Getting Started with the didhetero Package

Introduction

The didhetero package provides tools to construct doubly robust uniform confidence bands (UCB) for the group-time conditional average treatment effect (CATT) function given a pre-treatment covariate of interest in the staggered difference-in-differences (DiD) setup of Callaway and Sant’Anna (2021). The uniform inference procedures are developed by Imai, Qin, and Yanagi (2023) “Doubly Robust Uniform Confidence Bands for Group-Time Conditional Average Treatment Effects in Difference-in-Differences”.

Installation

Get the package from GitHub:

# install.packages("devtools") # if needed
devtools::install_github("tkhdyanagi/didhetero", build_vignettes = TRUE)

Package Function

The didhetero package provides the following functions:

catt_gt_continuous(): Doubly robust UCB for the CATT function given a continuous covariate.
catt_gt_discrete(): Doubly robust UCB for the CATT function given a discrete covariate.

Arguments

All package functions have the following 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 automatically constructed.
control_group: Which units to use the control group. Options are “nevertreated” and “notyettreated”. Default is “nevertreated”.
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.
biters: The number of bootstrap iterations to use. Default is 1000, which is only applicable if bstrap is TRUE.
uniformall: Boolean for whether or not to perform the uniform inference over \((g, t, z)\). Default is FALSE, and the uniform inference only over \(z\) is performed.
cores: The number of cores to use for parallel processing. The number of available cores can be checked with parallel::detectCores(). Default is 1.

The catt_gt_continuous() function has the following additional arguments:

bstrap: Boolean for whether or not to perform the multiplier bootstrap inference. Default is TRUE. If bstrap is FALSE, only the analytic critical value is used.
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.
bw: The scalar bandwidth used for the second- and third-stage estimation. Default is NULL, and the bandwidth is automatically selected.

Returns

The catt_gt_continuous() function returns a list that contains the following elements:

Estimate: A data.frame that contains the following elements:
- g: A group.
- t: A period.
- z: An evaluation point.
- est: A doubly robust estimate for CATT.
- se: A standard error.
- ci1_lower: The lower bound of the UCB based on the analytical method.
- ci1_upper: The upper bound of the UCB based on the analytical method.
- ci2_lower: The lower bound of the UCB via multiplier bootstrapping.
- ci2_upper: The upper bound of the UCB via multiplier bootstrapping.
- bw: The bandwidth.
Figure1: A list that contains the ggplot elements for the analytic UCBs.
Figure2: A list that contains the ggplot elements for the UCBs via multiplier bootstrapping.

The catt_gt_discrete() function returns 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.
- ci_lower: The lower bound of the UCB via multiplier bootstrapping.
- ci_upper: The upper bound of the UCB via multiplier bootstrapping.
Figure: A list that contains the ggplot elements for the UCB via multiplier bootstrapping.

Example: Continuous Covariate

We begin by generating artificial data using the datageneration() function.

# Load the package
library(didhetero)

# Generate artificial data
# n: The number of cross-sectional units
# tau: The length of time series
# continuous: Generate a continuous (resp. discrete) covariate if it is TRUE (resp. FALSE).
set.seed(1)
data1 <- datageneration(n = 1000, tau = 4, continuous = TRUE)

We can see the variables’ names in the dataset with:

head(data1)
#>   id period          Y G          Z
#> 1  1      1  3.4181061 4 -0.6264538
#> 2  1      2  7.1550896 4 -0.6264538
#> 3  1      3  6.8578708 4 -0.6264538
#> 4  1      4  8.0158122 4 -0.6264538
#> 5  2      1 -0.4197104 0  0.1836433
#> 6  2      2  0.7126766 0  0.1836433

We run the catt_gt_continuous() function to construct the doubly robust UCB for the CATT function given a continuous covariate \(Z\):

UCB1 <- catt_gt_continuous(yname = "Y",
                           tname = "period",
                           idname = "id",
                           gname = "G",
                           zname = "Z",
                           xformla = ~ Z,
                           data = data1,
                           zeval = seq(-1, 1, by = 0.1),
                           gteval = c(2, 2),
                           control_group = "nevertreated",
                           anticipation = 0,
                           alp = 0.05,
                           bstrap = TRUE,
                           biters = 1000,
                           porder = 2,
                           kernel = "gau",
                           bw = NULL,
                           uniformall = FALSE,
                           cores = 1)

The estimation and uniform inference results are given by:

head(UCB1$Estimate)
#>   g t    z       est        se   ci1_lower ci1_upper   ci2_lower ci2_upper
#> 1 2 2 -1.0 0.2607043 0.2347429 -0.30241607 0.8238246 -0.39944739 0.9208559
#> 2 2 2 -0.9 0.3715774 0.2268069 -0.17250543 0.9156603 -0.26625640 1.0094113
#> 3 2 2 -0.8 0.4965231 0.2197910 -0.03072936 1.0237755 -0.12158028 1.1146264
#> 4 2 2 -0.7 0.6233448 0.2141259  0.10968214 1.1370075  0.02117287 1.2255168
#> 5 2 2 -0.6 0.7411066 0.2095935  0.23831666 1.2438965  0.15168088 1.3305323
#> 6 2 2 -0.5 0.8423519 0.2060495  0.34806367 1.3366401  0.26289281 1.4218110
#>          bw
#> 1 0.4939719
#> 2 0.4939719
#> 3 0.4939719
#> 4 0.4939719
#> 5 0.4939719
#> 6 0.4939719

The figure of the resulting UCB computed with the analytic critical value is given by:

UCB1$Figure1
#> $g2_t2

The figure of the resulting UCB via multiplier bootstrapping is given by:

UCB1$Figure2
#> $g2_t2

Example: Discrete Covariate

Data generation:

set.seed(1)
data2 <- datageneration(n = 1000, tau = 4, continuous = FALSE)

Estimation and uniform inference:

UCB2 <- catt_gt_discrete(yname = "Y",
                         tname = "period",
                         idname = "id",
                         gname = "G",
                         zname = "Z",
                         xformla = ~ Z,
                         data = data2,
                         zeval = c(-1, 0, 1),
                         gteval = c(2, 2),
                         control_group = "nevertreated",
                         anticipation = 0,
                         alp = 0.05,
                         biters = 1000,
                         uniformall = FALSE,
                         cores = 1)

Results:

head(UCB2$Estimate)
#>   g t  z       est        se   ci_lower  ci_upper
#> 1 2 2 -1 0.2895654 0.1844509 -0.1664400 0.7455708
#> 2 2 2  0 1.1131381 0.2517058  0.4908630 1.7354132
#> 3 2 2  1 1.6688524 0.2803515  0.9757582 2.3619466

UCB2$Figure
#> $g2_t2

References

Callaway, B., & Sant’Anna, P. H. (2021). Difference-in-differences with multiple time periods. Journal of Econometrics, 225(2), 200-230. Link
Imai, S., Qin, L., & Yanagi, T. (2023). Doubly Robust Uniform Confidence Bands for Group-Time Conditional Average Treatment Effects in Difference-in-Differences. arXiv preprint arXiv:2305.02185. Link

Shunsuke Imai (imai.shunsuke.57n@st.kyoto-u.ac.jp), Lei Qin (dannychin524@gmail.com), Takahide Yanagi (yanagi@econ.kyoto-u.ac.jp)