Disasters with Unobservable Duration and Frequency: Intensified Responses and Diminished Preparedness

We study an economy subject to recurrent disasters when the frequency and duration of the disasters are unobservable parameters. Imprecise information about transition intensities increases the probability of the current state effectively lasting forever. In a disaster, uncertainty about duration makes disasters subjectively much worse and can make the welfare value of information extremely high. However, in advance of a disaster, uncertainty about the arrival rate can be welfare-increasing. Agents optimally invest less in mitigation than under full information and pay less for insurance against the next disaster.