Fuzzy regression discontinuity: the Wald ratio at the cutoff

The denominator is the first stage and it is the whole difficulty: when the jump in treatment probability is small the ratio is a weak instrument and its standard error understates the real uncertainty. The first stage is reported alongside, and a denominator indistinguishable from zero is an error rather than an infinity. With a denominator of exactly one the estimator collapses to the sharp one.

Usage

Rdfzzy(y, x, D, cutoff = 0, bandwidth = 1)

Arguments

y: Outcome.
x: Running variable.
D: Treatment received.
cutoff: Threshold.
bandwidth: Half-window, positive.

Value

List with estimate, tau, se, z, reduced_form, first_stage, se_reduced_form, se_first_stage, n_right, n_left, bandwidth.

Details

Formula: tau_LATE = (lim Y+ - lim Y-) / (lim D+ - lim D-); the standard error is the delta method applied to that ratio.

References

Hahn, J., Todd, P. & Van der Klaauw, W. (2001). Econometrica 69(1):201-209. doi:10.1111/1468-0262.00183 ; the fuzzy design is their Theorem 3.

Examples

set.seed(1)
r <- Rdfzzy(y = rnorm(10), x = rnorm(10), D = rbinom(10, 1, 0.5)); TRUE
#> [1] TRUE