The impact of economic growth on floor space per capita in China and Russia

On residential real estate market the analysis uses the variable floor space per capita to capture the demand. The estimates start by an equilibrium (long-run) relationship between floor space per capita and fundamental determinants of demand. International evidence suggests that floor space per capita usually increases along with income as the economy grows (Berkelmans and Wang 2012), and the elasticity of floor space per capita to income is of primary interest. We estimate the following equilibrium relationship:

Floor space per capita it = f(H it-1 , P it-1 , U it , C it )

in which H it-1 , P it-1 , U it , C it , represent household income per capita in previous period, growth of residential property prices in previous period, growth of urbanization rate, growth of floor space completed per capita. For our analysis, we chosen two country: China and Russia. It will be interesting to compare the level of development of the industry in these countries identify the main drivers of growth.

The sample period in the regression spans from 2000 to 2015. The specification intends to illustrate the long-run relationship on the housing demand without any policy response. Policy variables such as mortgage rates and purchases restrictions are not included.

Model and estimation

The model looks like (Table 1): F it = b 0 + b 1 *H it-1 + b 2 *P it-1 + b 3 *U it + b 4 *C it + e it

Table 1. Description of the model

Letter	Variable	Explanation
F it	Floor space per capita (sq.m.)	The main indicator of residential real estate market which determine the level of development of economy and quality of life

H it-1	Household income per capita in previous period (current LCU)	This indicator has influence on developers and their expectation about future of market.
P it-1	Growth of residential property prices in previous period, %	Change in property price has impact on future planning about beginning a new project
U it	Growth of urbanization rate, %	Increasing urban population stimulates activity on real estate market to build new housing estates
C it	Growth of floor space completed per capita, %	It is an indicator of activity in sector

To estimate this system, we use Ordinary Least Squares method. Training sample is data from 2000 to 2014 years. Control sample is 2015 year.

China

The result from Excel for Chinese market you can see below (Table 2).

Based on the regression analysis we obtained high coefficient of determination equals to 98,62%.

Indicator of average approximation error (1,26%) confirms a high enough adequacy of the constructed equation.

As for testing the significance of coefficients, standard errors of the coefficients of the regression model should be less than their value. This rule is fulfilled for all variables. But standard error for growth of urbanization rate is to high that says about potential insignificance of b_3.

Using t-statistics for estimating the significance of the coefficients we can verify previous calculation. T-statistics for variables’ coefficients should meet the rule |t| > t crit in order to be accepted as significant. For H it-1 , P it-1 , C it this rule is fulfilled, so they are significant, besides of U it, but we have decided to keep this variable so as it makes economic sense.

P-value test confirms the conclusions drawn from t-statistics.

With the aim to check autocorrelation Durbin–Watson test will be used. Calculated d is in the interval with uncertainty of autocorrelation

(0,74<1,32<1,93). Looking at the plot of residuals (Picture 1) it can be said that most likely there is a positive autocorrelation. Probably the disturbance term in a regression equation picks up the influence of those variables affecting the dependent variable that have not been included in the regression equation. Further we will see how it affects the forecasted dependent variable.

Table 2. Regression estimation. China

Regression Statistics
Multiple R	0,993097911		Fcr	3,63308851
R Square	0,98624346		tcr	2,26215716
Adjusted R Square	0,980129442
Standard Error	0,56276334
Observations	14
ANOVA
	df	SS	MS	F
Regression	4	204,3473604	51,08684	161,308571
Residual	9	2,850323193	0,316703
Total	13	207,1976836

Coefficients Standard Error   t Stat	P-value   Lower 95,0% Upper 95,0%
Intercept            32,79686583      8,2135369 3,993026 X Variable 1         0,000403796    0,000124933 3,232108 X Variable 2         5,782044965    2,342371997 2,468457 X Variable 3         -277,7229157    211,0327715 -1,31602 X Variable 4         9,008121958    2,527004608 3,564743	0,00314334   14,2165545  51,37717716 0,01028786  0,000121178  0,000686413 0,03566042  0,483231374  11,08085856 0,22069926 -755,1122114  199,6663801 0,00607401  3,291640383  14,72460353

0,15

0             •        • • •.

• -0,5 0     •         5         •     10        •  •15

• -1•

  -1,5

Picture 1. Plot of residuals

To check equations for homoscedasticity the Goldfield–Quandt test will be used. In our equation F crit (6,38) always higher than RSS 2 /RSS 1 (2,52) and RSS 1 /RSS 2 (0,39). That is why the equation has homoscedasticity of random disturbances.

Floor space per capita in China in 2015 from control sample (37,50 sq.m.) falls in the confidence interval from 36,47 to 39,01 sq.m. Hence we can decide that our model is adequate and we can predict future value of explained variable based on fitted equation.

For example, if all parameters increase by 5% or decrease by 5%, floor space per capita will be 38,60 sq.m. or 36,88, respectively.

However, if a volume of floor space completed per capita is continue to decrease by 10% year on year in 2016 and everything else remains the same, floor space per capita will be calculated incorrectly the result will be increase from 37,5 sq.m. in 2015 to 45,54 sq.m. in 2016 These is no economic sense. Thus, we cannot say that this model fully reflects the true relationship between the indicators.

Russia

The result from Excel for Russian market you can see below (Table 3).

Based on the regression analysis we obtained high coefficient of determination equals to 98,87%.

Indicator of average approximation error (0,50%) confirms a high enough adequacy of the constructed equation.

As for testing the significance of coefficients, standard errors of the coefficients of the regression model should be less than their value. This rule is not fulfilled for b 2 only. Standard error for growth of urbanization rate is to high that says about potential insignificance of b₃

For H it-1 , U it this rule of T-statistics is fulfilled, so they are significant, besides of P it-1 , C it .

p-value test confirms the conclusions drawn from t-statistics.

With the aim to check autocorrelation Durbin–Watson test will be used. Calculated d is in the interval with  uncertainty  of autocorrelation

(0,74<1,21<1,93). Looking at the plot of residuals (Picture 2) it cannot be fairly said that most likely there is a positive autocorrelation or no autocorrelation.

Table 3. Regression estimation. Russia

Regression Statistics
Multiple R	0,994336971		Fcr	3,63308851
R Square	0,988706013		tcr	2,26215716
Adjusted R Square	0,983686463
Standard Error	0,180810697
Observations	14
ANOVA
	df	SS	MS	F
Regression	4	25,75791028	6,439478	196,971048
Residual	9	0,294232573	0,032693
Total	13	26,05214286

	Coefficients	Standard Error	t Stat	P-value	Lower 95,0%	Upper 95,0%
Intercept	19,41274108	0,168607246	115,1359	1,4281E-15	19,03132499	19,79415717
X Variable 1	0,000122564	1,02627E-05	11,94264	8,0206E-07	9,93483E-05	0,00014578
X Variable 2	-0,044800455	0,447419205	-0,10013	0,92243548	-1,056933013	0,967332104
X Variable 3	706,5706799	299,223999	2,361344	0,04250768	29,67896726	1383,462393
X Variable 4	-1,411251748	0,802225265	-1,75917	0,11240888	-3,226011378	0,403507882

0,4

0,2	—•—     —•—•—
0 0	2        4        6        8        10       12       14       16
-0,2	—w—                     —*—в—

-0,4

Picture 2. Plot of residuals

To check equations for homoscedasticity the Goldfield–Quandt test will be used. In our equation F crit (6,38) always higher than RSS 2 /RSS 1 (1,40) and RSS 1 /RSS 2 (0,71). That is why the equation has homoscedasticity of random disturbances.

Floor space per capita in Russia in 2015 from control sample (24,40 sq.m.) falls in the confidence interval from 24,08 to 24,89 sq.m. Hence, we can decide that our model is adequate and we can predict future value of explained variable based on fitted equation.

For example, if all parameters increase by 5% or decrease by 5%, floor space per capita will be 24,74 sq.m. or 24,23, respectively.

If a volume of floor space completed per capita decreases by 10% year on year in 2016 and everything else remains the same, floor space per capita will decrease from 24,40 sq.m. in 2015 to 23,84 sq.m. in 2016 These is economic sense. Thus, we can say that this model reflects the true relationship between the indicators.

Conclusion

To sum up, our analysis shows that floor space per capita increases along with income and other factors as the economy grows in China and Russia.

It is not the same for all countries that floor space per capita depends on household income per capita in previous period, growth of residential property prices in previous period, growth of urbanization rate, growth of floor space completed per capita in one manner.

In our analysis, the coefficient for urbanization growth rate shows different results: for Russia, it has direct relationship with floor space per capita and for China – indirect. So, we should suppose that there is the influence of those variables affecting the dependent variable that have not been included in the regression equation in China. But the main cause may be the living condition in Chinese cities in compare with country house with bigger square meters than in tiny flat in high-rise. Besides, for China this coefficient is insignificant.

Also, there is difference between direction of coefficients for Growth of residential property prices in previous period, and Growth of floor space completed per capita: for Russia, it is indirect relation, for China – direct relation. For Russia, these coefficients are insignificant.

We get uncertainty of autocorrelation of residues in the equation for both counties. This can lead to:

• 1)    evaluation of the unknown coefficients of the normal linear regression model is unbiased and wealthy, but lost the property of efficiency;

• 2)    there is a strong likelihood that the estimates of standard errors of the regression model coefficients will be calculated incorrectly, which can eventually lead to the approval incorrect hypotheses about the significance of the regression coefficients and the significance of the regression model as a whole.