GK2011 (version 0.1.3)

estimate: estimate

Description

Estimators for Hybrid Experiments

Usage

estimate(rand, tr, y, iterations = 5000L)

Arguments

rand

An integer or logical vector specifying whether each observation is from the random (1) or self-selection (0) arm of the experiment.

tr

An integer or logical vector specifying whether each observation was treated (1) or control (0), regardless of the arm of the experiment.

y

A numeric vector specifying outcome values.

iterations

An integer specifying the number of bootstrap iterations used to estimate standard errors.

Value

A data.frame containing the following variables:

• Effect, a character vector of effect names (“t”, “t_s”, “t_n”, “naive”)
• Estimate, a numeric vector of effect estimates
• SE, a numeric vector of bootstrapped standard errors
• t, a t-statistic for the effect
• p, a two-tailed p-value

The return value will also carry an attribute “alpha”, indicating the estimated proportion $\alpha$.

Details

The package provides R implementations of the treatment effect estimators for hybrid (self-selection) experiments, as developed by Gaines and Kuklinski (2011). These functions estimate local average treatment effects for unobserved population subgroups inclined and disinclined to be treated, as revealed by a three-condition (two-arm) experimental design. In the design, participants are randomly assigned to one of three conditions: 1) treatment (T), 2) control (C), or 3) self-selection (S) of treatment or control. The design enables the estimation of three treatment effects:

1. First, the sample average treatment effect is estimated from conditions (1) and (2) as:\ $\hat{t} = \bar{Y}_{T} - \bar{Y}_{C}$
2. The effect for those inclined to choose treatment is given by:\ $\hat{t}_s = \frac{\bar{Y}_{S} - \bar{Y}_{C}}{\hat{\alpha}}$ where $\hat{\alpha}$ is the observed proportion of individuals in group S that choose T (rather than C).
3. The effect for those disinclined to choose treatment (or, equivalently, inclined to choose control) is given by:\ $\hat{t}_n = \frac{\bar{Y}_{T} - \bar{Y}_{S}}{1-\hat{\alpha}}$

By definition, the sample average treatment effect is an average of the other two effects.

References

Brian J. Gaines and James H. Kuklinski, (2011), "Experimental Estimation of Heterogeneous Treatment Effects Related to Self-Selection," American Journal of Political Science 55(3): 724-736.

See Also

ajps

Examples

# create fake data
set.seed(12345)
d <- 
data.frame(rand = c(rep(1, 200), rep(0, 100)),
           tr = c(rep(0, 100), rep(1, 100), rep(0, 37), rep(1, 63)),
           y = c(rnorm(100), rnorm(100) + 1, rnorm(37), rnorm(63) + 3))

# estimate effects
estimate(rand = d$rand, tr = d$tr, y = d$y)