Difference-in-difference and Treatment

[Calvin McHenry]

Hello,

I am supposed to use a difference and difference model to estimate the effect of mergers on the growth in R&D expenditures. I will be logging the R&D expenditures. I will also be using logSales as an independent variable. Then I need to follow the difference and difference model to create the interaction term between the treatment group and the firm type. The treatment in this case is a merger with a 1 used for each year when the firm merged. The firm type is a 1 for the firms that engaged in a merger and a 0 for the firms that did not merge during the time period of the study.

However, I am confused how to create the treatment variable.

My stata command comes out like this:

xtreg logR&D firmtype logSales

But I do not know how to make the Treatment variable for the treatment group. Then after that I need to make an interaction term between Treatment and firmtype.

[Bruce Weaver]

Hello Calvin. Sometimes, Google can be your friend. E.g., I just tried a search on <stata interaction vs difference in difference>, and a nice little slide show by Oscar Torres-Reyna (from Princeton University) appeared at the top of the list of results. Check it out.

[Fei Wang]

Calvin, I assume you have a firm-level balanced panel data where some firms merged at specific points of time while others never merged through the period of study. I also assume that your data have already included a variable (e.g., w_it) indicating the status of merger: w_it = 1 if firm i has merged at t; w_it = 0 if firm i has not merged at t. Let's first discuss the simplest case: Firms which merged at some time all merged at the same time. Then you may simply run the following regression to finish the DiD analysis.

xtreg logRD w i.timevar, fe vce(cluster panelvar)

w_it has already been the interaction of the two dimensions. If you are willing to generate the two dimensions, the procedure is as follows. Let's call the two variables d_i and p_t. d_i = 1 if firm i will eventually merge, and d_i = 0 if firm i will never merge. p_t = 1 for post-merger periods, and p_t = 0 for pre-merger periods.

bysort panelvar: egen tempvar = total(w)
gen d = (tempvar > 0)
sum timevar if w == 1
gen p = (timevar >= r(min))
drop tempvar

It's easy to verify that w = d * p. A very nice paper of Jeff Wooldridge (https://papers.ssrn.com/sol3/papers....act_id=3906345) proves that the following two regressions are equivalent.

xtreg logRD w i.timevar, fe vce(cluster panelvar)
reg logRD w d p, vce(cluster panelvar)

If the firms merged at different points of time, then it becomes the staggered DiD. There are several solutions, but still, I love Wooldridge's solution most. Essentially, you group the firms by the timing of mergers. A simple example: some firms merged at time A, some merged at time B, and the rest never merged. Then you would generate dA_i, dB_i, pA_t, pB_t. dA_i (or dB_i) = 1 if firm i merged at time A (or B), pA_t (or pB_t) = 1 for periods after time A (or B). Then DiD codes are:

reg logRD c.dA#c.pA c.dB#c.pB dA dB pA pB, vce(cluster panelvar)

Essentially there are two interaction terms capturing heterogenous effects of mergers. More details please refer to Wooldridge's paper (he also kindly provides Stata codes in his shared dropbox).