tiểu luận kinh tế lượng FACTORS AFFECTING THE HOUSING PRICE

FOREIGN TRADE UNIVERSITY
---------***--------

FACTORS AFFECTING THE HOUSING
PRICE

Student’s name:
Nguyễn Thùy Linh (1815520195)
Nguyễn Ngọc Quỳnh Trang (1815520233)
Trần Khánh Linh (1815520196)
Class: English 6 – K57 JIB

10 October 2019


Introduction
Econometrics is a specialized discipline in economics that seeks to statistically estimate
and estimate the relationship between economic variables. This provides analytical
methods along with the reciprocal interaction in terms of the amount of relationship
between them based on the data collected from reality. The methods and econometric
models in this subject help us to analyze and predict economic phenomena.
The modern real estate industry has become a pillar industry of the economy, and the
housing price is the key to the real estate industry. The housing price level is not only
related to the living standards of the masses but also related to global economic
development. However, in recent years, due to cyclical and regional real estate
development, there is an imbalance in the market of supply and demand. Together with
the increased raw material prices and costs, the house price is becoming more and higher.
The housing price is an extremely complex issue, to study the main influence factors and
to find out the change rules have important theoretical and practical significance to
promote the sustainable and healthy development of the residential real estate market.
Based on existing results, this assignment studies the relationship between Housing price

and its influencing factors based on the method of multiple linear regression analysis.
The aim is to find out the main factors of influencing the housing prices and to provide a
valuable reference for Viet Nam to regulate the housing market effectively.
The essay is divided into the following sections:
1. Chapter I: Literature Review
2. Chapter II: Methodology
3. Chapter III: Data


4. Chapter IV: Conclusion
In the process of teaming and running the model, we have tried to complete as best as we
can but can't avoid the shortcomings, hope that you can give suggestions for our next
essays to be more complete. We sincerely thank you!
I. Literature review
1. Theoretical basis
1.1. Housing price
The housing price indicator show indices of residential property price over time. Included
are rent price, real and nominal house price, and the ratios of price to rent and price to
income, the main elements of housing cost.
The nominal house price covers the sale of newly-built and existing dwellings. Following
the recommendation from RPPI (Residential Property Price Indices) manual. The real
house price is given by the ratio of the nominal price to the consumer’s expenditure
deflator in each country, both seasonally adjusted from the OECD national account
database.
The price to income ratio is the nominal house price divided by the nominal disposable
income per head and can be considered as a measure of affordability. The price to income
ratio í the nominal house price divided by the rent price and can be considered as a
measure of the profitability of house ownership.
1.2. House price Index
1.2.1. Definition

The House Price Index (HPI) is based on transactions involving conventional and
conforming mortgages on single-family properties. It is a weighted, repeat sales index,
measuring average price changes in repeat sales or refinancings on the same properties.
1.2.2. Advantage of house price index
The House Price Index (HPI) is one of many economic indicators that investors use to
keep a pulse on broader economic trends and potential shifts in the stock market.
The rise and fall of house prices can have big implications for the economy. Price
increases generally create more jobs, stimulate confidence and prompt higher consumer
spending. This paves for the way for greater aggregate demand, boosting gross domestic
product (GDP) and overall economic growth.
When prices fall, the opposite tends to happen. Consumer confidence is eroded and the
many companies profiting from the demand for real estate lay off staff. This can
sometimes trigger an economic recession.

2. Other theories
Meese and Wallace (1994) examine whether the real expected return on homeownership
is close to the real homeowner cost of capital by studying the relationship between price,
rent, and the cost of capital. Abraham and Hendershott (1993, 1996) study the
relationship between house prices, construction costs, real income growth, and interest
rates. They find that these factors explain half of the historical variation in house price
appreciation. Himmelberg et al. (2005) compare the level of housing prices with local
rent and income for a period of 25 years. But they fail to account, for example, for
differences in risk, property taxes, and maintenance expenses, and anticipated capital
gains from owning a home. Goodman and Thibodeau (2008) explore to what extent
house appreciation rates over the time period 2000–2005 can be attributed to economic
fundamentals and what portion can be attributed to speculation. According to these

authors, much of the appreciation is the result of inelastic supply and speculative motives
are present in less than half of the cities they examined.
There is a rapidly growing strand in the recent literature on housing price dynamics that
tries to identify the effects of various fundamental values on prices. Using simulation of
the U.S. housing market, Khandani et al. (2013) find that the declining interest rates and
the growth of the refinancing business contributed significantly to the recent housing
boom and the massive defaults during the bust.
II. Methodology
1. Economic Model
The model is illustrated as follow
Price = price
Number of rooms = rooms
the weighted distances to five employment centers in the Boston region= dist
full-value property-tax rate (per $lO,OOO)= proptax
Average student – teacher ratio by town= stratio
the proportion of the population that is lower status= lowstat
To demonstrate the relationship between housing price and other factors, the regression
function can be constructed as follows:
PRF:
E (Y| price, rooms, dist, proptax, stratio, lowstat) = β0 + β1rooms + β2 dist + β3proptax +
β4stratio + β5 lowstat + u
SRF: = 0 + 1 rooms + 2 dist + 3 proptax + 4 stratio + 5 lowstat

In which

β0

is the intercept of the regression model

βi

µ

is the slope coefficient of the independent variable

xi

is the disturbance of the regression model β

: estimator of Y
: estimator of βi

2. Quantitative Analysis
2.1. Data
- Data source: wooldridge: 111 Data Sets from "Introductory Econometrics: A Modern
Approach, 6e" by Jeffrey M. Wooldridge
- Data overview
- The structure of Economic data: cross-sectional data
- We had a summarizing table based on the above result:

Variables
Price
Rooms

Dist

Proptax

Explanation

Median housing price, $
Number of rooms

Weighted distance to 5 employ
centers
Property tax per 1000$

Type of variable
Dependent variable

Quantitative

Independent variable

Quantitative

Independent variable

Independent variable

Qualitative

Qualitative


Stratio

Average student – teacher ratio

Lowstat

% of people “lower status”

Independent variable

Quantitative

Independent variable

Qualitative

Expectation of parameters
Based on economics theories of housing price as well as other subjective and objective
factors, we hold some expectations for the model coefficients as follow:
-

β0: when all independent variables hold the value of 0, this coefficient stands for
the housing price, it cannot take the negative value. Therefore, we expect a

-

positive value for this coefficient. (+)
β1: The more rooms a house have, the higher its price it will be so we expect this to

-

be positive. (+)
β2: The further the weighted distances from a house to five employment centers is ,
the less people will want to live there, the lower its price will be so we expect this

-

to be negative. (-)
β3: The higher the Average student – teacher ratio by town is, the less number of
teachers live there, which means education doesn’t develop, so we expect this to

-

be negative (-)
β4 : The higher the property-tax rate is, the less people will want to live there, the

-

lower a house’s price will be , so we expect this coefficient to be negative. (-)
β5: The higher the proportion of the lower status population is, the less people will
want to live there,

the lower a house’s price will be ,

coefficient to be negative. (-)

so we expect this


2.2.

Estimation of econometric model

According to our hypothesis mentioned above (chapter I, part 1.3): We expect β 1, β2, β3,
β4, β5 to be positive (+).

2.3.

Building the experimental model

2.3.1. Checking correlation among variables:
Correlation coefficients, using the observations 1 - 506
5% critical value (two-tailed) = 0.0872 for n = 506
price
1.0000

rooms
0.6958
1.0000

dist
0.2493
0.2054
1.0000

proptax
-0.4671
-0.2921
-0.5344
1.0000

stratio
-0.5033
-0.3540
-0.2293
0.4542

1.0000

lowstat
-0.7264
-0.6096
-0.4956
0.5276
0.3654
1.0000

price
rooms
dist
proptax
stratio
lowstat

The correlation between rooms and price is: 0.6958 => moderate uphill correlation
relationship (+)
The correlation between proptax and price is: -0.4671 => moderate downhill correlation
relationship (-)
The correlation between stratio and price is: -0.5033 => moderate downhill correlation
relationship (-)
The correlation between lowstat and price is: -0.7264 => moderate downhill correlation
relationship (-)

2.3.2. Regression run:
Use OLS method in Gretl

Model 1: OLS, using observations 1-506
Dependent variable: price

Const

Coefficient
22346.6

Std. Error
4093.01

t-ratio
5.460

p-value
7.52e - 08

Rooms

4495.43

425.208

10.57

1.03e - 023 ***

Dist

−692.356

136.628

−5.067

5.68e - 07

***

Proptax

−65.1684

18.3575

−3.550

0.0004

***

Stratio

−830.982

123.544

−6.726

4.77e - 011 ***

Lowstat

−587.086

47.6695

−12.32

1.26e - 030 ***

Mean dependent var
Sum squared resid
R-squared
F(5, 500)
Log-likelihood
Schwarz criterion

22511.51
1.33e+10
0.688426
220.9508
−5041.183
10119.72

S.D. dependent var
S.E. of regression
Adjusted R-squared
P-value(F)
Akaike criterion

Hannan-Quinn

***

9208.856
5165.914
0.685310
4.2e-124
10094.37
10104.31

From the table, we have a sample regression model.
22346.6 + 4495.43
Economic significance of regression coefficients
= 4495.43: Other determinants are held constant. When the Number of rooms increases
by 1, the expected value of housing price increases by $
= −692.356: Other determinants are held constant, when the weighted distance to 5
employment centers in the Boston region centers increases by 1 unit, the expected value
of housing price decreases by 692.356 $


= −65.1684: Other determinants are held constant. full-value property-tax rate increases
by 1 (per $lO,OOO), the expected value of housing price decreases by 65.1684 $
β4 = −830.982: Other determinants are held constant. When the number of Average
student – teacher ratio by town increases by 1 unit, the expected value of housing price
decreases by 830.982 $
= −587.086: Other determinants are held constant. When the proportion of the lower
status - population increases by 1 unit, the expected value of housing price decreases by
587.086 $
The coefficient of determination R - squared = 0.688426 : all independent variables

(rooms, dist, proptax, stratio, lowstat) jointly explain 68,84% of the variation in the
dependent variable (price)

Hypothesis testing
Testing the significance of coefficients
*The t-test approach
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-

Testing the coefficient β1


• Hypothesis:
• ts = 10.57 ; tα/2; n-k = t0.025; ∞ = 1.96
• |ts|>|t0.025; ∞|
 Reject H0, β1 is statistically significant at 5%
-

Testing the coefficient β2
• Hypothesis:
• ts = −5.067 ; tα/2; n-k = t0.025; ∞ = 1.96
• |ts|>|t0.025; ∞|

 Reject H0, β2 is statistically significant at 5%
-

Testing the coefficient β3
• Hypothesis:
• ts = −6.726 ; tα/2; n-k = t0.025; ∞ = 1.96
• |ts|>|t0.025; ∞|

 Reject H0, β3 is statistically significant at 5%
-

Testing the coefficient β4
• Hypothesis:
• ts = −12.32 ; tα/2; n-k = t0.025; ∞ = 1.96
• |ts|>|t0.025; ∞|

 Reject H0, β4 is statistically significant at 5%
*The P-value approach
V
a
ri
a
bl
es
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Co peff value
ici
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ts
7.52e

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– 08
β1

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1.03e

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Pr

5.68e

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β3

ax
St

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β4

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4.77e

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β5


-

Testing the coefficient β1
• Hypothesis:
• p-value = 7.52e – 08 < α = 0.05
 Reject H0, β1 has the significance level of 5%

-

Testing the coefficient β2
• Hypothesis:
• p-value = 1.03e – 023 < α = 0.05
 Reject H0, β2 has the significance level of 5%

-

Testing the coefficient β3
• Hypothesis:
• p-value = 5.68e – 07 < α = 0.05

 Reject H0, β3 has the significance level of 5%

-

Testing the coefficient β4
• Hypothesis:
• p-value = 0.0004 < α = 0.05
 Reject H0, β4 has the significance level of 5%

-

Testing the coefficient β5
• Hypothesis:


• p-value = 4.77e – 011 < α = 0.05
 Reject H0, β5 has the significance level of 5%
Testing the overall significance of regression model
* The F test
-

Hypothesis:

-

According to the OLS result, Fs = 220.9508

-

F0.05(5, 500) = 2.2141

-

Fs = 220.9508 > 2.2141= F0.05(5, 500)
• Reject H0, accept H1

Not all slope coefficients are simultaneously zero. The model is statistically significant at
the level of 5 %.
Multicollinearity and heteroskedasticity testing
4.4.1. Multicollinearity Testing:
In statistics, multicollinearity (also collinearity) refers to predictors that are correlated
with other predictors in the model.I t is a phenomenon in which one predictor variable in
a multiple regression model can be linearly predicted from the others with a substantial
degree of accuracy.
In this situation the coefficient estimates of the multiple regression may change
erratically in response to small changes in the model or the data. To see if this model
contains collinearing variables or not, we are going to conduct the VIF (Variance
Inflation Factor) Test. If the value is above 10 then the reliableness of this model should
be doubted. The results are shown below:


Variance Inflation Factors
Minimum possible value = 1.0
Values > 10.0 may indicate a collinearity problem
rooms

1.689

dist 1.567
proptax 1.811

stratio

1.355

lowstat 2.253
VIF(j) = 1/(1 - R(j)^2), where R(j) is the multiple correlation coefficient
between variable j and the other independent variables
Belsley-Kuh-Welsch collinearity diagnostics:
Variance proportions
lambda

cond const rooms

dist proptax stratio lowstat

5.409 1.000 0.000 0.000 0.004 0.002 0.000 0.003
0.420 3.590 0.000 0.000 0.184 0.025 0.000 0.083
0.105 7.180 0.001 0.006 0.232 0.163 0.002 0.521
0.053 10.090 0.006 0.026 0.507 0.720 0.008 0.010
0.011 22.339 0.001 0.198 0.017 0.081 0.624 0.153
0.002 49.873 0.992 0.769 0.055 0.008 0.365 0.230
lambda = eigenvalues of inverse covariance matrix (smallest is 0.00217472)
cond = condition index
note: variance proportions columns sum to 1.0


As shown above, since there are no above-10 value, then this model contains no
collinearing variables

Heteroskedasticity test

Heteroskedasticity indicates that the variance of the error term is not constant, which
makes the least squares results no longer efficient and t tests and F tests results may be
misleading. . To see if this model contains heteroskedasticity or not, we are going to
conduct the White test. The result is shown below:

White's test for heteroskedasticity
OLS, using observations 1-506
Dependent variable: uhat^2
coefficient

std. error

t-ratio p-value

------------------------------------------------------------------const
rooms
dist

−8.49181e+07

5.88652e+08 −0.1443 0.8854

−9.13643e+07
−3.35641e+07

8.65234e+07 −1.056 0.2915
3.36979e+07 −0.9960 0.3197

stratio

6.82205e+07

3.89967e+07 1.749 0.0809 *

lowstat

−2.56011e+07

8.47812e+06 −3.020 0.0027

proptax

3.23871e+06

5.50795e+06 0.5880 0.5568

***

sq_rooms

9.36812e+06

4.31238e+06 2.172 0.0303 **

X2_X3

6.42436e+06

3.32528e+06 1.932 0.0539 *

X2_X4

−5.46664e+06

3.00685e+06 −1.818 0.0697

X2_X5

1.99124e+06 824605

X2_X6

324397

454680

2.415 0.0161 **
0.7135 0.4759

*


sq_dist

3.05526e+06 695127

4.395 1.36e-05 ***

X3_X4

−1.48792e+06 742138

−2.005 0.0455 **

X3_X5

1.85310e+06 415343

4.462 1.01e-05 ***

X3_X6

−1.15348e+06 188821

−6.109 2.06e-09 ***

sq_stratio −727829
X4_X5

−445159

X4_X6

122563

692425
300551
237353

−1.051 0.2937

−1.481 0.1392
0.5164 0.6058

sq_lowstat 633967

62364.3

10.17

X5_X6

40517.1

−4.781 2.32e-06 ***

21592.0

−0.4478 0.6545

−193712

sq_proptax −9668.99

3.89e-022 ***

Unadjusted R-squared = 0.458684
Test statistic: TR^2 = 232.094197,
with p-value = P(Chi-square(20) > 232.094197) = 0.000000

From the result we get p-value = 0.000000 0.05 -> reject . We conclude that the model

does have heteroskedascity mistake and that the variance of the error term is not constant.


Figure 1
In a well – fitted model, the variance of should be equal: var(ui)= E()= σ2
We would fix this problem by using robust standard errors relax the assumption that
errors are both independent and identically distributed and logarithmize all variables:
Model 3: OLS, using observations 1-506
Dependent variable: l_price
Heteroskedasticity-robust standard errors, variant HC1

Const
l_rooms
l_dist
l_proptax
l_stratio

Coefficient
12.3977
0.419812
−0.0934633
−0.219695
−0.439269

Std. Error
0.421337
0.164113
0.0246084
0.0317261
0.0705716

t-ratio
29.42
2.558
−3.798
−6.925
−6.224

p-value
<0.0001
0.0108
0.0002
<0.0001
<0.0001

***
**
***
***
***


l_lowstat

−0.438242

Mean dependent var
Sum squared resid
R-squared
F(5, 500)

Log-likelihood
Schwarz criterion

0.0363981

9.941057
22.62994
0.732450
231.7300
68.15458
−98.94995

−12.04

S.D. dependent var
S.E. of regression
Adjusted R-squared
P-value(F)
Akaike criterion
Hannan-Quinn

White's test for heteroskedasticity Null hypothesis: heteroskedasticity not present
Test statistic: LM = 123.579
with p-value = P(Chi-square(20) > 123.579) = 6.17482e-017
Test for normality of residual Null hypothesis: error is normally distributed
Test statistic: Chi-square(2) = 95.7256
with p-value = 1.63475e-021

<0.0001

***

0.409255
0.212744
0.729775
1.1e-127
−124.3092
−114.3633


Note that comparing the results with the earlier regression, none of the coefficient
estimates changed, but the standard errors and hence the t values are different, which
gives reasonably more accurate p values.
IV. Conclusion
The report attempts to analyze some factors that affect the housing price in Boston,
England in 2000. Through quantitative analysis of their potential relationship, a
regression model is built. According to the results , our initial expectations are proved
right - all significant influence housing price in Boston, England but in different ways.
This analysis can provide guidance on investigating residents’ expectations and
assumptions about their living area. Moreover, the decision - maker can also take
advantage of this report to design plans and adjust the housing price to fit with the
residents’ wishes. In the long term, the rational concept of housing consumption can
restrain the real estate market bubble, so that the prices will return to rational level.


After doing the problem- testing, we tried our best to fix Heteroscedasticity and
disnormality of residuals but we only can make Heteroscedasticity have BLUE
characteristics by using Robust regression. Some other mistakes still remain in the report
due to our limit understanding and knowledge. We hope that Dr. Tu Thuy Anh can give us
some corrections and constructive comment so that we can improve ourselves and

prepare better for our next reports in the future.

References
Daniel Liberto, 2019, House Price Index
Mishkin, F.S., 2007. Housing and the monetary transmission mechanism (No. w13518).
National Bureau of Economic Research.
Reed, R. and Reed, R., 2016. The relationship between house prices and demographic
variables. International Journal of Housing Markets and Analysis, 9(4), pp.520-537.


Megbolugbe Isaac, Marks Allen, and Schwartz Mary (1991) The Economic Theory of
Housing Demand: A Critical Review. Journal of Real Estate Research: 1991, Vol. 6, No.
3, pp. 381-393.
Introductory econometrics, Jeffrey Wooldridge, 2000
Basic Econometrics, Damodar N. Gujarati, 1978
Introduction to Econometrics, James H. Stock, Mark Watson, 2002
Econometric Analysis of Cross Section and Panel Data, Jeffrey Wooldridge, 2001
Econometric Analysis, William H. Greene, 1990
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