Measuring the Bid-Ask Spread: 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 paper provides a case the estimator would have downward bias. Such case satisfies the two conditions: (i) the buy (sell) order tends to follow buy (sell) order and (ii) the price change associated to such orders are small. 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 CFTC. The high-frequency data of the emissions market allows us to provide an empirical evidence.