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: zsong@cuhk.edu.hk; Yang, Department of Economics, The Chinese University of HongKong, E-mail: deyang@cuhk.edu.hk.

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.

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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.

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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.

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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,

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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

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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.

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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.

References

[1] Auerbach, Alan J. and Laurence J. Koltikoff (1987) “Dynamic Fiscal Policy,”Cambridge

University Press, Cambridge.

[2] Attanasio, Orazio P. and Agar Brugiavini (2003) “Social Security and Households’Sav-

ings,”Quarterly Journal of Economics, 118(3), 1075-1120.

[3] Beaudry, Paul and David A. Green (2000) “Cohort Patterns in Canadian earnings: As-

sessing the Role of Skill Premia in Inequality Trends,”Canadian Journal of Economics,

33(4), 907-936.

[4] Carroll, Christopher D. (1994), “How Does Future Income Affect Current Consumption?”

Quarterly Journal of Economics, 109(1), 111-147.

31

[5] Carroll, Christopher D., Jody Overland and David N. Weil (2000) “Saving and Growth

with Habit Formation,”American Economic Review, 90(3), 341-355.

[6] Carroll, Christopher D. and Lawrence H. Summers (1991) “Consumption Growth Parallels

Income Growth: Some New Evidence,”National Saving and Economic Performance, eds.

B.D. Bernheim and J.B. Shoven, Chicago: Chicago University Press.

[7] Chamon, Marcos and Eswar Prasad (2009) “Why Are Saving Rates of Urban Households

in China Rising?”American Economic Journal (Macroeconomics), forthcoming.

[8] Chen, Kaiji, Ayse Imrohoroglu and Selahattin Imrohoroglu (2006) “The Japanese Saving

Rate,”American Economic Review, 96(5), 1850-1858.

[9] Conesa, Juan C. and Dirk Krueger (1999) “Social Security Reform with Heterogeneous

Agents,”Review of Economic Dynamics, 2, 757-795.

[10] Davies, James and John Whalley (1991) “Taxes and Capital Formation: How Important

is Human Capital?” National Saving and Economic Performance, B. Bernheim and J.

Shoven (eds.), University of Chicago Press, Chicago, 1991.

[11] Deaton, Angus (1991) "Saving and Liquidity Constraints." Econometrica, 59(5): 1221-48.

[12] Deaton, Angus and Christina H. Paxson (1994) “Saving, growth and aging in Taiwan,”

In D. Wise, ed., Studies in the Economics of Aging, University of Chicago Press, Chicago,

IL.

[13] Deaton, Angus and Christina H. Paxson (2000) “Growth and Saving Among Individuals

and Households,”Review of Economics and Statistics, 82(2), 212-25.

[14] Dunaway, Steven and Vivek Arora (2007) “Pension Reform in China: The Need for a New

Approach,”IMF Working Paper 07/109.

[15] Heckman, James J., Lance J. Lochner, and Petra E. Todd (2006) “Fifty Years of Mincer

earnings Regressions,”Handbook of Education Economics, Vol. 1, Hanushek, E. and F.

Welch (eds.), The Netherlands: Elsevier.

[16] Feldstein, Martin S. (1974) “Social Security, Induced Retirement and Aggregate Capital

Accumulation,”Journal of Political Economy, 82(5), 905-926.

[17] Ge, Suqin, Dennis Tao Yang and Junsen Zhang (2010) "Populaiton Contro Policies and the

Chinese Household Saving Puzzle," Manuscript, The Chinese University of Hong Kong.

32

[18] Guvenen, Fatih (2007) “Learnings Your earnings: Are Labor Income Shocks Really Very

Persistent?”American Economic Review, 97(3), 687-712.

[19] Imrohoroglu, Ayse, Selahattin Imrohoroglu and Douglas H. Joines (1995) “A Life Cycle

Analysis of Social Security,”Economic Theory, 6, 83-114.

[20] Kambourov, Gueorgui and Iourii Manovskii (2005) “Accounting for the Changing life

cycle Profile of earnings,”mimeo.

[21] Lane, Philip R. and Gian Maria Lilesi-Ferretti (2007) "The External Wealth of Nations

Mark II: Revised and Extended Estimates of Foreign Assets and Liabilities, 1970-2004,"

Journal of International Economics 73, 223-250.

[22] Li, Zhigang and Mingqin Wu (2010) "Who Has Financed the Employer-Provided Pension

in China? A Triple-Track Story." Working Paper, University of Hong Kong.

[23] Lin, Dong-hai and Yu Ding (2007) “Social Security Pension New Deal: Assessing the Re-

placement Rate between Old and New,”Population & Economics, (1), 70-74 (in Chinese).

[24] Loayza, Norman, Klaus Schmidt-Hebbel and Luis Serven (2000) “What Drives Private

Saving Across the World?”Review of Economics and Statistics, 82(2), 165-181.

[25] Modigliani, Franco (1970) “The Life Cycle Hypothesis of Saving and Intercountry Differ-

ences in the Saving Ratio,” in Induction, Growth and Trade, eds. W. A. Eltis, M. FG.

Scott, and J. N. Wolfe, Oxford: Clarendon Press, 197-225

[26] Modigliani, Franco (1986) “Life Cycle, Individual Thrift, and the Wealth of Nations,”

American Economic Review, 76(3), 297-313,

[27] Modigliani, Franco and Shi Larry Cao (2004) “The Chinese Saving Puzzle and the life

cycle Hypothesis,”Journal of Economic Literature, 42(1), 145-170.

[28] Michaud, Pierre-Carl and Arthur van Soest (2006) “How Did the Elimination of the

Earings Test Above the Normal Retirement Age Affect Retirement Expectations,”mimeo,

University of Michigan.

[29] Paxson, Christina (1996) “Saving and Growth: Evidence from Micro Data,” European

Economic Review, 40(2), 255-288.

[30] Reimers, Cordelia and Marjorie Honig (1996) “Responses to Social Security by Men and

Women: Myopic and Far-Sighted Behavior,”Journal of Human Resources, 31(2), 359-382.

33

[31] Samwick, Andrew A. (2000) “Is Pension Reform Conducive to Higher Saving?”Review of

Economics and Statistics, 82(2), 264-272.

[32] Storesletten, Kjetil, Christopher I. Telmer and Amir Yaron (2004) “Consumption and

Risk Sharing over the Life Cycle,”Journal of Monetary Economics, 51, 609-633.

[33] Summers, Lawrence H. (1981) “Capital Taxation and Accumulation in a Life Cycle

Growth Model,”American Economic Review, 71(4), 533-544.

[34] Tobin, James (1967) “Life Cycle Saving and Balanced Growth,”in Ten Economic Studies

in the Tradition of Irving Fisher, John Wiley. 231-56.

[35] Wei, Shang-jin and Xiaobo Zhang (2009) “The Competitive Saving Motive: Evidence

from Rising Sex Ratios and Saving Rates in China,”NBER Working Paper 15093.

[36] Wen, Yi (2009) “Saving and Growth under Borrowing Constraints: Explaining the ’High

Saving Rate’Puzzle,”Federal Reserve Bank of St. Louis Working Paper 2009-045B.

[37] World Bank. 2010. World Development Indicators 2010, Washington, D.C.

[38] Yang, Dennis Tao, Junsen Zhang and Shaojie Zhou (2010) "Why Are Savign Rates So

High in China," Working Paper, The Chinese University of Hong Kong.

[39] Zhao, Yaohui, and Jianguo Xu (2002) “China’s Urban Pension System: Reforms and

Problems,”Cato Journal, 21(3), 395-414.

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

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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

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nt)

Panel A: Non-College Graduates

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Panel B: College Graduates

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Panel C: Non-College Graduates

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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

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0.1

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rela

tive

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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

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Panel A: Non-College Graduates

19922007

25 30 35 40 45 50 55-0.4

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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

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Panel A: The Aggregate Replacement Rate

UHSCYS

1992 1994 1996 1998 2000 2002 2004 200620

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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

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perc

ent

Panel A: Aggregate Saving Rates

model-1model-2data

25 30 35 40 45 50 55 606

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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

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age

perc

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Panel A: Non-College

modeldata

25 30 35 40 45 50 55 60

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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

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perc

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Panel A: Aggregate Saving Rate

model-1experiment 1experiment 2

25 30 35 40 45 50 55 608

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perc

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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

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perc

ent

Panel A: Aggregate Saving Rates

model-1model-2data

25 30 35 40 45 50 55 600

5

10

15

20

age

perc

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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.