Measuring the bid-ask spreads: a note on the potential downward bias of the Thompson–Waller estimator

Abstract

The upward bias of the widely used Thompson–Waller estimator has been pointed out in the literature. In contrast, the current article provides a case the estimator would have downward bias: frequent continuous arrivals of orders in the same side associated with a small price change. The upward bias might be cancelled out by downward bias, and the estimator might perform better than the other methods such as Wang–Yau–Baptiste used by the U.S. Commodity Futures Trading Commission. The high-frequency data of the emissions market allows us to provide an empirical evidence.