H.cdf {RATest}

Regression Discontinuity Design Permutation test

Description

Calculates the empirical CDF of the sample of W conditional on Z being close to the cutoff from either the left or right. Given the induced order for the baseline covariates

W^{-}_{[q]}, W^{-}_{[q-1]},\dots\le W^{-}_{[1]}

or

W^{+}_{[1]}, W^{+}_{[2]},\dots, W^{+}_{[q]}

, this function will calculate either

H^-_n(t)=\frac{1}{q}\sum_{i=1}^q I\{W^{-}_{[i]}\le t\}

or

H^+_n(t)=\frac{1}{q}\sum_{i=1}^q I\{W^{+}_{[i]}\le t\}

depending on the argument of the function. See section 3 in Canay & Kamat (2017).

Usage

H.cdf(W, t)

Arguments

W

Numeric. The sample of induced order statistics. The input can be either \{W^{-}_{[q]}, W^{-}_{[q-1]},\dots, W^{-}_{[1]}\} or \{W^{+}_{[1]}, W^{+}_{[2]},\dots, W^{+}_{[q]}\}.

t

Numeric. The scalar needed for the calculation of the CDF.

Value

Numeric. For a sample W=(w_1,\dots,w_n), returns the fraction of observations less or equal to t.

Author(s)

Maurcio Olivares

Ignacio Sarmiento Barbieri

References

Canay, I and Kamat V, (2018) Approximate Permutation Tests and Induced Order Statistics in the Regression Discontinuity Design. The Review of Economic Studies, 85(3): 1577-1608