Fuzzy regression discontinuity (Wald ratio)

Estimates \(\tau = \tau_y / \tau_w\), the ratio of the outcome discontinuity to the treatment discontinuity at the cutoff, each from a sharp local linear fit (Hahn, Todd and van der Klaauw 2001, Theorem 3). When treatment switches deterministically at the cutoff the denominator is 1 and the estimate reduces to the sharp one of morie_causrdd.

Usage

morie_causrddf(
  x,
  y,
  treat,
  cutoff = 0,
  h = NULL,
  h_treat = NULL,
  kernel = "triangular"
)

Arguments

x

Running variable.

y

Outcome.

treat

Treatment received (0/1 or a probability).

cutoff

Threshold, default 0.

h

Bandwidth for the outcome fit; NULL uses morie_causrddh on the outcome.

h_treat

Bandwidth for the first stage; NULL uses morie_causrddh on the treatment.

kernel

"triangular" (default) or "uniform".

Value

A list with estimate, se, ci, jump_outcome, jump_treatment, se_outcome, se_treatment, h_outcome, h_treatment, kernel, sharp_outcome, sharp_treatment, se_note, method.

References

Imbens, G. and Lemieux, T. (2008). Regression discontinuity designs: a guide to practice. Journal of Econometrics, 142(2), 615-635.

Examples

set.seed(1)
x <- runif(200, -1, 1)
y <- 0.5 * x + (x >= 0) * 0.3 + rnorm(200) * 0.1
treat <- as.integer((x >= 0) & (runif(200) < 0.85))
morie_causrddf(x, y, treat)
#> $estimate
#> [1] 0.2618832
#> 
#> $se
#> [1] 0.03638019
#> 
#> $ci
#> [1] 0.1905793 0.3331871
#> 
#> $jump_outcome
#> [1] 0.2520205
#> 
#> $jump_treatment
#> [1] 0.9623394
#> 
#> $se_outcome
#> [1] 0.03217331
#> 
#> $se_treatment
#> [1] 0.05271528
#> 
#> $h_outcome
#> [1] 0.5324359
#> 
#> $h_treatment
#> [1] 0.5895147
#> 
#> $kernel
#> [1] "triangular"
#> 
#> $sharp_outcome
#> $sharp_outcome$estimate
#> [1] 0.2520205
#> 
#> $sharp_outcome$se
#> [1] 0.03217331
#> 
#> $sharp_outcome$ci
#> [1] 0.1889620 0.3150791
#> 
#> $sharp_outcome$intercept_left
#> [1] 0.0019774
#> 
#> $sharp_outcome$intercept_right
#> [1] 0.2539979
#> 
#> $sharp_outcome$slope_left
#> [1] 0.4055003
#> 
#> $sharp_outcome$slope_right
#> [1] 0.5978381
#> 
#> $sharp_outcome$h
#> [1] 0.5324359
#> 
#> $sharp_outcome$kernel
#> [1] "triangular"
#> 
#> $sharp_outcome$n_left
#> [1] 61
#> 
#> $sharp_outcome$n_right
#> [1] 56
#> 
#> $sharp_outcome$n_used
#> [1] 117
#> 
#> $sharp_outcome$se_note
#> [1] "HC0 sandwich per side, sides independent; rdrobust vce='hc0' convention"
#> 
#> $sharp_outcome$method
#> [1] "sharp RDD, one-sided local linear fits at the cutoff"
#> 
#> 
#> $sharp_treatment
#> $sharp_treatment$estimate
#> [1] 0.9623394
#> 
#> $sharp_treatment$se
#> [1] 0.05271528
#> 
#> $sharp_treatment$ci
#> [1] 0.8590194 1.0656595
#> 
#> $sharp_treatment$intercept_left
#> [1] 0
#> 
#> $sharp_treatment$intercept_right
#> [1] 0.9623394
#> 
#> $sharp_treatment$slope_left
#> [1] 0
#> 
#> $sharp_treatment$slope_right
#> [1] -0.2102502
#> 
#> $sharp_treatment$h
#> [1] 0.5895147
#> 
#> $sharp_treatment$kernel
#> [1] "triangular"
#> 
#> $sharp_treatment$n_left
#> [1] 67
#> 
#> $sharp_treatment$n_right
#> [1] 66
#> 
#> $sharp_treatment$n_used
#> [1] 133
#> 
#> $sharp_treatment$se_note
#> [1] "HC0 sandwich per side, sides independent; rdrobust vce='hc0' convention"
#> 
#> $sharp_treatment$method
#> [1] "sharp RDD, one-sided local linear fits at the cutoff"
#> 
#> 
#> $se_note
#> [1] "delta method with independent jumps; the Imbens-Lemieux covariance term is omitted and documented"
#> 
#> $method
#> [1] "fuzzy RDD, Wald ratio of local linear jumps"
#>