Modeling a major source of economic resilience to disasters: recapturing lost production

Abstract

Terrorist attacks and natural disasters have potentially severe economic consequences in terms of property damage and business interruption. However, experience from the September 11 World Trade Center attack and other disasters indicates that the economy has a great deal of resilience. This refers to the ability to dampen the maximum potential economic output (business interruption) loss. One of the most prominent sources of resilience is the ability of businesses to reschedule, or recapture, lost production after the event. Although there have been applications of a fixed parameter recapture factor for each of several aggregated sectors of the economy, there has been little formal analysis of this resilience action. This study offers a theoretic framework for analyzing production rescheduling. It distinguishes the major conditions influencing two aspects that have previously been neglected: (1) the maximum time span over which the rescheduling can take place and (2) the likely decline of the maximum recapture as the business interruption increases. We divide the relevant time path into two periods after recovery. One is a function of a recaptured output path after recovery to the status of normal production. The other is a function for the maximum recaptured production, based on the recaptured output path. The recaptured output path function is assumed to follow a normal distribution function, and hence, total recaptured output follows the cumulative normal distribution function over time after productive capacity is restored. Also, we develop a new cumulative normal distribution function for interruption time duration, which is symmetric with respect to the output axis. This recapture function has unknown parameters. Empirical data on the recaptured amounts following an actual disaster can be used to estimate the parameters of this function using simulation methods.