tiểu luận kinh tế lượng tài chính factors that affect housing prices among location and region

We choose 6 variables: price, crime, nox, rooms, dist and proptax to do the research in which price is dependent variable and the other five are independent variables.. e variable label

I INTRODUCTION 3

1 Overall about econometrics 3

2 Why choosing OLS? 4

II QUESTION OF INTEREST 5

III ECONOMIC MODEL 5

1 Choosing the variables 5

2 Embedding that target in a general unrestricted model (GUM) 8 IV ECONOMETRICS MODEL 9

1 Population regression function (PRF) 9

2 Sample regression function (SRF) 9

V DATA COLLECTION 10

1 Data overview 10

2 Data description 10

VI ESTIMATION OF ECONOMETRIC MODEL 10

1 Checking the correlation among variables: 10

2 Regression run 12

VII CHECK MULLTICOLLINEARITY AND HETEROSCEDASTICITY 15

1 Multicollinearity 15

2 Heteroskedasticity 16

VIII HYPOTHESES POSTULATED 19

1 The t test 19

2 Confidence Intervals 21

3 P­ Value 22

4 Testing the overall significance: The F test 23

IX RESULT ANALYSIS AND POLICY IMPLICATION 24

X CONCLUSION 24

XI REFERENCES 25

Y Figure 1 7

Figure 9 21

I INTRODUCTION

1.Overall about econometrics

Econometrics   is   the   application   of   statistical   methods   to economic data and is described as the branch of economics that aims to give empirical content to economic relations. Precisely speaking,   it   is   the   quantitative   analysis   of   actual   economic problems,   based   on   the   concurrent   development   of   theory   and observation, related by appropriate methods of inference. It is understandable   that   economist   make   comparison   econometrics   is like an effective tool to convert mountains of data into extract simple relationships.

The reason why econometrics is effective is economics theory use   statistical   theory   and   mathematical   statistics   to   evaluate and   develop   econometrics   method   In   reality,   econometrics   help economists  to   assess  economic   theories,  developing   econometrics model, analyzing and forecasting the economic history.

Aware of the importance of econometrics to economic phenomena, our group decides to carry out a research of econometrics: “The factors that have influence on median housing price” and aim to analyze statistic and point out differences and their reason of price level.

The data set has 506 observations with 12 variables in total.

We choose 6 variables: price, crime, nox, rooms, dist and proptax

to do the research in which price is dependent variable and the other five are independent variables. The general method used in

This is the first time our group carry out an econometrics research, our performance is unavoidable to have many mistakes.

It would be a pleasure if we can receive the feedback from you to better ourselves next time.

2.Why choosing OLS?

Ordinary   least   squares (OLS)   is   a   type   of  linear   least squares  method for estimating the unknown  parameters  in a  linear regression  model   OLS   chooses   the   parameters   of   a  linear function  of   a   set   of  explanatory   variables  by   the   principle

of  least   squares :   minimizing   the   sum   of   the   squares   of   the differences   between   the   observed  dependent   variable  in   the given  dataset  and those predicted by the linear function. 

With the six selected variables, we use the OLS model because all regressions variable are exogenous variables, the effects of independent   variables   on   the   dependent   variable   are   linear effects. In  addition, the  estimates calculated  by means  of the least squares OLS are linear estimates that are not deviate and are better than others.

When using OLS, we have some basic assumptions:

1 The regression model is linear in the parameters

2 X values are fixed in repeated sampling, which means Xi and ui are uncorrelated 

3 Zero mean value of disturbance (E(ui)) =0)

4 Homoscedasticity or equal variance of ui : var(ui) = 

5 No correlation between disturbances

6 The model is correctly specified.

III ECONOMIC MODEL

According the provided data, the economic model used in this report is an empirical one. Note that the fundamental model is mathematical; with an empirical model, however, data is gathered for the variables and using accepted statistical techniques, the data are used to provide estimates of the model's values.

 size:        22,770  

e variable label

median housing  price, $

crimes committed per capita

nit ox concen;  parts per 100m

avg number of  rooms

wght dist to 5  employ centers

access. index to rad. hghwys

property tax per

$1000

stratio float %9.0g  

average student­ teacher ratio

perc of people  'lower status'

Figure 1

The above table reveal that this is the statistic of factors which have influence in housing price via 506 observations. After discussing   carefully,   our   group   jumped   into   a   conclusion   to choose   a   dependent   variable   Y:   Price,   independent   variable contains:

A brief description of each variable is given in Figure 1.

Name Meaning Expected

sign Dependent

8.59024 7

0.00 6

88.97 6

5.5497 83

1.15839

rooms 506

6.2840 51

0.70259

dist 506

3.7957 51

  price crime nox rooms dist proptax

corr price crime nox rooms dist proptax

We   can   see   from   the   matrix,   it   can   be   inferred   that   the correlation between price and each of the independent variable is decent enough to run the regression model. Specifically:

­ Correlation coefficient between price and crime is ­0.3879

=> price and crime have a moderate relationship.

­ Correlation coefficient between price and nox is ­0.426 => price and nox have a moderate relationship.

­ Correlation coefficient between price and rooms is 0.6958 => price and rooms  have a moderate relationship.

­ Correlation coefficient between price and dist is 0.2493 => price and dist have a weak relationship.

­ Correlation coefficient between price and proptax is ­0.4671

=> price and proptax have a moderate relationship.

Independent   variables   including   Rooms   and   Dist   have

correlation coefficient  larger than  0, which  means they  are in

directly   relationship   with   dependent   variable   The   highest

In   addition,   all   variables   have   correlation   coefficient   not

larger   than   0.8   so   this   model   does   not   have   multicollinearity

price Coef Err t P>t Conf Interval]

­ 136.3551 ­43.55923

0.02 3

­ 16877.67 ­1242.937

crime,   nox,   rooms,   dist,   proptax  all   have   statistically

significant effects on  price  at the 5% significant level (as all

  4 = ­791.2588 means that if weight distance to 5 employ centers increases 1 unit, average housing price will decrease by 791.2588

 Detect multicollinearity

o Method 1: Use cor command to examine multicollinearity

If   independent   variables   are   strongly   correlated   (r   >   0.8), multicollinearity may occur.

proptax ­0.4671 0.5828 0.667 ­0.2921 ­0.5344 1.0000 Figure 6

From   the   table   above,   we   can   easily   see   that   correlating coefficient   among   independent   variables   are   pretty   low   and   all smaller   than   0.8   As   a   result,   we   can   conclude   that multicollinearity does not occur in this model.

We   can   draw   a   conclusion   from   2   methods   above   that multicollinearity   not   too   worrisome   a   problem   for   this   set   of data.

2 Heteroskedasticity

Another   problem   that   our   model   can   suffer   from   when   being examined is heteroskedasticity. Heteroskedasticity may result in the   situation   that   some   least   squared   estimators   are   still unbiased but are no longer effective, along with that, estimators

of variances will become biased, thus lead to the reduction in effectiveness of our model.

When   the   assumption   of   variance   of   each   error   term   Ui   is unchanged when i moves from 1, 2 to n. It can also be rewritten as:

Var (U i ) = Var (U j ) i=1,2,3,…,n

j=1,2,3,…,n When that assumption is violated, heteroskedasticity appears

Causes

o   Essence of economic phenomena: If economic phenomena

is examined on subjects having difference in scale or they are examined under periods of time that are not similar in fluctuation level.

o   Model’s function is wrongly formatted, maybe because appropriate   variables   are   missing   or   function   analysis   is false.

o     cannot   fully   and   correctly   reflect   the   essence   of economic   phenomena   For   example,   external   observations appear   Bringing   in   or   eliminate   these   observations   does great impact on regression analysis.

o  Error tends to decrease as data collecting, conserving and processing techniques are improved

o  Behaviors in the past are learnt.

Hypothesis:   

         Prob > chi2  =   0.0000

We can see that Prob > chi2 = 0.0000 < 0.05 => We reject H 0 , accept H 1

We   can   conclude   that   heteroskedasticity   does   occur   in   this model

0.588 3

5937 9

Robust

price Coef Std. Err t P>t [95% Conf Interval]

crime ­150.0703 30.45247 ­4.93 0 ­209.9009 ­90.23976 nox ­1737.66 389.6642 ­4.46 0 ­2503.241 ­972.0787 rooms 7707.327 670.6304 11.49 0 6389.726 9024.928 dist ­791.2588 175.744 ­4.5 0 ­1136.546 ­445.9712 proptax ­89.95717 26.84788 ­3.35 0.001 ­142.7057 ­37.20862 _cons ­9060.303 5398.964 ­1.68 0.094 ­19667.75 1547.148 Figure 8

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.

c (500)

0.025  = 1.965 < |t s  | => Reject 

Conclusion:   nitrogen   oxide   concentrator   per   100m   has statistically signifincant effect on median housing price. Higher nitrogen oxide concentrator per 100m, lower median housing price Hypothesis:  

c (500)

0.025  = 1.965 < |t s  | => Reject 

Conclusion:   The   average   number   of   rooms   has   statistically signifincant   effect   on   median   housing   price,   higher   average number of rooms, higher median housing price.

Hypothesis:  

Conclusion weight distance to 5 employ centers has statistically signifincant   effect   on   median   housing   price,   higher  weight distance to 5 employ centers, lower median housing price.

Hypothesis:  

c (500)

0.025  = 1.965 < |t s  | => Reject 

Conclusion Property tax per $1000 has statistically signifincant effect on  median housing  price, higher  property tax  per $1000, lower median housing price.

X 5 5% (­142.7057  ; ­37.20862) Figure 9

We   can   see   that   for   all   coefficients,   0  doesn’t   belong   to   the confidence interval, so we reject the hypotheses H 0 : , , , , 

Conclusion: Number of crimes committed per capita, nitrogen oxide concentrator   per   100m,   the   average   number   of   rooms,  weight distance to 5 employ centers and property tax per $1000 all have statistically   signifincant   effect   on   median   housing   price  with the confidence level of 95%. 

In   particular,   with   the   sample   we   have,   the   estimated   result shows   that   one   more   crime   committed   decreases   median   housing price by 150.07$, holding other factors fixed.

Hypothesis testing: 

P­value = 0.0004 < α = 0.05 => Reject H 0

Nitrogen   oxide   concentrator   per   100m   has   statistically signifincant   effect   on   median   housing   price   Higher   nitrogen oxide concentrator per 100m, lower median housing price

In   particular,   with   the   sample   we   have,   the   estimated   result shows that one more unit in nitrogen oxide concentrator per 100m decreases median housing price by 1737.66$, holding other factors fixed.

Hypothesis testing: 

P­value = 0.0004 < α = 0.05 => Reject H 0

The average number of rooms has statistically signifincant effect

on median housing price, higher average number of rooms, higher

P­value = 0.0004 < α = 0.05 => Reject H 0

Weight   distance   to   5   employ   centers  has   statistically signifincant   effect   on   median   housing   price,   higher  weight distance to 5 employ centers, lower median housing price.

In   particular,   with   the   sample   we   have,   the   estimated   result shows that one more unit increased in weight distance to 5 employ centers decreases median housing price by 791.25$, holding other factors fixed.

Hypothesis testing: 

P­value = 0.0008 < α = 0.05 => Reject H 0

Property tax per $1000  has statistically signifincant effect on median housing price, higher property tax per $1000, lower median housing price. 

In   particular,   with   the   sample   we   have,   the   estimated   result shows   that   one   more   $   increased   in   property   tax   per   1000$ decreases median housing price by 89.96 $, holding other factors fixed.

we don’t reduce the model by dropping out this subset.

IX RESULT ANALYSIS AND POLICY IMPLICATION

From data analysis in previous sections, we have gained an  overall view of data set given in term of the satistical 

relationship between housing prices and each of the factors 

proposed. As mentioned at the beginning of this report, we aim to learn how security of the neighborhood, the air pollution, the  size of house, accessibility and the property tax are associated  with housing price. In other words, we are concerned about what 

is the willingness of buyers to pay for these components. 

Following the analysis of data, regression model run and 

hypothesis testing, it can be concluded that security of the  neighborhood, the air pollution, the size of house, accessibility and the property tax statistically affect the housing prices.  Therefore, tenants, investors or constructors should take all of  these ingredients into account when making deals.

X CONCLUSION

This   report   is   completed   on   the   dedicated   contribution   of each   member   and   the   knowledge   from   our   study   in   Econometrics This research has provided us with a good opportunity to practice what we have learned and to get a deeper understanding of data analysis and relevant testing. From this useful application, we hope   that   our   research   can   somehow   suggest   the   relationship between the housing prices and some other factors.

Again, due to the limitation of understanding and resources, our report may contain misinterpretations. We hope that teacher and readers can give us constructive comments on the report so that

we would improve ourselves and do better in the future.

1 http://pages.hmc.edu/evans/chap1.pdf

2 http://citeseerx.ist.psu.edu/viewdoc/download?

doi=10.1.1.926.5532&rep=rep1&type=pdf

3 D.A. Belsey, E. Kuh, and R. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, New York: Wiley (1990).