randomly assign treatment to control group with treated group's distribution

[Wenhan Yan]

I want to randomly assign a treatment to my control goup, I have state, year, and the treatment variable, in treatment group, only one year will be treated, and thus in my control group, I only want to assign one treatment to one state across entire period.

I have full 50 states, from 2012 to 2020, all my treatment start from 2016 and my treatment group has following distribution:

count	year
1	2016
3	2017
7	2018
9	2019
9	2020

this means I only have 1 state that is treated in 2016 and 3 states in 2017 and so on

Here is my data example with two states in treatment group and two states in control group

* Example generated by -dataex-. For more info, type help dataex
clear
input str20 state float(year cyear dif)
"Alabama"  2018    .  0
"Alabama"  2013    .  0
"Alabama"  2012    .  0
"Alabama"  2014    .  0
"Alabama"  2017    .  0
"Alabama"  2020    .  0
"Alabama"  2019    .  0
"Alabama"  2015    .  0
"Alabama"  2016    .  0
"Alabama"  2021    .  0
"Alaska"   2018    .  0
"Alaska"   2012    .  0
"Alaska"   2020    .  0
"Alaska"   2015    .  0
"Alaska"   2013    .  0
"Alaska"   2019    .  0
"Alaska"   2017    .  0
"Alaska"   2016    .  0
"Alaska"   2021    .  0
"Alaska"   2014    .  0
"Arizona"  2017 2018 -1
"Arizona"  2021 2018  3
"Arizona"  2016 2018 -2
"Arizona"  2012 2018 -6
"Arizona"  2015 2018 -3
"Arizona"  2014 2018 -4
"Arizona"  2019 2018  1
"Arizona"  2013 2018 -5
"Arizona"  2020 2018  2
"Arizona"  2018 2018  0
"Arkansas" 2012 2019 -7
"Arkansas" 2016 2019 -3
"Arkansas" 2020 2019  1
"Arkansas" 2013 2019 -6
"Arkansas" 2019 2019  0
"Arkansas" 2017 2019 -2
"Arkansas" 2015 2019 -4
"Arkansas" 2021 2019  2
"Arkansas" 2014 2019 -5
"Arkansas" 2018 2019 -1
end

cyear means the year state got the treatment, dif means the how far away from the treatment year. I tried following but when I try to random assign, I fail to let only one state get the treatment, in the end, my state can get more than one treatment:

gen ran=uniform()
gen treatment =. 
sort year  ran 
by year: replace treatment =(_n <= 1) if (year == 2016) & t ==.
by year: replace treatment =(_n <= 3) if (year == 2017) & t ==. 
by year: replace treatment =(_n <= 7) if (year == 2018) & t ==.
by year: replace treatment =(_n <= 9) if (year == 2019) & t ==.
by year: replace treatment =(_n <= 5) if (year == 2020) & t ==.

[George Ford]

This may help get things rolling

egen sid = group(state)
xtset sid year
g cyear_pseudo = cyear
g dif_pseudo = dif
egen controlx = sum(dif) , by(sid)
g control = controlx==0
g u = runiform()
bys sid: replace u = u[1]
summ u if control
replace cyear_pseudo = 2016 if control & u == `r(min)'
replace dif_pseudo = year - cyear_pseudo

[Wenhan Yan]

This may help get things rolling

egen sid = group(state)
xtset sid year
g cyear_pseudo = cyear
g dif_pseudo = dif
egen controlx = sum(dif) , by(sid)
g control = controlx==0
g u = runiform()
bys sid: replace u = u[1]
summ u if control
replace cyear_pseudo = 2016 if control & u == `r(min)'
replace dif_pseudo = year - cyear_pseudo

Hello George,

Thanks for the reply, I think the code only work for if I only want to have 1 random assignment right?

I have some thought these day and think following can work, but I don't know whether I will redraw for those already been drawed:

preserve 
tempfile control 
drop if treat == 1 
drop treat 
gen random = 1 
save `control', replace 

tempfile 2015
sample 5, count 
gen treat = 1 
gen t = 2015
save `2015', replace 
restore 

preserve 
use `control', clear
tempfile 2016 
sample 2, count 
gen treat = 1 
gen t = 2016
save `2016', replace 
restore 


preserve

clear

tempfile allyear

append using "`2015'" "`2016'"

duplicates drop id year, force

save `allyear', replace

restore 

*original dataset
use new_area, clear 
drop treat 
gen random = 0 
gen start = 0

append using `allyear'

by id year, sort: gen test =_N

*drop original and replace the new one 

drop if test == 2 & random == 0


*get the treatment year
by id, sort: egen t2=max(t)
by id, sort: egen treat2=max(treat)
*treatment period 
gen did0=1 if year >= t2 & treat2== 1 
replace did0=0 if did0 ==.

[George Ford]

you said "I only want to assign one treatment to one state across entire period". perhaps I misunderstood.

Do you want only one state to get a treatment in each round of a simulation, with all the others being a control?

[Wenhan Yan]

you said "I only want to assign one treatment to one state across entire period". perhaps I misunderstood.

Do you want only one state to get a treatment in each round of a simulation, with all the others being a control?

For my data, I already have Y for control and treatment group, but for control group I don't have treatment date, and I want to random assign one treatment to the control group

But since I need to following the treatment group distribution, I would randomly select some state to be treated in each year.

For example, in treament group, there are 1 state has been treated in 2016 and 3 states have been treated in 2017. And suppose in control group, Alabama is randomly selected as the one state treated in 2016. So in the following 2017, when I randomly draw 3 states in control group, I don't want Alabama in the set of control state to be drawed

[George Ford]

g control = mi(cyear)
forv i = 1/10 {
    capture drop fyear fdif u ru rru
    g fyear = cyear
    g fdif = dif
    g u = runiform() if year==2012 & control
    egen ru = rank(u)
    egen rru = min(ru), by(state)
    replace rru = . if rru>4
    replace fyear = 2016*(rru==1) + 2017*(rru>1) if !mi(rru)
    replace fdif = year - fyear if control
    ** dostuff
}

[Wenhan Yan]

g control = mi(cyear)
forv i = 1/10 {
capture drop fyear fdif u ru rru
g fyear = cyear
g fdif = dif
g u = runiform() if year==2012 & control
egen ru = rank(u)
egen rru = min(ru), by(state)
replace rru = . if rru>4
replace fyear = 2016*(rru==1) + 2017*(rru>1) if !mi(rru)
replace fdif = year - fyear if control
** dostuff
}

Thank you for the help, I think I figure it out by dropping the assigned states each year and then append them back:

set seed  1234

cap drop ran treatment



tempfile control
drop if t != .
gen ran=uniform()
gen treatment = .
save `control', replace 



use `control' ,clear 
tempfile 2016
sort year  ran 
by year: replace treatment =(_n <= 1) if (year == 2016) 
egen c16 = sum(treatment), by(state)
replace c16 = 2016 if c16 == 1 
replace cyear = c16 if c16 == 2016

save `2016', replace 

use `2016', clear 
tempfile 2017
drop if c16 == 2016 
sort year  ran 
by year: replace treatment =(_n <= 3) if (year == 2017) 
egen c17 = sum(treatment), by(state)
replace c17 = 2017 if c17 == 1 
replace cyear = c17 if c17 == 2017
save `2017', replace