highly preliminary draft life cycle earnings and saving in ......older workers, and cohort-speci–c...
TRANSCRIPT
Highly Preliminary Draft
Life Cycle Earnings and Saving in a Fast-Growing Economy∗
Zheng Michael SongChinese University of Hong Kong and Fudan University
Dennis Tao YangChinese University of Hong Kong
November 8, 2010
Abstract
This paper proposes an explanation for rising saving rates– particularlyamong young households– in fast-growing economies. When an economy em-barks on growth, the earnings of young workers rise more rapidly than those ofolder workers, and cohort-specific age-earnings profiles also become flattenedduring the transition period. We present robust empirical evidence on theselabor market changes during a period of extraordinary growth in China, andshow that once structural shifts in earnings have been incorporated, an oth-erwise standard intertemporal choice model can explain the observed savingbehavior. Our quantitative analysis, which is based on the dynamic optimiza-tion of heterogeneous agents, accounts well for the recent surge in householdsaving in China.
Keywords: Household saving, age-earnings profile, income growth, in-tertemporal choice, life cycle model, China.
JEL classification: E21, D91, O53
∗We would like to thank Marcos Chamon, Peter Diamond, Jing Han, Eswar Prasad, Richard Rogerson, KjetilStoresletten, Hongliang Zhang, Xiaodong Zhu, Fabrizio Zilibotti, and the seminar and conference participantsat The Chinese University of Hong Kong, Hong Kong University of Science and Technology, Shanghai JiaotongUniversity, University of Hong Kong, the Econometric Society World Congress in Shanghai, the First AnnualInternational Conference on the Chinese Economy at HKIMR, Shanghai Macro Workshop, Taipei InternationalConference on Growth, Trade and Dynamics, and Tsinghua Macro Workshop for their helpful comments. Anyremaining errors are our own. Contact information: Song, Department of Economics, The Chinese Universityof Hong Kong, E-mail: [email protected]; Yang, Department of Economics, The Chinese University of HongKong, E-mail: [email protected].
1 Introduction
Households save more in fast-growing economies. The experiences of Japan in the 1960s and
Korea and Taiwan in the 1970s and 1980s attest to this empirical regularity. More recently, the
national savings in emerging markets have also risen with their high rates of growth. Over the
1998-2008 period, average national savings as a percentage of GDP increased by 9.6 percentage
points in the BRIC countries (Brazil, Russia, India and China), reaching 34.4 percent in 2008,
a rate far above the world average of 22 percent (World Bank, 2009).1 This remarkable pattern
of rising savings in emerging markets has spurred tremendous interest in academic and policy
circles, not only because the phenomenon constitutes a challenge for the standard theory,2 but
also because it is viewed by some as a major source of global imbalances.3 Despite the rich
theoretical and policy implications of rising savings in high-growth environments, the primary
causes for them are still not well understood.4
This paper proposes an explanation for the rising saving rates– particularly those among
young households– observed in fast-growing economies. We argue that these rises in house-
hold saving are primarily the result of a structural shift in life cycle earnings associated with
economic growth. As an economy departs from a stable environment and embarks on fast-
paced growth, the earnings of young workers rise more rapidly than those of older workers,
resulting in a flattening of the age-earnings profile during the transition period. This reflects
the view that young workers with appropriate knowledge and skills are more productive in a
high-growth environment. The structural change in earnings boosts household saving rates
through two channels: while the older cohort saves more to smooth income growth for retire-
ment, the younger cohort saves more because of a new mechanism. Young workers earn more
1During this period, the real annual GDP growth of Brazil, China, India and Russia was 3.3, 9.8, 7.2 and6.9 percent, respectively, each exceeding the world average for GDP growth. The corresponding increases inthe national saving rates in these countries were 4.1, 7.8, 11.9 and 14.6 percentage points, respectively, reaching19.19, 49.22, 32.87 and 36.26 percent in 2008 (World Bank, 2009).
2The observation of high saving during high-growth episodes is diffi cult to reconcile with the representativeagent model in which forward-looking households with the standard preference would be expected to save lessin anticipation of a higher level of earnings in the future relative to their present income.
3Lane and Milesi-Ferretti (2007) reports a dramatic improvement in the external positions of assets andliabilities for emerging markets since the late 1990s, a period that coincides with the rising saving rates in majordeveloping countries documented here. This period has witnessed a worsening of the US’s external position,and, since 2001, the upward trend in the net foreign assets of other industrial countries has also been reversed.
4Although income growth can lead to increased saving in the life-cycle model (e.g., Modigliani, 1970) ormodels with habit formation (e.g., Deaton, 1992; Carroll, Overland and Weil, 2000), the quantitative effect hasbeen shown to be small (e.g., Paxson, 1996). The positive association between high growth and high saving isthus puzzling.
1
relative to older cohorts at the entry level. However, the future entry of new workers with
greater productivity will reduce their earnings growth due to diminishing returns in knowledge
and skills. Facing a flattened age-earnings profile, young workers thus have the incentive to
save more today to compensate for reduced earnings growth over their lifetimes.
Our motivation for forging a link between life cycle earnings and saving derives from the
two following empirical observations, made on the basis of the East Asian experience and a
newly available national sample of Urban Household Surveys (UHS) in China from 1992 to
2007. We analyze both in greater depth later in this paper.
1. Although increases in saving rates are observed across all age groups in high-growth
episodes, these increases are more pronounced among young families, thus appearing
to defy the typical hump-shaped age-saving profiles observed in developed economies.
For instance, amid Taiwan’s remarkable growth from 1976-1990, the saving rates of the
younger generations are found to have significantly outpaced those of their older coun-
terparts (Deaton and Paxson, 1994). Hayashi (1986) reports a similar pattern for Japan
in the early 1970s. The UHS data reveal the same trend in China between 1992 and
2007: with average annual income growth hovering at 8 percent, the country’s young
households boosted their rate of saving substantially (Figures 2 and 3).5
2. The 1992-2007 period in China also witnessed large upward shifts in the earnings of
younger workers, which were accompanied by a significant flattening of the cross-sectional
age-earnings profiles (Figures 4 and 5). Paxson (1996) documents similar pattern among
young Taiwanese workers in the 1970s and 1980s, in sharp contrast to the stable concave
earnings profile observed in other economies with a slower pace of growth. In addition
to this cross-sectional evidence, we also find evidence of entry-level earnings outpacing
average earnings and cohort-specific earnings profiles exhibiting flattening in China’s high
growth environment.
Although some of these empirical observations have been noted in the prior literature, they
have not been proposed as integral components of a coherent theory.
To illuminate the flattening of age-earnings profiles in a high-growth environment and its
impact on household saving decisions through a transparent mechanism, we develop a simple
four-period overlapping generations (OLG) model with closed-form solutions. When income
5Unless otherwise noted, our empirical evidence for China is based on the national UHS sample, which isdescribed in detail in the Data Appendix. See Chamon and Prasad (2010) and Yang et al. (2010) for additionaldescriptions of the saving behavior of urban Chinese households using the UHS data for selected provinces andtime periods.
2
growth is associated with the continual entry of more productive workers, this model is able
to generate the stylized features of the age-earnings profiles observed in China. When the
economy takes off and enters a growth regime, older workers choose a higher rate of saving for
the reason outlined above. The flattening of age-earnings profiles, however, means that the rise
in saving rate among young workers may be even more pronounced. These results are robust to
the incorporation of within-generation heterogeneity in worker types, the inclusion of a pension
system and alternative specifications of lifetime earnings expectations. The structural change
in age-earnings profiles thus provides a novel mechanism by which to explain the saving rate
rises witnessed in fast-growing economies, particularly among young households.
The question that remains is a quantitative one: To what extent can the flattened age-
earnings profiles associated with growth explain China’s rising household saving rates and
changing age-saving profiles? Between 1992 and 2007, the disposable incomes of Chinese ur-
ban households grew at a remarkable annual rate of 8 percent, whereas the aggregate urban
household saving rate grew at an even more phenomenal rate– from 16.6 to 27.6 percent. In
addition, consistent with Chamon and Prasad (2010), our national UHS sample also shows the
age-saving profile of Chinese urban households to exhibit a U-shaped pattern in recent years,
with younger and older households having high saving rates relative to their middle-aged
counterparts (see Figure 2A). The U-shaped increase in age-specific saving rates is even more
pronounced between the initial (1992-1993) and final (2006-2007) periods of the sample (see
Figure 2B). While a high saving rate is common among the young in fast-growing economies,
that among older workers appears unique to China. To account for these observations quan-
titatively, we turn to a more sophisticated OLG model in which one period corresponds to
one calendar year. Once the estimated structural changes in age-earnings profiles and pension
system reforms have been incorporated, the model with standard parameterization is able to
generate an increasing aggregate saving trend that is comparable to its empirical counterpart.
Moreover, the predicted increases in the saving rate over the life cycle fit reasonably well with
the U-shaped pattern observed in the data.
This paper is closely related to the literature on saving and growth. In a series of papers,
Modigliani and his coauthors (e.g., Modigliani, 1970; Modigliani and Cao, 2004) adopt the
life cycle approach to investigate how growth affects saving. They argue that stronger income
growth leads to higher aggregate saving because of the increased demand for wealth in the
economy. However, their predicted positive correlation between saving and growth can easily
be reversed in a representative agent model in which the saving rate tends to decline contem-
poraneously with consumer anticipation of ongoing income growth (e.g., Tobin, 1967; Carroll
3
and Summers, 1991). For this reason, economists have explored alternative channels– such as
habit formation (e.g., Carroll, Overland and Weil, 2000), the buffer-stock hypothesis (e.g., Car-
rol, 1992) and precautionary saving under borrowing constraints (e.g., Kimball, 1990; Deaton,
1991)– to explain the positive association between growth and saving. The quantitative effects
of these channels, however, have been shown to be too small to match the data (e.g., Paxson,
1996; Deaton and Paxson, 2000),6 and whether implicitly or explicitly, these studies have as-
sumed age-earnings profiles to be stationary. The present paper contributes to the literature
by investigating how growth affects saving decisions through changing age-earnings profiles.
We conduct our quantitative exercise employing a heterogeneous agents model with dy-
namic optimization on consumption and saving. Despite its widespread use in macroeconomics,
this framework typically assumes a stationary age-earnings profile,7 an assumption that runs
counter to the empirical evidence of age-earnings profiles flattening observed in fast-growing
economies. To the best of our knowledge, this paper is the first to incorporate structural
change in age-earnings profiles into quantitative analysis of an intertemporal decision.
This paper also contributes to the growing body of literature on household saving in China,8
which display features that the existing theory struggles to explicate. In an attempt to come
to a better understanding of recent Chinese household saving behavior, the existing literature
often resorts to factors that are unique to China, such as demographic structural changes
(Modigliani and Cao, 2004; Horioka and Wan, 2007), sharp increases in health and education
expenditures (Chamon and Prasad, 2010) and competitive saving motives stemming from the
marriage market as a result of the imbalance in the sex ratio (Wei and Zhang, 2009). To date,
no consensus has been reached on the major causes of the burgeoning household saving rate
in China. Different from earlier studies, our work highlights the structural change in life cycle
incomes– both the flattening of age-earnings profiles and the reduction in pension provisions–
as the primary cause. This also represents the first study to proffer a coherent explanation for
the U-shaped increase observed in the saving rate across age groups.
The reminder of the paper is organized as follows. Section 2 presents information on
6 In the analysis of national saving (rather than household saving), high saving and high growth can co-existin the neoclassical growth model due to the channel linking TFP growth, the rate of return to capital and theaggregate investment/saving rate (Chen et al., 2006). See Wen (2009) for a discussion of a growing economysubject to wealth uncertainty.
7See, for example, Auerbach and Koltikoff (1987). Idiosyncratic earnings shocks are introduced in laterstudies (e.g., Imrohoroglu et al., 1995; Storesletten et al., 2004). However, the average age-earnings profileremains stationary across cohorts.
8This is an important topic because the growth of China’s foreign reserves has been rather astonishing, risingfrom US$21 billion in 1992 (5% of annual GDP) to 2,130 billion in June 2009 (46% of GDP) and contributingto the current global imbalance. Explicating the reasons for the the increase in the Chinese saving rate maythus also help to shed light on the causes and even future direction of this imbalance.
4
Chinese household saving, including the sharp increase in the aggregate saving rate, the U-
shaped pattern in saving rates over the life cycle, and the high saving rates of the young
and college-educated. This section also presents data on earnings and pensions, including
cross-sectional evidence and cohort-based analysis to reveal the substantial flattening that has
occurred in China’s age-earnings profiles. Section 3 develops the simple four-period OLG model
to investigate the way in which growth can lead to the flattening of these profiles, an increase
in the aggregate household saving rate and the observed pattern in saving rates over the life
cycle. Quantitative exercises are conducted in Section 4, in which we demonstrate that our
model is able to closely replicate a number of puzzling facts quantitatively. Section 5 concludes
the paper.
2 Saving and Earnings Profiles: The Case of China
China provides an ideal laboratory for studying high saving in high-growth environments.
China introduced its first economic reforms in December 1978, aiming to reduce land collec-
tivization. Urban reforms took place in the early 1980s. Panel A of Figure 1 plots the urban
household disposable income, which grew at an annual rate of 5.1 percent in the 1982-1991
period. China started to move towards a full-fledged market economy in 1992. Economic
growth has accelerated since then. The annual income growth rate increased by 3 percentage
points to 8.1 percent in the 1992-2007 period. The solid line in Panel B plots the aggregate
urban household saving rate, which has featured an increasing trend since the early 1990. The
aggregate household saving rate has no obvious trend in the 1982-1991 period with a modest
income growth: the average saving rate was 11.7 percent. However, the average saving rate
nearly doubled and increased to 21.3 percent in the 1992-2007 period. These observations in
China are fully in line with the empirical regularity of high saving in high-growth episodes.
[Insert Figure 1]
2.1 Data
Figure 1 uses the aggregate data available at China Statistical Yearbooks. The household
data we use in the present paper come from 16 consecutive years of the UHS conducted by
China’s National Bureau of Statistics (NBS henceforth). The starting year is 1992, when NBS
began the use of standardized questionnaires. The latest data are from 2007. The UHS data
record basic conditions and detailed information on income, consumption, and demographic
characteristics of urban households in each calendar year. The data also reveal employment,
5
wages and individual characteristics of all household members. We use the full sample cov-
ering all provinces except Tibet because of missing surveys in certain years and the lack of
representation from this autonomous region.
The choice of households in UHS is based on the principle of random and representative
sampling, and the sampling method is consistent over all years.9 However, we discover that the
response rates for workers of state-owned and collective firms are systematically higher than
those of workers of other firms. Therefore, we deploy a resampling scheme that adjusts the
sample distribution of workers by ownership type to the national distribution figures. Details
on the resampling and a comparison between raw and resampled data are provided in the Data
Appendix. After resampling, our sample covers 14,730 households and 30,306 individuals in
1992, and the numbers increase to 36,821 and 71,131 in 2007 (see Table A1 in the appendix).
Savings are computed as the difference between disposable income and consumption ex-
penditure. Using alternative household saving definitions leaves no major changes to the facts
documented below, except for the saving rates after retirement (see the appendix for details).
Since saving rates after retirement are sensitive to saving definitions and quantitatively not
important, throughout the paper we will focus on household saving with the household head
age between 25 and 55 (for females) or 60 (for males), the offi cial retirement ages in China.10
The dotted line in Panel B of Figure 1 depicts the aggregate household saving rate in the
resampled UHS with age restrictions. One can see that our resampling and age restrictions
have limited impacts on the saving rate. The discrepancy between the solid and dotted lines
is below one percentage point in most years before 2002. The two lines almost coincide with
each other after that.
Earnings are referred to as the annual wages for adult workers engaged in wage employment.
Wage income consists of basic wage, bonus, subsidies and other labor-related income from
regular job. We deflate the annual wages to 2007 Yuan by province-specific urban consumption
price indices.11 Our sample for analysis include all workers aged 25-55 for females and 25-60 for
males, excluding employers, self-employed individuals, farm workers, retirees, students, those
re-employed after retirement, and workers whose real annual wages were below one half of the
real minimum wage.12
9NBS adopts a sampling scheme such that every 5 years they have a complete rotation of the urban householdsamples. Some changes to the questionnaires are also made along with the reshuffl ing of the samples.10Truncating the UHS data at age 80 would give essentially the same result. Quantitatively, it would lower
the aggregate saving rates by less than one percentage point.11See the appendix for the detailed descriptions of data sources, variable definitions and data adjustments.12Provincial-level minimum wages are available only in 2006 from the Ministry of Human Resources and Social
Security. To impute the minimum wages for the previous years, we calculate the ratios of the minimum wagesto the mean wages for each province in 2006. We use the product of these ratios and annual mean wages in
6
2.2 Age-Saving Profiles
Our UHS data begin from 1992, the year when China launched a new stage of reforms toward a
full-fledged market economy. As mentioned above, the real household disposable income grows
at an average annual rate of 8.1 percent from 1992 to 2007, 3 percentage points higher than
the rate in the 1982-1991 period. Associated with the acceleration of economic growth, the
aggregate household saving rate has increased remarkably since 1992, rising from 17 percent
in 1992 to 28 percent in 2007. The appendix shows that using alternative household saving
definitions reveals equally striking upward trends since 2002, when the relevant data for com-
puting saving rates became available. The pattern is also robust to alternative data sources,
such as the Flow of Funds Accounts reported in CSY (Yang et al., 2009).
Panel A of Figure 2 presents age-specific saving rates for the two periods of 1992-1993 and
2006-2007. Some age cells contain very limited number of observations; thus, we use the three-
age moving average to minimize the effect of measurement error. In the 1992-1993 period,
the saving rates are relatively flat before 45 and then increase towards the retirement age.
For the 2006-2007 period, a dramatic change is observed: The age-saving profile turns to a
U-shape. Using alternative saving definitions results in qualitatively similar profiles (see the
appendix for details), though the rise in the saving rate for age 50-60 may be less remarkable
under certain definitions. We can further eliminate the time-invariant age effects by taking the
difference of the two profiles.13 This yields the increase in the age-specific saving rate from
1992-1993 to 2006-2007, as depicted in Panel B of Figure 2. The U-shape pattern becomes
more pronounced: The average increase in the saving rate for those aged below 40 and above
50 is equal to 11.2 and 10.9 percent, respectively, whereas that for those middle-aged between
40 and 50 is only 8.3 percent. The rise in the saving rate of the young sharply contrasts the
typical hump-shaped or relatively flat age-saving profile in mature economies.
[Insert Figure 2]
To see whether the rise in the household saving rate has any structural pattern, we inves-
tigate two subsamples by household head education. Subsamples 1 and 2 include households
with high-school-and-below- (non-college henceforth) and college-and-above- (college hence-
forth) educated household head, respectively. Figure 3 plots the age-saving profiles of 1992-
1993 and 2006-2007 for the two subsamples. It is immediate that the main findings from
Figure 1 and 2 are robust to household head education. The rise in the household saving rate
each province as our estimates for province-specific minimum wages in 1992-2005 and 2007.13Age effects may be time-varing (for instance, the effects of changing age-specific household demographic
structures and family structures). See below for an investigation of the time-varing age effects.
7
is universal across the two subsamples and both subsamples feature a U-shaped increase in the
age-specific saving rate from 1992-1993 to 2006-2007.
[Insert Figure 3]
Although the main patterns in Figure 3 are qualitatively similar to those illustrated by
Figure 2, some quantitative differences are worth mentioning. A comparison between Panel C
and D shows that the increase in the saving rate of college graduates is substantially larger
than that of non-college graduates. From 1992 to 2007, the average saving rate for college
graduates increases by 12.6 percentage points, 2.7 percentage points higher than the increase
in the average saving rate for noncollege graduates. Reinforced by the increasing population
share of college graduates and the widening income gap between the two education groups, the
increase in the saving rate of the college educated alone can explain more than 40 percent of
the increase in the aggregate household saving rate over the sample period. The high saving
rate of young college graduates (those aged between 25 and 40) should be particularly noted.
It increases by 13 percentage points, which alone contributes to a 3-percentage-point increase
in the aggregate saving rate, about one fourth of the rise in the aggregate saving rate over the
sample period.
To summary, we have documented the following three main observations on Chinese house-
hold saving rates.
1. The aggregate household saving rate increases remarkably from 1992 to 2007. Moreover,
the household saving rate increases in all age and education groups.
2. The increase in the age-specific household saving rate features a U-shape, which is robust
to household head education.
3. Households with college-educated household heads increase their saving rate more than
those with non-college-educated household heads.
2.3 Age-Earnings Profiles
We first present cross-sectional age-earnings profiles and then examine the data statistically.
The dotted line in Figure 4 presents the cross-sectional relative age-earnings profiles in 1992-
1993, where workers of age 42 is used as the reference group to compute relative earnings. The
profile features the standard pattern: earnings increase in age, reach a peak at 57, and then
flatten until retirement. The earnings profile has changed dramatically afterwards. The solid
line in the figure presents the cross-sectional relative age-earnings profile in 2006-2007. The
8
flattening of the earnings profiles is evident: Workers at age 50 earn essentially the same as
those at age 30.
[Insert Figure 4]
Education is a key factor in determining labor earnings. In particular, the flattening cross-
sectional earnings profiles may reflect the fact that younger cohorts are better educated and,
therefore, earn more than earlier cohorts. To control for such an effect, we divide workers by
education, and then examine the cross-sectional earnings profile within each education group.
Panel A (or B) of Figure 5 depicts age-specific earnings for non-college (or college) educated
workers relative to the earnings at age 42 in that group. The flattening of the age-earnings
profile is also evident in both groups, though less dramatic than that in the full sample.
[Insert Figure 5]
2.3.1 Cohort-Specific Age-Earnings Profiles
The cross-sectional earnings profile does not necessarily reveal an individual’s earnings profile
over her life cycle. Moreover, the difference between any two cross-sectional earnings profiles
entails both cohort and year effects, while the earnings difference between any two age cells
along a cross-sectional profile comes from a combination of age and cohort effects. Due to these
concerns, we take an alternative approach: tracing the cohort-specific earnings by constructing
synthetic cohorts. A cohort is denoted by the year when individuals turn 25 and enter into our
sample. Therefore, individuals with the same entry year in repeated surveys across periods are
treated as being in the same cohorts.
To estimate cohort-specific earnings profiles, we use the following regression specification
used by Beaudry and Green (2000) and Kambourov and Manovskii (2009):
log y (i, t) = α0 + κ1z (i) + κ2z (i)2 + κ3z (i)x (i, t) (1)
+α1x (i, t) + α2x (i, t)2 + α3x (i, t)3 + α4 log Y (t) + ε (i, t) .
Here, the dependent variable, y (i, t), is the log annual earnings for a given cohort i in a given
year t. The regressors include the cohort entry year, z (i), and its square, an interaction of
age, x (i, t), and the cohort entry year, plus a polynomial of age.14 To control for the effect
of aggregate earnings shocks on individual earnings, we introduce log detrended aggregate
14Following Beaudry and Green (2000), the first cohort with entry year of 1957 in our sample is indexed bycohort 1. The following successive cohorts are counted up incrementally.
9
earnings, log Y (t), as an additional regressor.15 Specifically, Y (t) = Y (t) /Y0 (1 + g)t, where
g is set such that∑
t log Y (t) = 0. Since the sample contains 36 ages and 16 years, there
are a total of 576 observations. κ1 and κ3 are two parameters of interests that govern the
cohort-specific earnings profiles. First, when κ2 is close to zero, we may simply interpret κ1 as
the growth rate of the starting earnings. A larger κ1 implies a wider entry-level earnings gap
across cohorts. Second, κ3 captures change to the slope of the cohort-specific earnings profile.
A positive (or negative) κ3 implies a steepening (or flattening) of the earnings profile.
[Insert Table 1]
The estimated results are reported in Column (1) of Table 1. The positive and large
coeffi cient on the linear cohort term, κ1, suggests a high growth of the entry-level earnings,
which contributes to the flattening of the cross-sectional earnings profiles in Figure 4. This is
also in accordance with Modigliani-Paxson’s postulation on the change in life cycle earnings in
a growing economy (e.g. Modigliani, 1986; Paxson, 1996); i.e., the aggregate growth manifests
itself in an upward shift of the age-earnings profile from cohort to cohort. More specifically,
the estimated κ1 implies an average annual growth rate of 12 pecent for the starting earnings
at age 25 over the sample period, much higher than the growth rate of 7.5 percent for the
aggregate earnings.16
Another key coeffi cient on the age-cohort interaction, κ3, is negative and significant. This
suggests that the cohort-specific age-earnings profile has been flattening from cohort to cohort.
In other words, although young cohorts earn more at the entry level relative to older cohorts,
their earnings will actually grow at a lower rate. A combination of the large κ1 and the
negative κ3 results in a quantitatively sizable effect on the life cycle earnings growth. For the
2007 cohort, for instance, the estimates imply that their earnings would grow at an average
annual rate of 5.0 percent over the life cycle, substantially lower than the rate of 7.1 percent
for the 1992 cohort.
As a robustness check, we replace the detrended aggregate earnings, log Y (t), with year
dummies. In this case, an identification condition is needed since cohort, age and year are a
linear combination of each other. Following Deaton and Paxson (1994), we add two restrictions
such that (i) year dummy coeffi cients sum up to zero, and (ii) year dummy coeffi cients are
orthogonal to a time trend. Column (2) reports the estimated results. The coeffi cient of
interest, κ3, remains negative and highly significant, though the absolute value drops from
15Beaudry and Green (2000) use unemployment rates, which are actually flat and not informative in China.16Here, we ignore the statistically insignificant κ2.
10
0.0011 to 0.0008. All the other estimates are essentially the same as those in Column (1).17
The specification (1) can easily be extended to estimate group- and cohort-specific earnings
profiles.
log y (i, j, t) = α0 (j) + κ1 (j) z (i) + κ2 (j) z (i)2 + κ3 (j) z (i)x (i, t) (2)
+α1 (j)x (i, t) + α2 (j)x (i, t)2 + α3 (j)x (i, t)3 + α4 (j) log Y (t) + ε (i, j, t) ,
where y (i, j, t) denotes the earnings of individuals with age i in group j at period t. Column
(3) to (4) in Table 1 report estimation results for groups of the non-college-educated and
college-educated, respectively. Interestingly, the estimates of κ1 and κ3 change considerably
across the two groups. κ1 in Column (3) shows that the entry-level earnings of the non-college-
educated grow at a rate that is closer to the average earnings growth rate. In contrast, κ1
in Column (4) shows that the growth rate of the entry-level earnings of the college-educated
young workers is substantially higher than the average earnings growth rate. Nevertheless, the
negative and statistically significant coeffi cient on the quadratic cohort term, κ2, suggests that
the entry-level earnings growth has been slowing down.
κ3 is negative in both education groups, marginally significant for non-college-educated
workers but highly significant for college-educated workers. The estimated absolute value of
κ3 for the college-educated equals 0.0019, much larger than that in the full sample regression.
That is to say, the flattening of the cohort-specific earnings profiles is more pronounced for the
college-educated. For the 2007 cohort, their estimated annual earnings growth rate over the
life cycle is 4.2 percent, nearly half of the rate of 7.9 percent for the 1992 cohort.1819
Beaudry and Green (2000) and Kambourov and Manovskii (2009) find a similar flattening
of the cohort-specific earnings profile in Canada and the U.S., respectively. The flattening
of the earnings profile in China is more prominent on average. For instance, Kambourov
and Manovskii (2009) report an estimated κ3 of −0.004 in the PSID data, with a magnitude
much smaller than the one in Column (1) of Table 1. Beaudry and Green (2000) document a
17The Chinese government started reforming the central-planned economy in 1978. Therefore, cohorts enteringthe labor market after the reform might have age-earnings profiles different from earlier cohorts. To isolate age-earnings profiles of the “lucky generations,”we run the same regressions for a subsample of cohorts with entryyears later than 1978. The subsample contains 376 observations, less than two-thirds of the full sample. Theestimated κ3 is still negative, marginally significant under the Beaudry-Green specification but highly significantunder the Deaton-Paxson specification. The detailed results are provided in the technical appendix.18The estimates of α4 (j) also exhibit substantial heterogeneity across education groups. It varies from 0.90
for the non-college educated to 1.11 for the college-educated, implying that earnings of the college-educated tendto be more volatile over the business cycle. This may provide an explanation, through precautionary savingmotives, for the higher saving rate of the college-educated, which is complementary to our explanation providedbelow. We will leave it as an interesting extension for future research.19Using the Deaton-Paxson specification gives similar results. The details are provided in the technical
appendix.
11
strong flattening of the earnings profile for high-school educated men in Canada. However, the
overall picture is less clear as κ3 becomes statistically insignificant for university educated men.
Moreover, no evidence suggests that the entry-level earnings outstrip the average earnings in
these two developed economies as observed in China.
2.4 Pension
Pension has been found important for saving decision over the life cycle (e.g., Attanasio and
Brugiavini, 2003). This subsection provides facts about the Chinese pension system, which has
undergone a series of reforms since the late 1990s. The original pension system was primarily
based on state and urban collective enterprises in the central-planned economy. Retirees re-
ceived generous pensions from their employers, with a replacement rate that could be as high
as 80 percent (see, e.g., OECD, 2007). The work-unit-based system has a low coverage, though.
Many non-state-owned entreprises has no pension scheme for their employees. The coverage
rate, measured by the ratio of the number of workers covered by the system to the urban
employment, was only 44 percent in 1992.20 The old system has been under severe financial
distress since the late 1980s mainly due to a growing disproportion between the numbers of
contributors and beneficiaries (Zhao and Xu, 2002). To deal with the issue, the government
initiated a transition from the traditional Pay-As-You-Go system (PAYGO henceforth) to a
partially-funded one in the early 1990s. A new system was implemented after the State Coun-
cil issued “A Decision on Establishing a Unified Basic Pension System for Enterprise Workers
(Document 26)”in 1997.
The reformed system consists of three pillars. The first pillar, funded by 17 percent wage
taxes paid by enterprises, guarantees a replacement rate of 20 percent of local average wage
for retirees with a minimum of 15 years of contribution. The second pillar provides pensions
from individual accounts financed by a contribution of 3 and 8 percent wage taxes paid by
enterprises and workers, respectively. The third pillar adds to individual accounts through
voluntary contribution. The return of individual accounts is adjusted according to bank deposit
rates. The system also defines monthly pension benefits from individual accounts equaling the
account balance at retirement divided by 120. The targeted replacement rate of the system is
58.5 percent. Suppose that the wage growth rate is equal to the interest rate. For a worker
who contributes to the system for 35 years (from age 25 to 60), her pension benefits should be
equal to 20 percent of the average wages (the first pillar) plus 38.5 percent of her wage before
retirement.20Data source: China Statistical Yearbook (2009).
12
More recently, a new reform was implemented after the State Council issued “A Decision
on Improving the Basic Pension System for Enterprise Workers (Document 38)”in 2005. The
reform adjusted the proportion of taxes paid by enterprises and individuals and the proportion
of contribution for individual accounts. Individual accounts are now funded by the wage
taxes of 8 percent paid by workers only. Moreover, the reform changed the pension benefits
substantially. The replacement rate of an individual is now determined by years of contribution:
A one year contribution increases the replacement rate of an wage index averaged from local
and individual wages by one percentage point.21
The pension reform was cohort-specific. There were three types of cohorts when the pension
reform took place: Cohorts enter into the labor market after 1997 (xinren), cohorts retired
before 1997 (laoren) and cohorts in between (zhongren). Pension contributions and benefits
of xinren are entirely determined by the new rule. According to Item 5 in Document 26, the
government commits to pay laoren the same pension benefits as those in the old system subject
to an annual adjustment by wage growth and inflation. For zhongren, their contributions follow
the new rule, while their benefits consist of two components: (1) pensions from the new system
identical to those for xinren, and (2) a transitional pension that smoothens the pension gap
between loaren and xinren.
We next present a quantitative assessment of the evolution of the Chinese pension system.
Due to the lack of data on historic earnings, the actual replacement rate is hard to obtain.
Thus, we compute the aggregate replacement rate as a percentage of average pensions per
retiree over average wages per worker instead. Chinese Statistical Yearbook (CSY) reports
the “Pensions for Retired and Resigned Persons per capita” up to 2005. This variable is
divided by the “Average Wage of Staff and Workers” to generate a proxy for the aggregate
replacement rate. The solid line in Panel A of Figure 6 plots the results from 1992 through
2007. The aggregate replacement rate was above 80 percent in the early 1990s, consistent with
the impressionistic view that the original work-unit-based pension system entails generous
inter-generational redistribution. The 1997 reform cut pension benefits substantially for those
newly retired workers (zhongren), driving the aggregate replacement rate to fall in the late
1990s. The declining trend continued in the 2000s. The aggregate replacement rate dropped
to 58 percent in 2005. Dunaway and Arora (2007) report a similar dramatic pattern. They
show that the replacement rate of average manufacturing wages declined from 82 percent in
2000 to 68 percent in 2005.
[Insert Figure 6]
21However, the article did not state explicitly how to compute the wage index.
13
Although the generosity of the system has been reduced dramatically through these reforms,
a targeted replacement rate close to 60 percent still stands high and is actually higher than
the rate in most OECD countries (OECD, 2007).22 However, the actual replacement rate
can be much lower due to the widespread payment evasion. To reduce pension contributions,
enterprises have the incentive of reporting lower wages. The system requires a contribution
rate of 20 percent from enterprises, while the actual rate is about 5 percent according to
the enterprise survey conducted by NBS (see Li and Wu, 2010). This implies that the wages
reported by enterprises is only one-fourth of the actual ones and the pension system pays only 5
percent of the actual average wages from the first pillar. Our UHS data reveal a similar pattern
for individual contributions. The average individual contribution rate from 2002 to 2007 was
4.1 percent, about half of the offi cial rate. For a worker who contributes to the system for 35
years, the second pillar provides pension benefits equaling 14 percent of her actual wages, if we
maintain the assumption that the wage growth rate equals the interest rate. In other words,
the replacement rate adjusted by the actual contribution rate would be equal to 19 percent,
only one-third of the targeted rate.
The overestimated aggregate replacement rate from CSY can also be seen from the UHS
pension data. Since 2002, UHS has adopted a new definition of pension that covers a lot
more items other than the narrowly-defined pension, such as the reimbursement of medical
expenditure from enterprises and the public health care system. To maintain data consistency,
we compute the aggregate replacement rate as a ratio of the average pension (broadly defined)
per pension beneficiary over the average earnings per worker for the 2002-2007 period. The
result is plotted by the dotted line in Panel A of Figure 6. The aggregate replacement rate
from UHS also features a downward trend, declining from 61.8 percent in 2002 to 52.4 percent
in 2007. Although the aggregate replacement rate from UHS overestimates the actual rate, it
is still significantly lower than that from CSY. In 2002, for instance, the rate from UHS equals
61.8 percent, about 10 percentage points below that from CSY. This is in line with the view
that enterprises under-report wage bills.
The payment evasion leads to low pension coverage at the extensive margin. Panel B of
Figure 6 plots the aggregate replacement rate adjusted by pension coverage, computed as the
ratio of the number of workers contributing to the system to the total urban employment. The
adjusted replacement rate from CSY (the solid line) has a similar downward trend as that in
Panel A. The level is, however, less than half of the unadjusted rate because of the average
22The new reform of 2005 announced a targeted replacement rate of 59.2 percent. Although the rate is 0.7percentage points higher than the target of the 1997 reform, the actual replacement rate has been found to fall(e.g. Lin and Ding, 2007).
14
coverage rate of 44 percent in the 1992-2005 period. The downward trend of the replacement
rate from UHS in the 2002-2007 period disappears after being adjusted by pension coverage.23
This reflects a recent increase in the coverage rate, which rises from 45 percent in 2002 to 52
percent in 2007.
3 A Four-Period OLG Model
We have shown the dramatic changes in the age-earnings profiles in China over the period
associated with fast economic growth. The cohort effects on the starting earnings and the
flattening of the age-earnings profiles are particularly remarkable. We now formulate a simple
model in order to address two questions. First, how can economic growth lead to the observed
changes in the age-earnings profiles? Second, how these changes affect the aggregate saving
rate as well as the life-cycle saving pattern? We shall use a four-period OLG model with simple
analytical results, to make the underlying mechanism highly transparent. A full-fledged OLG
model will be presented in the next section, in which the observed age-earnings profiles are
imposed to deliver quantitative implications for saving.
The economy is populated by four overlapping generations with equal mass, referred to as
the young, middle-aged, old and retired. In each period, individuals, except for the retired,
supply one unit of labor inelastically. The after-tax earnings of the young, middle-aged and
old at period t are denoted by w1t , w2t and w
3t , respectively. The retirees at period t receive
pensions of pt. We abstract away taxes and, thus, how pensions are financed. Alternatively,
we may introduce a balancing government budget, allowing the tax rate to be endogenously
determined by pensions. Such an extension will not change our main results.
3.1 The Flattening of the Age-Earnings Profiles in a Growing Economy
Our first objective is to provide a simple theory for the flattening of both cross-sectional and
cohort-specific age-earnings profiles in a growth environment. The theory should also deliver
predictions consistent with other empirical findings documented above. We shall see that
increasing effi cient units of labor by cohorts can explain all the facts when the production has
a diminishing return to labor. Specifically, individuals born at t are endowed with ht effi cient
units of labor, which will hold constant over their life time. The aggregate production follows
Yt = AtHαt , α < 1,
23The pension coverage rate in UHS is computed as the ratio of the number of workers with positive pensioncontributions to the number of total workers.
15
where Ht stands for the aggregate effi cient units of labor and At is the aggregate production
effi ciency. α < 1 reflects the diminishing returns to labor. A competitive labor market implies
that
wit =αAt
H1−αt
ht+i−1, (3)
where αAt/H1−αt is the equilibrium wage rate per effi cient labor. At is set to a constant and
normalized to unity in the benchmark analysis for notational convenience. The assumption
will be relaxed below.
We compare age-earnings profiles in two regimes. The zero-growth regime is defined as the
steady state where ht+1 = ht = 1; i.e., each cohort has the same effi cient units of labor. As a
result, both the slopes of the steady-state cross-sectional and cohort-specific earnings profiles
are equal to 0. The growth regime is referred to as an economy where ht > ht−1; i.e., the new
cohort enters with more effi cient units of labor relative to the previous cohort. Since effi cient
units of labor for each cohort remain constant over the life cycle, income growth in this regime
is entirely driven by more effi cient units of labor brought by newly-born cohorts.
Let the economy stay in the zero-growth regime for t < T , and then switch to the growth
regime for t ≥ T . The aggregate human capital evolves such that HT−1 = 3, HT = 2 + hT ,
HT+1 = 1 + hT + hT+1 and Ht = ht−2 + ht−1 + ht for t ≥ T + 2. The associated individual
earnings profiles from period T − 1 to T + 1 are summarized in Table 2.
Table 2
T − 1 T T + 1young w1T−1 = α
H1−αT−1
w1T = αH1−αT
hT w1T+1 = αH1−αT+1
hT+1
middle-aged w2T−1 = αH1−αT−1
w2T = αH1−αT
w2T+1 = αH1−αT+1
hT
old w3T−1 = αH1−αT−1
w3T = αH1−αT
w3T+1 = αH1−αT+1
Two properties emerge from Table 2, which can directly be compared with the data. First,
the growth flattens the cross-sectional earnings profile since hT+1 > hT > 1. Intuitively, young
workers born at period T and afterwards are endowed with more effi cient units of labor and,
therefore, earn more relative to previous cohorts in the growth regime. Second, for young
workers at period T , w2T+1/w1T characterizes the slope of their cohort-specific earnings profile
between period T and T + 1, which is strictly lower than that for young workers at period
T − 1:w2T+1w1T
=
(2 + hT
1 + hT + hT+1
)1−α<
(3
2 + hT
)1−α=
w2Tw1T−1
. (4)
Similarly, for the middle-aged at period T , w3T+1/w2T characterizes the slope of their cohort-
specific earnings profile over period T and T + 1, which is strictly lower than that for the
16
middle-aged at period T−1 since w3T+1/w2T = w2T+1/w
1T and w
3T /w
2T−1 = w2T /w
1T−1. Therefore,
more effi cient units of labor brought by the young cohort lower the earnings of earlier cohorts,
resulting in the flattening of the cohort-specific earnings profile. Here, diminishing returns to
labor play a key role. If α = 1, the slope of the cohort-specific earnings profile will remain
unchanged. These two properties on the flattening of the age-earnings profiles are in line with
the facts observed in China.
We may also compare the slope of the cohort-specific earnings profile after period T with
that in the zero-growth regime. As will be shown below, such a comparison helps revealing
how the growth affects saving decision. Denote wit as the earnings as if the economy is in the
zero-growth regime, where the slope of the profile is governed by wit/wi−1t−1 = 1. Since
w3T+2w2T+1
=
(1 + hT + hT+1
hT + hT+1 + hT+2
)1−α< 1, (5)
w3T+1w2T
=w2T+1w1T
=
(2 + hT
1 + hT + hT+1
)1−α< 1, (6)
the cohort-specific earnings profiles in the growth regime for cohorts born at period T − 1 and
T are also flatter than the profiles in the zero-growth regime.
In addition to the flattening of age-earnings profiles, the model delivers another impli-
cation that can be confronted with the data. The entry-level earnings growth rates are
equal to hT (3/ (2 + hT ))1−α and (hT+1/hT ) ((2 + hT ) / (1 + hT + hT+1))1−α for period T and
T + 1, respectively, while the average earnings growth rates are equal to ((2 + hT ) /3)α and
((1 + hT + hT+1) / (2 + hT ))α, respectively. Since hT+1 > hT > 1, the increasing effi cient units
of labor by cohorts imply that the entry-level earnings grow faster than the average earnings.
This is indeed consistent with the empirical finding from Table 1: The starting earnings grow
at a rate of 12 percent, four-percentage-point higher than the average earnings growth rate.
The simple model has a counterfactual feature though: The middle-aged and the old earn
less as the economy grows due to the lower wage rate per effi cient unit of labor, while the
cross-sectional earnings profile shifts upwards in the data. The inconsistency can be fixed by
allowing At to grow exogenously at period T and afterwards.24 The earnings of the middle-
aged and the old will grow as the economy moves to the growth regime. In this case, the
flattening of the cohort-specific earnings profile requires a more restrictive condition:
(1 + hT + hT+1) / (2 + hT )
(2 + hT ) /3>
1 + χT+11 + χT
, (7)
24Appendix 6.1 provides a simple theory of endogenizing the growth of At by introducing human capitalexternality.
17
where χT+1 ≡ (AT+1/AT )1
1−α−1 stands for the adjusted technical progress rate. If χT+1 ≤ χT ,the condition is reduced to
hT+1 >1 + hT + h2T
3,
which must hold true since hT+1 > hT . In other words, a continuous growth of effi cient units of
labor by cohorts, together with a non-accelerating aggregate productivity growth, can account
for the observed flattening of the cohort-specific earnings profile. Similarly, (5) and (6) should
be rewritten as
HT+2
HT+1=
hT + hT+1 + hT+21 + hT + hT+1
> 1 + χT+2, (8)
HT+1
HT=
1 + hT + hT+12 + hT
> 1 + χT+1. (9)
So, if the aggregate effi cient units of labor outstrips the aggregate productivity, the earnings
profiles in the growth regime for cohorts born at T − 1 and T will be flatter than the ones in
the zero-growth regime.
The above findings are summarized in Proposition 1.
Proposition 1 Consider an economy that is in the zero-growth regime for t < T and switches
to the growth regime afterwards, with ht > ht−1 and At ≥ At−1 for t ≥ T . Assume that (7),
(8) and (9) hold true. Then,
(i) The cross-sectional earnings profile shifts upwards and becomes flatter for t ≥ T .(ii) Cohorts born in period T − 1 and T face flatter cohort-specific earnings profiles from
period T − 1 to T + 1.
(iii) The cohort-specific earnings profiles in the growth regime for cohort born at period
T − 1 and T are flatter than the ones in the zero-growth regime.
(iv) The entry-level earnings grow faster than the average earnings do.
To understand the underlying mechanism of the flattening of age-earnings profiles, we
formalize how increasing effi cient units of labor by cohorts shape individual earnings growth
under a production technology with diminishing returns. Despite highly hypothetical, the
model generally captures the stylized features of the age-earnings profiles we observe from the
fast-growing economy of China described in Section 2.3.
18
3.2 Saving Decision
We now examine how the growth affects saving decision. The preferences of a young individual
born at period t are represented by
4∑i=1
βi−1u(cit+i−1
), (10)
where u (·) is a standard twice differentiable and strictly concave utility function, β denotesthe discount factor, and cit stands for the consumption of an individual of age i at period t.
The young individual chooses the optimal saving decision by maximizing (10) subject to her
intertemporal budget constraint:
4∑i=1
cit+i−1
(1 + r)i−1=
3∑i=1
wit+i−1
(1 + r)i−1+
pt+3
(1 + r)3,
where r is the interest rate and pt+3 stands for pension benefits of an individual born at period
t. Denote ait the asset of age i at the beginning of period t. Individuals are born with no assets;
i.e., a1t = 0.
For expositional ease, we restrict our attention to the case with β = 1 + r = 1, where
the Euler equation implies an equalized consumption flow over the life time. In the technical
appendix, which is available from our website, we relax the assumption and show that our main
results are robust to a large set of parameter values. Moreover, to focus on the role of earnings
profiles, we assume away within-cohort heterogeneity and let pt = 0 ∀t in the benchmark forsimplicity. These assumptions will be relaxed below, to understand how changes in group-
specific age-earnings profiles and pensions influence the aggregate saving rate as well as the
saving rates over the life cycle.
The assumption β = 1 + r = 1 implies the following age-saving profile:
sr1t =3
4− 1
4
(w2t+1 + w3t+2
w1t
), (11)
sr2t =3
4− 1
4
(w1t−1 + w3t+1
w2t
), (12)
sr3t =3
4− 1
4
(w1t−2 + w2t−1
w3t
), (13)
where srit denotes the saving rate of age i at period t. These results are straightforward and
standard. In particular, (11), (12) and (13) show that saving rates increase in the current
earnings and decrease in the past and future earnings. In other words, the age-saving profile
appears to “track”the age-earnings profile for consumption smoothing.
19
3.3 Growth and Saving
Whether the growth can be anticipated affects saving decisions when the economy switches to
the growth regime. An anticipated earnings growth provides the incentive of borrowing against
the future, and a realization of the anticipated growth will naturally increase saving rates. To
make the analysis stark, we focus on how an unanticipated growth affects saving decision. In
line with the above set-up, the economy is in the zero-growth regime for t < T , where the
asset-earnings ratios follow (11) and (12):
a2tw2t
=1
4,
a3tw3t
=1
2. (14)
Here, a2t and a3t denote the assets of the middle-aged and the old at the beginning of period t,
respectively. Following Proposition 1, the unanticipated growth at period T leads to
wiT > wiT−1 = wiT , (15)
w2Tw1T
<w2T−1w1T−1
= 1,w3Tw2T
<w3T−1w2T−1
= 1, (16)
w2T+1w1T
<w2T+1w1T
= 1,w3T+2w2T+1
<w3T+1w2T
<w3T+1w2T
= 1. (17)
(15) shows an upward shift in the cross-sectional earnings profile. The profile turns flatter, as
indicated by (16). (17) suggests that the cohort-specific earnings profiles in the growth regime
are flatter than the ones in the old regime. All the properties come from Proposition 1.
Define ∆srit ≡ srit− srit−1 the increase of saving rate of age i over period t and t−1. When
the unanticipated earnings growth arrives at period T , we have
∆sr1T =1
4
(1−
w2T+1w1T
)+
1
4
(1−
w3T+2w1T
)︸ ︷︷ ︸the effect of the slope of the earnings profile
> 0. (18)
The inequality in (18) comes from (17). The flattening cohort-specific age-earnings profile
implies a lower earnings growth rate over the lifetime, which leads to a high saving rate. We
referred to this as the effect of the slope of the earnings profile.
The increase in the saving rate of the middle-aged is equal to
∆sr2T =1
12
(1− w2T
w2T
)︸ ︷︷ ︸
the effect of current earnings
+1
3
(1−
w3T+1w2T
)︸ ︷︷ ︸
the effect of the slope of the earnings profile
> 0, (19)
where (14) is used for substituting out a2T /w2T . The inequality in (19) comes from (15) and
(17). Compared with the middle-aged in the zero-growth regime, the period-T middle-aged
20
would like to increase their saving rate for two reasons. First, their current earnings, w2T , are
higher than their anticipated earnings, w2T . Holding the age-earnings profile unchanged, this,
referred to as the effect of current earnings, would increase the saving rate.25 Second, the same
effect of the slope of the earnings profile as that in (18) yields a higher saving rate.
Finally, ∆sr3T can be written as
∆sr3T =1
4
(1− w3T
w3T
)︸ ︷︷ ︸
the effect of current earnings
> 0, (20)
where (14) has been used for substituting out a3T /w3T . The inequality in (20) comes from
(15). The old at period T increase their saving rate simply because they earn more than their
ancestors. The effect of the slope of the earnings profile does not apply to the old since they
receive zero earnings after retirement.
The main results are summarized in Proposition 2.
Proposition 2 Consider an economy that is in the zero-growth regime for t < T and switches
unanticipatedly to the growth regime afterwards, with ht > ht−1 and At ≥ At−1 for t ≥ T .
Assume that (7), (8) and (9) hold true, and that β = 1 + r = 1. Then,
(i) ∆s1T > 0, ∆s3T = 0 and ∆s3T > 0.
(ii) The aggregate saving rate increases at period T .
The above highly stylized four-period model illustrates a key implication from the flattening
of cohort earnings profiles. ∆sriT > 0 for all i implies that ∆srT > 0; i.e., the aggregate saving
rate will increase when the economic growth occurs at period T .26 This sharply contrasts the
prediction of the representative agent model that the aggregate saving rate will fall at period
T if the future growth is suffi ciently high.
3.3.1 Two Extensions
We have shown that a flattening of the cohort-specific age-earnings profile can explain the first
two empirical facts on saving documented in Section 2.2. We now extend the above framework
to incorporate within-generation heterogeneity, to shed some lights on the third empirical fact
on saving. Denote wijt as the wage of an individual of age i with education level j. The
assumptions of (15) and (17) are maintained for all j. Without loss of generality, let wijt be
25Note that a zero asset position will shut down such an effect. In other words, after controling for the cohortage-earnings profile, the saving rate will be independent of the current earnings when a2T = 0.26 Including dissavings of the retirees from aggregate savings will lead to the same result since their dissavings
remain unchanged from period T − 1 to T .
21
increasing in j. If j refers to education levels, the increasing wijt in j will capture the return
to education. We further assume that wijT /wijT = wijT /w
ijT−1 is increasing in j, while w
2jT+1/w
1jT ,
w3jT+2/w1jT and w3jT+1/w
2jT are all decreasing in j. The increasing wijT /w
ijT (or equivalently,
wijT /wijT−1) implies a faster earnings growth as j increases. The decreasing w
2jT+1/w
1jT , w
3jT+2/w
1jT
and w3jT+1/w2jT imply a more pronounced flattening of the cohort earnings profile as j increases.
These assumptions are a simple reflection of the two empirical observations illustrated by
Table 1 in Section 2.3.1. First, the higher growth of the starting earnings of college graduates,
captured by the larger κ1 Column (4), suggests that they have a higher wijT /w
ijT . Second,
the cohort earnings profile of college graduates is flatter than that of non-college graduates
according to the larger absolution value of κ3 in Column (4). Under these assumptions, the
model predicts an increasing ∆sijT in j, which is consistent with the third empirical fact on the
Chinese household saving rates.
Another important extension is to introduce a pension system. The facts presented in
Section 2.4 shows that the reform maintains pension benefits for the retired but cuts benefits
for the working generations. Assume that the reform occurs at the beginning of period T . For
the cohort born at period T − 2 (the old at period T ), their pension after the reform will be
less than the anticipated pension from the old system. This provides the incentive for the old
to increase their saving rate. We shall see in Section 4 that a full-fledged quantitative model
with the observed changes in pension benefits can match the significant increase in the saving
rate of the old in the data.
3.4 Myopic Expectation
So far we have implicitly assumed that individuals hold perfect foresight on their future earnings
after the economy takes off at period T . Although theoretically appealing, perfect foresight
may be far from the way individuals form their expectations in a rapidly-changing economy like
China. With a former central-planned economy transformed into a rather sophisticated market
economy in less than two decades, information about future earnings must be limited, while
past information quickly becomes obsolete. Individuals, therefore, may naturally rely more on
the current information to form expectations. In fact, a number of studies have even found
empirical evidence supporting myopic behaviors in developed economies. Reimers and Honig
(1996) provides an example. They show that male workers in the U.S. respond only to current
pension benefits and do not take into account changes in future benefits. For these concerns,
this subsection adopts myopic expectation, as a robustness check for the above findings.
Throughout the paper, myopic expectation is referred to as the case in which individuals use
22
the current cross-sectional age earnings profile to forecast their future earnings. Specifically,
denoting Et[wit+k
]as the myopic expectation on wit+k at period t, we have
Et[wit+k
]= wit. (21)
Assume (15) and (16) based on the cross-sectional evidence on the age-earnings profile in
Figure 4. It is immediate that
∆sr1T =1
4
(1− w2T
w1T
)+
1
4
(1− w3T
w1T
)︸ ︷︷ ︸
the effect of the slope of the earnings profile
> 0, (22)
∆sr2T =1
12
(1−
w2T−1w2T
)︸ ︷︷ ︸
the effect of current earnings
+1
3
(1− w3T
w2T
)︸ ︷︷ ︸
the effect of the slope of the earnings profile
> 0. (23)
Here, we abstract away within-cohort heterogeneity and pension for simplicity. The increase
in the saving rate of the old under myopic expectation is identical to (20) since expectation
becomes irrelevant for those who will retire in one period. Despite the different ways of forming
expectations, (22) and (23) delivers essentially the same results as (18) and (19). The reason
is simple: The cross-sectional age-earnings profile also features a flattening process similar to
the cohort-based profile. Therefore, the age-saving profile will shift upwards, and the young
will increase their saving rate due to the effect of the slope of the earnings profile, irrespective
of perfect foresight or myopic expectation. The main findings are thus robust to alternative
ways of expectations.27
We have shown that in a highly stylized life cycle framework, higher starting earnings,
together with a flattening of the age-earnings profile, can not only increase the aggregate saving
rate, but result in a U-shape increase in the age-specific saving rates. Moreover, the increase
in the saving rate is larger for individuals experiencing a more pronounced flattening of the
earnings profile. The next section will use a more sophisticated model, to assess quantitatively
how the observed changes in the earnings profiles in China would affect household savings at
the aggregate level and over the life cycle.
4 A Full-Fledged OLG Model
In this section, we incorporate changes in the age-earnings profiles observed in China to an
otherwise standard life-cycle model. Our aim is to provide a quantitative assessment on the
27We can further extend the model by introducing within-cohort heterogeneity and pension in a way similarto those under perfect foresight. The results are obvious and, hence, omitted.
23
extent the observed facts can explain the Chinese household saving puzzle over the period
1992 to 2007 (including the surge of the aggregate household saving rate and the U-shaped
increase in the age-specific saving rates). Given such a goal, the above four-period OLG model,
where one period corresponds to twenty years, would be inadequate. Therefore, we extend the
model to a full-fledged OLG model, where one period corresponds to one calendar year and
individuals live up to 75 periods after entering labor market.
Individuals start working at age 1 and retire at age Tr. Each Individual receives an
endowment of human capital at birth, and supplies one unit of labor inelastically in each
period. We use wijt to denote the after-tax earnings of an individual of age i with endowment
j at period t. Similarly, pijt stands for the pensions of a retiree of age i with endowment j at
period t. Lifetimes are uncertain. Let πi denote the unconditional survival rate up to age i,
with π1 = 1. The survival rate conditional on being alive at age i− 1 is thus equal to πi/πi−1.
4.1 Perfect Foresight
To compute individuals’optimal saving rates, we need to specify how the expectations on future
earnings are formed. There are two alternative approaches in the literature of life cycle analysis:
adopting either perfect foresight (e.g., Auerbach and Kotlikoff, 1987) or myopic expectation
(e.g., Davies and Whalley, 1991). In this subsection, we assume that, as in the four-period
model, individuals hold perfect foresight on their earnings, which are drawn from the estimated
cohort-based age earnings profiles.28 An alternative myopic expectation approach will be taken
as a robustness check.
Preferences for an individual of age i = n with endowment j are represented by
T∑i=n
δiπiπnu(cijt+i−n
), (24)
where δi ≡ Πiτ=nβτ and βτ denotes the subjective discount factor at age τ . We allow the
age-specific discount factor to incorporate time-invariant life-cycle elements affecting saving
decision. In particular, βτ is calibrated to match the age-saving profile in 1992. The individual
worker chooses the optimal saving decision by maximizing (24) subject to the following budget
28 Individuals can also foresee perfectly the evolution of demographic structures to form expectations on theirpension benefits.
24
constraint:
T∑i=n
cijt+i−n
(1 + r)i−n= I
(Tr∑i=n
wijt+i−n
(1 + r)i−n+
T∑i=Tr+1
pijt+i−n
(1 + r)i−n
)(25)
+ (1− I)T∑i=n
pijt+i−n
(1 + r)i−n+ (1 + r) aijt ,
where I is an indicator function with I = 1 for n ≤ Tr and I = 0 otherwise, and aijt denotes
the asset position of an individual with age i and endowment j at period t.
Following the documentation of the Chinese pension system and its reforms in Section 2.4,
there are three types of cohorts when the reform took place in 1997. We assume that for xinren
(i.e., cohorts enter into the labor market after 1997), their pension benefits follow the new rules
specified by Documents 26 and 38, adjusted by the actual contribution rates. Specifically,
their annual pension benefits are equal to the sum of 20 percent of the average wages (the first
pillar) and the individual account balance at retirement divided by 10 (the second pillar). In
Document 38, workers contribute 8 percent of their earnings to their individual accounts. The
return to individual accounts is equal to the interest rate, r. For notational convenience, we
define
Yt ≡∑i
∑j
φ (i, j, t)wijt (26)
as the average wages at period t, where φ (i, j, t) denotes the population density for age i group
j at period t. In addition, define
W ijt ≡
1
Tr
t−i+Tr∑τ=t−i+1
Rτ−(t−i+1)wτ−t+ijτ (27)
as the average life-time earnings of workers j born at t − i + 1. Pension benefits can thus be
written as
pijt = θ1 · 20% · Yt + θ2 · 8% ·W ijt ·
Tr
10, (28)
where θ1 and θ2 denote the adjustment rates for the first and second pillars, respectively,
according to the actual contribution rates.
For laoren (cohorts retired before 1997), their pension is equal to pijt + τ , where pijt follows
(28). τ captures the discrepancy between laoren’s pension in the old system and their pension in
the new system as if they were xinren. Note that for simplicity, we assume τ to be independent
of cohorts and years. Nevertheless, with the presence of pijt , laoren’s pension also varies across
cohorts and years. This reflects the annual adjustment according to wage growth and inflation,
which are assumed to affect laoren’s and xinren’s pensions by an equal amount.
25
Zhongren (cohorts between xinren and laoren) can be further classified into two groups. For
zhongren aged 45 and below in 1997, they can work for at least fifteen years before retirement
and become fully entitled to the pension of the new system. In practice, they receive virtually
zero transitional pension. So, we treat them as xinren and allow their pension to follow (28).
For zhongren aged above 45 in 1997, their pension is set to pijt +x · τ , where x equals 1 for the
cohort aged 60 in 1997, decreases linearly for cohorts aged between 46 and 59, and finally falls
to zero for the cohort aged 45 in 1997. The cohort-specific component, x · τ , can be considereda transitional pension that smoothens the gap between loaren’s and xinren’s pensions.
Denote srijt as the saving rate of individuals with age i and type j at period t. The aggregate
saving rate can be computed by aggregating individual saving rates over i and j:
srt =
∑Tri
∑j φ (i, j, t) srijt w
ijt∑Tr
i
∑j φ (i, j, t)wijt
. (29)
To be consistent with the data, we exclude the saving rates of the retirees. The cross-sectional
age-saving profile at period t contains the average saving rates of individuals of age i ∈ [1, T r]:
srit =
∑j φ (i, j, t) srijt w
ijt∑
j φ (i, j, t)wijt. (30)
4.1.1 Benchmark Parameterization
Agents enter the economy at age 25 and live until 100 (N = 76). Let Tr = 36 as the retirement
age for male workers in China is 60. The annual interest rate is set to 3 percent, which is slightly
higher than the government bond returns in the period of 1992-2007 but much lower than the
stock market returns over the period. We assume a log preference so that the intertemporal
elasticity of substitution is equal to one. The survival rates are obtained by the actual age-
conditional survival rates from the 2005 population consensus (China Statistical Yearbook,
2006). The population density, φ (i, j, t), follows the actual density in the UHS data. We let
φ (i, j, t) = φ (i, j, 2007) for t > 2007.
The age-specific discount factors, βi, are calibrated to match the initial age-saving profile.
Since the saving rates of retirees are excluded, we simply let βi = βTr for i > Tr and choose
βTr such that the initial saving rate for workers at the retirement age is equal to that in the
data. βi for i < Tr can thus be calibrated recursively. Figure A-1 in the appendix plots the
calibrated age discount factors, with a mean of 0.978. Alternatively, we may assume an age-
independent β and calibrate it to the initial aggregate household saving rate. This would lead
to essentially the same increase in the age-specific saving rates, though the initial age-saving
profile in data cannot be perfectly matched.
26
The cohort-specific age-earnings profiles follow (1), with α4 = 0 and all other coeffi cients
being equal to the estimates in column (1) of Table 1. Two remarks are in order. First, we
abstract away within-cohort heterogeneity in the benchmark parameterization. Second, α4 = 0
implies no aggregate earnings shocks, which are consistent with our model setup. Moreover, it
helps to isolate the effect of the growth on saving decision. The estimated coeffi cients are also
used to predict future earnings after 2007. The out-of-sample projection suggests the economy
would continue to grow for years to come: The predicted aggregate earnings growth rate will
be above 5 percent until 2038. Pension benefits pijt are computed by according to (28). Since
we do not have the complete life-time earnings data for those who entered the labor market
before 1992. only the earnings after 1992 are used to compute their average life-time wages.
Section 2.4 has presented the evidence of the payment evasion. In particular, enterprises
contribute only 5 percent of wages, which is one-fourth of the offi cial rate. We then set the
adjustment rate for the first pillar, θ1, to 0.25. Similarly, since the actual contribution rate of
workers is about half of the offi cial rate, θ2 is set to 0.5. If wage growth is equal to the interest
rate, (28) implies a replacement rate of 19 percent for xinren. τ is calibrated such that the
aggregate replacement rate equals the rate adjusted by pension coverage of 37 percent in 1992
(Panel B of Figure 6).
Finally, we back out the initial age asset distribution based on the main assumption that the
cross-sectional age-earnings and age-saving profiles before 1992 are equal to the 1992 profiles
adjusted by the ratios of the year-t aggregate household earnings and saving rate to the 1992
income and saving rate, respectively. The aggregate household saving rate is available from
CSY for the 1982-1991 period. We assume that the saving rate before 1982 equals 12 percent,
the average rate in the 1982-1991 period. Household earnings data are not available. We
approximate earnings growth by disposable income growth, which is available from CSY for
the 1982-1991 period. The annual household earnings growth is set to 2 percent for periods
before 1982. Under these assumptions, the 1992 asset-earnings ratio starts from zero at age 25
and peaks at 2.5 at retirement.
4.1.2 Results
The aggregate household saving rate, srt, is plotted in Panel A of Figure 7. Solid and dotted
lines represent the simulated results and actual data, respectively. The model predicts a take-
off of the aggregate saving rate since 1992, with a trend similar to that in the data. Note that
subjective discount factors are chosen to match the initial age-saving profile and, hence, the
initial aggregate saving rate. However, the dynamics of the aggregate saving rate is entirely
27
endogenous. The rise in the saving rate is quantitatively large. The aggregate saving rate
increases by 10.1 percentage points, only one percentage point lower than the increase in the
data. Panel B displays the increase in the age-specific saving rates, sri2007− sri1992. Consistentwith the argument in Section 3, the model indeed features a U-shaped increase that matches
the data (dotted line) reasonably well. The young increase savings due to the flattening of
their age-earnings profile, while the old increase savings partly due to the increased earnings,
and partly due to the less generous pension system.
[Insert Figure 7]
We then allow within-cohort heterogeneity by introducing different education endowments
at birth.29 Let j ∈ {H,C}, representing high-school-and-below and college-and-above educatedindividuals. Their age-earnings profiles follow (2), with α4 (j) = 0 and all the other coeffi cients
being equal to estimates in Columns (3) and (4) of Table 1. We maintain the initial asset-
earnings ratios in the benchmark parameterization for both non-college and college graduates,
and recalibrate βi to match the initial age-saving profile. This yields a mean of βi of 0.971.
The dashed lines in Figure 7 plot the simulation results, which are similar to those in the
benchmark model. Figure 8 shows that college graduates increase their saving rate much
more than non-college graduates do. This is mainly driven by the more flattened age-earnings
profiles for college graduates. The coeffi cient governing the flatterning of the profile, κ3, is
equal to −0.0019 for college graduates, more than double than that for non-college graduates.
The simulated increase in the saving rate of non-college graduates is broadly in line with
the data (the dotted line), while college graduates increase their saving rate too much in the
simulation. Note that the simulated results is based on inidvidual saving decision, while the
saving data are available only at the household level. We will use family education structures
to simulate household saving rates in the next section, which will match better the increase in
the age-specific saving rates in the data.
[Insert Figure 8]
We now check the parameter sensitivity of the above findings. First, note that by calibrat-
ing age-specific discount rates, βi, to match the initial age-saving profile, the intertemporal
elasticity of substitution will have no effects on the increase of saving rates. Changing σ only
leads to different calibrated values of βi. For instance, lowering σ from 1 to 0.5 yields a mean
of recalibrated βi of 0.96. Thus, we analyze sensitivity to the remaining two key parameters:
29The initial age asset distribution is assumed to be the same as that in the benchmark case.
28
The adjustment parameters of the pension system, θ1 and θ2. Specifically, we use the model
with no education heterogeneity as the benchmark case and perturb one of the parameters in
each experiment. The first and second experiments increase θ1 and θ2 by half, respectively.
The results are plotted in Figure 9. The higher replacement rates lead to the lower saving
rates. However, our main findings are robust to these alternative parameterizations.
[Insert Figure 9]
Our quantitative analysis shows that, once incorporating the observed changes in age-
earnings profiles, an otherwise standard life cycle model can account well for the recent surge
in household saving as well as the U-shaped increase in the age-specific saving rates. However,
it is also worth pointing out that the model is less successful in matching the rise in the saving
rate of college graduates. Note that the model presented above is very simple and abstracts
away household characteristics. The fitness will be improved substantially when adjustments
are made for controlling family structures (to be written).
4.2 Myopic Expectation
This subsection adopts myopic expectation as an alternative approach. In the context of the
present paper, following (21), myopic expectation is referred to as the case in which individ-
uals use the current cross-sectional age-earnings profile to forecast their future earnings. In
other words, everyone expects that the current cross-sectional age-earnings profile will remain
unchanged indefinitely. Consequently, any change in the profile in the future will be perceived
as an unanticipated permanent one.
We further assume that individuals hold a myopic expectation on pensions; i.e., they expect
future their pension benefits to be the same as those for the current retirees. The myopic
expectation on pension benefits follows
Et
[pijt+i−n
]= pijt . (31)
In principle, individuals can form forward-looking expectations on their pensions by perceiving
payment rules of the system. However, as discussed in Section 2.4, the Chinese pension system
has undergone a series of reforms, transiting from the original work-unit-based system to the
current PAYGO mixed with individual accounts. The dramatically changing pension schemes
provide additional justification for the myopic expectation in (31).30
30Michaud and van Soest (2006) show that even in the U.S., workers tend to misperceive the complicatedrules of the social security system.
29
Finally, we assume that the current pension benefits are evenly distributed across retirees
and are equal to the average wages multiplied by the aggregate replacement rate adjusted by
pension coverage:
pijt = ψt · Yt. (32)
4.2.1 Parameterization
Following the same procedure, we calibrated the age-specific discount factors, βi, to match the
initial age-saving profile. The mean of βi is equal to 0.968. Let wijt and ψt be equal to the
observed earnings and the adjusted aggregate replacement rates. As before, we consider two
model economies. The first model has no within-cohort heterogeneity, where wijt equals the
average wage of age i, and the second one introduces different education endowments. All the
other parameter values are identical to those in Section 4.1.1 under perfect foresight.
4.2.2 Results
The aggregate household saving rate simulated from the first model with no education hetero-
geneity is plotted by the solid line in Panel A of Figure 10. The simulated saving rate increases
by 9 percentage points, two percentage points lower than the increase in the data. Panel B
displays the increase in the age-specific saving rates from 1992 to 2007, which also features a
U-shape. The reason is identical to that in the case of perfect foresight. The flattening of the
cross-sectional earnings profile encourages the young to save more, while the old increase saving
for the reduction in pension benefits. We then allow within-cohort heterogeneity by introduce
different education endowments at birth, with recalibrated βi. The dashed lines in Figure 10
plot the simulation results. The basic features carry over to the second model, though the
simulated increase in the saving rate of the young is less dramatic. The reason can be seen
from Figure 4 and 5. The flattening of the cross-sectional earnings profile in Figure 4 is partly
driven by the fact that younger cohorts are better educated. Controlling for education leads
to a less pronounced flattening of the profile (see Figure 5), which implies a lower saving rate
of the young.
[Insert Figure 10]
5 Concluding Remarks
The life cycle and permanent income hypotheses represent a simple and elegant paradigm
that can be used to understand the determinants of consumption and saving decisions. While
30
the theory has succeeded in unifying a wide range of diverse phenomena, it is diffi cult to
reconcile with the positive relationship between saving and income growth found in fast growing
economies or in cross-country regression analysis: Anticipating higher future income, forward-
looking consumers with standard utility should save less, not more.
This paper addresses theoretically and empirically the puzzle in the context of the fast
growing economy of China. Our analysis suggests a new channel for growth to affect saving
through the age-earnings profile. Using a unique national household survey covering the period
1992-2007, instead of observing stationary age-earnings profiles as assumed either explicitly or
implicitly in past studies, we found that rapid income growth in China has dramatically raised
the entry-level earnings of successive cohorts. We also found that the cohort-specific age-
earnings profiles have become flattened. These observations can naturally occur in the growth
featuring a continual entry of young workers who are more productive than earlier cohorts.
Our quantitative analysis showed that an otherwise standard life cycle model can account well
for the recent surge in the aggregate household saving as well as the U-shaped increase in the
age-specific saving rates, once we incorporated changes in the age-earnings profiles and pension
benefits in China during the 1992-2007 period.
A rising saving rate is a widely observed phenomenon in fast growing economies, including
the newly industrialized countries in East Asia and more recently the BRICs. Whether the
mechanism proposed in this paper could well explain the rise in saving in other high-growth
environments remains a challenge to validate. We will leave the question for future research.
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6 Appendix
6.1 Endogenizing the Growth of A
We assume that the technology level, At, is determined by the aggregate effi cient units of labor,
or human capital, Ht:
At = H1−α+γt .
Here, 1−α+ γ measures the externality of human capital. Denote ht as the human capital of
an individual born at period t. Individual earnings are thus equal to
wit = αHγt h
it−i+1. (33)
Note that αHγt is the equilibrium wage rate per unit of human capital. We assume γ > 0 to
ensure that the wage rate is increasing in the aggregate human capital.
34
In the zero-growth regime, ht is constant and normalized to unity. The cohort size is
also nomalized to unity such that Ht = 1. So, both the slopes of the cross-sectional and the
cohort-specific earnings profiles are equal to 0.
When the economy switches to the growth regime, newly-born cohorts enter the labor
market with higher human capital. Specifically, the cohort born at period t is associated with
human capital ht, with ht > 1 and ht+1 > ht, for t ≥ T . The aggregate human capital followsHT = 2 + hT , HT+1 = 1 + hT + hT+1 and Ht = ht−2 + ht−1 + ht for t ≥ T + 2. Individual
earnings profiles are summarized in Table A-2.
Table A-2T − 1 T T + 1
young w1T−1 = αHγT−1 w1T = αHγ
ThT w1T+1 = αHγT+1hT+1
middle-aged w2T−1 = αHγT−1 w2T = αHγ
T w2T+1 = αHγT+1hT
old w3T−1 = αHγT−1 w3T = αHγ
T w3T+1 = αHγT+1
The flattening of the cross-sectional earnings profile, (16), is immediate since hT > 1. The
slopes of the cohort-specific earnings profile for the young and the middle-aged are equal to
(HT−1/HT )γ and (HT /HT+1)γ for cohorts born at period T − 1 and T , respectively. So, we
need2 + hT
3>
1 + hT + hT+12 + hT
⇒
hT+1 >1 + hT + h2T
3
to have a flattened earnings profile for later cohorts. The exactly same argument applies for
the slopes of the earnings profile for cohorts born at period T −2 and T −1, respectively. Note
that hT+1 > hT is suffi cient for the above condition. (7) will be no longer required. In other
words, a continuous growth of human capital embodied in the new cohorts alone can account
for the observed flattening of the cohort-specific earnings profile.
Finally, note that
w2T+1w1T
=w3T+1w2T
=
(HT
HT+1
)γ,w3T+2w2T+1
=
(HT+1
HT+2
)γ.
It is immediate thatHT+1
HT=
1 + hT + hT+12 + hT
> 1,
HT+2
HT+1=hT + hT+1 + hT+2
1 + hT + hT+1> 1,
which ensure the validity of (8) and (9).
35
The above model can not only provide a microfoundation for the flattening earnings profiles
in the four-period model, but also deliver a key prediction that is in line with our empirical
finding. Suppose that we observe only individual earnings from period T − 1 to period T + 1.
36
Figure 1 The Aggregate Urban Household Income and Saving
1985 1990 1995 2000 20052000
4000
6000
8000
10000
12000
14000
year
inco
me
(in 2
007
Yua
n)Panel A: Urban Household Disposable Income (in 2007 Yuan)
1985 1990 1995 2000 20055
10
15
20
25
30
year
savi
ng ra
te (i
n pe
rcen
t)
Panel B: The Aggregate Urban Household Saving Rate
CSYUHS
Figure 1: Panel A plots the Chinese urban household disposable income from 1982 to 2007 in 2007 Yuan. Data source: China Statistical Yearbook (CSY), various issues. Plot B plots the Chinese urban household saving rate. The solid and dotted lines stand for data from CSY and UHS, respectively. Saving rate is equal to (disposable income – consumption expenditure)/disposable income.
Figure 2 Cross-Sectional Age-Saving Profiles
25 30 35 40 45 50 5510
15
20
25
30
35
40
age
savi
ng ra
te (p
erce
nt)
Panel A: Average Saving Rates by Age of Household Head
1992-19932006-2007
25 30 35 40 45 50 555
10
15Panel B: Increase of Saving Rates by Age of Household Head
age
incr
ease
of s
avin
g ra
te
Figure 2: The dotted and solid lines in Panel A refer to the cross-sectional age-saving profiles averaged over 1992-1993 and 2006-2007 (weighted by the number of observations in each age cell), respectively. The line in Panel B plots the increase of the age-specific saving rate from 1992-1993 to 2006-2007 (namely, the difference between the two profiles in Panel A). Three-age moving average is used to smooth the age-saving profiles.
Figure 3 Cross-Sectional Age-Saving Profiles by Education
30 40 5010
15
20
25
30
35
40
age
savi
ng ra
te (p
erce
nt)
Panel A: Non-College Graduates
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20
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30
35
40
age
savi
ng ra
te (p
erce
nt)
Panel B: College Graduates
30 40 504
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age
incr
ease
of s
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g ra
te
Panel C: Non-College Graduates
30 40 50
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10
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14
age
incr
ease
of s
avin
g ra
tePanel D: College Graduates
1992-19932006-2007
1992-19932006-2007
Figure 3: The dotted and solid lines refer to the cross-sectional age-saving profiles averaged over 1992-1993 and 2006-2007 (weighted by the number of observations in each age cell), respectively. Three-age moving average is used to smooth the age-saving profiles. Panel A and B plot the age-saving profile for households with household head who is non-college graduate (Panel A) and college graduate (Panel B). Panel C and D plot the increase in the age-specific age rate from 1992-1993 to 2006-2007 for households with household head who is non-college graduate (Panel C) and college graduate (Panel D).
Figure 4 Cross-Sectional Life-Cycle Earnings Profiles
25 30 35 40 45 50 55-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
age
log
rela
tive
earn
ings
19922007
Figure 4: The dotted and solid lines refer to the cross-sectional age-earnings profiles in 1992 and 2007, respectively. Relative earnings are computed as the ratio of earnings to earnings at age 42.
Figure 5 Cross-Sectional Age-Earnings Profiles by Education
25 30 35 40 45 50 55-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
age
log
rela
tive
earn
ings
Panel A: Non-College Graduates
19922007
25 30 35 40 45 50 55-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
age
log
rela
tive
earn
ings
Panel B: College Graduates
19922007
Figure 5: The dotted and solid lines refer to the cross-sectional age-earnings profiles in 1992 and 2007. Panel A and B plot the age-earnings profile for households with household head who is non-college graduate (Panel A) or college graduate (Panel B). Relative earnings are computed as the ratio of earnings to earnings at age 42 within each group.
Figure 6 The Aggregate Replacement Rate
1992 1994 1996 1998 2000 2002 2004 200650
60
70
80
90
year
the
repl
acem
en ra
te (p
erce
nt)
Panel A: The Aggregate Replacement Rate
UHSCYS
1992 1994 1996 1998 2000 2002 2004 200620
25
30
35
40
year
the
repl
acem
en ra
te (p
erce
nt)
Panel B: The Aggregate Replacement Rate Adjusted by Pension Coverage
UHSCYS
Figure 6: The solid line in Panel A is the aggregate replacement rate as the ratio of pensions for retired and resigned persons per capita over average wage of staff and workers. Data source: China Statistical Yearbook (2006). The dotted line in Panel A is the aggregate replacement rate as the ratio of average pensions per pension beneficiary over average earnings per worker. Data source: UHS. The solid and dotted lines in Panel B are the aggregate replacement rate adjusted by pension coverage in CSY and UHS, respectively. The adjusted rate is equal to the unadjusted rate in Panel A multiplied by the pension coverage rate.
Figure 7 Simulation Results under Perfect Foresight
1992 1994 1996 1998 2000 2002 2004 2006 200816
18
20
22
24
26
28
year
perc
ent
Panel A: Aggregate Saving Rates
model-1model-2data
25 30 35 40 45 50 55 606
8
10
12
14
16
age
perc
ent
Panel B: Increase of Saving Rates by Age from 1992 to 2007
model-1model-2data
Figure 7: Solid and dashed lines are the simulated results from model-1 (no within-cohort heterogeneity) and model-2 (within-cohort heterogeneity of education levels), respectively. Panel A and B plot the increase of saving rate at the aggregate level and over the life cycle, respectively, under the benchmark parameterization (see the text for details). Dotted lines plot the increases in the data.
Figure 8 The Simulated Increase of the Age-Specific Saving Rate
25 30 35 40 45 50 55 604
6
8
10
12
14
age
perc
ent
Panel A: Non-College
modeldata
25 30 35 40 45 50 55 60
8
10
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14
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18
20
age
perc
ent
Panel B: College
modeldata
Figure 8: Solid lines the simulated results from the extended model containing within-cohort heterogeneity of education levels, under the benchmark parameterization (see the text for details). Panel A and B plot the increase of saving rate for non-college and college graduates, respectively. Dotted lines plot the increases in the data.
Figure 9 Robustness Check under Perfect Foresight
1992 1994 1996 1998 2000 2002 2004 200615
20
25
30
year
perc
ent
Panel A: Aggregate Saving Rate
model-1experiment 1experiment 2
25 30 35 40 45 50 55 608
10
12
14
16
age
perc
ent
Panel B: Increase of the Saving Rate by Age from 1992 to 2007
model-1experiment 1experiment 2
Figure 9: Panel A and B plot the sensitivity of the increase in the aggregate saving rate and the age-specific saving rate, respectively. See the text for details on the two experiments.
Figure 10 Simulated Results under Myopic Expectation
1992 1994 1996 1998 2000 2002 2004 200615
20
25
30
year
perc
ent
Panel A: Aggregate Saving Rates
model-1model-2data
25 30 35 40 45 50 55 600
5
10
15
20
age
perc
ent
Panel B: Increase of the Saving Rate by Age from 1992 to 2007
model-1model-2data
Figure 10: Solid and dashed lines are the simulated results from model-1 (no within-cohort heterogeneity) and model-2 (within-cohort heterogeneity of education levels), respectively. Panel A and B plot the increase of saving rate at the aggregate level and over the life cycle, respectively, under the benchmark parameterization (see the text for details). Dotted lines plot the increases in the data.
Table 1 Regressions on Cohort-Specific Age-Earnings Profiles Dep. Variable Log of real annual earnings (1) (2) (3) (4) Full sample Full sample Non-college College Cohort 0.1210***
(3.94) 0.1109***
(22.11) 0.0968***
(2.68) 0.2044***
(4.24) Cohort2 -0.0002
(-0.98) -0.0001 (-0.90)
-0.0002 (-0.82)
-0.0009** (-2.46)
Cohort*Age -0.0011** (-2.37)
-0.0008*** (-10.25)
-0.0008 (-1.44)
-0.0019*** (-2.68)
Age 0.3080*** (9.32)
0.2979*** (41.60)
0.2116*** (5.45)
0.3271*** (6.31)
Age2 -0.0042*** (-11.55)
-0.0040*** (-16.07)
-0.0024*** (-5.71)
-0.0033*** (-5.79)
Age3 0.0000*** (12.18)
0.0000*** (12.15)
0.0000*** (5.45)
0.0000*** (4.78)
Detrended aggregate earnings
1.0351*** (12.12)
- 0.8973*** (8.94)
1.1055*** (8.24)
Year Dummies No Yes No No Obs. 576 576 576 Ad. R2 0.9831 0.9687 0.9709 Note: Column (1) and (2) are the full sample regressions with the specification in Beaudry and Green (2000) and that in Deaton and Paxson (1994), respectively. Using the Beaudry-Green specification, Column (3) and (4) report results from subsamples of workers who are non-college graduate and college graduate, respectively. t statistics are in parentheses. ***, ** and * stand for significance at 1%, 5% and 10%, respectively.