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ECMT: Econometric Applications Problem

Set 2 Solutions

Semester 2 2022

Question 1.

(i) When cigs = 0, predicted birth weight is 119.7 ounces. When cigs = 20, b—wght = 109.49. This is approximately an 8.6 per cent decline.

(ii) No. There are many other factors that can influence birthweight, particularly overall health of the mother and the quality of antenatal (prenatal) care. These may be correlated with cigarette smoking during pregnancy. Further, some factors (like caffeine consumption, diet in general) can affect birthweight and may also be correlated with cigarette smoking.

(iii) (iii) If we want a predicted bwght of 125, then cigs = (125 − 119.77)/( −0.524) = −10.18, or about −10 cigarettes! This does not make sense, and shows what may happen when we try to predict something as complicated as birth weight with only a single explanatory variable. The largest predicted birthweight is necessarily 119.77. However, almost 700 of the births in the sample had a birth weight higher than 119.77.

(iv) In fact 1176 out of 1388 women did not smoke while pregnant (approximately 85 per cent) – which is a very large fraction of the sample. Since we use only cigs to explain birth weight, we have only one predicted birth weight at cigs = 0. The predicted birth weight is necessarily roughly in the middle of the observed birth weights at cigs = 0, and so we will under predict high birth weights.

 

Question 2.

(i) Yes. We expect feduc to have a positive effect on e一duc. This effect may arise due to the fam- ily budget constraint fathers with higher education have greater earnings capacity which is related to higher family incomes and hence ability to fund children’s education. The pos- itive effects may also work through preferences – fathers with higher education may value education more than other fathers, encouraging higher educational attainment among their

children, all else equal (i.e. ceteris paribus). To find the increase in feduc necceary to increase predicted education by 1 year, holding other factors constant, solve:

educ = 1 = 0.210 × ∆feduc

1 = 0.21 × ∆feduc

feduc =

= 4.76

(ii) Holding meduc and feduc constant, and each additional sibling leads to a decline in expected years of education by 0.094 years (or equivalently, it takes more than an additional 10 siblings for predicted education to decline by 1 year, other things equal!). This is a small effect.

(iii) Since the number of siblings is the same, but meduc and feduc are both different, the coeffi- cients on meduc and feduc both need to be taken into account. The predicted difference in education between B and A is 0.431 × 8 + 0.210 × 8 = 3.448 + 1.680 = 5.128 years.

 

Question 3. Computer Exercise: Explaining House Prices

(i) Housing price summary statistics:

price

sqrmtr

lotsize

bdrms

min

111, 000

134

125

2

max

815, 000

446

11585

7

mean

292, 649

233.35

1058

3.5678

(ii) Estimated equation:

p—rice = −11.751 + 1.0183 sqmtr + 0.0196 lotsize + 12.914 bdrms n = 118,     R2  = 0.6367

(iii) Holding square-metres of floor area and lotsize constant, ∆p—rice  =  12.914 × ∆bdrms  =

12.914 × 1 = 12.914. Therefore the expected increase in the price for a house with one more bedroom, other things equal, is $12, 914.

(iv) Now p—rice  = 1.0183 × ∆sqrmtr + 12.914 × ∆bdrms  = 1.0183 × 28 + 12.914 × 1 =

28.512+12.914 = 41.4264 or $41, 426. This is much larger than the effect in part (iii) because the extra bedroom is associated with greater floor area (or size) of the house.

(v) Approximately 63.37% (this is the R2  statistic).

(vi) The predicted price is:

p—rice1  = −11.751 + 1.0183 × 280 + 0.0196 × 766 + 12.914 × 6

= −11.751 + 285.124 + 15.0136 + 77.484

= 365.8706

or $365, 871.

(vii) The residual for the first observation is: 1  = 320.000 − 365.871 = −45.871. This suggests that the buyer underpaid for the house (i.e. the actual selling price was less than the expected price based on the regression model) – and hence looks to have got a bargain. However, there are many features of a house apart from sqmtr, lotsize and bdrms – which affect price and have not been controlled for in the regression model.  This could be problematic in getting reliable estimates of the true causal relationship.

Note:  STATA output gives p—rice1  = 365.845 and 1  = −45.845. The difference is rounding error (STATA is more precise than my calculations based on 3 decimal places).