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ECMT6007/6702: Econometric Applications Problem Set 2 Semester 2 2022
发布时间：2022-09-04
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ECMT6007/6702: Econometric Applications
Problem Set 2
Semester 2 2022
Question 1. The data set BWGHT .RAW contains data on births to women in the US. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 139 births:
b—wght = 119.77 − 0.514 cigs
(i) What is the predicted birth weight when cigs = 0 ? What about when cigs = 20 (one pack per day)? Comment on the difference.
(ii) Does the simple regression necessarily capture a casual relationship between the child’s birth
weight and the mother’s smoking habits? Explain.
(iii) To predict a birth weight of 125 ounces what would cigs have to be? Comment.
(iv) The proportion of women in the sample who do not smoke while pregnant is about 0.85. Does this help reconcile your finding from part (iii)?
Question 2. The data in WAGES2 .RAW on working men was used to estimate the following equation:
e一duc = 10.36 − 0.094 sibs + 0.431 meduc + 0.210 feduc n = 722, R2 = 0.314
where educ is years of schooling, sibs is number of siblings, meduc is mother’s years of schooling, and feduc is father’s years of schooling.
(i) Does feduc have the expected effect ? Explain. Holding sibs and meduc fixed, by how much does feduc have to increase to increase predicted years of eduction by one year? (NB: a non- integer answer is acceptable.)
(ii) Discuss the interpretation of the coefficient on sibs.
(iii) Suppose that Man A has no siblings, and his mother and father each have 9 years of education.
Man B has no siblings, and his mother and father each have 17 years of education. What is the predicted difference in years of education between A and B?
Question 3. Computer Exercise: Explaining House Prices
(i) Download the data set hprice2 .dta from the Canvas web page. What are the average values of price, sqrmtr, lotsize and bdrms in the sample? What are the minimum and max-
imum values of each variable?
(ii) Estimate the model:
price = β0 + β1 sqrmtr + β2 lotsize + β3 bdrms + u
where price is the house price measured in thousands of dollars, sqrmtr is the size (i.e. floor area) ofthe house measured in square-metres, lotsize is the land area ofthe property in square- metres and bdrms is the number of bedrooms. Write out the results in the usual form.
(iii) What is the estimated increase in price for a house with one more bedroom, holding square metres of floor area and lotsize constant?
(iv) What is the estimated increase in price for a house with an additional bedroom that is 28 square metres in size? Compare this to your answer in part (iii) – why are they different?
(v) What percentage of the variation in price is explained by square metres of floor area, lotsize and number of bedrooms?
(vi) The first house in the sample has sqrmtr = 280, lotsize = 766 and bdrms = 6. Find the
predicted selling price for this house from the OLS regression model.
(vii) The actual selling price of the first house in the sample was $320,000 (i.e. price = 320). Find the residual for this house (e.g. calculate this by hand). Does it suggest that the buyer underpaid or overpaid for the house?
Note: The data set hprice2 .dta has 118 observations and 5 variables. The variables corresponds
to:
1. price (measured in dollars)
2. bdrms (number of bedrooms)
3. lotsize (or land area in square-metres)
4. sqrmtr (floor area of the house measures in square-metres)
5. fed (indicator variable, = 1 if the house is Federation style, = 0 otherwise) These data are in STATA (‘.dta’) format.
