Can Rising Housing Prices Explain China's High Household ... Rising Housing Prices Explain China’s...

FEDERAL RESERVE BANK OF ST. LOUIS REVIEW MARCH/APRIL 2011 67

Can Rising Housing Prices Explain China’s High Household Saving Rate?

Xin Wang and Yi Wen

China’s average household saving rate is one of the highest in the world. One popular view attrib-utes the high saving rate to fast-rising housing prices and other living costs in China. This articleuses simple economic logic to show that rising housing prices and living costs per se cannot explainChina’s persistently high household saving rate. Although borrowing constraints and demograph-ic changes can help translate housing prices to the aggregate saving rate, quantitative simulationsusing Chinese data on household income, housing prices, and demographics indicate that risingmortgage costs contribute at most 5 percentage points to the Chinese aggregate household savingrate, given the down payment structure of China’s mortgage markets. (JEL D14, D91, E21, I31, R21)

Federal Reserve Bank of St. Louis Review, March/April 2011, 93(2), pp. 67-87.

cent after the early 1990s and peaked in 1994 and2003 with values of 27 percent and 26 percent,respectively.

Such a persistently high aggregate householdsaving rate is extraordinary compared with devel-oped nations such as the United States, which hashad an average household saving rate of 2 percentsince the early 1990s. However, the high Chinesesaving rate is not unique. Figure 2 shows thehousehold saving rates for Japan and Korea inthe postwar period. Both economies had a highhousehold saving rate—above 20 percent—duringtheir rapid economic growth periods (Japan inthe mid-1970s and Korea from 1987 to 1994).2

A ccording to Friedman’s (1957) per-manent income hypothesis, rationalconsumers should save less whentheir income is growing fast because

the need to save is reduced when people expectto be richer in the future than they are today.However, the reality in China is the opposite:China, as one of the fastest-growing economies,has an average household saving rate among thehighest in the world.

“Aggregate household saving rate” is definedin this paper as the ratio of net changes in aggre-gate household financial wealth (e.g., bankdeposits, government bonds, and stocks) to aggre-gate household disposable income.1 Figure 1shows that the average Chinese household savingrate was around 2 percent in 1978 (the first yearof economic reform) and rose rapidly thereafter.The saving rate stabilized at around 20 to 25 per-

1 Notice that our definition of the saving rate does not include changesin household nonfinancial wealth (such as housing investment).

2 These data are based on the Organisation for Economic Co-operationand Development database, Hayashi (1986), and Bai and Qian(2009). We are unable to find reliable household saving data forIndia. However, according to a report from the Centre for Monitor -ing Indian Economy, India’s household saving rate (includinginvestment in fixed assets) in 2001 was 24 percent. This numberrose to 35 percent in 2007 and 36 percent in 2008. Based on suchinformation, India’s household saving rate has reached a levelsimilar to China’s.

Xin Wang is a doctoral student in the School of Economics and Management at Tsinghua University in Beijing, China. Yi Wen is an assistantvice president and economist at the Federal Reserve Bank of St. Louis and professor of economics at Tsinghua University. The authors thankCarlos Garriga, David Wheelock, Michael Z. Song, Weilong Zhang, and seminar participants at Tsinghua University and People’s Universityfor helpful comments and Zhengjie Qian for sharing data.

© 2011, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect theviews of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

http://research.stlouisfed.org/econ/wen

Wang and Wen

68 MARCH/APRIL 2011 FEDERAL RESERVE BANK OF ST. LOUIS REVIEW

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Household Saving Rate (percent)

Figure 1

Chinese Household Saving Rate (1978-2006)

SOURCE: Bai and Qian (2009).

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ChinaJapanSouth Korea

Figure 2

Cross-Country Comparison of Household Saving Rates (1968-2007)

Why the Japanese saved so much during therapid stage of economic development is still anopen question (see, e.g., Hayashi, 1986). Hence,it is not surprising that the high Chinese savingrate appears puzzling, especially given China’srapid income growth.

The high saving rate of Chinese householdsnot only poses a challenge to economic theory,but also has become a source of recent politicalcontroversy and trade disputes with the UnitedStates and its other major trading partners. Forexample, the former Chairman of the FederalReserve, Alan Greenspan, alleged that the highChinese saving rate was likely the culprit of the recent American subprime mortgage crisisbecause it caused low interest rates in the worldfinancial markets, which pushed Americanstoward excessive consumption and housingfinance (Greenspan, 2009). Current ChairmanBen Bernanke (2005) also argued that the “globalsaving glut” is partly responsible for the increasein the U.S. current account deficit.

What are the causes of the high Chinese savingrate? A growing segment of the macro literaturehas focused on understanding this phenomenon.Many factors have been proposed as possiblecauses, including rapid income growth, agingpopulation, lack of social safety nets and unem-ployment insurance, precautionary savingmotives, cultural tradition of thrift, high costs of education and health care, and rising housingprices, among others.3 In particular, Wei andZhang (2009) propose that the unbalanced sexratio in China leads to competitive saving behav-ior in the marriage markets, which may signifi-cantly raise the aggregate household saving ratebecause men with adequate wealth accumulation(e.g., enough savings to buy houses) are morelikely to attract marriage partners. Such competi-tive behavior further drives up housing pricesand reinforces this competitive saving behavior.Chamon and Prasad (2010) argue that the rapidlyrising private burdens of housing, education, and

health care are the most important contributingfactors. They also conjecture that the impact ofthese factors on saving can be amplified by under-developed financial and credit markets.

Indeed, the rapidly rising housing prices andother living costs in China are serious socioeco-nomic problems and have attracted much atten-tion from the news media and policymakers. InBeijing and Shanghai, for example, the averagehousing price-to-income ratio (for a 27.0-square-meter [300-square-foot] living space) is about 12.4

Specifically, a young married couple needs to savetheir entire income (a 100 percent saving rate)for 12 years to afford a 55.74-square-meter (600-square-foot) apartment.5 Hence, it is not surpris-ing that rising housing prices have been perceivedas one of the most important factors underlyingChina’s high aggregate household saving rate.

But can rising housing prices really explainthe persistently high household saving rate inChina? This is not only an empirical question,but also a theoretical one with broad implicationsfor developing economies. To the best of ourknowledge, little theoretical work has been doneto carefully and quantitatively address this ques-tion. Based on simple economic logic and quan-titative analysis, our answer to this question isbasically “No.”

More specifically, we show the following:

• In the absence of economic growth andborrowing constraints, the aggregate house-hold saving rate of an economy is inde-pendent of housing prices.

• Only under the following combined condi-tions will high housing prices significantlyincrease the aggregate household saving

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3 This literature includes Modigliani and Cao (2004); Overland andWeil (2000); Horioka (1990); Horioka and Wan (2007); Chen,Imrohoroglu, and Imrohoroglu (2006); Song, Storesletten, andZilibotti (2011); Yuan and Song (1999, 2000); and Wen (2009),among others.

4 According to China Statistical Yearbook (2007), in 2006 the aver-age living space per person was 27.1 square meters (291.7 squarefeet) in urban areas and 30.7 square meters (323.9 square feet) inrural areas. However, the average living space for new homebuyersis greater than 30 square meters (322.9 square feet).

5 According to China Statistical Yearbook (2008), in 2007 the nation-wide average housing price was 3,645 yuan per square meter,10,661 yuan for Beijing, and 8,253 yuan for Shanghai. In 2007,the average disposable income per capita was 13,786 yuan nation-wide, 21,989 yuan in Beijing, and 23,623 yuan in Shanghai. Hence,if the living space per person is 30 square meters (322.9 squarefeet), the ratio of housing price to disposable income would be7.93 for the nation, 14.55 for Beijing, and 10.48 for Shanghai.

rate: (i) Agents have severe borrowing con-straints with zero possibility of obtainingmortgage loans, (ii) over time, the popu-lation of potential future homebuyersincreases rapidly relative to current home-buyers, and (iii) housing prices rise fasterthan household income. However, theseconditions are inconsistent with Chinesereality. Quantitative simulations based onChinese time-series data for householdincome, housing prices, demographic struc-ture, and mortgage down payment require-ments show that rising housing prices cancontribute at most 5 percentage points tothe aggregate saving rate.

The intuition is simple: Suppose the onlyreason to save is to buy a house. Regardless ofthe level of housing prices, income saved forfuture housing purchases by future homebuyers(called “would-be homebuyers” in this paper) isalways canceled by housing expenditures of thecurrent homebuyers in the measured aggregatesaving ratio. In other words, as soon as a personspends his or her past savings to purchase a good,the average lifetime saving rate for that individualimmediately becomes zero. If part of the expen-diture is financed by bank loans against the buyer’sfuture income, the average lifetime saving rate atthe moment of the home purchase is negativebecause the buyer must continue to save in thefuture to repay the loans until the debt is com-pletely repaid. Hence, if the population is notgrowing and housing prices are constant, theaggregate saving rate across all cohorts at anypoint in time is independent of housing prices,regardless of borrowing constraints.

On the other hand, if housing prices are rap-idly growing, then the population share of futurehomebuyers is effectively increasing relative tothat of current homebuyers. In this case, theexpenditures of the current homebuyers cannotcompletely cancel the savings of the would-behomebuyers. Because young cohorts need to savemore and for longer periods under borrowingconstraints when housing prices increase, this isequivalent to a continuous expansion of the pop-ulation size of the saving cohort relative to the

dissaving cohort. In other words, both housing-price growth and borrowing constraints areequivalent to population growth in terms of theirimpact on the aggregate saving rate. We call suchequivalence the “population effect.” Under suchpopulation effect, housing prices may play animportant role in determining the aggregate savingrate. However, if household income increases atroughly the same rate as housing prices (as is thecase in China), then the anticipated rising perma-nent income would reduce the need to save andcancels the population effect. In fact, the rapidgrowth in household income is the key force driv-ing the rapidly rising housing prices in China,given the scarcity of habitable land in China.

Therefore, our analysis clarifies a popularconfusion or misunderstanding that attributes thehigh aggregate household saving rate in China torising housing prices and other costs of living.The same logic can also be applied to discreditsimilar theories that view the rising private bur-den in education, childbearing, health care, mar-riage, and so on in China as the major factorscontributing to China’s high aggregate householdsaving rate.

Our analysis also reveals a potential tensionor conflict between survey data and economicanalysis. Suppose survey data unambiguouslyindicate that cost-of-living factors are the primarymotive for each household to increase its savingrate. Such empirical facts by no means imply thatrising living costs are responsible for the persis -tently high aggregate household saving ratebecause incomes saved for any spending needswill always be consumed at later stages of life.Hence, such types of savings will cancel acrosshouseholds among different cohorts. Even if sav-ings are not entirely spent within a person’s life-time and become bequests, they would reducethe children’s need to save by exactly the sameamount. Thus, any such type of savings should becanceled through aggregation across age cohorts.

Hayashi (1986) analyzes the possible causesof Japan’s high household saving rate in the 1960sand 1970s. His analysis includes discussionsregarding the possible impact of rising housingprices on the saving behavior of Japanese house-

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holds. In particular, using regression analysis, hefinds that the average household saving rate of agiven Japanese city is independent of that city’saverage housing prices.6 Based on this finding,Hayashi concludes that rising housing prices perse are not the cause of Japan’s high householdsaving rate because of the “saving-expenditurecancellation” effects across population and agecohorts. This conclusion is similar to ours. How -ever, Hayashi did not conduct detailed theoreti-cal analysis to rigorously prove the point, so hisanalysis is not generalizable and may not applyto China. In particular, he did not consider thepossibility that under severe borrowing con-straints, rising housing prices may significantlyincrease the aggregate household saving rate.

In this paper, we choose a simple consumption-saving model to illustrate our points, yet withoutthe loss of generality. In the model, many vari-ables (such as household income, housing prices,optimal age of homebuyers, and demographicstructure) are deliberately kept exogenous so thatcomparative statistics can be easily obtained usingChinese data. The only endogenous optimizationbehavior derived from the model is consumptionsmoothing over a person’s lifetime subject toborrowing constraints. This framework providesthe simplest setup to calibrate the model usingvarious Chinese time-series data.

The remainder of the paper is organized asfollows. The next section presents a benchmarkconsumption-saving model without borrowingconstraints and studies the effects of housingprices on the aggregate household saving rate. Insubsequent sections we extend the analysis toinclude borrowing constraints, conduct robustnessanalysis, and consider other extensions of the basicmodel. The final section summarizes our findingsand includes some policy recommendations.

THE BASIC MODELConstant Income and Housing Prices

Suppose shelter (housing) is an indivisibleand necessary consumption good that depreci-ates completely at the end of a homeowner’s life.Given household income, increases in housingprices will force individual consumers to savemore (and for a longer period) to afford a house.This positive association between housing pricesand individual saving behavior may be why peo-ple view rising housing prices as a cause of thehigh aggregate saving rate in China. However,this view suffers from the fallacy of aggregation:It ignores the fact that when people purchasehouses, they generate negative savings to society,canceling other people’s positive savings.

More specifically, suppose that (i) the interestrate is zero and there is no discounting in thefuture,7 (ii) each individual’s only purpose forsaving at a young age is to buy a house in middleage, and (iii) there are no debts or bequests at birthor after death. Clearly, in such a society, eachperson’s average lifetime saving rate should beexactly zero. Although a higher housing pricewill increase an individual’s saving rate beforepurchasing a house, it does not change the aver-age lifetime saving rate because at the moment ofhome purchase, all of the buyer’s positive savingsare exactly canceled by the current expenditure.Therefore, if the population is stable over time(i.e., each age cohort has the same number ofindividuals), then the aggregate saving rate isalso zero, independent of housing prices.

Formally, imagine an economy where allagents have the same momentary utility func-tion, and a typical consumer lives for T periodswith a constant income flow

–Y in each period.

Each consumer needs to buy a house in period t + 1 � T,8 the price of a house is M >

–Y, and there

are no borrowing constraints except the zero debt

Wang and Wen


6 Hayashi also estimated the saving rates of homeowners, would-behomebuyers, and non-homeowners who do not plan to own housesin rural and urban areas. He argued that if housing prices have asignificant impact on a household’s saving rate, then the savingrate of would-be homebuyers should be significantly higher thanthe other two types of households, and urban households shouldhave a higher saving rate than rural households. However, he didnot find such differences in the Japanese data.

7 Our results are robust to these assumptions.

8 Because t can take arbitrary values, we can calibrate it usingChinese data. Making it endogenous complicates the analysis dra-matically without additional gains. An additional advantage ofkeeping t exogenous is that we need not worry about how andwhen housing enters the utility function. That is, we can ignorethe utility value of housing without loss of generality.

requirement and the assumption of 100 percentdepreciation of a house at the end of a home-owner’s life. Naturally, we also need to assume T–Y > M to ensure that each consumer is able to

afford a house with his or her lifetime income.Under these conditions, because of the zero inter-est rate and no discounting, the marginal utilityof consumption (C ) is exactly the same acrosstime, so utility maximization implies that theconsumer will save a constant amount of his orher personal income flow each period to smoothconsumption.

Formally, the maximization problem isstated as follows:

Notice that we have deliberately omitted housingconsumption in the utility function to simplifythe analysis. This is an innocuous assumptionbecause shelter is a necessary consumption goodand the wealth effect generated from a house, ifit exists, will only decrease the incentive for sav-ing rather than increase it. The optimal solutionto the above problem is

That is, consumption is perfectly smoothed andequals a constant. However, notice that the totalexpenditure in period t+1 equals consumptionplus the housing expenditure: Ct+1 + M. This

max:

s.t.:� � .=1

u C

C M TY

T

T

ττ

ττ

( )

+ ≤

=∑

∑

1

C YMTτ = − .

typical consumer’s expenditure, savings, andsaving rate in each period of his or her lifetimeare reported in Table 1.

The first line of Table 1 indicates the con-sumer’s living period (or age), the second linetotal expenditures in each period, the third lineadditional savings in each period, and the last linethe saving rate in each period, which is definedas the ratio of additional savings to income.

Notice that the consumer’s saving rate isalways

in each period except in period t+1. In periodt+1, because of the additional expenditure of thehousing purchase, the saving rate is negative,

The consumer’s average lifetime saving rate is

(1)

Because the negative savings incurred at themoment of a home purchase exactly cancel thepositive savings in the other periods, housingprices are irrelevant to the consumer’s lifetimesaving rate.

To compute the aggregate household savingrate in this economy with many different agecohorts for a particular period, we need to aggre-gate the saving rate of each age cohort in thatperiod. There exist two measures (or definitions)of the aggregate saving rate:

Lifetime� average� saving� rate .= − ==∑ M

TY

M

Y

T

τ 10

MTY

MTY

MY

− < 0.

Wang and Wen


Table 1Saving Behavior of Individual Consumers

Period: 1 … t t+1 t+2 … T

Expenditure–Y – M/T …

–Y – M/T

–Y – M/T + M

–Y – M/T …

–Y – M/T

Savings M/T … M/T M/T … M/T

Saving rate … …

M

TM−

M

TY

M

TY

M

TY

M

Y−

M

TY

M

TY

(i) The average of the personal saving rateacross cohorts weighted by the population shareof each age cohort—namely,

(2)

where ατ represents the population share ofcohort τ in the total population, and

represents the saving rate of cohortτ . (ii) The ratio of aggregate saving to aggregate

income in the same period:

(3)

where ατ still denotes the population share ofcohort τ , Sτ denotes the savings of cohort τ , andYτ the income of cohort τ .

We can call definition (i) the “average house-hold saving rate” and definition (ii) the “aggregatehousehold saving rate.” Clearly, if all cohorts havethe same income levels and identical populationshares, the two definitions are equivalent. How -ever, if different cohorts have different incomelevels and population shares (e.g., because ofincome growth and population growth), the twomeasures of the aggregate saving rate are not iden-tical. Because definition (ii) depends only onmacro data and is consistent with the data pre-sented in Figures 1 and 2, we adopt definition (ii)in equation (3) as the measure of the aggregatehousehold saving rate for the remainder of thispaper.

Assume for a moment identical populationshares across cohorts (we relax this assumptionin the next section); then

in equation (3). In this case, because income andhousing prices are time invariant, we can computethe aggregate household saving rate in equation(3) using information provided in Table 1 to obtain

S sT

==∑ατ ττ 1

,

sSYτ

τ

τ=

SS

Y

T

T= =

=

∑

∑

α

α

τ ττ

τ ττ

1

1

,

ατ =1T

(4)

namely, the aggregate saving rate is zero andindependent of housing prices.

Hence, under the maintained assumptions of constant income and demographics, changesin the level of housing prices do not affect theaggregate saving rate, although they do affectindividuals’ saving rates. In other words, even if 99 percent of the total population is saving forfuture home purchases, the other 1 percent (home-buyers) can generate just enough negative savingsto cancel the would-be homebuyers’ positivesavings, resulting in a zero aggregate saving rate.This logic of aggregation is simple but not alwaysrecognized.

However, does the conclusion continue tohold if income and housing prices grow over time?In a sense, continuously rising housing pricesimply that young cohorts must continuouslyincrease their saving rate and save for a longerperiod to afford a house. Consequently, the rela-tive population share of would-be homebuyerswill become larger than that of current homebuy-ers (even without population growth), and thispopulation effect may result in a positive aggre-gate saving rate, holding income constant. On theother hand, if income is also growing over time,the effective share of would-be homebuyers rela-tive to homebuyers will shrink because the needto save is reduced (a negative population effect),everything else equal. Therefore, if income andhousing prices are growing at the same time, theirpopulation effects may (at least partially) canceleach other, leading to insignificant changes inthe aggregate saving rate. This issue is the focusof the next subsection.

Time-Varying Income and HousingPrices

In a model with time-varying income andhousing prices, a consumer born in period 1 whoneeds to purchase a house in period t+1 solvesthe following problem:

ST

S

TY

MT

M

Y

T

T

T

T= =

−==

=

=

=

∑

∑

∑

∑

1

101

1

1

1

ττ

τψ

τ

τ

,

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The optimal solution is given by

where

denotes a consumer’s permanent income (i.e.,average lifetime income). Total expenditure inperiod t+1 is C + Mt+1.

Suppose the optimal age for each consumerto become a homeowner is t+1 periods after birth.Suppose at the present moment this cohort ofhomebuyers faces housing price M0 and has per-manent income

–Y0. We call this age group “cohort

t+1” or “homebuyer cohort.” Based on such nota-tions, the generation one period younger thancohort t+1 is called “cohort t,” who will becomehomebuyers in the next period and face housingprice M1 and permanent income

–Y1. Analogously,

the generation one period older than the home-buyer cohort is called “cohort t+2,” who havealready bought a house one period ago when thehousing price was M–1 and permanent incomewas

–Y–1. Similarly, at the present moment all gen-

max:

s.t.:� � .=1 =1

u C

C M Y

T

T

t

T

ττ

ττ

ττ

( )

+ ≤

=

+

∑

∑ ∑

1

1

C YM

Tt

τ = − +1 ,

YT

YT

==∑1

1τ

τ

erations younger than the homebuyer cohort arecalled cohorts {1,2,…,t }; these consumers willface housing prices {Mt,Mt–1,…,M1} and perma-nent income {

–Yt,

–Yt–1,…,

–Y1}, respectively, when

they purchase homes in the future. Also, at themoment all generations older than the homebuy-ers are called cohorts {t+2,t+3,…,T }; and eachperson in these cohorts bought a house withprice {M–1,M–2,…,M–T+t–1} and permanent income{–Y–1,

–Y–2,…,

–Y–T+t–1}, respectively, in the past.

Based on the above notations, we can tabulatethe incomes, savings, and saving rates of differentage cohorts at the present moment. The first linein Table 2 shows the age of different cohorts at thepresent moment, the second line their respectivepermanent income levels, the third line the hous-ing prices they face when becoming a homeowner,the fourth line their current level of savings, andthe last line their respective saving rate at thepresent moment. The table shows that at the sametime point different age cohorts have differentsaving rates because permanent income andhousing prices are changing over time. How ever,regardless of age, the saving rate of each cohortis a function of the housing price-to-income ratio�M/

–Y � facing that particular cohort.Therefore, if the housing price-to-income

ratio remains constant over time despite growinghousing prices and permanent income, then dif-ferent age cohorts (except the homebuyer cohort)have the same saving rate, whereas the home-

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Table 2Saving Behavior of Different Age Cohorts

Age cohorts: 1 … t t+1 t+2 … T

Permanent income–Yt …

–Y1

–Y0

–Y–1 …

–Y–T+t+1

Housing price Mt … M1 M0 M–1 … M–T+t+1

Savings Mt /T … M1 /T M–1 /T … M–T+t+1 /T

Saving rate … …

1−( )T M

T0

M

TYt

t

M

TY1

1

1−( )T M

TY0

0

M

TY−

−

1

1

M

TYT t

T t

−

−

+ +1

+ +1

buyer cohort always has a negative saving ratethat offsets the positive savings of the othercohorts. Hence, the average saving rate acrosscohorts is exactly zero because each cohort isweighted identically by the factor 1/T in comput-ing the societal average saving rate.

However, because by definition the aggregatesaving rate is the ratio of aggregate saving to aggre-gate income, instead of the weighted sum ofindividuals’ saving rates, the measured aggregatesaving rate is not necessarily zero but dependson the current housing price-to-aggregate incomeratio. That is, the negative savings of the home-buyer cohort (cohort t+1) may receive a lower(or higher) weight than 1/T if equation (3) is usedas our measure of the aggregate saving rate. Forexample, if the ratio of cohort t+1’s housing price(M0) to aggregate income equals 1/T, then themeasured aggregate saving rate is still zero. How -ever, if that ratio is greater than 1/T, then the meas-ured aggregate saving rate is less than zero becausethe negative savings caused by the homebuyercohort more than offsets the total savings fromother cohorts due to time-varying housing pricesand income; if that ratio is less than 1/T, the meas-ured aggregate saving rate is positive.

To sort these effects, consider first the case inwhich permanent income and housing prices haveconstant growth rates according to the equations–Yτ = �1 + a�–Yτ–1 and Mτ = �1 + b�Mτ–1, respectively,where the growth rates a and b are both constants.Notice that if annual income grows at a constantrate, then the permanent income also grows atthe same constant rate. Under these conditions,the aggregate saving rate is given by

(5)

If a ≠ 0 and b ≠ 0, equation (5) can be simplified to

ST

S

TY

M bT

T t

t

T t

t

T t= =

+( )=− + +

=− + +

=− + +∑

∑

1

1

1

1

1

0

ττ

ττ

τ

τ 110

01

1

t

T t

t

M

Y a

∑

∑

−

+( )=− + +

τ

τ

.

SMY

bT

b

b

a

T t T

T

=

+( ) − +( )

− +( ) −

+( )

− + +

− +

0

0

11 1 1

1 11

1 tt

Ta

a+ − +( )

− +( )1

1 1

1 1

,

which depends only on the housing price-to-income ratio of the current homebuyer cohort.

For example, suppose a = b = 10 percent, T = 40, and t = 15.9 Then equation (5) gives anaggregate saving rate of 2.14 percent, which istrivial compared with the 20 percent Chineseaggregate saving rate. On the other hand, it ispossible to obtain an aggregate saving rate of 20percent in the model if we allow the growth rateof permanent income and housing prices to be50 percent per year, which is hard to imagine inreality. Therefore, when housing prices and per-manent income grow at the same rate within anempirically plausible range, housing prices arestill largely irrelevant to the aggregate saving rate.

Calibration 1. We now use actual Chinesedata to calibrate the model. Suppose that peoplestart working at age 21 and retire at age 60; thus,we set the total working years T = 40. Also sup-pose that the average homebuyer’s age is 35—that is, people must work and save for 15 yearsbefore buying a house. This implies that t = 15in our model (e.g., in Table 2). Suppose that indi-viduals in the homebuyer cohort (cohort t+1)become homeowners in the year 2007; in thatyear the housing price-to-income ratio in Chinawas 7.93, so we set M0/

–Y0 = 8. According to the

Chinese Statistical Yearbook (2008), from 1978to 2007 the growth rate of average family incomewas 12.57 percent in rural areas and 13.58 percentin urban areas; hence we set a = 0.13. Accordingto the China Macroeconomic Infor ma tion NetworkDatabase, the average growth rate of housingprices was 9.02 percent per year between 1991and 2008; hence we set b = 0.09. Entering thesenumbers into equation (5), the estimated aggre-gate saving rate equals 1 percent: That is, risinghousing prices explain only 1 percentage pointof China’s aggregate household saving rate, sub-stantially below the actual 27 percent saving ratein 2007.

Moreover, even if the growth rate of housingprices exceeds that of income, the impact of ris-ing housing prices on the aggregate saving rate isstill quite limited. For example, when the growth

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9 T = 40 and t = 15 imply that each individual needs to work for 15years to afford a house and work for 40 years to retire (income isassumed to be zero after retirement).

rate of household income is 10 percent per year,the average growth rate of housing prices must bealmost 20 percent per year to reach an aggregatesaving rate of 20 percent in the model. Althougha 20 percent annual growth rate in housing pricesis possible for a short period, we have not seensuch a high average growth rate over a 10-yearperiod in China or anywhere else in the world.

Calibration 2. The above calibration analysisis based on the assumption that the growth ratesof income and housing prices are constant overtime. If we allow the growth rate of income andhousing prices to vary over time, how does thisaffect our results? Because the simple model isno longer analytically tractable under uncer-tainty, we assume perfect foresight to gain intu-ition. When the growth rates of both income andhousing prices are time varying, Table 2 impliesthat the aggregate household saving rate is deter-mined by

(6)

As before, using 2007 as the base year for cur-rent homebuyers (cohort t+1), M0 = P2007, whereP2007 denotes the average housing price in 2007.Recall that we use a 40-year window to computethe permanent income based on 40 years of aver-age household income between year 2007 – t andyear 2007 + T – t – 1, where T = 40. For example,the permanent income of cohort t+1 is denoted by

Using the same method, we can also estimatethe permanent incomes of cohorts {1,2,…,t } andcohorts {t+2,t+3,…,T}.10 By entering the estimatedvalues of housing prices facing homebuyers ofdifferent age cohorts, {Mt,Mt–1,…,M0,…,M–T+t–1},and the corresponding permanent incomes,

ST

M M

Y

T t

t

T t

t=−

=− + +

=− + +

∑

∑

1

10

1

ττ

ττ

.

YT

Yjj t

T t

02007

2007 11== −

+ − −

∑ .

{–Yt,

–Yt–1,…,

–Y0,…,

–Y–T+t–1}, into equation (6), we

obtain an aggregate saving rate of 0.61 percent.Therefore, regardless of how the model is cali-brated, we conclude that in the absence of bor-rowing constraints, rising housing prices alonecannot explain China’s aggregate household sav-ing rate.

BORROWING CONSTRAINTSAND DEMOGRAPHICS

Our basic model makes two importantassumptions: (i) Consumers can completelysmooth their consumption over a working life-time by using future income to finance currentmortgage payments. (ii) The population or demo-graphic structure does not change over time.These assumptions are not realistic and may biasour results.

Assumption (i) would be innocuous if house-hold income, housing prices, and populationwere constant over time. To understand this point,suppose consumers cannot borrow at all. Thencohort t+1 must increase its saving rate at ayounger age to accumulate just enough money topay off the entire mortgage before period t+1. Inthis case, if income and housing prices do notgrow over time, the aggregate saving rate is stillzero because the negative savings generated bycohort t+1 in the housing market still completelycancel the total positive savings from cohorts{1,2,…,t }. However, if income and housing pricesgrow over time, assumption (i) is no longer innocu-ous and borrowing constraints may greatly mag-nify the positive impact of housing prices on theaggregate saving rate.

The assumption of a constant population sizedoes not allow our model to capture any transi-tional dynamics outside the steady state. Hence,the demographic structure is also important forthe robustness of our analysis and conclusionsand should be considered. Formal analyses withassumptions (i) and (ii) relaxed are presentedbelow. We consider first the case with borrowingconstraints and then the case with a time-varyingpopulation structure.

Wang and Wen


10 Computing young cohorts’ permanent income requires the use ofincome data after 2009. Since such data do not exist, we extrapo-late by assuming a 10 percent annual growth rate after 2009. Weprovide the sensitivity analyses in a later section.

Borrowing Constraints

To facilitate future analysis, we first considerconstant income and housing prices under bor-rowing constraints. If agents cannot borrow atall and the optimal timing for purchasing a homeis still t+1 periods after birth (we examine therobustness of the results to this assumption later),the would-be homebuyers must then increasetheir saving rates before period t+1. This impliesthat from period 1 to t the saving rate is M/t, andoptimal consumption is –Y – M/t. Between periodt+2 and period T, the optimal consumption levelis –Y and the saving rate is zero. In period t+1, totalexpenditure (consumption plus housing pur-

chase) is –Y + M. These statistics are summarizedin Table 3.

Compared with Table 1, the addition of bor-rowing constraints raises the individual’s savingrate from M/T to M/t; however, the average life-time saving rate is still zero. Hence, if the popu-lation share of each age cohort is the same, theaggregate saving rate is also zero.

Now with time-varying income and housingprices, the effective share of each cohort is nolonger the same because of the population effect.In this case, we can use a method similar to thatused for Table 2 to compute each age cohort’ssaving rate under borrowing constraints. Theseresults are summarized in Table 4.

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Table 3Saving Behavior of Individuals under Borrowing Constraints*


Expenditure–Y – M/t …

–Y – M/t

–Y + M

–Y …

–Y

Savings M/t … M/t –M 0 … 0

Saving rate … 0 … 0

NOTE: *Constant income and housing prices.

M

tY

M

tY

−M

Y

Table 4Saving Behavior of Different Age Cohorts under Borrowing Constraints*



–Y1

–Y0

–Y–1 …

–Y–T+t+1


Savings Mt /t … M1 /t –M0 0 … 0

Saving rate … 0 … 0

NOTE: *Time-varying income and housing prices.

M

tYt

t

M

TYt

t

−M

Y0

0

Each generation purchases houses t+1 periodsafter birth. At a particular moment, the currenthomebuyer generation is called cohort t+1, andthis cohort faces housing price M0 and permanentincome

–Y0. The one-period-younger generation is

cohort t; this cohort will be buying houses in thenext period, facing housing price M1 and perma-nent income

–Y1, and this generation’s current sav-

ing rate is M1/t. Analogously, the one-period-oldergeneration is cohort t+2; these individuals havealready bought houses in the last period, facedhousing price M–1 and permanent income

–Y–1, and

their current saving rate is 0, in contrast to themodel in Table 2. All cohorts proceed in a similarfashion.

Suppose permanent income and housingprices grow over time according to the equations–Yτ = �1 + a�–Yτ–1 and Mτ = �1 + b�Mτ–1, respectively,where the growth rates a and b are both constant.Under such conditions, the aggregate saving rateis given by

(7)

which can be simplified to

It can be shown that the aggregate saving ratewith borrowing constraints is larger than thatwithout borrowing constraints. The intuition isas follows. Without borrowing constraints, whenhousing prices increase, the average saving rateof would-be homebuyers is larger than that ofthe current homeowners because of the popula-tion effect. With borrowing constraints, this pop-ulation effect is significantly magnified becausethe saving rate of all homeowners is now zero. Inother words, in computing the aggregate savings,the population weight of would-be homebuyersis increased from 1/T to 1/t, while the population

S

M bt

M

Y a

t

T t

t=

+( ) −

+( )=

=− + +

∑

∑

0

10

01

1

1

τ

τ

τ

τ

,

SM

Y

bt

b

b

a

t

T t

=

+( ) − +( )

− +( ) −

+( )−

− + +

0

01

1 1 1

1 11

11 1++( )

− +( )a

a

T

1 1

.

weight of the current homeowners is decreasedfrom 1/T to 0. Because the aggregate income ofall cohorts is the same, the ratio of aggregate sav-ings to aggregate income (the aggregate savingrate) has increased under borrowing constraints.

Calibration. As in the previous analysis (withtime-varying income and housing prices), we setT = 40, t = 15, M0/

–Y0 = 8, a = 0.13, and b = 0.09.

Substituting these values into equation (7) givesan aggregate saving rate of 16.66 percent. Alterna -tively, if we allow the growth rate of income andhousing prices to vary over time (as in actualChinese data), under the assumption of perfectforesight, the aggregate saving rate is given by

(8)

Using the same method adopted in a previoussection, namely, choosing 2007 as the base yearfor the current homebuyers (cohort t+1), estimat-ing and computing the associated values forhousing prices {Mt,Mt–1,…,M0,…,M–T+t–1} andpermanent incomes {

–Yt,

–Yt–1,…,

–Y0,…,

–Y–T+t–1}, and

substituting the results into equation (8) gives anaggregate saving rate of 19.22 percent, higher thanthat implied by equation (7).

Clearly, under severe borrowing constraints(i.e., no borrowing at all), using actual Chinesetime-series data for housing prices and incomeimplies estimates of the aggregate saving rate thatmatch the actual Chinese household saving ratequite well. It thus appears that rising housingprices can explain China’s high household sav-ing rate if borrowing constraints are taken intoaccount. But is this really the case?

Not really. In reality, the degrees of borrowingconstraints are not as severe as assumed in theprevious analysis. Typically, homebuyers needto pay only one-third of the housing price as adown payment and can borrow at least two-thirdswith the mortgage. But how would a slightlyrelaxed borrowing constraint affect our quantita-tive result?

To be conservative, we assume that the downpayment requirement is as high as 50 percent of

S

M

tM

Y

t

T t

t=−=

=− + +

∑

∑

ττ

ττ

10

1

.

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the house price.11 In this case, the borrowingconstraints do not bind if each generation’s opti-mal time for buying a house is after working for20 years (because of sufficient savings). However,as long as each generation still needs to purchasehouses after working for only 15 years (as assumedpreviously), borrowing constraints will still bindfor every generation with an empirically plausi-ble growth rate of income and housing prices. Atypical individual’s saving behavior given theseconditions is shown in Table 5.

Between period 1 and period t of an individ-ual’s lifetime, a consumer’s annual saving is M/2t(see Table 5); in period t+1, the total past savingsare just enough to pay for the 50 percent downpayment, so the consumer needs to borrow theother 50 percent from future income to pay forthe mortgage. Thus, in period t+1 the buyer’shousing expenditure is M and saving is

afterward, future saving for each period is always

MT t

M2 −( ) − ;

MT t2 −( ) .

Based on such information and assumingtime-varying income and housing prices, we canuse the methods outlined in the previous sectionsto compute each cohort’s saving rate at the samepoint of time (Table 6). As shown, if permanentincome and housing prices follow a constantgrowth rule,

–Yτ = �1 + a�–Yτ–1 and Mτ = �1 + b�Mτ–1,

then the aggregate saving rate is given by

(9)

In such a case, we use Chinese data to set T = 40,t = 15, M0/

–Y0 = 8, a = 0.13, and b = 0.09. Substi -

tuting these values into equation (9) gives anaggregate saving rate of 4.17 percent.

On the other hand, if the growth rates ofincome and housing prices are time varying, theaggregate saving rate is given by

(10)

Using the same method as before, by setting2007 as the base year for homebuyers (cohortt+1) and computing the associated housing prices{Mt,Mt–1,…,M0,…,M–T+t–1} and permanent incomes

S

M bt

M bT t

M

Y

t

T t=

+( ) ++( )−( ) −

= =− + +∑ ∑0

1

0

1

0

0

0

12

12

τ

τ

τ

τ

111

+( )=− + +

∑ aT t

t τ

τ

.

S

M

t

M

T tM

Y

t

T t

T t

t=+

−( ) −= =− + +

=− + +

∑ ∑

∑

ττ

ττ

ττ

1 1

0

0

1

2 2.

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11 In China, the down payment required for home loans has beenabout one-third of the purchase price until recently. Now the downpayment for the first house is one-third and that for the secondhouse is one-half of the purchase price (some people in Chinaown more than one home for investment purposes).

Table 5Saving Behavior of Individuals with 50 Percent Down Payment*


Expenditure–Y – M/t …

–Y – M/t

–Y + M

–Y …

–Y

Savings M/2t … M/2t …

Saving rate … …

NOTE: *Constant income and housing prices.

M

2tY

M

2 T t Y

M

Y−( ) −

M

2 T tM

−−( )

M

2 T t−( )M

2 T t−( )

M

2tY

M

2 T t Y−( )M

2 T t Y−( )

{–Yt,

–Yt–1,…,

–Y0,…,

–Y–T+t–1}, equation (1) implies an

aggregate saving rate of 4.34 percent.We can make the following conclusions from

the above analyses: Borrowing constraints cansignificantly amplify the positive effects of hous-ing prices on the aggregate saving rate. However,as long as the borrowing constraints are not toosevere (i.e., with a 50 percent down payment),12

the effects of rising housing prices on the aggre-gate saving rate are quite moderate, less than 5percentage points.

Our analysis also indicates that, relative torising housing prices and other living costs, bor-rowing constraints may play a more importantrole in explaining China’s high household savingrate. This also explains why more than a decadeof rising U.S. housing prices before the recentfinancial crisis did not induce a high householdsaving rate: American families are much less bor-rowing constrained than Chinese households.Our conclusion is consistent with the analysis ofWen (2009), who shows in a general equilibriumgrowth model that borrowing constraints not onlyinduce a high precautionary saving rate underincome uncertainty, but also make this precau-tionary saving rate an increasing function ofincome growth. Thus, a high income growth rate

can lead to a high aggregate saving rate underborrowing constraints and income uncertainty.

Demographics

As with income and housing price changes,a changing population should have no impact onthe aggregate saving rate without borrowing con-straints. Thus, this section considers only caseswith borrowing constraints.

If the population changes over time, the pop-ulation weights ατ in equation (3) for differentcohorts must be adjusted accordingly whencomputing the aggregate saving rate. Thus, if Wτdenotes cohort τ’s share in total population andassuming that permanent income and housingprices follow the equations

–Yτ = �1 + a�–Yτ–1 and

Mτ = �1 + b�Mτ–1, then the aggregate saving ratebased on equation (3) is given by

(11)

which is analogous to equation (7).Based on the population shares of individu-

als 21 to 60 years of age provided in ChinaPopulation and Employment Statistics Yearbook(2008), assuming that working ages are from 21to 60, the average homebuyer’s age is 35 (i.e., he

SW

M bt

W M

W Y a

t

T t

t=

+( ) −

+( )=

=− + +

∑

∑

τ

τ

τ

ττ

τ

0

10 0

01

1

1,

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12 The actual down payment requirement in China is less than 50percent. Assuming a smaller value further reduces the impact ofhousing prices on the aggregate saving rate.

Table 6Saving Behavior of Different Age Cohorts with 50 Percent Down Payment*



–Y1

–Y0

–Y–1 …

–Y–T+t+1


Savings Mt /2t … M1 /2t …

Saving rate … …

NOTE: *Time-varying income and housing prices.

M

2tYt

t

M

2tY1

1

M

2 T t Y

M

Y0

0

0

0−( ) −

M

2 T tM0

0−−( )

M

2 T t–1

−( )M

2 T tT t– + +

−( )1

M

2 T t Y–1

–1−( )M

2 T t YT t

T t

−

−−( )+ +1

+ +1

or she must work for 15 years to buy a house);using the average income growth and housingprice growth in China, equation (11) implies anaggregate saving rate of 10.47 percent, lower thanthe value with constant population. If we allowa 50 percent down payment for the mortgage, theimplied aggregate saving rate is negative (–0.75percent), also lower than the value with constantpopulation.

If we allow the growth rates of income andhousing prices to vary over time, under 100 per-cent borrowing constraints (100 percent downpayment), the aggregate saving rate is given by

(12)

Using a similar calibration method as in the pre-vious section by choosing 2007 as the base yearfor the homebuyer cohort, the implied aggregate

SW

Mt

W M

W Y

t

T t

t=−

=

=− + +

∑

∑

ττ

τ

τ ττ

10 0

1

.

Wang and Wen


saving rate is 11.32 percent, lower than the valuewith constant population. If we allow a 50 percentdown payment, the implied aggregate saving rateis –1.62 percent, also lower than the value withconstant population.

The reason that taking the demographicstructure into account yields a lower aggregatesaving rate, everything else equal, is that in recentyears the homebuyer cohort is at its peak in termsof its population share. Therefore, the negativesavings generated by this cohort receives largerweight than other cohorts. Figure 3 plots thedemographic structure in China based on ChinaPopulation and Employment Statistics Yearbook(2008), given the assumption that working agesare between 21 and 60 and the average home-buyer’s age is 35. The homebuyer cohort peakedaround 2007.

If the base year of the homebuyer cohort ismoved to other years, such as 2005 or earlier, orif we change the assumed age of homebuyers,the implied aggregate saving rate will differ only

1.57

1.57

1.58

1.92

1.73

1.52

1.58

1.38

1.21 1.22 1.23

1.39

1.25

1.24

1.30

1.281.24

1.38

1.44 1.57

1.66 1.78

1.86

2.06

1.92

2.09

1.72

1.94

1.97

1.91

2.20

1.69

0.94

1.09

1.21

1.46

1.66

1.49

1.59

0.00

0.50

1.00

1.50

2.00

2.50

21 26 31 36 41 46 51 56

Age

Population Share (percent)

1.59

Figure 3

Population Shares of Different Age Cohorts in 2007

SOURCE: China Statistical Yearbook.

insignificantly from the values obtained above.The reason is simple: Unless the population hasbeen sharply declining so that the populationshare of the homebuyer cohort is always signifi-cantly larger than that of the would-be home-buyer cohorts (which is inconsistent with Chinesedata), taking the demographic structure intoaccount cannot strengthen the effect of risinghousing prices on the aggregate saving rate.

Summary of Analyses

The previous analyses covered three scenar-ios: (i) time-varying income and housing prices,(ii) borrowing constraints, and (iii) demographicchanges. The results are briefly summarized inTable 7. The first column lists the assumptions,the second column shows the correspondingequation used to compute the aggregate savingrate, and the last column shows the numericalvalue of the aggregate saving rate.

The first three rows in Table 7 show thatwithout borrowing constraints and demographicchanges, rising housing prices contribute little tothe aggregate saving rate: less than 1 percent. Thesubsequent two rows show that under completeborrowing constraints (with zero possibility toborrow), rising housing prices can have large

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effects on the aggregate saving rate, ranging from16.66 to 19.22 percent. However, such effects arequickly dampened once the degree of borrowingconstraints is reduced. For example, with a 50percent down payment requirement, the aggre-gate saving rate is reduced to 4.17 percent and4.34 percent, respectively, depending on the spe-cific income process. In addition, if China’sdemographic structure is taken into account, thelast two rows in the table show that the savingrate is reduced further: down to –0.75 percentand –1.62 percent, respectively. Therefore, givenChinese time-series data on household income,mortgage prices, borrowing costs, and demo-graphics, we can conclude that the aggregatehousehold saving rate is essentially unrelated tohousing prices.

MORE SENSITIVITY ANALYSESDifferent Extrapolations

In the previous analyses, we extrapolated thefuture growth rates of permanent income andhousing prices beyond 2009 when consideringthe effects of time-varying income and housingprices. For example, in equation (10) we assumedfuture growth rates of income and housing prices

Table 7Aggregate Saving Rate under Different Assumptions

Assumptions Equation Saving rate (%)

No BC, constant {D, I, P} (4) 0.00

No BC, constant D, constant growth in {I, P} (5) 1.00

No BC, constant D, time-varying growth in {I,P} (6) 0.61

100% BC, constant D, constant growth in {I,P} (7) 16.66

100% BC, constant D, time-varying growth in {I,P} (8) 19.22

50% BC, constant D, constant growth in {I,P} (9) 4.17

50% BC, constant D, time-varying growth in {I,P} (10) 4.34

Time-varying D, 100% BC, constant growth in {I,P} (11) 10.47

Time-varying D and growth in {I,P}, 100% BC (12) 11.32

Time-varying D, 50% BC, constant growth in {I,P} –0.75

Time-varying D and growth in {I,P}, 50% BC –1.62

NOTE: BC, borrowing constraints; D, population; I, income; P, housing price; 100% BC, full down payment.

of 10 percent per year after 2009. In the following,we conduct sensitivity analyses on equation (10)by considering other possible growth rates forfuture income and housing prices. Let us assumea 50 percent down payment requirement andthat future growth rates of income and housingprices take the values of 8 percent, 9 percent, 10percent, 11 percent, and 12 percent, respectively.The implied aggregate saving rates under thesepossible future growth rates for income and hous-ing prices are reported in Table 8, where the toppanel assumes a constant demographic structureand the bottom panel considers a time-varyingpopulation.

First, Table 8 shows that, given the growthrate of housing prices (i.e., the columns), theaggregate saving rate decreases as the growthrate of income increases. This is consistent withthe permanent income hypothesis. Second, theaggregate saving rate increases when housingprices are growing faster, given the income growth(i.e., the rows). The main reason for this increaseis the existence of borrowing constraints. Third,the aggregate saving rate is highest (as high as8.34 percent) when the expected future income

growth rate is 8 percent and that of housing pricesis 12 percent. However, if we reduce the downpayment requirement from 50 percent to 33 per-cent, the aggregate saving rate becomes essentiallyzero. Even if the down payment remains 50 per-cent, taking into account China’s demographicstructure (lower panel in Table 8) also reducesthe implied aggregate saving rate from 8.34 per-cent to 1.40 percent. Therefore, unless peopleexpect that (i) housing prices will grow muchfaster than 12 percent per year, (ii) future incomegrowth is significantly lower than 8 percent peryear, and (iii) the borrowing constraints are moresevere than the 50 percent down payment require-ment, housing prices cannot explain China’s per-sistently high aggregate household saving rate.

Other Possible Extensions

Our analysis so far is based on a simple eco-nomic model. However, our simple model can befurther enriched. In this subsection, we discusssome possible extensions and the likely effectsof such extensions on our results.

Endogenous Timing of Home Purchase. Theoptimal timing of home purchase t in our model

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Table 8Sensitivity Analysis for Different Future Growth Rates*

Expected housing price growth (%)

8 9 10 11 12

Expected income growth (%)

8 1.81 3.24 4.79 6.48 8.34

9 1.73 3.09 4.57 6.19 7.95

10 1.64 2.93 4.34 5.87 7.55

11 1.55 2.77 4.10 5.55 7.13

12 1.46 2.60 3.85 5.22 6.70

Time-varying population (%)

8 –4.44 –3.16 –1.77 –0.25 1.40

9 –4.26 –3.04 –1.70 –0.24 1.35

10 –4.07 –2.90 –1.62 –0.23 1.29

11 –3.87 –2.76 –1.55 –0.22 1.23

12 –3.67 –2.61 –1.46 –0.21 1.16

NOTE: *For individuals with 50 percent down payment.

is exogenous and is calibrated using the averagehomebuyer’s age (working years). If we can makethis variable endogenous, the model has thepotential to explain the difference in the optimalage of homebuyers across countries. However,even if this variable is endogenized, we stillneed to calibrate the other parameters so thatthe model-predicted timing of home purchasematches that in the data. This is not much differ-ent from exogenously setting t = 15, as we didherein. Therefore, even if t were endogenous, ourresults would still hold under similar calibrations.

Inclusion of Wealth Effects. In our simplemodel, a shelter is a pure consumption good andgenerates a constant lifetime utility. In reality, ashelter is also a capital good because it may yieldcapital gains when housing prices appreciate,which may generate positive wealth effects.However, this simplification does not hurt ouranalysis. If shelters were introduced into ourmodel as a capital good (or durable consumptiongood), the situation is the same for the would-behomebuyer cohorts when the housing priceincreases; but for the current homeowners, itimplies that their wealth would increase, whichwould decrease their saving incentives and miti-gate the positive impact of rising housing priceson lifetime savings. Such a wealth effect mayexplain why the aggregate household saving ratein developed countries has been declining overthe past decade. For example, Case, Quigley,and Shiller (2006), whose empirical analysis isbased on U.S. cross-country and cross-state data,find that for every 10 percent increase in hous-ing prices, the consumption-to-income ratioincreases by 1.1 percent and the saving ratedecreases by 1.1 percent. These authors explaintheir findings based on the wealth effect. Hence,introducing a wealth effect into our model wouldonly strengthen our conclusion that rising hous-ing prices cannot explain China’s high aggregatesaving rate.

Depreciation Less than 100 Percent. Theprevious analyses are based on the assumptionthat a house has zero market value at the end ofa homeowner’s life. This assumption is not real-istic, but it is an innocuous assumption and doesnot affect our main results. The reason is simple:

If homeowners could sell houses at the end oftheir lifetimes, they could then borrow againstthe home equity to increase consumption whenyoung and use the proceeds from mortgage salesto repay their debt at the end of life. This wouldeffectively relax borrowing constraints and reduceeach individual’s saving rate before buying ahouse. More specifically, if the market value ofthe house does not change over time and can becollateralized, an individual would then haveno need to save before purchasing a home,would incur a negative saving rate (or positiveborrowing) equivalent to the market value ofthe house when purchasing a home, and wouldincur a positive saving rate when selling thehome at the end of life. Thus, the average life-time saving rate would still be zero.

The Hump-Shaped Curve of Lifetime Income.Our model assumes that household income iseither constant or increasing over time, but inreality income follows a life cycle with aninverted-U shape: Personal income peaks inmiddle age. However, our results are not sensi-tive to this income pattern. First, in our modelthe measured income is household or familyincome, not individual income. Householdincome is less hump-shaped than individualincome unless both husband and wife are iden-tical wage earners. Second, and more important,the primary concern for a hump-shaped incomeprofile is that agents are more borrowing con-strained at a young age. But in our model wehave set the optimal age of home purchase as35 (i.e., 15 years after joining the workforce),which is roughly the peak year of lifetime income.Thus, our calibration makes the concern of bor-rowing constraints due to a hump-shaped incomepattern less relevant. In addition, our calibrationof the down payment requirement of 50 percenthas effectively overestimated the actual degreeof borrowing constraints; we showed that, evenunder a 50 percent down payment requirement,the influence of rising housing prices on the aggre-gate saving rate is insignificant. Hence, takinginto account the inverted-U curve of lifetimeincome should not change our results significantly.

Bequests. In China, many parents give moneyto their children to buy houses because the

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children cannot afford the high mortgage costs.Hence, one popular view is that such altruismraised China’s aggregate saving rate. We can usea version of our simple model to show that thisview is incorrect because it again suffers fromthe fallacy of aggregation. The intuition is sim-ple: Bequests from parents reduce their children’sneed to save; hence, at the aggregate level,bequests may have little effect on the averagehousehold saving rate.

CONCLUSIONOur analysis shows the following: (i) Without

borrowing constraints and population growth,the aggregate household saving rate is essentiallyindependent of rising housing prices. (ii) Account -ing for China’s demographics reduces the aggre-gate saving rate because the ratio of homebuyersto non-homebuyers has been increasing, whichincreases the weights of the negative savings ofthe homebuyers in aggregate savings. (iii) Underborrowing constraints the aggregate saving ratecan become quite sensitive to housing prices;however, with realistic degrees of borrowing con-straints (such as allowing for a 50 percent downpayment), rising housing prices can generate anaggregate saving rate of 4.17 percent withoutconsidering the Chinese demographic structure(this value becomes zero if the demographic struc-ture is taken into account). These values are toosmall to explain China’s 20 percent aggregate sav-ing rate. Therefore, our analysis clarifies a popu-lar misunderstanding or fallacy that attributes therapidly rising costs of living, such as housing,education, health care, and so on, to China’shigh aggregate household saving rate. This viewignores the saving-expenditure cancellationeffect across cohorts.

If the rapidly rising housing prices and othercosts of living are not responsible for the per-sistently high Chinese saving rate, what factorsactually cause such saving? We believe that largeuninsurable uncertainty and severe borrowingconstraints in conjunction with rapid incomegrowth may provide the answer to China’s highhousehold saving rate. For example, Wen (2009)shows that when individuals face large unin-sured idiosyncratic risk and severe borrowingconstraints, their marginal propensity to savebecomes a positive function of the growth rateof their permanent income. Thus, rapid incomegrowth could imply an extremely high householdsaving rate when financial markets are incomplete.In particular, Wen (2009) shows that a standardbuffer-stock saving model with incomplete finan-cial markets could generate a 30 percent aggregatehousehold saving rate when the income growthrate is 10 percent per year. In this case, an indi-vidual’s expenditure does not completely cancelhis or her precautionary saving because of theneed for a buffer stock at any moment in life. Inother words, it is optimal to always maintain apositive stock of personal saving as self-insuranceagainst unpredictable shocks.

Our findings also have some policy implica-tions. Although rapidly rising housing pricesmay have adverse welfare effects on would-behomebuyers, policies designed to reduce hous-ing prices may be effective in reducing the indi-vidual saving rate of young people but will notbe effective in reducing the aggregate saving rate.In comparison, policies designed to reduce bor-rowing constraints and improve the efficiency ofthe financial system may prove more effective inreducing the aggregate saving rate.

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