How should I test for parallel trend assumption in case of repeated cross-sectional data?

[Jheelum Sarkar]

I have a repeated cross-sectional dataset on time-use which I am using to estimate the impact of a certain shock. My outcome of interest is time spent by individuals (men and women) on particular activity. There are two rounds of data available before the shock happened and one round of data after the shock.

I am curious to know how I can test for parallel trend assumption in this case using Stata.

[Ali Bahrami Sani]

you can use ``honestdid" command. Furter information here.

[Jeff Wooldridge]

As a start, add D*t to the usual DID regression where D is a binary indicator of whether a unit belongs to the eventually treated group. It gives a difference-in-difference-in-differences estimate on D*post, and a simple test.

[Ali Bahrami Sani]

As a start, add D*t to the usual DID regression where D is a binary indicator of whether a unit belongs to the eventually treated group. It gives a difference-in-difference-in-differences estimate on D*post, and a simple test.

Hi Jeff,

I am wondering how we can test the trend after the estimation of DiDiD? Is there any further info. you can provide?

[Jeff Wooldridge]

That can’t be done with T = 3. I know how to do test whether the linear trend is sufficient with at least three treatment periods. But I’m currently on a flight. And, remember, DiDiD already removes heterogeneous linear trends, so it sets a pretty high bar.

[Jheelum Sarkar]

Thank you for your comments! I tried using the following command:
didregress ( paid_labor_time) (shock), group( District ) time( Sub_Round )

Here, the dependent variable ( paid_labor_time) is amount of time spent per day by individuals located in a district-d during a sub round-t (measured in minutes per day);
Independent variable (shock) is the intervention, that is, the occurrence of the shock.
The fixed effects variables are district and sub round. There are total three sub rounds: two sub rounds before the shock happened and one sub round after the shock happened.

Followed this, I have used the following commands to get some pre-trend parallel trend status:

estat ptrends
estat trendplots

The output are enclosed as the images. My concern: while I find Prob > F =0.4563, the graphical diagnostics are not giving me parallel trend type. May I request you to explain why does this happen? I am unable to figure that out.

[Jheelum Sarkar]

Additionally, my another concern is:
when I use the command: reg paid_labor_time time_dummy shock affected, r
the result is statistically significant at 1% level and the coefficient is 88.045
But when I am using the command: didregress ( paid_labor_time) (shock), group( District ) time( Sub_Round )
the result is loosing its statistical significance.

Can anyone explain why is that happening?

[George Ford]

your regression does not have district or sub_round fixed effects as does didregress.

[Jheelum Sarkar]

Thank you for explaining. Does that mean DID is not suitable choice? One thing to note is that my treatment dummy is at district level. Can this problem of fixed effect happen because my treatment is already at district level?

[George Ford]

DID is fine if the conditions are met (2 groups, 2 periods, neither treated in first period, 1 treated in second period, and so forth).

If you want to reproduce what didregress produces, you need a regression with unit and time fixed effects (reghdfe).