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Cutoff Threshold
Predetermined discontinuity point where the probability of receiving treatment changes abruptly, serving as the basis for causal identification in regression discontinuity.
Forcing Variable
Continuous variable determining treatment assignment relative to the cutoff threshold, assumed to be random locally around the threshold to ensure causal validity.
Bandwidth
Window around the cutoff threshold selected for analysis, balancing bias and variance in the estimation of the local treatment effect.
Sharp RD
Configuration where treatment changes deterministically when crossing the threshold, creating a perfect discontinuity in the treatment probability.
Fuzzy RD
Variant where the treatment probability changes probabilistically at the threshold, requiring estimation techniques similar to instrumental variables.
McCrary Test
Density test verifying the fundamental assumption of no manipulation of the forcing variable around the cutoff threshold.
Local Treatment Effect
Average causal effect estimated for marginal units at the threshold boundary, representing the effect for individuals indifferent to treatment.
Continuity Validation
Empirical verification that covariates exhibit continuity at the threshold, supporting the assumption of local random assignment.
Polynomial Function
Functional specification controlling for the relationship between the forcing variable and the outcome on each side of the threshold.
Local Estimator
Weighted estimation method giving more importance to observations near the threshold to minimize specification bias.
Robustness
Sensitivity of estimates to methodological choices such as bandwidth, polynomial degree, and kernel function used.
Intention to Treat Effect
Effect of eligibility for treatment rather than actual treatment, often the primary effect estimated in fuzzy RD designs.
Calonico Criterion
Bandwidth selection methodology optimized to minimize asymptotic bias while controlling variance in RD estimation.
Assignment Density
Observed distribution of the forcing variable used to detect potential strategic manipulations around the threshold.
Optimization Window
Range of forcing variable values where the bias-variance tradeoff is optimal for causal effect estimation.
Jump Discontinuity
Instantaneous change in the average outcome when crossing the threshold, representing the causal effect identified in sharp RD.
Robust Inference
Statistical methods accounting for uncertainty in bandwidth selection and functional specification for hypothesis testing.