Is there a paradox of pledgeability?

We show that in the limited-commitment framework of Donaldson, Gromb, and Piacentino (2019), firm value always increases in the fraction of cash flows that can be pledged as collateral. That is, pledgeability increases investment efficiency and relaxes a firm's financing constraint. We derive this conclusion using the same contracts considered by the authors and generalize the result to an arbitrary number of states. We also show that the first best can always be implemented by a nonstate-contingent secured debt contract, which differs from the ones they consider.