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EC3380

Summer Examinations 2020/21

Econometrics 2: Microeconometrics

Section A: Answer ALL SEVEN questions

(For questions 1-3) The United Kingdom, like in many other countries, prioritised the elderly in the rollout of COVID-19 vaccines, ahead of other age cohorts. Suppose that you are in a fictional country where only the over-70s got the vaccine.

Your data consists of COVID-19 case counts, and vaccinations per week, age bracket, and narrow geographical units (such as the Lower-layer Super Output areas, or LSOAs, of which there are over 30,000 in England and Wales). You also have data on the population headcount and socio-demographic composition at the same level.

1. Using the potential outcome notation, define the average treatment effects on the treated (ATT), the average treatment effects on the untreated (ATU), and the conditional versions. Be specific about the quantities that can, or cannot, be observed by the empiricist. Should the policymaker be interested in estimating the ATE, ATU or both? Can you give examples of conditional versions that may also be of interest? (10 marks)

2. Formulate identiﬁcation approach(es) to estimate the causal eﬀect of the vaccine on COVID-19 case counts using variations of the diﬀerences-in-diﬀerences approach. You can explore the timing of the vaccine rollout and/or the allocation of treatment to over- and under-70s. You must write the econometric speciﬁcation in full and explain, in intuitive terms, the identiﬁcation strategy you pursue. (10 marks)

3. What considerations should one take into account when specifying the standard errors in the regression above? What type of standard errors should be implemented, and why?

(10 marks)

4. Suppose that you estimate a dynamic diﬀerences-in-diﬀerences with treatment implementation at T = 0. The omitted period is T = -4. You observe the following eﬀects before and after the implementation. What diagnosis do you make? Which solutions could you suggest to achieve a causal identiﬁcation? (10 marks)

400 300 200 100 0
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	−4 −3 −2 −1 0 +1 +2 +3 +4

(For questions 5-7) The months of lockdown in the United Kingdom were particularly challenging for the mental health of youth, as widely reported. In questions 5 to 7 as follows we consider a hypothetical interventions to improve the mental health of this cohort, and the consequences for

the Econometric speciﬁcations that should be implemented.

5. Suppose that a research institute is interested in testing two interventions. First, the administration of Cognitive Behavioural Therapy (CBT) onto the research participants. CBT is described as “(...) a talking therapy that can help you manage your problems by changing

the way you think and behave.” The second intervention is designed to promote the practice of sports which are known to release endorphins and might improve the mental health of the participants.

The research institute is interested in evaluating the eﬀects of the two interventions, both as

standalone and combined, and randomised participants into four groups:

1. Control group with no intervention.

2. CBT-only group.

3. Exercise-only group.

4. CBT + exercise group.

What is the empirical speciﬁcation that you could implement to evaluate the eﬀects of CBT and exercise interventions? The research institute is also interested in learning whether the CBT and exercise interventions are complements or substitutes. How can you address this question? Also comment on some potential drawbacks of this research design.

(10 marks)

6. Let’s now focus on a single intervention through delivery of Cognitive Behavioural Therapy

(CBT) to students. Suppose now that allocation is no longer random. In fact, the government oﬀers the therapy to all students with household income level below x* and with grades below z* . That is, eligibility can be summarised in the Figure below:

7. The research institute is tasked to better understand the causes of mental health issues. To do so, they deﬁne a binary variable yi = 1 for individuals i with any episode of mental health issue in the past year, and yi = 0 otherwise. The explanatory variables are: xi1 is parental income, and xi2 are minutes of sport per day. They postulate that:

P (yi = 1 ∣xi1, xi2) = G (β0 + β1 xi1 + β2 xi2 + β3 xi(2)2 )

where G is the Gaussian or Logistic distribution. You are interested in the marginal eﬀect of sports per day on yi . Can you derive the marginal eﬀects, and the marginal eﬀect at the mean? What limitation do you see in this case? (10 marks)

Section B: Answer ONE question

8. Every time we walk into the supermarket, we make a decision on whether to buy certain goods or not. In fact, we do NOT purchase most of the goods – in other words, we consume exactly zero of most products, and some positive quantity of a few other products. We may write our optimal decision of purchasing a certain good as

y∗i = xiβ + i

where i ∼ N(0, σ 2 ). However, yi ∗ is not necessarily observed. In fact, we observe zero purchase (yi = 0) if, in fact, the optimal decision would have been to purchase a negative amount yi ∗ < 0. This is also known as the Tobit model. We can equivalently write

yi = max{0, xiβ + i}

(a) What are the probabilities P(yi = 0∣xi) and P(yi > 0∣xi)? (9 marks)

(b) What would be the maximum likelihood function for this case? In fact, the likelihood f will be on the following format:

f(yi∣xi) = [●] ■ ⋅ [▲] ⭑ .

you can write your answer in terms of defining what ●, ■, ▲ and ⭑ are. (16 marks)

9. The paper “Long-term Consequences of Vietnam-Era Conscription: New Estimates Using Social Security Data” by Angrist, Chen and Song (American Economic Review, 2011) estimates the effect of military service of earnings and working status of veterans.

The paper is included along with this exam for completeness but you do NOT need to read or look through the paper to answer the questions that follow.

(a) Suppose that you regressed outcomes yi on the veteran status V ETi and a set of controls xi ,

yi = β ⋅ VETi + Xi ′ γ + i

where i is a random disturbance term. Would β reflect the causal estimate? Why? Give as many examples as possible and use the omitted variable bias formula to make your argument. (6 marks)

(b) The authors propose to instrument the veteran status with a random draft number that is correlated with eligibility. Comment on whether this may be a suitable instrument, if using the instrument would identify β, the empirical speciﬁcations to be used, and the interpretation of the proposed causal impact. (14 marks)

(c) The following table shows the results for earnings and working status (you may suppose that =1 if working). Columns (2) and (5) show the 2SLS results. Columns (3) and (6) show the OLS results. What is your conclusion regarding the eﬀects of military service on earnings and working status? What can you learn about selection biases from this table? (10 marks)