Fused extended two-way fixed effects

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

The treatment-effect fusion penalty defaults to a within-/between-cohort geometry (fusion_structure = "cohort") and also supports an event-study geometry (fusion_structure = "event_study", fusing effects at the same time since treatment across cohorts) or a fully custom fusion_matrix. See the fusion_structure / fusion_matrix arguments below and vignette("fusion_structure_vignette", package = "fetwfe") for guidance on choosing.

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,
  allow_no_never_treated = TRUE,
  se_type = "default",
  lambda_selection = "cv",
  cv_folds = 10L,
  cv_seed = NULL,
  ci_type = c("simultaneous", "pointwise"),
  fusion_structure = c("cohort", "event_study"),
  fusion_matrix = NULL,
  gls = TRUE
)

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.) Either a character vector containing the names of the columns for covariates (e.g., covs = c("x1", "x2")), or a one-sided formula (e.g., covs = ~ x1 + x2) – the formula form mirrors the convention used by did::att_gt(xformla = ...). Only additive bare variable names are supported in the formula form; for derived variables, compute them in the data frame first and pass via the character-vector form. 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 G 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 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.

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 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.

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.

allow_no_never_treated

(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.

se_type

Character; one of "default", "conservative", or "cluster". "default" returns the tight Gaussian variance sqrt(att_var_1 + att_var_2) from Theorem (c$'$) under Assumption (Psi-IF); this is asymptotically exact for the package's default cohort sample-proportions estimator and for every standard propensity-score estimator that satisfies (Psi-IF) (multinomial logit, any GLM on W | X, kernel/series regression of 1{W = g} on X). "conservative" returns the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c); use only if the propensity-score estimator violates (Psi-IF) (e.g., a Robins-Rotnitzky-augmented doubly-robust estimator, which the package does not currently implement). "cluster" is 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); only meaningful when q < 1 (the bridge oracle property is required), and for q >= 1 the SE will be NA regardless of se_type. The default value of "default" corresponds to the new tight Gaussian default introduced in version 1.12.0; previous versions used the conservative Cauchy-Schwarz formula as the default. To recover the prior conservative default behavior, pass se_type = "conservative".

lambda_selection

Character; method for selecting the bridge penalty parameter lambda. Either "cv" (10-fold cross-validation on cv.grpreg; the v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default for v1.12.0 and earlier). The default changed in v1.13.0 to address a finite-sample bias issue documented in simulation studies (see issue #164): under the prior BIC default, the overall-ATT estimator was biased toward zero at moderate sample sizes, producing 95% confidence intervals whose empirical coverage was as low as 0.00 in some regimes. Cross-validation restores near-nominal coverage in every regime tested. To recover the prior behavior — for example, when reproducing analyses run against v1.12.0 or earlier — pass lambda_selection = "bic". See the inference vignette section "Choosing the bridge penalty parameter" for details.

cv_folds

Integer; number of folds for the CV path. Ignored when lambda_selection = "bic". Default is 10.

cv_seed

Integer or NULL; the seed passed to set.seed() immediately before the cv.grpreg() call, controlling fold assignment. If NULL (the default), the seed defaults internally to as.integer(N * T) so consecutive calls on the same dataset are reproducible without the user having to specify a seed. The seed actually used is stored on the returned object as cv_seed. Ignored when lambda_selection = "bic".

ci_type

Character; one of "simultaneous" (default) or "pointwise". Controls the confidence-interval bounds reported for the cohort-specific ATTs (in catt_df) and the event-study effects (from eventStudy(), shown by print / summary / plot, and surfaced by broom::tidy() on the fitted object and on the eventStudy() / cohortStudy() outputs). "simultaneous" reports parametric simultaneous (family-wise, uniform) bands computed via simultaneousCIs(): each family's band covers all of its effects jointly with probability 1 - alpha, matching the default presentation of did::aggte(cband = TRUE). "pointwise" reports per-effect Wald intervals (each covers its own effect with probability 1 - alpha, no joint guarantee — the behavior of versions <= 1.15.1). Both the interval bounds and the per-cohort p-values (p_value) follow ci_type: under "simultaneous" the p_value is the single-step max-T multiplicity- adjusted p-value matching the band, under "pointwise" the per-cohort Wald p-value (#200). The standard errors (se) and selection flags (selected) are identical under both settings, and the overall-ATT confidence interval (a single scalar) is unaffected. When standard errors are unavailable (q >= 1, or a rank-deficient design) the bounds are NA under both settings. Default is "simultaneous".

fusion_structure

Character; one of "cohort" or "event_study". "cohort" (the default) uses the within-cohort / between-cohort two-way fusion penalty. "event_study" instead fuses treatment effects at the same time since treatment (event time e = t - g) across cohorts. The event-study penalty carries the same theoretical guarantees as the default (Faletto 2025); only the treatment-effect fusion structure changes.

fusion_matrix

(Optional.) Numeric matrix or NULL (the default). An advanced-use override: a user-supplied num_treats x num_treats forward differences matrix D_N for the treatment-effect block, encoding an arbitrary fusion structure beyond the two built-ins. When non-NULL it overrides fusion_structure for the treatment-effect block only (the fixed-effect blocks are unchanged); the estimator uses solve(fusion_matrix) internally. The rows/columns are interpreted in the cohort-major (g, t) order used internally for the treatment effects (the order getFirstInds() / getTreatInds() encode): row/column i corresponds to base treatment effect i, with cohort g occupying rows first_inds[g]:(first_inds[g + 1] - 1) ordered by event time. num_treats equals T * G - G * (G + 1) / 2. fusion_matrix must be a finite, invertible numeric matrix of that exact dimension (otherwise fetwfe() stops). Under the paper's fixed-dimension scoping, any finite invertible D_N of that dimension inherits the paper's inferential guarantees: the theory depends on D_N only through its invertibility and singular-value bounds (Assumption (D) of Faletto 2025), which a fixed invertible matrix automatically satisfies, and swapping in a different D_N from this class changes only constant factors. A numerically near-singular (ill-conditioned) D_N still yields a valid point estimator but emits a warning() that its inverse may be unreliable. Default is NULL (use the built-in fusion_structure).

gls

(Optional.) Logical; default TRUE. When TRUE, the design is GLS-whitened using REML-estimated (or supplied) variance components — the standard, efficient path. When FALSE, fetwfe() skips GLS whitening and variance-component estimation entirely, fitting on the un-whitened (fusion-transformed) design. This is the high-dimensional (p >= NT) path: REML cannot estimate the variance components there (the p < N(T - 1) REML guard would otherwise stop the fit), and whitening buys efficiency, not validity — the debiasedATT() cluster-robust sandwich standard error needs no Omega (paper Decision D1). A gls = FALSE fit has calc_ses = FALSE (no within-selection oracle standard errors) and un-whitened internal$X_final / internal$y_final; pass it to debiasedATT() for a valid cluster-robust SE. add_ridge = TRUE is not supported, and supplied sig_eps_sq / sig_eps_c_sq are ignored, under gls = 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. Under the default se_type = "default", the SE is the tight Gaussian variance sqrt(att_var_1 + att_var_2) (Theorem (c$'$) under Assumption (Psi-IF); paper line 1233 onwards). Assumption (Psi-IF) is satisfied by the package's default cohort sample-proportions estimator hat_pi_g = N_g / N (and by multinomial logit, any GLM on W | X, and kernel/series regression of 1{W = g} on X), so the default SE is asymptotically exact for the package's default estimator. Under se_type = "conservative" (or in version <= 1.11.7 by default), the SE is the Cauchy-Schwarz upper bound sqrt(att_var_1 + att_var_2 + 2 * sqrt(att_var_1 * att_var_2)) from Theorem (c). When indep_counts is provided, the two-sample exact formula sqrt(att_var_1 + att_var_2) is used regardless of se_type. If q >= 1, this will be NA.

att_p_value

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.

att_selected

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.

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 data frame (with S3 class c("catt_df", "data.frame")) displaying the cohort names (cohort), average treatment effects (estimate), standard errors (se), 1 - alpha confidence interval bounds (ci_low, ci_high), 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 catt_df S3 class makes [[ / $ / [ access on the pre-1.11.0 Title-Case column names (Cohort, Estimated TE, SE, ConfIntLow, ConfIntHigh, P_value) stop() with a migration message pointing to the new name. See NEWS.md for the rename table.

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 number of selected features (excluding the always-present intercept) at 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 number of selected features (excluding the always-present intercept) at 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 the selection method recorded in lambda_selection. 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 number of selected features (excluding the always-present intercept) in the chosen model. 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.

lambda_selection

Character scalar; either "cv" (10-fold cross-validation on cv.grpreg; v1.13.0+ default) or "bic" (BIC over the grpreg lambda grid; the prior default). Mirrors the lambda_selection argument the user passed.

cv_folds

Integer scalar; the cv_folds value used when lambda_selection = "cv", NA_integer_ when lambda_selection = "bic".

cv_seed

Integer scalar; the seed actually fed to set.seed() immediately before cv.grpreg() was called. Defaults to as.integer(N * T) when the user did not pass a seed. NA_integer_ when lambda_selection = "bic".

fusion_structure

Character scalar; the fusion_structure argument the user passed ("cohort" or "event_study"), recording which fusion-penalty differences matrix was used for the treatment effects.

fusion_matrix

The user-supplied custom forward differences matrix D_N (a num_treats x num_treats numeric matrix), or NULL if none was supplied. When non-NULL it overrode fusion_structure for the treatment-effect block; the estimator used solve(fusion_matrix) internally. See the fusion_matrix argument.

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.

G

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

R

Deprecated alias for G, retained for backward compatibility; populated with the same value. Use G. Will be removed in a future release.

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.

calc_ses

Logical indicating whether standard errors were calculated. Same as $internal$calc_ses; duplicated at top level for parity with etwfe(), betwfe(), and twfeCovs() (#180).

cohort_probs_overall

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

indep_counts_used

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

se_type

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

ci_type

Character scalar; the ci_type argument the user passed ("simultaneous" or "pointwise"), controlling whether the reported catt_df / eventStudy() confidence-interval bounds are simultaneous (family-wise) or pointwise.

y_mean

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.

response_col_name

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

time_var, unit_var, treatment

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).

covs

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

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.

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.

variance_components

A list exposing the two variance pieces (att_var_1, att_var_2) plus their paper-notation counterparts (V_1, V_2) and the unit-scaled variance estimators (tilde_v_N, hat_v_N, tilde_v_N_C, tilde_v_N_C_pi_hat, tilde_v_N_C_pi_hat_cons, tilde_v_N_cons) catalogued at paper line 2006. The Wald CI is [hat_T_N +- qnorm(1-alpha/2) * sqrt(tilde_v_N / N)] (paper Eq. conf.int.form). New in v1.12.0 (issue #141 + #146).

first_year

Integer or numeric scalar; the first (earliest) time_var value in the panel after idCohorts() processing. Consumed by eventStudy() to map cohort_probs' cohort labels (treatment-start years) to 1-based panel-time-index offsets when the labels are integer-coercible. New in v1.13.3 (issue #174).

d_inv_treat

The inverted custom treatment-effect fusion block solve(fusion_matrix) (a num_treats x num_treats numeric matrix), or NULL if no fusion_matrix was supplied. Consumed by eventStudy() and simultaneousCIs() so the access-time bands reuse the same fusion block the fit used (#236).

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).

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.

Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67(1), 1-48. doi:10.18637/jss.v067.i01 .

Patterson, H. D., & Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika, 58(3), 545-554.

Pinheiro, J. C., & Bates, D. M. (2000). Mixed-Effects Models in S and S-PLUS. Springer.

See also

vignette("fusion_structure_vignette", package = "fetwfe") for guidance on choosing between the cohort (default) and event-study fusion penalties and on supplying a custom fusion_matrix.

Author

Gregory Faletto

Examples

# `bacondecomp` (which supplies the `divorce` data) is a Suggests-only
# dependency, so guard the example on its availability. The fit is wrapped in
# \donttest{} because it is slower than a toy example.
# \donttest{
if (requireNamespace("bacondecomp", quietly = TRUE)) {
  library(bacondecomp)

  data(divorce)

  # Stevenson & Wolfers (2006): the effect of unilateral ("no-fault") divorce
  # reforms on female suicide rates. Restrict to the female subset
  # (`sex == 2`); `changed` is already the absorbing 0/1 reform indicator, and
  # the elasticity-scaled female suicide rate is the response.
  divorce_f <- divorce[divorce$sex == 2, ]

  # Reproduces the empirical application in Faletto (2025, Sec. 8.2). The 9
  # states already treated by 1964 are auto-dropped as first-period-treated,
  # and `murderrate` is auto-dropped (missing in 1964 for one state); both are
  # reported as (expected) warnings. The noise variances are supplied
  # (precomputed by REML) to keep the example fast and reproducible; the
  # default lambda_selection is "cv" (10-fold cross-validation).
  res <- fetwfe(
      pdata = divorce_f,
      time_var = "year",
      unit_var = "st",
      treatment = "changed",
      covs = c("murderrate", "lnpersinc", "afdcrolls"),
      response = "suiciderate_elast_jag",
      sig_eps_sq = 0.0344,
      sig_eps_c_sq = 0.1507,
      add_ridge = TRUE,
      q = 0.5)

  # FETWFE estimates an overall ATT of roughly -6% on the elasticity-scaled
  # female suicide rate, with a 95% confidence interval that excludes zero.
  # The selection step retains heterogeneous cohort effects (several cohorts
  # are pruned to exactly zero), rather than fusing to a single common effect.
  print(res, max_cohorts = Inf)
}
#> Warning: 9 units were removed because they were treated in the first time period: AK, LA, MD, NC, OK, UT, VA, VT, WV
#> Warning: 1 covariate(s) were removed because they contained missing values in the first time period for at least one unit:  murderrate
#> Fused Extended Two-Way Fixed Effects Results
#> ===========================================
#> 
#> Overall Average Treatment Effect (ATT):
#>   Estimate:   -0.0602
#>   Std. Error: 0.0188
#>   P-value:    0.001376
#>   Selected:   TRUE
#>   95% CI:    [-0.0970, -0.0233]
#> 
#> Cohort Average Treatment Effects (CATT) [simultaneous 95% CI]:
#>  cohort    estimate          se       ci_low      ci_high      p_value selected
#>    1969  0.00000000 0.000000000  0.000000000  0.000000000           NA    FALSE
#>    1970 -0.44401171 0.046498180 -0.572555501 -0.315467911 0.000000e+00     TRUE
#>    1971 -0.02633974 0.020112012 -0.081939211  0.029259735 8.474215e-01     TRUE
#>    1972 -0.01611957 0.009359074 -0.041992646  0.009753503 5.468636e-01     TRUE
#>    1973 -0.06452464 0.013062067 -0.100634602 -0.028414670 7.037395e-06     TRUE
#>    1974 -0.03001991 0.012978739 -0.065899516  0.005859696 1.707508e-01     TRUE
#>    1975  0.00000000 0.000000000  0.000000000  0.000000000           NA    FALSE
#>    1976 -0.04379642 0.063672429 -0.219818270  0.132225427 9.976219e-01     TRUE
#>    1977 -0.12389080 0.024178412 -0.190731799 -0.057049799 2.691903e-06     TRUE
#>    1980 -0.04013226 0.061547270 -0.210279123  0.130014613 9.984244e-01     TRUE
#>    1984  0.00000000 0.000000000  0.000000000  0.000000000           NA    FALSE
#>    1985  0.14972560 0.050875421  0.009080967  0.290370243 2.880518e-02     TRUE
#> 
#> Event-Study Average Treatment Effects (per event time) [simultaneous 95% CI]:
#>  event_time n_cohorts     estimate          se      ci_low    ci_high   p_value
#>           0        12  0.000000000 0.000000000  0.00000000 0.00000000        NA
#>           1        12  0.007021230 0.008967259 -0.01711252 0.03115498 0.9599013
#>           2        12  0.007021230 0.008967259 -0.01711252 0.03115498 0.9598298
#>           3        12 -0.002432030 0.012215187 -0.03530699 0.03044293 0.9999999
#>           4        12 -0.003617641 0.011148464 -0.03362171 0.02638642 0.9999595
#>           5        12 -0.003617641 0.011148464 -0.03362171 0.02638642 0.9999596
#>           6        12 -0.011132396 0.014720658 -0.05075037 0.02848558 0.9668442
#>           7        12 -0.021202910 0.015683174 -0.06341132 0.02100550 0.6427008
#>           8        12 -0.037944910 0.018119407 -0.08671000 0.01082018 0.1978968
#>           9        12 -0.037944910 0.018119407 -0.08671000 0.01082018 0.1982691
#>   ... and 22 more event times.
#> 
#> Model Details:
#>   Units (N)           : 42
#>   Time periods (T)    : 33
#>   Treated cohorts (G) : 12
#>   Covariates (d)      : 2
#>   Features (p)        : 908
#>   Selected size       : 38
#>   Lambda*             : 0.0004
# }