├── .DS_Store ├── .Rbuildignore ├── .gitignore ├── DESCRIPTION ├── LICENSE ├── Meta └── vignette.rds ├── NAMESPACE ├── R ├── conformal.R ├── estimators.R ├── scinference.R └── ttest.R ├── README.md ├── man └── scinference.Rd ├── scinference.Rproj └── vignettes ├── .DS_Store └── scinference.Rmd /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/kwuthrich/scinference/567c6889ce0a1d269a62d415b88aa6baf723a3fe/.DS_Store -------------------------------------------------------------------------------- /.Rbuildignore: -------------------------------------------------------------------------------- 1 | ^.*\.Rproj$ 2 | ^\.Rproj\.user$ 3 | ^doc$ 4 | ^Meta$ 5 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | .Rproj.user 2 | .Rhistory 3 | .RData 4 | .Ruserdata 5 | doc 6 | Meta 7 | -------------------------------------------------------------------------------- /DESCRIPTION: -------------------------------------------------------------------------------- 1 | Package: scinference 2 | Title: Inference for synthetic controls 3 | Version: 0.0.0.9000 4 | Authors@R: 5 | person(given = "Kaspar", 6 | family = "Wuthrich", 7 | role = c("aut", "cre"), 8 | email = "kwuthrich@ucsd.edu") 9 | Description: This package implements inference procedures for conformal inference. 10 | License: use_gpl3_license() 11 | Encoding: UTF-8 12 | LazyData: true 13 | Roxygen: list(markdown = TRUE) 14 | RoxygenNote: 7.1.1 15 | Imports: 16 | limSolve, 17 | CVXR 18 | Suggests: 19 | knitr, 20 | rmarkdown 21 | VignetteBuilder: knitr 22 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /Meta/vignette.rds: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/kwuthrich/scinference/567c6889ce0a1d269a62d415b88aa6baf723a3fe/Meta/vignette.rds -------------------------------------------------------------------------------- /NAMESPACE: -------------------------------------------------------------------------------- 1 | # Generated by roxygen2: do not edit by hand 2 | 3 | export(scinference) 4 | -------------------------------------------------------------------------------- /R/conformal.R: -------------------------------------------------------------------------------- 1 | # Moving block permutations 2 | movingblock <- function(Y1,Y0,T1,T0,theta0,estimation_method,lsei_type){ 3 | T01 <- T0+T1 4 | 5 | Y1_0 <- Y1 6 | Y1_0[(T0+1):T01] <- Y1[(T0+1):T01]-theta0 7 | 8 | if (estimation_method=="classo"){ 9 | u.hat <- classo(Y1_0,Y0)$u.hat 10 | } 11 | if (estimation_method=="sc"){ 12 | u.hat <- sc(Y1_0,Y0,lsei_type)$u.hat 13 | } 14 | if (estimation_method=="did"){ 15 | u.hat <- did(Y1_0,Y0)$u.hat 16 | } 17 | sub.size <- T1 18 | u.hat.c <- c(u.hat,u.hat) 19 | S.vec <- matrix(NA,T01,1) 20 | for (s in 1:(T01)){ 21 | S.vec[s,1] <- sum(abs(u.hat.c[s:(s+sub.size-1)])) 22 | } 23 | p <- mean(S.vec>=S.vec[T0+1]) 24 | return(p) 25 | } 26 | 27 | # All/iid permutations (use random subsample of size n_perm all permutations) 28 | iid <- function(Y1,Y0,T1,T0,theta0,estimation_method,n_perm,lsei_type){ 29 | T01 <- T0+T1 30 | 31 | Y1_0 <- Y1 32 | Y1_0[(T0+1):T01] <- Y1[(T0+1):T01]-theta0 33 | 34 | if (estimation_method=="classo"){ 35 | u.hat <- classo(Y1_0,Y0)$u.hat 36 | } 37 | if (estimation_method=="sc"){ 38 | u.hat <- sc(Y1_0,Y0,lsei_type)$u.hat 39 | } 40 | if (estimation_method=="did"){ 41 | u.hat <- did(Y1_0,Y0)$u.hat 42 | } 43 | post.ind <- ((T0+1):T01) 44 | pre.ind <- (1:T0) 45 | S.vec <- matrix(NA,n_perm,1) 46 | 47 | Sq <- sum(abs(u.hat[post.ind])) 48 | for (r in 1:n_perm){ 49 | u.hat.p <- u.hat[sample(1:T01,replace=F)] 50 | S.vec[r,1] <- sum(abs(u.hat.p[post.ind])) 51 | } 52 | p <- 1/(n_perm+1)*(1+sum(S.vec>=Sq)) 53 | return(p) 54 | } 55 | 56 | # Confidence interval via test inversion 57 | confidence_interval <- function(Y1,Y0,T1,T0,estimation_method,alpha,ci_grid,lsei_type){ 58 | 59 | lb <- ub <- rep(NA,T1) 60 | for (t in 1:T1){ 61 | indices <- c(1:T0,T0+t) 62 | Y1_temp <- Y1[indices] 63 | Y0_temp <- Y0[indices,] 64 | 65 | ps_temp <- rep(NA,length(ci_grid)) 66 | for (ind in 1:length(ci_grid)){ 67 | Y1_0_temp <- Y1_temp 68 | Y1_0_temp[(T0+1)] <- Y1_temp[(T0+1)] - ci_grid[ind] 69 | if (estimation_method=="classo"){ 70 | u_hat <- classo(Y1_0_temp,Y0_temp)$u.hat 71 | } 72 | if (estimation_method=="sc"){ 73 | u_hat <- sc(Y1_0_temp,Y0_temp,lsei_type)$u.hat 74 | } 75 | if (estimation_method=="did"){ 76 | u_hat <- did(Y1_0_temp,Y0_temp)$u.hat 77 | } 78 | ps_temp[ind] <- mean(abs(u_hat)>=abs(u_hat[(T0+1)])) 79 | } 80 | ci_temp <- ci_grid[ps_temp>alpha] 81 | lb[t] <- min(ci_temp,na.rm=TRUE) 82 | ub[t] <- max(ci_temp,na.rm=TRUE) 83 | } 84 | 85 | return(list(lb=lb,ub=ub)) 86 | } 87 | -------------------------------------------------------------------------------- /R/estimators.R: -------------------------------------------------------------------------------- 1 | # difference-in-differences 2 | did <- function(Y1,Y0){ 3 | u.hat <- Y1 - mean(Y1-rowMeans(Y0)) - rowMeans(Y0) 4 | return(list(u.hat=u.hat)) 5 | } 6 | 7 | # synthetic control 8 | sc <- function(Y1,Y0,lsei_type){ 9 | J <- dim(Y0)[2] 10 | e <- matrix(1,1,J) 11 | f <- 1 12 | g <- diag(x=1,J,J) 13 | h <- matrix(0,J,1) 14 | w.hat <- limSolve::lsei(A=Y0,B=Y1,E=e,F=f,G=g,H=h,type=lsei_type)$X 15 | u.hat <- Y1-Y0%*%w.hat 16 | return(list(u.hat=u.hat,w.hat=w.hat)) 17 | } 18 | 19 | # constrained lasso 20 | classo <- function(Y1,Y0){ 21 | J <- dim(Y0)[2] 22 | w <- CVXR::Variable((J+1)) 23 | objective <- CVXR::Minimize(mean((Y1-cbind(1,Y0)%*%w)^2)) 24 | prob <- CVXR::Problem(objective,constraints = list(sum(abs(w[2:(J+1)])) <= 1)) 25 | result <- CVXR::solve(prob) 26 | w.hat <- result$getValue(w) 27 | u.hat <- Y1 - cbind(1,Y0)%*%w.hat 28 | return(list(u.hat=u.hat,w.hat=w.hat)) 29 | } 30 | 31 | -------------------------------------------------------------------------------- /R/scinference.R: -------------------------------------------------------------------------------- 1 | #' Inference estimation_methods for synthetic control 2 | #' 3 | #' The function \code{scinference} implements the inference methods for synthetic controls proposed by Chernozhukov et al. (2020a,b). 4 | #' The methods apply to a canonical synthetic control setup with 1 treated unit and J control units. 5 | #' The treated unit is untreated for the first \code{T0} periods and treated for the remaining \code{T1=T-T0} periods. 6 | #' 7 | #' @param Y1 outcome data for treated unit (T x 1 vector) 8 | #' @param Y0 outcome data for control units (T x J matrix) 9 | #' @param T1 number of post-treatment periods 10 | #' @param T0 number of pre-treatment periods 11 | #' @param inference_method inference method; conformal inference ("conformal",default), t-test ("ttest") 12 | #' @param alpha significance level; default \code{alpha} = 0.1 13 | #' @param ci logical, indicating whether pointwise confidence intervals are reported; default \code{ci=FALSE} 14 | #' @param theta0 null hypothesis for treatment effect trajectory (T1 x 1 vector or scalar if constant effects null); default \code{theta0}=0 15 | #' @param estimation_method estimation method; difference-in-differences ("did"), synthetic control ("sc", default), constrained lasso ("classo"). Note that constrained lasso is not implemented for the t-test. 16 | #' @param permutation_method permutation method; moving block permutations ("mb", default), iid permutations ("iid") 17 | #' @param ci_grid grid for the confidence interval 18 | #' @param n_perm number of permutation (relevant for iid permutations); default = 5000 19 | #' @param lsei_type option for lsei (package limSolve) used for sc; default = 1 20 | #' @param K K>1 number of cross-fits for t-test; default = 2 21 | #' @return conformal inference: p-value for testing the null that \code{theta=theta0} and pointwise CI (lower bounds and upper bounds) if \code{ci=TRUE}; t-test: ATT estimate, standard error, and confidence interval 22 | 23 | #' @export 24 | scinference <- 25 | function(Y1, 26 | Y0, 27 | T1, 28 | T0, 29 | inference_method = "conformal", 30 | alpha = 0.1, 31 | ci = FALSE, 32 | theta0 = 0, 33 | estimation_method = "sc", 34 | permutation_method = "mb", 35 | ci_grid = NULL, 36 | n_perm = 5000, 37 | lsei_type = 1, 38 | K = 2) { 39 | 40 | # preliminaries 41 | if(length(Y1)!=(T0+T1)) stop("length of Y1 needs to be equal to T") 42 | if(dim(Y0)[1]!=(T0+T1)) stop("number of rows in Y0 needs to be equal to T") 43 | if(!(inference_method %in% c("conformal","ttest"))) stop("The selected inference method is not available") 44 | 45 | if(inference_method == "conformal"){ 46 | 47 | if(!(estimation_method %in% c("did","sc","classo"))) stop("The selected estimation method is not implemented for conformal inference") 48 | if(!(permutation_method %in% c("iid","mb"))) stop("The selected class of permutations is not available") 49 | if(length(theta0)!=1){ 50 | if(length(theta0)!=T1){ 51 | stop("length of theta0 should be T1") 52 | } 53 | } 54 | 55 | # p-value for overall null hypothesis 56 | 57 | if(permutation_method == "mb") { 58 | p_val <- movingblock(Y1=Y1,Y0=Y0,T1=T1,T0=T0,theta0=theta0,estimation_method=estimation_method,lsei_type=lsei_type) 59 | } 60 | if(permutation_method == "iid") { 61 | p_val <- iid(Y1=Y1,Y0=Y0,T1=T1,T0=T0,theta0=theta0,estimation_method=estimation_method,n_perm=n_perm,lsei_type=lsei_type) 62 | } 63 | 64 | # pointwise confidence intervals 65 | 66 | if(ci==TRUE){ 67 | if(is.null(ci_grid)){ 68 | stop("no grid specified for confidence interval") 69 | } 70 | obj <- confidence_interval(Y1=Y1,Y0=Y0,T1=T1,T0=T0,estimation_method=estimation_method,alpha=alpha,ci_grid=ci_grid,lsei_type=lsei_type) 71 | ub <- obj$ub 72 | lb <- obj$lb 73 | } else { 74 | lb <- NA 75 | ub <- NA 76 | } 77 | return(list(p_val=p_val,lb=lb,ub=ub)) 78 | 79 | } 80 | 81 | if(inference_method == "ttest"){ 82 | 83 | if(!(estimation_method %in% c("did","sc"))) stop("The selected estimation method is not implemented for the t-test") 84 | if(K==1) stop("K must be strictly than 1") 85 | if(estimation_method == "did"){ 86 | obj <- did.cf(Y1,Y0,T1,T0,K) 87 | } 88 | if(estimation_method == "sc"){ 89 | obj <- sc.cf(Y1,Y0,T1,T0,K,lsei_type) 90 | } 91 | 92 | att <- obj$tau.hat 93 | se <- obj$se.hat 94 | lb <- att - qt(1-alpha/2,df=K-1)*se 95 | ub <- att + qt(1-alpha/2,df=K-1)*se 96 | 97 | return(list(att=att,se=se,lb=lb,ub=ub)) 98 | 99 | } 100 | 101 | } 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | -------------------------------------------------------------------------------- /R/ttest.R: -------------------------------------------------------------------------------- 1 | # t-test 2 | 3 | sc.cf <- function(Y1,Y0,T1,T0,K,lsei_type){ 4 | 5 | T01 <- T0 + T1 6 | r <- min(floor(T0/K),T1) 7 | 8 | Y1.pre <- Y1[1:T0] 9 | Y0.pre <- Y0[1:T0,] 10 | Y1.post <- Y1[(T0+1):T01] 11 | Y0.post <- Y0[(T0+1):T01,] 12 | 13 | tau.mat <- matrix(NA,K,1) 14 | for (k in 1:K){ 15 | Hk <- (T0-(r*K))+seq((k-1)*r+1,k*r,1) 16 | w.Hk <- sc(Y1.pre[-Hk],Y0.pre[-Hk,],lsei_type=lsei_type)$w.hat 17 | tau.mat[k,1] <- mean(Y1.post-Y0.post%*%w.Hk) - mean(Y1.pre[Hk]-Y0.pre[Hk,]%*%w.Hk) 18 | } 19 | 20 | tau.hat <- mean(tau.mat) 21 | se.hat <- sqrt(1+((K*r)/T1))*sd(tau.mat)/sqrt(K) 22 | t.hat <- tau.hat/se.hat # this has a t_{K-1} distribution 23 | 24 | return(list(t.hat=t.hat,tau.hat=tau.hat,se.hat=se.hat)) 25 | } 26 | 27 | did.cf <- function(Y1,Y0,T1,T0,K){ 28 | 29 | T01 <- T0 + T1 30 | r <- min(floor(T0/K),T1) 31 | 32 | Y1.pre <- Y1[1:T0] 33 | Y0.pre <- Y0[1:T0,] 34 | Y1.post <- Y1[(T0+1):T01] 35 | Y0.post <- Y0[(T0+1):T01,] 36 | 37 | tau.mat <- matrix(NA,K,1) 38 | for (k in 1:K){ 39 | Hk <- (T0-(r*K))+seq((k-1)*r+1,k*r,1) 40 | tau.mat[k,1] <- mean(Y1.post-rowMeans(Y0.post)) - mean(Y1.pre[Hk]-rowMeans(Y0.pre[Hk,])) 41 | } 42 | 43 | tau.hat <- mean(tau.mat) 44 | se.hat <- sqrt(1+((K*r)/T1))*sd(tau.mat)/sqrt(K) 45 | t.hat <- tau.hat/se.hat # this has a t_{K-1} distribution 46 | 47 | return(list(t.hat=t.hat,tau.hat=tau.hat,se.hat=se.hat)) 48 | } 49 | 50 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # scinference 2 | This R package implements the inference methods for synthetic and counterfactual controls proposed by Chernozhukov et al. (2020a,b). The papers are available here: https://arxiv.org/abs/1712.09089 https://arxiv.org/abs/1812.10820 3 | # Installation 4 | ``` 5 | install.packages("remotes") 6 | library(remotes) 7 | remotes::install_github("kwuthrich/scinference") 8 | library(scinference) 9 | ``` 10 | # Support 11 | Kaspar Wuthrich: kaspar.wuethrich@gmail.com 12 | -------------------------------------------------------------------------------- /man/scinference.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/scinference.R 3 | \name{scinference} 4 | \alias{scinference} 5 | \title{Inference estimation_methods for synthetic control} 6 | \usage{ 7 | scinference( 8 | Y1, 9 | Y0, 10 | T1, 11 | T0, 12 | inference_method = "conformal", 13 | alpha = 0.1, 14 | ci = FALSE, 15 | theta0 = 0, 16 | estimation_method = "sc", 17 | permutation_method = "mb", 18 | ci_grid = NULL, 19 | n_perm = 5000, 20 | lsei_type = 1, 21 | K = 2 22 | ) 23 | } 24 | \arguments{ 25 | \item{Y1}{outcome data for treated unit (T x 1 vector)} 26 | 27 | \item{Y0}{outcome data for control units (T x J matrix)} 28 | 29 | \item{T1}{number of post-treatment periods} 30 | 31 | \item{T0}{number of pre-treatment periods} 32 | 33 | \item{inference_method}{inference method; conformal inference ("conformal",default), t-test ("ttest")} 34 | 35 | \item{alpha}{significance level; default \code{alpha} = 0.1} 36 | 37 | \item{ci}{logical, indicating whether pointwise confidence intervals are reported; default \code{ci=FALSE}} 38 | 39 | \item{theta0}{null hypothesis for treatment effect trajectory (T1 x 1 vector or scalar if constant effects null); default \code{theta0}=0} 40 | 41 | \item{estimation_method}{estimation method; difference-in-differences ("did"), synthetic control ("sc", default), constrained lasso ("classo"). Note that constrained lasso is not implemented for the t-test.} 42 | 43 | \item{permutation_method}{permutation method; moving block permutations ("mb", default), iid permutations ("iid")} 44 | 45 | \item{ci_grid}{grid for the confidence interval} 46 | 47 | \item{n_perm}{number of permutation (relevant for iid permutations); default = 5000} 48 | 49 | \item{lsei_type}{option for lsei (package limSolve) used for sc; default = 1} 50 | 51 | \item{K}{K>1 number of cross-fits for t-test; default = 2} 52 | } 53 | \value{ 54 | conformal inference: p-value for testing the null that \code{theta=theta0} and pointwise CI (lower bounds and upper bounds) if \code{ci=TRUE}; t-test: ATT estimate, standard error, and confidence interval 55 | } 56 | \description{ 57 | The function \code{scinference} implements the inference methods for synthetic controls proposed by Chernozhukov et al. (2020a,b). 58 | The methods apply to a canonical synthetic control setup with 1 treated unit and J control units. 59 | The treated unit is untreated for the first \code{T0} periods and treated for the remaining \code{T1=T-T0} periods. 60 | } 61 | -------------------------------------------------------------------------------- /scinference.Rproj: -------------------------------------------------------------------------------- 1 | Version: 1.0 2 | 3 | RestoreWorkspace: No 4 | SaveWorkspace: No 5 | AlwaysSaveHistory: Default 6 | 7 | EnableCodeIndexing: Yes 8 | UseSpacesForTab: Yes 9 | NumSpacesForTab: 2 10 | Encoding: UTF-8 11 | 12 | RnwWeave: Sweave 13 | LaTeX: pdfLaTeX 14 | 15 | AutoAppendNewline: Yes 16 | StripTrailingWhitespace: Yes 17 | LineEndingConversion: Posix 18 | 19 | BuildType: Package 20 | PackageUseDevtools: Yes 21 | PackageInstallArgs: --no-multiarch --with-keep.source 22 | PackageRoxygenize: rd,collate,namespace 23 | -------------------------------------------------------------------------------- /vignettes/.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/kwuthrich/scinference/567c6889ce0a1d269a62d415b88aa6baf723a3fe/vignettes/.DS_Store -------------------------------------------------------------------------------- /vignettes/scinference.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: "Inference for synthetic control methods: the scinference package" 3 | author: "Victor Chernozhukov, Kaspar Wuthrich, Yinchu Zhu" 4 | output: rmarkdown::html_vignette 5 | date: "`r Sys.Date()`" 6 | vignette: > 7 | %\VignetteIndexEntry{Inference for synthetic control methods: the scinference package} 8 | %\VignetteEngine{knitr::rmarkdown} 9 | %\VignetteEncoding{UTF-8} 10 | --- 11 | 12 | ```{r, include = FALSE} 13 | knitr::opts_chunk$set( 14 | collapse = TRUE, 15 | comment = "#>" 16 | ) 17 | ``` 18 | 19 | # Introduction 20 | 21 | The package scinference implements the inference methods for synthetic control and related methods proposed in the following two papers: 22 | 23 | "An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls" written by V. Chernozhukov, K. Wuthrich, and Y. Zhu (2020). The paper is available here: https://arxiv.org/abs/1712.09089. 24 | 25 | "Practical and robust t-test based inference for synthetic control and related methods" written by V. Chernozhukov, K. Wuthrich, and Y. Zhu (2020). The paper is available here: https://arxiv.org/abs/1812.10820. 26 | 27 | # Overview 28 | 29 | The package can be used to make inferences in settings with one treated unit and $J\ge 1$ control units, where the treated unit is untreated for the first $T_0$ time periods and treated for the remaining $T_1$ periods. 30 | 31 | ## Conformal inference 32 | The package computes p-values for the null hypothesis that $H_0:(\theta_{T_0+1},\dots,\theta_{T_0+T_1})=(\theta^0_{T_0+1},\dots,\theta^0_{T_0+T_1})$, where $(\theta_{T_0+1},\dots,\theta_{T_0+T_1})$ is the vector of treatment effects in the post-treatment period. The p-values can be computed using moving block and iid permutations. If ci=TRUE, the package also computes pointwise $(1-\alpha)$ confidence intervals for $\theta_t$ for all $T_0+1\le t \le T_0+T_1$. 33 | 34 | ## T-test 35 | 36 | The package computes the debiased estimator of the ATT over time, $T_1^{-1}\sum_{t=T_0+1}^{T_0+T_1}\theta_t$, including $(1-\alpha)$ confidence intervals. Note that this method requires $T_1$ to be large. 37 | 38 | ## Estimators of the counterfactuals 39 | The package implements three different estimators of the counterfactuals: difference-in-differences, canonical synthetic control, constrained Lasso. Note that the implementation of synthetic control uses only pre-treatment outcomes as predictors and does not accommodate additional covariates. Moreover, the t-test is currently only available for difference-in-differences and synthetic control. 40 | 41 | # Examples 42 | 43 | The package is available for download on github. 44 | ```{r install} 45 | library(scinference) 46 | ``` 47 | ## Conformal inference 48 | 49 | We start by illustrating conformal inference using some simulated data. We consider a setup with $J=50$, $T_0=50$, and $T_1=5$. The control data as generated as iid normal; the outcome equals a weighted average of the contemporaneous control outcomes with sparse weights $(1/3,1/3,1/3,0,\dots,0)$. The treatment effect is constant and equal to $2$ for all periods. 50 | ```{r setup} 51 | set.seed(12345) 52 | 53 | J <- 50 54 | T0 <- 50 55 | T1 <- 5 56 | 57 | w <- rep(0,J) 58 | w[1:3] <- 1/3 59 | Y0 <- matrix(rnorm((T0+T1)*J),(T0+T1),J) 60 | Y1 <- Y0 %*% w + rnorm(T0+T1) 61 | 62 | Y1[(T0+1):(T0+T1)] <- Y1[(T0+1):(T0+T1)] + 2 63 | ``` 64 | We start by testing the null hypothesis $H_0:\theta=(4,4,4,4,4)'$. We compare the results for all three estimation methods and for both types of permutations. By default, the p-value based on the iid permutations is computed using 5000 randomly-drawn permutations. 65 | ```{r null} 66 | scinference(Y1,Y0,T1=T1,T0=T0,theta0=4,estimation_method="sc",permutation_method="mb")$p_val 67 | scinference(Y1,Y0,T1=T1,T0=T0,theta0=4,estimation_method="did",permutation_method="mb")$p_val 68 | scinference(Y1,Y0,T1=T1,T0=T0,theta0=4,estimation_method="classo",permutation_method="mb")$p_val 69 | 70 | scinference(Y1,Y0,T1=T1,T0=T0,theta0=4,estimation_method="did",permutation_method="iid")$p_val 71 | scinference(Y1,Y0,T1=T1,T0=T0,theta0=4,estimation_method="sc",permutation_method="iid")$p_val 72 | scinference(Y1,Y0,T1=T1,T0=T0,theta0=4,estimation_method="classo",permutation_method="iid")$p_val 73 | ``` 74 | Next, we compute pointwise confidence intervals using the synthetic control method. This requires specifying a grid (see Algorithm 1 in the corresponding paper). 75 | ```{r ci} 76 | 77 | obj <- scinference(Y1,Y0,T1=T1,T0=T0,estimation_method="sc",ci=TRUE,ci_grid=seq(-2,8,0.1)) 78 | 79 | plot(1, ylab="", xlab="Time", main="90% pointwise CIs",xlim = c(1,5), ylim=c(-1,7), type="n") 80 | lines(1:5, obj$lb, lwd = 2) 81 | lines(1:5, obj$ub, lwd = 2) 82 | abline(h=0,col="darkgrey", lwd=1) 83 | ``` 84 | 85 | ## T-test 86 | We start by generating some data. Note that the t-test requires a large number of post treatment periods. We use a similar DGP as before. 87 | ```{r data_ttest} 88 | set.seed(12345) 89 | 90 | J <- 30 91 | T0 <- 30 92 | T1 <- 30 93 | 94 | w <- rep(0,J) 95 | w[1:3] <- 1/3 96 | Y0 <- matrix(rnorm((T0+T1)*J),(T0+T1),J) 97 | Y1 <- Y0 %*% w + rnorm(T0+T1) 98 | 99 | Y1[(T0+1):(T0+T1)] <- Y1[(T0+1):(T0+T1)] + 2 100 | ``` 101 | We apply the t-test with synthetic control and $K\in \{2,3\}$ to estimate the ATT over time and 90% confidence intervals. 102 | ```{r ttest} 103 | ttest_K2 <- scinference(Y1,Y0,T1=T1,T0=T0,inference_method="ttest",K=2) 104 | ttest_K2$att 105 | ttest_K2$se 106 | ttest_K2$lb 107 | ttest_K2$ub 108 | ttest_K3 <- scinference(Y1,Y0,T1=T1,T0=T0,inference_method="ttest",K=3) 109 | ttest_K2$se 110 | ttest_K3$att 111 | ttest_K3$lb 112 | ttest_K3$ub 113 | ``` 114 | 115 | 116 | 117 | --------------------------------------------------------------------------------