Skip to contents

Calculate Robustness Values

robustness_values.Rd

Calculate Robustness Values

Usage

robustness_values(w, z, y, X = NULL)

Arguments

w

the instrument vector, a numeric (double) vector with no NA values

z

the treatment vector, a numeric (double) vector with no NA values

y

the outcome vecctor, a numeric (double) vector with no NA values

X

an optional matrix of covariates to residualize on

Value

a dataframe containing robustness values with the following columns:

  • Method The method for the associated Robustness Value:

    • SOO - Selection on observables

    • IV - Instrumental variables

    • ExogenousIV - Instrumental variables, where exogeneity is known to be satisfied (as in a randomized experiment)

    • ExcludableIV - Instrumental variables, where the exclusion restriction is known to be satisfied

  • RV the robustness value

  • rho_1, rho_2, rho_3 The parameters used to achieve this robustness value

  • bias The bias achieved at this combination of parameters

  • assumption gap the largest gap between partial correlations that are assumed to be zero (only relevant for ExogenousIV and ExcludableIV) and the actual value found by the optimizer. This should be negligible and close to the machine tolerance.

Examples

create_simulation <- function(n=10^7, rho = .5) {
 w <- rnorm(n)
 z <- sqrt(rho)*w + sqrt(1-rho)*rnorm(n)
 y <- 2*z + rnorm(n)

 return(list(
   w = w, 
   z = z, 
   y = y
 ))
}


strong_instrument_data <- create_simulation(rho = .90)
weak_instrument_data <- create_simulation(rho = .01)

robustness_values(
 strong_instrument_data$w, 
 strong_instrument_data$z, 
 strong_instrument_data$y
)
#> # A tibble: 4 × 8
#>   method           rv        rho_1 rho_2 rho_3  bias assumption_gap estimate
#>   <chr>         <dbl>        <dbl> <dbl> <dbl> <dbl>          <dbl>    <dbl>
#> 1 Soo          0.463  0.197        0.681 0.681  2.00  0                 2.00
#> 2 Iv           0.0199 0.0384       0.975 0.145  2.00  0                 2.00
#> 3 ExogenousIV  0.0199 0.0000000370 0.975 0.145  2.00  0.0000000370      2.00
#> 4 ExcludableIV 0.720  0.848        0.535 1.000  2.00  0.00000000152     2.00

robustness_values(
 weak_instrument_data$w, 
 weak_instrument_data$z, 
 weak_instrument_data$y
)
#> # A tibble: 4 × 8
#>   method            rv       rho_1 rho_2 rho_3  bias assumption_gap estimate
#>   <chr>          <dbl>       <dbl> <dbl> <dbl> <dbl>          <dbl>    <dbl>
#> 1 Soo          0.827   0.00744     0.910 0.910  2.00    0               2.00
#> 2 Iv           0.00463 0.0680      0.974 0.464  2.00    0               2.00
#> 3 ExogenousIV  0.0406  0.000000333 0.975 0.457  2.00    0.000000333     2.00
#> 4 ExcludableIV 0.00956 0.0978      0.975 0.457  2.00    0.000000426     2.00