tests/testthat/test_nocovariates.R

In DRDID: Doubly Robust Difference-in-Differences Estimators

context("Equivalence between estimation methods with no covariates")

test_that("All estimation methods agree when there are no covariates", {

  # Let us generate some panel data
  #-----------------------------------------------------------------------------
  # DGP 1 used by Sant'Anna and Zhao (2020) (Panel data case)
  # Sample size
  n <- 500
  # pscore index (strength of common support)
  Xsi.ps <- .75
  # Researcher always observes Z
  #-----------------------------------------------------------------------------
  # Mean and Std deviation of Z's without truncation
  mean.z1 <- exp(0.25/2)
  sd.z1 <- sqrt((exp(0.25) - 1) * exp(0.25))
  mean.z2 <- 10
  sd.z2 <- 0.54164
  mean.z3 <- 0.21887
  sd.z3 <-   0.04453
  mean.z4 <- 402
  sd.z4 <-  56.63891
  #-----------------------------------------------------------------------------
  set.seed(1234)
  # Gen covariates
  x1 <- stats::rnorm(n, mean = 0, sd = 1)
  x2 <- stats::rnorm(n, mean = 0, sd = 1)
  x3 <- stats::rnorm(n, mean = 0, sd = 1)
  x4 <- stats::rnorm(n, mean = 0, sd = 1)

  z1 <- exp(x1/2)
  z2 <- x2/(1 + exp(x1)) + 10
  z3 <- (x1 * x3/25 + 0.6)^3
  z4 <- (x1 + x4 + 20)^2

  z1 <- (z1 - mean.z1)/sd.z1
  z2 <- (z2 - mean.z2)/sd.z2
  z3 <- (z3 - mean.z3)/sd.z3
  z4 <- (z4 - mean.z4)/sd.z4

  x <- cbind(x1, x2, x3, x4)
  z <- cbind(z1, z2, z3, z4)
  #-----------------------------------------------------------------------------
  # Gen treatment groups
  # Propensity score
  pi <- stats::plogis(Xsi.ps * (- z1 + 0.5 * z2 - 0.25 * z3 - 0.1 * z4))
  d  <- as.numeric(runif(n) <= pi)
  #-----------------------------------------------------------------------------
  # Generate aux indexes for the potential outcomes
  index.lin <- 210 + 27.4*z1 + 13.7*(z2 + z3 + z4)
  index.unobs.het <- d * (index.lin)
  index.att <- 0

  #This is the key for consistency of outcome regression
  index.trend <- 210 + 27.4*z1 + 13.7*(z2 + z3 + z4)

  #v is the unobserved heterogeneity
  v <- stats::rnorm(n, mean = index.unobs.het, sd = 1)

  #Gen realized outcome at time 0
  y0 <- index.lin + v + stats::rnorm(n)

  # gen outcomes at time 1
  # First let's generate potential outcomes: y_1_potential
  y10 <- index.lin + v + stats::rnorm(n, mean = 0, sd = 1) +#This is the baseline
    index.trend #this is for the trend based on X

  y11 <- index.lin + v + stats::rnorm(n, mean = 0, sd = 1) +#This is the baseline
    index.trend + #this is for the trend based on X
    index.att # This is the treatment effects

  # Gen realized outcome at time 1
  y1 <- d * y11 + (1 - d) * y10
  #-----------------------------------------------------------------------------
  #Gen id
  id <- 1:n
  #-----------------------------------------------------------------------------
  # Put in a "wide" data frame
  dta_wide <- as.data.frame(cbind(id = id, y1 = y1, y0 = y0, d = d,
                                  x1 = z1, x2= z2, x3 = z3, x4 = z4))
  # Make "long" data
  dta_long <- as.data.frame(cbind(id = id, y = y1, d = d, post = T,
                                  x1 = z1, x2= z2, x3 = z3, x4 = z4))
  dta_long <- as.data.frame(rbind(dta_long,cbind(id = id, y = y0, d = d, post = F,
                                                 x1 = z1, x2= z2, x3 = z3, x4 = z4)))
  dta_long <- dta_long[order(dta_long$id),]
  #-----------------------------------------------------------------------------
  #-----------------------------------------------------------------------------
  # Use the different estimators to compute ATT
  #-----------------------------------------------------------------------------
  # Panel Data
  or.did_panel <- ordid(yname="y",
                        tname = "post",
                        idname = "id",
                        dname = "d",
                        xformla= NULL,
                        data = dta_long,
                        panel=T,
                        boot = F)

  std_ipw.did_panel <- ipwdid(yname="y",
                              tname = "post",
                              idname = "id",
                              dname = "d",
                              xformla= NULL,
                              data = dta_long,
                              panel=T,
                              boot = F)

  dr_trad.did_panel <- drdid(yname="y",
                             tname = "post",
                             idname = "id",
                             dname = "d",
                             estMethod = "trad",
                             xformla= NULL,
                             data = dta_long,
                             panel=T,
                             boot = F)

  dr_imp.did_panel <- drdid(yname="y",
                            tname = "post",
                            idname = "id",
                            dname = "d",
                            estMethod = "imp",
                            xformla= NULL,
                            data = dta_long,
                            panel=T,
                            boot = F)

  # Pretending data was repeated cross section
  or.did_rc <- ordid(yname="y",
                     tname = "post",
                     idname = "id",
                     dname = "d",
                     xformla= NULL,
                     data = dta_long,
                     panel=F,
                     boot = F)

  std_ipw.did_rc <- ipwdid(yname="y",
                           tname = "post",
                           idname = "id",
                           dname = "d",
                           xformla= NULL,
                           data = dta_long,
                           panel=F,
                           boot = F)

  dr_trad.did_rc <- drdid(yname="y",
                          tname = "post",
                          idname = "id",
                          dname = "d",
                          estMethod = "trad",
                          xformla= NULL,
                          data = dta_long,
                          panel=F,
                          boot = F)

  dr_imp.did_rc <- drdid(yname="y",
                         tname = "post",
                         idname = "id",
                         dname = "d",
                         estMethod = "imp",
                         xformla= NULL,
                         data = dta_long,
                         panel=F,
                         boot = F)
  #-----------------------------------------------------------------------------
  # Check if all point estimates are equal (both panel and repeated cross section)
  expect_equal(dr_imp.did_panel$ATT, or.did_panel$ATT)
  expect_equal(dr_trad.did_panel$ATT, or.did_panel$ATT)
  expect_equal(std_ipw.did_panel$ATT, or.did_panel$ATT)
  expect_equal(dr_imp.did_rc$ATT, or.did_panel$ATT)
  expect_equal(dr_trad.did_rc$ATT, or.did_panel$ATT)
  expect_equal(std_ipw.did_rc$ATT, or.did_panel$ATT)
  expect_equal(or.did_rc$ATT, or.did_panel$ATT)


  # Check if all standard errors are equal (only panel data)
  expect_equal(dr_imp.did_panel$se, or.did_panel$se)
  expect_equal(dr_trad.did_panel$se, or.did_panel$se)
  expect_equal(std_ipw.did_panel$se, or.did_panel$se)

  # Check if all standard errors are equal (only repeated cross section data)
  expect_equal(dr_imp.did_rc$se, or.did_rc$se)
  expect_equal(dr_trad.did_rc$se, or.did_rc$se)
  expect_equal(std_ipw.did_rc$se, or.did_rc$se)

})