One of the largest car-insurance companies in the country, Allstate Corp., and a smaller Midwestern auto insurer are refunding hundreds of millions of dollars to their policyholders, citing a dramatic drop in accident claims from Americans hunkered down in their homes.

Allstate said it would dispatch more than $600 million in shelter-in-place payback checks, while American Family Mutual Insurance Co. said it is returning $200 million to its smaller policyholder base.

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