Title: Fused Extended Two-Way Fixed Effects
Version: 1.5.0
Maintainer: Gregory Faletto <gfaletto@gmail.com>
Depends: R (≥ 4.1.0)
Description: Calculates the fused extended two-way fixed effects (FETWFE) estimator for unbiased and efficient estimation of difference-in-differences in panel data with staggered treatment adoption. This estimator eliminates bias inherent in conventional two-way fixed effects estimators, while also employing a novel bridge regression regularization approach to improve efficiency and yield valid standard errors. Also implements extended TWFE (etwfe) and bridge-penalized ETWFE (betwfe). Provides S3 classes for streamlined workflow and supports flexible tuning (ridge and rank-condition guarantees), automatic covariate centering/scaling, and detailed overall and cohort-specific effect estimates with valid standard errors. Includes simulation and formatting utilities, extensive diagnostic tools, vignettes, and examples. See Faletto (2025) (<doi:10.48550/arXiv.2312.05985>).
URL: https://github.com/gregfaletto/fetwfePackage
BugReports: https://github.com/gregfaletto/fetwfePackage/issues
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.3.2
Imports: expm, glmnet, grpreg, Matrix (≥ 1.6-0)
Suggests: bacondecomp, knitr, rmarkdown, dplyr, did
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2025-07-02 06:27:29 UTC; gregfaletto
Author: Gregory Faletto ORCID iD [aut, cre]
Repository: CRAN
Date/Publication: 2025-07-02 16:20:12 UTC

Convert data formatted for att_gt() to a dataframe suitable for fetwfe() / etwfe()

Description

attgtToFetwfeDf() reshapes and renames a panel dataset that is already formatted for did::att_gt() (Callaway and Sant'Anna 2021) so that it can be passed directly to fetwfe()oretwfe()⁠from the⁠fetwfe' package. In particular, it

Usage

attgtToFetwfeDf(
  data,
  yname,
  tname,
  idname,
  gname,
  covars = character(0),
  drop_first_period_treated = TRUE,
  out_names = list(time = "time_var", unit = "unit_var", treatment = "treatment",
    response = "response")
)

Arguments

data

A data.frame in long format containing at least the four columns used by did::att_gt(): outcome yname, time tname, unit id idname, and the first‑treatment period gname (which is 0 for the never‑treated group).

yname

Character scalar. Name of the outcome column.

tname

Character scalar. Name of the time variable (numeric or integer). This becomes time in the returned dataframe.

idname

Character scalar. Name of the unit identifier. Converted to character and returned as unit_var.

gname

Character scalar. Name of the group variable holding the first period of treatment. Values must be 0 for never‑treated, or a positive integer representing the first treated period.

covars

Character vector of additional covariate column names to carry through (default character(0)). These columns are left untouched and appear after the required columns in the returned dataframe.

drop_first_period_treated

Logical. If TRUE (default), units that are already treated in the first sample period are removed before creating the treatment dummy. fetwfe() would do this internally, but dropping them here keeps the returned dataframe cleaner.

out_names

A named list giving the column names to use in the resulting dataframe. Defaults are list(time = "time", unit = "unit", treatment = "treatment", response = "y"). Override if you prefer different names (for instance, to keep the original yname). The vector must contain exactly these four names.

Value

A data.frame with columns time, unit, treatment, y, and any covariates requested in covars, ready to be fed to fetwfe()/etwfe(). All required columns are of the correct type: time is integer, unit is character, treatment is integer 0/1, and y is numeric.

References

Callaway, Brantly and Pedro H.C. Sant'Anna. "Difference-in- Differences with Multiple Time Periods." Journal of Econometrics, Vol. 225, No. 2, pp. 200-230, 2021. doi:10.1016/j.jeconom.2020.12.001, https://arxiv.org/abs/1803.09015.

Examples

## toy example ---------------------------------------------------------------
## Not run: 
library(did)  # provides the mpdta example dataframe
data(mpdta)

head(mpdta)

tidy_df <- attgtToFetwfeDf(
  data  = mpdta,
  yname = "lemp",
  tname = "year",
  idname = "countyreal",
  gname = "first.treat",
  covars = c("lpop"))

head(tidy_df)

## End(Not run)

## Now you can call fetwfe()  ------------------------------------------------
# res <- fetwfe(
#   pdata      = tidy_df,
#   time_var   = "time_var",
#   unit_var   = "unit_var",
#   treatment  = "treatment",
#   response   = "response",
#   covs       = c("lpop"))

Bridge-penalized extended two-way fixed effects

Description

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).

Usage

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
)

Arguments

pdata

Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.

time_var

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.

unit_var

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).

treatment

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").

response

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.

covs

(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().

indep_counts

(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.)

sig_eps_sq

(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.

sig_eps_c_sq

(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.

lambda.max

(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.

lambda.min

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

nlambda

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

q

(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.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

A named list with the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

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.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

lambda.max

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.)

lambda.max_model_size

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.

lambda.min

Either the provided lambda.min or the one that was used, if a value wasn't provided.

lambda.min_model_size

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.

lambda_star

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.

lambda_star_model_size

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.

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

Author(s)

Gregory Faletto

References

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.

Examples

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

Run BETWFE on Simulated Data

Description

This function runs the bridge-penalized extended two-way fixed effects estimator (betwfe()) on simulated data. It is simply a wrapper for betwfe(): it accepts an object of class "FETWFE_simulated" (produced by simulateData()) and unpacks the necessary components to pass to betwfe(). So the outputs match betwfe(), and the needed inputs match their counterparts in betwfe().

Usage

betwfeWithSimulatedData(
  simulated_obj,
  lambda.max = NA,
  lambda.min = NA,
  nlambda = 100,
  q = 0.5,
  verbose = FALSE,
  alpha = 0.05,
  add_ridge = FALSE
)

Arguments

simulated_obj

An object of class "FETWFE_simulated" containing the simulated panel data and design matrix.

lambda.max

(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. For lambda <= 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. 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.

lambda.min

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

nlambda

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

q

(Optional.) Numeric; determines what L_q penalty is used for the fusion 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.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

A named list with the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

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.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

lambda.max

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.)

lambda.max_model_size

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.

lambda.min

Either the provided lambda.min or the one that was used, if a value wasn't provided.

lambda.min_model_size

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.

lambda_star

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.

lambda_star_model_size

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.

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

Examples

## Not run: 
  # Generate coefficients
  coefs <- genCoefs(R = 5, T = 30, d = 12, density = 0.1, eff_size = 2, seed = 123)

  # Simulate data using the coefficients
  sim_data <- simulateData(coefs, N = 120, sig_eps_sq = 5, sig_eps_c_sq = 5)

  result <- betwfeWithSimulatedData(sim_data)

## End(Not run)

Extended two-way fixed effects

Description

Implementation of extended two-way fixed effects. Estimates overall ATT as well as CATT (cohort average treatment effects on the treated units).

Usage

etwfe(
  pdata,
  time_var,
  unit_var,
  treatment,
  response,
  covs = c(),
  indep_counts = NA,
  sig_eps_sq = NA,
  sig_eps_c_sq = NA,
  verbose = FALSE,
  alpha = 0.05,
  add_ridge = FALSE
)

Arguments

pdata

Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.

time_var

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.

unit_var

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).

treatment

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").

response

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.

covs

(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().

indep_counts

(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.)

sig_eps_sq

(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.

sig_eps_c_sq

(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.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

A named list with the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

A standard error for the ATT. If the Gram matrix is not invertible, this will be NA.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

A named vector containing the (asymptotically exact) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

Author(s)

Gregory Faletto

References

Wooldridge, J. M. (2021). Two-way fixed effects, the two-way mundlak regression, and difference-in-differences estimators. Available at SSRN 3906345. doi:10.2139/ssrn.3906345.

Extended Two-Way Fixed Effects Output Class

Description

S3 class for the output of etwfe().

Convert data prepared for etwfe::etwfe() to the format required by fetwfe() and fetwfe::etwfe()

Description

etwfeToFetwfeDf() reshapes and renames a panel dataset that is already formatted for etwfe::etwfe() (McDermott 2024) so that it can be passed directly to fetwfe()oretwfe()⁠from the⁠fetwfe' package. In particular, it

Usage

etwfeToFetwfeDf(
  data,
  yvar,
  tvar,
  idvar,
  gvar,
  covars = character(0),
  drop_first_period_treated = TRUE,
  out_names = list(time = "time_var", unit = "unit_var", treatment = "treatment",
    response = "response")
)

Arguments

data

A long-format data.frame that you could already feed to etwfe().

yvar

Character. Column name of the outcome (left-hand side in your fml).

tvar

Character. Column name of the time variable that you pass to etwfe() as tvar.

idvar

Character. Column name of the unit identifier (the variable you would cluster on, or pass to etwfe(..., ivar = idvar) if you were using unit FEs).

gvar

Character. Column name of the “first treated” cohort variable passed to etwfe() as gvar. Must be 0 for never-treated units, or the (strictly positive) first treated period.

covars

Character vector of additional covariate columns to keep (default character(0)).

drop_first_period_treated

Logical. Should units already treated in the very first sample period be removed? (fetwfe() will drop them internally anyway, but doing it here keeps the returned dataframe clean.) Default TRUE.

out_names

Named list giving the column names that the returned dataframe should have. The default (time, unit, treatment, y) matches the arguments usually supplied to fetwfe(). Do not change the names of this list – only the values – and keep all four.

Value

A tidy data.frame with (in this order)

References

McDermott G (2024). etwfe: Extended Two-Way Fixed Effects. doi:10.32614/CRAN.package.etwfe doi:10.32614/CRAN.package.etwfe, R package version 0.5.0, https://CRAN.R-project.org/package=etwfe.

Examples

## toy example ---------------------------------------------------------------
## Not run: 
library(did)  # provides the mpdta example dataframe
data(mpdta)

head(mpdta)

tidy_df <- etwfeToFetwfeDf(
  data  = mpdta,
  yvar = "lemp",
  tvar = "year",
  idvar = "countyreal",
  gvar = "first.treat",
  covars = c("lpop"))

head(tidy_df)


## End(Not run)
## Now you can call fetwfe()  ------------------------------------------------
# res <- fetwfe(
#   pdata      = tidy_df,
#   time_var   = "time_var",
#   unit_var   = "unit_var",
#   treatment  = "treatment",
#   response   = "response",
#   covs       = c("lpop"))

Run ETWFE on Simulated Data

Description

This function runs the extended two-way fixed effects estimator (etwfe()) on simulated data. It is simply a wrapper for etwfe(): it accepts an object of class "FETWFE_simulated" (produced by simulateData()) and unpacks the necessary components to pass to etwfe(). So the outputs match etwfe(), and the needed inputs match their counterparts in etwfe().

Usage

etwfeWithSimulatedData(
  simulated_obj,
  verbose = FALSE,
  alpha = 0.05,
  add_ridge = FALSE
)

Arguments

simulated_obj

An object of class "FETWFE_simulated" containing the simulated panel data and design matrix.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

A named list with the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

A standard error for the ATT. If the Gram matrix is not invertible, this will be NA.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

A named vector containing the (asymptotically exact) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

Examples

## Not run: 
  # Generate coefficients
  coefs <- genCoefs(R = 5, T = 30, d = 12, density = 0.1, eff_size = 2, seed = 123)

  # Simulate data using the coefficients
  sim_data <- simulateData(coefs, N = 120, sig_eps_sq = 5, sig_eps_c_sq = 5)

  result <- etwfeWithSimulatedData(sim_data)

## End(Not run)

Fused extended two-way fixed effects

Description

Implementation of fused extended two-way fixed effects. Estimates overall ATT as well as CATT (cohort average treatment effects on the treated units).

Usage

fetwfe(
  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
)

Arguments

pdata

Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.

time_var

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.

unit_var

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).

treatment

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").

response

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.

covs

(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().

indep_counts

(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.)

sig_eps_sq

(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.

sig_eps_c_sq

(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.

lambda.max

(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.

lambda.min

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

nlambda

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

q

(Optional.) Numeric; determines what L_q penalty is used for the fusion 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.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

An object of class fetwfe containing the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

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.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

lambda.max

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.)

lambda.max_model_size

The size of the selected model corresponding to 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.

lambda.min

Either the provided lambda.min or the one that was used, if a value wasn't provided.

lambda.min_model_size

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.

lambda_star

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.

lambda_star_model_size

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.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

alpha

The alpha level used for confidence intervals.

internal

A list containing internal outputs that are typically not needed for interpretation:

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

calc_ses

Logical indicating whether standard errors were calculated.

The object has methods for print(), summary(), and coef(). By default, print() and summary() only show the essential outputs. To see internal details, use print(x, show_internal = TRUE) or summary(x, show_internal = TRUE). The coef() method returns the vector of estimated coefficients (beta_hat).

Author(s)

Gregory Faletto

References

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.

Examples

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 <- fetwfe(
    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)

# Print results with internal details
print(res, max_cohorts = Inf)

Fused Extended Two-Way Fixed Effects Output Class

Description

S3 class for the output of fetwfe().

Run FETWFE on Simulated Data

Description

This function runs the fused extended two-way fixed effects estimator (fetwfe()) on simulated data. It is simply a wrapper for fetwfe(): it accepts an object of class "FETWFE_simulated" (produced by simulateData()) and unpacks the necessary components to pass to fetwfe(). So the outputs match fetwfe(), and the needed inputs match their counterparts in fetwfe().

Usage

fetwfeWithSimulatedData(
  simulated_obj,
  lambda.max = NA,
  lambda.min = NA,
  nlambda = 100,
  q = 0.5,
  verbose = FALSE,
  alpha = 0.05,
  add_ridge = FALSE
)

Arguments

simulated_obj

An object of class "FETWFE_simulated" containing the simulated panel data and design matrix.

lambda.max

(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. For lambda <= 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. 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.

lambda.min

(Optional.) Numeric. The smallest lambda penalty parameter that will be considered. See the description of lambda.max for details. Default is NA.

nlambda

(Optional.) Integer. The total number of lambda penalty parameters that will be considered. See the description of lambda.max for details. Default is 100.

q

(Optional.) Numeric; determines what L_q penalty is used for the fusion 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.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

An object of class fetwfe containing the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

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.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

lambda.max

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.)

lambda.max_model_size

The size of the selected model corresponding to 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.

lambda.min

Either the provided lambda.min or the one that was used, if a value wasn't provided.

lambda.min_model_size

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.

lambda_star

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.

lambda_star_model_size

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.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

alpha

The alpha level used for confidence intervals.

internal

A list containing internal outputs that are typically not needed for interpretation:

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

calc_ses

Logical indicating whether standard errors were calculated.

The object has methods for print(), summary(), and coef(). By default, print() and summary() only show the essential outputs. To see internal details, use print(x, show_internal = TRUE) or summary(x, show_internal = TRUE). The coef() method returns the vector of estimated coefficients (beta_hat).

Examples

## Not run: 
  # Generate coefficients
  coefs <- genCoefs(R = 5, T = 30, d = 12, density = 0.1, eff_size = 2, seed = 123)

  # Simulate data using the coefficients
  sim_data <- simulateData(coefs, N = 120, sig_eps_sq = 5, sig_eps_c_sq = 5)

  result <- fetwfeWithSimulatedData(sim_data)

## End(Not run)

Generate Coefficient Vector for Data Generation

Description

This function generates a coefficient vector beta for simulation studies of the fused extended two-way fixed effects estimator. It returns an S3 object of class "FETWFE_coefs" containing beta along with simulation parameters R, T, and d. See the simulation studies section of Faletto (2025) for details.

Usage

genCoefs(R, T, d, density, eff_size, seed = NULL)

Arguments

R

Integer. The number of treated cohorts (treatment is assumed to start in periods 2 to R + 1).

T

Integer. The total number of time periods.

d

Integer. The number of time-invariant covariates. If d > 0, additional terms corresponding to covariate main effects and interactions are included in beta.

density

Numeric in (0,1). The probability that any given entry in the initial sparse coefficient vector theta is nonzero.

eff_size

Numeric. The magnitude used to scale nonzero entries in theta. Each nonzero entry is set to eff_size or -eff_size (with a 60 percent chance for a positive value).

seed

(Optional) Integer. Seed for reproducibility.

Details

The length of beta is given by

p = R + (T - 1) + d + dR + d(T - 1) + \mathit{num\_treats} + (\mathit{num\_treats} \times d)

, where the number of treatment parameters is defined as

\mathit{num\_treats} = T \times R - \frac{R(R+1)}{2}

.

The function operates in two steps:

  1. It first creates a sparse vector theta of length p, with nonzero entries occurring with probability density. Nonzero entries are set to eff_size or -eff_size (with a 60\

  2. The full coefficient vector beta is then computed by applying an inverse fusion transform to theta using internal routines (e.g., genBackwardsInvFusionTransformMat() and genInvTwoWayFusionTransformMat()).

Value

An object of class "FETWFE_coefs", which is a list containing:

beta

A numeric vector representing the full coefficient vector after the inverse fusion transform.

theta

A numeric vector representing the coefficient vector in the transformed feature space. theta is a sparse vector, which aligns with an assumption that deviations from the restrictions encoded in the FETWFE model are sparse. beta is derived from theta.

R

The provided number of treated cohorts.

T

The provided number of time periods.

d

The provided number of covariates.

seed

The provided seed.

References

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.

Examples

## Not run: 
  # Generate coefficients
  coefs <- genCoefs(R = 5, T = 30, d = 12, density = 0.1, eff_size = 2, seed = 123)

  # Simulate data using the coefficients
  sim_data <- simulateData(coefs, N = 120, sig_eps_sq = 5, sig_eps_c_sq = 5)

## End(Not run)

Generate Coefficient Vector for Data Generation

Description

This function generates a coefficient vector beta along with a sparse auxiliary vector theta for simulation studies of the fused extended two-way fixed effects estimator. The returned beta is formatted to align with the design matrix created by genRandomData(), and is a valid input for the beta argument of that function. The vector theta is sparse, with nonzero entries occurring with probability density and scaled by eff_size. See the simulation studies section of Faletto (2025) for details.

Usage

genCoefsCore(R, T, d, density, eff_size, seed = NULL)

Arguments

R

Integer. The number of treated cohorts (treatment is assumed to start in periods 2 to R + 1).

T

Integer. The total number of time periods.

d

Integer. The number of time-invariant covariates. If d > 0, additional terms corresponding to covariate main effects and interactions are included in beta.

density

Numeric in (0,1). The probability that any given entry in the initial sparse coefficient vector theta is nonzero.

eff_size

Numeric. The magnitude used to scale nonzero entries in theta. Each nonzero entry is set to eff_size or -eff_size (with a 60 percent chance for a positive value).

seed

(Optional) Integer. Seed for reproducibility.

Details

The length of beta is given by

p = R + (T - 1) + d + dR + d(T - 1) + \mathit{num\_treats} + (\mathit{num\_treats} \times d)

, where the number of treatment parameters is defined as

\mathit{num\_treats} = T \times R - \frac{R(R+1)}{2}

.

The function operates in two steps:

  1. It first creates a sparse vector theta of length p, with nonzero entries occurring with probability density. Nonzero entries are set to eff_size or -eff_size (with a 60\

  2. The full coefficient vector beta is then computed by applying an inverse fusion transform to theta using internal routines (e.g., genBackwardsInvFusionTransformMat() and genInvTwoWayFusionTransformMat()).

Value

A list with two elements:

beta

A numeric vector representing the full coefficient vector after the inverse fusion transform.

theta

A numeric vector representing the coefficient vector in the transformed feature space. theta is a sparse vector, which aligns with an assumption that deviations from the restrictions encoded in the FETWFE model are sparse. beta is derived from theta.

References

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.

Examples

## Not run: 
  # Set parameters for the coefficient generation
  R <- 3         # Number of treated cohorts
  T <- 6         # Total number of time periods
  d <- 2         # Number of covariates
  density <- 0.1 # Probability that an entry in the initial vector is nonzero
  eff_size <- 1.5  # Scaling factor for nonzero coefficients
  seed <- 789    # Seed for reproducibility

  # Generate coefficients using genCoefsCore()
  coefs_core <- genCoefsCore(R = R, T = T, d = d, density = density,
  eff_size = eff_size, seed = seed)
  beta <- coefs_core$beta
  theta <- coefs_core$theta

  # For diagnostic purposes, compute the expected length of beta.
  # The length p is defined internally as:
  #   p = R + (T - 1) + d + d*R + d*(T - 1) + num_treats + num_treats*d,
  # where num_treats = T * R - (R*(R+1))/2.
  num_treats <- T * R - (R * (R + 1)) / 2
  p_expected <- R + (T - 1) + d + d * R + d * (T - 1) + num_treats + num_treats * d

  cat("Length of beta:", length(beta), "\nExpected length:", p_expected, "\n")

## End(Not run)

Compute True Treatment Effects

Description

This function extracts the true treatment effects from a full coefficient vector as generated by genCoefs(). It calculates the overall average treatment effect on the treated (ATT) as the equal-weighted average of the cohort-specific treatment effects, and also returns the individual treatment effects for each treated cohort.

Usage

getTes(coefs_obj)

Arguments

coefs_obj

An object of class "FETWFE_coefs" containing the coefficient vector and simulation parameters.

Details

The function internally uses auxiliary routines getNumTreats(), getP(), getFirstInds(), getTreatInds(), and getActualCohortTes() to determine the correct indices of treatment effect coefficients in beta. The overall treatment effect is computed as the simple average of these cohort-specific effects.

Value

A named list with two elements:

att_true

A numeric value representing the overall average treatment effect on the treated. It is computed as the (equal-weighted) mean of the cohort-specific treatment effects.

actual_cohort_tes

A numeric vector containing the true cohort-specific treatment effects, calculated by averaging the coefficients corresponding to the treatment dummies for each cohort.

Examples

## Not run: 
# Generate coefficients
coefs <- genCoefs(R = 5, T = 30, d = 12, density = 0.1, eff_size = 2, seed = 123)

# Compute the true treatment effects:
te_results <- getTes(coefs)

# Overall average treatment effect on the treated:
print(te_results$att_true)

# Cohort-specific treatment effects:
print(te_results$actual_cohort_tes)

## End(Not run)

Generate Random Panel Data for FETWFE Simulations

Description

Generates a random panel data set for simulation studies of the fused extended two-way fixed effects (FETWFE) estimator by taking an object of class "FETWFE_coefs" (produced by genCoefs()) and using it to simulate data. The function creates a balanced panel with N units over T time periods, assigns treatment status across R treated cohorts (with equal marginal probabilities for treatment and non-treatment), and constructs a design matrix along with the corresponding outcome. The covariates are generated according to the specified distribution: by default, covariates are drawn from a normal distribution; if distribution = "uniform", they are drawn uniformly from [-\sqrt{3}, \sqrt{3}]. When d = 0 (i.e. no covariates), no covariate-related columns or interactions are generated. See the simulation studies section of Faletto (2025) for details.

Usage

simulateData(
  coefs_obj,
  N,
  sig_eps_sq,
  sig_eps_c_sq,
  distribution = "gaussian",
  guarantee_rank_condition = FALSE
)

Arguments

coefs_obj

An object of class "FETWFE_coefs" containing the coefficient vector and simulation parameters.

N

Integer. Number of units in the panel.

sig_eps_sq

Numeric. Variance of the idiosyncratic (observation-level) noise.

sig_eps_c_sq

Numeric. Variance of the unit-level random effects.

distribution

Character. Distribution to generate covariates. Defaults to "gaussian". If set to "uniform", covariates are drawn uniformly from [-\sqrt{3}, \sqrt{3}].

guarantee_rank_condition

(Optional). Logical. If TRUE, the returned data set is guaranteed to have at least d + 1 units per cohort, which is necessary for the final design matrix to have full column rank. Default is FALSE, in which case no such condition is enforced.

Details

This function extracts simulation parameters from the FETWFE_coefs object and passes them, along with additional simulation parameters, to the internal function simulateDataCore(). It validates that all necessary components are returned and assigns the S3 class "FETWFE_simulated" to the output.

The argument distribution controls the generation of covariates. For "gaussian", covariates are drawn from rnorm; for "uniform", they are drawn from runif on the interval [-\sqrt{3}, \sqrt{3}] (which ensures that the covariates have unit variance regardless of which distribution is chosen).

When d = 0 (i.e. no covariates), the function omits any covariate-related columns and their interactions.

Value

An object of class "FETWFE_simulated", which is a list containing:

pdata

A dataframe containing generated data that can be passed to fetwfe().

X

The design matrix X, with p columns with interactions.

y

A numeric vector of length N \times T containing the generated responses.

covs

A character vector containing the names of the generated features (if d > 0), or simply an empty vector (if d = 0)

time_var

The name of the time variable in pdata

unit_var

The name of the unit variable in pdata

treatment

The name of the treatment variable in pdata

response

The name of the response variable in pdata

coefs

The coefficient vector \beta used for data generation.

first_inds

A vector of indices indicating the first treatment effect for each treated cohort.

N_UNTREATED

The number of never-treated units.

assignments

A vector of counts (of length R+1) indicating how many units fall into the never-treated group and each of the R treated cohorts.

indep_counts

Independent cohort assignments (for auxiliary purposes).

p

The number of columns in the design matrix X.

N

Number of units.

T

Number of time periods.

R

Number of treated cohorts.

d

Number of covariates.

sig_eps_sq

The idiosyncratic noise variance.

sig_eps_c_sq

The unit-level noise variance.

References

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.

Examples

## Not run: 
  # Generate coefficients
  coefs <- genCoefs(R = 5, T = 30, d = 12, density = 0.1, eff_size = 2, seed = 123)

  # Simulate data using the coefficients
  sim_data <- simulateData(coefs, N = 120, sig_eps_sq = 5, sig_eps_c_sq = 5)

## End(Not run)

Generate Random Panel Data for FETWFE Simulations

Description

Generates a random panel data set for simulation studies of the fused extended two-way fixed effects (FETWFE) estimator. The function creates a balanced panel with N units over T time periods, assigns treatment status across R treated cohorts (with equal marginal probabilities for treatment and non-treatment), and constructs a design matrix along with the corresponding outcome. When gen_ints = TRUE the full design matrix is returned (including interactions between covariates and fixed effects and treatment indicators). When gen_ints = FALSE the design matrix is generated in a simpler format (with no interactions) as expected by fetwfe(). Moreover, the covariates are generated according to the specified distribution: by default, covariates are drawn from a normal distribution; if distribution = "uniform", they are drawn uniformly from [-\sqrt{3}, \sqrt{3}].

When d = 0 (i.e. no covariates), no covariate-related columns or interactions are generated.

See the simulation studies section of Faletto (2025) for details.

Usage

simulateDataCore(
  N,
  T,
  R,
  d,
  sig_eps_sq,
  sig_eps_c_sq,
  beta,
  seed = NULL,
  gen_ints = FALSE,
  distribution = "gaussian",
  guarantee_rank_condition = FALSE
)

Arguments

N

Integer. Number of units in the panel.

T

Integer. Number of time periods.

R

Integer. Number of treated cohorts (with treatment starting in periods 2 to T).

d

Integer. Number of time-invariant covariates.

sig_eps_sq

Numeric. Variance of the idiosyncratic (observation-level) noise.

sig_eps_c_sq

Numeric. Variance of the unit-level random effects.

beta

Numeric vector. Coefficient vector for data generation. Its required length depends on the value of gen_ints:

  • If gen_ints = TRUE and d > 0, the expected length is p = R + (T-1) + d + dR + d(T-1) + num\_treats + num\_treats \times d, where num\_treats = T \times R - \frac{R(R+1)}{2}.

  • If gen_ints = TRUE and d = 0, the expected length is p = R + (T-1) + num\_treats.

  • If gen_ints = FALSE, the expected length is p = R + (T-1) + d + num\_treats.

seed

(Optional) Integer. Seed for reproducibility.

gen_ints

Logical. If TRUE, generate the full design matrix with interactions; if FALSE (the default), generate a design matrix without any interaction terms.

distribution

Character. Distribution to generate covariates. Defaults to "gaussian". If set to "uniform", covariates are drawn uniformly from [-\sqrt{3}, \sqrt{3}].

guarantee_rank_condition

(Optional). Logical. If TRUE, the returned data set is guaranteed to have at least d + 1 units per cohort, which is necessary for the final design matrix to have full column rank. Default is FALSE, in which case no such condition is enforced.

Details

When gen_ints = TRUE, the function constructs the design matrix by first generating base fixed effects and a long-format covariate matrix (via generateBaseEffects()), then appending interactions between the covariates and cohort/time fixed effects (via generateFEInts()) and finally treatment indicator columns and treatment-covariate interactions (via genTreatVarsSim() and genTreatInts()). When gen_ints = FALSE, the design matrix consists only of the base fixed effects, covariates, and treatment indicators.

The argument distribution controls the generation of covariates. For "gaussian", covariates are drawn from rnorm; for "uniform", they are drawn from runif on the interval [-\sqrt{3}, \sqrt{3}].

When d = 0 (i.e. no covariates), the function omits any covariate-related columns and their interactions.

Value

An object of class "FETWFE_simulated", which is a list containing:

pdata

A dataframe containing generated data that can be passed to fetwfe().

X

The design matrix. When gen_ints = TRUE, X has p columns with interactions; when gen_ints = FALSE, X has no interactions.

y

A numeric vector of length N \times T containing the generated responses.

covs

A character vector containing the names of the generated features (if d > 0), or simply an empty vector (if d = 0)

time_var

The name of the time variable in pdata

unit_var

The name of the unit variable in pdata

treatment

The name of the treatment variable in pdata

response

The name of the response variable in pdata

coefs

The coefficient vector \beta used for data generation.

first_inds

A vector of indices indicating the first treatment effect for each treated cohort.

N_UNTREATED

The number of never-treated units.

assignments

A vector of counts (of length R+1) indicating how many units fall into the never-treated group and each of the R treated cohorts.

indep_counts

Independent cohort assignments (for auxiliary purposes).

p

The number of columns in the design matrix X.

N

Number of units.

T

Number of time periods.

R

Number of treated cohorts.

d

Number of covariates.

sig_eps_sq

The idiosyncratic noise variance.

sig_eps_c_sq

The unit-level noise variance.

References

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.

Examples

## Not run: 
  # Set simulation parameters
  N <- 100           # Number of units in the panel
  T <- 5             # Number of time periods
  R <- 3             # Number of treated cohorts
  d <- 2             # Number of time-invariant covariates
  sig_eps_sq <- 1    # Variance of observation-level noise
  sig_eps_c_sq <- 0.5  # Variance of unit-level random effects

  # Generate coefficient vector using genCoefsCore()
  # (Here, density controls sparsity and eff_size scales nonzero entries)
  coefs_core <- genCoefsCore(R = R, T = T, d = d, density = 0.2, eff_size = 2, seed = 123)

  # Now simulate the data. Setting gen_ints = TRUE generates the full design
  matrix with interactions.
  sim_data <- simulateDataCore(
    N = N,
    T = T,
    R = R,
    d = d,
    sig_eps_sq = sig_eps_sq,
    sig_eps_c_sq = sig_eps_c_sq,
    beta = coefs_core$beta,
    seed = 456,
    gen_ints = TRUE,
    distribution = "gaussian"
  )

  # Examine the returned list:
  str(sim_data)

## End(Not run)

Two-way fixed effects with covariates and separate treatment effects for each cohort

Description

WARNING: This function should NOT be used for estimation. It is a biased estimator of treatment effects. Implementation of two-way fixed effects with covariates and separate treatment effects for each cohort. Estimates overall ATT as well as CATT (cohort average treatment effects on the treated units). It is implemented only for the sake of the simulation studies in Faletto (2025). This estimator is only unbiased under the assumptions that treatment effects are homogeneous across covariates and are identical within cohorts across all times since treatment.

Usage

twfeCovs(
  pdata,
  time_var,
  unit_var,
  treatment,
  response,
  covs = c(),
  indep_counts = NA,
  sig_eps_sq = NA,
  sig_eps_c_sq = NA,
  verbose = FALSE,
  alpha = 0.05,
  add_ridge = FALSE
)

Arguments

pdata

Dataframe; the panel data set. Each row should represent an observation of a unit at a time. Should contain columns as described below.

time_var

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.

unit_var

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).

treatment

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").

response

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.

covs

(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().

indep_counts

(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.)

sig_eps_sq

(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.

sig_eps_c_sq

(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.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

A named list with the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

A standard error for the ATT. If the Gram matrix is not invertible, this will be NA.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

A named vector containing the (asymptotically exact) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

Author(s)

Gregory Faletto

References

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.

Run twfeCovs on Simulated Data

Description

This function runs the bridge-penalized extended two-way fixed effects estimator (twfeCovs()) on simulated data. It is simply a wrapper for twfeCovs(): it accepts an object of class "FETWFE_simulated" (produced by simulateData()) and unpacks the necessary components to pass to twfeCovs(). So the outputs match twfeCovs(), and the needed inputs match their counterparts in twfeCovs().

Usage

twfeCovsWithSimulatedData(
  simulated_obj,
  verbose = FALSE,
  alpha = 0.05,
  add_ridge = FALSE
)

Arguments

simulated_obj

An object of class "FETWFE_simulated" containing the simulated panel data and design matrix.

verbose

Logical; if TRUE, more details on the progress of the function will be printed as the function executes. Default is FALSE.

alpha

Numeric; function will calculate (1 - alpha) confidence intervals for the cohort average treatment effects that will be returned in catt_df.

add_ridge

(Optional.) Logical; if TRUE, adds a small amount of ridge regularization to the (untransformed) coefficients to stabilize estimation. Default is FALSE.

Value

A named list with the following elements:

att_hat

The estimated overall average treatment effect for a randomly selected treated unit.

att_se

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.

catt_hats

A named vector containing the estimated average treatment effects for each cohort.

catt_ses

If q < 1, a named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort.

cohort_probs

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.

catt_df

A dataframe displaying the cohort names, average treatment effects, standard errors, and 1 - alpha confidence interval bounds.

beta_hat

The full vector of estimated coefficients.

treat_inds

The indices of beta_hat corresponding to the treatment effects for each cohort at each time.

treat_int_inds

The indices of beta_hat corresponding to the interactions between the treatment effects for each cohort at each time and the covariates.

sig_eps_sq

Either the provided sig_eps_sq or the estimated one, if a value wasn't provided.

sig_eps_c_sq

Either the provided sig_eps_c_sq or the estimated one, if a value wasn't provided.

X_ints

The design matrix created containing all interactions, time and cohort dummies, etc.

y

The vector of responses, containing nrow(X_ints) entries.

X_final

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.

y_final

The final response after multiplying on the left by the square root inverse of the estimated covariance matrix for each unit.

N

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).

T

The number of time periods in the final data set.

R

The final number of treated cohorts that appear in the final data set.

d

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).

p

The final number of columns in the full set of covariates used to estimate the model.

Examples

## Not run: 
  # Generate coefficients
  coefs <- genCoefs(R = 5, T = 30, d = 12, density = 0.1, eff_size = 2, seed = 123)

  # Simulate data using the coefficients
  sim_data <- simulateData(coefs, N = 120, sig_eps_sq = 5, sig_eps_c_sq = 5)

  result <- twfeCovsWithSimulatedData(sim_data)

## End(Not run)