Produces a table of benchmark values for c_outcome and c_predictor in
ei_sens() for each covariate, following the methodology of Chernozhukov
et al. (2024).
Arguments
- spec
An ei_spec object.
- preproc
An optional function which takes in a
ei_specobject (specwith one covariate removed) and returns a modified object that includes modified object. Useful to apply any preprocessing, such as a basis transformation, as part of the benchmarking process.
References
Chernozhukov, V., Cinelli, C., Newey, W., Sharma, A., & Syrgkanis, V. (2024). Long story short: Omitted variable bias in causal machine learning (No. w30302). National Bureau of Economic Research.
Examples
data(elec_1968)
spec = ei_spec(elec_1968, vap_white:vap_other, pres_ind_wal,
total = pres_total, covariates = c(educ_elem, pop_urban, farm))
ei_bench(spec)
#> # A tibble: 9 × 7
#> covariate predictor outcome c_outcome c_predictor confounding est_chg
#> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 educ_elem vap_white pres_ind_wal 0.0859 0.609 0.686 0.0272
#> 2 educ_elem vap_black pres_ind_wal 0.0859 1 -0.827 -0.148
#> 3 educ_elem vap_other pres_ind_wal 0.0859 1 0.0880 0.422
#> 4 pop_urban vap_white pres_ind_wal 0.0680 0.151 -0.940 -0.0195
#> 5 pop_urban vap_black pres_ind_wal 0.0680 0.104 0.863 0.0578
#> 6 pop_urban vap_other pres_ind_wal 0.0680 0.0560 0.245 0.322
#> 7 farm vap_white pres_ind_wal 0.125 0.275 -0.563 -0.0203
#> 8 farm vap_black pres_ind_wal 0.125 0.102 0.420 0.0377
#> 9 farm vap_other pres_ind_wal 0.125 0.289 0.471 1.72
# preprocess to add all 2-way interactions
ei_bench(spec, preproc = function(s) {
z_cols = match(attr(s, "ei_z"), names(s))
s_out = s[-z_cols]
z_new = model.matrix(~ .^2 - 1, data = s[z_cols])
s_out = cbind(s_out, z_new)
ei_spec(s_out, vap_white:vap_other, pres_ind_wal,
total = attr(s, "ei_n"), covariates = colnames(z_new))
})
#> # A tibble: 9 × 7
#> covariate predictor outcome c_outcome c_predictor confounding est_chg
#> <chr> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 educ_elem vap_white pres_ind_wal 0.193 0.797 0.422 0.0308
#> 2 educ_elem vap_black pres_ind_wal 0.193 1 -0.0493 -0.0187
#> 3 educ_elem vap_other pres_ind_wal 0.193 0.113 -0.549 -1.22
#> 4 pop_urban vap_white pres_ind_wal 0.0860 0.143 -0.586 -0.0152
#> 5 pop_urban vap_black pres_ind_wal 0.0860 0.210 0.526 0.0681
#> 6 pop_urban vap_other pres_ind_wal 0.0860 -0.345 -1 -0.359
#> 7 farm vap_white pres_ind_wal 0.254 0.700 -0.294 -0.0237
#> 8 farm vap_black pres_ind_wal 0.254 0.617 0.486 0.160
#> 9 farm vap_other pres_ind_wal 0.254 1 0.162 1.08