Demographic change and the saving rate of Japanesehouseholds: the aggregate effect is almost nil
Oleksandr Movshuk∗
Department of Economics, University of Toyama,3190 Gofuku, Toyama, 930-8555, Japan
E-mail: movshuk@eco.u-toyama.ac.jp
November 7, 2012
Preliminary draft
Abstract
In this paper, I examined how much changes in demographic structure might account for the sharp decline in the saving rate of Japanese households since the early
1990s. Using household data from the National Survey of Family Income and Expenditure, I estimated age-saving profiles for five major household types (singles,
couples with children, couples without children, single parents with children, andmulti-generation households). After applying these estimates to the actual age structure of Japanese households between 1990 and 2005, I found that changes in demographic structure had only modest effects on the saving rate of Japanese households.
I also predicted the future contribution of demographic structure on the saving rate,using projections of Japan’s household structure by age in 2010–2030. The projected
effect of population structure reduced the household saving rate, but the effect was
remarkably small, by just 0.01 percentage points from 2010 to 2030. Overall, themicro-level evidence in this paper does not support the conventional view that the
recent decline in the saving rate of Japanese households is mainly due to the effectof population aging.

∗ I am indebted to the Research Centre for Information and Statistics of Social Science, Institute of

Economic Research, Hitotsubashi University, and to the National Statistics Center of Japan for supporting
my application to obtain anonymous data from the National Survey of Family Income and Expenditure.
A previous version of this paper circulated as “Household saving in different family types: evidence
from Japanese micro data”. I am benefitted from the comments by Nobuaki Hoshino, Naoki Makita,Akihiko Noda, Craig Parsons and Xu Guangjian. I gratefully acknowledge financial support from theGrant-in-Aid for Scientific Research (C) 22530207 from the Japan Society for the Promotion of Science(JSPS).

1 Introduction
In this paper I present evidence from Japanese micro data that population aging could
have a negligible impact on the household saving rate, both in the past and in the
future. This finding runs against the conventional view that the rapid drop in Japan’ssaving rate, from around 15 percent in the early 1990s to almost zero in recent years(Figure 1), mainly reflects the effect of population aging (Horioka, 2008; Hoshi and
Kashyap, 2011). The link between population aging and declining saving rate stems
from the life-cycle hypothesis (LCH) of Modigliani and Brumberg (1954). The LCH
postulates a humped-shaped saving profile over the life cycle, with a principal claim thatsavings become negative for aged and retired individuals (Horioka, 2006). Due to rapid
population aging, the share of aged and retired individuals has increased substantiallyin Japan, while the share of working-age population has declined. If age-saving profiles
are sufficiently humped-shaped over the life cycle, the aggregate effect of these two
secular trends in Japan’s population structure should reduce the saving rate of Japanesehouseholds.
The importance of demographic structure for explaining Japanese household savings
was pointed by Horioka (1991), while Dekle (2005) and Koga (2006) provided recent empirical support that Japan’s demographic structure had a significant effect on the decline
in household saving rate since the early 1990s. But the evidence in these studies was
based on aggregate data for household saving rate and the share of major age groups.
Such macro-level data are well-known to have serious limitations. First, demographic
trends are typically slow, and may pick up the effect of other slowly changing trends,
such as a secular trend that makes personal saving less important to households, withthe effect similar across different age groups (Bosworth et al., 1991, p. 197). Second, theslow pace of the population aging does not fit well with nonlinear changes in the savingrate of Japanese households, with a particularly rapid declines in some years, and nochange at all in other years (Iwaisako and Okada, 2010).
Rather than using macro data, a number of studies examined the link between population structure and household saving with micro-level data that measure saving decisions of specific households. With micro data, it is possible to account for various
household characteristics that are important for explaining differences in saving decisions. In addition, micro data allow controlling for secular trends in the saving rate at
the macro level (by using time dummy variables for general period effects). In contrast,
the aggregate data could misinterpret these general period effects for the contributionof demographic trends.
Curiously, the micro studies have repeatedly reached the opposite conclusion to
studies with aggregate data, with a common finding that changes in the population
structure have very small effects on household savings. Weil (1994) provides a comprehensive summary of earlier micro-level studies. More recent micro-level evidence for1small demographic effects was reported by Parker (2000) for the United States, Jappelli
and Pagano (1999)), Baldini and Mazzaferro (2000) for Italy, Demery and Duck (2006)
for the United Kingdom, and Park and Rhee (2005) for South Korea. As shown in Figure
1, all these countries experienced significant decline in household saving rates in recent
years, yet changes in the demographic structure of these countries had very minor estimated effect. A much more significant effect was from uniform changes across different
age groups, presumably reflecting a common macroeconomic effect on the saving rate,
rather than changes in the share of different age groups with different propensities tosave.
Compared with other countries, micro-level evidence for Japanese households remains scant. One of the earliest study was done by Bosworth et al. (1991), who useddata from the Family Saving Survey between 1970 and 1989. The study concluded that“differences in saving rates among age groups are simply not large enough to generate
major demographic effects on the aggregate saving rate” (p. 220-221). In addition, thestudy examined a long-term correlation between the population aging in Japan and thedecline in household saving rate, but concluded that “the relationship does not appear
causal” (p. 221).
Subsequently, Ito and Tsuri (2006) calculated the expected contribution of demographic factors to Japanese saving rate from 2000 to 2050. Saving rates for different ages
were based on the National Survey of Family Income and Expenditure for 1999. Since
the original data were available for households only, the paper used a special set of
equivalence scales to derive individual-based saving rates. These saving rates were thenapplied to mid-point population projections from the National Institute of Populationand Social Security Research (IPSS). The net effect of demographic change was minor,
with saving rate declining from around 35 to 32 percent during 2000-2050.
More recently, Iwaisako and Okada (2010) used raw age-saving profiles from theFamily Income and Expenditure Survey (FIES) in 1997, and calculated the contribution of demographic change to the declining household saving rate from 1997 to 2008.
The paper found that changes in the demographic structure contributed 2.5 percentage
points to the decline in the saving rate, with a residual drop by 5.9 percentage points
still unexplained (p. 11). Finally, Hoshi and Ito (2012) used the data from the FIES, andcalculated average saving rates for different age brackets from 2000 to 2010. Then the
study applied these saving rates to mid-point population projections from the IPSS for2010 to 2050. The net effect of the population aging was estimated to be larger then inconceptually similar study by Ito and Tsuri (2006), with demographic factors reducing
the saving rate by around 6 percentage points from 2010 to the end of the 2040s.
The previous micro-level studies for Japan calculated the aggregate effect of demographic structure with only raw saving rates for different age groups, with no adjustments for effects from other determinants of household savings. In contrast, this paper
estimates age-saving profiles from a semiparametric model of household saving that2controls not only for the age effect, but also for other factors of household saving, suchas differences across birth cohorts, aggregate period effects that that are the same acrossdifferent ages and birth cohorts, and household characteristics that may be importantfor explaining differences in saving behavior.
Compared with previous studies, the paper makes three major contributions. First,
as already mentioned, instead of using unadjusted age-saving propensities, the paper
used regression-based estimates for age, cohort and period effects, and identified separately the contribution of each of these effects on the past and future changes in household saving rate.
Second, the paper dealt with a possible heterogeneity in the saving behavior in different family types. The LCH focuses mostly on the saving behavior of individuals, rather
than households, who save in preparation for old age. So the LCH largely neglects theimpact of family structure, as well as children, on saving behavior. In the extreme case,the stripped-down version of the LCH assumes that individuals stay single, and raise no
children. In consequence, there is particularly scant empirical evidence on whether different family arrangements have effect on household saving profiles over the life cycle1 .
Paxson (1996), Attanasio et al. (1999) and Fernández-Villaverde and Krueger (2007) previously demonstrated that changes in family structure have large effects on age-saving
profiles. However, these studies estimated only linear effects from family structure,with demographic variables (such as the number of adults and children in households)
included among linear parametric effects. In contrast, I examined the impact of family
structure with a flexible semiparametric model, and estimated age-saving profiles acrossdifferent family types by nonparametric terms that allow nonlinear effects on savings.
Third, the paper used consistently household weights (rather than the combinationof household and population weights) for calculating the aggregate effects on household saving rates. In most previous studies, saving rates were differentiated by theage of household head, but projections of future demographic structure were typicallytaken from population projections that refer to individuals, rather than households. To
get consistency between households and individuals in population structure, the conventional approach needs to make a number of assumptions, including fixed average
size of households over time, and a special set of equivalence scales to convert household data to individuals. In contrast, this paper uses the same aggregation structureof households, both at the estimation stage to derive age-saving profiles, and at theaggregation stage to calculate the net effect of demographic change.
To preview major findings, the paper found that different family arrangements havemuch more complex effects on savings than could be captured by conventional linear
specifications of demographic effects. However, these differences in age-saving profiles
were insufficient to produce a large effect from demographic structure on the saving
1 Such family arrangements include decisions to live with a partner, or to stay single, and whether toraise children, once again as a couple, or as a single parent.

3

rate of Japanese households, both in the past, and in the future. Three major findings
stand out.
First, the paper found that households without children started to reduce their savingrate much earlier than predicted by the LCH, with the peak saving rate reached as early
as in mid-40s. On the other hand, households with children had peak saving rates at anolder age, in the late 50s. Evidently, it is the presence of children, and not the prospectof old age that motivates households to maintain high saving rates up to the retirement
age.
Second, the paper examined whether the presence of aged and retired household
members, as emphasized by Horioka (2006), might reduce the overall savings by households. To examine this key prediction of the LCH, I estimated the net effect on household saving rate from aged and retired members, with two groups of households that
had such household members. When only one aged and retired household members,
the net effect on saving rate was negative and statistically significant. However, the scaleof the effect was small, by less than one percentage point. Moreover, with two aged andretired household members, their effect on the saving rate turned insignificant, providing little support to the central implication of the life-cycle hypothesis in Japanese micro
data.
Third, when I applied estimated age effects on household savings to to the actual
age structure of Japanese households between 1990 and 2005, the past changes in demographic structure had only modest effects on the aggregate saving rate of households,
with essentially no net effect over the span from 1990 to 2005. When I predicted thefuture contribution of demographic structure, using mid-point projections of Japan’s
household structure by age until 2030, the demographic effect was again negligible, by
only 0.1 percentage points from 2010 to 2030. Overall, the micro-level evidence in thispaper does not support the conventional view that the recent decline in the saving rateof Japanese households is mainly due to the effect of population aging.
The paper is organized as follows. Section 2 describes the estimation of life-cycle profiles by semiparametric models, and introduces the varying-coefficient model of Hastie
and Tibshirani (1993), which was used to specify differentiated age effects on savings.
Section 3 outlines main features of semiparametric estimation. Section 4 explains data
sources, and describes major adjustments to the original household data. Estimation
results are reported in Section 5, while Section 6 offers major conclusions.

2 Model specification
2.1 Basic models of household savings with a single nonparametriceffect.
I start with a conventional life-cycle model household consumption, then proceed to aclosely-related model of household income, from which it will be trivial to derive a base-4

line model of household saving. Households are assumed to smooth their consumption
over life cycle, and the level of consumption depends on the lifetime stock of household
wealth. Specifically, consumption is a fraction of household’s lifetime wealth, which
depends on the age of household head:ci,t = δ ( agei ) Wi exp (ε i,t )(1)

where ci,t is consumption expenditures of household i at time t, Wi is the total lifetime
wealth of household, and ε i,t is the regression disturbance.
Parameter δ ( agei ) defines the age profile of consumption, and reflects changing composition of households, and varying needs of household members over the life-cycle.
After taking logs of (1), we obtain an additive specification that includes age and wealtheffects on consumption. The specification is further extended by a vector of observable variables zi,t , which includes demographic effects (namely, the average number ofadults and children per household), and other household characteristics, such as regionof residence, occupation, education, race, marital status, gender, and similar controls forhousehold head:ln (ci,t ) = log (δ ( agei )) + log (Wi ) + β′ zi,t + ε i,t(2)

The baseline model (2) is specified for individual households, but Japanese household data for this study do not have a panel dimension. So model (2) is re-expressed interms of groups of households, or household cohorts, that can be traced across over time.
The household cohorts are identified by the birth year of household head. Let a birthyear be denoted by c, so that c = t − age, where t is the current year. After averaging (2)across birth cohorts c, we getlog (cc,t ) = log (δ ( agec )) + αc + β′ zc,t + ε c,t(3)

where c identifies a particular birth cohort, and αc is the average logarithm of lifetime
wealth of households belonging to cohort c.
To account for the time variation in household consumption, specification (3) is extended by a set of year dummies Dt for observation years t = 1, . . . , T. In addition,
the age effect log (δ ( agec )) is replaced by a flexible function of age, specified by aset of dummy variables Da . Similarly, the fixed effect from different birth cohorts αc
is estimated by a matrix Dc with cohort dummies, resulting in the baseline model ofhousehold consumption with age, cohort and period effects:log (consc,t ) = α′a,cons Da + α′c,cons Dc + α′t,cons Dt + β′cons zc,t + ε c

5(4)Next, I specify regression model for household income, from which it will be trivial
to derive a model for household savings. Following Paxson (1996), the life-cycle profile
of household income is specified similarly to the consumption model (4):log (incc,t ) = α′a,inc Da + α′c,inc Dc + α′t,inc Dt + β′inc zc,t + ε c(5)where incc,t denotes disposable income of households belonging to cohort c at time t.
To obtain the model of household savings, I use the following approximation: whenincome incc,t and consumption consc,t are not much different, log (incc,t ) − log (consc,t ) ≈incc,t −consc,t, which in turn equals to the saving rate src,t . Thus, by subtracting equationincc,t(5) from (4), we obtain the baseline model of household savings:
src,t = α′a Da + α′c Dc + α′t Dt + β′ zc,t + ε c(6)with adjustments in model’s parameters (for example, α a = α a,inc − α a,cons ).
However, this model has a serious limitation: the exact linear relationship among
age a, birth cohort c, and current year t (i.e., current year minus age equals the birthyear). Due to the exact collinearity, it is not possible to estimate (6) by linear regression
estimators, unless some restrictions are introduced in the three interlinked effects.
Fernández-Villaverde and Krueger (2007) proposed to solve the identification problem by replacing age dummies Da with a smooth nonlinear function of age, which I will
denote by f ( a). With this substitution, model (6) becomes a semiparametric model witha single nonparametric component f ( a), and the parametric part including the rest of
explanatory variables (namely, cohort and period dummies Dc and Dt , and other control
variables in vector zc,t ):src,t = f ( a) + α′c Dc + α′t Dt + β′ zc,t + ε c(7)This semiparametric specification imposes only a mild restriction on the age effectf ( a), which is assumed to be a smooth function of age. Apart from this restriction, theshape of f ( a) is unspecified, and its estimate depends entirely on the data.
In first three models, the nonparametric age effect f ( a) is left unchanged, and threealternative specifications for the parametric part are considered. In particular, I examined whether the estimate of nonparametric age effect f ( a) would change much withthree different parametric specifications in Models 1-3. In Model 1, the parametric part
included only cohort and period effects:
sri,t = f ( a) + α′c Dc + α′t Dt + ε i,t6(8)demogr,
In Model 2, the parametric part was extended by demographic variables zi,twhich included three groups of variables: the number of adults and children, living inhousehold, and the number of aged and retired members of household:demogrsri,t = f ( a) + α′c Dc + α′t Dt + β′ zi,t

+ ε i,t(9)other , such as the marital status
Finally, Model 3 included the rest of control variables zi,tof household head, region of residence, industry of occupation, type of employment
contract, and similar controls:
demogrsri,t = f ( a) + α′c Dc + α′t Dt + β′ zi,tother
+ γ′ zi,t+ ε i,t(10)

2.2 Varying-coefficient models of household savings
In Model 4, I retained the parametric part of Model 3, and replaced the nonparametricage effect f ( a) with separate age effects on saving for different family types. These
differentiated age effects were specified by the varying-coefficient model of Hastie andTibshirani (1993).
A distinctive feature of the varying-coefficient model is that nonparametric effects
interact with categorical variables (such as different family types). Consider a general
semiparametric model that has the parametric part θ ′ X and a single nonparametric termf (z). Assuming that θ ′ X and f (z) are additive effects, the response variable y is specified
by y = θ ′ X + f (z) + ε, where ε is the conventional error term.
Let d be a dummy variable with two distinct values, d1 and d2 . In the varyingcoefficient model, the shape of nonparametric effect f (z) depends on values of thedummy variable d:y = θ ′ X + f ( z ) d1 + f ( z ) d2 + ε(11)with f (z)d1 and f (z)d2 denoting two separate estimates of nonparametric effects, depending whether d takes the value d1 or d2 .
The general specification (11) can be used to derive age effects on savings from different family types. Let households be divided into five family types:
1. single households,
2. couple with no children,
3. couple with children,
4. single parent with children,
5. extended (i.e., non-nuclear) family.

7

Using this classification, Model 4 was specified with a matrix of dummy variables
D f for five family types, and corresponding differentiated age effects f ( a) f :5demogrsri,t = ∑ f ( a) f D f + α′c Dc + α′t Dt + β′ zi,tother
+ γ′ zi,t+ ε i,t(12)f

The varying coefficient model (12) essentially introduces heterogeneity in nonparametric age effects, and keeps the same parametric specification for different household
types. This allows using the complete data sample, from which we can obtain separate
nonparametric estimates of age-saving profiles for different family types.

3 Estimation method
To save space, I will discuss only main issues in estimating semiparametric models inthis paper. When estimating semiparametric models with a single nonparametric termf ( a), three problems have to be solved:
1. how to represent the smooth function f ( a),2. how to specify a smoothness parameter that controls the trade-off between smoothness and goodness-of-fit in estimated f ( a),3. how to select the smoothness parameter in a data-dependent way.
These three problems are addressed in a library of semiparametric estimators mgcv2
Wood (2012) in statistical package R R Development Core Team (2012). First, the mgcv
library provides a large number of basis functions to approximate the smooth functionf ( a). Second, the library provides a large number of penalty functions and smoothness parameters, which could control the trade-off between the smoothness and fit
in estimated fˆ( a). Third, the library provides a data-dependent selection of smoothness parameters. Two alternative approaches are available, either by minimizing thegeneralized cross validation (gcv) statistics (Craven and Wahba, 1979), or by solving amixed model for variance components that maximizes the restricted maximum likelihood (REML) statistic (Ruppert et al., 2003).
When interpreting the output from the mgcv library, one parameter is particularly
useful: the estimated number of degrees of freedom for approximating non-parametricterms. Let this parameter be denoted by v. When v = 1, this implies that the nonparametric term can be approximated by a single variable with linear effect. On theother hand, higher values of v indicate increasingly complex patterns that require moredegrees of freedom.
The upper limit for v is the sample size, but in practice much smaller values areused. The default value of v in the mgcv library is 10. But this provides only an initial
estimate for v, and the library then estimates a data-dependent value of v, which could
be in the range between 1 and the initial choice of v.
2 The acronym mgcv stands for ‘modified generalized cross validation’84 Data
Data for Japanese households were were taken from the National Survey of Family
Income and Expenditure (NSFIE) for 1989, 1994, 1999, and 2004. The raw data were
provided by the National Statistics Center of Japan, as a random sub-sample with 80
percent of the original sample. Detailed description of the NSFIE is available in Hayashi(1997) and Kitamura et al. (2003), and I will provide only information that is relevant forinterpreting results in this paper.
A typical wave of the NSFIE collects data from almost 60 thousand households. The
survey provides exceptionally detailed information on living conditions of households,
including annual income, consumption expenditures of a large number of goods andservices, financial assets and liabilities, demographic and employment status of household members, their education level, and many other characteristics.
The random sub-samples with 80 percent of original households included about
3,500 households with single members, and 44,500 households with two and morehousehold members. The combined sample size for 4 waves of NSFIE was 192,599
households, but due to data cleaning, the final sample contained 168,058 households.
In subsequent subsections, I explain definitions of major variables, discuss major
data adjustments, and explain in more details the data-cleaning process.

4.1 Variable definitions.
The saving rate was defined as the difference between disposable income and nondurable consumption, normalized by disposable income. Disposable income and nondurable consumption broadly followed definitions in Hayashi (1997).
Specifically, disposable income was the difference between gross income and nonliving expenditures, which included taxes and social security contributions. Gross income mainly contained wages, income from assets (such as dividend and interest income), income in kind, and social security benefits. For households that owned housing, gross income also included the imputed rent from owner-occupied housing. Remittances from outside households were not classified as income. Non-living expenditures
included taxes (such as income tax, resident tax, and other tax categories) and social
security contributions (such as public pension fees, health insurance fees, and the like).
Nondurable consumption was equal to the total consumption expenditures, less expenditures on durable goods. To identify expenditures on durable goods, I used the
NSFIE’s classification into four expenditure types: durable goods, semi-durable goods,
non-durable goods, and services. Then nondurable consumption was calculated byomitting the first category from the total consumption expenditures. Following Hayashi(1997), I included in consumption expenditures the imputed rent of homeowners, andexcluded remittances to the outside of households.

94.2 Data adjustments
The NSFIE is conducted during the three-month period from September to November.
While data for gross household income cover the whole calendar year, consumption expenditures refer only to the survey period. To remove the impact of seasonal factors, I
extrapolated the expenditure data for the full year. Similarly to Hayashi (1997) and Kitamura et al. (2003), I calculated seasonal adjustment coefficients for major consumption
expenditures, using comparable categories from another household survey in Japan, theFamily Income and Expenditure Survey (FIES). Unlike the NSFIE, the FIES is conducted
over the whole calendar year. While these surveys have different sample coverage ofhouseholds, and other conceptual differences, they are broadly comparable in the coverage of workers’ households. Using 10 major consumption categories in NSFIE and
FIES for workers’ households, I calculated seasonal adjustment coefficients as the ratioof reported values in FIES and NSFIE in the same calendar year. Then these coefficientswere used to extrapolate major consumption categories in the NSFIE data to the wholecalendar year.
Another adjustment was made to the age of household head in multi-generation
households. Hayashi (1997, p. 425) noted that the design of NSFIE may create a sample
selection bias when classifying household heads in such households. He also suggesteda solution, by re-defining the head of multi-generation household as a member fromyounger generation, and I also used the Hayashi adjustment in this paper.

4.3 Missing data
The NSFIE data does not contain information for taxes and social security contributions
for so-called ‘other households’, which in practice contain mostly individual proprietors.
The data are missing for NSFIE waves in 1999 and 2004, while the earlier waves in 1989
and 1994 report taxes and social security contributions. Since these data are required
to calculate disposable incomes, I imputed the missing observations in 1999 and 2004,
using regression coefficients from 1989 and 1994 data.
Specifically, I predicted the rate of tax payments and social security contributionsfor 1999 and 2004, using parameter estimates from ‘other households’ in 1989 and 1994.
The rate of tax payments and social security contributions was predicted by annual
income, gender and age of household head, region of residence, and a year dummy
for 1989. Predictions were calculated by a routine for multiple-imputations of missing
observations in software STATA (version 12). To avoid predictions of unrealistic tax
rates, I imposed restriction that predicted tax rates remain in the interval between 0
and 1.

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4.4 Data cleaning
When cleaning the NSFIE data, I first omitted households that were flagged as unreliable. As shown in Table 1, this criterion reduced the sample size from 192,599 to 189,107
households.
I also omitted households with top-coded observations in the following three categories: (a) high annual income3 , (b) households with many members (namely, 8 andmore household members), and (c) households with advanced age of household head(i.e., 85 year and more). In addition, I omitted households that had negative estimates ofdisposable income or nondurable consumption. These criteria reduced the sample size
to 186,732 households.
Finally, I omitted households that were likely to be outliers, using both tails in the
distribution of saving rates, with cut-offs at 5 and 95 percentiles. This resulted in the
final sample of 168,058 households.

4.5 Alternative data sources for family types
In this paper, households were classified into 5 family types, as discussed in subsection
2.2. Table 2 compares the household composition by family types, using published reports of the NSFIE, and the population census of Japan. Panel (a) reports family sharesfrom published NSFIE reports, which are based on the complete sample of households.
In contrast, family shares in Panel (b) are calculated from the 80 percent subset of the
NSFIE data, while Panel (c) shows family shares in the final sample of 168,058 households that remained after data cleaning. Overall, differences between family shares inPanels (a), (b) and (c) are minor, always less than 1 percentage point, indicating thatthe sub-sample of NSFIE data in this paper was broadly comparable to the survey’s fullsample.
In addition, Panel (d) reports family shares from the most comprehensive data
source, the population census of Japan. Similarly to the NSFIE, the census is conducted
every five years. However, there is a one year shift between the NSFIE and the population census, so that the NSFIE for 1989 can be compared only to the Population Census
for 1990.
As shown in Panels (a) and (d), there are minor differences in the coverage of family
types by the NSFIE and population census. For single households, population sharesconverged over time, but other family types had differences in the range of 2-4 percentage points. In particular, the NSFIE evidently over-samples couples (both with children
and without children), while single parents with children and non-nuclear households
are under-sampled. Due to these differences in the household structure, I calculated the
3 The upper limit for single households was 10 million yen, while for households with two or moremembers, it was 25 million yen.

11

impact of demographic structure with both NSFIE and population census. In practice,these alternative household weights produced very similar results.

5 Results
5.1 Estimates of age-cohort-period effects on household savings
Estimation results for Models 1 and 2 are reported in Table 3. The nonparametric partof these models was the same, with only a nonparametric term f ( a) for age effect, while
the parametric part of Model 2 differed by several demographic variables. The overall
goodness-of-fit is measured by the ratio of explained deviance. It is similar to the R2
statistic in linear regression models4 , with higher values indicating a better fit. As shownin the bottom of Table 3, Model 2 had a higher goodness of fit compared with Model 1,
6.94 and 3.97 percent, respectively.
Estimates of cohort effect in both models showed increasing saving rates for more
recently born cohorts, with almost all effects having statistically significant estimates.
For example, compared with the control category, the birth cohort 1905 - 1909, the savingrate of birth cohort 1975-1979 was 9.33 percentage points higher in Model 1. In contrast,
estimates of period effects were relatively modest, always less than 2 percentage points
in both models.
Estimates for demographic effects in Model 2 indicated a relatively large impact on
the saving rate, especially for different numbers of adults. The control category washouseholds with no adult members (defined by the age between 18 and 65 years old).
The addition of one adult increased saving rate by 8.58 percentage points, and by asmuch as 16.5 percentage points for 4 and more adults. Conversely, children reduced
household saving rates, by around 5 percentage points. Finally, the estimated effect ofaged and retired household members was statistically significant and positive, which
does not support the LCH. For example, with only one aged and retired household
member, the saving rate increased by almost 2 percentage points. The positive effectwas even larger for two and more such members, by 5.57 percentage points.
Nonparametric estimate of age effect for Models 1 and 2 is shown in Panels (a) and(b) of Figure 2. As reported at the bottom part of Table 3, the number of estimateddegrees of freedom was 7.10 and 7.08, respectively, indicating a complicated structureof age effects in both models. The nonparametric estimate of age effect shows that thesaving rate was increasing up to the middle age, but then declined during the late 40s
and 50s. When demographic effects were added to Model 2, this greatly decreased the4 Estimated semiparametric models belong to the normal family of generalized linear models with identi-

cal link function, and their deviance is made up of the sum of squared residuals. The ratio of explained
deviance compares deviances of two models: the null model with just the intercept term, and the alternative model with all explanatory
 variables. Let these deviances by D0 and D1 , respectively. Then thedeviance explained is ( D0 − D1 ) D0 .

12amplitude of variation in the age effect on saving, and produced an unexpected jumpin the saving rate for oldest households.
Table 4 reports estimates for Models 3 and 4. The the goodness of fit was the highest
for Model 4, with the ratio of explained deviance increased from 11.2 in Model 3 to 12.0
in Model 4.
When the full set of parametric controls was added to Models 3 and 4, some cohort
effects were no longer statistically significant (especially this applies to recently-borncohorts). In contrast, all estimates of period effects became significant, with a generalincrease in the saving rate by 2-3 percentage points compared with the control year 1989.
The positive effect from adult members became much smaller compared with Models 1
and 2. On the other hand, little change occurred for the effect of children, who reduced
household saving rate in the range of 2-6 percentage points. Finally, the effect from aged
and retired household members was negative, but was statistically significant only inhouseholds that had only one such a member.
Estimates for new parametric effects in Models 3 and 4 produced a few relatively
large effects. Compared with the control category of single households, all other family
types had higher saving rates, with a particularly large difference for extended households, which increased the saving rate by almost 6 percentage points. A similarly large
effect was from differences in employment status, with difference of 7.8 percentage
points between full-time workers (the control category) and part-time workers.
Nonparametric estimates of age effects on saving for Model 3 are plotted in Panel (c)of Figure 2. With the full set of parametric controls, the variation in age-saving profile
was greatly reduced, to only 6 percentage points over the whole life cycle. Moreover,the saving rate of aged households declined much less, indicating that a substantial partof reduced saving rate in Models 1 and 2 was explained away by extra control variablesof Model 3.
Figure 3 reports estimates of differentiated age profiles for different family types inModel 4. Panel (a) shows that the saving rate of single households rose up to the early
40s, but then was declining until early 60s, and then stayed mostly flat. The estimatedprofile does not fit well with the conventional life-cycle theory of savings. In particular,
single households started to reduce their saving rate much too early, and did not show aclear reduction in saving rate in old age. For couples without children, estimated saving
profile turned out similar to single households, with the only difference that peak savingrate was reached about ten years later.
Households with children, including couples and single parents, provided the closest
match with the humped-shaped profile of savings; it is ironic that the life-cycle theory
largely ignores these family types. In particular, couples with children and single parents greatly reduced their saving rate in the old age (Panels (c) and (d) of Figure 3). As
for the the saving profile for multi-generation households in Panel (e), its interpretation13

is difficult because these households combine members at different stages of their life
cycle.
Out of four considered models, which one can be considered as the best one? The
ratio of explained deviance selects Model 4. The same conclusion is reached by the
Akaike Information Criterion (AIC), as reported at the bottom of Tables 3 and 4. Though
Model 4 used a large number of parameters to approximate nonparametric effects age
effects in different family types, this complexity was more than counter-balanced bygreatly improved fit, which led to the superior AIC score for Model 4, with Model 3
showing a slightly worse performance. In consequence, I used Model 4 to derive theaggregate contribution of age, cohort and period effects on household saving rates.

5.2 Calculation of aggregate demographic effects
In this sub-section I calculate the aggregate effect on household saving rates that can be
attributed to differences in age and cohort structure of the population, and other factorsthat were estimated in Model 4. Table 5 illustrates the calculation for the age effect,using the population structure of Japan from the population census in 2005.
The original nonparametric estimates of age effects in Figure 3 does not show point
estimates for specific ages, but interval estimates in the age range from 20 to 84 years.
These interval estimates of nonparametric effects were averaged by 5-year bands (namely,
20-24, 25-29, 30-34, . . . , 80-84), and the corresponding point estimates are reported in
the left side in Table 5. For example, age effect among single households in the age
range 20-24 was -3.28 percentage points, which corresponds to the original nonparametric estimate in Panel (a) of Table 4, with the only difference that average point estimatesin Table 5 are multiplied by 100.
The second column of Table 5 shows average point estimates for couples, with theage group of 20-24 years having -6.34 percentage point reduction in the saving rate. The
relatively large negative effect for the second family type for the youngest age group isevident by comparing Panels (a) and (b) of Figure 3.
The right side of Table 5 shows weights by different age groups across five family
types in 2005. Using these weights and point estimates of age effects, I calculated theaggregate effects on household saving rate from the Japan’s age structure in 2005 forfive different household types. For example, the aggregate effect for single households
was -1.52 percentage points, reflecting negative age effects for single households among
the youngest and oldest age groups, and the relative concentration of single households
among youngest and oldest age groups. Similarly, the aggregate effect for the second
family type, couples without children, was -1.82 percentage points. This estimate reflects
two distinctive feature of couples without children: first, the relative prevalence of aged
households, and relatively large negative age effects for couples that are older than 60
years old.

14

The aggregate effect for the next two family groups (couples with children and single parents with children) were positive, at 0.11 and 1.09 percentage points, while theestimate for extended households for -1.14 percentage points. To calculate the total
contribution of age structure on household saving rate, these separate contributions forfive family types were multiplied by corresponding weights in populations structure(namely, 0.292 for single households, 0.196 for couples, etc.). The resulting estimate of
the net change in household saving rate for 2005 was -0.82 percentage points (shown in
the last row of Figure 5).
The contribution from changing structure of birth cohorts was calculated in a similar
way. The left side of Table 6 shows two sets of parameter estimates for cohort effects.
The first set includes all estimates of cohort effects from Model 4, which were alreadyreported in Table 4. Around half of these estimates turned out statistically insignificant,as illustrated by Figure 4. The first birth cohort is used as a control category, with zerocoefficient.
As shown in Figure 4, subsequent birth cohorts from 1920-1914 to 1930-1934 hadstatistically significant positive estimates, followed by a long sequence of insignificant
cohort effects, with only a single significant (and negative) estimate for the youngest
birth cohort of 1980-1984. Due to the large number of insignificant estimates, I also
used a second set of cohort estimates, which were significant at 5 percent level, while
insignificant ones were zero.
The right side of Table 6 contains weights for different birth cohorts, which were
calculated from different rounds of NSFIE survey in 1989, 1994, 1999 and 2004. With
each subsequent survey, the share of a given birth cohort declines. For example, household heads that were born in 1920-1924 accounted for 5.1 percent of households in 1989,
but for only 2.4 percent of households in 2004. As shown in Figure 4, older birth cohorts tended to have relatively high saving rate, with increased saving rate by around
4 percentage points for those born between 1910 and 1929. As the older birth cohorts
decreased their share in the household structure over time, the net effect of the cohort
effects is expected to be negative.
The bottom part of Table 6 illustrates this trend in the historical contribution ofcohort effect. For example, the aggregate contribution of cohort effect in 1989 was 1.81
percentage points with all estimates of cohort effects, and 1.25 percentage points with
only significant estimates. But with declining share of birth cohorts with relatively highsaving rates, the aggregate contribution from birth cohorts declined continuously, anddropped to 1.24 percentage points in 2004 with all estimates for cohort effects, while
significant estimates also produced the estimate of 0.70 percentage points, which was
lower compared with estimates for previous years.
Table 7 summarizes contributions to household saving rate from age, cohort andperiod effects. It contains two alternative estimates for different age structure amonghouseholds. The first estimate uses household weights from different round of pop-

15

ulation census of Japan (namely, in 1990, 1995, 2000 and 2005)5 . The second estimate
uses household weights in NSFIE samples (namely the final sample of 168,058 households that I obtained after data cleaning, as shown in Table 1). Using this second set ofweights, I got very similar estimates for the aggregate contribution of age structure. For
example, the estimate with NSFIE weights in 1989 was -0.68 percentage points, which
was not much different from the estimate of -0.82 percentage points, derived in Table 5
with weights from 1990 population census.
Table 7 also reports two estimates for the aggregate contribution of cohort effects(namely, with all and only significant estimates) that were calculated in Table 6. Finally,
estimates for period effect are taken from parameter estimates for year dummies inModel 4 (reported in Table 4). The control category for period effects was the first survey
year (1989), against which the household saving rate increased by 1.83 percentage points
in 1994, by 2.67 percentage points in 1999 and by 1.75 percentage points in 2004.
Compared with these changes in period effect on saving rates, how large was variation in the contribution of age and cohort effects? Similarly to the contribution of period
effect, I set the aggregate contribution of age and cohort effects in 1989 (or 1990 in thecase of census weights) to zero, and calculated net change over time in these effects compared with the initial level. The bottom part of Table 7 reports these net changes in age
and cohort effects over time. I begin with the net effect from changes in age structure ofhouseholds. With census weights for household weights, these was almost no change in
the aggregate age effect over time; in fact, the aggregate contribution in 2005 turned out
exactly the same as it was in 1990. With NSFIE weights, changes in the age structure
also had a minor negative effect on household saving rate, by -0.16 percentage points in2004 compared with 1989.
Compared with surprising small effect from changes in age structure, the aggregate
effect from the changing composition of birth cohorts was more pronounced. It reducedsaving rate by 0.57 percentage points from 1989 to 2004 with all estimates of cohort
effect, and by 0.55 percentage points with only significant estimates. But taking into
account that the net aggregate effect was spread over 20 years, the impact from cohort
effect on the saving rate is essentially nil.
Table 8 reports estimates of aggregate contribution of age and cohort effects, using
mid-point projections of household structure by age by National Institute of Populationand Social Security Research (2008). The projections are available in five-year intervals
from 2010 to 2030.
The aggregate effect from the age structure of households is around 0.80 percentage
point, and changes little over time. In fact, the estimate for 2030 is very close to its levelin 2010, indicating that differences in the age structure of households may have negligible impact on the future household saving rate. The aggregate effect from different birth
5 Table 5 have already illustrated the calculation with these weights for year 2005.

16

cohorts showed a more noticeable change. For example, with only significant estimatesof cohort effects, the aggregate saving rate dropped from 0.33 percentage points to -0.35
percentage points in 2030, reflecting the reduced share of cohorts with relatively highsaving rates. However, this change in 0.68 percentage points over the span of 20 years
implies that at annual rate, the effect on saving rate is just -0.03 percentage points a year.

6 Conclusion.
Using micro data from the National Survey of Family Income and Expenditure, this paper estimated the effect of age, birth cohorts and other factors on changes in householdsaving rates in Japan. Four major findings stand out in estimates of these effects.
First, I found that different types of households had vastly different age-saving profiles, with little evidence of a common saving pattern among households. Consequently,
studies that assume uniform age-saving profiles across different family types are likely
to miss the substantial diversity in saving behavior. Second, the estimates produced little
evidence to support a humped-shaped profile of savings, as predicted by the life-cycle
hypothesis of savings. For example, households without children started to decrease
their saving rate much earlier that postulated by the life-cycle theory, and this pattern
was evident both for single households, and for couples. Moreover, I found even lessevidence of humped-shaped savings in other family types, with a notable absence of
reduced saving saving rate among aged households in most family types. Fourth, whenhouseholds were differentiated by the number of aged and retired household members,
the presence of such members did not significantly reduce the rate of household savings,
indicating that dissaving in the old age may be largely absent in the Japanese household
data.
Using the estimates of age effects, I calculated the aggregate effect from demographic
structure on the household saving rate in Japan. At a given point of time, the aggregate
effect from different age groups was negative, but very small in magnitude, always
within one percentage point. Moreover, the variation in the aggregate age effect overtime was even less evident, indicating a negligible impact on the household saving ratefrom changing age structure in Japan.
Why the age compositional effect of the life-cycle theory turned out of such a limited
scale in Japan? One possible reason is that estimated age-saving profiles did not havelarge enough variation in humped-shaped savings, with a particular lack of sufficiently
steep declines in the saving rate of aged households. In fact, for some family types, thesaving rate did not decline in the old age, but either stayed flat, or even increased.
Compared with the small effect from differences in the age structure of Japanesehouseholds, changes in the composition of birth cohorts had a larger effect on the saving rate. In particular, I found that older birth cohorts of Japanese households wererelatively higher saving rates, but the difference across cohorts mostly disappeared after

17

the baby-boom generation. Since the population aging reduces the population share ofolder birth cohorts with relatively high saving rates, the aggregate cohort effect has been
reducing the rate of household savings, by about -0.6 percentage points, with the effectspread over 1989–2004.
The paper also applied the estimates of age and cohort effects on savings to projections of the future structure of Japanese households by age and family types. Onceagain, the net change in the contribution of the age effect was only 0.01 percentage
points over 2010–2030, while the corresponding estimate for the aggregate cohort effectwas only -0.6 percentage points, with an average annual change by just -0.03 percentage
points.
In general, the results in this paper agree with other micro-level evidence on thelittle importance of demographic factors for aggregate household savings. Rather thandemographics, a more important factor seems to be uniform changes in saving behavior
across different age and cohort groups, when for some unknown reason, people decideto save their saving behavior, and the new applies equally to all age and cohort groups.
These changes in parallel across different demographic groups were pointed by Bosworth
et al. (1991), and have been subsequently identified among households in other countries(Deaton and Paxson, 2000). In this paper, I also found that these common changes insaving behavior, expressed by large estimated period effects, were important among
Japanese households too, especially in comparison with the small compositional effects
from the demographic structure. But what drives these common changes in saving
behavior remains a puzzle.

18

Figure 1. Household saving rates (%).
The figure plots household saving rates, calculated from national accounting system
SNA93. Italy, Japan and Korea report household saving on a net basis (namely, excluding consumption of fixed capital by households and unincorporated businesses), whilegross saving rates are reported by the United Kingdom and the United States. Household include the household sector and non-profit institutions that serve households.
24
20
16
12
8
4
0
1990

1995

2000
ITALY
UK

2005
JAPAN
USA

2010
KOREA

Source: OECD (2012).

Table 1. Changes in the sample size at different stages of data cleaning
1. Original sample size
2. Less households, marked for unreliable data
3. Less households with top-coded income
4. Less households with negative disposable income or nondurable consumption
5. Less households with topped-up age (85 y.o.)
6. Less households in 5% tails of saving rate’s distribution

19

192,599
189,107
187,786
187,401
186,732
168,058

Table 2. Comparison of different data sources for family type shares.
Singles Couples Couples & Single parents Non-nuclear
child(ren) & child(ren) households(a) NSFIE (published report)
1989
19.9
1994
21.1
1999
27.7
2004
29.1

16.2
19.2
20.9
22.8

44.1
42.2
36.7
34.1

3.2
3.2
3.7
4.2

16.6
14.2
11.1
9.9

(b) NSFIE (80% subset of micro data)
1989
19.2
15.8
1994
20.5
18.7
1999
26.9
20.4
2004
28.2
22.0

42.8
40.6
35.3
32.8

2.2
3.0
3.1
3.6

19.9
17.3
14.3
13.3

(c) NSFIE (after cleaning)
1989
17.7
1994
18.8
1999
24.6
2004
26.7

15.8
19.0
21.0
22.3

44.6
42.6
37.5
34.7

2.0
2.5
2.6
3.2

19.9
17.1
14.3
13.1

(d) Population census
1990
23.0
1995
25.5
2000
27.4
2005
29.2

15.4
17.3
18.8
19.6

37.5
34.5
32.3
30.3

6.7
7.0
7.6
8.3

17.3
15.6
13.9
12.6

5.0
5.2
5.3
6.0

19.7
18.5
17.5
16.1

(e) Comprehensive Survey of People’s Living Conditions
1989
20.0
16.0
39.3
1995
22.6
18.4
35.3
1998
23.9
19.7
33.6
2004
23.4
21.9
32.7

20

Table 3. Regression estimates with a general age effect on household savings
The table reports estimates of regression models (8), (9), and (10), with a single nonparametric effect for general age effect f ( age) . Dependent variable is the saving rate ofhouseholds (in percent). Acronym ‘edf’ stands for the number of estimated degrees of
freedom for nonparametric terms.

Model 1Model 2Estimate t-value

Estimate t-value

30.33
2.90
2.53
4.36
5.35
4.77
4.69
5.04
5.46
6.14
7.45
8.18
9.78
9.14
9.33
5.21
0.55
0.31
-1.74

18.91
3.50
3.01
4.86
5.30
4.15
3.50
3.36
3.79
4.14
5.26
5.59
6.82
6.01
5.78
1.15
1.06
1.40
-0.16
8.58
15.43
17.66
16.45
-4.85
-4.94
-5.77
1.95
5.57

Parametric effects
Intercept
Cohort (1910-14)
Cohort (1915-19)
Cohort (1920-24)
Cohort (1925-29)
Cohort (1930-34)
Cohort (1935-39)
Cohort (1940-44)
Cohort (1945-49)
Cohort (1950-54)
Cohort (1955-59)
Cohort (1960-64)
Cohort (1965-69)
Cohort (1970-74)
Cohort (1975-79)
Cohort (1980-84)
Year = 1994
Year = 1999
Year = 2004
Adults = 1
Adults = 2
Adults = 3
Adults ≥ 4Children = 1
Children = 2
Children ≥ 3
Age>65 & retired = 1
Age>65 & retired ≥ 2

24.90
2.18
1.99
3.51
4.29
3.82
3.77
4.07
4.43
5.00
6.08
6.70
8.01
7.44
7.44
3.75
3.92
2.10
-11.14

Nonparametric effects
edf

edf

7.10***

7.08***

Deviance explained (%)
AIC score

3.97
1,519,359

6.94
1,514,101

Number of households

168,058

168,058f ( age)
Model-selection criteria

21

15.49
2.68
2.41
3.98
4.31
3.38
2.86
2.75
3.11
3.41
4.34
4.62
5.63
4.91
4.62
0.83
7.61
9.31
-0.97
33.65
57.11
61.40
55.31
-27.78-26.83-22.67
13.21
24.23

Figure 2. Nonparametric estimates of general age-saving profiles.
The figure reports estimated age-saving profiles in Models 1, 2 and 3 that use a common nonparametric term for the age effect on savings, and differ only in the composition of parametric effects.
Model 1 contains only cohort and period effects, Model 2 adds two demographic variables (thenumber of adults and children), while Model 3 has the most extensive list of control variables.
Detailed parameter estimates for Models 1, 2, and 3 are given in Table 1. The y-axes reports theestimated number of degrees of freedom to approximate nonparametric age effects.
(a) Model 1: Age−Cohort−Year(b) Model 2: Add demographics(c) Model 3: Additional controls
0.10

0.05

0.05

0.05

0.00

0.00

0.00

s(age,7.1)s(age,7.06)

0.10

s(age,7.08)

0.10

−0.05

−0.05

−0.05

−0.10

−0.10

−0.10

−0.15

−0.15

−0.15

20

30

40

50

age

60

70

80

20

30

40

50

age

22

60

70

80

20

30

40

50

age

60

70

80

Table 4. Regression estimates with differentiated age effects on household saving
The table reports estimates of semiparametric models (10) and (12). The dependent variable
is the saving rate of households (in percent).
Model 3Model 4

Estimate t-value

Estimate t-value

34.36
4.80
3.80
4.97
4.87
3.24
2.43
1.53
0.94
0.61
0.96
0.76
1.45
-0.26
-1.60
-5.76
1.89
2.84
2.08
-0.38
1.20
1.89
0.04
-4.35
-4.82
-5.95
-1.12
-0.42

27.47
3.76
3.11
4.16
4.05
2.70
2.03
1.28
0.79
0.52
0.81
0.64
1.21
-0.22
-1.30
-4.21
13.77
18.87
12.37
-1.25
2.65
3.76
0.08
-22.99-23.11-21.87
-4.89
-1.17

35.88
4.34
3.32
4.66
4.62
2.90
2.11
1.40
0.83
0.48
0.76
0.70
1.64
0.26
-0.87
-5.25
1.83
2.67
1.75
-1.49
-0.64
-1.29
-2.93
-2.38
-3.14
-4.43
-0.60
-0.50

27.37
3.40
2.71
3.86
3.78
2.35
1.70
1.12
0.66
0.38
0.58
0.53
1.22
0.19
-0.60
-3.31
12.55
14.70
7.68
-4.10
-1.26
-2.34
-5.12
-11.30-13.46-15.17
-2.39
-1.29

0.29
0.56
2.69
5.88
-1.69
-8.15
1.55
-7.03

1.07
1.70
7.01
13.86
-17.57-26.939.51-38.48

1.72
1.44
1.80
5.85
-1.73
-7.79
1.51
-6.72

4.88
3.83
4.20
12.71
-18.07-25.679.29-35.84

Parametric effects
Intercept
Cohort (1910-14)
Cohort (1915-19)
Cohort (1920-24)
Cohort (1925-29)
Cohort (1930-34)
Cohort (1935-39)
Cohort (1940-44)
Cohort (1945-49)
Cohort (1950-54)
Cohort (1955-59)
Cohort (1960-64)
Cohort (1965-69)
Cohort (1970-74)
Cohort (1975-79)
Cohort (1980-84)
Year = 1994
Year = 1999
Year = 2004
Adults = 1
Adults = 2
Adults = 3
Adults ≥ 4Children = 1
Children = 2
Children ≥ 3
Age>65 & retired = 1
Age>65 & retired ≥ 2
Different family types:
Family type 2: Couple only
Family type 3: Couple & child(ren)Family type 4: Parent & child(ren)Family type 5: Multi-generation
3 major metropolitan districts
Job contract: part-time
Job contract: none
Head of household: female
Nonparametric effects
edf

edf

f(age)
7.06
f(age):family type 1 (Single)
f(age):family type 2 (Couple only)f(age):family type 3 (Couple & child(ren))f(age):family type 4 (parent & child(ren))f(age):family type 5 (Multi-generation)

8.20
7.31
7.90
7.39
7.59

Model-selection criteria
Deviance explained (%)
AIC score

11.2
1,506,136

12.0
1,504,714

Number of households

168,058

168,058

23

Figure 3. Age-saving profiles across different household types inModel 4.
The figure reports estimated age-saving profiles in Model 4, specified by equation (12).
Detailed parameter estimates are given in Table 2. The y-axes reports the estimatednumber of degrees of freedom to approximate the shape of age effect.
(a) Single households(b) Couple only

0.15

0.15

0.10

0.10

(c) Couple & child(ren)
0.15

0.00

s(age,7.9):family3s(age,7.31):family2s(age,8.2):family1

0.10
0.05

0.05

0.00

−0.05

−0.05

0.05

0.00

−0.05

−0.10

−0.10

−0.15

−0.15

−0.10

20

30

40

50

60

70

80

20

30

40

50

60

70

80

20

30

40

50

age
(e) Multi−generation family

0.15

0.15

0.10

0.10

s(age,7.59):family5s(age,7.39):family4(d) Single parent & child(ren)

0.05

0.00

−0.05

0.05

0.00

−0.05

−0.10

−0.10

20

30

40

50

age

60

70

80

20

30

40

50

age

24

60

70

80

60

70

80

Figure 4. Age-saving profiles across different household types in Model 4.
The figure reports 95% confidence intervals for cohort effects on savings, estimated byModel 4. Birth cohorts are denoted by the mid-point of corresponding 5-year interval(for example, 1907 on the x-axis denotes the birth cohort of 1905-1909).

ϴ

ϲ

ϰ

Ϯ

Ϭ
ϭϵϬϳ

ϭϵϭϮ

ϭϵϭϳ

ϭϵϮϮ

ϭϵϮϳ

ϭϵϯϮ

ϭϵϯϳ

ϭϵϰϮ

ͲϮ

Ͳϰ

Ͳϲ

Ͳϴ

ͲϭϬ

25

ϭϵϰϳ

ϭϵϱϮ

ϭϵϱϳ

ϭϵϲϮ

ϭϵϲϳ

ϭϵϳϮ

ϭϵϳϳ

ϭϵϴϮ

Table 5. Calculation of the aggregate age effect in 2005.
The table reports point estimates of age effects on the saving rate for different family types, and theage structure for these family types in 2005. Age structure is based on weights from the population
census. The following abbreviations for family types are used: S = single households, C = couples,
C & Ch = couples with children, S & Ch = single parents with children, Ex = extended (non-nuclear)households.
Point estimates of the age effects

Age group:
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84

Weight by age group in 2005

SC

C & Ch

S&C

Ext

S

C

C & Ch

S&C

Ext

-3.28
-3.58
-1.70
2.14
4.80
2.93
0.26
-1.98
-3.46
-2.26
-1.50
-2.57
-4.67

-6.34
-3.61
-1.09
0.63
1.85
3.78
4.36
0.67
-4.81
-4.48
-2.69
-1.82
-1.16

-12.29
-7.94
-4.30
-1.47
0.18
0.25
1.82
2.71
1.53
2.52
3.68
3.47
2.23

-8.35
-6.50
-5.28
-4.41
-3.57
-2.34
2.67
5.46
3.92
7.26
6.67
3.08
1.93

2.19
2.07
2.25
2.09
1.06
0.09
1.01
0.34
-3.09
-3.52
-3.47
-4.17
-4.94

0.155
0.115
0.096
0.071
0.057
0.051
0.063
0.079
0.067
0.066
0.070
0.064
0.046

0.006
0.040
0.063
0.045
0.033
0.030
0.055
0.110
0.147
0.161
0.151
0.108
0.050

0.007
0.039
0.104
0.127
0.129
0.120
0.124
0.130
0.091
0.060
0.038
0.021
0.009

0.007
0.025
0.059
0.085
0.110
0.121
0.135
0.139
0.095
0.074
0.062
0.050
0.037

0.016
0.023
0.029
0.038
0.060
0.090
0.132
0.167
0.127
0.104
0.093
0.077
0.045

-1.14

0.292

0.196

0.303

0.083

0.126

Change in the saving rate for the family type:
-1.52

-1.82

0.11

Aggregate change in the saving rate:

1.09

-0.82

26

Table 6. Calculation of the aggregate cohort effect
The table reports point estimates of cohort effects on the saving rate for different family types,
and the cohort structure for these family types. Cohort weights are calculated from the NSFIE
data of 168,058 households. The following abbreviations for family types are used: S = single
households, C = couples, C & Ch = couples with children, S & Ch = single parents withchildren, Ex = extended (non-nuclear) households.
Estimates
All
Birth cohorts:
1905-09
1910-14
1915-19
1920-24
1925-29
1930-34
1935-39
1940-44
1945-49
1950-54
1955-59
1960-64
1965-69
1970-74
1975-79
1980-84

0.00
4.34
3.32
4.66
4.62
2.90
2.11
1.40
0.83
0.48
0.76
0.70
1.64
0.26
-0.87
-5.25

Weights by cohorts

Only significant

1989

0.00
4.34
3.32
4.66
4.62
2.90
2.11

0.007
0.017
0.036
0.051
0.076
0.090
0.101
0.124
0.144
0.138
0.104
0.074
0.039

1994

0.010
0.023
0.048
0.081
0.084
0.089
0.113
0.128
0.130
0.109
0.092
0.062
0.031

1999

0.013
0.036
0.068
0.086
0.090
0.099
0.112
0.111
0.100
0.097
0.083
0.077
0.028

-5.25

2004

0.024
0.058
0.083
0.095
0.100
0.103
0.101
0.096
0.092
0.091
0.080
0.056
0.022

Change in the saving rate due to cohort effect:
1.81
1.25

With all estimates
With only significant estimates

27

1.74
1.15

1.52
0.96

1.24
0.70

Table 7. Summary of aggregate age, cohort and period effects in historical changesof household saving rate in Japan.
The table summarizes the aggregate contribution of age, cohort and period effects on householdsaving rate from 1989/1990 to 2004/2005. The contribution of age effect in 2005 (with census
weights) is taken from Table 5. Two alternative contributions from cohort effects is taken from
Table 6. The contribution of period effects is taken from parameter estimates for Model 4 inTable 4.
1989/1990 1994/1995 1999/2000 2004/2005(a) Annual point estimates:
Age effecta. Census weights
b. NSFIE weights
Cohort effecta. All coefficientsb. Significant coefficients

-0.82
-0.68

-0.86
-0.75

-0.85
-0.86

-0.82
-0.84

1.81
1.25

1.74
1.15

1.52
0.96

1.24
0.70

0.00

1.83

2.67

1.75

0.00
0.00

-0.04
-0.08

-0.04
-0.19

0.00
-0.16

0.00
0.00

-0.07
-0.10

-0.28
-0.29

-0.57
-0.55

(b) Change in effect compared with 1989/1990:
Period effectAge effecta. Census weights
b. NSFIE weights
Cohort effecta. All coefficientsb. Significant coefficients

Table 8. Projected effect of the demographic structure on household saving ratein Japan
The table summarizes the aggregate contribution of age and cohort effects on future householdsaving rates. Household weight are taken from mid-point projections by National Institute ofPopulation and Social Security Research (2008). Calculations in Panels (a) and (b) may notagree due to rounding errors.
2010

2015

2020

2025

2030

-0.80

-0.72

-0.68

-0.71

-0.80

0.85
0.33

0.76
0.18

0.60
0.00

0.36
-0.32

0.22
-0.35

0.09

0.13

0.09

0.01

-0.09
-0.15

-0.24
-0.33

-0.49
-0.65

-0.63
-0.68

(a) Annual point estimates:
Age effectCohort effecta. All coefficientsb. Significant coefficients(b) Change in effect compared with 2010:
Age effectCohort effecta. All coefficientsb. Significant coefficients28

References
Attanasio, O. P., Banks, J., Meghir, C. and Weber, G. (1999) Humps and bumps in lifetime
consumption, Journal of Business & Economic Statistics, 17, 22–35.
Baldini, M. and Mazzaferro, C. (2000) Demographic transition and household saving in
Italy, working paper, University of Bologna.
Bosworth, B., Burtless, G. and Sabelhaus, J. (1991) The decline in saving: Evidence fromhousehold surveys, Brookings Papers on Economic Activity, 1, 183–241.
Craven, P. and Wahba, G. (1979) Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross validation,
Numerische Mathematik, 31, 377–403.
Deaton, A. S. and Paxson, C. (2000) Growth, demographic structure, and national savingin Taiwan, Population and Development Review, 26, 141–173.
Dekle, R. (2005) Understanding Japanese saving: does population aging matter?, RoutledgeCurzon studies in the growth economies of Asia, Routledge.
Demery, D. and Duck, N. (2006) Demographic change and the UK savings rate, Applied
Economics, 38, 119–136.
Fernández-Villaverde, J. and Krueger, D. (2007) Consumption over the life cycle: Factsfrom Consumder Expenditure Survey data, The Review of Economics and Statistics, 89,
552–565.
Hastie, T. and Tibshirani, R. (1993) Varying-coefficient models, Journal of the Royal Statistical Society. Series B (Methodological), 55, 757–796.
Hayashi, F. (1997) Life cycle and bequest savings: Evidence from a large cross-section ofJapanese households, in Understanding saving: evidence from the United States and Japan(Ed.) F. Hayashi, The MIT Press, Cambridge, pp. 407–476.
Horioka, C. Y. (1991) The determinants of Japan’s saving rate: The impact of the age
structure of the population and other factors, Economic Studies Quarterly, 42, 237–253,
now called Japanese Economic Review.
Horioka, C. Y. (2006) Do the elderly dissave in Japan?, in Long-Run Growth and ShortRun Stabilization: Essays in Memory of Albert Ando (Ed.) L. R.Klein, Edward Elgar,
Cheltenham, UK and Northampton, MA:, pp. 129–136.
Horioka, C. Y. (2008) The flow of household funds in Japan, Public Policy Review, 4,
37–52.
Hoshi, T. and Ito, T. (2012) Defying Gravity: How long will Japanese government bondprices remain high?, Working paper no. 18287, National Bureau of Economic Research.
Hoshi, T. and Kashyap, A. (2011) Why did Japan stop growing?, Tech. rep., National
Institute for Research Advancement.
Ito, T. and Tsuri, M. (2006) Macroeconomic impacts of aging in Japan on the balance of
current accounts, in Shoshika Keizai Bunseki [Economic analysis of declining birth rate](Eds.) N. Takayama and O. Saito, Touyo Keizai Shinbunsha, pp. 141–172.
Iwaisako, T. and Okada, K. (2010) Understanding the decline in Japan’s saving rate in
the new millennium, Discussion Paper Series 10A-06, Policy Research Institute, theMinistry of Finance (Japan).
Jappelli, T. and Pagano, M. (1999) The determinants of savings: Lessons from Italy, in
Accounting for saving: financial liberalization, capital flows, and growth in Latin America
and Europe (Ed.) C. Reinhart, Inter-American Development Bank.
Kitamura, Y., Takayama, N. and Arita, F. (2003) Household savings and wealth distribution in Japan, in Life-cycle savings and public policy : a cross-national study of six countries(Ed.) A. Borsch-Supan, Academic Press, Amsterdam, Boston, pp. 148–203.

29

Koga, M. (2006) The decline of Japan’s saving rate and demographic effects, The Japanese
Economic Review, 57, 312–321.
Modigliani, F. and Brumberg, R. H. (1954) Utility analysis and the consumption function: an interpretation of cross-section data, in Post-Keynesian Economics (Ed.) K. K.
Kurihara, Rutgers University Press, New Brunswick, pp. 388–436.
National Institute of Population and Social Security Research (2008) Household Projections for Japan: 2005-2030 (in Japanese), Tech. rep., National Institute of Populationand Social Security Research.
OECD (2012) OECD Economic Outlook Annex Tables, vol. 2012 Issue 1, OECD - Organisation for Economic Co-operation and Development.
Park, D. and Rhee, C. (2005) Saving, growth, and demographic change in Korea, Journalof the Japanese and International Economies, 19, 394–413.
Parker, J. A. (2000) Spendthrift in America? on two decades of decline in the U.S. saving
rate, in NBER Macroeconomics Annual 1999, Volume 14 (Eds.) B. S. Bernanke and J. J.
Rotemberg, National Bureau of Economic Research, vol. 14, pp. 317–387.
Paxson, C. (1996) Saving and growth: Evidence from micro data, European Economic
Review, 40, 255–288.
R Development Core Team (2012) R: A Language and Environment for Statistical Computing,
R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org.
Ruppert, D., Wand, M. P. and Carroll, R. J. (2003) Semiparametric Regression, Cambridge
University Press, Cambridge.
Weil, D. N. (1994) The saving of the elderly in micro and macro data, The Quarterly
Journal of Economics, 109, 55–81.
Wood, S. N. (2012) Package ‘mgcv’ (version 1.7-22), http://cran.r-project.org/web/
packages/mgcv/mgcv.pdf.

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