augsynth: Augmented Synthetic Control Method

The augsynth package implements the Augmented Synthetic Control Method (ASCM) through three distinct approaches depending on your experimental design:

1. single_augsynth: Used for the classic synthetic control approach involving a single treated unit.
2. multisynth: Used when estimating treatment effects for multiple treated units with staggered adoption.
3. augsynth_multiout: Used for a single treated unit when there are multiple outcomes to analyze.

You can include additional covariates to balance simultaneously with the pre-treatment outcomes by adding them to the formula after a pipe (|) symbol.

Usage:

• Formula format: outcome ~ treatment | covariate1 + covariate2.
• If covariates vary during pre-treatment periods, multisynth uses their average pre-treatment value by default.
• Use the cov_agg argument to provide a custom aggregation function if the default average is not desired.

Note: The auxiliary covariates must be present in the dataframe passed to multisynth().

# Example: Including per capita income and student-teacher ratio as covariates
ppool_syn_cov <- multisynth(lnppexpend ~ cbr | perinc_1959 + studteachratio_1959,
                            State, year, analysis_df_covs)

To install the augsynth package, you need the devtools package. You can install devtools from CRAN and then use devtools::install_github() to pull the latest version of augsynth directly from the GitHub repository.

# Install devtools if not already installed
install.packages("devtools", repos='http://cran.us.r-project.org')
# Install augsynth from github
devtools::install_github("ebenmichael/augsynth")

To use the multisynth function for estimating treatment effects with staggered adoption, your dataset must include a treatment status column. This column should indicate whether a unit (e.g., a state) is treated in a specific year.

In the provided example, a column cbr is created where a value of 1 indicates the unit is under treatment and 0 indicates it is not. Additionally, ensure that the year the treatment was adopted is represented (e.g., using Inf for units that are never treated) to facilitate logical comparisons.

library(magrittr)
library(dplyr)
library(augsynth)

# Example data preparation
data %>%
    filter(!State %in% c("DC", "WI"),
           year >= 1959, year <= 1997) %>%
    mutate(YearCBrequired = ifelse(is.na(YearCBrequired), 
                                   Inf, YearCBrequired),
           cbr = 1 * (year >= YearCBrequired)) -> analysis_df

You can include auxiliary covariates in the augmentation by adding them to the formula after a pipe |.

• Aggregation: By default, time-invariant covariates are created by averaging the auxiliary covariates over the pre-intervention period (dropping NA values). Use cov_agg to specify a custom aggregation function.
• Mechanism: The lagged outcomes and auxiliary covariates are jointly balanced by the SCM, and the ridge outcome model includes both.

# Include covariates in the formula
covsyn <- augsynth(lngdpcapita ~ treated | lngdpcapita + log(revstatecapita) + 
                                           log(revlocalcapita) + log(avgwklywagecapita) + 
                                           estabscapita + emplvlcapita,
                   fips, year_qtr, kansas,
                   progfunc = "ridge", scm = TRUE)

To fit ridge ASCM on the residuals of the initial model, use the residualize = TRUE argument. You can pass the lambda value from a previous augmentation to ensure consistency.

# Fit on residuals using lambda from a previous model (asyn)
covsyn_resid <- augsynth(lngdpcapita ~ treated | lngdpcapita + log(revstatecapita) + 
                                           log(revlocalcapita) + log(avgwklywagecapita) + 
                                           estabscapita + emplvlcapita,
                   fips, year_qtr, kansas,
                   progfunc = "ridge", scm = TRUE, 
                   lambda = asyn$lambda,
                   residualize = TRUE)

To reduce L2 imbalance, you can augment the synthetic control with an outcome model. Setting progfunc = "Ridge" fits a ridge regression model.

• Hyperparameter Tuning: If lambda is not specified, it is determined via cross-validation.
• Cross-Validation: You can visualize the cross-validation MSE by setting plot_type = "cv" in the plot() function.
• CV Selection: By default, the procedure selects the maximal lambda with MSE within one standard deviation of the minimal MSE. To select the lambda that strictly minimizes the CV MSE, set min_1se = FALSE.

# Augment with Ridge regression
asyn <- augsynth(lngdpcapita ~ treated, fips, year_qtr, kansas,
                progfunc = "Ridge", scm = TRUE)

# Plot cross-validation MSE
plot(asyn, plot_type = "cv")

To perform an Augmented Synthetic Control analysis, prepare a panel dataset containing the following variables:

• outcome: The measure of interest.
• trt: The treatment indicator.
• unit: The unit indicator.
• time: The time variable.
• t_int: The intervention time.

Use the augsynth function with a formula interface to estimate the effect.

asyn <- augsynth(outcome ~ trt, unit, time, t_int, data)

After fitting a model with multisynth(), use the summary() function to compute treatment effects (ATT), standard errors, and confidence intervals using the wild bootstrap.

Arguments:

• alpha: The significance level for confidence intervals (default is 0.05).

Output:

• The summary object contains global and individual L2 imbalance metrics.
• The $att component is a dataframe containing point estimates, standard errors, and confidence limits.
• In the att dataframe, Time = NA represents the effect averaged across all post-treatment periods.

# Compute effects and confidence intervals
ppool_syn_summ <- summary(ppool_syn)

# Access the ATT dataframe
att_data <- ppool_syn_summ$att

To find a synthetic control using only pre-intervention outcomes (without auxiliary covariates), use the augsynth() function. You must provide a formula in the form outcome ~ treatment, the unit identifier, the time variable, and the dataset. Setting progfunc = "None" and scm = TRUE performs a standard Synthetic Control Method (SCM) fit.

Note: If t_int (intervention time) is not provided, the code will attempt to automatically determine it from the treatment column.

library(augsynth)
# Basic SCM fit
syn <- augsynth(lngdpcapita ~ treated, fips, year_qtr, kansas,
                progfunc = "None", scm = TRUE)

A simple outcome model is the unit fixed effect model. This can be included by setting fixedeff = TRUE in the augsynth() call.

# Augment with unit fixed effects
desyn <- augsynth(lngdpcapita ~ treated, fips, year_qtr, kansas,
                   progfunc = "none", scm = TRUE, fixedeff = TRUE)