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EC3380

Summer Examinations 2018/19

Econometrics 2: Microeconometrics

1. Deﬁne wi = 1 if individual i received a treatment, and wi = 0 otherwise. According to the potential outcomes framework, y1i is the outcome of individual i if she/he gets the treatment and y0i is the outcome of individual i if she/he does not get the treatment.
Consider the diﬀerence:
D = B(y1i~wi = 1) _ B(y0i~wi = 0)
where B is the expectation operator.
(a) Can B(y1i~wi = 1) and B(y0i~wi = 0) be observed from the data? (3 marks)
(b) What is the interpretation of the counterfactual term B(y0i~wi = 1)? Is it observed
directly from the data? (3 marks)
(c) Decompose D into the eﬀect of the treatment on the treated and selection bias.
(5 marks)
(d) How does random assignment solves the selection bias? (3 marks)

Preamble to Questions 2-6: Tackling climate change is one of the most important issues of our

times. In the following questions, you will be asked to consider how microeconometric methods may

be applied to evaluate the eﬀects of climate change, as well as to evaluate the eﬀects of policies that governments worldwide are implementing to preserve forests and the nature.

2. Between July and November 2018, wildﬁres engulfed the state of California in the United States. It is known that wildﬁres dramatically increase the number of air pollutants. In fact, an article in the New York times on November 18th 2018 entitled “Air Quality in California: Devastating Fires Lead to a New Danger” mentioned that:

“The wildﬁres that have laid waste to vast parts of California are presenting

In this question, you will assess the suitability of the Diﬀerences-in-Diﬀerences method to

analyse the eﬀects of wildﬁres on health.

The outcome variable yit is the number of patients admitted to the hospitals in county i at time t due to respiratory diseases, typically caused by air pollutants. The explanatory variable xit is equal to 1 if county i experienced wild ﬁres at time t, and zero otherwise.

(a) Write the diﬀerences-in-diﬀerences regression. Note that diﬀerent counties may experience wildﬁres at diﬀerent points in time. (5 marks)

(b) Spell out the main identiﬁcation assumption of the Diﬀerences-in-Diﬀerences method.

(4 marks)

(c) How could you verify if the identiﬁcation assumption above is likely to hold? In particular, which regression model could you implement to verify if the data supports that assumption? (4 marks)

(d) What alternative regression models could you implement if the data does not support the main identiﬁcation assumption of the Diﬀerences-in-Diﬀerences method? (3 marks)

(e) Pollution from wildﬁres travel through air, and may aﬀect neighbouring counties to those that experienced wildﬁres. This is referred to as “spillover eﬀect” since the control units suﬀer partially the eﬀect of the treated units. Are spillover eﬀects a threat to identiﬁcation of treatment eﬀects? If so, what would be the direction of the bias?

(3 marks)

3. Standard or classical standard errors assume that eit ～ N(0, σ2 ), where N (µ, σ2 ) is the Normal distribution with mean µ and variance σ 2 , and independent across units. Under heteroskedasticity, the variance of the error σ is allowed to vary with i, that is,

eit ～ N(0, σi(2)), but it is still assumed as independent across units. In EC338 you have seen a third option: clustered standard errors.

(a) Describe what clustered standard errors are, and how it generalizes the hypothesis that errors are independent across units. (5 marks)

(b) Describe how hypothesis testing can be aﬀected if the units suﬀer common shocks but the researcher utilizes the classical standard errors instead. (3 marks)

(c) Should clustering be implemented in the forest ﬁre application in Question 2? More speciﬁcally, which level of clustering could be appropriate? Justify your answer. (Hint: there is more than one answer to this question. Any answer will be accepted as long as appropriately justiﬁed.) (3 marks)