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scpi_illustration.R
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scpi_illustration.R
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################################################################################
## SCPI R Package
## R-file for Empirical Illustration - Single Treated Unit
## Authors: Matias D. Cattaneo, Yingjie Feng, Filippo Palomba and Rocio Titiunik
################################################################################
### Clear R environment
rm(list = ls(all = TRUE))
### Install R library
# install.packages('scpi')
### Load SCPI package
library(scpi)
library(ggplot2)
library(latex2exp)
###############################################################################
# SINGLE TREATED UNIT
###############################################################################
### Load data
data <- scpi_germany
####################################
### Set options for data preparation
id.var <- "country" # ID variable
time.var <- "year" # Time variable
period.pre <- seq(from = 1960, to = 1990, by = 1) # Pre-treatment period
period.post <- (1991:2003) # Post-treatment period
unit.tr <- "West Germany" # Treated unit (in terms of id.var)
unit.co <- setdiff(unique(data$country), unit.tr) # Donors pool
outcome.var <- "gdp" # Outcome variable
cov.adj <- NULL # Covariates for adjustment
features <- NULL # No features other than outcome
constant <- FALSE # No constant term
report.missing <- FALSE # To check where missing values are
cointegrated.data <- TRUE # Belief that the data are cointegrated
####################################
### Data preparation
df <- scdata(df = data, id.var = id.var, time.var = time.var, outcome.var = outcome.var,
period.pre = period.pre, period.post = period.post,
unit.tr = unit.tr, unit.co = unit.co, cov.adj = cov.adj, features = features,
constant = constant, cointegrated.data = cointegrated.data)
####################################
### SC - point estimation with simplex
est.si <- scest(data = df, w.constr = list(name="simplex"))
# Use print or summary methods to check results
print(est.si)
summary(est.si)
est.si2 <- scest(data = df, w.constr = list(p = "L1", dir = "==", Q = 1, lb = 0))
summary(est.si2)
####################################
### SC - plot results
scplot(result = est.si, fig.path = ".",
fig.name = "germany_est", fig.format = "png", plot.range = (1960:2003),
label.xy = list(x.lab = "Year", y.lab = "GDP per capita (thousand US dollars)"),
event.label = list(lab = "Reunification", height = 10))
####################################
### SC - point estimation with lasso
est.lasso <- scest(data = df, w.constr = list(name="lasso"))
summary(est.lasso)
est.lasso2 <- scest(data = df, w.constr = list(p = "L1", dir = "<=", Q = 1, lb = -Inf),
solver="OSQP")
summary(est.lasso2)
####################################
### SC - point estimation with ridge
est.ridge <- scest(data = df, w.constr = list(name="ridge"))
summary(est.ridge)
Qest <- est.ridge$est.results$w.constr$Q
est.ridge2 <- scest(data = df, w.constr = list(p = "L2", dir = "<=", Q = Qest, lb = -Inf))
summary(est.ridge2)
####################################
### SC - point estimation with L1-L2
est.l1l2 <- scest(data = df, w.constr = list(name="L1-L2"))
summary(est.l1l2)
est.l1l2.2 <- scest(data = df, w.constr = list(p = "L1-L2", dir = "==/<=", Q = 1,
Q2 = Qest, lb = 0))
summary(est.l1l2.2)
####################################
### SC - point estimation with least squares
est.ls <- scest(data = df, w.constr = list(name="ols"))
summary(est.ls)
est.ls2 <- scest(data = df, w.constr = list(p = "no norm", dir = NULL, Q = NULL, lb = -Inf))
summary(est.ls2)
####################################
## Set options for inference
u.alpha <- 0.05 # Confidence level (in-sample uncertainty)
e.alpha <- 0.05 # Confidence level (out-of-sample uncertainty)
rho <- NULL # Regularization parameter (if NULL it is estimated)
rho.max <- 1 # Maximum value attainable by rho
sims <- 200 # Number of simulations
u.order <- 1 # Degree of polynomial in B and C when modelling u
u.lags <- 0 # Lags of B to be used when modelling u
u.sigma <- "HC1" # Estimator for the variance-covariance of u
u.missp <- T # If TRUE then the model is treated as misspecified
e.lags <- 0 # Degree of polynomial in B and C when modelling e
e.order <- 1 # Lags of B to be used when modelling e
e.method <- "gaussian" # Estimation method for out-of-sample uncertainty
cores <- 1 # Number of cores to be used by scpi
w.constr <- list(name = "simplex") # Simplex-type constraint set
set.seed(8894)
pi.si <- scpi(data = df,u.order = u.order, u.lags = u.lags, u.sigma = u.sigma,
u.missp = u.missp, sims = sims, e.order = e.order, e.lags = e.lags,
e.method = e.method, cores = cores, w.constr = w.constr, u.alpha = u.alpha,
e.alpha = e.alpha, rho = rho, rho.max = rho.max)
# Use print or summary methods to check results
print(pi.si)
summary(pi.si)
####################################
### SC - plot results
scplot(result = pi.si, fig.path = ".",
fig.name = "germany_unc", fig.format = "png", plot.range = (1960:2003),
label.xy = list(x.lab = "Year", y.lab = "GDP per capita (thousand US dollars)"),
x.ticks = NULL, e.out = T, event.label = list(lab = "Reunification", height = 10))
########################################################
# Sensitivity Analysis for 1997 using subgaussian bounds
########################################################
set.seed(8894)
res.si <- scpi(data = df, sims = sims, e.method = "gaussian", e.order = e.order, e.lags = e.lags,
u.order = u.order, u.lags = u.lags, u.sigma = u.sigma, u.missp = u.missp,
cores = cores, w.constr = list(name = "simplex"), lgapp = "linear")
e.alpha <- 0.05 # default level in scpi
sens <- c(0.25, 0.5, 1, 1.5, 2)
time <- c(1997)
emean <- res.si$inference.results$e.mean
esig <- sqrt(res.si$inference.results$e.var)
sc.l.0 <- res.si$inference.results$CI.in.sample[,1,drop = F]
sc.r.0 <- res.si$inference.results$CI.in.sample[,2,drop = F]
y <- res.si$data$Y.post
for (l in 1:length(time)) {
ssc.l.1 <- ssc.r.1 <- c()
e.mean <- emean[time[l]-1990]
sig <- esig[time[l]-1990]
sig.seq <- sens * sig
for (s in 1:length(sig.seq)) {
eps <- sqrt(-log(e.alpha/2)*2*(sig.seq[s]^2))
ssc.l.1[s] <- sc.l.0[time[l]-1990] + e.mean - eps
ssc.r.1[s] <- sc.r.0[time[l]-1990] + e.mean + eps
}
sen.dat <- data.frame(t=c(1:5), lb1=ssc.l.1, ub1=ssc.r.1,
lb=rep(sc.l.0[time[l]-1990], 5),
ub=rep(sc.r.0[time[l]-1990], 5),
lab=as.factor(sens))
plot <- ggplot() + theme_bw() +
theme(panel.grid.major = element_blank(),
panel.grid.minor = element_blank()) +
labs(x="sd. of e", y="GDP per capita (thousand US dollars)")
plot <- plot + geom_errorbar(data=sen.dat, aes(x=lab, ymin=lb1, ymax=ub1),
col="maroon", width=0.2, linetype=5) +
geom_errorbar(data=sen.dat, aes(x=lab, ymin=lb, ymax=ub),
col="blue", width=0.2, linetype=1) +
geom_hline(yintercept = y[time[l]-1990], linetype=1, linewidth=0.3, alpha=0.8) +
annotate("text", x=5.4, y=y[time[l]-1990]-.1,label="Y(1)", size=3.5) +
scale_x_discrete(labels=c(parse(text=TeX("$0.25\\hat{\\sigma}$")),
parse(text=TeX("$0.5\\hat{\\sigma}$")),
parse(text=TeX("$\\hat{\\sigma}$")),
parse(text=TeX("$1.5\\hat{\\sigma}$")),
parse(text=TeX("$2\\hat{\\sigma}$"))))
}
################################################################################
### Other examples of data preparation
## multiple features
df <- scdata(df = data, id.var = id.var, time.var = time.var, outcome.var = outcome.var,
period.pre = period.pre, period.post = period.post,
unit.tr = unit.tr, unit.co = unit.co, cov.adj = cov.adj, features = c("gdp", "trade"),
constant = constant, cointegrated.data = cointegrated.data)
## multiple features and feature-specific covariate adjustment
df <- scdata(df = data, id.var = id.var, time.var = time.var, outcome.var = outcome.var,
period.pre = period.pre, period.post = period.post,
unit.tr = unit.tr, unit.co = unit.co, features = c("gdp", "trade"),
cov.adj = list('gdp' = c("constant","trend"), 'trade' = c("constant")),
constant = constant, cointegrated.data = cointegrated.data)
## multiple features and feature-specific covariate adjustment (just for one of the two features)
df <- scdata(df = data, id.var = id.var, time.var = time.var, outcome.var = outcome.var,
period.pre = period.pre, period.post = period.post,
unit.tr = unit.tr, unit.co = unit.co, features = c("gdp", "trade"),
cov.adj = list('gdp' = c("constant","trend"), 'trade' = c()),
constant = constant, cointegrated.data = cointegrated.data)
## Specifying features for different pre-treatment periods or just use pre-treatment averages
# I) we want to include "trade" just for some selected periods, i.e., 1960, 1970, 1980, 1990
tradeUnselPeriods <- setdiff(period.pre, seq(1960, 1990, by = 10)) # period NOT to be included
data$tradeAux <- data$trade # copy of the feature of interest
data$tradeAux[data$year %in% tradeUnselPeriods] <- NA
df <- scdata(df = data, id.var = id.var, time.var = time.var, outcome.var = outcome.var,
period.pre = period.pre, period.post = period.post,
unit.tr = unit.tr, unit.co = unit.co, features = c("gdp", "tradeAux"),
cov.adj = list('gdp' = c("constant","trend"), 'tradeAux' = c("constant")),
constant = constant, cointegrated.data = cointegrated.data)
df$B
# II) we want to include just the pre-treatment average of "infrate"
dataAux <- subset(data, year <= 1990) # select just pre-treatment periods
dataAuxAgg <- aggregate(dataAux$infrate, by = list(dataAux$country), FUN = mean, na.rm = TRUE) # take average
names(dataAuxAgg) <- c("country", "infrateAvg")
data <- merge(data, dataAuxAgg, by = c("country")) # merge back
data$infrateAvg[data$year != 1990] <- NA # any period would work, 1990 is arbitrary
df <- scdata(df = data, id.var = id.var, time.var = time.var, outcome.var = outcome.var,
period.pre = period.pre, period.post = period.post,
unit.tr = unit.tr, unit.co = unit.co, features = c("gdp", "infrateAvg"),
cov.adj = list("gdp" = c("constant", "trend")),
constant = constant, cointegrated.data = cointegrated.data)
df$B