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 – 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: Chapter I: Literature Review Chapter II: Methodology Chapter III: Data 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 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 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 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: = + rooms + dist + proptax + stratio + 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 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 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 - 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 employment centers in the Boston region centers increases by 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 (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 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 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 V C a oe ri ffi trati o a b ci l en e ts s R 10.5 o o β1 m s D −5 is β 067 t P −3 r 550 o pt β3 a x S −6 tr 726 at β4 io L −12 o 32 w β st at - 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 R Co peff value ici en ts 7.52e o o – 08 β1 m s D 1.03e ist β2 – 023 Pr 5.68e o – 07 pt β3 ax St 0.000 ti β4 o L 4.77e o – 011 w st at 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 % 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 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