Leverage Dynamics with Reputation

This work analyzes the classic trade-off theory of capital structure in a dynamic model where the firm does not have any commitment power. The equilibrium analyzed in this paper depends on the firm's whole history (reputation) instead of the firm's current income and debt level. This paper proves that under this non-Markov structure, the firm may repurchase its outstanding debt, which breaks the Leverage Ratchet effect discussed in Admati, DeMarzo, Hellwig, and Pfleiderer (2018). This paper also proves that under mild conditions, the equity value in a non-Markov equilibrium can be higher than the equity value in the Markov equilibrium, the one depicted in DeMarzo and He (2021). Interestingly, with some conditions, the firm can achieve the first best equity value as if the firm has commitment power. In this case, reputation is a perfect substitute for commitment power.