Answer the following questions: (a) Each of the methods for estimating causal ee

Question

Answer the following questions:
(a) Each of the methods for estimating causal eects except for one has a potential debilitating aw. List the various ways we discussed for estimating causal impacts and their associated potential aw.

(b) Comment on the following statement: “There is an inverse relationship between how close your data are to a randomized controlled experiment and the complication of the appropriate methodology with which to analyze the data.”

(c) Explain how the Hausman test of random vs. xed eects diers or is similar to the equaleects assumption of between and within eects.

(d) Explain carefully how a two-way xed eects estimation solves an omitted-variables problem

Explanation / Answer

c)A Haussmann test compares the coefficient vectors from two estimators. If they are both consistent estimators, then their point estimates should not differ greatly, whereas if one of the estimators is inconsistent, its point estimates are likely to differ widely from those of a consistent estimator. In the current context, the FE estimator is always consistent, but inefficient under the null hypothesis that cov(xit, ai) = 0. RE is both consistent and relatively efficient under that null hypothesis, but inconsistent under the alternative.

d)A fixed effects regression uses the variation within an entity to make identification in order to control for unobserved differences across entities, rather than comparing apples and oranges. (Ex: compare Arizona today to Arizona tomorrow rather than comparing Arizona to New York) The aim of a fixed effects estimator is to remove (or estimate) this linear entity specific fixed effect. For example, if i stand for state, the interpretation of i is a state-specific intercept. If the dependent variable is crime, then a large i means that state I has a lot of crime on average, and a low i means state I has less crime than average. Also time fixed effects are useful in dealing with omitted variables that don’t vary across entities yet vary over time.

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