household Saving: Concepts and Measurement

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