Doubly robust LATE / LATT with a binary instrument

Formula front-end mirroring the Stata drlate three-equation syntax. The outcome, treatment and instrument arguments are formulas whose LHS give the outcome \(Y\), treatment \(W\) and (binary) instrument \(Z\), and whose RHS give the covariates for the outcome model, treatment model and instrument propensity-score model respectively.

Usage

drlate(
  outcome,
  treatment,
  instrument,
  data,
  method = c("ipwra", "ipw", "aipw", "ra"),
  estimand = c("late", "latt"),
  ps = c("logit", "cbps", "ipt"),
  outcome_family = c("linear", "logit", "poisson"),
  treatment_family = c("logit", "linear", "poisson"),
  normalize = TRUE,
  vce = c("robust", "cluster", "bootstrap"),
  cluster = NULL,
  boot_reps = 400L,
  boot_seed = NULL,
  weights = NULL,
  pstolerance = 1e-05,
  osample = FALSE
)

Arguments

outcome: Outcome equation, e.g. y ~ x1 + x2.
treatment: Treatment equation, e.g. d ~ x1 + x2.
instrument: Instrument propensity-score equation, e.g. z ~ x1 + x2.
data: A data frame.
method: Estimator: "ipwra" (default), "ipw", "aipw", or "ra".
estimand: "late" (default) or "latt" (LATE on the treated).
ps: Instrument PS method: "logit" (default), "cbps", or "ipt".
outcome_family: Outcome QMLE family: "linear" (default), "logit", "poisson".
treatment_family: Treatment QMLE family: "logit" (default), "linear", "poisson".
normalize: Logical; normalized vs unnormalized IPW/AIPW moments. Ignored (normalized by construction) for "ipwra" and "ra".
vce: Variance type: "robust" (default), "cluster", or "bootstrap". "cluster" requires a cluster variable; "bootstrap" uses boot_reps nonparametric resamples (see boot_reps/boot_seed).
cluster: Optional cluster variable: a column name in data or a length-n vector. Required when vce = "cluster".
boot_reps: Number of nonparametric bootstrap resamples when vce = "bootstrap". Default 400.
boot_seed: Optional integer RNG seed for vce = "bootstrap" reproducibility.
weights: Optional pweights: a column name in data or a length-n vector. Defaults to all ones.
pstolerance: Overlap tolerance; fitted instrument PS must lie in [pstolerance, 1 - pstolerance]. Default 1e-5.
osample: Logical; if TRUE, instead of erroring on overlap violations the returned object carries an osample logical vector flagging them.

Value

An object of class "drlate": a list with coef (named late/num/denom), vcov (3x3), nobs, method, estimand, ps, outcome_family, treatment_family, normalize, vce, call, dmeanz0/dmeanz1 (sample mean of the treatment when Z=0 and when Z=1), and (when osample=TRUE) osample.

References

Słoczyński, T., Uysal, S. D., and Wooldridge, J. M. (2022). Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment. arXiv:2208.01300. doi:10.48550/arXiv.2208.01300

Examples

# Small simulated instrumental-variables example (runs in <1s).
set.seed(1)
n <- 200
x <- rnorm(n)
z <- rbinom(n, 1, plogis(0.3 * x))             # binary instrument
d <- rbinom(n, 1, plogis(-0.2 + 0.8 * z + 0.3 * x))  # treatment
y <- 1 + 0.5 * d + 0.4 * x + rnorm(n)          # outcome
dat <- data.frame(y, d, z, x)

# Default: doubly robust IPWRA LATE (logit PS, linear outcome, logit treatment)
fit <- drlate(y ~ x, d ~ x, z ~ x, data = dat)
fit
#> 
#> Local average treatment effect                    Number of obs = 200
#> Estimator       : IPWRA
#> Outcome model   : linear
#> Treatment model : logit
#> Instrument model: logit (MLE)
#> 
#>       Estimate Std. Err.      z  P>|z| [95% Conf. Interval]
#> late    0.7142    0.6675 1.0700 0.2846    -0.5940    2.0225
#> num     0.1627    0.1552 1.0479 0.2947    -0.1416    0.4669
#> denom   0.2277    0.0659 3.4545 0.0006     0.0985    0.3569
coef(fit)
#>      late       num     denom 
#> 0.7142439 0.1626520 0.2277261 

# AIPW with an inverse-probability-tilting instrument propensity score
drlate(y ~ x, d ~ x, z ~ x, data = dat, method = "aipw", ps = "ipt")
#> IPT weights are normalized; setting normalize = FALSE
#> 
#> Local average treatment effect                    Number of obs = 200
#> Estimator       : AIPW (normalized)
#> Outcome model   : linear
#> Treatment model : logit
#> Instrument model: logit (IPT)
#> 
#>       Estimate Std. Err.      z  P>|z| [95% Conf. Interval]
#> late    0.7142    0.6675 1.0701 0.2846    -0.5940    2.0224
#> num     0.1627    0.1552 1.0479 0.2947    -0.1416    0.4669
#> denom   0.2277    0.0659 3.4548 0.0006     0.0985    0.3569

# LATE on the treated (LATT)
drlate(y ~ x, d ~ x, z ~ x, data = dat, estimand = "latt")
#> 
#> Local average treatment effect on the treated     Number of obs = 200
#> Estimator       : IPWRA
#> Outcome model   : linear
#> Treatment model : logit
#> Instrument model: logit (MLE)
#> 
#>       Estimate Std. Err.      z  P>|z| [95% Conf. Interval]
#> late    0.7184    0.6646 1.0809 0.2798    -0.5843    2.0210
#> num     0.1636    0.1546 1.0579 0.2901    -0.1395    0.4666
#> denom   0.2277    0.0660 3.4500 0.0006     0.0983    0.3571