staggered {staggered}

Calculate the efficient adjusted estimator in staggered rollout designs

Description

This functions calculates the efficient estimator for staggered rollout designs proposed by Roth and Sant'Anna.

Usage

staggered(
  df,
  i = "i",
  t = "t",
  g = "g",
  y = "y",
  estimand = NULL,
  A_theta_list = NULL,
  A_0_list = NULL,
  eventTime = 0,
  beta = NULL,
  use_DiD_A0 = ifelse(is.null(A_0_list), TRUE, FALSE),
  return_full_vcv = FALSE,
  return_matrix_list = FALSE,
  use_last_treated_only = FALSE,
  compute_fisher = FALSE,
  num_fisher_permutations = 500,
  skip_data_check = FALSE
)

Arguments

df

A data frame containing panel data with the variables y (an outcome), i (an individual identifier), t (the period in which the outcome is observe), g (the period in which i is first treated, with Inf denoting never treated)

i

The name of column containing the individual (cross-sectional unit) identifier. Default is "i".

t

The name of the column containing the time periods. Default is "t".

g

The name of the column containing the first period when a particular observation is treated, with Inf denoting never treated. Default is "g".

y

The name of the column containing the outcome variable. Default is "y".

estimand

The estimand to be calculated: "simple" averages all treated (t,g) combinations with weights proportional to N_g; "cohort" averages the ATEs for each cohort g, and then takes an N_g-weighted average across g; "calendar" averages ATEs for each time period, weighted by N_g for treated units, and then averages across time. "eventstudy" returns the average effect at the ”event-time” given in the parameter EventTime. The parameter can be left blank if a custom parameter is provided in A_theta_list. The argument is not case-sensitive.

A_theta_list

This parameter allows for specifying a custom estimand, and should be left as NULL if estimand is specified. It is a list of matrices A_theta_g so that the parameter of interest is sum_g A_theta_g Ybar_g, where Ybar_g = 1/N sum_i Y_i(g)

A_0_list

This parameter allow for specifying the matrices used to construct the Xhat vector of pre-treatment differences. If left NULL, the default is to use the scalar set of controls used in Callaway and Sant'Anna. If use_DiD_A0 = FALSE, then it uses the full vector possible comparisons of (g,g') in periods t<g,g'.

eventTime

If using estimand = "eventstudy", specify what eventTime you want the event-study parameter for. The default is 0, the period in which treatment occurs. If a vector is provided, estimates are returned for all the event-times in the vector.

beta

A coefficient to use for covariate adjustment. If not specified, the plug-in optimal coefficient is used. beta =0 corresponds with the simple difference-in-means. beta = 1 corresponds with the Callaway and Sant'Anna estimator when using the default value of use_DiD_A0 = TRUE.

use_DiD_A0

If this parameter is true, then Xhat corresponds with the scalar used by Callaway and Sant'Anna, so the Callaway and Sant'Anna estimator corresponds with beta=1. If it is false, the Xhat is a vector with all possible comparisons of pairs of cohorts before either is treated. The latter option should only be used when the number of possible comparisons is small relative to sample size.

return_full_vcv

If this is true and estimand = "eventstudy", then the function returns a list containing the full variance-covariance matrix for the event-plot estimates in addition to the usual dataframe with the estimates

return_matrix_list

If true, the function returns a list of the A_0_list and A_theta_list matrices along with betastar. This is used for internal recursive calls to calculate the variance-covariance matrix, and will generally not be needed by the end-user. Default is False.

use_last_treated_only

If true, then A_0_list and A_theta_list are created to only make comparisons with the last treated cohorts (as suggested by Sun and Abraham), rather than using not-yet-treated units as comparisons. If set to TRUE (and use_DiD_A0 = TRUE), then beta=1 corresponds with the Sun and Abraham estimator.

compute_fisher

If true, computes a Fisher Randomization Test using the studentized estimator.

num_fisher_permutations

The number of permutations to use in the Fisher Randomization Test (if compute_fisher = TRUE). Default is 500.

skip_data_check

If true, skips checks that the data is balanced and contains the colums i,t,g,y. Used in internal recursive calls to increase speed, but not recommended for end-user.

Value

resultsDF A data.frame containing: estimate (the point estimate), se (the standard error), and se_neyman (the Neyman standard error). If a vector-valued eventTime is provided, the data.frame contains multiple rows for each eventTime and an eventTime column. If return_full_vcv = TRUE and estimand = "eventstudy", the function returns a list containing resultsDF and the full variance covariance for the event-study estimates (vcv) as well as the Neyman version of the covariance matrix (vcv_neyman). (If return_matrix_list = TRUE, it likewise returns a list containing lists of matrices used in the vcv calculation.)

References

Roth, Jonatahan, and Sant'Anna, Pedro H. C. (2021), 'Efficient Estimation for Staggered Rollout Designs', arXiv: 2102.01291, https://arxiv.org/abs/2102.01291.

Examples

# Load some libraries
library(dplyr)
library(purrr)
library(MASS)
set.seed(1234)
# load the officer data and subset it
df <- pj_officer_level_balanced
group_random <- sample(unique(df$assigned), 3)
df <- df[df$assigned %in% group_random,]
# Calculate efficient estimator for the simple weighted average
staggered(df = df,
  i = "uid",
  t = "period",
  g = "first_trained",
  y = "complaints",
  estimand = "simple")
# Calculate efficient estimator for the cohort weighted average
staggered(df = df,
  i = "uid",
  t = "period",
  g = "first_trained",
  y = "complaints",
  estimand = "cohort")
# Calculate efficient estimator for the calendar weighted average
staggered(df = df,
  i = "uid",
  t = "period",
  g = "first_trained",
  y = "complaints",
  estimand = "calendar")
# Calculate event-study coefficients for the first 24 months
# (month 0 is instantaneous effect)
eventPlotResults <- staggered(df = df,
  i = "uid",
  t = "period",
  g = "first_trained",
  y = "complaints",
  estimand = "eventstudy",
  eventTime = 0:23)
eventPlotResults %>% head()