Performing the synthetic control method using glmnet. This allows easily validating the model using LOOCV

lasso_synthetic_control.R

# Implementing synthetic control using glmnet
library(tidyverse)
library(tidysynth)
library(glmnet)

# we need a wide dataset, only cigsale
smoking_w <- 
  smoking |> 
  select(state, year, cigsale) |> 
  pivot_wider(names_from = state, values_from = cigsale)

# LOOCV LASSO
X_pre <- model.matrix(California ~ . - year + 0, data = smoking_w |> filter(year <= 1988))
X_post <- model.matrix(California ~ . - year + 0, data = smoking_w |> filter(year > 1988))
y_pre <- smoking_w |> filter(year <= 1988) |> pull(California)
y_post <- smoking_w |> filter(year > 1988) |> pull(California)

cv.fit <- cv.glmnet(X_pre, y_pre, lower.limits = 0, upper.limits = 1, nfolds = nrow(X_pre), grouped = FALSE)
yhat <- predict(cv.fit, newx = rbind(X_pre, X_post), s = "lambda.1se")

plot(x = 1970:2000, y = c(y_pre, y_post), type = "l", xlab = "Year", ylab = "Cigarette sales", 
     main = "Synthetic control using LASSO", bty = "L")
lines(x = 1970:2000, y = yhat, lty = 2)
mtext("With leave-one-out cross-validation", line = 0.5)
text(2000, tail(y_post, 1), "California", c(1.15, 0))
text(2000, tail(yhat, 1), "Synthetic California", c(1.15, 0))