The literature on the effects of bank market power on access to credit has produced many results that are sometimes contradictory. Yet, this paper draws attention to a problematic aspect of traditional measures of bank market power, which are based on unconsolidated data and ignore the national market power of groups. This results in an underestimation that I propose to correct. Using a panel of more than 55,000 French covering the period 2006-2017, I consider a set of both unconsolidated and consolidated measures of bank market power (structural and non-structural). My results strongly support the market power hypothesis which emphasizes the virtues of competition on interest rate setting. While unconsolidated measures of bank market power do not affect the cost of credit, I find that consolidated measures increase the interest rate charged. This effect is stronger for small and opaque firms and is concentrated on long-term loans. These findings highlight the need to take into account bank capital linkages to fully assess the implications of bank market power.