Permutation-based tests for discontinuities in event studies

Bugni, Federico A.; Li, Jia

We propose using a permutation test to detect discontinuities in an underlying economic model at a 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. An empirical illustration on a recent sample of daily S&P 500 returns is provided.