The perm excludes part of the mandated increase.
Sanga ’20 [Sarath; February 2020; Professor of Law at Northwestern University, Ph.D. in Economics from the University of California at Berkeley, J.D. from Yale University; Journal of Law and Economics, “Network Effects in Corporate Governance,” vol. 63]
The proof is given in Section A4 in the Appendix. Intuitively, the legal quality estimator uses the first postshock cohort to measure the immediate change in Delaware's share of new firms. However, that cohort responds not only to the increase in Delaware's legal quality but also to the (expected) increase in its future network size. Delaware's share of the first postshock cohort is therefore greater than what the quality effect alone would have induced. Similarly, the network effect estimator uses firms from the second postshock cohort and onward to measure subsequent changes in Delaware's share of new firms. This estimator is a lower bound because it excludes the part of the increase in Delaware's share of the first postshock cohort that was due to the expected increase in network size. Note that this logic does not depend on the accuracy of firms' predictions, the ability of firms to reincorporate, or the total number of firms; the validity of the bounds depends only on firms' beliefs that a positive quality shock will (weakly) increase Delaware's network size. The bounds are thus valid even if firms systematically underestimate Delaware's future network size.