A Julia package for Regression Discontinuity analyses.
This package is still experimental (and results should be double-checked for any empirical work). Please report any issues you encounter.
We demonstrate the basic functionality of the package using the U.S. House Elections dataset of Lee (2008).
julia> using RegressionDiscontinuity
julia> data = RDData(RegressionDiscontinuity.Lee08())The following estimates the sharp RDD estimate using local linear regression without any kind of bias correction. It uses a rectangular kernel and the Imbens-Kalyanaraman bandwidth.
julia> fit(NaiveLocalLinearRD(kernel = Rectangular(), bandwidth = ImbensKalyanaraman()), data.ZsR, data.Ys)Local linear regression for regression discontinuity design
⋅⋅⋅⋅ Naive inference (not accounting for bias)
⋅⋅⋅⋅ Rectangular kernel (U[-0.5,0.5])
⋅⋅⋅⋅ Imbens Kalyanaraman bandwidth
⋅⋅⋅⋅ Eicker White Huber variance
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h τ̂ se bias z p-val Lower 95% Upper 95%
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Sharp RD estimand 0.462024 0.08077 0.0087317 unaccounted 9.25 <1e-99 0.0636562 0.0978838
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The following estimates the sharp RDD estimate for the min-max optimal estimator of Imbens and Wager (2019).
The estimate assumes a bound of 14.28 on the second derivative of the conditional mean functions for the outcome in the Lee data. The optimization uses a user specified solver. The fastest option is Mosek, which is free for academics. An open source alternative is Hypatia.jl, but it is currently slower for this problem.
julia> using RegressionDiscontinuity
julia> using MosekTools
julia> fit(ImbensWagerOptRD(B=14.28, solver=Mosek.Optimizer), data.ZsR, data.Ys)Imbens-Wager (2019) optimized regression discontinuity design
Max Second Derivative Bound: 14.28
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τ̂ se max bias Lower 95% Upper 95%
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Sharp RD estimand 0.0592235 0.0197343 0.0101986 0.0159069 0.10254
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We conduct inference using Noise-Induced Randomization (NIR), as described in EIWW. We apply NIR, assuming the sensitivity model 𝒯₀ on a regression discontinuity design artificially constructed from test scores in early childhood (data from the Early Childhood Longitudinal Study).
julia> using RegressionDiscontinuity
julia> using Empirikos
julia> using MosekTools
julia> ecls_tbl = RegressionDiscontinuity.raw_table(RegressionDiscontinuity.ECLS_EIWW())
julia> Zs = NormalSample.(ecls_tbl.Z, minimum(ecls_tbl.SE))
julia> ZsR = RunningVariable(Zs, -0.2, :≥)
julia> Ys = ecls_tbl.Y
julia> nir = NoiseInducedRandomization(; solver=Mosek.Optimizer)
julia> nir_fit = fit(nir, ZsR, Ys)RD analysis with Noise Induced Randomization (NIR)
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τ̂ se max bias Lower 95% Upper 95% CI halfwidth
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Weighted RD estimand 0.355071 0.0232147 0.0109893 0.304914 0.405229 0.0501575
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The following estimates a test of manipulation of the running variable based on McCrary (2008).
julia> using RegressionDiscontinuity
julia> fit(McCraryTest(), data.ZsR)The McCrary (2008) test for manipulation in the
running variable for RDD.
⋅⋅⋅⋅ Bin size: 0.0112
⋅⋅⋅⋅ Bandwidth size: 0.2426
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θ̂ σ̂ z p-val
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McCrary Test 0.102688 0.0798507 1.29 0.1984
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