pwfe: Fitting the Weighted Fixed Effects Model with Propensity...
In insongkim/wfe: Weighted Linear Fixed Effects Regression Models for Causal Inference

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

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)

`formula`	a symbolic description of the model for estimating propensity score. The formula should not include dummmies for fixed effects. The details of model specifications are given under ‘Details’.
`treat`	a character string indicating the name of treatment variable used in the models. The treatment should be binary indicator (integer with 0 for the control group and 1 for the treatment group).
`outcome`	a character string indicating the name of outcome variable.
`data`	data frame containing the variables in the model.
`pscore`	an optional character string indicating the name of estimated propensity score. Note that pre-specified propensity score should be bounded away from zero and one.
`unit.index`	a character string indicating the name of unit variable used in the models. The index of unit should be factor.
`time.index`	a character string indicating the name of time variable used in the models. The index of time should be factor.
`method`	method for weighted fixed effects regression, either `unit` for unit fixed effects; `time` for time fixed effects. The default is `unit`.
`within.unit`	a logical value indicating whether propensity score is estimated within unit. The default is `TRUE`.
`qoi`	one of `"ate"` or `"att"`. The default is `"ate"`. `"fd"` and `"did"` are not compatible with `pwfe`.
`estimator`	an optional character string `"fd"` indicating whether the first-difference estimator will be used.
`C.it`	an optional non-negative numeric vector specifying relative weights for each unit of analysis.
`White`	a logical value indicating whether White misspecification statistics should be calculated. The default is `TRUE`.
`White.alpha`	level of functional specification test. See White (1980) and Imai . The default is `0.05`.
`hetero.se`	a logical value indicating whether heteroskedasticity across units is allowed in calculating standard errors. The default is `TRUE`.
`auto.se`	a logical value indicating whether arbitrary autocorrelation is allowed in calculating standard errors. The default is `TRUE`.
`unbiased.se`	logical. If `TRUE`, bias-asjusted heteroskedasticity-robust standard errors are used. See Stock and Watson (2008). Should be used only for balanced panel. The default is `FALSE`.
`verbose`	logical. If `TRUE`, helpful messages along with a progress report of the weight calculation are printed on the screen. The default is `TRUE`.

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 (2018).

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.

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.

`coefficients`	a named vector of coefficients
`residuals`	the residuals, that is respons minus fitted values
`df`	the degree of freedom
`W`	weight matrix calculated from the model. Row and column indices can be found from unit.name, time.name.
`call`	the matched call
`causal`	causal quantity of interest
`estimator`	the estimating method
`unit.name`	a vector containing unique unit names
`unit.index`	a vector containing unique unit index number
`time.name`	a vector containing unique time names
`time.index`	a vector containing unique time index number
`method`	call of the method used
`vcov`	the variance covariance matrix
`White.alpha`	the alpha level for White specification test
`White.pvalue`	the p-value for White specification test
`White.stat`	the White statistics
`x`	the design matrix
`y`	the response vector
`mf`	the model frame

In Song Kim, Massachusetts Institute of Technology, insong@mit.edu and Kosuke Imai, Princeton University, imai@harvard.edu

Imai, Kosuke and In Song Kim. (2018) “When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data?" American Journal of Political Science, Forthcoming.

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.

wfe for fitting weighted fixed effect models.

### 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
## Not run: 

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)

## End(Not run)