mlSC: Multi-level Synthetic Control Estimator

This package implements the multi-level SC estimator (mlSC) for the treatment effect for a single, treated, aggregated unit in panel data with multiple levels of aggregation, as proposed in Bottmer (2025). We observe matrices of outcomes at the disaggregate and the aggregate level. Treatment is assigned at the aggregate level and the goal is to obtain a treatment effect estimate at the aggregate level. The package captures cases for a single aggregated treated unit, possibly over multiple time periods (where treatment is assumed to never turn off). The multi-level SC estimator will use the disaggregated data as a starting point to estimate a synthetic control for the entire aggregated treated unit. It augments the objective function by adding a hierarchical penalty parameter that shrinks the flexible solution towards the classical synthetic control estimator that treats each state as a single unit. The penalty parameter is estimated using either (1) cross-validation over time or (2) a heuristic.

This package is currently in beta and the functionality and interface is subject to change.

Installation

Install this library using pip:

pip install multi-levelSC

Example

In this example, data at the county- and state-level is simulated from a hierarchical linear latent factor model. Then, the multi-level SC estimator is applied, using the heuristic to estimate the penalty parameter. Alternatively, if the user can use cross-validation over time by specifying "cross-validation" as the lambda_est method (and additionally a lambda_grid, if desired).

#####################
### Generate data ###
#####################

np.random.seed(42)

# --- Parameters ---
N_states = 10
counties_per_state = 10 # each state has the same number of counties in this example
n_c = np.full(N_states, counties_per_state)  # array of number of counties per state
T = 20

# Standard deviations for each component
sigma_time = 1.0       # time factor scale
sigma_state = 0.8      # state loading scale
sigma_county = 0.5     # county-level deviation scale
sigma_eps = 0.3        # idiosyncratic noise scale

# --- Generate latent factors ---
# Single time factor (T × 1)
time_factor = np.random.normal(0, sigma_time, size=(T, 1))

# State-level loadings (N_states × 1)
state_loadings = np.random.normal(0, sigma_state, size=(N_states, 1))

# County-level deviations (N_states * counties_per_state × 1)
n_counties = N_states * counties_per_state
county_components = np.random.normal(0, sigma_county, size=(n_counties, 1))

# --- Map counties to states ---
state_idx = np.repeat(np.arange(N_states), counties_per_state)
county_in_state_idx = np.tile(np.arange(counties_per_state), N_states)

# --- Combine state and county effects ---
county_loadings = state_loadings[state_idx] + county_components  # (n_counties × 1)

# --- Generate outcome matrix at disaggregate level ---
# data_c_{s,c,t} = county_loading_sc * time_factor_t + ε_{s,c,t}
eps = np.random.normal(0, sigma_eps, size=(n_counties, T))
data_c = county_loadings @ time_factor.T + eps  # (n_counties × T)

# --- Population weights within each state ---
# Each county gets equal weight = 1 / number of counties in its state
w_c = [np.full(n_c[s], 1 / n_c[s]) for s in range(N_states)] # IMPORTANT: this needs to be a list of arrays!

# --- Aggregate data by state using population weights ---
data_s = np.zeros((N_states, T))
for s in range(N_states):
    # Weighted average across all counties in state s
    counties_in_s = np.where(state_idx == s)[0]
    data_s[s, :] = np.average(data_c[counties_in_s, :], axis=0, weights=w_c[s])

# --- Treated unit and time period ---
idx = 0
t = 19

################
### Analysis ###
################

# Import estimator
from multi_level_sc_estimator.mlSC import mlSC_estimator

# Define data sets, treated unit, treated period, population weights (w_c) and how to estimate lambda.
mlSC_results = mlSC_estimator(data_s,data_c, idx, n_c, t, w_c, lambda_est = "heuristic")

# Display results
tau_hat = mlSC_results[0]
lambda_hat = mlSC_results[1]
w_hat = mlSC_results[2]

References

Lea Bottmer. Synthetic Control with Disaggregated Data, 2025. [link]