Parallel trends assumption - pooled cross sectional data

[Guest]

I am analyzing the impact of time spent on tablets (>5 hours per day vs. <5 hours per day) on parents' perceptions of their children's productivity. parents' perception of their children's productivity is a binary outcome (improved, decreased). There was a policy change in 2017 aimed at encouraging students to use tablets more for their studies per day.

I have cross-sectional data from 2016 (pre-policy) and 2019 (post-policy).
Here's the main finding so far:

• Over time, time spent on tablets increased among students.
• Parents of children using tablets for >5 hours per day reported that their children's productivity decreased over time.
• Parents of children using tablets for <5 hours per day also reported that their children's productivity decreased over time.
• However, in both 2016 and 2019, a higher percentage of parents whose children used tablets for <5 hours per day reported improvements in productivity compared to parents whose children used tablets for >5 hours per day.

I want to use a Difference-in-Differences (DiD) approach to estimate the impact of tablets on parents' perceptions of their children's productivity. Since I only have two time periods (2016 and 2019), I am also unsure about how to justify the parallel trends assumption.

gen treatment = (tablet_time_spent== ">5_hours")
gen post_policy= (year == 2019)

collapse (mean) productivity_perception, by(year treatment)
twoway (line productivity_perception year if treatment == 1, lcolor(blue) lwidth(medium) lpattern(solid) legend(label(1 "Tablet Time >5"))) ///
(line productivity_perception year if treatment == 0, lcolor(red) lwidth(medium) lpattern(dash) legend(label(2 "Tablet Time <5"))), ///
title("Trends in Parents' Perception of Children's Productivity by Tablet Time") ///
xlabel(2016 2019))



My data looks like this (ofc these arent true values)

Tablet_time_spent Parents' Perception of Children's Productivity year
>5 increased 2016
>5 decreased 2016
<5 decreased 2016
>5 increased 2016
<5 decreased 2016
.
.
.
<5 increased 2019
<5 increased 2019
<5 increased 2019
>5 decreased

I would really appreciate any help. Thank you.

(my variables are a bit different from the ones I have mentioned but they have the same type/characteristics and the idea is pretty much the same)





I was looking at another thread and didreg was recommended:

didregress (parents' Perception of Children's Productivity) (treatment), group(region) time(year)

but I am getting this error
invalid group specification
None of the groups defined by region is a control.

[Jared Greathouse]

You need panel data. Cross sectional data=no Difference-in-Differences

Edit: and who is the control group here?

[Maxence Morlet]

Perhaps OP meant repeated cross-sectional data?

@jared: I would have to give this more thought, but what if you have a cross-section, and a variable indicating date of birth, defining time. Do you think a DiD would be feasible there?

[Jared Greathouse]

I sort of think it would be backwards, no? Maybe if this is a cohort study, maybe people in Cohort 1997 (me) were exposed to a treatment in 2011, but people born in 1998 (someone a year younger than me) were not.

So here, the cohort defines the group. And, assuming we collect data on everyone in each cohort (say) from their date of birth to 2014, then yeah, assuming the other cohort follows common trends to mine, I think DiD is possible here.

I think you're right about the repeated cross section point, though, which is essentially what you an I just discussed.


However this doesn't speak to OPs issues. Guest says that Stata says that no unit is defined as a control. what this suggests, but I cannot tell because no data is given, that all regions did the policy, but some people in those regions were less exposed than others?

I guess the main thing I'm confused about is the policy. Guest writes

There was a policy change in 2017 aimed at encouraging students to use tablets more for their studies per day.

okay fine. But why is treatment coded like

gen treatment = (tablet_time_spent== ">5_hours")

Treatment for DiD is (usually) defined by time, not the quasi-continuous time variable, as this wound suggest a regression discontinuity (or, a difference-in-discontinuities approach).

The bottom line is, I think for us to comment better, we need to firstly see a data example, but we also need precise definitions of who was exposed to the policy and when.

[Guest]

Sorry, I meant repeated cross-sections. I was thinking of adding students who spent more than 5 hours per day on tablets in the treatment group, while those who spent less than 5 hours in the control group. Over time, more students across the country began spending more than 5 hrs on tablets for studies (and that could be due to a policy aimed at encouraging this behavior). I want to investigate how this increased usage is influencing perceptions, specifically whether spending more time on tablets is changing a particular perception. I think changing the variable names might be causing confusion though they are very similar. Thank you so much!

[Jared Greathouse]

I was thinking of adding students who spent more than 5 hours per day on tablets in the treatment group, while those who spent less than 5 hours in the control group.

Why?

[Guest]

I am sorry for the late response. I figured that I wasn't on the track. Thanks