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We propose using a permutation test to detect discontinuities in anunderlying economic model at a known cutoff point. Relative to the existingliterature, we show that this test is well suited for event studies based ontime-series data. The test statistic measures the distance between theempirical distribution functions of observed data in two local subsamples onthe two sides of the cutoff. Critical values are computed via a standardpermutation algorithm. Under a high-level condition that the observed data canbe coupled by a collection of conditionally independent variables, we establishthe asymptotic validity of the permutation test, allowing the sizes of thelocal subsamples to be either be fixed or grow to infinity. In the latter case,we also establish that the permutation test is consistent. We demonstrate thatour high-level condition can be verified in a broad range of problems in theinfill asymptotic time-series setting, which justifies using the permutationtest to detect jumps in economic variables such as volatility, tradingactivity, and liquidity. These potential applications are illustrated in anempirical case study for selected FOMC announcements during the ongoingCOVID-19 pandemic.

Permutation-based tests for discontinuities in event studies