Trimming Bounds

Usage

estimator_trim(
  Y,
  Z,
  R = NULL,
  R1 = NULL,
  Attempt = NULL,
  R2 = NULL,
  strata = NULL,
  alpha = 0.05,
  se = c("analytic", "bootstrap", "none"),
  sims = 1000,
  data
)

Arguments

Y: The (unquoted) outcome variable, or a formula outcome ~ treatment for use with declare_estimator(.method = estimator_trim). Must be numeric.
Z: The (unquoted) assignment indicator variable. Must be numeric and take values 0 or 1. Ignored when Y is a formula.
R: The single-stage response indicator: unquoted column name, or a quoted string column name when using the formula interface. Must be numeric and take values 0 or 1. Supply either R (single-stage) or R1/Attempt/R2 (double-sampling).
R1: The initial sample response indicator. Unquoted or quoted string column name. Must be numeric and take values 0 or 1.
Attempt: The follow-up attempt indicator. Unquoted or quoted string column name. Must be numeric and take values 0 or 1.
R2: The follow-up response indicator. Unquoted or quoted string column name. Must be numeric and take values 0 or 1.
strata: Not supported; supplying any value raises an error.
alpha: The desired significance level. 0.05 by default.
se: How to obtain standard errors. "analytic" (the default) uses the closed-form asymptotic variance of Lee (2009), Proposition 3, and is available for the single-stage R path only. "bootstrap" resamples units within treatment arm and works for both paths. "none" returns bounds alone.
sims: Number of bootstrap replicates when se = "bootstrap". 1000 by default.
data: A dataframe. Must be given by name: data is the last argument, so passing it positionally assigns it to another argument.

Value

A named numeric vector containing lower_bound and upper_bound, the trimming bound estimates; lower_se and upper_se, their standard errors; ci_lower and ci_upper, the joint Imbens-Manski confidence interval; and the intermediate quantities used to build them. All elements are NA when monotonicity is violated. Pass to tidy() for a data frame.

Details

The analytic variance has four contributions: the variance of the retained (trimmed) outcomes, the variance from estimating the trimming threshold, the variance from estimating the trimming proportion, and the variance of the control-group respondent mean. The third of these is often the largest, so treating the trimming proportion as known would understate the uncertainty substantially.

Lee's derivation assumes the bounds are interior points, which fails when the two response rates are equal: the trimming proportion is then zero, the bounds collapse to a point, and the standard errors are not trustworthy. This case warns.

References

Lee, David S. (2009). Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects. Review of Economic Studies 76(3):1071-1102.

Tauchmann, Harald (2014). Lee (2009) Treatment-Effect Bounds for Nonrandom Sample Selection. Stata Journal 14(4):884-894.

Examples

set.seed(343)
N <- 1000
Y_0 <- sample(1:5, N, replace = TRUE, prob = c(0.1, 0.3, 0.3, 0.2, 0.1))
Y_1 <- sample(1:5, N, replace = TRUE, prob = c(0.1, 0.1, 0.4, 0.3, 0.1))
Z <- rbinom(N, 1, 0.5)
Y_star <- Z * Y_1 + (1 - Z) * Y_0

# Treated units respond at a higher rate, so the missingness is nonignorable
R <- rbinom(N, 1, prob = 0.7 + 0.1 * Z)
Y <- Y_star
Y[R == 0] <- NA
df <- data.frame(Y, Z, R)

# Single-stage: trimming bounds under monotonicity, with Lee (2009) standard errors
estimator_trim(Y, Z, R = R, data = df)
#>     upper_bound     lower_bound       Out0_mono      Out1L_mono      Out1U_mono 
#>      0.64239649      0.01761468      2.93353474      2.95114943      3.57593123 
#> control_group_N   treat_group_N               Q              f1              f0 
#>    331.00000000    417.00000000      0.16385742      0.18713450      0.32032854 
#>          pi_r_1          pi_r_0              yU              yL        lower_se 
#>      0.81286550      0.67967146      2.00000000      4.00000000      0.09007908 
#>        upper_se        ci_lower        ci_upper 
#>      0.09972250     -0.13055222      0.80642541 

# Bootstrap standard errors instead
estimator_trim(Y, Z, R = R, se = "bootstrap", sims = 200, data = df)
#>     upper_bound     lower_bound       Out0_mono      Out1L_mono      Out1U_mono 
#>      0.64239649      0.01761468      2.93353474      2.95114943      3.57593123 
#> control_group_N   treat_group_N               Q              f1              f0 
#>    331.00000000    417.00000000      0.16385742      0.18713450      0.32032854 
#>          pi_r_1          pi_r_0              yU              yL        lower_se 
#>      0.81286550      0.67967146      2.00000000      4.00000000      0.08467663 
#>        upper_se        ci_lower        ci_upper 
#>      0.09880524     -0.12166598      0.80491665