  We propose using a permutation test to detect discontinuities in an
underlying economic model at a known cutoff point. Relative to the existing
literature, we show that this test is well suited for event studies based on
time-series data. The test statistic measures the distance between the
empirical distribution functions of observed data in two local subsamples on
the two sides of the cutoff. Critical values are computed via a standard
permutation algorithm. Under a high-level condition that the observed data can
be coupled by a collection of conditionally independent variables, we establish
the asymptotic validity of the permutation test, allowing the sizes of the
local 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 that
our high-level condition can be verified in a broad range of problems in the
infill asymptotic time-series setting, which justifies using the permutation
test to detect jumps in economic variables such as volatility, trading
activity, and liquidity. These potential applications are illustrated in an
empirical case study for selected FOMC announcements during the ongoing
COVID-19 pandemic.
