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To show the second claim (๐‘ŠโŠฅ โŠฅ๐ท,๐‘|๐‘ˆ), we have that, P[๐‘Š=๐‘ค|๐ท=๐‘‘,๐‘=๐‘ง,๐‘ˆ ]=P[๐‘Š(๐‘ˆ,๐œ‚ ๐‘ค)=๐‘ค|๐ท=๐‘‘,๐‘=๐‘ง,๐‘ˆ ] =P[๐‘Š(๐‘ˆ,๐œ‚ ๐‘ค)=๐‘ค|๐‘ˆ ], where the first line follows from Assumption 2d (exclusion), th

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econ.EM 1

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2025 1

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CONDITIONAL 1

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Placebo Discontinuity Design

econ.EM ยท 2025-07-16 ยท conditional ยท novelty 7.0

Even when strategic manipulation makes the running variable jump at the cutoff, the treatment effect can be recovered by subtracting the placebo outcome's discontinuity, weighted by a local instrumental variable estimate, from the usual RDD estimate.

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  • Placebo Discontinuity Design econ.EM ยท 2025-07-16 ยท conditional ยท none ยท ref 2

    Even when strategic manipulation makes the running variable jump at the cutoff, the treatment effect can be recovered by subtracting the placebo outcome's discontinuity, weighted by a local instrumental variable estimate, from the usual RDD estimate.