# Exercise 1

This exercise will involve estimating causal effect parameters using a difference-in-differences identification strategy that involves conditioning on covariates in the parallel trends assumption and possibly allows for anticipation effects.

In particular, we will use data from the National Longitudinal Study of Youth to learn about causal effects of job displacement (where job displacement roughly means “losing your job through no fault of your own” — a mass layoff is a main example).

To start with, load the data from the file job_displacement_data.RData by running

load("job_displacement_data.RData")

which will load a data.frame called job_displacement_data. This is what the data looks like

head(job_displacement_data)
       id year group income female white occ_score
1 7900002 1984     0  31130      1     1         4
2 7900002 1985     0  32200      1     1         3
3 7900002 1986     0  35520      1     1         4
4 7900002 1987     0  43600      1     1         4
5 7900002 1988     0  39900      1     1         4
6 7900002 1990     0  38200      1     1         4

You can see that the data contains the following columns:

• id - an individual identifier
• year - the year for this observation
• group - the year that person lost his/her job. group=0 for those that do not lose a job in any period being considered.
• income - a person’s wage and salary income in this year
• female - 1 for females, 0 for males
• white - 1 for white, 0 for non-white

For the results below, we will mainly use the did package which you can install using install.packages("did"), and you can load it using

library(did)

## Question 1

We will start by computing group-time average treatment effects without including any covariates in the parallel trends assumption.

1. Use the did package to compute all available group-time average treatment effects.
1. Bonus Question Try to manually calculate $$ATT(g=1992, t=1992)$$. Can you calculate exactly the same number as in part (a)?
1. Aggregate the group-time average treatment effects into an event study and plot the results. What do you notice? Is there evidence against parallel trends?
1. Aggregate the group-time average treatment effects into a single overall treatment effect. How do you interpret the results?

# Question 2

A major issue in the job displacement literature concerns a version of anticipation. In particular, there is some empirical evidence that earnings of displaced workers start to decline before they are actually displaced (a rough explanation is that firms where there are mass layoffs typically “struggle” in the time period before the mass layoff actually takes place and this can lead to slower income growth for workers at those firms).

1. Is there evidence of anticipation in your results from Question 1?
1. Repeat parts (a)-(d) of Question 1 allowing for one year of anticipation.

# Question 3

Now, let’s suppose that we think that parallel trends holds only after we condition on a person sex and race (in reality, you could think of including many other variables in the parallel trends assumption, but let’s just keep it simple). In my view, I think allowing for anticipation is desirable in this setting too, so let’s keep allowing for one year of anticipation.

1. Answer parts (a), (c), and (d) of Question 1 but including sex and white as covariates.
1. By default, the did package uses the doubly robust approach that we discussed during our session. How do the results change if you use a regression approach or propensity score re-weighting?

# Question 4

Finally, the data that we have contains a variable called occ_score which is roughly a variable that measures the occupation “quality”. Suppose that we (i) are interested in including a person’s occupation in the parallel trends assumption, (ii) are satisfied that occ_score sufficiently summarizes a person’s occupation, but (iii) are worried that a person’s occupation is a “bad control” (in the sense that it could be affected by the treatment).

1. Repeat parts (a), (c), and (d) of Question 1 but including occ_score in the parallel trends assumption. Continue to allow for 1 year of anticipation effects.
1. What additional assumptions (with respect to occupation) do you need to make in order to rationalize this approach?