MSC.jl

MSC.jl implements multivariate synthetic control for high-dimensional disaggregated panels. It is designed for settings with many treated units and many controls where fitting one synthetic-control model per treated unit is expensive.

The package includes:

• fit_msc and predict_counterfactual for matrix-level MSC estimation.
• msc_estimate for panel-matrix and long-table ATT estimation.
• panel_matrices for balanced common-adoption panel conversion.
• Cross-validated regularization over the MSC penalty path.
• Treated-unit counterfactuals, effect curves, unit effects, and weight tables.
• Time-placebo and control-unit placebo routines.
• A lightweight RecipesBase plotting recipe.
• Synthetic data generators and a paper-application replication scaffold.

Where To Start

• Use Getting Started for the matrix API.
• Use DataFrame Panels for long panel data.
• Use Paper Application for the county-unemployment application from Shen, Song, and Abadie.
• Use Examples for runnable scripts.

The paper application script uses the local BLS data file and prints the replication comparison directly:

control counties       MSC.jl 438     paper 438
treated counties       MSC.jl 2674    paper 2,674
pre-treatment months   MSC.jl 147     paper 147
April 2020 ATT, pp     MSC.jl 4.9552  paper 5.06

The estimator fits

Y_pre = X_pre * Theta + E

with the sparse multivariate square-root Lasso objective

min_Theta (1 / sqrt(T0)) * ||Y_pre - X_pre * Theta||_* + lambda * ||Theta||_1

where X_pre is T0 x n_controls, Y_pre is T0 x n_treated, and Theta maps control outcomes to treated-unit counterfactuals.

Installation

using Pkg
Pkg.add(url = "https://github.com/xiangao/MSC.jl")

For local development:

using Pkg
Pkg.develop(path = "/home/xao/projects/software/MSC.jl")

Quick Start

using MSC
using Statistics

sim = simulate_msc(ncontrols = 20, ntreated = 5, T0 = 50, T1 = 6, tau = 1.2, seed = 1)

est = msc_estimate(
    sim.Y,
    sim.N0,
    sim.T0;
    nlambda = 8,
    nfolds = 4,
    max_iter = 800,
    tol = 1e-6,
)

round(est.estimate, digits = 3)

1.179

The fitted object stores treated-unit counterfactuals and diagnostics:

(
    effects = round.(unit_effects(est), digits = 3),
    prefit = round(prefit_rmse(est.fit, sim.Y[1:sim.N0, 1:sim.T0]', sim.Y[(sim.N0 + 1):end, 1:sim.T0]'), digits = 3),
    nonzero_weights = size(weights_table(est; atol = 1e-8), 1),
)

(effects = [1.184, 1.183, 1.165, 1.195, 1.167], prefit = 0.047, nonzero_weights = 22)

See the vignettes and examples pages for complete workflows.