. plus voluntary contributions to, minus payments from, individual retirement
accounts and pension funds where withdrawals may be made only after retirement
or a pre-specified age
. plus amortization of, minus take-u p of, consumer loans.
In turn, active discretionary real saving consists of
. Purchases of, minus sales of, real estate (including owner-occupied housing)
. plus expenditures in upkeep and improvem ent of housing, minus
depreciation
. plus amortization of, minus take-up of, mortgages
. plus purchases of, minus sales of, gold and other jewellery.
10
Finally, a word on inflation. In the budget constraint, Eq. (2.1), we have defined
all variables in real terms. This includes the return on financial assets, r
t
A
t
. Normally,
disposable income is defined as net labor income plus total (net) asset income, but
this grossly overstates the true measure and can provide a misleading picture of
current trends. In Table 2.2 we show the importance of this issue for Italy in the
recent past (1995–1998), when nominal returns fell from 12.2% to 4.9% and
inflation fell from 5.2% to 2%: the aggregate, uncorrected personal saving rate
appears to be falling from 19.4% in 1995 to 15.4%, but once the disposable income
measure is corrected for inflation the saving rate is in fact quite stable over time.
11
2.5 AGGREGATION AND ESTIMATION
When we plot the saving age profile by cohort, we are effectively estimating the
equation
S
h
t
¼ f ðage
h
t
; yob
h
; tÞþ"
h
t
TABLE 2.2 Macroeconomic Indicators for Italy
1995 1996 1997 1998
Long-term (10-year) interest rate
a
on government debt 12.21% 9.40% 6.86% 4.88%
CPI inflation 5.2% 4.0% 2.0% 2.0%
Personal sector saving rate 19.4% 19.1% 17.2% 15.4%
Personal sector saving rate (inflation adjusted) 14.4% 14.8% 14.2% 14.2%
Disposable income growth 4.7% 5.5% 2.8% 2.2%
Source: Bank of Italy — Relazione del Governatore 1998
a
All interest and growth rates are nominal.
10
See Bo
¨
rsch-Supan (2001a).
11
This adjustment is routinely carried out by the Bank of Italy.
52 Chapter 2 Household Saving: Concepts and Measurement
by instrumental variables (two-stage least squares), where the set of instruments
includes all nonredundant year-cohort dummies. Thus, in the first stage the
estimator works out cohort averages for each year and in the second stage these are
regressed on the explanatory variables (that are perfectly fitted by the instruments:
by construction there is no within-year cohort cell variability in age, year of birth,
or time).
If further regressors are considered, the cohort averaging technique fails to
exploit all available information in estimation (on this point, see Attanasio, 1998)
and is in fact less widely used (see Attanasio and Weber, 1994). Suppose, for instance,
we wish to control for the effects of education, but do not wish to define cohorts
on the basis of both year of birth and education. We could for instance specify
S
h
t
¼ lðage
h
t
ÞþD
h
c
þ D
t
þ Educ
h
þ "
h
t
where Educ
h
represents the years of education (that we assume not to vary over
time). This equation can be estimated on individual data or on average cohort data:
estimates will not be identical be cause cohort averaging does not exploit within-
cell variability in education.
A natural and sometimes usefu l extension of this is to add further time-varying
explanatory variables that reflect household structure (number of household
members, number of children, and so on). The estimated age profile will now have
a different interpretation because it is conditional on no demographic changes
taking place.
Let us now look at
s
h
t
¼ f ðage
h
t
; yob
h
; tÞþ
h
t
where the dependent variable is
s
h
t
¼
S
h
t
Y
h
t
i.e., the saving rate (where the denominator can be either an income measure or
a consumption measure).
If we use average cohort techniques in this context we estimate the age profile
for the average saving rate within each cohort. This is not the cohort saving rate,
defined as
s
c
t
¼
S
c
t
Y
c
t
¼
P
h2c
S
h
t
P
h2c
Y
h
t
As we have seen, the two are related as follows:
s
c
t
¼
X
h2c
!
h
t
s
h
t
where !
h
t
¼ Y
h
t
=Y
c
t
is the income or consumption share of household h within
the cohort.
2.5 Aggregation and Estimation 53
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