STATA assignment Background information question 1: The file HOUSES contains dat

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STATA assignment

Background information question 1:

The file HOUSES contains data on house sales from a well-known building society in UK for different postcode sectors in Staffordshire. The data was collected over a short period of time when house prices were not trending and thus can be treated as cross sectional data. The files contain data on several variables:

IDNUM = case number
Price = price in £s
Age = age in years
Size = the size in square metres

And the following dummy variables that are equal to 1 in the case indicated 0 elsewhere.
Terr = 1 if terraced
Det = 1 if detached
Semi = 1 if semi-detached
Garage = 1 if there is at least 1 garage
CHF = 1 if there is full central heating
Bath2P = 1 if there are 2 or more bathrooms

Using the data provided to you on both locations, estimate and fully interpret the results of a hedonic house price estimation of the form: LnPrice = ß1+ß2AGE+ß3SIZE+ß4GARAGE+ ……+ut where Ln is the natural logarithm. You should carefully consider the specification and any type of diagnostic tests and indicators you consider of importance, given this type of model and data. Do you consider that autocorrelation is a problem with this data?

(I ran the following commands in STATA and gained the following tables:)

. gen time = _n

. tsset time
time variable: time, 1 to 153
delta: 1 unit

. estat bgodfrey, lag(1)

Breusch-Godfrey LM test for autocorrelation
---------------------------------------------------------------------------
lags(p) | chi2 df Prob > chi2
-------------+-------------------------------------------------------------
1 | 10.555 1 0.0012
---------------------------------------------------------------------------
H0: no serial correlation

. dwstat

Durbin-Watson d-statistic( 8, 153) = 1.451573

(ii) It has been suggested in the literature that heteroscedasticity related to age is present in hedonic house price models. Test for this and suggest appropriate action, if necessary. (You are not expected to re-estimate the model)

Price age size Lerr det Chr bath2p garage Berti regreBB note: det tted because of collinearity of Oba 153 7, 115 125.61 Model 6.0604e+10 B. 6577e+09 0.0000 Residunal. 9.9943e+09 115 68926103-1 0.8581 R-aquared. 0.B516 B302-2 Total 7.0599e+10 152 464463946 Root MSE Price Pro-lt. [95& Conf. I 137-7739 25-60166 5.34 0.000 BB-769B -B6-77796 2.969B 31.59832 9.62 0.000 aize 261.5876 101.3519 10317.69 2B61-51 3.61 0.000 15973.34 -4662.027 o omitted) det. 79-1473B 0.05 0.959 3150.306 2991-111 1553.717 12599.26 2523-BB4 4.99 0.000 7610-905 175B7-61. B15., 6383 2178.853 0.37 0.709 3190.776 5122.052 senti. -3981.49 2434-912 1.64 0.1 04 B793-996 B31-0153 20452-e 36037-91. 20645.35 4145-065 6-91 0.000

Explanation / Answer

i) Null hypothesis: There is no serial correlation (Autocorrelation).

Alternative hypothesis: There is a serial correlation (Autocorrelation

From the given test,

Chisquare value= 10.555

P-value is 0.0012 <0.05

Hence we reject the null hypothesis at 5% level of significance.

Hence autocorrelation is a problem for this data.

ii) To check the homoscedasticity of a data,

Null hypothesis: The data is homoscedastic (i.e having equal variance of all variable)

Alternative hypothesis: The data is heteroscedastic (i.e not having equal variance of all variable, atleast one is different)

so we use the F-test for this test,

from the bove analysis,

F-value is =125.61

p-value is 0.0 < 0.05 hence we reject the null hypothesis at 5% level of significance.

hence The data is heteroscedastic.

Therefore heteroscedasticity related to age is present in hedonic house price models.

If we check the R^2=0.8584 that means model is good. so we need not to worry about the heteroscedasticity.

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