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Short communication

Are house prices too high in China

Ling SHEN

School of Business East China University of Science and Technology Meilong Road 130 Shanghai 200237 China

a r t i c l e i n f o a b s t r a c t

Article histo ry

Received 10 November 2010Received in revised form 15 September 2011

Accepted 24 March 2012

Available online 12 May 2012

This short note defines a new measurement of housing affordability in terms of permanent

income Using this new measurement we find that housing affordability in China is verystrong relative to other developed economies although the ratio of housing prices to current

income in China is much higher than those of developed nations

copy 2012 Elsevier Inc All rights reserved

JEL class ification

C43

E25

E64

R31

Keywords

Housing affordability

Price-to-income ratio

Growth

China

With house prices soaring in key cities more and more investors and economists worry that China has the next great real

estate bubble waiting to be burst1 The Chinese government is worrying too In recent months many regulation policies have

been implemented in order to stop the rising trend of house prices in Chinese cities for example increasing downpayments to

40 for Chinese families buying a second home stopping new loans for a third home and forbidding selling apartments to non-

residents of the cities

Many of these arguments and policies have mentioned two basic pieces of information First new house prices in 70 large and

middle-sized cities have been increasing very rapidly over the past decade In particular new house prices grew by average

annual rate of 235 in 20092 Second the housing price-to-income ratio in urban China is much higher than the average level of

developed nations For instance the report ldquothe Analysis of Real Estate Trends in Shanghairdquo by Li Xunlei3 reports an average ratio

of 10 for Chinas largest cities Similarly the Economic Blue Bulletin by the Chinese Academy of Social Sciences also shows that the

housing price-to-income ratio reached 83 for urban residents in China in 2008

In addition on January 19 2010 the National Bureau of Statistics of China published the 2009 National Real Estate Market

Situation that shows the national average new house price was 4695 CNYm 2 in 2009 Thus an apartment of 100 m2 costs about

470000 CNY According to the National Bureau of Statistics the per capita disposable income of urban residents in 2009 was

17175 CNY while annual household income was 51525 CNY for a family of three Thus in 2009 the average housing price-to-

China Economic Review 23 (2012) 1206ndash1210

We would like to thank Prof Guoqiang Tian and the Editor for t heir helpful suggestions All possible errors are of course mine

E-mail address vwldehotmailcom1 For example Daily Finance reported ldquoGlobal Economys next threat Chinas Real Estate Bubblerdquo on January 5 2010 by Charles Hugh Smith CNN senior writer

Chris Isidore worried ldquoIs China another real estate bubblerdquo on April 15 2010 on CNN Moneycom and the Wall Street Journal even earlier proclaimed ldquoChinas

Housing Bubble Troublerdquo on November 20 2009 by Andrew Peaple2 Data source the National Bureau of Statistics of China3 Li Xunlei is the Director of Research Institute in Guotai-Junan Securities Co which is one of the biggest in China

1043-951X$ ndash see front matter copy 2012 Elsevier Inc All rights reserveddoi101016jchieco201203008

Contents lists available at SciVerse ScienceDirect

China Economic Review

8132019 Are house prices too high in Chinapdf

httpslidepdfcomreaderfullare-house-prices-too-high-in-chinapdf 25

income ratio was 91 for urban residents in China which is approximately consistent with the above data By contrast according

to Demographia International (2010) which computes median housing price-to-income ratios for 227 regions the comparable

national data are 29 for the US 51 for the UK and 68 for Australia

These data have been widely quoted However the theoretical underpinnings of the concept of affordability have received

little attention from academics Given the housing price-to-income ratios quoted above it is easy to arrive at the conclusion that

Chinas house prices are much less affordable than are those of the US which may then be amplified to the existence of a large

bubble in the Chinese real estate market giving rise to public misunderstandings However if we take a dynamic point of view

to examine Chinas housing affordability and consider differences in the real estate tax system we may come to different conclusions

This note constructs a new measurement of the housing price-to-permanent income ratio through which we can better

compare housing affordability among regions with different growth rates Then we apply our methodology to data on China and

on developed countries

The literature on housing affordability tends to focus either on the ratio of house prices to current income or on the proportion

of income to mortgage repayments (eg Gan amp Hill 2009 Stone 2006) In addition previous studies have mostly discussed the

distribution of affordability in particular for low income families (Hulchanski 1995 Kutty 2005) Since the housing reforms in

1998 the Chinese housing market has attracted more and more concerns among academic researchers For example Sato (2006)

discusses housing inequality and housing poverty in urban China in the late 1990s while Wang Yang and Liu (2010) shed light

on the impact of urban economic openness on realestate prices in 35 Chinese cities Further Gan Yin and Zang (2010) investigate the

impact of housing reforms on the consumption of durables in China However none of these studies measures housing affordability

using an international comparison

We consider a representative agent living infinitely in an economy with a nominal growth rate g that has a current income y0

The interest rate is r Hence for g ner hisher present value of the income in N periods is

y0

1thorn g 1thornr

N

minus1

1thorn g 1thornr minus1

264

375

For g br the permanent income is y01thornr r minus g

forallNrarrinfin For g gt r the permanent income approaches infinity If g = r lifetime income is

N y0 Because housing choices are likely to be made based on lifetime income rather than on current income4 we construct a

housing price-to-permanent income ratio (PPIR) instead of the ratio of house prices to current income (PCIR) Theoretically the

PPIR is consistent with the permanent income hypothesis Hence it is better than the PCIR to measure housing affordability

because it takes into consideration income growth

De1047297nition 1 The house price to permanent income ratio (PPIR) is defined as

X y0

1thorn g 1thornr minus1

1thorn g 1thornr

N

minus1equiv X

y0

β

where X is the house price

Because X y0

is the PCIR the factor β is the ratio of the PPIR to the PCIR which depends on g r and N If the annual growth rate

of income is the same as the interest rate the factor β is equal to 1N= For a comparison among different regions it is reasonable to

assume that N is equal for all hence the comparison of PPIRs is the same as comparing PCIRs for the case of g = r

For g ner it is also possible to use the PCIR instead of the PPIR for comparisons if these regions have exactly the same growth

rates and interest rates However Table 1 shows that they are different in general The annual growth rates in nominal GDP and

lending interest rates during 1990ndash2009 for selected developed economies and China are shown in Table 1

We find from above table that lending interest rates are similar for these economies except Australia and New Zealand

Further GDP growth rates (as the proxy of income growth rate) are similar except in China and Ireland In particular these two

economies have a greater GDP growth rate than lending interest rate Hence we are able to apply β frac14 r minus g 1thornr to calculate the PPIRs forthese economies except China and Ireland

For China and Ireland we cannot apply β frac14 r minus g 1thornr because g gt r Intuitively we cannot assume that the annual growth rates in

income for these two economies can stay at such a high level forever Instead we assume that they grow at the current growth

rate g for N periods and that the growth rate then falls below r to be equal to the average level of the other five economies namely

475 Hence China and Ireland have a permanent income

y0

1thorn g 1thornr

N

minus1

1thorn g 1thornr minus1

0B

1CA thorn

1 thorn g

1 thorn r

Nminus1 1 thorn g prime

r minus g prime

264

375 eth1THORN

where5 g prime= 475 For N = 15 the comparable values for these two economies are 0097 and 0031 respectively (Table 2)

4

Quigeley and Raphael (2004) mention this however they do not consider it in a formal framework5 See Appendix A

1207L Shen China Economic Review 23 (2012) 1206 ndash1210

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From this new point of view although the UK has a higher PCIR than the US its affordability is higher because of the highereconomic growth rate and lower interest rate Moreover Australia and New Zealand are less affordable from both perspectives

although they have high economic growth rates too This is because these two economies have high interest rates

The novel result lies in China Because of its extreme economic growth as well as a relatively low interest rate (compared with

the average level of other economies) its housing affordability is extremely high in terms of the PPIR (ie the value of the PPIR is

extremely low) However it has a very low housing affordability in terms of the PCIR (91) This dramatic result comes from

different implicit assumptions the PCIR comes from a static viewpoint whereas the PPIR stems from a dynamic one As Chinas

growth behaves differently relative to developed economies we should take the growth rate into consideration Of course this

consideration (PPIR) implicitly assumes that the current growth rate of income (1328) and the interest rate (772) are

sustainable in China for at least N years (eg N = 15) Thus we can test the robustness of this result in two aspects N and r

First even if China could only grow at this rate for 10 years (N=10) its housing affordability (PPIR=0134) is still similar to

that of Australia and New Zealand Table 3 shows that the qualitative result still holds when N varies from 5 to 30 Another aspect

to understand the case of China is to test whether high housing affordability is sustainable if the interest rate rises For example

we can assume that the interest rate rises to the level so that r minus

g is same as the average level of the other five economies exceptIreland namely 3 Then the PPIR of China is 0235 also similar to that of New Zealand Table 3 also shows similar calculations for

when the interest rate varies from 1428 to 1828

From the above discussion we know that we can get different judgments about housing affordability when we use different

measurements namely the PPIR or the PCIR It is difficult to say which is better in general For those economies growing at similar

rates and with similar interest rates the PCIR is a good simplified version of the PPIR Both produce similar results However for

those growing at different rates the permanent income hypothesis implies that the PPIR is able to measure housing affordability

better than can the PCIR In practice investors use these ratios to estimate the potential ldquohousing bubblerdquo Hence it is ofinterest to

see which one can make better predictions using historical data

Chinese statistical yearbooks have reported average new apartment prices per m2 every year since 1997 Hence we can

estimate the PCIR by assuming a 100 m2 apartment and a family of three (as above) From 1997 to 2009 the growth rate of

disposable income of Chinese urban residents was 10 and we assume r =7 Because this annual growth rate was successfully

achieved for more than 10 years we can use Eq (1) assuming N= 10 to calculate historical PPIRs

From Table 4 we know that the PCIR in China was even higher in the past decade Hence if wewould use the PCIR to estimate thepossible ldquohousing bubblerdquo we would conclude that China had a great bubble 12 years ago An investor at that time was not worried

because the PPIR (016) was not high compared with those of developed economies (006ndash026) If an investor did buy an apartment

on the basis of this judgment in 1997 heshe would find that hisher own PCIR decreased rapidly from 129 to 3886 by 2009 In fact

we can divide the past 12 years into two periods The first one is from 1997 to 2003 In this period the annual growth rate of income

was 83 and house prices rose by 28 every year Hence the PCIR decreased from 129 to 93 The second period is from 2003 to

2009 Although house prices grew by 115 every year income grew at a similar level Hence the PCIR was stable We thus cannot

conclude a ldquohousing bubblerdquo in China simply by comparing the Chinese PCIR with those of other developed nations

Now we turn to the real estate tax system In the US a typical case of developed economies there is a real estate tax for owning

a house which is τ of the current value every year However there is no such user fee in China 7 This difference implies that US

6 If heshe bought an apartment in 1997 at 1997 prices hisher apartment price is 1047297xed from then on However hisher income increased to 17175 CNY over

the next 12 years Hence in 2009 hisher PCIR is 388 not 91 This is important for the investor who borrows from the 1047297nancial market when heshe buys an

apartment7

China announced such a tax reform at the beginning of 2011 In Chongqing and Shanghai some owners whose houses are particular large will pay anadditional real estate tax

Table 2

PPIRs and PCIRs

Source PCIRs are quoted from Demographia International (2010) Chinas data are from the estimation on page 1

Australia Canada Ireland New Zealand UK US China

PCIRs 68 37 37 57 51 29 91

PPIRs (I) 021 006 026 008 009

PPIRs (II) 0031 0097

PPIRs (I) are calculated by the form β = (r minus g )(1+r ) for those countries r gt g For Ireland and China PPIRs (II) are calculated under the assumption that they

retain their current growth rates for 15 years which then fall to the average level namely 475

Table 1

Growth rates in nominal GDP and lending interest rates (1990ndash2009)

Australia Canada Ireland New Zealand UK US China

r 940 612 605 1020 601 700 772

g 603 439 781 512 438 383 1328

r ndash g 337 173 minus176 508 163 317 minus556

Notes r is the lending interest rate and g is the annual growth rate in nominal GDP (in USD) All data are derived from the World Bank Databank httpdata

worldbankorg

1208 L Shen China Economic Review 23 (2012) 1206 ndash1210

8132019 Are house prices too high in Chinapdf

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house prices are not the total cost of owning a house Hence in order to compare housing affordability in China and the US we

construct a second ratio namely the total housing cost-to-permanent income ratio (TPIR)

De1047297nition 2 The total housing cost to the permanent income (TPIR) is defined as

X thorn Z eth THORN

y0

β

where Z is the present value of real estate tax

For the simple case where X is constant over time Z frac14 X τ r TRIP frac14 PPIR 1 thorn τ r

If we assume τ =2 for the six economies

mentioned in Demographia International (2010) housing affordability in China is even higher relative to others (Table 5)

As housing is non-traded and inherently local talking about affordability at a national level is not convincing enough

Therefore I follow Demographia International to compare two main Chinese cities Shanghai and Beijing with seven other

metropolises in the abovementioned developed countries We calculate the growth rate of income for those metropolises in

developed countries using data from Demographia International Annual reports (2006ndash2010) and continue to use the above

interest rates because they are country-specific For China we collect data from statistic yearbooks (2006ndash2010) The results are

shown in Table 6

Similar to the comparison at the national level it seems that there were housing bubbles in Los Angeles and in the two Chinese

cities in 2005 in terms of PCIRs Their higher PCIRs imply that the housing in these regions is much less affordable relative toelsewhere However we come to different conclusions in terms of PPIRs Chinese cities show a greater housing affordability

because of higher growth rates of income (about 113) If an investor in Beijing in 2005 had believed PPIRs instead of PCIRs and

indeed bought an apartment heshe would find that the value of hisher apartment had increased by 19 per year for the

following five years Some may argue that by using PPIRs investors in Los Angeles might come to the wrong conclusion because

house prices there decreased at an annual rate of 63 for the next five years The reason for this lies in the calculation of PPIRs (I)

which implies that the current growth rate is sustainable forever This is obviously not true for Los Angeles Hence if we use PPIRs

Table 3

The robustness test of the case of China

N 5 10 15 20 25 30

PPIR 0188 0134 0098 0073 0055 0041

r 1428 1528 1628 1728 1828

PPIR 0080 0158 0235 0310 0385

Notes we only change the value of N from 5 to 30 while the PPIR varies from 0188 to 0041 which is similar to that of developed economies If we raise the

interest rate to 1428 or even to 1828 the PPIR still shows us that Chinese housing affordability is similar to that in Australia and New Zealand

Table 4

PCIRs and PPIRs in China over the past decade

Source data are derived from the Chinese Statistic yearbook (2010) httpwwwstatsgovcntjsjndsj2010indexehhtm

Disposable income of Chinese urban residents (CNY) Average new apartment price per m2 (CNY) PCIR PPIR

1997 5160 1997 129 016

1998 5425 2063 127 016

1999 5854 2053 117 015

2000 6280 2112 112 014

2001 6860 2170 105 013

2002 7703 2250 97 012

2003 8472 2359 93 012

2004 9422 2714 96 0122005 10493 3168 101 013

2006 11760 3367 95 012

2007 13786 3864 93 012

2008 15781 3801 80 010

2009 17175 4695 91 012

Notes the PCIR= (new apartment price 100)(income 3) the PPIR is calculated by assuming g =10 r =7 N=10 and g prime=5

Table 5

PPIRs and TPIRs

Australia Canada Ireland New Zealand UK US China

PPIRs (I) (II) 021 006 0031 026 008 009 0097

TPIRs 0255 008 008 031 0106 0116 0097

Notes PPIRs are from Table 2 while the TPIR is from TRIP frac14 PPIR 1 thorn τ r

which reflects the difference in real estate tax systems

1209L Shen China Economic Review 23 (2012) 1206 ndash1210

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(II) instead of PPIRs (I) by assuming the current growth rate can continue for five years and then decrease to the average level

namely 3 PPIRs have a normal conclusion

We conclude from this new measurement of housing affordability that Chinas housing affordability is relatively high if we

consider the PPIR instead of the PCIR The key factors are the high economic growth rate and low interest rate in China If we were

to call it a ldquobubblerdquo it would be interesting to test whether it would be sustainable if the low interest rate rose or the high growth

rate declined The above results show that Chinese housing is still affordable compared with New Zealand and Australia in terms

of the PPIR We believe that this novel result is useful for better understanding the case of China and other rapidly growing

economies

Appendix A

We consider an economy with current income y0 growing at g gt r for the first N periods and then the growth rate falls to g br

Then the present value (PV ) of the permanent income is as follows

PV frac14XNminus1

t frac140

y0

1 thorn g

1 thorn r

t

thornXinfint frac14N

yNminus1

1 thorn g prime

1 thorn r

t minusNthorn1

frac14 y0

1 thorn g

1 thorn r

N

minus1

1 thorn g

1 thorn r

minus1

thorn yNminus1

1 thorn g prime

r minus g prime

frac14 y0

1 thorn g 1 thorn r

Nminus1

1 thorn g

1 thorn r

minus1

thorn 1 thorn g

1 thorn r

Nminus1 1 thorn g

prime

r minus g prime

2666437775

References

Chinese Statistic yearbook (2010) httpwwwstatsgovcntjsjndsj2010indexehhtmDemographia International (2010) httpwwwdemographiacom Gan Li Yin Zhichao amp Zang Wenbin (2010) The impact of housing reform on durables consumption in China China Economic Review 21 55ndash64Gan Q amp Hill R J (2009) Measuring housing affordability Looking beyond the median Journal of House Economy 18 115ndash125Hulchanski J D (1995) The concept of housing affordability Six contemporary uses of the housing expenditure-to-income ratio Housing Studies 10(4) 471ndash491Kutty N K (2005) A new measure of housing affordability Estimates and analytical results Housing Policy Debate 16 (1) 113ndash142Quigeley J M amp Raphael S (2004) Is housing unaffordable Why isnt it more affordable The Journal of Economic Perspectives 18(1) 191ndash214

Sato Hiroshi (2006) Housing inequality and housing poverty in urban China in the late 1990s China Economic Review 17 37ndash50Stone M (2006) What is housing affordability The case for the residual income approach Housing Policy Debate 17 (1) 151ndash184The 2009 National Real Estate Market Situation Published by National Bureau of Statistics of China httpwwwstatsgovcn Wang Songtao Yang Zan amp Liu Hongyu (2010) Impact of urban economic openness on real estate prices evidence from thirty-five cities in China China

Economic Review httpdxdoiorg 101016jchieco201008007World Bank Databank httpdataworldbankorg

Table 6

PPIRs and PCIRs at a city level in 2005

Sources Data on non-Chinese cities are from Demographia International PCIRs are from its annual report (2006) and the growth rate of income is calculated from

its reports (2006ndash2010) The interest rate is from the World Bank as in Table 1 Chinas data are from various Chinese statistical yearbooks (2006ndash2010)

New York Los Angeles Toronto London Dublin Sydney Auckland Beijing Shanghai

PCIRs 79 112 44 69 60 85 66 105 108

Growth 256 481 022 156 591 12 38 1128 1132

PPIRs (I) 0328 0229 0243 0289 0008 0639 0385

PPIRs (II) 0393 0155 0141 0144

PPIRs (I) are calculated by the form β = (r minus g )(1+r ) for those countries r gt g For Beijing and Shanghai PPIRs (II) are calculated under the assumption that they

can keep the current growth rate for 15 years which then falls to the average level namely 3 For Los Angeles and Dublin N=5

1210 L Shen China Economic Review 23 (2012) 1206 ndash1210