ECOM30002 ECOM90002 ECONOMETRICS 2

Due date: 11:59 pm on Thursday, 18 August, 2022

Section 1
A country has been ravaged by a pest. The economy is struggling, with 3 of the country’s 6 equally
large economic sectors set to end the financial year with losses. The government is considering a
reform package, but it would have heterogeneous effects on the economy.
The following table characterises the potential outcomes of the reform, where Y 1i denotes sector
i’s potential profits (for Y 1i > 0) or losses (for Y 1i < 0) if it were subjected to the reform, and Y 0i
denotes i’s potential profits or losses if it were not subjected to the reform:
Sector Y 0i Y 1i
a 7.0 16.0
b -4.0 12.0
c -8.0 -3.0
d 14.0 13.5
e 0.5 -0.5
f -4.0 -10
Consider the following three different ways of assigning the treatment:
(i) the reform applies to every sector in the economy;
(ii) adoption of the reform is voluntary (assume that each sector acts as a single profit-maximising
agent that has perfect information of the sector’s potential outcomes);
(iii) the reform only applies to sectors set to post a loss without the reform.
1. What is the average effect of the treatment on the treated (ATT) for each case (i), (ii), and
(iii)?
2. Does any of the three ATTs above correspond to the average treatment effect (ATE)? Ex-
plain.
3. Calculate the OLS coefficients for the regression of Y i on X i for case (iii).
4. Calculate the selection bias for case (iii), and give an intuitive explanation of why the OLS
regression does or does not estimate a causal effect in this case.

Section 2
The following equation describes the median house price in a community i (price i ) as depending
on the amount of pollution (nox i for nitrogen oxide pollutants, NO X ) and the average number of
rooms in houses in the community (rooms i ):
log(price i ) = β ‘
0 + β
‘
1 log(nox i ) + β
‘
2 rooms i + V
‘
i .
(1)
5. What are the probable signs of β ‘
1
and β ‘
2 ? What is the interpretation of β ‘ 1 ? Explain.
6. Why might nox i (or more precisely, log(nox i )) and rooms i be negatively correlated? If this
is the case, does the simple regression of log(price i ) on log(nox i ) produce an upward or a
downward biased estimator of β ‘
1 ? Explain.
7. Using the data in houseprices.csv, estimate the following equation
log(price i ) = β s
0 + β
s
1 log(nox i ) + V
s
i
, (2)
as well as equation (1) and report your results in an appropriate table.
8. Is the relationship between the simple and multiple regression estimates of the elasticity of
price with respect to NO X what you would have predicted, given your answer in part 6?
Explain.
9. Do arguments like those in part 6 imply that β ‘
1
is definitely closer to the true elasticity than
β s
1 ? Discuss (including what might be meant by “true elasticity”).

Section 3
A researcher is interested in the effect of family size on mothers’ employment.
Specifically, the researcher uses a sample of women with either two or more children to estimate
the causal effect of a third birth (ThirdBirth i =1 if mother i has three or more children, 0 if she
has two) on whether the mother is employed (Employed i =1 if i is employed, 0 otherwise). The
instrument used for third birth is an indicator of the second birth being twins (Twins i =1 if mother
i’s second and third children are twins, 0 otherwise).
The researcher reports the following results.
Employed i ThirdBirth i Employed i
OLS OLS IV
(1) (2) (3)
ThirdBirth i -0.167 -0.083
(0.002) (0.017)
Twins i 0.625
(0.011)
Notes: Cells contain coefficient estimates. Robust standard errors in parentheses.
The mean of Employed i is 0.528. Column headers indicate dependent variable
and estimator.
10. Give an appropriate interpretation of the OLS estimate from Column (1).
11. Explain why the OLS estimate is unlikely to represent the causal effect of having more than
two children on employment for the population in question, giving concrete examples that
apply to this setting.
12. Interpret the estimated first stage slope, and calculate the first stage intercept.
13. Do you think the instrument is relevant? Explain why or why not.
14. Do you think the instrument is exogenous? Explain why or why not.
15. Give an appropriate interpretation of the IV estimate from Column (3). Compare the IV
and OLS estimates of the coefficient on ThirdBirth i , discussing if the results are compatible
with what you hypothesised in part 11 of this question.