Only use the data from 1987 and 1988 construct the

Question

Econometrics 706 - Difference in Differences

Problem 1 - Take the data set jtrain1 (also from from https://www.stata.com/texts/eacsap/). This has data on firms and the amount of job training they get.

a) Only use the data from 1987 and 1988. Construct the difference in differences estimator in two different ways:

i) Construct the 4 means (control, treatment × before, after)

ii) Run the regression

hrsemp_it = β₀ + β₁grant_it + β₂1(year = 1988) + β₃E_i + u_it

where E_i is a dummy variable for being a treatment (i.e. someone who would receive the grant in 1988).

iii) Run the fixed effect regression:

hrsemp_it = θ_i + β₁grant_it + β₂1(year = 1988) + u_it

Do you get exactly the same answer, why or why not?

b) Now (using all the data rather than 2 years) include a firm specific time trend in the model in two different ways:

i) use the x_i command (something like xi: reg y x i.fcode*year)

ii) For each firm, run a regression of x and y on an intercept and a time trend, take the residuals and run them on each other (not sure the cleanest way to do this, but you could again use egen with by)

Problem 2 - Now use the data set regm.raw.gz that you can get from the computer software part of my website.

You can read it into stata using the comand: infile coll merit male black asian year state chst using regm.raw

Now run the difference in difference model 4 different ways

a) Standard regression using all data (constructs standard errors 3 ways, robust, cluster by state year, cluster by state)

b) Standard regression using all data but weighted so that all states get the same weight

c) Now take the mean of all variable by state × year and run the diff in diff regression (robust se, and clustering by states)

d) Do the same as in c, but weight by state so it looks like the population

How does this all compare?