Optimal individualized treatment regime chosen by DR-DiD value

An individualized rule is chosen by maximising its estimated value over a restricted class. The class here is the threshold rules 1{W_j > c}; the value of a rule is the doubly robust DiD ATT among the units it targets. Candidate thresholds are the deciles of each covariate, so the search is finite and deterministic; subgroups without both treatment arms, or smaller than min_frac of the sample, are skipped. No sample splitting is done, so the reported maximum is optimistic; the complementary group's ATT is reported beside it.

Usage

Itr2dd(y, D, W, min_frac = 0.25)

Arguments

y

Outcome change dY.

D

Treatment indicator, 0 or 1.

W

Covariates the rule may use, one row per unit.

min_frac

Smallest admissible targeted share of the sample.

Value

List with estimate, se, feature, threshold, n_targeted, share_targeted, att_complement, att_overall, se_overall, gain, n_rules, n, method.

Details

Formula: d* = argmax_{j,c} tau_hat({i : W_ij > c}).

References

Athey and Imbens (2017), The state of applied econometrics, Journal of Economic Perspectives 31(2):3-32, doi:10.1257/jep.31.2.3 ; Sant'Anna and Zhao (2020), Journal of Econometrics 219(1):101-122. doi:10.1016/j.jeconom.2020.06.003

Examples

set.seed(1)
Itr2dd(y = rnorm(40), D = rbinom(40, 1, 0.5), W = matrix(rnorm(80), 40, 2))
#> $estimate
#> [1] 0.5430192
#> 
#> $se
#> [1] 0.6689697
#> 
#> $feature
#> [1] 1
#> 
#> $threshold
#> [1] -0.06689735
#> 
#> $n_targeted
#> [1] 16
#> 
#> $share_targeted
#> [1] 0.4
#> 
#> $att_complement
#> [1] -0.5463016
#> 
#> $att_overall
#> [1] -0.252466
#> 
#> $se_overall
#> [1] 0.3120899
#> 
#> $gain
#> [1] 0.7954852
#> 
#> $n_rules
#> [1] 10
#> 
#> $n
#> [1] 40
#> 
#> $method
#> [1] "d*(W) = argmax_{j,c} DR-DiD ATT on {W_j > c}, Athey & Imbens (2017)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"