Research summary: We study how two dimensions of reputation (i.e., generalized favorability and being known) and attribution of crisis responsibility affect firm value at the onset of a crisis. Analyzing 126 corporate crises befalling publicly listed firms in China from 2008 to 2014, we find that generalized favorability serves as a buffer, while being known can be a burden, in influencing firm value. We also find that the buffering effect of generalized favorability is stronger when the attribution of crisis responsibility is low (vs. high). In addition, there is a negative interaction effect between the two dimensions of reputation such that the buffering effect of generalized favorability weakens when firms are better known. We discuss our contributions to research on corporate reputation and crisis management. Managerial summary: Corporate reputation is an intangible asset, especially at the onset of a corporate crisis. This research sheds light on the “double‐edged sword” of corporate reputation by examining the effects of two reputation dimensions (i.e., being liked and being known) on firm value. Our results suggest that well‐liked firms can leverage their generalized favorability among stakeholders to assuage firm value loss, whereas well‐known firms may have to better communicate with stakeholders to overcome the burden of stakeholders' attention that escalates firm value loss. To better cope with the onset of a crisis, firms should therefore enhance their generalized favorability and simultaneously avert stakeholders' excessive attention. In addition, well‐liked firms can further buffer against the loss in firm value by reducing the perceived intentionality of a crisis. Copyright © 2017 John Wiley & Sons, Ltd.