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ECONOMICS 340: ECONOMIC RESEARCH METHODS
Instructions:
1. You may type your answers below, write them on separate sheets and scan your answers,
or type them on a separate document.
2. For all hypothesis tests, please use a 5% significance level. For critical values, you can
use the link on Canvas, any critical value calculator of your choosing, or these below:
https:
www.danielsoper.com/statcalc/calculator.aspx?id=10 (t critical value)
https:
www.danielsoper.com/statcalc/calculator.aspx?id=4 (F critical value)
3. At the end of the paper, there are tables of regression results and other information that
will help with solving the problems. Please show your work as a basis to receive partial
credit if your answers are inco
ect.
3. The exam will be worth a total of 100 points.
This assignment contains 3 short answer questions with multiple parts.
https:
www.danielsoper.com/statcalc/calculator.aspx?id=10
https:
www.danielsoper.com/statcalc/calculator.aspx?id=4
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1. In “Hedonic Price Models and Sun-and-Beach Package Tours: The Norwegian Case” by
Christer Thrane (Journal of Travel Research, Vol. 43, Fe
uary 2005, XXXXXXXXXX), the author
examines the price of popular winter vacation tourist packages to the Canary Islands to
escape the Norwegian winter. Table 1 on page 6 of the exam shows the list of variables in
the paper, and Table 2 shows the regression results where the natural logarithm of the
package price is used as the dependent variable, and other variables enter the regression as
they appear in Table 1. The “Difference (%)” shows the expected percent change in package
prices if the dummy is 1 versus 0 if the variable is significant, which is a reliable estimate of
the effects of each dummy on prices since the dependent variable is logged. Model 2 differs
from model 1 in the regression results with the addition of the star rating of the destination
hotel as an independent variable.
a. Should the authors be concerned about functional form or heteroscedasticity issues in
either regression? Why or why not? (10 points)
. Please interpret the parameter estimate on the “DISTBEACH” variable in model 2.
What effect does the hotel’s distance from the beach have on the package price?
Please be careful with the units. (6 points)
c. When the authors conducted a robustness check (model 2) to add the effect of the star
ating to the original model (model 1), the dummy for there being a restaurant at the
hotel (REST), the dummy for there being free TV at the hotel (TV), and the dummy
for if the hotel is the tour operator’s own resort (RESORT) became insignificant.
That is, we cannot reject the null hypothesis that each parameter is 0 individually for
those three variables in model 2 whereas we could reject the null hypotheses in model
1. Why do you think that is? (6 points)
d. A tour package has the following attributes:
- A tour by the company Saga on the island of Tenerife at Saga’s resort
hotel built in 1993 that is 100 meters from the beach.
- Hotel has air conditioning, an on-site restaurant, free TV, 24 hour
eception, and a swimming pool for children.
- The rooms at the hotel are apartment style (not bungalow) with 3
ooms.
- If other features are not listed here, they are not included in the
package.
What would be model 1’s predicted price of the package in Norwegian krone?
(10 points)
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2. Suppose that you were hired to examine if there is a link between property values and
proximity to the Fullerton Airport. You use Redfin to collect housing prices and distance to
the Fullerton Airport from 317 home sales in zip code XXXXXXXXXXcontains airport) sold within
the last year. The Redfin data also provides you information about other factors that affect
local housing prices. The core regression that you run is as follows:
ln(??????) = ?1 + ?2????i + ?3ln(???????)? + ?4????? + ?5?????
2 + ?6ln(?????)
+ ?7????ℎ? + ?8????????? + ??
?????:???????????????ℎ?ℎ???(?????????)
????:???????????????ℎ???(????????????)
???????:?????????ℎ???????(????????????)
????:????ℎ???????????
????:??????????????????ℎ???
????ℎ:?????????????:1???ℎ????????ℎ????????????(??ℎ????)
????????:????????ℎ???????????????????????(????????????)
ln( ) : ??????????????ℎ?????????
You also run a series of diagnostic tests to identify potential problems with
heteroscedasticity, imperfect multicollinearity, and functional form issues. The results of
these regressions are in tables starting on page 7. Please consult them as you answer the
questions below.
a. Suppose that you want to test the functional form of your core regression. Please perform
a regression equation specification e
or test (RESET). In your answer, please clearly
provide the null and alternative hypothesis of your test, the test statistic that you will use,
the critical value of your test statistic/p value of your statistic, and the result of the test.
(10 points)
. Based on your results of the RESET from part a, would you recommend changing the
functional form of the regression? Why or why not? (6 points)
c. Now you want to run a general test for heteroscedasticity on the core regression. Please
perform the White test. In your answer, please clearly provide the null and alternative
hypothesis of your test, the test statistic that you will use, the critical value of your test
statistic/p value of your statistic, and the result of the test. (10 points)
d. Based on your results of the White test from part d, would you estimate the regression
any differently to account for any heteroscedasticity? Why or why not? (6 points)
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e. Please perform an F test of the claim that the year the home was built has no effect on
housing prices (?4 = 0, ?5 = 0). In your answer, please clearly provide the null and
alternative hypothesis of your test, the test statistic that you will use, the critical value of
your test statistic, and the result of the test. (10 points)
f. Please interpret the parameter estimate for the lot size variable in the core regression
(regression 1, ?3̂ = XXXXXXXXXXWhat effect does an increase in the lot size have on the local
home prices? (Hint: please be careful with the units). (6 points)
g. Please perform the F test of the model as a whole on the core regression (regression 1).
In your answer, please clearly provide the null and alternative hypothesis of your test, the
test statistic that you will use, the critical value of your test statistic, and the result of the
test. (10 points)
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3. Suppose that you are trying to model the determinants of high infant mortality. You have
data at the county level about the infant mortality rate (Infant), per capita income (Income),
and the number of doctors per 100,000 people (Docs) from 102 u
an counties in the United
States. Suppose that you want to choose between the linear and log-log functional forms for
the regression:
??????? = ?1 + ?2????? + ?3??????? + ??
ln(???????) = ?1 + ?2 ln(?????) + ?3 ln(???????) + ??
You estimate each regression and perform the MacKinnon-White-Davidson test. The test
egressions are:
??????? = ?1 + ?2????? + ?3??????? + ?4?1,? + ??
ln(???????) = ?1 + ?2 ln(?????) + ?3 ln(???????) + ?5?2,? + ??
?1,? = ln(???????̂ )− ???????̃
?2,? = exp(???????̃ )− ???????̂
???????̂ :?????????????????????????????
???????̃ :???????????????? ln(???????) ?????ℎ? ??? − ??? ?????
You obtain the following parameter estimates from the test regressions:
?4̂ = 17.626; ??(?4̂) = 12.472
?5̂ = −0.239; ??(?5̂) = 0.039
Does the test indicate that you should prefer the linear or the log-log model? If so, which
one should you prefer? Please show your work. (10 points)
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Tables for Problem 1
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Regression Results for Problem 2
(Note: 4 regression results total below, you need to figure out which regression(s) provide you
information for each part)
Variables included:
?????:???????????????ℎ?ℎ???(?????????)
????:???????????????ℎ???(????????????)
???????:?????????ℎ???????(????????????)
????:????ℎ???????????
????:??????????????????ℎ???
????ℎ:?????????????:1???ℎ????????ℎ????????????(??ℎ????)
????????:????????ℎ???????????????????????(????????????)
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Regression 1 (Core regression):
ln(??????) = ?1 + ?2????i + ?3ln(???????)? + ?4????? + ?5?????
2 + ?6ln(?????)
+ ?7????ℎ? + ?8????????? + ??
ln(): natural logarithm function
Parameter Standard E
or of
Variable Estimate (�̂�) Parameter Estimate (??(�̂�)) t p-value of t
Constant
XXXXXXXXXX XXXXXXXXXX96E-05
SQFT
XXXXXXXXXX63E XXXXXXXXXX54E-22
??(???????)
XXXXXXXXXX XXXXXXXXXX14E-10
????
XXXXXXXXXX XXXXXXXXXX
????^?
6.18E-05 1.57E XXXXXXXXXX
??(????)
XXXXXXXXXX XXXXXXXXXX
?????
XXXXXXXXXX XXXXXXXXXX4E-13
????????
XXXXXXXXXX XXXXXXXXXX
R Squared
0.8574 Explained Sum of
Squares (ESS)
20.712
3.445
24.157
F Statistic (Model as a
Whole)
265.4
(p-value:
0.00001)
Residual Sum of
Squares (RSS)
Sample size 317
Total Sum of Squares
(TSS)
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Regression 2:
ln(??????) = ?1 + ?2????i + ?3ln(???????)? + ?4ln(?????) + ?5????ℎ? + ?6????????? +
??
Parameter Standard E
or of
Variable Estimate (�̂�) Parameter Estimate (??(�̂�)) t p-value of t
Constant
XXXXXXXXXX XXXXXXXXXX2E-226
SQFT
XXXXXXXXXX43E XXXXXXXXXX76E-42
??(???????)
XXXXXXXXXX XXXXXXXXXX
??(????)
XXXXXXXXXX XXXXXXXXXX
?????
XXXXXXXXXX XXXXXXXXXX67E-23
????????
XXXXXXXXXX XXXXXXXXXX
R Squared
0.8388 Explained Sum of
Squares (ESS)
20.264
3.893
24.157
F Statistic (Model as a
Whole)
323.8
(p-value:
0.00001)
Residual Sum of
Squares (RSS)
Sample size 317
Total Sum of Squares
(TSS)
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Regression 3:
ln(??????) = ?1 + ?2????i + ?3ln(???????)?