[SOLVED] Socga2332 lab 9

Logistics
• Quiz explanations
Part 1: Replication Project Tips
1.1 Samples
• For the 1990 sample, use the 1% metro sample
• For the 2010 sample, use the single-year ACS sample, not 3- or 5-year pooled sample
• If you read pp.1046 carefully, you will notice that Rs with the top and bottom earning percentile are excluded
– You can create percentiles using quantile(ma$WEEKEARN, seq(0.01,1,0.01)), suppose your dataframe is ma, and the weekly earning variable is WEEKEARN
1.2 Variables
• Use BPL rather than NATIVITY
• The latter has no valid values for most samples
• Use HISPAN to exclude Hispanic Whites and Hispanic Blacks
• Use CLASSWKR to determine whether R is in a public sector or not
– You should look at CLASSWKRD, which gives detailed classification of CLASSWKR
• Use CPI99 to adjust inflation for INCWAGE
• The main dependent variable is the logged form of weekly earnings
– You will need WKSWORK1 and WKSWORK2 to measure the number of weeks worked last year. WKSWORK1 always gives the best continuous estimate, but when WKSWORK1 is not available, you should turn to
WKSWORK2
• To estimate potential years of experience, the formula is given by LMEXP = AGE – EDUYEAR – 6 – EDUYEAR needs to be estimated
– Codes for this process are available in the code folder
1.3 Duncan’s Dissimilarity Index
• In Table A1a and A1b, you will notice that there is a dissimilarity index. This is a very commonly used measure of occupational segregation.
– The standard Duncan’s Dissimilarity/Segregation Index is given by:
1 X
D = n ai − bi
2 A Bi=1
where ai and bi is the number of White and Black workers in occupation group i. A and B represents the total number of White and Black workers.
• Instead of using hundreds of OCC1990 categories, you will use 2-digit aggregated categories of OCC1990
– Codes are available on Brightspace
– Use the merge() function
1.4 General Instructions
• It is totally okay if you cannot get exactly the same numbers! I also couldn’t.
• But they should be close enough. If they deviate a lot, you need to explain your speculations why the numbers differ this much.
Part 2: Causality: The Potential Outcome Framework
2.1 The Fundamental Problem of Causal Inference
• The modern way of thinking about causality is to think about outcomes in a counterfactual approach
• For example, the effect of a policy treatment on an outcome Y , is to think about the difference between Yit, i.e., the potential outcome of individual i receiving the treatment, and Yic, i.e., the potential outcome of the same individual, if not receiving the treatment. Either one of the two terms is never observed.
– Notation-wise, Y c and Y t are both potential outcomes (i.e., Rubin’s approach)
– ATE is defined as ATE = E[Yit] − E[Yic] = E[Yit − Yic]
– We can only observe E[Yit|Di = 1] and E[Yic|Di = 0]
2.2 Naive Estimation of the Average Treatment Effect
• At the population level, the average treatment effect (ATE) is defined as:
τ = ATE = E[Yit − Yic] = E[Yit] − E[Yic]
* Since we do not observe the population level Y T or Y C, the naive approach to estimate the population level ATE uses the following equation:
τˆ = E[Yit|Di = 1] − E[Yic|Di = 0]
• which calculates the difference in the expected value of Yi in the observed treated group (E[Yit|Di = 1]) and the expected value of Yi in the observed control group (E[Yic|Di = 0]).
• The estimated naive ATE will be unbiased if the assignment to treatment is purely random.
2.3 Selection Bias
• However, if there are selection bias that lead to certain kinds of unit to go into the treatment or control group, the naive estimator will be biased.
τˆ = E[Yit|Di = 1] − E[Yic|Di = 0]
= E[Yit|Di = 1] − E[Yic|Di = 1]+E[Yic|Di = 1] − E[Yic|Di = 0]

| {z } | {z }
ATT selection bias
where E[Yit|Di = 1]−E[Yic|Di = 1] is the treatment effect on the treated and E[Yic|Di = 1]−E[Yic|Di = 0] is the selection bias. You can think of it as the baseline difference of Yi if both the treatment and the control group are not treated.
• There is also a definition of the treatment effect on the control (ATC), which can be expressed as E[Yit|Di = 0] − E[Yic|Di = 0]
• E[Y ic|Di = 1,Xi] − E[Yic|Di = 0,Xi] = 0

| {z } selection bias
– This is a strong assumption, i.e., strong ignorability assumption
– Failure to satisfy the assumption will lead to omitted variable bias, or selection bias, or the violation of zero-conditional mean assumption
Part 2 Exercise
Assuming you know both potential outcomes Yit and Yic on the same individual, as well as their realized outcomes. Answering the following questions:

1. Calculate ATE:
2. Calculate ATT:
3. Calculate ATC:
4. Naive estimate of the ATE:
5. What causes the naive ATE to deviate from the true ATE in this example?
Part 3: Some Examples of Causal Inferential Studies
• The most straightforward approach is to manipulate treatment assignment to be completely random.
In this case, selection bias is zero, by design.
• Effect of neighborhood stigma on economic transactions, The Proceedings of the National Academy of
Sciences (PNAS)
– Random assignment of seller’s neighborhood information on an online market
• The mark of a criminal record, AJS
– Random assignment of racial background of job seekers with criminal record
• Exposure to Opposing Views can Increase Political Polarization: Evidence from a Large-Scale Field Experiment on Social Media, PNAS
– Random assignment of Republican or Democrats voters to follow twitter accounts from elected officials and opinion leaders with opposing political views
• In many cases, experiments with random assignment is either unethical or unfeasible. People therefore turn to natural experiments, where assignment of treatment is quasi-random.
Nation building through foreign intervention: Evidence from discontinuities in military strategies, QJE
• Quasi-random assignment of bombing and airstrikes in the Vietnam War
Lifetime earnings and the Vietnam era draft lottery: evidence from social security administrative records,
AER
• Quasi-random assignment of military participation in the Vietnam War
• Instrumental variables are seen as quasi-experiments if their variations come from certain social or natural designs
• Commitment through Sacrifice: How Longer Ramadan Fasting Strengthens Religiosity and Political Islam, ASR
– IV from the time-shifting feature of Ramadan that makes the fasting duration vary from year to year
• Community and the Crime Decline: The Causal Effect of Local Nonprofits on Violent Crime, ASR
– IV from nonprofit organizations in art, media, and medical industries to instrument local nonprofit organizations targeting violent crimes