PROBLEM:

I am examining how mobility fell during a COVID lockdown in two types of communities, slums and non-slums. I have data on > 500,000 cell phones on a daily basis for several months. During that period, the government imposed a lockdown. For simplicity, assume that the data start on 1 March 2020 and the lockdown is 1 April - 30 April 2020, and I am only looking in those two months. I want to study if the effect of the lockdown differed across the two communities, but want to measure that in 2 ways.

1/ Was mobility lower in non-slums than slums during the lockdown
2/ Did mobility decline more during lockdown in non-slums measured as a percentage of pre-lockdown mobility

In addition, I want to identify changes in mobility within devices (ie, the phones). Importantly, each device is associated with a time-invariant community type (slum or non-slum).

And to make it even more complicated, the device id variable is a string.

I am using Stata 16.

ATTEMPTED SOLUTION:

Ordinarily, I would do the following:

reghdfe mobility lockdown if slum==0, a(device_id)
eststo nonslum
reghdfe mobility lockdown if slum==1, a(device_id)
eststo slum
suest nonslum slum, vce(cl device)
test _[slum_lockdown] - _[nonslum_lockdown] = 0
test (_[slum_lockdown]/(_[slum_cons])) - (_[nonslum_lockdown]/(_[nonslum_cons])) = 0

But suest doesn't work with reghdfe.
So then I tried reg with factors.

egen cell = group(device_id)
reg mobility lockdown i.cell if slum==0
eststo nonslum
reg mobility lockdown i.cell if slum==1
eststo slum
suest nonslum slum, vce(cl device)

But I have > 500,000 devices. I can't set maxvar high enough.
So, I try using predict instead.

gen lockdown_slum = lockdown * slum
reghdfe mobility lockdown lockdown_slum, a(device_id)
predict nonslum_level if slum==0, xb
predict nonslum_level_se if slum==0, stdp
predict slum_level if slum==1, xb
predict slum_level_se if slum==1, stdp

The question is how to test the difference in predictions to test hypothesis 1. Moreover, how to test hypothesis 2?

Any advice would be much appreciated.