This study investigates if the use of a Big 6 auditor is increasing in the firm's endogenous propensity to generate accruals. High‐accrual firms have greater scope for aggressive and/or opportunistic earnings management and therefore have an incentive to hire a Big 6 auditor to provide assurance that reported earnings are credible. For a large sample of NASDAQ firms over the period 1975–1994 we find that the likelihood of using a Big 6 auditor is increasing in firms' endogenous propensity for accruals. Even though Big‐6‐audited firms have higher levels of total accruals, we also find they have lower amounts of estimated discretionary accruals. This finding is consistent with Big 6 auditors constraining aggressive and potentially opportunistic reporting of accruals.