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

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.