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Introduction to SCMs: Synthetic Control Methods with Specification Curve Analysis

SCMs Package Authors

2026-10-22

Introduction

The SCMs package provides a comprehensive implementation of synthetic control methods with advanced specification curve analysis and machine learning integration. This vignette introduces the key concepts and basic usage patterns.

What are Synthetic Control Methods?

Synthetic control methods allow researchers to estimate the causal effect of an intervention on a treated unit by constructing a “synthetic” version of the treated unit using a weighted combination of control units. The method is particularly useful for:

Policy evaluation with a single treated unit (e.g., a state, country, or firm)
Settings where randomized experiments are not feasible
Time series data with pre- and post-treatment periods

Why Specification Curve Analysis?

Traditional synthetic control studies typically present results from a single specification. However, researchers must make many modeling choices:

Which pre-treatment characteristics to match on?
How to aggregate covariates over time?
Which optimization constraints to use?
What feature weighting scheme to employ?

Specification curve analysis systematically varies these choices and examines the distribution of treatment effect estimates across all reasonable specifications. This approach:

Increases transparency by showing the full range of plausible estimates
Assesses robustness by revealing whether conclusions depend on specific choices
Identifies drivers of variation in results through SHAP value analysis

Package Highlights

The SCMs package offers several innovations:

Comprehensive specification spaces: Systematically vary modeling choices
SHAP integration: Use machine learning to understand what drives variation in results
Advanced inference: Both Abadie placebo tests and bootstrap methods
Performance optimization: Handle large specification curves efficiently
Professional visualization: Publication-ready plots with ggplot2

Basic Workflow

A typical analysis follows this pattern:

Prepare data: Panel data in long format
Run specification curve: Systematically vary modeling choices
Visualize results: Examine the distribution of treatment effects
Interpret patterns: Use SHAP values to understand variation
Draw conclusions: Assess robustness and policy implications

Quick Start Example

Let’s demonstrate the package with a simple example using simulated data.

library(SCMs)
library(data.table)
library(ggplot2)

# For reproducibility
set.seed(123)

Create Example Data

# Create panel data for demonstration
states <- c("California", "Texas", "New York", "Florida", "Illinois")
years <- 1990:2010

# Generate full panel
panel_data <- expand.grid(
  state = states,
  year = years,
  stringsAsFactors = FALSE
)

# Convert to data.table for efficiency
setDT(panel_data)

# Add outcome variable with treatment effect for California after 2000
panel_data[, gdp := 100 + (year - 1990) * 1.5 + rnorm(.N, 0, 3)]
panel_data[state == "California" & year > 2000, gdp := gdp + 8]

# Add covariates
panel_data[, population := 1000 + (year - 1990) * 50 + rnorm(.N, 0, 100)]
panel_data[, investment := 20 + gdp * 0.15 + rnorm(.N, 0, 5)]

# Display sample of data
head(panel_data, 10)
#>          state  year       gdp population investment
#>         <char> <int>     <num>      <num>      <num>
#>  1: California  1990  98.31857   995.4972   35.34401
#>  2:      Texas  1990  99.30947   921.5096   36.11486
#>  3:   New York  1990 104.67612   833.2058   41.86380
#>  4:    Florida  1990 100.21153   961.9773   32.45141
#>  5:   Illinois  1990 100.38786  1091.8997   30.09564
#>  6: California  1991 106.64519   992.4653   44.37526
#>  7:      Texas  1991 102.88275  1110.7964   33.22660
#>  8:   New York  1991  97.70482   888.2117   31.04039
#>  9:    Florida  1991  99.43944  1044.4438   28.73455
#> 10:   Illinois  1991 100.16301  1101.9407   28.60087

Basic Synthetic Control Analysis

Let’s start with a single specification to understand the core methodology:

# Prepare synthetic control data
scdata_result <- scdata(
  df = panel_data,
  id.var = "state",
  time.var = "year", 
  outcome.var = "gdp",
  period.pre = 1990:2000,
  period.post = 2001:2010,
  unit.tr = "California",
  unit.co = c("Texas", "New York", "Florida", "Illinois"),
  covagg = list(
    list(var = "population"),
    list(var = "investment")
  )
)

# Estimate synthetic control weights
scest_result <- scest(
  data = scdata_result,
  w.constr = list(name = "simplex"),
  feature_weights = "uniform"
)

# View results
print(scest_result)
summary(scest_result)

Specification Curve Analysis

Now let’s examine robustness by varying multiple modeling choices:

# Define covariate specifications to test
covariate_specs <- list(
  # Basic specification
  basic = list(
    label = "basic",
    operations = list(
      list(var = "population", compute = "mean"),
      list(var = "investment", compute = "mean")
    )
  ),
  
  # Include outcome lags
  with_lags = list(
    label = "with_lags", 
    operations = list(
      list(var = "outcome_var", partition_periods = list(type = "by_period")),
      list(var = "population", compute = "mean"),
      list(var = "investment", compute = "mean")
    )
  ),
  
  # Population only
  population_only = list(
    label = "population_only",
    operations = list(
      list(var = "population", compute = "mean")
    )
  )
)

# Run specification curve analysis
analysis_params <- list(
  outcomes = "gdp",
  covagg = covariate_specs,
  col_name_unit_name = "state",
  name_treated_unit = "California",
  treated_period = 2001,
  min_period = 1990,
  end_period = 2010,
  col_name_period = "year",
  feature_weights = c("uniform", "optimize"),
  outcome_models = c("none", "ridge"),
  constraints = list(
    list(name = "simplex"),
    list(name = "lasso", Q = 0.1)
  ),
  donor_sample = "all",
  constants = FALSE,
  inference_type = "placebo",
  inference_config = list(verbose = TRUE)
)

spec_results <- run_spec_curve_analysis(
  dataset = panel_data,
  params = analysis_params,
  cores = 1  # Use 1 core for vignette
)

# View specification curve
plot(spec_results)

Understanding the Output

Treatment Effect Distribution

The specification curve shows:

X-axis: Individual specifications (sorted by effect size)
Y-axis: Treatment effect estimates
Points: Each specification’s estimate
Colors: SHAP values indicating which features drive the estimates

Key Interpretations

Central tendency: Where do most estimates cluster?
Range: How wide is the distribution of plausible effects?
Outliers: Are there specifications with very different results?
Patterns: Do certain modeling choices systematically affect results?

Statistical Inference

The package provides two inference approaches:

Abadie Placebo Tests: Compare treated unit’s post/pre RMSPE ratio to control units
Bootstrap Methods: Construct null distributions for hypothesis testing

SHAP Value Interpretation

SHAP (SHapley Additive exPlanations) values help understand:

Which pre-treatment features are most predictive
How feature importance varies across specifications
Whether results are driven by specific covariates

Next Steps

This introduction covered the basic concepts and workflow. To learn more:

Complete Workflow vignette: Step-by-step analysis with real data
Advanced Features vignette: Customization, optimization, and extensions
Package documentation: help(package = "SCMs")

The synthetic control method with specification curve analysis provides a powerful framework for causal inference with observational data. The SCMs package makes these advanced methods accessible while maintaining statistical rigor and computational efficiency.

References

Abadie, A., Diamond, A., & Hainmueller, J. (2010). Synthetic control methods for comparative case studies. Journal of the American Statistical Association, 105(490), 493-505.
Simonsohn, U., Simmons, J. P., & Nelson, L. D. (2020). Specification curve analysis. Nature Human Behaviour, 4(11), 1208-1214.
Ben-Michael, E., Feller, A., & Rothstein, J. (2021). The augmented synthetic control method. Journal of the American Statistical Association, 116(536), 1789-1803.

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They may not be fully stable and should be used with caution. We make no claims about them.
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