wfe (version 1.2)

pwfe: Fitting the Weighted Fixed Effects Model with Propensity Score Weighting

Description

pwfe is used to fit weighted fixed effects model for causal inference after transforming outcome variable based on estimated propensity score. pwfe also derives the regression weights for different causal quantity of interest.

Usage

pwfe(formula, treat = "treat.name", outcome, data, pscore = NULL,
     unit.index, time.index = NULL, method = "unit", within.unit = TRUE,
     qoi = c("ate", "att"), estimator = NULL, C.it = NULL,
     White = TRUE, White.alpha = 0.05,
     hetero.se = TRUE, auto.se = TRUE, unbiased.se = FALSE,
     verbose = TRUE)

Value

pwfe returns an object of class "pwfe", a list that contains the components listed below. The function summary (i.e., summary.pwfe) can be used to obtain a table of the results.coefficientsa named vector of coefficientsresidualsthe residuals, that is respons minus fitted valuesdfthe degree of freedomWweight matrix calculated from the model. Row and column indices can be found from unit.name, time.name.callthe matched callcausalcausal quantity of interestestimatorthe estimating methodunit.namea vector containing unique unit namesunit.indexa vector containing unique unit index numbertime.namea vector containing unique time namestime.indexa vector containing unique time index numbermethodcall of the method usedvcovthe variance covariance matrixWhite.alphathe alpha level for White specification testWhite.pvaluethe p-value for White specification testWhite.statthe White statisticsxthe design matrixythe response vectormfthe model frame

Details

To fit the weighted unit (time) fixed effects model with propensity score weighting, use the syntax for the formula, ~ x1 + x2, where x1 and x2 are unit (time) varying covariates. One can provide his/her own estimated pscore which can be used to transform the outcome varialbe. If so, one does not need to specify formula. If pscore is not provided, bayesglm will be used to estimate propensity scores. If within.unit = TRUE, propensity score will be separately estimated within time (unit) when method is unit (time). Otherwise, propensity score will be estimated on entire data at once. The estimated propensity scores will be used to transform the outcome variable as described in Imai and Kim (2011). pwfe calculates weights based on different underlying causal quantity of interest: Average Treatment Effect (qoi = "ate") or Average Treatment Effect for the Treated (qoi = "att"). One can further set estimating methods: First-Difference (estimator ="fd") or Difference-in-differences (estimator = "did"). To specify different ex-ante weights for each unit of analysis, use non-negative weights C.it. For instance, using the survey weights for C.it enables the estimation fo the average treatement effect for the target population.

References

Imai, Kosuke and In Song Kim. (2012) ``On the Use of Linear Fixed Effects Regression Models for Causal Inference.'' Technical Report, Department of Politics, Princeton University. available at http://imai.princeton.edu/research/FEmatch.html Stock, James and Mark Watson. (2008) ``Heteroskedasticity-Robust Standard Errors for Fixed Effect Panel Data Regression'' Econometrica, 76, 1. White, Halbert. (1980) `Using Least Squares to Approximate Unknown Regression Functions.'' International Economic Review, 21, 1, 149--170.

See Also

wfe for fitting weighted fixed effect models.

Examples

### NOTE: this example illustrates the use of wfe function with randomly
### generated panel data with arbitrary number of units and time.

## generate panel data with number of units = N, number of time = Time
N <- 10 # number of distinct units
Time <- 15 # number of distinct time

## generate treatment variable
treat <- matrix(rbinom(N*Time, size = 1, 0.25), ncol = N)
## make sure at least one observation is treated for each unit
while ((sum(apply(treat, 2, mean) == 0) > 0) | (sum(apply(treat, 2, mean) == 1) > 0) |
       (sum(apply(treat, 1, mean) == 0) > 0) | (sum(apply(treat, 1, mean) == 1) > 0)) {
  treat <- matrix(rbinom(N*Time, size = 1, 0.25), ncol = N)
}
treat.vec <- c(treat)

## unit fixed effects
alphai <- rnorm(N, mean = apply(treat, 2, mean))

## geneate two random covariates
x1 <- matrix(rnorm(N*Time, 0.5,1), ncol=N)
x2 <- matrix(rbeta(N*Time, 5,1), ncol=N)
pscore <- matrix(runif(N*Time, 0,1), ncol=N)
x1.vec <- c(x1)
x2.vec <- c(x2)
pscore <- c(pscore)

## generate outcome variable
y <- matrix(NA, ncol = N, nrow = Time)
for (i in 1:N) {
    y[, i] <- alphai[i] + treat[, i] + x1[,i] + x2[,i] + rnorm(Time)
}
y.vec <- c(y)

## generate unit and time index
unit.index <- rep(1:N, each = Time)
time.index <- rep(1:Time, N)

Data.str <- as.data.frame(cbind(y.vec, treat.vec, unit.index, x1.vec, x2.vec))
colnames(Data.str) <- c("y", "tr", "strata.id", "x1", "x2")

Data.obs <- as.data.frame(cbind(y.vec, treat.vec, unit.index, time.index, x1.vec, x2.vec, pscore))
colnames(Data.obs) <- c("y", "tr", "unit", "time", "x1", "x2", "pscore")


############################################################
# Example 1: Stratified Randomized Experiments
############################################################

## run the weighted fixed effect regression with strata fixed effect.
## Note: the quantity of interest is Average Treatment Effect ("ate")
## and the standard errors allow heteroskedasticity and arbitrary
## autocorrelation.


### Average Treatment Effect
ps.ate <- pwfe(~ x1+x2, treat = "tr", outcome = "y", data = Data.str, 
               unit.index = "strata.id", method = "unit", within.unit = TRUE,
               qoi = "ate", hetero.se=TRUE, auto.se=TRUE)
## summarize the results
summary(ps.ate)

### Average Treatment Effect for the Treated
ps.att <- pwfe(~ x1+x2, treat = "tr", outcome = "y", data = Data.str, 
               unit.index = "strata.id", method = "unit", within.unit = TRUE,
               qoi = "att", hetero.se=TRUE, auto.se=TRUE)
## summarize the results
summary(ps.att)


############################################################
# Example 2: Observational Studies with Unit Fixed-effects
############################################################

## run the weighted fixed effect regression with unit fixed effect.
## Note: the quantity of interest is Average Treatment Effect ("ate")
## and the standard errors allow heteroskedasticity and arbitrary
## autocorrelation.

### Average Treatment Effect
ps.obs <- pwfe(~ x1+x2, treat = "tr", outcome = "y", data = Data.obs, 
               unit.index = "unit", time.index = "time",
               method = "unit", within.unit = TRUE,
               qoi = "ate", hetero.se=TRUE, auto.se=TRUE)

## summarize the results
summary(ps.obs)

## extracting weigths
summary(ps.obs)$Weights

### Average Treatment Effect with First-difference

ps.fd <- pwfe(~ x1+x2, treat = "tr", outcome = "y", data = Data.obs,
              unit.index = "unit", time.index = "time",
              method = "unit", within.unit = TRUE,
              qoi = "ate", estimator = "fd", hetero.se=TRUE, auto.se=TRUE)

## summarize the results
summary(ps.fd)


############################################################
# Example 3: Estimation with pre-specified propensity score
############################################################

### Average Treatment Effect with Pre-specified Propensity Scores

mod.ps <- pwfe(treat = "tr", outcome = "y", data = Data.obs, pscore = "pscore",
               unit.index = "unit", time.index = "time",
               method = "unit", within.unit = TRUE,
               qoi = "ate", hetero.se=TRUE, auto.se=TRUE)

## summarize the results
summary(mod.ps)