Package {fetwfe}

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).

Character scalar. Name of the outcome column.

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

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

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.

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.

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.

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

Logical. If TRUE, a message() reports the count of first-period-treated unit-period rows dropped when drop_first_period_treated = TRUE. Default FALSE (silent).

An object of class "betwfe".

A panel data.frame with the response column under x$response_col_name. Any sort order; first-period-treated units are auto-trimmed.

Unused.

An object of class "etwfe".

A panel data.frame with the response column under x$response_col_name. Any sort order; first-period-treated units are auto-trimmed.

Unused.

An object of class "fetwfe".

A panel data.frame with one row per unit-period (any sort order — augment auto-sorts), containing the response column under the same name used at fit time (see x$response_col_name). First-period-treated units, if present, are auto-trimmed.

Unused.

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 by REML on the linear mixed-effects model y ~ X + (1 | unit) via lme4::lmer (Bates et al. 2015; Patterson & Thompson 1971). 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 by REML via lme4::lmer on the linear mixed-effects model y ~ X + (1 | unit) (Bates et al. 2015; Patterson & Thompson 1971). 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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). "cluster" is only meaningful when q < 1 (the bridge oracle property is required); for q >= 1 the SE will be NA regardless of se_type. Default is "default".

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 two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback).

Logical scalar; TRUE if att_hat is not exactly zero, FALSE otherwise. BETWFE uses bridge regression directly on the coefficients (rather than on the fused restrictions used by FETWFE); under the bridge oracle property of Kock (2013), att_selected = FALSE is an analogous asymptotic statement that the truth is zero under a sparsity assumption different from the one Theorem 6.2 establishes for FETWFE. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

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, 1 - alpha confidence interval bounds, per-cohort p-values (P_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), P_value is NA.

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.

Numeric scalar; mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the response column name in the original pdata. Consumed by augment.betwfe().

Character scalars; the corresponding arguments the user passed. Consumed by augment.betwfe() when auto-aligning a user-supplied panel to the fitted design.

Character vector; the original covs argument (pre-factor- expansion). Consumed by augment.betwfe().

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

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

(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.

(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 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.

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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). "cluster" is only meaningful when q < 1 (the bridge oracle property is required); for q >= 1 the SE will be NA regardless of se_type. Default is "default".

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 two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback).

Logical scalar; TRUE if att_hat is not exactly zero, FALSE otherwise. BETWFE uses bridge regression directly on the coefficients (rather than on the fused restrictions used by FETWFE); under the bridge oracle property of Kock (2013), att_selected = FALSE is an analogous asymptotic statement that the truth is zero under a sparsity assumption different from the one Theorem 6.2 establishes for FETWFE. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

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, 1 - alpha confidence interval bounds, per-cohort p-values (P_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), P_value is NA.

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.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

Numeric scalar; mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the response column name in the original pdata. Consumed by augment.betwfe().

Character scalars; the corresponding arguments the user passed.

Character vector; the original covs argument (pre-factor- expansion).

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 by REML on the linear mixed-effects model y ~ X + (1 | unit) via lme4::lmer (Bates et al. 2015; Patterson & Thompson 1971). 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 by REML via lme4::lmer on the linear mixed-effects model y ~ X + (1 | unit) (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the OLS-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). Default is "default".

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

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

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA. Standard post-OLS interpretation; ETWFE does not perform selection.

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

A named vector containing the (asymptotically exact) 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, 1 - alpha confidence interval bounds, and per-cohort p-values (P_value). No selected column; ETWFE does not perform selection.

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.

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.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed. Consumed by ⁠augment.<class>()⁠ when auto-aligning a user-supplied panel to the fitted design.

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally). Consumed by ⁠augment.<class>()⁠.

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

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

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

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).

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.

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

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.

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

Logical. If TRUE, a message() reports the count of first-period-treated unit-period rows dropped when drop_first_period_treated = TRUE. Default FALSE (silent).

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

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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the OLS-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). Default is "default".

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

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

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA. Standard post-OLS interpretation; ETWFE does not perform selection.

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

A named vector containing the (asymptotically exact) 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, 1 - alpha confidence interval bounds, and per-cohort p-values (P_value). No selected column; ETWFE does not perform selection.

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.

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.

The alpha level used for confidence intervals.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed.

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally).

A fitted object of class "fetwfe", "etwfe", or "betwfe".

(Optional) Significance level for confidence intervals. Defaults to x$alpha (the alpha used at fit time).

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 by REML on the linear mixed-effects model y ~ X + (1 | unit) via lme4::lmer (Bates et al. 2015; Patterson & Thompson 1971). 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 by REML via lme4::lmer on the linear mixed-effects model y ~ X + (1 | unit) (Bates et al. 2015; Patterson & Thompson 1971). 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 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.

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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). "cluster" is only meaningful when q < 1 (the bridge oracle property is required); for q >= 1 the SE will be NA regardless of se_type. Default is "default".

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 two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback). See the package vignette section "Testing the zero-effect null" for interpretation guidance under selection consistency.

Logical scalar; TRUE if att_hat is not exactly zero (i.e., at least one cohort's bridge-penalized coefficient survived selection), FALSE otherwise. Under FETWFE Theorem 6.2 (restriction selection consistency), att_selected = FALSE is the asymptotic statement that the truth is zero. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

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, 1 - alpha confidence interval bounds, per-cohort p-values (P_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), P_value is NA — the inferential content lives in selected.

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 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.

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 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.

The alpha level used for confidence intervals.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed. Consumed by ⁠augment.<class>()⁠ when auto-aligning a user-supplied panel to the fitted design (e.g., dropping first-period-treated units the estimator removed internally, and sorting rows to match the design matrix's internal ⁠(unit, time)⁠ order).

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally). Consumed by ⁠augment.<class>()⁠.

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.

theta_hat

The vector of estimated coefficients in the transformed (fused) space, including the intercept as the first element.

calc_ses

Logical indicating whether standard errors were calculated.

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

(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.

(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 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.

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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the bridge-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). "cluster" is only meaningful when q < 1 (the bridge oracle property is required); for q >= 1 the SE will be NA regardless of se_type. Default is "default".

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 two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA (e.g., under the bridge solver's selected-out fallback). See the package vignette section "Testing the zero-effect null" for interpretation guidance under selection consistency.

Logical scalar; TRUE if att_hat is not exactly zero (i.e., at least one cohort's bridge-penalized coefficient survived selection), FALSE otherwise. Under FETWFE Theorem 6.2 (restriction selection consistency), att_selected = FALSE is the asymptotic statement that the truth is zero. For ridge (q = 2) the bridge solver does not zero coefficients, so this will typically be TRUE.

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, 1 - alpha confidence interval bounds, per-cohort p-values (P_value), and a selected logical flag (TRUE when the bridge penalty left the cohort's CATT nonzero). For selected-out cohorts (selected = FALSE), P_value is NA — the inferential content lives in selected.

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 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.

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 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.

The alpha level used for confidence intervals.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

Numeric scalar; the mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the name of the response column in the original pdata. Consumed by ⁠augment.<class>()⁠.

Character scalars; the time_var / unit_var / treatment arguments the user passed. Consumed by ⁠augment.<class>()⁠ when auto-aligning a user-supplied panel to the fitted design (e.g., dropping first-period-treated units the estimator removed internally, and sorting rows to match the design matrix's internal ⁠(unit, time)⁠ order).

Character vector; the original covs argument the user passed (before any factor expansion the estimator performed internally). Consumed by ⁠augment.<class>()⁠.

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.

theta_hat

The vector of estimated coefficients in the transformed (fused) space, including the intercept as the first element.

calc_ses

Logical indicating whether standard errors were calculated.

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

Integer. The total number of time periods.

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

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

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).

(Optional) Integer. Seed for reproducibility.

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

Integer. The total number of time periods.

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

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

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).

(Optional) Integer. Seed for reproducibility.

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

An object of class "betwfe".

Unused.

An object of class "etwfe".

Unused.

An object of class "fetwfe".

Unused.

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

Integer. Number of units in the panel.

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

Numeric. Variance of the unit-level random effects. Must be non-negative; 0 is allowed (yields a panel with no unit-level random effects).

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

(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.

Integer. Number of units in the panel.

Integer. Number of time periods.

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

Integer. Number of time-invariant covariates.

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

Numeric. Variance of the unit-level random effects. Must be non-negative; 0 is allowed (yields a panel with no unit-level random effects).

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.

(Optional) Integer. Seed for reproducibility.

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

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

(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.

An object of class "FETWFE_tes" returned by getTes().

Logical; include conf.low / conf.high columns. Defaults to TRUE to match the sibling tidy methods and preserve pre-#84 backward compatibility. Population-truth objects have no sampling distribution, so the CI columns are always filled with NA_real_ when included.

Numeric in (0, 1). Accepted for broom-convention parity but unused (no CIs to compute for a population truth); validated regardless. Defaults to 0.95 (FETWFE_tes objects do not carry an alpha slot, so there is no fitted-object value to default to).

Unused.

An object of class "betwfe" returned by betwfe().

Logical; include CI columns.

Numeric in (0, 1); defaults to 1 - x$alpha.

Unused.

An object of class "etwfe" returned by etwfe().

Logical; include CI columns.

Numeric in (0, 1); defaults to 1 - x$alpha.

Unused.

An object of class "eventStudy" returned by eventStudy().

Logical; include conf.low / conf.high columns.

Numeric in (0, 1). Confidence level for the CI columns; defaults to 0.95 (eventStudy() does not store the alpha it was called with, so there is no fitted-object value to default to).

Unused.

An object of class "fetwfe" returned by fetwfe().

Logical. If TRUE (default), conf.low and conf.high columns are included.

Numeric in (0, 1). Confidence level for the CI columns. Defaults to 1 - x$alpha (faithful to the alpha used at fit time; deviates from broom::tidy.lm's 0.95 default by design).

Unused; present for S3 compatibility.

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 the conservative standard error formula will be used).

(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 by REML on the linear mixed-effects model y ~ X + (1 | unit) via lme4::lmer (Bates et al. 2015; Patterson & Thompson 1971). 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 by REML via lme4::lmer on the linear mixed-effects model y ~ X + (1 | unit) (Bates et al. 2015; Patterson & Thompson 1971). Default is NA.

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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the OLS-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). Default is "default".

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

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

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA. Standard post-OLS interpretation; twfeCovs does not perform selection.

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

A named vector containing the (asymptotically exact) 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, 1 - alpha confidence interval bounds, and per-cohort p-values (P_value). No selected column; twfeCovs does not perform selection.

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.

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.

Numeric scalar; mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the response column name in the original pdata. Reserved for future augment() / predict() methods.

Character scalars; the corresponding arguments the user passed.

Character vector; the original covs argument (pre-factor- expansion).

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

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

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.

(Optional.) Logical; if TRUE (default) and the input panel contains no never-treated units, the panel is auto-truncated by dropping time periods at and after the latest cohort's start time — the units in that latest cohort then serve as the never-treated comparison group in the retained sub-panel — with a warning naming the dropped periods. If FALSE, the estimator stops with an error in this case (the package's behavior prior to version 1.5.6). The argument has no effect when the input already contains never-treated units. Default is TRUE.

Character; one of "default" (the package's Assumption-F1-based standard error from the paper) or "cluster" (an experimental unit-clustered Liang-Zeger sandwich SE on the OLS-selected support; see the companion vignette inference_vignette for the formula, the assumptions, and the theory-pending caveat). Default is "default".

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

A standard error for the ATT. If indep_counts was provided, this standard error is asymptotically exact; otherwise, it is asymptotically conservative. If the Gram matrix is not invertible, this will be NA.

A two-sided p-value for the overall ATT against the null H_0: tau = 0, computed as ⁠2 * pnorm(-|att_hat / att_se|)⁠. NA if att_se is zero or NA. Standard post-OLS interpretation; twfeCovs does not perform selection.

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

A named vector containing the (asymptotically exact, non-conservative) standard errors for the estimated average treatment effects within each cohort. If the Gram matrix is not invertible, the entries are NA.

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, 1 - alpha confidence interval bounds, and per-cohort p-values (P_value). No selected column; twfeCovs does not perform selection.

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.

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.

Logical indicating whether standard errors were calculated.

A vector of the estimated cohort probabilities on the overall sample (treated and untreated), used in computing the variance of the overall ATT.

Logical scalar; TRUE if a valid indep_counts argument was provided and used for asymptotically-exact ATT inference, FALSE otherwise.

Character scalar; the se_type argument the user passed ("default" or "cluster").

Numeric scalar; mean of the original (pre-centering) response. Stored so downstream methods (augment(), predict()) can return fitted values on the original-response scale.

Character scalar; the response column name in the original pdata.

Character scalars; the corresponding arguments the user passed.

Character vector; the original covs argument (pre-factor- expansion).