Implementation of extended two-way fixed effects with a bridge penalty. Estimates overall ATT as well as CATT (cohort average treatment effects on the treated units).
betwfe(
pdata,
time_var,
unit_var,
treatment,
response,
covs = c(),
indep_counts = NA,
sig_eps_sq = NA,
sig_eps_c_sq = NA,
lambda.max = NA,
lambda.min = NA,
nlambda = 100,
q = 0.5,
verbose = FALSE,
alpha = 0.05,
add_ridge = FALSE
)A named list with the following elements:
The estimated overall average treatment effect for a randomly selected treated unit.
If q < 1, a standard error for the ATT. If
indep_counts was provided, this standard error is asymptotically exact; if
not, it is asymptotically conservative. If q >= 1, this will be NA.
A named vector containing the estimated average treatment effects for each cohort.
If q < 1, a named vector
containing the (asymptotically exact, non-conservative) standard errors for
the estimated average treatment effects within each cohort.
A vector of the estimated probabilities of being in each
cohort conditional on being treated, which was used in calculating att_hat.
If indep_counts was provided, cohort_probs was calculated from that;
otherwise, it was calculated from the counts of units in each treated
cohort in pdata.
A dataframe displaying the cohort names,
average treatment effects, standard errors, and 1 - alpha confidence
interval bounds.
The full vector of estimated coefficients.
The indices of beta_hat corresponding to
the treatment effects for each cohort at each time.
The indices of beta_hat corresponding to the
interactions between the treatment effects for each cohort at each time and
the covariates.
Either the provided sig_eps_sq or
the estimated one, if a value wasn't provided.
Either
the provided sig_eps_c_sq or the estimated one, if a value wasn't
provided.
Either the provided lambda.max or the one
that was used, if a value wasn't provided. (This is returned to help with
getting a reasonable range of lambda values for grid search.)
The size of the selected model corresponding
lambda.max (for q <= 1, this will be the smallest model size). As
mentioned above, for q <= 1 ideally this value is close to 0.
Either the provided lambda.min or the one
that was used, if a value wasn't provided.
The
size of the selected model corresponding to lambda.min (for q <= 1, this
will be the largest model size). As mentioned above, for q <= 1 ideally
this value is close to p.
The value of lambda chosen
by BIC. If this value is close to lambda.min or lambda.max, that could
suggest that the range of lambda values should be expanded.
The size of the model that was selected. If
this value is close to lambda.max_model_size or lambda.min_model_size,
That could suggest that the range of lambda values should be expanded.
The design matrix created containing all interactions, time and cohort dummies, etc.
The vector of
responses, containing nrow(X_ints) entries.
The design matrix after applying the change in coordinates to fit the model and also multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.
The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.
The final number of units that were in the data set used for estimation (after any units may have been removed because they were treated in the first time period).
The number of time periods in the final data set.
The final number of treated cohorts that appear in the final data set.
The final number of covariates that appear in the final data set (after any covariates may have been removed because they contained missing values or all contained the same value for every unit).
The final number of columns in the full set of covariates used to estimate the model.
Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.
Character; the name of a single column containing a variable for the time period. This column is expected to contain integer values (for example, years). Recommended encodings for dates include format YYYY, YYYYMM, or YYYYMMDD, whichever is appropriate for your data.
Character; the name of a single column containing a variable for each unit. This column is expected to contain character values (i.e. the "name" of each unit).
Character; the name of a single column containing a variable
for the treatment dummy indicator. This column is expected to contain integer
values, and in particular, should equal 0 if the unit was untreated at that
time and 1 otherwise. Treatment should be an absorbing state; that is, if
unit i is treated at time t, then it must also be treated at all times
t + 1, ..., T. Any units treated in the first time period will be removed
automatically. Please make sure yourself that at least some units remain
untreated at the final time period ("never-treated units").
Character; the name of a single column containing the response for each unit at each time. The response must be an integer or numeric value.
(Optional.) Character; a vector containing the names of the columns for covariates. All of these columns are expected to contain integer, numeric, or factor values, and any categorical values will be automatically encoded as binary indicators. If no covariates are provided, the treatment effect estimation will proceed, but it will only be valid under unconditional versions of the parallel trends and no anticipation assumptions. Default is c().
(Optional.) Integer; a vector. If you have a sufficiently
large number of units, you can optionally randomly split your data set in
half (with N units in each data set). The data for half of the units should
go in the pdata argument provided above. For the other N units, simply
provide the counts for how many units appear in the untreated cohort plus
each of the other R cohorts in this argument indep_counts. The benefit
of doing this is that the standard error for the average treatment effect
will be (asymptotically) exact instead of conservative. The length of
indep_counts must equal 1 plus the number of treated cohorts in pdata.
All entries of indep_counts must be strictly positive (if you are concerned
that this might not work out, maybe your data set is on the small side and
it's best to just leave your full data set in pdata). The sum of all the
counts in indep_counts must match the total number of units in pdata.
Default is NA (in which case conservative standard errors will be calculated
if q < 1.)
(Optional.) Numeric; the variance of the row-level IID noise assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated using the estimator from Pesaran (2015, Section 26.5.1) with ridge regression. Default is NA.
(Optional.) Numeric; the variance of the unit-level IID noise (random effects) assumed to apply to each observation. See Section 2 of Faletto (2025) for details. It is best to provide this variance if it is known (for example, if you are using simulated data). If this variance is unknown, this argument can be omitted, and the variance will be estimated using the estimator from Pesaran (2015, Section 26.5.1) with ridge regression. Default is NA.
(Optional.) Numeric. A penalty parameter lambda will be
selected over a grid search by BIC in order to select a single model. The
largest lambda in the grid will be lambda.max. If no lambda.max is
provided, one will be selected automatically. When q <= 1, the model
will be sparse, and ideally all of the following are true at once: the
smallest model (the one corresponding to lambda.max) selects close to 0
features, the largest model (the one corresponding to lambda.min) selects
close to p features, nlambda is large enough so that models are
considered at every feasible model size, and nlambda is small enough so
that the computation doesn't become infeasible. You may
want to manually tweak lambda.max, lambda.min, and nlambda to try
to achieve these goals, particularly if the selected model size is very
close to the model corresponding to lambda.max or lambda.min, which could
indicate that the range of lambda values was too narrow or coarse. You can
use the function outputs lambda.max_model_size, lambda.min_model_size, and
lambda_star_model_size to try to assess this. Default is NA.
(Optional.) Numeric. The smallest lambda penalty
parameter that will be considered. See the description of lambda.max for
details. Default is NA.
(Optional.) Integer. The total number of lambda penalty
parameters that will be considered. See the description of lambda.max for
details. Default is 100.
(Optional.) Numeric; determines what L_q penalty is used for the
regularization. q = 1 is the lasso, and for 0 < q < 1, it is
possible to get standard errors and confidence intervals. q = 2 is ridge
regression. See Faletto (2025) for details. Default is 0.5.
Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.
Numeric; function will calculate (1 - alpha) confidence intervals
for the cohort average treatment effects that will be returned in catt_df.
(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.
Gregory Faletto
Faletto, G (2025). Fused Extended Two-Way Fixed Effects for Difference-in-Differences with Staggered Adoptions. arXiv preprint arXiv:2312.05985. https://arxiv.org/abs/2312.05985. Pesaran, M. H. . Time Series and Panel Data Econometrics. Number 9780198759980 in OUP Catalogue. Oxford University Press, 2015. URL https://ideas.repec.org/b/oxp/obooks/9780198759980.html.
set.seed(23451)
library(bacondecomp)
data(divorce)
# sig_eps_sq and sig_eps_c_sq, calculated in a separate run of `fetwfe(),
# are provided to speed up the computation of the example
res <- betwfe(
pdata = divorce[divorce$sex == 2, ],
time_var = "year",
unit_var = "st",
treatment = "changed",
covs = c("murderrate", "lnpersinc", "afdcrolls"),
response = "suiciderate_elast_jag",
sig_eps_sq = 0.1025361,
sig_eps_c_sq = 4.227651e-35,
verbose = TRUE)
# Average treatment effect on the treated units (in percentage point
# units)
100 * res$att_hat
# Conservative 95% confidence interval for ATT (in percentage point units)
low_att <- 100 * (res$att_hat - qnorm(1 - 0.05 / 2) * res$att_se)
high_att <- 100 * (res$att_hat + qnorm(1 - 0.05 / 2) * res$att_se)
c(low_att, high_att)
# Cohort average treatment effects and confidence intervals (in percentage
# point units)
catt_df_pct <- res$catt_df
catt_df_pct[["Estimated TE"]] <- 100 * catt_df_pct[["Estimated TE"]]
catt_df_pct[["SE"]] <- 100 * catt_df_pct[["SE"]]
catt_df_pct[["ConfIntLow"]] <- 100 * catt_df_pct[["ConfIntLow"]]
catt_df_pct[["ConfIntHigh"]] <- 100 * catt_df_pct[["ConfIntHigh"]]
catt_df_pct
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