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Fast Interactive Fixed Effects (IFE) for Generalized Synthetic Control

Source: R/RcppExports.R
gsc_ife_cpp.Rd

Implements Xu (2017) IFE model with optional covariate adjustment and optional additive fixed effects (Xu 2017, Remark 3). When X_co has p > 0 slices, alternates the two steps of Bai (2009): factors: truncated SVD of Y_tilde = Y_co - X_co * beta beta: inverse(sum_i X_i' M_F X_i) sum_i X_i' M_F Y_i, with the loadings concentrated out through the annihilator M_F of the factors When X_co has 0 slices (default), falls back to the plain 3-step estimator. Additive effects are swept out of the control panel by the within transformation first; on a balanced panel this solves the joint least squares problem exactly, and the effects are recovered from the means of the residual.

Usage

gsc_ife_cpp(
  Y_co,
  Y_tr_pre,
  r,
  X_co,
  X_tr_pre,
  max_iter = 1000L,
  tol = 1e-08,
  force = "none"
)

Arguments

Y_co

Control units outcome matrix (T x N_co)

Y_tr_pre

Treated units pre-treatment outcomes (T_pre x N_tr)

r

Number of latent factors (must be <= min(T, N_co)); 0 is allowed with additive effects

X_co

Time-varying covariate cube (T x N_co x p). Pass an empty cube (0 slices) for the covariate-free estimator.

X_tr_pre

Time-varying covariate cube for treated units in the pre-treatment window (T_pre x N_tr x p). Required for correct Step 2 loading estimation per Xu (2017): lambda_hat is estimated from Y_tr_pre - X_tr_pre * beta (covariate- demeaned). Pass an empty cube (0 slices) to skip demeaning (backward-compatible, but biased when beta != 0).

max_iter

Maximum iterations of the covariate loop (default 1000)

tol

Convergence tolerance on relative beta change (default 1e-8)

force

Additive fixed effects: "none" (default), "unit", "time" or "two-way".

Value

A list with components:

  • F: estimated time factors (T x r).

  • L_co: control-unit factor loadings (N_co x r).

  • L_tr: treated-unit factor loadings (N_tr x r).

  • Y_tr_hat: estimated treated-unit counterfactual outcomes (T x N_tr), additive effects included, covariate contribution excluded.

  • Y_co_hat: fitted control outcomes on the same basis (T x N_co).

  • singular_values: singular values from the final truncated SVD.

  • beta: estimated covariate coefficients (p x 1), empty when no covariates are supplied.

  • mu, alpha_co, alpha_tr, xi: grand mean, unit effects of the control and treated units, and time effects (zero where force leaves them out).

  • n_iter: iterations of the covariate loop (0 without covariates).

  • converged: whether the covariate loop met tol within max_iter (always TRUE without covariates).