微观计量经济学代写 微观计量经济学的因果推理

ECON7360: Causal Inference for Microeconometrics

Problem Set 2

微观计量经济学代写 Answer all questions and clearly label all your answers. When using STATA to conduct empirical analysis, you should show your…

Instruction

Answer all questions and clearly label all your answers. When using STATA to conduct empirical analysis, you should show your STATA commands and outputs (e.g., attach the STATA log- fifile to your assignment as an appendix). You will lose 2 points whenever you fail to provide STATA commands or outputs. When you are asked to explain or discuss something, your response should be concise. You should upload this assignment (in PDF or Word format) via the “Turnitin” submission link (in the “Homework/Problem Set 2” folder under “Assessment”) Do not hand in a hard copy. You are allowed to work on this assignment in groups; that is, you can discuss how to answer these questions with your group members. However, this is not a group assignment, which means that you must answer all the questions in your own words and submit your report separately. The marking system will check the similarity, and UQ’s student integrity and misconduct policies on plagiarism apply.

A.DID and Panel Data Regression (60 points)

Background 微观计量经济学代写

The following empirical questions are based on:

McKinnish, T., 2005. “Importing the Poor Welfare Magnetism and Cross-Border Welfare Migration.” Journal of human Resources, 40(1), pp.57–76.

The research question is whether poor families in the U.S. migrate to states with higher welfare benefifits. The main empirical diffiffifficulty is to show that migrants to high-benefifit states are moving for welfare benefifits, rather than other state amenities (such as strong labor markets) that tend to be positively correlated with welfare benefifits.

Most studies of welfare migration, including this one, focus on the Aid to Families with Dependent Children (AFDC) program. AFDC was a welfare program that provided cash payments to low-income single mothers.1 Even though it was a federal welfare program, states set their own benefifit levels, generating sizeable difffferences in generosity across states. An important feature for the purpose of this paper is that benefifit levels are set at the state level. They do not vary by county within a state.

Assume that the costs of between-state migration are lower for individuals located close to state borders.

Consider the simple example for a country with two states illustrated below. The top state is the high-benefifit state and the bottom state is the low-benefifit state. Area HB contains the counties of the high-benefifit state that border on the other state, and area LB is likewise defifined for the low-benefifit state. Areas HI and LI are the interiors of the two states. If the assumption of difffferential migration costs is correct, then, the border counties in area HB should disproportionately draw migrants from the border counties in area LB. As a result, area LB should exhibit signifificantly lower per capita AFDC expenditures than area LI, which can be thought of as evidence of welfare migration. To examine this, in what follows, you will need

to use the data set Welfmig2.dta to conduct a series of DID-type analyses. Welfmig2.dta contains observations for all counties in the 48 continental states for the years 1970–1990. It contains the following variables:

• AFDCExp: Log of per capita AFDC expenditures in county.
• AFDCBen: Monthly AFDC benefifit in state (benefifit for a family of 4, in 100s of dollars).
• neardist: Distance from county to the closest neighbor state (in miles).
• NeighborBen: Monthly AFDC benefifit in the closest neighboring state (in 100s of dollars).
• state: State ID code.
• year: Year, 1970–1990.

Note that AFDCExp, neardist, and NeighborBen vary at the county level. AFDCBen and state vary only at the state level.

Questions 微观计量经济学代写

1. (6 points) Defifine a border county as one with neardist ≤ 25. Create a dummy variable Border25 for border counties. Create a dummy variable BenDiff indicating if the closest neighbor state’s benefifits is higher than own state’s benefifits (then the dummy should take the value of 1). Create a variable Border25xBenDiff as the interaction between Border25 and BenDiff.
2. (10 points) Using only 1979 observations, regress AFDCExp on AFDCBen, NeighborBen, Border25, BenDiff, and Border25xBenDiff. Which coeffiffifficient does capture the welfare migration effffect? Can you fifind evidence of welfare migration? Explain.

3. (4 points) Now re-run the regression in Q2 but control for state fifixed effffects. A convenient way to do so is to use STATA’s xtreg command with option “fe i(state)”.2 Can the coeffiffifficient on AFDCBen be identifified? Why?

4.(10 points) Compare the estimation results obtained in Q2 and Q3. Comment on your fifindings. Hint: Read the research question background and think about potential OVB.

5. (10 points) Re-run the regression in Q3 using all observations (1970–1990). Can the coeffiffifficient on AFDCBen be identifified now? Why? What has happened to the SE of the coeffiffiffi-cient on BenDiff? Explain. What has happened to the coeffiffifficient on Border25xBenDiff?

6. (10 points) Create and add year fifixed effffects to the regression model in Q5. Can you tell a story for why the effffect of AFDCBen changes a lot when controlling for year fifixed effffects? Explain why the coeffiffifficient on Border25xBenDiff only changes a little.

7. (10 points) Does the welfare migration effffect change over time? Create an indicator variable for the years 1980-1990 and interact it with all included regressors (other than year dummies) of the regression model in Q6 to test this hypothesis.

Regression Discontinuity Design (40 points) 微观计量经济学代写

Consider the paper by Melissa Dell (2010) who uses a regression discontinuity design (RDD) to analyze the persistence of institutions. The relevant data set is dell.dta.

The variables included in the data set are:

• mita: Mita Dummy.
• distance: Distance to Mita boundary.
• infants: number of infants in household.
• children: number of children in household.
• adults: number of adults in household.
• elevation: elevation.
• slope : slope.
• bfe4 *: boundary segment fifixed effffects.
• hh consumpition: household consumption.
• cusco: dummy for whether the observation is in Cusco.
• ubigeo: clustering variable.

Questions 微观计量经济学代写

1. (5 points) Replicate the fifirst 3 columns of panel C in Table 2 of Dell (2010). (Note: she conditions the regression on cusco!=1; the clustering command she uses is: robust cluster (ubigeo))

2. (10 points) Generate interaction variables between mita and the polynomial specifification of distance. How could you adjust the regression equation to allow the functional form of the running variable to be difffferent on both sides of the Mita discontinuity? Can you include the interaction variables you generated? Show the regression results when you estimate this specifification.
3. 3 (10 points) Construct a standard two-dimensional regression discontinuity graphs where the running variable is distance to the mita and the outcome variable is household consumption to show the difffferences from the cutoffff. Repeat this when the distance to the mita is 100, 75, and 50 km. Apply (a) a quadratic and (b) a linear fifitting.

4. (5 points) Repeat the exercise in Q3 but this time put on the y-axis the control variables: slope and elevation. Use a quadratic fifitting.

5. (10 points) Suppose you are worried about sorting at the threshold. Can you carry out the McCrary (2008) test? Is there evidence for sorting around the threshold? Repeat this exercise when the distance to the mita is 100, 75, and 50 km.