The Problem

The First Step Insurance Agency is one of the largest car insurance agencies in Massachusetts. The agency has hundreds of agents and hundreds of thousands of insurance policies. In order to stay profitable and competitive the agency must spend thousands of man hours not only investigating suspicious claims, but also investigating its own agents. The insurance giant is concerned that some of its agents have not been investigating the claims assigned to them thoroughly enough, resulting in overpayment to the policy holder and a loss for the company. The company is also concerned that some agents are simply inflating their claim payouts. The company needs to investigate the moral hazard of its agents.

By examining the data representing a group of agents working for First Stage Insurance Agency, is it possible to determine whether any single agents losses differ significantly enough from First Stages average to warrant further investigation of that agent?

Background Information

The size of the insurance industry indicates that people are eager to pay to avoid risk. They pay and get nothing if fortune smiles on them, whereas if misfortune strikes, they break even because the insurance should just pay back the value lost in the misfortune.

Sometimes, however, people do better than break even when misfortune strikes, and this possibility has greatly interested economists. If, for example, the misfortune costs a person $1000, but insurance will pay $2000, the insured person has no incentive to avoid the misfortune and may act to bring it on. This tendency of insurance to change behavior is called moral hazard.

Sometimes moral hazard is dramatic. Fire insurance encourages arson, automobile insurance encourages accidents, and disability insurance encourages dismemberment. In a story in its December 23, 1974 issue, The Wall Street Journal reported this bizarre instance of moral hazard:

“There is a macabre case of “Nub City,” a small Florida town that insurance investigators decline to identify by its real name because of continuing disputes over claims. Over 50 people in the town have suffered ‘accidents’ involving the loss of various organs and appendages, and claims of up to $300,000 have been paid out by insurers. Their investigators are positive the maimings are self-inflicted; many witnesses to the ‘accidents’ are prior claimants or relatives of the victims, and one investigator notes that ‘somehow they always shoot off parts they seem to need least.”

Moral hazard does not require that people intentionally cause the misfortune. If they simply take fewer measures to prevent the misfortune, the same outcome occurs.

Background information taken from Moral Hazard and Adverse Selection.

Materials Included

A long version and a short version of this project are provided. Both versions ask similar questions about a data set from First State Insurance agents; however, the data set used in the long version is significantly larger. Computer software such as Microsoft Excel is therefore highly recommended for data analysis of the long version, whereas the short version may be completed either with computer software or by hand.

Both versions of the project contain the following information:

• A database which includes the loss in dollars per agent for agents working for First Stage Insurance Agency.
• Suggested student activities and solutions.
• Helpful student tutorials regarding:
  • Box and whisker plots
  • Normal curves, and construction and interpretation of histograms
  • Hypothesis testing with the z-statistic
• A standard normal probability table