Choosing an RD estimator¶

0. TL;DR flowchart¶

Is the treatment deterministic at the cutoff (P(D=1|X>=c)=1)?
  YES -> SHARP RD
  NO  -> Does the cutoff shift treatment PROBABILITY?
          YES -> FUZZY RD (Wald ratio)
          NO  -> RD is not identified; consider bunching/DiD

What is the running variable behaviour at the cutoff?
  Continuous density          -> Standard local polynomial (sp.rdrobust)
  Discrete (time-based)        -> RDiT (sp.rdit)
  Kink (derivative jump)       -> RKD (sp.rkd)
  Two running variables        -> sp.rd2d
  Multiple cutoffs             -> sp.rdmulti
  Randomisation (near cutoff)  -> Local randomization (sp.rdrandinf)

1. The default: sharp RD with CCT-robust CI¶

r = sp.rdrobust(df, y='y', x='running_var', c=0.0,
                kernel='triangular', bwselect='mserd')
r.summary()

This is the Calonico-Cattaneo-Titiunik (2014) procedure: - Triangular kernel + MSE-optimal bandwidth - Bias-corrected point estimate - Robust standard errors accounting for bias correction

Do not use naive local-linear regression — it underestimates standard errors by ignoring bias.

2. Fuzzy RD¶

r = sp.rdrobust(df, y='y', x='running_var', c=0.0, fuzzy='treatment_var')

Fuzzy RD identifies a LATE for compliers. Also report: - First-stage jump in treatment probability (r.model_info['first_stage']) - Kitagawa test for instrument validity (sp.kitagawa_test)

3. Decision tree for method variants¶

Situation	Method
Standard continuous-x sharp RD	`sp.rdrobust`
Standard fuzzy RD	`sp.rdrobust(..., fuzzy='d')`
Discrete running variable (e.g., date)	`sp.rdit`
Kink design (slope jump, not level)	`sp.rkd`
Two-dimensional cutoff	`sp.rd2d`
Multiple cutoffs (school-district boundaries)	`sp.rdmulti`
Near-cutoff local randomization	`sp.rdrandinf`
Heterogeneous effects	`sp.rdhte`, `sp.rd_forest`
ML-based extrapolation beyond cutoff	`sp.rd_extrapolate`
Honest inference (Armstrong-Kolesar)	`sp.rd_honest`
Manipulation / bunching at cutoff	`sp.bunching` + `sp.rddensity`

4. Mandatory diagnostics¶

Every RD paper must report these. StatsPAI packages them all:

# 1. Density continuity (no manipulation)
sp.rddensity(df, x='running_var', c=0.0)
sp.mccrary_test(df, x='running_var', c=0.0)

# 2. Covariate balance across the cutoff
sp.rdbalance(df, x='running_var', c=0.0, covariates=[...])

# 3. Placebo cutoffs
sp.rdplacebo(df, y='y', x='running_var',
             true_cutoff=0.0, placebo_cutoffs=[-0.5, 0.5])

# 4. Bandwidth sensitivity
sp.rdbwsensitivity(df, y='y', x='running_var', c=0.0)

# 5. Power
sp.rdpower(df, y='y', x='running_var', c=0.0, tau=[0.1, 0.5, 1.0])

Or in one call:

r = sp.rdrobust(df, y='y', x='running_var', c=0.0)
r.next_steps()  # prints the priority-ordered checklist

5. Bandwidth selection¶

bwselect='mserd' (default) is MSE-optimal and RD-specific. Other options:

`bwselect`	When to use
`'mserd'`	Default — MSE-optimal, common bandwidth
`'msetwo'`	Different bandwidths on each side of cutoff
`'cerrd'`	Coverage-error-rate optimal (better for CI coverage)
`'certwo'`	CER-optimal, two bandwidths
`'cct'`	Exact R `rdrobust` parity; requires `statspai[rd-cct]`
Fixed `h=`	Specified by you (for robustness checks)

Rule of thumb: use mserd for point estimates, run cerrd as a robustness check for CI coverage.

6. Polynomial order¶

Default p=1 (local linear). Gelman & Imbens (2019) argue strongly against high-order polynomials. Report p=2 (local quadratic) as a sensitivity check, not as the preferred specification. p>=3 is almost never justified.

7. Reading the output¶

r = sp.rdrobust(df, y='y', x='x', c=0.0)
r.estimate         # Point estimate (bias-corrected)
r.se               # Robust SE
r.ci               # Robust CI
r.model_info['bandwidth_h']    # Chosen bandwidth h
r.model_info['bandwidth_b']    # Bias-correction bandwidth b
r.model_info['n_effective_left'], ['n_effective_right']  # Obs used
r.tidy()           # Includes conventional, bias-corrected, robust rows
r.glance()         # Nobs, bandwidth, kernel, estimator
r.plot()           # Falls back to coefplot; use sp.rdplot for binscatter

8. When NOT to use RD¶

No clear discontinuity: check sp.rdplot first; if the plot doesn't show a jump, there's nothing to estimate.
Bunching at cutoff: McCrary/RD density tests will flag this. Use sp.bunching instead.
Running variable is choice variable: identification fails. Use IV or DiD.

For Agents¶

Pre-conditions - running variable x is continuous with support on both sides of c - treatment assignment is determined by the cutoff c (sharp) or probabilistically at c (fuzzy) - sufficient mass of observations within the optimal bandwidth

Identifying assumptions - Continuity of potential outcomes in x at c (Hahn, Todd, van der Klaauw 2001) - No manipulation of x at c (McCrary density test) - Local randomization only in a neighborhood of c — extrapolation away from c is not identified - Covariate balance at c (optional but recommended)

Failure modes → recovery

Symptom	Exception	Remedy	Try next
McCrary density test p < 0.05	`AssumptionViolation`	Use donut-hole RD (donut=<δ>) or partial-identification bounds.	`sp.rdrobust`
Covariate imbalance at cutoff (sp.rdbalance rejects)	`AssumptionViolation`	Include covariates as controls, narrow bandwidth, or report as caveat.
Effect unstable across bandwidth halvings	`AssumptionWarning`	Report sp.rdbwsensitivity and sp.rd_honest (Armstrong-Kolesár honest CI).	`sp.rd_honest`
Placebo cutoffs show significant 'effects'	`AssumptionViolation`	The RD signal is noise; seek an alternative identification strategy.	`sp.bounds`

Alternatives (ranked) - sp.rd_honest - sp.rdrbounds - sp.bounds

Typical minimum N: 500