Handling time-varying covariates in Difference-in-Differences

[Ridwan Sheikh]

Dear all,

I have a following setup:

I am using Difference-in-Differences to examine the impact of some policy intervention (POLICY) enacted in 2004 on firm outcomes. Therefore, POLICY is an indicator that takes the value of 1 for years on and after 2004. My treatment (TREAT) take the vale of 1 for high-tech (treatment) firms and 0 for low-tech firms (control). My question is how to accomodate covariates in this case to mitigate post-treatment bias (bad control problem). In some paper, the authors use two approaches to include covariates:

(1) They mention, "All the pre-reform firm characteristics (sales, R&D) are measure as an average for years 2002 and 2003"

I am not clear, what that means. Suppose the sales for firm A in 2002 is 7 million and in 2003 is 9 million, the average for Firm A, therefore, become (7 + 9)/2 = 16 , we calculate sales for other firrms accordingly. Should we put the value of 16 for all other years. I am not sure, if they mean something like this, when these authors mention, "All the pre-reform firm characteristics (sales, R&D) are measure as an average for years 2002 and 2003" .

Note that, using covariates in this way makes them time-constant and will be subsumed in firm fixed effects, the authors do not include firms fixed effects here.

Please show me the STATA codes to implement DiD that handles covariates in this way.

(2) In another approach/specification, they mention, "We use assets and capital intensity in (𝑡− 1) period.

What does this mean, using the covariate value in t-1 =2003 period. I mean, what values does the given covariate assume for other yeras in DiD regression.

Here, they use firm fixed effects.

Please help me with the STATA codes that implements DiD using covariates in t-1 period.

Thanks,

[George Ford]

just egen conditional on pre-treatment data by id. You don't want any control that may be affected by the treatment, which is why they do this. The mean, by the way, is 8 not 16. If you want coefficients on those means, use CRE.

[Carlo Lazzaro]

Ridwan:
regarding the second approach you mention, Stata will give you back something similar (lag=1):

. set obs 3
Number of observations (_N) was 0, now 3.

. g id=1

. g year=_n+2025

. g asset=2000*runiform()

. tsset id year

Panel variable: id (strongly balanced)
 Time variable: year, 2026 to 2028
         Delta: 1 unit

. g wanted=L.asset
(1 missing value generated)

. list

     +---------------------------------+
     | id   year      asset     wanted |
     |---------------------------------|
  1. |  1   2026   697.7434          . |
  2. |  1   2027   533.7714   697.7434 |
  3. |  1   2028   273.2926   533.7714 |
     +---------------------------------+

.