ECOM114 Applied Econometrics (Applied Micro) 2021
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ECOM114 Applied Econometrics (Applied Micro)
2021
SECTION A – This section is worth 30 marks in total and consists of 3 questions. Each question is worth 10 marks. Answer ALL questions from this section. Be as formal as possible in all your answers.
1. Ability bias
We want to estimate a Mincer equation:
= + + +
where is the wage of individual i, is years of education, is a vector of individual controls (e.g. age, gender, etc.) and is an error term. However, we are concerned that unobserved ability may bias our estimate of the coefficient .
a. [4 marks] Derive and sign the ability bias (ignore the vector of controls when
deriving the bias).
b. [6 marks] Now, suppose we have a measure of IQ for each individual in our sample
(not included in the vector ). Can we use this variable as an instrument for schooling and obtain consistent estimates of ? Provide a formal argument to support your argument.
2. Panel data
Consider the model:
= + +
where: the subscript i defines individuals ( = 1, … , ) and the subscript t defines time periods ( = 1, … , ); is a matrix of time varying controls; is an unobservable time-
invariant individual effect; and is an idiosyncratic error term. We assume: (i) the two
unobservables components are mean-independent: ( | ) = 0; (ii) the idiosyncratic temporary shock is not serially correlated: ( , ) = 2 , where = 1 if = and 0 otherwise; (iii) strict exogeneity: ( |1, … , , ) = 0 .
a. [3 marks] Assume random effects. Is there an endogeneity problem if we estimate
the equation above with OLS? Which estimator(s) would allow to obtain consistent estimates of the vector of parameters ? Explain formally.
b. [4 marks] Assume fixed effects. Is there an endogeneity problem if we estimate the
equation above with OLS? Which estimator(s) would allow to obtain consistent estimates of the vector of parameters ? Explain formally.
c. [3 marks] Assume that y_it is the number of litres of beer consumed by individual i
in each month t and the main regressor of interest x_it is individual monthly income. We are interested in estimating the income elasticity of beer consumption. Explain why assuming random rather than fixed effects in estimating this regression may lead to opposite conclusions. (Hint: use graphs to illustrate your argument).
3. Schools, Teacher and RCT
Consider the following paper: Duflo, Esther, Rema Hanna, and Stephen P. Ryan. 2012. "Incentives Work: Getting Teachers to Come to School." American Economic Review, 102 (4): 1241-78.
a. [5 marks] Briefly discuss Table 1 in the Appendix that reports balance tests at
baseline from Duflo, Hanna, and Ryan. (2012). In particular, does the fact that the differences in outcomes between treatment and control group are not statistically
significant imply that the treatment had no effect? Explain.
b. [5 marks] Which treatment (or treatments) was (were) used in this paper? Briefly
describe it (them)?
SECTION B: This section is worth 40 marks in total and consists of one question. Be as formal as possible in all your answers.
Question B1 - Randomised experiment [40 marks]
Consider a randomised experiment. Z is the variable that is randomly assigned (i.e. = 1 if the individual i was randomly assigned to the treatment) while D is the treatment of interest (i.e. = 1 if the individual i took the treatment).
a. [4 marks] After having defined the “Fundamental Problem of Causal Inference” ,
explain how a randomised experiment allows us to overcome it.
b. [4 marks] Define “selection into treatment” . Are there different types of
selection? Which ones?
c. [3 marks] Does randomization always remove any concern about selection into
treatment?
d. [4 marks] The experiment may determine changes in the behaviour of subjects
in the treatment and/or control groups that are induced by the experimental evaluation itself. How are these effects called? Explain whether they may threaten the identification of causal effects in randomized experiments.
e. [7 marks] Assume perfect compliance.
i. Formally define perfect compliance.
ii. Formally show which parameter is identified by a randomised experiment with
perfect compliance. Explain the interpretation of that parameter.
f. [8 marks] Consider now the Intention to Treat effect (ITT).
i. Formally define the ITT.
ii. Briefly discuss the following statement: “To be valid and to prevent the
reintroduction of selection bias, an analysis needs to focus on groups created by the initial randomisation. One must compare all those initially allocated to the treatment group with all those initially randomised to the comparison group, whatever their actual behaviour and their actual treatment status.”
iii. Explain under which conditions the ITT identifies an Average Treatment Effect
(ATE).
g. [10 marks] Suppose we have one-sided compliance (i.e. all those randomised
out do not get the treatment, while those randomised in can choose not to take the treatment).
i. Precisely explain the following expression (i.e. define denominator and
numerator of the fraction on the right hand side and explain which parameter is identified on the left hand side of the equation:
( | = 1) − ( | = 0)
ii. Using the equality ( = 1| = 1) = ( | = 1) − ( | = 0), show
that the expression above can be rewritten as a Wald estimator. What is the Wald estimator? What is the link between the IV estimator and the Wald estimator?
iii. Discuss whether the random assignment variable satisfies the two conditions for being a valid and relevant instrument for treatment status .
SECTION C: This section is worth 30 marks and includes two questions. Answer ONLY ONE question. Be as formal as possible in all your answers.
Questions C1 – Education and School Construction [30 marks]
a. [8 marks] Briefly discuss the main identification challenges in estimating returns
to schooling in Mincer equations. Be as formal as possible.
b. [10 marks] Consider the paper by Esther Duflo (2001) “Schooling and labor
market consequences of school construction in Indonesia: Evidence from an unusual policy experiment. “ , American Economic Review, that was discussed during the course. Briefly explain her estimation strategy. Be as formal as possible.
c. [12 marks] Discuss the empirical findings reported in Table 2 from Duflo (2001)
– see the appendix to this paper. In particular: i) write and explain the estimating equation used to obtain these estimates; ii) contrast and explain the estimates reported in panel A and panel B; iii) explain the rationale for the inclusion of the control variables (see last two rows in the table).
Question C2 – Cops and robbers [30 marks]
a. [10 marks] Consider the paper by Draca, Machin and Witt (2011) “Panic on the
streets of London: Police, crime, and the July 2005 terror attacks.” American Economic Review, which was discussed during the course. Briefly explain their estimation strategy. Be as formal as possible.
b. [10 marks] Briefly discuss Table 3 from Draca, Machin and Witt (2011), which is
shown in the appendix to this paper. In particular, note that in the pre-period crime
rate in untreated areas (T=0) was half the crime rate in treated areas (T=1). Is this a violation of the common trend assumption of the Difference-in-Differences? Explain with a graph.
c. [10 marks] Suppose you had cross-sectional data on crime rates and police
deployment (e.g. number of officer hours per day) in different neighbourhoods of one city. Would you expect to find a positive or negative correlation between these two variables? Explain the main identification challenges in estimating the causal effect of police on crime. Would you be able to identify a causal effect if you had longitudinal data? Explain. Be as formal as possible.
2022-05-05