Prior research on the Big 4 oligopoly in the US audit market has attempted to examine the relation between competition among Big 4 auditors in local audit markets and audit quality using the inverse of the Herfindahl market concentration index as a proxy for competition. However, these prior studies (Boone et al. 2012; Newton et al. 2013) report conflicting results. Moreover, other research suggests that oligopolistic markets can be competitive, i.e., supplier concentration does not imply lack of competition (Cabral 2017; Oster 1999; Scherer 1996; Sheth and Sisodia 2002). Hence, a potential explanation for the conflicting evidence on the relation between auditor concentration and audit quality is that concentration need not necessarily imply reduced competition. Although the Herfindahl index is a generally accepted metric of market concentration, to our knowledge there is no generally accepted measure of competition (Cabral 2017). In this paper, we use the notion of counterfactual fees chargeable by auditors and develop a novel metric of fee competition at the client-level. We first validate our competition metric by showing that greater fee competition is associated with a higher likelihood of the client switching to another Big 4 auditor. We then utilize our competition metric to investigate competing views on the consequences of price competition among Big 4 auditors for Big 4 audit quality in US local audit markets.1 In particular, we shed light on whether the relation between price competition and audit quality is impacted by the incumbent Big 4 auditor’s market power and the quality of the client. Specifically, we operationalize audit fee competition as the audit fee charged by the incumbent Big 4 auditor less the lowest projected (counterfactual) audit fee that would be charged by any other Big 4 auditor for that particular engagement, scaled by client total assets. The projected fee is based on cross-sectional audit fee regressions estimated by year, industry, and each Big 4 auditor, controlling for client-specific, auditor-specific and local audit market-specific factors.2 For audit engagements that have a lower counterfactual fee from any other Big 4 auditor, the audit fee competition metric is positive, implying that the incumbent auditor faces fee competition. By contrast, for audit engagements that do not have a lower counterfactual fee, the audit fee competition metric is negative, implying that the incumbent faces no fee competition.