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Does large volatility help?—stochastic population forecasting technology in explaining real estate price process

Abstract

This paper investigates the association between real estate demand and the volatility of population changes. In a financial liberalized housing market, the housing mortgage loan implies insurance function to homeowners through the default option. Larger expected volatilities in the population imply a higher value of the default option. When analyzing the impact of the long-term population development on housing prices, the traditional deterministic population forecasting employed by previous research provides limited credibility. By means of the newly developed stochastic population forecasting methodology and counterfactual numerical simulations, we found a huge volatility associated with long-term population forecasting. A positive correlation between the expected volatility of population changes and real estate demand is ascertained.

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Fig. 1
Fig. 2

Notes

  1. Hoynes and McFadden (1994)

  2. The Supreme People’s Court of the People’s Republic of China.

  3. http://www.yicai.com/news/2010/06/366162.html

  4. Software R has been adopted to generate the multivariate normal distributed variables for changes in population, housing stock, and income. The singular value decomposition method was used in generating the multivariate normal distributed variables.

  5. The data is from the 2009 Shanghai Statistics Yearbook. For the variables of income, population and housing supply, we use the published data on individual average disposable income, residential population and the area of newly constructed residential dwellings as the proxies.

  6. For the minimum age of childbearing, β 4, we found that estimates were invariably equal to 15 years.

  7. 17.38, 17.32, and 16.76 million are for 2015, 2030, and 2040, respectively.

  8. The price is published for January 2007 on http://www.ehomeday.com.

  9. It is obtained by (predicted population mean in Year 2030 – population in Year 2000)/ population in Year 2000.

  10. It is obtained by ((upper bound of 95% confidence interval – population in Year 2000)/ population in Year 2000)^2.

  11. The “equivalent” population concept has been introduced by Mankiw and Weil (1989) and employed extensively afterwards. The core of “equivalent” population is to transform the nominal population number into another population number, which denotes an artificial population size as if all the people are at the same age group.

  12. 1.86, 5.03, and 10.08 million are for group younger than 25 years old, middle age group between 25 and 55 years old, and the old group with age above 55 years old, respectively.

  13. \({\rm log}\left( {Y_t } \right)_{\rm adj} = {\rm log}\left( {Y_t } \right)-log\left( {Y_t } \right)_{\rm hat} ,\,\quad {\rm where} \quad {\rm log}\left( {Y_t } \right)_{\rm hat} =\hat {\gamma }_0 +\hat {\gamma }_1 {\rm log}\left( {N_t } \right)+\hat {\gamma }_2 {\rm log}\left( {K_t } \right).\)

    \({\rm log}\left( {K_t } \right)_{\rm adj} = {\rm log}\left( {K_t } \right)-{\rm log}\left( {K_t } \right)_{\rm hat} ,\quad {\rm where} \quad {\rm log}\left( {K_t } \right)_{\rm hat} =\hat {\lambda }_0 +\hat {\lambda }_1 \,{\rm log}\left( {N_t } \right).\)

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Acknowledgements

We would like to thank the anonymous referees, Nico Keilman, James M. Poterba, Olav Bjerkholt, John K. Dagsvik, Erik Biorn, Kaiji Chen, and Ke Wang for their valuable comments. We also gratefully acknowledge the support of National Natural Science Foundation of China (Research Project: #70632002, Fudan University, China) and the sponsor from Shanghai Pujiang Program.

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Correspondence to Xuehui Han.

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Appendix

Appendix

Starting from Eq. 14, we can get

$$ \label{A1} P=\frac{1}{K}\ast N\ast (W+(1-m)Y)\ast s. $$
(29)

Based on Eq. 29, we can have

$$ \begin{array}{rll} \label{A2} \hfill {\mathop P\limits^\bullet } &=& \frac{\left( {\frac{1}{K'}\times N'\times (W+(1-m)Y')\times s} \right)-\left( {\frac{1}{K}\times N\times (W+(1-m)Y)\times s} \right)}{\left( {\frac{1}{K}\times N\times (W+(1-m)Y)\times s} \right)}, \\ &=& \frac{\left( {\frac{1}{K'}\times N'\times (W+(1-m)Y')\times s} \right)}{\left( {\frac{1}{K}\times N\times (W+(1-m)Y)\times s} \right)}-1, \\ &=& \left[ {\left( {\frac{K}{K'}\times \frac{N'}{N}\times \frac{(W+(1-m)Y')}{(W+(1-m)Y)}} \right)} \right]-1. \end{array} $$
(30)

The variance of \(\mathop P\limits^\bullet \) can be expressed as

$$ \begin{array}{rll} \label{A3} {\rm var}(\mathop P\limits^\bullet ) &=& {\rm var}\left( {\frac{K}{K'}\times \frac{N'}{N}\times \frac{(W+(1-m)Y')}{(W+(1-m)Y)}} \right), \\ {\rm var}(\mathop P\limits^\bullet ) &=& {\rm var}\left( {\frac{K}{K'}} \right)+ {\rm var}\left( {\frac{N'}{N}} \right)+ {\rm var}\left( {\frac{(W+(1-m)Y')}{(W+(1-m)Y)}} \right)\\ && + \ {\rm cov}\left(\frac{K}{K'},\frac{N'}{N}\right)+{\rm cov}\left( {\frac{K}{K'},\frac{(W+(1-m)Y')}{(W+(1-m)Y)}} \right) \\ && + \ {\rm cov}\left(\frac{N'}{N},\frac{(W+(1-m)Y')}{(W+(1-m)Y)}\right), \\ &=& {\rm var}\left( {\frac{K}{K'}} \right)+ {\rm var}\left( {\frac{N'}{N}} \right)+ {\rm var}\left( {\frac{(1-m)Y'}{(W+(1-m)Y)}} \right) \\ && + \ {\rm cov}\left(\frac{K}{K'},\frac{N'}{N}\right)+{\rm cov}\left( {\frac{K}{K'},\frac{(W+(1-m)Y')}{(W+(1-m)Y)}} \right) \\ && + \ {\rm cov}\left(\frac{N'}{N},\frac{(W+(1-m)Y')}{(W+(1-m)Y)}\right). \end{array} $$
(31)

To get the testable empirical counterpart of the Eq. 29, we first transform the variable into logarithm.

$$ {\rm log}\left( P \right)= {\rm log}\left( N \right)+ {\rm log}\left( {W+(1-m)Y} \right)- {\rm log}\left( K \right)+ {\rm log}\left( s \right), $$

Then, we have the empirical regression specification as

$$ \label{A4} {\rm log}\left( {P_t } \right)=\alpha +\beta _1 {\rm log}\left( {N_t } \right)+\beta _2 {\rm log}\left( {Y_t } \right)+\beta _3 {\rm log}\left( {K_t } \right)+\varepsilon _t . $$
(32)

If we regress Eq. 32 directly, it is going to be serious multicollinearities between the variables as testified by the correlations in Table 9. Therefore, we use the adjusted income and housing supplyFootnote 13 as the regressor instead. The regression results are presented in Table 10.

Table 9 Correlations between housing price, population, income, and housing supply
Table 10 Estimation results of Eq. 32
Table 11 Forecast of net immigration for year 2006 to 2021 (Units: 10,000)
Table 12 Events of cohort of new arrival of floating population of 1995 till 1997 (Units: 1,000)
Fig. 3
figure 3

New residential land area allocated in Shanghai from 1995 to 2008. Source: 2002 and 2009 Shanghai statistics yearbook. For years before 2000, the new residential land volumes are published by the Statistics Yearbook 2000. For years after 2000, the new residential land areas are not published directly. Rather, the traded land volumes are published, which include both the new and the re-traded land. To proxy the new land volume, we subtract the residential volume of the “movers” from the total number

Fig. 4
figure 4

Age-specific birth rates, empirical values, and gamma curve fit for selected years

Fig. 5
figure 5

Stochastic predictions for TFR for Shanghai, with restriction (0.4–6)

Fig. 6
figure 6

Stochastic predictions for mean age at childbearing for Shanghai

Fig. 7
figure 7

Stochastic prediction for variance at age of childbearing for Shanghai

Fig. 8
figure 8

Stochastic predictions for life expectance at birth, male

Fig. 9
figure 9

Stochastic predictions for life expectance at birth, female

Fig. 10
figure 10

Stochastic population forecasting for 2015

Fig. 11
figure 11

Stochastic populations forecasting for 2030

Fig. 12
figure 12

Population pyramid in 2000

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Cheng, Y., Han, X. Does large volatility help?—stochastic population forecasting technology in explaining real estate price process. J Popul Econ 26, 323–356 (2013). https://doi.org/10.1007/s00148-010-0349-1

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Keywords

  • Default option
  • Volatilities
  • Stochastic population forecasting

JEL Classification

  • D81
  • D91
  • J11