EC3380 Econometrics 2: Microeconometrics 2020/21

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EC3380

Summer Examinations 2020/21

Econometrics 2: Microeconometrics

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 on

regression above? What type o

(10 marks)

ake into account when specifying the standard errors in the f standard errors should be implemented, and why?

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)

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:

explore the thresholds in eligibility for the programme? (10 marks)

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)

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

yi(*) = xi β + fi

where fi ∼ N (0, σ2 ). 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, xi β + fi }

(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 ) = [●]■ . [A]★ .

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

(c) Write the log-likelihood and the function to be maximised.(5 marks)











2022-05-25