The following is based on hearsay from Mexicans:
1. Many people of means in Mexico City buy kidnapping insurance.
2. If you are taken, the kidnappers and the insurance companies have a close working relationship. The kidnappers and the company will speak, and a mutual transfer will be arranged. No one need send a chopped off ear to establish that they have you.
3. Most kidnappers much prefer to kidnap someone with insurance. The transaction runs more smoothly and everyone behaves professionally. (There are, by the way, some “rogue” kidnapppers who behave in nasty ways and spoil the market for everybody.)
4. Didn’t Yoram Barzel and Eugene Fama, among others, teach us that the limits of the firm are arbitrary? If the kidnappers and the companies trade with such low transaction costs, can we not think of the kidnappers as part of the firm, in some sense? Or shall I say that the insurance company is part of the kidnappers?
5. Can we not think of the insurance company as an institution that helps the kidnappers make credible commitments? The company certifies which kidnappers will in fact return a live body in return for the money. The company is a kind of Better Business Bureau for the kidnappers.
6. The victims pay the nominal costs of this service. You might think this a coup for the kidnappers, but of course the long-term incidence of the charge is less clear. In any case, it is more important to have the insurance company pay greater immediate heed to what the potential victims want.
7. The general presence of kidnapping insurance may make the potential victims worse off. True, if you are kidnapped you much prefer to have the insurance. But if no insurance were possible, the costs of kidnapping would be much higher to the kidnappers. Kidnappings would be less frequent, albeit more costly for the victim.
8. The insurance confers positive externalities on those, such as myself, who are obviously uninsured [hey, kidnappers, if it is not obvious, here's hoping you read MR!]. Presumably I am seen as a tourist, not as a local CEO of a wealthy American multinational. My chance of being kidnapped is much lower, as in relative terms I am a difficult target to extract wealth from. It is much more likely that I am robbed.
Here is an earlier MR post on the economics of kidnapping; it also includes some simple data.