program multisite_regLATE, eclass
version 14.2
syntax varlist(min=4 max=4 numeric) [if] [aweight] [, fs y0 controls(varlist numeric) mediators(varlist numeric)]
preserve
// Display an error and exit the command in cases...
if "`controls'" == "" & "`mediators'" == "" & "`y0'" == "" & "`fs'" == ""{
di as error "Error: No LATEs predictor specified."
exit 200
}
qui{
// Drop variables from memory.
capture drop mediators
capture drop controls
// Store the four variables properly.
local v=1
foreach var of local varlist{
if `v' == 1 {
local outcome `var'
}
else if `v' == 2 {
local treatment `var'
}
else if `v' == 3 {
local instrument `var'
}
else if `v' == 4 {
local site `var'
}
local v = `v' + 1
}
// Count number of explanatory variables
local num_controls : word count `controls'
local num_med : word count `mediators'
local num_var = `num_controls' + `num_med'
local prior = 0
if "`y0'" != ""{
local num_var = `num_var' + 1
local prior = `prior' + 1
}
if "`fs'" != ""{
local num_var = `num_var' + 1
local prior = `prior' + 1
}
// Store names of variables for future display
if "`fs'" != ""{
if "`y0'" != ""{
local varnames = "`fs' `y0' `mediators' `controls'"
}
else{
local varnames = "`fs' `mediators' `controls'"
}
}
else{
if "`y0'" != ""{
local varnames = "`y0' `mediators' `controls'"
}
else{
local varnames = "`mediators' `controls'"
}
}
// Keeping if sample
if `"`if'"' != "" {
keep `if'
}
// In case missing observations
drop if `outcome'==.
// Drop site lack of observations
bys `site': egen multisiteITT_n1s = total(`instrument')
bys `site': gen multisiteITT_ns = _N
gen multisiteITT_n0s = multisiteITT_ns - multisiteITT_n1s
drop if multisiteITT_n1s < 2 | multisiteITT_n0s < 2
drop multisiteITT_ns multisiteITT_n1s multisiteITT_n0s
// Calculate ITT and FS
levelsof `site', local(levels)
local num_site : word count `levels'
* index for site to start
local s = 1
* weight vector
matrix ws = J(`num_site',1,0)
* weight vector
matrix wtildes = J(`num_site',1,0)
* FSs vector
matrix FSs = J(`num_site',1,0)
* ITTs vector
matrix ITTs = J(`num_site',1,0)
* site index vector
matrix site = J(`num_site',1,0)
* loop over sites
local s=1
foreach y of local levels {
sum `treatment' [`weight' `exp'] if `instrument'==1 & `site'==`y'
scalar Dbar1=r(mean)
scalar nt=r(N)
sum `treatment' [`weight' `exp'] if `instrument'==0 & `site'==`y'
scalar Dbar0=r(mean)
sum `outcome' [`weight' `exp'] if `instrument'==1 & `site'==`y'
scalar Ybar1=r(mean)
scalar nt=r(N)
sum `outcome' [`weight' `exp'] if `instrument'==0 & `site'==`y'
scalar Ybar0=r(mean)
scalar nc=r(N)
scalar n_s=nt+nc
// ws fill
matrix ws[`s',1] = n_s/_N
// ws tilde fill
matrix wtildes[`s',1] = n_s/(_N/`num_site')
// FSs fill
matrix FSs[`s',1] = Dbar1- Dbar0
// ITTs fill
matrix ITTs[`s',1] = Ybar1- Ybar0
// site index fill
matrix site[`s',1] = `y'
local s=`s'+1
}
local total_obs = _N
matrix data = ITTs, FSs, ws, site, wtildes
svmat data
rename data1 ITTs
rename data2 FSs
rename data3 ws
rename data4 site
rename data5 wtildes
// Calculate ITT and FS effects
sum ITTs [aw=ws]
scalar ITT= r(mean)
sum FSs [aw=ws]
scalar FS= r(mean)
matrix multiplier = [1 \ -ITT/FS]
// Calculate influence function of LATEs
matrix A = ITTs, FSs
matrix B = A * multiplier
matrix phi_late = (1/FS) * B
// Matrix of store coefficient of beta estimates
matrix betas = J(`num_var',2,0)
// When FS specified
if "`fs'" != ""{
local fsi = 1
* To store the estimates of beta_ITT_med_j
multisite_regITT `outcome' `instrument' `site' [`weight' `exp'], fs(`treatment')
matrix beta = e(coefficients)
matrix betas[`fsi',1]= beta[1,1]
matrix phi_itts_`fsi'= phi_4s
* To store the estimates of beta_FS_med_j
multisite_regITT `treatment' `instrument' `site' [`weight' `exp'], fs(`treatment')
matrix beta = e(coefficients)
matrix betas[`fsi',2]= beta[1,1]
matrix phi_fss_`fsi'= phi_4s
* Compute the influence function on LATE
matrix phi_lates_`fsi'= phi_itts_`fsi'- (ITT/FS)*phi_fss_`fsi'- betas[`fsi',2]*phi_late
svmat phi_lates_`fsi'
* V_beta^LATE: sample variance of phi_lates
matrix accum V_beta_`fsi'= phi_lates_`fsi', deviations noconstant
matrix V_beta_`fsi' = V_beta_`fsi' /((r(N)-1)*r(N))
}
// When y0 specified
if "`y0'" != ""{
if "`fs'" != ""{
local yi = 2
}
else{
local yi = 1
}
* To store the estimates of beta_ITT_y0_j
multisite_regITT `outcome' `instrument' `site' [`weight' `exp'], y0
matrix beta = e(coefficients)
matrix betas[`yi',1]= beta[1,1]
matrix phi_itts_`yi'= phi_4s
* To store the estimates of beta_FS_y0_j
multisite_regITT `treatment' `instrument' `site' [`weight' `exp'], y0
matrix beta = e(coefficients)
matrix betas[`yi',2]= beta[1,1]
matrix phi_fss_`yi'= phi_4s
* Compute the influence function on LATE
matrix phi_lates_`yi'= phi_itts_`yi'- (ITT/FS)*phi_fss_`yi'- betas[`yi',2]*phi_late
svmat phi_lates_`yi'
* V_beta^LATE: sample variance of phi_lates
matrix accum V_beta_`yi'= phi_lates_`yi', deviations noconstant
matrix V_beta_`yi' = V_beta_`yi' /((r(N)-1)*r(N))
}
// Loop over mediators
if "`mediators'" != ""{
* Tracking index of mediator
local i=1
foreach med of local mediators{
local medi = `prior' + `i'
* To store the estimates of beta_ITT_med_i
multisite_regITT `outcome' `instrument' `site' [`weight' `exp'], mediators(`med')
matrix beta = e(coefficients)
matrix betas[`medi',1]= beta[1,1]
matrix phi_itts_`medi'= phi_4s
* To store the estimates of beta_FS_med_i
multisite_regITT `treatment' `instrument' `site' [`weight' `exp'], mediators(`med')
matrix beta = e(coefficients)
matrix betas[`medi',2]= beta[1,1]
matrix phi_fss_`medi'= phi_4s
* Compute the influence function on LATE
matrix phi_lates_`medi'= phi_itts_`medi'- (ITT/FS)*phi_fss_`medi'- betas[`medi',2]*phi_late
svmat phi_lates_`medi'
* V_beta^LATE: sample variance of phi_lates
matrix accum V_beta_`medi'= phi_lates_`medi', deviations noconstant
matrix V_beta_`medi' = V_beta_`medi' /((r(N)-1)*r(N))
* Update tracking index
local i=`i'+1
}
}
// Loop over controls
if "`controls'" != ""{
* Tracking index of mediator
local j=1
foreach con of local controls{
local coni = `prior' +`num_med' + `j'
* To store the estimates of beta_ITT_med_j
multisite_regITT `outcome' `instrument' `site' [`weight' `exp'], controls(`con')
matrix beta = e(coefficients)
matrix betas[`coni',1]= beta[1,1]
matrix phi_itts_`coni'= phi_4s
* To store the estimates of beta_FS_med_j
multisite_regITT `treatment' `instrument' `site' [`weight' `exp'], controls(`con')
matrix beta = e(coefficients)
matrix betas[`coni',2]= beta[1,1]
matrix phi_fss_`coni'= phi_4s
* Compute the influence function on LATE
matrix phi_lates_`coni'= phi_itts_`coni'- (ITT/FS)*phi_fss_`coni'- betas[`coni',2]*phi_late
svmat phi_lates_`coni'
* V_beta^LATE: sample variance of phi_lates
matrix accum V_beta_`coni'= phi_lates_`coni', deviations noconstant
matrix V_beta_`coni' = V_beta_`coni' /((r(N)-1)*r(N))
* Update tracking index
local j=`j'+1
}
}
// Calculate the cov(late, x) term
matrix sigma_LATE_x = betas*multiplier
matrix list sigma_LATE_x
// Display the output table
* Number of Sites and Total Observations
local num_sites = `num_site'
local k = rowsof(sigma_LATE_x)
* Create the Output Matrix
matrix mat_res_XX = J(`k', 6, .)
local rownames `varnames'
}
* Loop over betas to display
forval i = 1/`k' {
matrix mat_res_XX[`i', 1] = sigma_LATE_x[`i', 1] // Estimate
matrix mat_res_XX[`i', 2] = V_beta_`i'[1,1]^(1/2) // Standard Error
matrix mat_res_XX[`i', 3] = sigma_LATE_x[`i', 1] - 1.96 * V_beta_`i'[1,1]^(1/2) // Lower bound
matrix mat_res_XX[`i', 4] = sigma_LATE_x[`i', 1] + 1.96 * V_beta_`i'[1,1]^(1/2) // Upper bound
matrix mat_res_XX[`i', 5] = `num_sites' // Number of Sites
matrix mat_res_XX[`i', 6] = `total_obs' // Total Observations
}
matrix rownames mat_res_XX = `rownames'
matrix colnames mat_res_XX = "Estimate" "SE" "95% LB" "95% UB" "# Sites" "# Units"
* Display the Table
di "{hline 80}"
di _skip(13) "{bf:Sign of Univariate Regression Coefficients of LATEs on Explanatory Variables}"
di "{hline 80}"
noisily matlist mat_res_XX, border(rows)
di as text "The development of this package was funded by the European Union (ERC, REALLYCREDIBLE,GA N°101043899)."
restore
end