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Uniform Inference for Group-Time Conditional Average Treatment Effects Given a Continuous Covariate

catt_gt_continuous.Rd

`catt_gt_continuous` computes doubly robust estimates and uniform confidence bands for the group-time conditional average treatment effect (CATT) function given a continuous pre-treatment covariate in the staggered difference-in-differences setup of Callaway and Sant'Anna (2021) for balanced panel data. See Imai, Qin, and Yanagi (2025) for more details.

Usage

catt_gt_continuous(
  yname,
  tname,
  idname,
  gname,
  zname,
  xformla,
  data,
  zeval,
  gteval = NULL,
  pretrend = FALSE,
  control_group = "notyettreated",
  anticipation = 0,
  alp = 0.05,
  bstrap = TRUE,
  biters = 1000,
  porder = 2,
  kernel = "gau",
  bwselect = "IMSE1",
  bw = NULL,
  uniformall = TRUE
)

Arguments

yname

The name of the outcome

tname

The name of the time periods

idname

The name of the cross-sectional IDs

gname

The name of the groups. "G = 0" indicates the never treated group.

zname

The name of the scalar continuous covariate for which the group-time conditional average treatment effects are estimated

xformla

A formula for the covariates to include in the model. It should be of the form `~ X1 + X2`. `xformla` should include `zname` as a covariate.

data

The name of data.frame that contains the balanced panel data

zeval

The vector of the evaluation points z

gteval

The vector or matrix of the evaluation points g and t. If it is a vector, the first and second elements indicate g and t, respectively. If it is a matrix, the first and second columns indicate g's and t's, respectively. Default is `NULL` and `gteval` is constructed automatically.

pretrend

Boolean for whether or not to perform the uniform inference for CATT in the pre-treatment periods (i.e., conditional pre-trends). This parameter is only applicable if `gteval = NULL`. Default is `FALSE`.

control_group

Which units to use the control group. Options are "nevertreated" and "notyettreated". Default is "notyettreated".

anticipation

The number of time periods before participating in the treatment where units can anticipate participating in the treatment and therefore it can affect their untreated potential outcomes. Default is 0.

alp

The significance level. Default is 0.05.

bstrap

Boolean for whether or not to perform weighted bootstrapping. Default is `TRUE`. If bstrap is `FALSE`, only the analytical critical value is used.

biters

The number of bootstrap iterations. This parameter is only applicable if bstrap is `TRUE`. Default is 1000.

porder

The polynomial order used for the second- and third-stage estimation. Options are 1 and 2, which correspond to the local linear and quadratic regressions, respectively. Default is 2.

kernel

The kernel function used for the local polynomial regressions. Options are "gau" for the Gaussian kernel and "epa" for the Epanechnikov kernel. Default is "gau".

bwselect

The bandwidth selection method used for the second- and third-stage estimation. Options are "IMSE1", "IMSE2", "US1", and "manual". "IMSE1" and "IMSE2" mean the IMSE-optimal bandwidths for the local linear and quadratic regressions, respectively. "US1" means the rule-of-thumb undersmoothing bandwidth for the local linear regression. "manual" means the manual selection and bw should be specified in this case. Default is "IMSE1", which is recommended for use with `porder = 2`.

bw

The bandwidth used for the second- and third-stage estimation. Default is `NULL` and the bandwidth is chosen automatically. This parameter is only applicable if bwselect is "manual", and should be a scalar or a vector whose length equals to the number of rows of gteval.

uniformall

Boolean for whether or not to perform the uniform inference over (g, t, z). Default is `TRUE`, and the uniform inference over (g, t, z) is performed. If `FALSE`, the uniform inference only over z is performed.

Value

A list that contains the following elements.

Estimate

A data.frame that contains the following elements.
g: The group.
t: The period.
z: The covariate value.
est: The doubly robust estimate of CATT.
se: The standard error.
ci1_lower: The lower bound of the analytical UCB.
ci1_upper: The upper bound of the analytical UCB.
ci2_lower: The lower bound of the bootstrap UCB.
ci2_upper: The upper bound of the bootstrap UCB.
bw: The bandwidth.

Figure1

A list that contains the ggplot elements for the analytical UCB

Figure2

A list that contains the ggplot elements for the bootstrap UCB

References

Callaway, B., & Sant’Anna, P. H. (2021). Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2), 200-230.

Imai, S., Qin, L., & Yanagi, T. (2025). Doubly robust uniform confidence bands for group-time conditional average treatment effects in difference-in-differences. arXiv preprint arXiv:2305.02185.

Examples

if (FALSE) { # \dontrun{

data <- datageneration(
  n = 500,
  tau = 4
)

output <- catt_gt_continuous(
  yname = "Y",
  tname = "period",
  idname = "id",
  gname = "G",
  zname = "Z",
  xformla = ~ Z,
  data = data,
  zeval = seq(-1, 1, by = 0.1),
  gteval = c(2, 2),
  pretrend = FALSE,
  control_group = "notyettreated",
  anticipation = 0,
  alp = 0.05,
  bstrap = TRUE,
  biters = 1000,
  porder = 2,
  kernel = "gau",
  bwselect = "IMSE1",
  bw = NULL,
  uniformall = TRUE
)

} # }