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ECON60052

代考微观经济学 You have 3 hours to answer the questions, however this exam is based on a response time of 2 hours and 15 minutes.

MICRO ECONOMETRICS – MOCK EXAM

Answer ALL questions. 100 marks in total.

INSTRUCTIONS SPECIFIC TO THIS EXAM:

• This is an Open Book examination.
• Answer all questions. You can achieve 100 points in total. Unanswered questions receive a mark of zero.

• You must not impersonate another candidate or allow yourself to be impersonated. You must not look at the work or copy from another candidate, or allow anyone to copy from yourself. You should not directly quote from lecture materials, internet sources or other material. Every answer must be written in their own words to avoid plagiarism.All work submitted by you must be your own work.

• You have 3 hours to answer the questions, however this exam is based on a response time of 2 hours and 15 minutes. You should not expect to spend the entire time period working on this exam. The additional time is to be used to submit your paper on the virtual learning environment.  代考微观经济学

• Your answers could be typed or hand-written (and scanned to a single file that can be submitted) or a combination of a typed answer with included images of algebra or figures.

• You must correctly enter your registration number and the course code (ECON60052) on your answer.

• Candidates are expected to demonstrate to the examiners a competent knowledge of all computations.

• Candidates are also advised that the examiners attach considerable importance to the clarity with which answers are expressed.
• Candidates must not write more than is needed. Many questions have some kind of limit (excluding formulae) — and candidates will be penalised for exceeding these limits.The limits are very generous: good answers can be shorter. Where a question includes a word limit you have to include a word count for your answer (excluding formulae).

Answer all questions.  代考微观经济学

1. [18 Marks] In all parts to this question, choose one or more correct answer(s). Choosing a wrong answer loses points. If the number of negative points exceeds the number of positive points, your total for this question is zero.

(a) Which of the following is true in a Randomized Controlled Trial:

1. The Intention-to-Treat Effect is equal to the Average Treatment Effect under perfect compliance.

2. The Intention-to-Treat Effect divided by the share of compliers equals the Local Average Treatment Effect.  代考微观经济学

3. The Intention-to-Treat Effect is always larger than or equal to the Local Average Treatment Effect.

(b) Consider the following model: y = β0 + β1x + u, where y is an outcome of interest,x an endogenous regressor and u an error term. Imagine you have a valid instrument

1. z. Instrumenting x1 with z results in:
2. Estimating the model: y = β0 + β1z + v by OLS.
3. Estimating the model y = β0 + β1xˆ + v by OLS, where xˆ is the predicted value of a regression of the endogenous regressor on the instrument.

3. An unbiased estimator βˆ 1.
4. A consistent estimator βˆ 1.

(c) Using the same model as in (b), the Zero Conditional Mean assumption fails if:

1. There are variables explaining the outcome not included in the regression.
2. There are variables explaining the outcome not included in the regression which are correlated with x.

3. E(u|x) ≠ 0.

(d) In a Differences-in-Differences framework, the Common Trend assumption:

1. Means that the treated and untreated groups follow the same trend in absence of the treatment.

2. Is required to identify the Average Treatment Effect on the Treated.  代考微观经济学
3. Is often supported by a visual analysis comparing the outcomes of both groups before and after the treatment occurs.

(e) In an instrumental variable setup, the Hausman test:

1. Is valid even if the instrument does not meet the exclusion restriction.
2. Assumes exogeneity under the null.
3. Assumes that the difference between the two-stage-least squares estimator and the OLS estimator goes to zero under the null.

(f) Suppose one is interested in the effectiveness of a medical treatment to combat contagious diseases. To study the effect, treatment is randomized at the individual level within a single village. Without further information, which of the following is likely:

1. A failure of the Stable Unit Treatment Value Assumption.
2. That the potential outcome for one individual only depends on the treatment received by this unit.

3. That there are spillover problems.

(g) In a Panel Data model:

1. Fixed Effects and First Difference estimators yield the same result if they esti-mate the same model for two time periods.

2. The Fixed Effects, the Random Effects and the Pooled OLS estimators require strict exogeneity.

3. Random Effects allows the inclusion of non-time-varying regressors.

(h) The simple Moulton factor:

1. Illustrates that as the group size N goes to infinity, the Moulton problem van-ishes.

2. Quantifies by how much one overestimates precision by ignoring intraclass cor-relation.

3. Is unity if the intraclass correlation is equal to 1.

(i) Assuming that the First Stage assumption holds, The Bloom result:

1.Shows that under the exclusion restriction, independence and additionally un-der monotonicity, the Local Average Treatment Effect is equal to the Average Treatment Effect on the Treated in an eligibility design.

2.Shows that under exclusion restriction and independence, the Local Average Treatment Effect is equal to the Average Treatment Effect on the Treated in an eligibility design.

3.Applies to a Randomized Controlled Trial design with one-sided imperfect com-pliance.

2.[25 Marks] This question is inspired by the paper from Gerber et al. (2009) “Does the Me-dia Matter? A Field Experiment Measuring the Effect of Newspapers on Voting Behavior and Political Opinions”.  代考微观经济学

Gerber, A. S., D. Karlan, and D. Bergan (2009): “Does the Media Matter? A Field Experiment Measuring the Effect of Newspapers on Voting Behavior and Political Opinions,” American Economic Journal: Applied Economics, 1, 35–52.

The authors run a randomized experiment to measure the effect of political news content on political behavior and opinions.

One month prior to the Virginia gubernatorial election in November 2005 the authors run a short survey to a random selection of households. 3347 individuals reported not to receive the Post or the Times in the household and responded to all questions. The authors randomly assigned these individuals to get subscriptions to either the Post or the Times for about 10 weeks. The control group did not get either paper in the framework of this experiment. The randomization was carried out using stratification. The variables times, post and paper are binary variables being equal to one or zero. Define times = 1 if the household received the times treatment, post = 1 if the household received the post treatment and paper = 1 if the household received either treatment.  代考微观经济学

One week after the election, the authors conducted a follow-up survey in which individuals were asked about several outcomes such as their voting behavior and readership.The authors had further access to a state administrative dataset including voter turnout data for the november 2005 and 2006 elections.

(a) [7 Marks] You are interested in the voting outcome from the 2006 elections (voted2006g) using administrative data. (i) Write down a simple model to identify both treatment effects, post and times, in a single regression without additional controls / strata.

(ii) State all population parameters as functions of conditional expectations and ex-plain what they mean in this context. Explain which individuals form the control group.

(b) [5 Marks] Consider the following information on voted2006g:

Estimate the treatment effects for the post and times treatment and carefully in-terpret.

[Note: you do not need to consider additional controls and can assume that the results are significantly different from zero. The values are obtained without any data cleaning procedures and are therefore very different from the original results from the paper.]  代考微观经济学

(c) [9 Marks] Table 2 of the paper is reproduced below. (i) Explain how the authors obtain the estimates for this table and draw an overall conclusion from each column.

(ii) Explain why the authors might provide such a table and the implication for the experimental design. (iii) Does this information have some implications on the

identified causal effect from part (b)?

[Note: do not interpret each single number and do only discuss panel A].

Figure 1: Table 2 from Gerber et al. (2009).

(d) [4 Marks] How does the table relate to an instrumental variable approach? Explain briefly in words.

3.[25 Marks] Consider the following regression model estimated using a balanced panel with three time periods:

yit = β0 + β1xit + ai + uit, t = 1, 2, 3

Where xit is a binary variable which is e.g. equal to 1 if married and 0 otherwise. yit is an outcome of interest, ai an unobserved individual effect and uit an error term. The First Difference (FD) estimator is the same as estimating the following model using OLS:

∆yit = β1∆xit + ∆uit, t = 2, 3

Where ∆xit = xit − xt−1,i. There are identical expressions for ∆uit and ∆yit.  代考微观经济学

There are seven different types of individuals creating seven groups of size n. .

• ns stayers: individuals who do not change their marital status.
• nqe early quitters: individuals who are married in t = 1 but got divorced and are not married anymore in t = 2 and t = 3.

• …

(a) List the missing groups indicating how their marriage status changes over time.

(b) Write down an algebraic expression for the Pooled OLS estimate of ∆yit on ∆xit and show that (i) the stayers do not contribute to this expression and that (ii) only two groups contribute to the expression during both periods of the differenced equation.

4.[32 Marks] Consider the following model:

Yi = β0 + β1Di + β2(Xi − xo) + ui

where Yi is an outcome variable of interest, Di is an indicator variable which is equal to 1 when individual i receives treatment, Xi is an additional control variable centered at point xo, and ui is an error term with certain properties. You are interested in β1, the effect of receiving treatment.

Suppose the econometrician is interested in the effect on school outcomes of a summer school remediation programme for poorly performing school children. Di represents the participation in the programme and Xi the student’s grade in mathematics.

(a) Within the context of this model and example, explain the concept of self-selection into treatment and why this is problematic for the estimation of the model without further assumptions on the relationship between Di and Xi .  代考微观经济学

(b) Using this example, what does the formal relationship between Di and Xi need to be so that one can correctly estimate the model using Regression Discontinuity (RD) methods?

(c) (i) What is the key assumption about the potential outcomes Y (d), d = {0, 1} and Xi that needs to be satisfied in order to estimate a causal effect using Sharp RD estimation of the above model? (ii) Explain intuitively why, under this assumption,the econometrician is able to estimate the causal effect of Di on Yi in this context and name the causal effect.

(d) Explain the difference between the parametric and the non-parametric identification of the effect of Di on Yi using Sharp RD methods and explain what the “variance bias-tradeoff” means in this context.

(e) In order to estimate this question using Fuzzy RD methods, specifically Mixed RD,what would the relationship between Di and Xi have to be like? Explain formally in this context.

(f) Show formally that in the Mixed Design, the difference in the expected outcomes approaching the threshold from above and below (limε→0 E [Y |X = x0 ± ε]) divided by the limit of the expected program participation approaching the threshold from above (limε→0 E [D|X = x0 + ε]), is equal to the Average Treatment Effect on the Treated at the threshold. Explain each step in detail and state all relevant assump-tions.

 

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