Research Division Federal Reserve Bank of St. Louis Working Paper Series

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1 Research Division Federal Reserve Bank of S. Louis Working Paper Series Can Rising Housing Prices Explain China s High Household Saving Rae? Xin Wang and Yi Wen Working Paper 2-48A hp://research.slouisfed.org/wp/2/2-48.pdf November 2 FEDERAL RESERVE BANK OF S. LOUIS Research Division P.O. Box 442 S. Louis, O 6366 he views expressed are hose of he individual auhors and do no necessarily reflec official posiions of he Federal Reserve Bank of S. Louis, he Federal Reserve Sysem, or he Board of Governors. Federal Reserve Bank of S. Louis Working Papers are preliminary maerials circulaed o simulae discussion and criical commen. References in publicaions o Federal Reserve Bank of S. Louis Working Papers (oher han an acknowledgmen ha he wrier has had access o unpublished maerial) should be cleared wih he auhor or auhors.

2 Can Rising Housing Prices Explain China s High Household Saving Rae? * Xin Wang singhua Universiy Yi Wen Federal Reserve Bank of S. Louis & singhua Universiy Absrac: China s average household saving rae is one of he highes in he world. One popular view aribues he high saving rae o fas rising housing prices and oher coss of living in China. his aricle uses simple economic logic o show ha rising housing prices and living coss per se canno explain China s high household saving rae. Alhough borrowing consrains and demographic changes can help ranslae housing prices o he aggregae saving rae, quaniaive simulaions using Chinese daa on household income, housing prices, and demographics indicae ha rising morgage coss conribue a mos 5 percenage poins o he Chinese aggregae household saving rae, given he down-paymen srucure of China s morgage markes. Keywords: Chinese Economy, Housing, Saving Rae, Borrowing Consrains. JEL Codes: D4, D9, E2, I3, R2 * We hank Jiandong Ju, Yue Liu, Qing Liu, Xingzhen Shi, Xiaoxia Wang, Zhiru Wei, Binzhen Wu, Weilong Zhang, and Xiaohan Zhong for helpful commens and Zhengjie Qian for sharing daa.

3 Inroducion According o Friedman s (957) permanen income hypohesis, raional consumers should save less when heir income is growing faser, because he need o save is reduced when people expec o be richer in he fuure han hey are oday. However, he realiy in China is he opposie: As one of he fases-growing economies, China s average household saving rae is among he highes in he world. Aggregae household saving rae is defined in his paper as he raio of ne changes in aggregae household financial wealh (e.g., bank deposis, governmen bonds, and socks) o aggregae household disposable income. Figure shows ha he average Chinese household saving rae was around 2% in 978 (he saring year of economic reform) and rose rapidly hereafer. he saving rae sabilized around 2% o 25% afer he early 99s and peaked in 994 and 23 wih values of 27% and 26%, respecively. Household Saving Rae (%) Year Figure. Chinese Household Saving Rae (978-26) 2 Such a high aggregae household saving rae is exraordinary compared wih Noice ha our definiion of he saving rae does no include changes in household nonfinancial wealh (such as housing invesmen). 2 Daa source: Bai and Qian (29). 2

4 developed naions such as he Unied Saes, which has had an average household saving rae of 2% since he early 99s (Figure 2). 3 However, he high Chinese saving rae may no be unique. Figure 2 also shows he household saving raes for Japan from 968 o 976 and Korea from 983 o 99 when hese wo economies experienced similar economic growh and had household saving raes similar o China. 4 Why he Japanese saved so much during he rapid sage of economic developmen is sill an open quesion (see, e.g., Hayashi, 986). Hence, i is no surprising ha he high Chinese saving rae appears puzzling, especially given China s rapid income growh. 3. Household Saving Rae (%) Year Unied Saes Japan Korea China Korea (983-99) Japan ( ) Figure 2. Cross-Counry Comparison of Household Saving Raes (998-26) he high saving rae of Chinese households no only poses a challenge o economic heory, bu also has become a source of recen poliical conroversy and 3 Daa source: OECD Economic Oulook 985 daabase, Hayashi (986), and Bai and Qian (29). 4 We are unable o find reliable household saving daa for India. However, according o a repor from he Cenre for onioring Indian Economy, India s household saving rae in 2 was 24%, including invesmen in nonfinancial wealh. his number rose o 34.8% in 27, 36% in 28, and was expeced o be 24% in 29. Based on such informaion, India s household saving rae has reached a level similar o China s. 3

5 rade dispues wih he Unied Saes and oher major rading parners of China. For example, he former chairman of he Federal Reserve, Alan Greenspan, alleged ha he high Chinese saving rae was he culpri of he recen American subprime morgage crisis because i caused low ineres raes in he world financial markes, which pushed Americans oward excessive consumpion and housing finance. 5 Wha are he causes of he high Chinese saving rae? A growing lieraure has aemped o undersand his phenomenon and many facors have been proposed as possible causes, including rapid income growh, aging populaion, lack of social safey nes and unemploymen insurance, precauionary saving moives, culural radiion of hrif, high coss of educaion and healh care, and rising housing prices, among ohers. 6 In paricular, Wei and Zhang (29) propose ha he unbalanced sex raio in China leads o compeiive saving behavior in he marriage markes, which may significanly raise he aggregae household saving rae because men wih adequae wealh accumulaion (e.g., enough savings o buy houses) have a greaer chance o arac marriage parners. Such compeiive behavior furher drives up housing prices and reinforces he compeiive saving behavior. Chamon and Prasad (2) argue ha he rapidly rising privae burden of housing, educaion, and healhcare are he mos imporan conribuing facors. hey also conjecure ha he impac of hese facors on saving can be amplified by underdeveloped financial and credi markes. Indeed, he rapidly rising housing prices and oher coss of living (such as educaion and healhcare) in China have become serious socioeconomic problems and araced much aenion from he news media and policymakers. In he ciies of Beijing and Shanghai, for example, he average housing price-o-income raio (for a 3-square-foo living space) is abou 2. 7 Namely, a young married couple needs o save heir enire income (a % saving rae) for 2 years o afford a 6-square-foo 5 From a speech by Alan Greenspan, he Fed Didn' Cause he Housing Bubble, Wall Sree Journal, arch, his lieraure includes odigliani and Cao (24), Carroll, Overland, and Weil (2), Horioka and Wan (27), Chen, Imrohoroglu and Imrohoroglu (26), Yuan and Song (999, 2), and Wen (29). 7 According o he China Saisical Yearbook (27), in 26 he average living space per person was 27. square meers in urban areas and 3.7square meers in rural areas. However, he average living space for new homebuyers is greaer han 3 square meers. 4

6 aparmen for heir family. 8 his means ha, even wih bank loans wih a one-hird down-paymen arrangemen and a 33% household saving rae, a ypical working couple sill needs o save for 2 years o buy a small aparmen. Hence, i is no surprising ha rising housing prices have been perceived as one of he mos imporan facors underlying China s high aggregae household saving rae. Can rising housing prices really explain he high household saving rae in China? his is no only an empirical quesion, bu also a heoreical one wih broad implicaions for developing economies. o he bes of our knowledge, lile heoreical work has been done o carefully and quaniaively address his quesion. Based on simple economic logic and quaniaive analysis, our answer o he above quesion is No. ore specifically, we show he following: In he absence of economic growh and borrowing consrains, he aggregae household saving rae of an economy is independen of housing prices. Only under he following combined condiions namely (i) agens are severely borrowing consrained wih zero possibiliy of obaining morgage loans, (ii) he relaive populaion of would-be homebuyers o homebuyers increases rapidly over ime, and (iii) housing prices rise much faser han household income will high housing prices significanly increase he aggregae household saving rae. However, hese condiions are inconsisen wih Chinese realiy. Quaniaive simulaions based on Chinese ime-series daa for household income, housing prices, demographic srucure, and morgage down-paymen requiremen show ha rising housing prices can conribue a mos 5 percenage poins o he aggregae saving rae. he inuiion is simple: Suppose he only reason o save is o buy a house. Regardless of he level of housing prices, income saved for fuure housing purchases by would-be homeowners is always canceled by housing expendiures of homebuyers in he measured aggregae saving raio. In oher words, as soon as a person spends his 8 According o China Saisical Yearbook (28), in 27 he naionwide average housing price was 3,645 yuan per square meer,,66 yuan for Beijing and 8,253 yuan for Shanghai. In 27, he average disposable income per capia was 3,786 yuan naionwide, 2,989 yuan in Beijing and 23,623 yuan in Shanghai. Hence, if he living space per person is 3 square meers, he housing price-o-disposable income raio would be 7.93 for he naion, 4.55 for Beijing, and.48 for Shanghai. 5

7 or her pas savings o purchase a good, he average lifeime saving rae for ha individual immediaely becomes zero. If par of he expendiure is financed by bank loans agains he buyer s fuure income, he average lifeime saving rae a he momen of he home purchase is even negaive because he buyer mus coninue o save in he fuure o repay he loans unil he deb is compleely repaid. Hence, if he populaion is no growing and housing prices are consan, he aggregae saving rae across all cohors a any poin in ime is independen of housing prices, regardless of borrowing consrains. On he oher hand, if housing prices are rapidly growing, hen he populaion share of would-be homebuyers is effecively increasing relaive o ha of he homebuyers. In his case, he expendiures of he homebuyers canno compleely cancel he savings of he would-be homebuyers. Because young cohors need o save more and for longer periods under borrowing consrains when housing prices increase, his is equivalen o a coninuous expansion of he populaion size of he saving cohor relaive o he dissaving cohor. In oher words, boh housing-price growh and borrowing consrains are equivalen o populaion growh in erms of heir impac on he aggregae saving rae. We call such equivalence he populaion effec in his paper. Under such populaion effecs, housing prices may play an imporan role in deermining he aggregae saving rae. However, if household income increases a roughly he same rae as ha of housing prices (as is he case in China), hen he anicipaed rising permanen income would reduce he need o save and cancels he populaion effecs. In fac, he rapid growh in household income is he mos imporan driving force behind he rapidly rising housing prices in China. herefore, our analysis clarifies a popular confusion or misundersanding ha aribues he high aggregae household saving rae in China o rising housing prices and oher coss of living. he same logic can also be applied o discredi similar heories ha view he rising privae burden in educaion, childbearing, healhcare, marriage, and so on in China as he key conribuing facors o China s high aggregae household saving rae. Our analysis also reveals a poenial ension beween survey daa and economic 6

8 analysis. Suppose survey daa unambiguously indicae ha living-cos facors are he primary moive for each household o increase is saving rae. Such empirical facs by no means imply ha rising living coss are responsible for he persisenly high aggregae household saving rae because incomes saved for any spending needs will always be consumed a laer sages of life. Hence, such ypes of savings will cancel across households among differen cohors. Even if savings are no enirely spen wihin a person s lifeime and become bequess, hey would reduce he children s need o save by exacly he same amoun. hus, any such ype of savings should be canceled hrough aggregaion across age cohors. Hayashi s (986) aricle, Why Is Japan s Saving Rae So Apparenly High? analyzes he possible causes of Japan s high household saving rae in he 96-7s. His analysis includes discussions regarding he possible impac of rising housing prices on Japanese household saving behavior. In paricular, using regression analysis, he found ha he average household saving rae of a given Japanese ciy is independen of ha ciy s average housing prices. 9 Based on his finding, Hayashi concludes ha rising housing prices per se are no he cause of Japan s high household saving rae because of he saving-expendiure cancellaion effecs across populaion and cohors. his conclusion is similar o ours. However, Hayashi did no conduc deailed heoreical analysis o rigorously prove he poin, so his analysis is no generalizable and may no apply o China. In paricular, he did no consider he possibiliy ha under severe borrowing consrains rising housing prices may significanly increase he aggregae household saving rae. In his paper, we choose a simple consumpion-saving model o illusrae our poins, ye wihou he loss of generaliy. In he model, many variables (such as household income, housing prices, he opimal age of homebuyers, and he demographic srucure) are deliberaely kep exogenous so ha comparaive saisics 9 Hayashi also esimaed he saving raes of homeowners, would-be homebuyers, and non-homeowners who do no plan o own houses in rural and urban areas, respecively. He argued ha if housing prices have significan impac on a household s saving rae, hen he saving rae of would-be homebuyers should be significanly higher han he oher wo ypes of households, and urban households should have a higher saving rae han rural households. Bu he did no find such differences in he Japanese daa. 7

9 can be easily conduced using Chinese daa. he only endogenous opimizaion behavior derived from he model is consumpion smoohing over a person s lifeime subjec o borrowing consrains. his framework provides he simples seup o calibrae he model using various Chinese ime-series daa. he remainder of he paper is organized as follows. Secion 2 presens a benchmark consumpion-saving model wihou borrowing consrains and sudies he effecs of housing prices on aggregae household saving rae. Secion 3 exends he analysis o borrowing consrains. Secions 4 and 5 conduc robusness analysis and consider oher exensions of he basic model. Secion 6 concludes he paper wih some policy recommendaions. 2 he Basic odel 2. Consan Income and Housing Prices Suppose sheler (housing) is an indivisible and necessary consumpion good. Given income, increases in housing prices will force individual consumers o save more (and for a longer period) o afford a house. his posiive associaion beween housing prices and individual saving behavior may be why people view rising housing prices as a cause of he high aggregae saving rae in China. However, his view suffers from he fallacy of aggregaion: I ignores he fac ha when people purchase houses, hey generae negaive savings o sociey, canceling oher people s posiive savings. ore specifically, suppose ha (i) he ineres rae is zero and here is no discouning in he fuure, (ii) each individual s only purpose for saving a a young age is o buy a house in middle age, and here are no debs or bequess a birh or afer deah. Clearly, in such a sociey each person s average lifeime saving rae should be exacly zero. Alhough a higher housing price will increase an individual s saving rae before purchasing a house, i does no change he average lifeime saving rae because a he momen of home purchase, all of he buyer s posiive savings are exacly Our resuls are robus o hese assumpions. 8

10 canceled by he curren expendiure. herefore, if he populaion is sable over ime (i.e., each age cohor has he same number of individuals), hen he aggregae saving rae is also zero, independen of housing prices. Formally, imagine an economy where all agens have he same momenary uiliy funcion, and a ypical consumer lives for periods wih a consan income flow Y in each period. he consumer needs o buy a house in period +, he price of a house is > Y, and here are no borrowing consrains excep he zero-deb requiremen a he end of life. Naurally, we also need o assume Y > o ensure ha each consumer is able o afford a house wih his or her lifeime income. Under hese condiions, because of he zero ineres rae and no discouning, he marginal uiliy of consumpion ( C ) is exacly he same across ime, so uiliy maximizaion implies ha he consumer will save a consan amoun of his or her personal income flow each period o smooh consumpion. Formally, he maximizaion problem is saed as: max: = ( ) u C s..: C Y. = Noice ha we have deliberaely omied housing consumpion in he uiliy funcion o simplify he analysis. his is an innocuous assumpion because sheler is a necessary consumpion good and he wealh effec generaed from a house, if exiss, will only decrease he incenive for saving raher han increase i. he opimal soluion o he above program is C = Y. ha is, consumpion is perfecly smoohed and equals a consan. However, noice ha he oal expendiure in period + equals consumpion plus he housing Because can ake arbirary values, we can calibrae i using Chinese daa. aking i endogenous complicaes he analysis dramaically wihou addiional gains. An addiional advanage of keeping exogenous is ha we need no worry abou how and when housing eners he uiliy funcion. ha is, we can ignore he uiliy value of housing wihou loss of generaliy. 9

11 expendiure: C + +. his ypical consumer s expendiure, savings, and saving rae in each period of his/her lifeime are repored in able. able. Individual Consumer s Saving Behavior Period + +2 Expendiure Y Y Y + Y Y Savings Saving Rae Y Y Y Y Y Y he firs row of able indicaes he consumer s living period (or age), he second row oal expendiures in each period, he hird row addiional savings in each period, and he las row saving rae in each period, which is defined as he raio of addiional savings o income. Noice ha he consumer s saving rae is always Y in each period excep in period +. In period +, because of he addiional spending on he housing purchase, he saving rae is negaive, <. he consumer s average lifeime Y Y saving rae is given by Life-ime Average Saving Rae = =. () Y Y Because he negaive savings incurred a he momen of a home purchase exacly cancel he oher periods posiive savings, housing prices are irrelevan o he consumer s lifeime saving rae. o compue he aggregae household saving rae in his economy wih many differen age cohors for a paricular period, we need o aggregae he saving rae of each age cohor in ha period. here exis wo measures (or definiions) of he aggregae saving rae: (i) he average of he personal saving rae across cohors weighed by he populaion share of each age cohor namely, =

12 S = α s, (2) = where α represens he populaion share of cohor in he oal populaion, and s S = represens he saving rae of cohor. Y (ii) he raio of aggregae saving o aggregae income in he same period: S = = = α S α Y, (3) where α sill denoes he populaion share of cohor, S denoes he savings of cohor, and Y he income of cohor. We can call definiion (i) he average household saving rae and definiion (ii) he aggregae household saving rae. Clearly, if all cohors have he same income levels and idenical populaion shares, he wo definiions are equivalen. However, if differen cohors have differen income levels and populaion shares (e.g., because of income growh and populaion growh), he wo measures of he aggregae saving rae are no idenical. Because definiion (ii) depends only on macro daa and is consisen wih he daa presened in Figures and 2, we adop definiion (ii) in equaion (3) as he measure of he aggregae household saving rae for use hroughou he res of his paper. Assume for a momen idenical populaion shares across cohors (we will relax his assumpion in he nex secion); hen α = in equaion (3). In his case, because income and housing prices are ime invarian, we can compue he aggregae household saving rae in equaion (3) using informaion provided in able o obain S S = = = = = Y ψ= = Y. (4) Namely, he aggregae saving rae is zero and independen of housing prices.

13 Hence, under he mainained assumpions of consan income and demographics, changes in he level of housing prices do no affec he aggregae saving rae, alhough hey do affec individuals saving raes. In oher words, even if 99% of he oal populaion is saving for fuure home purchases, he oher % (homebuyers) can generae jus enough negaive savings o cancel he would-be homebuyers posiive savings, resuling in a zero aggregae saving rae. his logic of aggregaion is simple bu no always recognized. However, does he conclusion coninue o hold if income and housing prices grow over ime? In a sense, coninuously rising housing prices imply ha young cohors mus coninuously increase heir saving rae and save for a longer period o afford a house. Consequenly, he relaive populaion share of he would-be homebuyers will ge larger han ha of homebuyers (even wihou populaion growh) and his populaion effec may resul in a higher aggregae saving rae, holding income consan. On he oher hand, if income is also growing over ime, he effecive size of he would-be homebuyers relaive o homebuyers will shrink because he need o save is reduced (a negaive populaion effec), everyhing else equal. herefore, if income and housing prices are growing a he same ime, heir populaion effecs may (a leas parially) cancel each oher, leading o insignifican changes in he aggregae saving rae. his issue is he focus of he nex subsecion. 2.2 ime-varying Income and Housing Prices In a model wih ime-varying income and housing prices, a consumer born in period who needs o purchase a house in period + solves he following problem: max: = ( ) u C he opimal soluion is given by s..: C + Y. + = = C = Y 2 +.

14 where Y = Y = denoes a consumer s permanen income (i.e., average lifeime income). oal expendiure in period + is C+ +. Suppose he opimal age for each consumer o become a homeowner is + periods afer birh. Suppose a he presen momen his cohor of homebuyers faces housing price and has permanen income Y. We call his age group cohor +. Based on such noaions, he generaion one period younger han he homebuyer cohor is called cohor, who will become homebuyers in he nex period and face housing price and permanen income Y. Analogously, he generaion one period older han he homebuyers is called cohor + 2, who have already bough a house one period ago when he housing price was and permanen income was Y. By he same oken, a he presen momen all generaions younger han he homebuyers are called cohors {, 2,, }, respecively, and hese would-be homebuyers will face housing prices {,,..., } and permanen income { Y, Y,..., Y}, respecively. Also, a he momen all generaions older han he homebuyers are called cohors { 2, 3,, } + +, respecively, and hese homeowners once bough a house wih prices {, 2,..., + } and permanen income { Y, Y 2,..., Y + } in he pas. Based on he above noaions, we can abulae he incomes, savings, and saving raes of differen age cohors a he presen momen. he firs row in able 2 shows he age of differen cohors a he presen momen, he second row heir respecive permanen income levels, he hird row he housing prices hey face when becoming a homeowner, he fourh row heir curren level of savings, and he las row heir respecive saving rae a he presen momen. he able shows ha a he same ime 3

15 poin differen age cohors have differen saving raes because permanen income and housing prices are changing over ime. However, regardless of age cohor, he saving rae of each cohor is a funcion of he housing price-o-income raio ( Y ) facing ha paricular cohor. able 2. Saving Behavior of Differen Age Cohors Age Cohor + +2 Permanen Y Y Y Y Income Y ++ Housing ++ Price Savings ( ) ++ Saving Rae Y Y ( ) Y Y Y herefore, if he price-o-income raio Y remains consan over ime despie growing housing prices and permanen income, hen differen age cohors (excep he homebuyer cohor) have he same saving rae, whereas he homebuyer cohor always has a negaive saving rae. Hence, he average saving rae across cohors is exacly zero because each cohor is weighed idenically by he facor / in compuing he socieal average saving rae. However, because by definiion he aggregae saving rae is he raio of aggregae saving o aggregae income, insead of he weighed sum of individuals saving raes, he measured aggregae saving rae is no necessarily zero bu depends on he curren housing price-o-aggregae income raio. ha is, he negaive savings of he homebuyer cohor (cohor + ) may receive a lower (or higher) weigh han if equaion (3) is used as our measure of he aggregae saving rae. For example, if he raio of cohor + s housing price ( ) o aggregae income equals, hen he 4

16 measured aggregae saving rae is sill zero; however, if ha raio is greaer han, hen he measured aggregae saving rae is less han zero because he negaive savings caused by he homebuyer cohor more han cancels he oal savings from oher cohors due o ime-varying housing prices and income; and if ha raio is less han, he measured aggregae saving rae is posiive. o sor ou hese effecs, consider firs he case where permanen income and housing prices have consan growh raes according o he law of moion: Y = ( + ay ) and ( b) = +, respecively, where he growh rae a and b are boh consans. Noice ha if annual income grows a a consan rae, hen he permanen income also grows a he same consan rae. Under hese condiions, he aggregae saving rae is given by ( + b) S = ++ = ++ Y Y ( + a) = ++ = ++ S = = If a and b, equaion (5) can be simplified o. (5) S = Y ++ ( b ) ( + b) ( + b) ( + a) ++ ( + a ) ( + a) +, which depends only on he price-o-income raio of he curren homebuyer cohor. For example, suppose a = b= %, = 4, and = 5. 2 hen equaion (5) gives an aggregae saving rae of 2.4%, which is rivial compared wih he 2% Chinese aggregae saving rae. On he oher hand, i is possible o obain an aggregae saving rae of 2% in he model if we allow he growh rae of permanen income and housing prices o be 5% per year, which is hard o imagine in realiy. herefore, when housing prices and permanen income grow a he same rae, housing prices are sill irrelevan o he aggregae saving rae. 2 = 4 and = 5 imply ha each individual needs o work for 5 years o afford a house and work for 4 years o reire (income is assumed o be zero afer reiremen). 5

17 Calibraion. We now use acual Chinese daa o calibrae he model. Suppose ha people sar working a age 2 and reire a age 6; hus, we se he oal working years = 4. Also suppose ha he average homebuyer s age is 35 ha is, people mus work and save for 5 years before buying a house. his implies ha = 5 in our model (e.g., in able 2). Suppose ha individuals in he homebuyer cohor ( cohor + ) become homeowners in he year 27; in ha year he housing price-o-income raio in China was 7.93, so we se Y = 8. According o Chinese Saisical Yearbook (28), from 978 o 27 he growh rae of average family income is 2.57% in rural areas and 3.58% in urban areas; hence we se a =.3. According o Zhong Hong acro Daabase, he average growh rae of housing prices was 9.2% per year beween 99 and 28, hence we se b =.9. Enering hese numbers ino equaion (5), he esimaed aggregae saving rae equals %. ha is, rising housing prices explain only percenage poin of China s aggregae household saving rae, subsanially below he acual 27% saving rae in 27. oreover, even if he growh rae of housing prices exceeds ha of income, he impac of rising housing prices on aggregae saving rae is sill quie limied. For example, when he growh rae of household income is % per year, o reach an aggregae saving rae of 2% in he model, he average growh rae of housing prices mus be almos 2% per year. Alhough a 2% annual growh rae in housing prices is possible for a shor period, we have no seen such a high average growh rae over a -year period in China or anywhere else in he world. Calibraion 2. he above calibraion analysis is based on he assumpion ha he growh raes of income and housing prices are consan over ime. If we allow he growh rae of income and housing prices o vary over ime, how does his affec our resuls? Because he simple model is no longer analyically racable under uncerainy, we assume perfec foresigh o gain inuiion. When he growh raes of boh income and housing prices are ime varying, able 2 implies ha he aggregae household saving rae is deermined by 6

18 S = = ++ = ++ Y. (6) As before, using 27 as he base year for curren homebuyers (cohor + ): = P, where P 27 denoes he average housing price in 27. Recall ha we 27 use a 4-year window o compue he permanen income based on 4 years of average household income beween year 27 and year 27 +, where = 4. For example, he permanen income of cohor + is given by Y 27+ = Yj. j= 27 By he same mehod, we can also esimae he permanen incomes of cohors {, 2,, } and cohors { 2, 3,, } {,,,,, } Enering he esimaed values of housing prices facing homebuyers of differen age cohors, { Y, Y,, Y,, Y ++ }.6%., and he corresponding permanen incomes ino equaion (6), we obain an aggregae saving rae of herefore, regardless of how he model is calibraed, we conclude ha in he absence of borrowing consrains, rising housing prices canno explain China s aggregae household saving rae. 3 Borrowing Consrains and Demographics he basic model in Secion 2 makes wo imporan assumpions: (i) Consumers can compleely smooh heir consumpion over a working lifeime by using fuure income o finance curren morgage paymens. (ii) he populaion or demographic srucure does no change over ime. hese assumpions are no realisic and may bias our resuls. Assumpion (i) would be innocuous if household income, housing prices, and 3 Compuing young cohors permanen income needs o use income daa afer 29. Since such daa do no exis, we exrapolae by assuming a % annual growh rae afer 29. We provide he sensiiviy analysis in Secion 4. 7

19 populaion were consan over ime. o undersand his, suppose consumers canno borrow a all. hen cohor + mus increase is saving rae a a younger age o accumulae jus enough money o pay off he enire morgage before period +. Even in his case, if income and housing prices do no grow over ime, he aggregae saving rae is sill zero because he negaive savings generaed by cohor + in he housing marke sill compleely cancel he oal posiive savings from cohors {, 2,, }. However, if income and housing prices grow over ime, assumpion (i) is no longer innocuous and borrowing consrains may grealy magnify he posiive impac of housing prices on he aggregae saving rae. he assumpion of a consan populaion size does no allow our model o capure any ransiional dynamics ouside he seady sae. Hence, considering he demographic srucure is also imporan for he robusness of our analysis and conclusions. Formal analyses wih he assumpions (i) and (ii) relaxed are presened below. We consider firs he case wih borrowing consrains (Secion 3.) and hen consider he case wih a ime-varying populaion srucure (Secion 3.2). 3. Borrowing Consrains o faciliae fuure analysis, we firs consider consan income and housing prices under borrowing consrains. If agens canno borrow a all, assuming ha he opimal period for home purchase is sill + periods afer birh (we examine he robusness of he resuls o his assumpion laer), would-be homebuyers mus hen increase heir saving raes before period +. his implies ha from period o he saving rae is /, opimal consumpion is Y. Beween period + 2 and period, he opimal consumpion level is Y and he saving rae is zero. In period +, oal expendiure (consumpion plus housing purchase) is Y summarized in able hese saisics are 8

20 able 3. Individual Saving Behavior under Borrowing Consrains (Consan Income and Housing Prices) Period + +2 Expendiure Y Y Y + Y Y Saving Saving Rae Y Y Y Compared wih able, borrowing consrains raise he individual s saving rae from o ; however, he average lifeime saving rae is sill zero. Hence, if he populaion share of each age cohor is he same, he aggregae saving rae is also zero. Now wih ime-varying income and housing prices, he effecive share of each cohor is no longer he same because of he populaion effec. In his case, we can use a mehod similar o ha used for able 2 o compue each age cohor s saving rae under borrowing consrains. he resuls are summarized in able 4. able 4. Saving Behavior of Differen Cohors under Borrowing Consrains (ime-varying Income and Housing Prices) Age Cohor + +2 Permanen Y Y Y Y Income Y ++ Housing ++ Price Saving Saving Rae Y Y Y Each generaion purchases houses + periods afer birh. In a paricular momen, he curren homebuyer generaion is called cohor +, and his cohor 9

21 faces housing price and permanen income Y. he one-period-younger generaion is called cohor, his cohor will be buying houses in he nex period, facing housing price and permanen income Y, and his generaion s curren saving rae is. Analogously, he one-period-older generaion is called cohor + 2, hese individuals have already bough houses in he las period, faced housing price and permanen income Y, and his generaion s curren saving rae is, in conras o he model in able 2. All cohors proceed in a similar fashion. Suppose he laws of moion for permanen income and housing prices are given, respecively, by Y = ( + ay ) and ( ) = + b, where he growh raes a and b are boh consan. Under such condiions, he aggregae saving rae is given by S = = = ++ ( + b) Y ( + a), (7) which can be simplified o S = Y ( + b ) ( + b) ( + b) ( + a) ++ ( + a ) ( + a). I can be shown ha he aggregae saving rae under borrowing consrains is larger han ha wihou borrowing consrains. he inuiion is as follows. Wihou borrowing consrains, when housing prices increase, he average saving rae of would-be homebuyers is larger han ha of he homeowners because of he populaion effec. Wih borrowing consrains, his populaion effec is significanly amplified because he saving rae of all homeowners is now zero. In oher words, in compuing he aggregae savings, he populaion weigh of would-be homebuyers is increased from o, while he populaion weigh of he homeowners is decreased from 2

22 o. Because he aggregae income of all cohors is he same, he raio of aggregae savings o aggregae income (he aggregae saving rae) has increased under borrowing consrains. Calibraion. As in he previous analysis in Secion 2.2, se = 4, = 5, Y = 8, a =.3, and b =.9. Subsiuing hese values ino equaion (7) gives an aggregae saving rae of 6.66%. Alernaively, if we allow he growh rae of income and housing prices o vary over ime (as in acual Chinese daa), under he assumpion of perfec foresigh, he aggregae saving rae is given by: S = = = ++ Y. (8) Using he same mehod adoped in Secion 2.2 namely, choosing 27 as he base year for he curren homebuyers (cohor + ), esimaing and compuing he associaed values for housing prices {,,,,, } incomes { Y, Y,, Y,, Y ++ } and permanen ++, and subsiuing he resuls ino equaion (8) gives an aggregae saving rae of 9.22%, higher han ha implied by equaion (7). Clearly, under severe borrowing consrains (i.e., no borrowing a all), using acual Chinese ime-series daa for housing prices and income implies esimaes of he aggregae saving rae ha maches he acual Chinese household saving rae quie well. I hus appears ha rising housing prices can explain China s high household saving rae if borrowing consrains are aken ino accoun. Or is i so? No really. In realiy, he degrees of borrowing consrains are no as severe as assumed in he previous analysis. ypically, homebuyers only need o pay one-hird of he housing price as a down paymen and can borrow a leas wo-hirds wih he morgage. he quesion is, how would a slighly relaxed borrowing consrain affec our quaniaive resul? o be conservaive, assume ha he down-paymen requiremen is as high as 2

23 5% of he house. 4 In his case, he borrowing consrains do no bind if each generaion s opimal ime for buying a house is afer working for 2 years (because of sufficien savings). However, as long as each generaion sill needs o purchase houses afer working only for 5 years (as assumed before), borrowing consrains will sill bind for every generaion wih an empirically plausible growh rae of income and housing prices. Under hese condiions, a ypical individual s saving behavior is shown in able 5. able 5. Individual s Saving Behavior wih 5% Down Paymen Period + +2 Expendiure Y Y Y + Y Y Saving 2 2 2( ) 2( ) 2( ) Saving rae 2Y 2 Y 2( ) Y Y 2( ) Y 2( ) Y As able 5 shows, beween period and period of an individual s lifeime, a consumer s annual saving is 2 ; in period +, he oal pas savings are jus enough o pay for he 5% down paymen, so he consumer needs o borrow he oher 5% from fuure income o pay for he morgage. hus, in period + he buyer s housing expendiure is and saving is 2 ( ) ; aferward, fuure saving each period is always. 2( ) Based on such informaion and assuming ime-varying income and housing prices, we can use he mehods oulined in he previous secions o compue each cohor s saving rae a he same momen (able 6). 4 In China he down paymen required for home loans has been abou one-hird of he purchase price unil very recenly. Now he down paymen for he firs house is one-hird and ha for he second house is 5%. 22

24 able 6. Saving Behavior of Differen Cohors wih 5% Down Paymen Age Cohor + +2 Permanen Income Housing Price Y Y Y Y Y Saving 2 2 ( ) 2 2( ) 2 ++ ( ) Saving Rae 2Y 2 Y 2( ) Y Y ( ) 2 Y 2 ( ) ++ Y ++ Y In able 6, if permanen income and housing prices follow a consan growh rule, = ( + ay ) and ( b) = +, hen he aggregae saving rae is given by S = ( + ) ( + ) 2 2( ) b b + = = ++ = ++ Y ( + a). (9) In such a case, we use Chinese daa o se = 4, = 5, Y = 8, a =.3, and b =.9. Subsiuing hese values ino equaion (9) gives an aggregae saving rae of 4.7%. On he oher hand, if he growh raes of income and housing prices are ime varying, he aggregae saving rae is given by S = = = = ++ ( ) Y. () Using he same mehod as before, by seing 27 as he base year for homebuyers (cohor + ) and compuing he associaed housing prices {,,,,, } and permanen incomes { Y, Y,, Y,, Y ++ } ++ equaion () implies an aggregae saving rae of 4.34%. 23, herefore, from he above analyses we can make he following conclusions:

25 Borrowing consrains can significanly amplify he posiive effecs of housing prices on he aggregae saving rae. However, as long as he borrowing consrains are no oo severe (i.e., wih a 5% down paymen), 5 he effecs of rising housing prices on he aggregae saving rae are minimal. Our analysis also indicaes ha, relaive o rising housing prices and oher coss of living, borrowing consrains may be a more imporan and essenial facor for China s high household saving rae. his also explains why rising housing prices in he Unied Saes for more han a decade before he recen financial crisis did no induce a high household saving rae: American families are much less borrowing consrained han Chinese households. Our conclusion is consisen wih he analysis of Wen (29), who shows in a general-equilibrium growh model ha borrowing consrains no only induce a high precauionary saving rae under income uncerainy bu also make his precauionary saving rae an increasing funcion of income growh. So a high income growh can lead o a high aggregae saving rae under borrowing consrains and income uncerainy. 3.2 Demographics Similar o he cases of income and housing price changes, a changing populaion should have no impac on he aggregae saving rae wihou borrowing consrains. hus, his secion considers only he cases wih borrowing consrains. If he populaion changes over ime, he populaion weighs α in equaion (3) for differen cohors mus be adjused accordingly when compuing he aggregae saving rae. hus, leing W denoe cohor s share in oal populaion and assuming ha permanen income and housing prices follow he laws of moion, Y = ( + ay ) and ( b) equaion (3) is given by = +, hen he aggregae saving rae based on 5 he acual down-paymen requiremen in China is less han 5%. Assuming a smaller value furher reduces he impac of housing prices on aggregae saving rae. 24

26 S = = W = ++ ( + b) WY W ( + a), () which is analogous o equaion (7). Based on he populaion shares of age 2 o age 6 provided in China Populaion and Employmen Saisics Yearbook (28), assuming ha working ages are from 2 o 6, he average homebuyer s age is 35 (i.e., he or she mus work for 5 years o buy a house), using he average income growh and housing price growh in China, equaion () implies an aggregae saving rae of.47%, lower han he value under consan populaion. If we allow a 5% down paymen for he morgage, he implied aggregae saving rae is negaive (-.75%), also lower han he value wih consan populaion. If we allow he growh raes of income and housing prices o be ime varying, under % borrowing consrains (% down paymen), he aggregae saving rae is given by S = = W = ++ W WY. (2) Using a similar calibraion mehod as in he previous secion by choosing 27 as he base year for he homebuyer cohor, he implied aggregae saving rae is.32%, lower han he value wih consan populaion. If we allow a 5% down paymen, he implied aggregae saving rae is -.62%, also lower han he value wih consan populaion. he reason ha consideraion of demographic srucure yields a lower aggregae saving rae, everyhing else equal, is ha in recen years he homebuyer cohor is a is peak in erms of is populaion share. herefore, he savings generaed by his cohor receives larger weigh. Figure 3 plos he demographic srucure in China based on China Populaion and Employmen Saisics Yearbook (28), under he assumpion ha working ages are beween 2 and 6 and he average homebuyer s age is

27 Figure 3 shows ha he homebuyer cohor peaked around 27. Suppose he base year of he homebuyer cohor is moved o oher years, such as 25 or earlier, or if we change he assumed age of homebuyers, he implied aggregae saving rae will be only insignificanly differen from he value obained earlier under he assumpion of consan populaion. he reason is simple: Unless he populaion has been sharply declining so ha he populaion share of he homebuyer cohor is always significanly larger han ha of he would-be homebuyer cohors (which is inconsisen wih Chinese daa), aking he demographic srucure ino accoun canno srenghen he effec of rising housing prices on he aggregae saving rae. 2.5 Populaion Share (%) Age Figure 3. Populaion Shares of Differen Age Cohors in 27 (Daa source: China Saisics Yearbook). 3.3 Summary We have discussed hree scenarios in he previous analyses: (a) ime-varying income and housing prices, (b) borrowing consrains, and (c) demographic changes. 26

28 he resuls are briefly summarized in able 7. he firs column liss he assumpions, he second column shows he corresponding equaion used o compue he aggregae saving rae, and he las column shows he numerical value of he aggregae saving rae. able 7. Aggregae Saving Rae under Differen Assumpions Assumpions Equaion Saving Rae(%) No BC, consan {D, I, P} (4). No BC, consan D, consan growh in {I, P} (5). No BC, consan D, ime-varying growh in {I,P} (6).6 % BC, consan D, consan growh in {I,P} (7) 6.66 % BC, consan D, ime-varying growh in {I,P} (8) % BC, consan D, consan growh in {I,P} (9) 4.7 5% BC, consan D, ime-varying growh in {I,P} () 4.34 ime-varying D, % BC, consan growh in {I,P} ().47 ime-varying D and growh in {I,P}, %BC (2).32 ime-varying D, 5% BC, consan growh in {I,P} -.75 ime-varying D and growh in {I,P}, 5% BC -.62 Noe: BC sands for borrowing consrains, D for populaion, I for income, P for housing prices, and % BC for full down-paymen. he firs hree rows in able 7 show ha wihou borrowing consrains and demographic changes, rising housing prices conribue very lile o he aggregae saving rae: less han %. he subsequen wo rows show ha under complee borrowing consrains (wih zero possibiliy o borrow), rising housing prices can have very large effecs on aggregae saving rae, ranging from 6.66% o 9.22%. However, such effecs are quickly dampened once he degree of borrowing consrains is reduced. For example, wih a 5% down-paymen requiremen, he aggregae saving rae is reduced o 4.7% and 4.34%, respecively, depending on he specific income process. In addiion, if China s demographic srucure is aken ino accoun, he las wo rows in he able show ha he saving rae is reduced furher: down o -.75% and -.62%, respecively. herefore, we can conclude ha, given Chinese ime-series daa on household income, morgage prices, borrowing coss, and demographics, he aggregae household saving rae is essenially unrelaed o housing prices. 27

29 4 ore Sensiiviy Analyses 4. Differen Exrapolaions In he previous analyses, we exrapolaed he fuure growh raes of permanen income and housing prices beyond 29 when considering he effecs of ime-varying income and housing prices. For example, in equaion () we have assumed ha fuure growh raes of income and housing prices are boh % per year afer 29. In he following, we conduc sensiiviy analyses on equaion () by considering oher possible growh raes for fuure income and housing prices. Assume a 5% down paymen requiremen and ha he fuure growh raes of income and housing prices ake he values of {8%, 9%, %, %, 2%}, respecively. he implied aggregae saving raes under hese possible fuure growh raes for income and housing prices are repored in able 8, where he op panel assumes a consan demographic srucure and he boom panel considers a ime-varying populaion. able 8. Sensiiviy Analysis for Differen Fuure Growh Raes (5% Down Paymen) Expeced Housing-Price Growh 8% 9% % % 2% Expeced Income Growh Consan Populaion 8%.8% 3.24% 4.79% 6.48% 8.34% 9%.73% 3.9% 4.57% 6.9% 7.95% %.64% 2.93% 4.34% 5.87% 7.55% %.55% 2.77% 4.% 5.55% 7.3% 2%.46% 2.6% 3.85% 5.22% 6.7% ime-varying Populaion 8% -4.44% -3.6% -.77% -.25%.4% 9% -4.26% -3.4% -.7% -.24%.35% % -4.7% -2.9% -.62% -.23%.29% % -3.87% -2.76% -.55% -.22%.23% 2% -3.67% -2.6% -.46% -.2%.6% Firs, able 8 shows ha, given he growh rae of housing prices, he aggregae 28

30 saving rae decreases as he growh rae of income rises. his is consisen wih he permanen-income hypohesis. Second, he aggregae saving rae increases when housing prices are growing faser, given he income growh. he main reason for his is he exisence of borrowing consrains. hird, he aggregae saving rae is he highes (as high as 8.34%) when he expeced fuure income growh rae is 8% and ha of housing prices is 2%. However, if we reduce he down-paymen requiremen from one-half o one-hird, he aggregae saving rae becomes essenially zero. Even if he down paymen remains 5%, aking ino accoun China s demographic srucure (lower panel in able 8) also reduces he implied aggregae saving rae from 8.34% o.4%. herefore, unless people expec housing prices o grow much faser han 2% per year, ha fuure income growh is significanly lower han 8% a year, and ha he borrowing consrains are more severe han he 5% down-paymen requiremen, housing prices canno explain China s high aggregae household saving rae. 4.2 Oher Possible Exensions Our analysis so far is based on a simple economic model. However, our simple model can be furher enriched. In his secion we discuss some possible exensions and he likely effecs of such exensions on our resuls. (a) aking he iming of Home Purchase Endogenous he opimal iming of home purchase in our model is exogenous and is calibraed using he average homebuyer s age (working years). If we can make his variable endogenous, he model has he poenial o explain he difference in he opimal age of homebuyers across counries. However, even if his variable is endogenized, we sill need o calibrae he oher parameers so ha he model-prediced iming of home purchase maches ha in he daa. his is no much differen from exogenously seing = 5, as we did in his paper. herefore, even if were endogenous, our resuls would sill hold under similar calibraions. (b) Including Wealh Effecs In our simple model housing is a consumpion good and generaes a consan 29

31 lifeime uiliy. In realiy, housing is also a capial good because i may yield capial gains when housing prices appreciae, which may generae posiive wealh effecs. However, his simplificaion does no hur our analysis. If shelers were inroduced ino our model as a capial good (or durable consumpion good), he siuaion is he same for he would-be homebuyer cohors when housing price increases; bu for he homeowners, i implies ha heir wealh would increase, which would decrease heir saving incenives and miigae he posiive impac of rising housing prices on lifeime savings. Such a wealh effec may explain why he aggregae household saving rae in developed counries has been declining in he pas decade. For example, Case, Quigley, and Shiller s (26) empirical analysis based on cross-counry and cross-sae daa for he Unied Saes finds ha for every % increase in housing prices, he consumpion-o-income raio increases by.% and he saving rae decreases by.%. hese auhors explain heir findings based on he wealh effec. Hence, inroducing a wealh effec ino our model would only srenghen our conclusion ha rising housing prices canno explain China s high aggregae saving rae. (c) he Hump-Shaped Curve of Lifeime Income Our model assumes ha household income is eiher consan or increasing over ime. Bu in realiy income follows a life cycle wih an invered-u shape: Personal income peaks in middle age. However, our resuls are no sensiive o his income paern. Firs, in our model he measured income is household or family income, no individual income. Household income is less hump-shaped han individual income unless boh husband and wife are idenical wage earners. Second and more imporanly, he mos imporan concern for a hump-shaped income profile is ha agens are more borrowing consrained a a young age. Bu in our model we have se he opimal age of home purchase as 35 (i.e., 5 years afer sar working), which is roughly he peak year of lifeime income. hus, our calibraion makes he concern of borrowing consrains due o a hump-shaped income paern less relevan. In addiion, our calibraion of he down-paymen requiremen of 5% has effecively overesimaed he acual degree of borrowing consrains; we showed ha even under 3