Appendix 1: Proof of Investors’ Binding Borrowing Constraint

PROOF:

Use the Kuhn-Tucker condition to check whether the collateral constraint is binding. We have

μt[mtpth(htI+htRI)btI]=0

If (11) is not binding, then µt = 0. We can write the investor’s FOC Equation (18) as:

Ut,cII(ctI,htI,ntI)=βI𝔼t[(1+it)Ut+1,cII(ct+1)Iht+1)Int+1I)](42)

At steady state, we have

βI(1+i)=1

However from (6), we know βR(1 + i) = 1 at steady state. With parameter restrictions that βR > βI, therefore βI (1 + i) < 1, contradiction. Therefore we cannot have µt = 0. Therefore, µt > 0, and thus we have btI=mtpth(htI+htRI). Q.E.D.

Appendix 2: System of Steady-State Conditions

This appendix lays out the system of equilibrium conditions in steady state.

cR+prhR=YN+idR(43)
UhRR(cR,hR)=ptrUcRR(cR,hR)(44)
UnRR(cR,hR)=WUcRR(cR,hR)(45)
1=βR(1+i)(46)
cI+phδ(hI+hRI)+ibtI=YN+I+prhRI(47)
[1βI(1δ)]UcII(cI,hI)ph=UhII(cI,hI)+μmph(48)
[1βI(1δ)]UcII(cI,hI)ph=UcII(cI,hI)pr+μmph(49)
[1βI(1+i)]UcII(cI,hI)=μ(50)
bI=mphhI(51)
bDev=WnDev+pll(52)
Yh=A(nDev)γ(l)1γ(53)
W=γAph(nDev)γ1(l)1γ1+i(54)
pl=(1γ)Aph(nDev)γ(l)γ1+i(55)
Y=A(NG)α(56)
W=Aα(NG)α1(57)
δ(hI+hRI)=yh(58)
(1ϕ)hRI=ϕhR(59)
(1ϕ)bDev+(1ϕ)bI=ϕdR(60)
NG+(1ϕ)NnDev=N(61)
(1ϕ)Nl=L¯(62)

Appendix 3: Parameter Calibration

The discount factor of the renters (βR,ss) is calibrated by matching the steady-state interest rate to the average deposit rate in China. To proxy for the steady-state level, we use the average one-year benchmark deposit rate in China from 2000 to 2018 (from People’s Bank of China), which equals 2.42 percent.

The weight on housing services by renters ( j) and weight on housing services by investors (κ) are chosen to match another steady-state object, which is the housing GDP as a share of the total GDP. That is, we set the following expression to the average value-added of housing to GDP ratio in China from 2000 to 2018 in the data (from China Statistical Yearbooks in these years):

(1ϕss)Nysshpssh+ϕssNhRpR(1ϕss)Nysshpssh+ϕssNhRpR+Yss=0.05,

where φss is the share of renters in households population and equals 0.255, as discussed in the main text; (1ϕss)Nysshpssh is the housing value-added produced by real estate developers (due to the one-to-one mapping between real estate developers and housing investors, this also equals the market value of houses purchased by housing investors); φssNhRpR is the housing value-added consumed by renters; Yss is the steady-state output of non-housing production. yssh,pssh,hR,pR,Yss are all general equilibrium objects that depend on both j and κ.

The share of labor in housing production (γ) is calibrated to match the average share of labor costin the total cost of real estate developers. There is no official data on this share. Therefore, we manually calculate it for each of the five large real estate developers in China from 2010 to 2019, including China Overseas Land and Investment, China Vanke, China Evergrande Group, Country Garden, and Sunac China Holdings. In each year, we take the weighted average of the labor cost shares (across the five companies) as the share for the whole industry. We then calibrate/estimate 7 as the average share across all available years (2010–2019), which equals 5.74 percent.

Finally, the depreciation rate of houses (δ) takes the standard value from Iacoviello (2005). The discount factor of the investors I) and share of labor in goods production (α) take values from Gete (2020), which also studies the housing market and also assumes that the non-housing sector uses labor as the only input.

References

  • Allen, Franklin, Jun Qian, and Xian Gu, 2017, “An Overview of China’s Financial System,” Annual Review of Financial Economics, ISSN: 1941–1375.

    • Search Google Scholar
    • Export Citation
  • Amstad, Marlene, Guofeng Sun, and Wei Xiong, Forthcoming, The Handbook of China’s Financial System.

  • Anglin, Paul M., David Dale-Johnson, Yanmin Gao, and Guozhong Zhu, 2014, “Patterns of Growth in Chinese Cities: Implications of the Land Lease,” Journal of Urban Economics, 83: 87107.

    • Search Google Scholar
    • Export Citation
  • Arrow, Kenneth, 1964, “The Role of Securities in the Optimal Allocation of Risk Bearing,” Review of Economic Studies, 31 (2): 9196.

    • Search Google Scholar
    • Export Citation
  • Bai, Chong-En, Chang-Tai Hsieh, and Zheng (Michael) Song, 2016. “The Long Shadow of China’s Fiscal Expansion,” Brookings Papers in Economic Activity.

    • Search Google Scholar
    • Export Citation
  • Bai, Chong-En and Yingyi Qian, 2010, “Infrastructure Development in China: The Cases of Electricity, Highways, and Railways,” Journal of Comparative Economics, 38, 3451.

    • Search Google Scholar
    • Export Citation
  • Brunnermeier, Markus, Michael Sockin, and Wei Xiong, 2017, “China’s Gradualistic Economic Approach and Financial Markets,” American Economic Review Papers & Proceedings, 107 (5): 608613.

    • Search Google Scholar
    • Export Citation
  • Chen, Zhuo, Zhiguo He, and Chun Liu, 2020, “The Financing of Local Government in China: Stimulus Loan Wanes and Shadow Banking Waxes,” Journal of Financial Economics, 137 (1): 4271.

    • Search Google Scholar
    • Export Citation
  • Chen, Ting, Laura Xiaolei Liu, Wei Xiong, and Li-An Zhou, 2017, “Real Estate Boom and Misallocation of Capital in China,” Working Paper.

    • Search Google Scholar
    • Export Citation
  • Chen, Kaiji, Jue Ren, and Tao Zha, 2018, “The Nexus of Monetary Policy and Shadow Banking in China,” American Economic Review, 108 (12): 38913936.

    • Search Google Scholar
    • Export Citation
  • Chen, Kaiji, and Yi Wen, 2017, “The Great Housing Boom of China,” American Economic Journal: Macroeconomics, 9 (2): 73114.

  • Du, Zaichao, and Lin Zhang, 2015, “Home-Purchase Restriction, Property Tax and Housing Price in China: A Counterfactual Analysis,” Journal of Econometrics, 188 (2): 558568.

    • Search Google Scholar
    • Export Citation
  • Gan, Li, Feng Li, Xiaomeng Lu, Bofu Deng, Jiandong Luo, Hongyang Wang, Tao Jiang, Liangyan Guo, Sitong Chen, and Xiang Wang, 2016, “Assessment Report on Chinese Household Finance Portfolio Risks,” Neo Capital Report.

    • Search Google Scholar
    • Export Citation
  • Gao, Huina, Zhi Liu, and Yue Long, 2019, “Residential Land Supply and Housing Prices in China: An Empirical Analysis of Large Cities,” Chapter 15, by Rebecca Chiu, Zhi Liu, and Bertrand Renaud (ed.), International Housing Market Experience and Implications for China.

    • Search Google Scholar
    • Export Citation
  • Gete, Pedro, 2020, “Expectations and the Housing Boom and Bust: An Open Economy View,” Journal of Housing Economics, 49, September.

  • Glaeser, Edward, Wei Huang, Yueran Ma, and Andrei Shleifer, 2017, “A Real Estate Boom with Chinese Characteristics,” Journal of Economic Perspectives, 31(1): 93116.

    • Search Google Scholar
    • Export Citation
  • Liu, Chang, and Wei Xiong, 2018, “China’s Real Estate Market,” NBER Working Paper #25297.

  • McKinnon, Ronald I., 1973, Money and Capital in Economic Development, Washington, D.C.: Brookings Institution.

  • Mei, Dongzhou, Xiaoyong Cui, and Yu Wu, 2018, “House Price Fluctuation, Land Finance and Business Cycle in China,” (in Chinese) Economic Research Journal, 1: 3549.

    • Search Google Scholar
    • Export Citation
  • Minetti, Raoul, Tao Peng, and Tao Jiang, 2019, “Keeping Up with the Zhangs and House Price Dynamics in China,” Journal of Economic Dynamics and Control, 109.

    • Search Google Scholar
    • Export Citation
  • He, Hui, Huang, Feng, Liu, Zheng, and Dongming Zhu, 2018, “Breaking the ’Iron Rice Bowl:’ Evidence of Precautionary Savings from the Chinese State-Owned Enterprises Reform,” Journal of Monetary Economics, 94: 94113.

    • Search Google Scholar
    • Export Citation
  • He, Hui, Lei Ning, and Dongming Zhu, 2019, “The Impact of Rapid Ageing and Pension Reform on Savings and the Labor Supply: The Case of China,” IMF Working Paper 19/61.

    • Search Google Scholar
    • Export Citation
  • Huang, Yukon, 2017, “Cracking the China Conundrum: Why Conventional Economic Wisdom Is Wrong,” Oxford University Press.

  • Iacoviello, Matteo, 2005, “House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle,” American Economic Review, 95 (3): 739764.

    • Search Google Scholar
    • Export Citation
  • IMF, 2019, People’s Republic of China: 2019 Article IV Consultation Staff Report, IMF Country Report No. 19/266.

  • Rajan, Raghuram G., 2006, “Has Finance Made the World Riskier?European Financial Management, 12(4): 499533.

  • Rungskunroch, Panrawee, Yuwen Yang, and Sakdirat Kaewunruen, 2020, “Does High-Speed Rail Influence Urban Dynamics and Land Pricing?Sustainability,, 12 (7).

    • Search Google Scholar
    • Export Citation
  • Shaw, Edward S., 1973, Financial Deepening in Economic Development, New York: Oxford University Press.

  • Shepard, Wade, 2015, Ghost Cities of China: The Story of Cities without People in the World’s Most Populated Country. London: Zed Books.

    • Search Google Scholar
    • Export Citation
  • Shi, Yu, 2018, “Sectoral Booms and Misallocation of Managerial Talent: Evidence from the Chinese Real Estate Boom,” IMF Working Paper 18/221.

    • Search Google Scholar
    • Export Citation
  • Wang, Zhi, Qinghua Zhang, and Li-An Zhou, 2019, “Career Incentives of City Leaders and Urban Spatial Expansion in China,” Review of Economics and Statistics, August.

    • Search Google Scholar
    • Export Citation
  • Woodworth, Max D., and Jeremy L. Wallace, 2017, “Seeing Ghosts: Parsing China’s ‘Ghost City’ Controversy,” Urban Geography, 38(8): 12701281.

    • Search Google Scholar
    • Export Citation
  • Wu, Jing, Joseph Gyourko, and Yongheng Deng, 2016, “Evaluating the Risk of Chinese Housing Markets: What We Know and What We Need to Know,” China Economic Review, 39: 91114.

    • Search Google Scholar
    • Export Citation
  • Xiong, Wei, 2019, “The Mandarin Model of Growth,” Princeton University Working Paper.

  • Yang, Zan, Ying Fan, and Liqing Zhao, 2018, “A Reexamination of Housing Price and Household Consumption in China: The Dual Role of Housing Consumption and Housing Investment,” Journal of Real Estate Finance and Economics, 56: 472499.

    • Search Google Scholar
    • Export Citation
  • Zhang, Longmei, Ray Brooks, Ding Ding, Haiyan Ding, Hui He, Jing Lu, and Rui C. Mano, 2018, “China’s High Savings: Drivers, Prospects, and Policies,” IMF Working Paper 18/277.

    • Search Google Scholar
    • Export Citation
  • Zhang, Chuanchuan, Shen Jia, Rudai Yang, 2016, “Housing Affordability and Housing Vacancy in China: The Role of Income Inequality,” Journal of Housing Economics, 33: 414.

    • Search Google Scholar
    • Export Citation
  • Zhao, Yunhui, 2020, “US Housing Market during COVID-19: Aggregate and Distributional Evidence,” COVID Economics, 50 (September): 113154.

    • Search Google Scholar
    • Export Citation
1

We are grateful for the helpful discussions during the presentation to the China team (with Helge Berger, Fei Han, Kenneth Kang, and other team members); for the comments received during the formal review stage (from Katharina Bergant, Diego Alejandro Cerdeiro, Junghwan Mok, Cian Ruane) and at the surveillance meeting; and for the helpful discussions with Zhuo Chen (Tsinghua), Martin Cihak, Ding Ding, Jack Favilukis (UBC), Wei Guo, Dong He, Zhiguo He (Chicago), Zhongxia Jin, Petya Koeva Brooks, Ivo Krznar, Li Lin, Jianhai Lin, Yang Liu, Wojciech Maliszewski, Paul Mathieu, Alex Murray (Finance Canada), Xiaohui Sun, Rengming Xie, TengTeng Xu, Wentao Xiong (Harvard), Daria Zakharova, Fudong Zhang (Tsinghua), Tianxiao Zheng, and especially Chuqiao Bi and Tao Zha (Atlanta Fed). We also thank Tiana Wang for her research assistance.

2

The rising trend of the housing price in the US is also not reversed by the COVID-19, as discussed in Zhao (2020).

3

Incomplete markets are markets where the number of Arrow-Debreu securities is less than that of states of nature (Arrow, 1964). This shortage of securities will likely restrict individuals from transferring the desired level of wealth among states. In the case of financial markets, market incompleteness practically means the available investment channels (for savers) or financing channels (for borrowers) are inadequate for savers/borrowers to optimally allocate resources over time.

4

We could extend our model to include the stock market; however, for the “rich” households who can afford the down payments for multiple houses, housing is still a preferred investment under reasonable parameterizations. Therefore, for simplicity we did not add this market.

5

The source can be found here. In addition, China’s overseas investment in 2018 fell 9.6 percent, as the Chinese government’s crackdown on capital flight continued (South China Morning Post, September 13, 2019).

6

The lively-updated supplementary materials are available here.

7

Liu and Xiong (2018) review the historical development of China’s real estate market.

8

Chen and Wen (2017) finds that China’s housing boom can be interpreted as a rational bubble emerging naturally from its economic transition.

9

Chen, Ren, and Zha (2018) also study the rise of shadow banking activities in China, although their focus is not on the housing market per se.

10

Based on data from 2001 to 2012, Glaeser and others (2017) document that China’s housing vacancy rate rose sharply after 2009. And as of February 2019, one-fifth of China’s urban housing stock had been bought and left vacant (Bloomberg, February 27, 2019).

11

For example, the housing price per square meter in Ordos City dropped from RMB 20,000 to RMB 3,000 (QQ News, April 2, 2020).

12

Separately, Brunnermeier, Sockin, and Xiong (2017) study the macroeconomic implications of China’s financial market liberalization, and find that China’s current, more liberal financial system poses challenges for the government to experiment with a temporary stimulus that could be reversed easily soon after its inception.

13

The same comment applies to other 2020 data in subsequent figures. The GDP estimate can be found here.

14

All the numbers presented in Figure 3 and Figure 4 have been cross-checked against numbers published elsewhere.

1

More specifically, as explained later, the Nt households as a whole (including all renters and all investors) own the non-housing consumption goods producers and equally split the (off-equilibrium) profit from these producers. Hence, for an individual renter (and an individual investor), the total income from these producers equals Wt+YtWtNtNt=YtNt, where Wt is the wage.

2

Below is one analog that may help better understand our proposal: The current financial system in China is like an “arranged marriage” where corporates with dramatically different risk profiles are forced to “marry” the dominant and risk-averse banks; by contrast, what we propose is similar to “free marriage” where “men” (a variety of financial institutions, including banks and nonbanks) and “women” (corporates) can freely match with each other based on their risk profiles/preferences. But to ensure the fairness and efficiency of this “free marriage market”, some strict rules have to be put in place. And the current issue of emerging fake P2P platforms in China is just like disclosing false information on a dating site.

Incomplete Financial Markets and the Booming Housing Sector in China
Author: Mr. Tamim Bayoumi and Mr. Yunhui Zhao