icsw.tsls {icsw}

Two-stage least squares with inverse complier score weighting

Description

Estimate average treatment effects using two-stage least squares with a binary instrument and binary treatment and weighting with inverse complier scores (probabilities of compliance). Optionally, bootstrap the entire estimation process for the purpose of hypothesis testing and constructing confidence intervals.

Usage

icsw.tsls(D, X, Y, Z, W, weights = NULL,
  R = 0, estimand = c("ATE", "ATT"),
  min.prob.quantile = NULL,
  min.prob = NULL, ...)

icsw.tsls.fit(D, X, Y, Z, W, weights,
  estimand = c("ATE", "ATT"),
  min.prob.quantile = NULL,
  min.prob = NULL, ...)

Arguments

D

Binary treatment of interest.

X

Matrix of covariates for two-stage least squares. Add a constant if desired (see examples).

Y

Outcome.

Z

Binary instrument.

W

Matrix of covariates for compliance model.

weights

Observation weights.

R

Number of bootstrap replicates.

estimand

Whether to estimate average treatment effect (default) or average treatment effect on the treated.

min.prob.quantile

Compliance scores are truncated to this quantile of positive compliance scores.

min.prob

Compliance scores are truncated to this value.

...

Additional arguments to compliance.score.

Value

If R = 0 or icsw.tsls.fit is called directly, a model fit, as described in lm.wfit.

If R > 0, a list with elements

fitted.model

A model fit, as returned by lm.wfit.

coefs.boot

p by R matrix of model coefficients for each of R bootstrap replicates.

coefs.se.boot

Vector of standard deviations of coefficients under bootstrap resampling (i.e., bootstrap standard errors).

Author(s)

Peter M. Aronow <[e-mail]>; Dean Eckles <[e-mail]>; Kyle Peyton <[e-mail]>

References

Peter M. Aronow and Allison Carnegie. (2013). Beyond LATE: Estimation of the average treatment effect with an instrumental variable. Political Analysis.

See Also

compliance.score for calculating compliance scores used in example.

tsls.wfit for regression via 2SLS with weights.

Examples

# Load example dataset, see help(FoxDebate) for details
data(FoxDebate)

# Ipw reweighting step Aronow and Carnegie (2013) use for missing data
covmat <- with(FoxDebate, cbind(partyid, pnintst, watchnat, educad, readnews, gender, 
                                income, white))

# IPW reweighting step Aronow and Carnegie (2013) use for missing data
Ymis <- is.na(FoxDebate[, "infopro"])

IPWweight <- 1 / (1 - predict(glm(Ymis ~ covmat, family = binomial(link = "probit")),
                                  type = "response"))
IPWweight[Ymis] <- 0

N <- length(FoxDebate[, "infopro"])
alpha <- 0.275

# Compute the ATE of watching the Fox Debate on knowledge . This replicates the 
#   ATE from column 2 of Table 1 in Aronow and Carnegie (2013) 
icsw.out <- with(FoxDebate, icsw.tsls(D = watchpro, X = cbind(1, covmat), 
                                          Y = infopro, Z = conditn, W = covmat,
                                          min.prob.quantile = 1 / (N^alpha),
                          weights = IPWweight))
round(icsw.out$coefficients["D"], 2)

# Example with bootstrap (this takes awhile!)
icsw.out <- with(FoxDebate, icsw.tsls(D = watchpro, X = cbind(1, covmat), 
                                      Y = infopro, Z = conditn, W = covmat,
                                      min.prob.quantile = 1 / (N^alpha), 
                                      weights = IPWweight, R = 1000))

# Display vector of coefficients
icsw.out$coefficients

# Display vector of (bootstrapped) SEs
icsw.out$coefs.se.boot