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 satis...es 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

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... y the CFTC. The high-frequency data of the emissions market allows us to provide an empirical evidence.