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.

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 supply¹³ 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

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

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

Fig. 5

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

Fig. 6

Stochastic predictions for mean age at childbearing for Shanghai

Fig. 7

Stochastic prediction for variance at age of childbearing for Shanghai

Fig. 8

Stochastic predictions for life expectance at birth, male

Fig. 9

Stochastic predictions for life expectance at birth, female

Fig. 10

Stochastic population forecasting for 2015

Fig. 11

Stochastic populations forecasting for 2030

Fig. 12

Population pyramid in 2000