Life-Cycle Savings and Public Policy

relatively high-quality compared with income data, as in diary-based surveys. When

consumption is instead known to be affected by major underreporting, the

traditional measure may be preferable. In fact, households who und erreport their

expenditure most will appear to save more, and their saving rate will be further

inflated if the denominator is C

t

rather than income.

One drawback of working with saving rates is the nontrivial relation between

the individual level data and the corresponding aggregate variable. Suppose we

plot the mean saving rate for a given age group against time, i.e., we take means

of the saving rates of individual households h of age a at time t. The resulting

statistic is not the average (or aggregate) saving rate of the a age group in period t,

defined as:

s

a

t

¼

S

a

t

Y

a

t

¼

P

h2a

S

h

t

P

h2a

Y

h

t

where Y denotes either ‘‘income’’ or consumption, according to the chosen

measure. The two are related as follows:

s

a

t

¼

X

h2a

!

h

t

s

h

t

where !

h

t

¼ Y

h

t

=Y

a

t

is the ‘‘income’’ or consumption share of household h within

the age group. If we want to study the time pattern for s

a

t

we must weigh the

individual saving rates by !

h

t

.

An approximation that works well at the aggregate level is sometimes used

(Deaton and Paxson, 1994):

s

t

’ lnðY

t

ÞlnðC

t

Þ

This approximation is again not defined for negative or zero income and can be

quite inaccurate at the individual level, but has the advantage of being less sensitive

to outliers. The relation between the average saving rate and the corresponding

aggregate variable is known and exact when both income and consumption are

lognormally distributed.

2.3 WHY COHORT ANALYSIS?

We are interested in the age profile of household saving (or of the savin g rate). But

we don’t normally observe the same individuals through time long enough to be

able to plot individual age profiles. Sometimes we only have wealth at a moment

in time (individual saving cannot be computed); some other time we observe

income and consumption flows for a single period (individual saving can be

computed, but only for a particular age).

2.3 Why Cohort Analysis? 39

If we plot saving against age in a cross section, the resulting profile will link

individuals born in different years. This may produce misleading evidence on age

effects if individuals born in different years are different in their resources or

preferences (Shorrocks, 1975). If we have access to several cross sections over time,

we can address this issue by using cohort analysis.

We define a cohort as a group of individuals born in the same calendar year.

By construction, cohort members age together (in this sense a cohort can be

considered as a synthetic individual). Note there is no within-cohort age variability

over any one observation year. Wider cohorts can be defined, including all

individuals born within a certain year band (5-year cohorts, for instance), but care

must be taken to define the age of each individual as the cohort mid-age.

Narrower cohorts can be defined, by selecting individuals who meet certain time-

invariant criteria (race, sometimes education and region).

When dealing with households, cohorts are normally defined on the basis of the

year of birth of the household head. This is correct if the head does not change over

time. Within couples the head is often the male, but this choice is of little

consequence if the age difference between spouses is not large. Howev er, the

presence of more than one adult within the household does raise the issue of

who takes the relevant consumption/saving decisions. There can be doubts on the

ability of the unitary model to interpret the data, particularly when both spouses

work. A simple example is provided in Browning (1995): given that women survive

longer, there will be disagreement within married couples on saving. The higher

the bargaining power of wives, the higher the household saving rate will be.

The case of multiple-adult (or composite) households poses further important

problems, discussed in Deaton and Paxson (2000). At the very least, household

income and consumption should be attributed to the various household members,

and not just to the head, before age profiles can be drawn. As we show in Table 2.1,

the presence of young adults living with their parents is extremely common in at

least two of the countries studied in this book (Italy and Japan). If the choice of

leaving home relates to wealth, income, or consumption, we face a problem of

TABLE 2.1 Proportion of Young Adults Living with Parent(s)

Country Male aged 25–29 Female aged 25–29 Male aged 30–34 Female aged 30–34

Germany 32 12 14 3.5

Italy 76 50 32 19.5

Japan 59 48 37 28

Netherlands 27 6 6 1.5

UK 21 9.5 6.5 4

USA 19 12 8 5.5

Source: OECD (2000).

40 Chapter 2 Household Saving: Concepts and Measurement