Introduction to Econometrics
Worksheet week # 7
1. Answer the following questions about a data on the sales prices of houses in the UK.
The variables in this study are:
HPRICEi Sales price for house i
ASSESSi Assessed price of house i
LOTSIZEi Size of lot (in m2) for house i
BDRMSi Number of bedrooms for house i
BATHi Number of bathrooms for house i
OCEANi Dummy variable indicating that house i is located within 10 miles of the ocean
LAKEi Dummy variable indicating that house i is located within 10 miles of the lake
URBANi Dummy variable indicating that house i is located in an area classified as urban
INTERCEPT Intercept in the model
SSE Sum of squared residuals
Table 1 lists coefficients with standard errors in parentheses below the coefficients.
Table 1: Results of regressions
Dependent variable HPRICEi, n = 238
(1) (2) (3) (4) (5) (6) (7)
ASSESSi 0.90 0.90 0.91 0.90 0.89 0.90
(0.03) (0.03) (0.03) (0.03) (0.03) (0.03)
LOTSIZEi 0.0035 0.00059 0.00059 0.00057 0.00058 0.00059 0.00060
(0.00002) (0.00002) (0.00002) (0.00002) (0.00002) (0.00002) (0.00002)
BDRMSi 11.5 9.74 7.65 8.74 10.43
(2.32) (3.11) (3.29) (3.54) (3.77)
BATHi 3.57 3.78
(2.24) (1.11)
OCEANi 15.6 14.32 16.76 15.32 14.56
(11.43) (5.21) (4.32) (4.98) (7.01)
URBANi 9.54 10.29 12.32
(8.99) (5.43) (5.22)
LAKEi 11.36 12.87 11.98
(4.28) (8.32) (6.43)
INTERCEPT 261.9 -38.91 -40.30 -43.21 - 36.54 -42.37 -38.44
(11.98) (6.78) (7.32) (6.99) (5.87) (7.22) (9.43)
SSE 145.69 142.99 136.66 134.54 135.38 135.22 136.54
R2
0.143 0.158882 0.196118 0.208588 0.203647 0.204588 0.196824
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(a) Using the reported regressions, could you test whether the value of the house
due to lot size near water was different from the value of the lot away from the
water at the 5% level, controlling for assessed value, lot size and the number of
bedrooms? If so, perform the test. If not, explain what results you would need
to do the test.
(b) Could you test whether bathrooms change the house value controlling for assessed
value, lot size and the number of bedrooms at the 5% level? If so, perform
the test. If not, explain what results you would need to do the test.
(c) Can you test whether the assessed value and number of bedrooms are jointly
significant, controlling for lot size? If yes, perform the test at 5% level. If not,
explain what you would need to perform this test.
(d) Could you test whether all 7 of the listed variables (excluding the intercept) are
jointly significant at the 5% level? Be sure to state any assumptions you are
making.
2. Consider the following model:
log(price) = β0+β1 log(assess)+β2 log(sqrft)+β3 log(lotsize)+β4 d bdrms+ε , (1)
where price is house price, assess is the assessed housing value (before the house
was sold), lotsize is size of the lot (in feet), sqrft is square footage, and d bdrms is
a dummy variable indicating if the house has more than 3 bedrooms.
(a) Use the data housing.gdt to estimate the model (1). First transform the first
four variables in logarithms, then construct the dummy variable as
d bdrms =
1 if bdrms > 3
0 otherwise
and run the regression. Interpret the coefficients.
(b) Now, suppose we would like to test whether the assessed housing price is a
rational valuation: if this is the case, then a 1% change in assess should be
associated with a 1% change in price. In addition, lotsize, sqrft, and d bdrms
should not help to explain log(price), once the assessed value has been controlled
for. Define the hypotheses to be tested, the test statistic, and explain how would
you conduct the test. Then test for rational valuation in Gretl.
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