# Insurance companies

Insurance companies make a living trying to correctly assess the probability of particularm events, and also the probability of certain individuals incurring in given types…

Insurance companies make a living trying to correctly assess the probability of particularm events, and

also the probability of certain individuals incurring in given types of accidents.Imagine for a second that we have access (legally of course) to data on individuals that haveinsured their cars in New York State. The insurance company (Let’s call is Patakazo Inc.)gives us a set of demographic and socio-economic variables, among them the probability thateach of those drivers will incur in an accident in the next year.a) If the average probability of an accident of those insured with Patakazo is 7%, and theaverage value of the cars insured by the same company is \$23,000, what is the averagepremium paid by New Yorkers insured with Patakazo if we assume the insurance companymakes zero economic profits.b) Can you write an econometric model that tries to explain using a set of variables theaccident probabilities provided by the insurance companyc) Spell out which variables do you think belong in your econometric model and what do youthink would be the sign of their coefficients if we were to use OLS to estimate the model.4d) If I told you that a regression that tries to explain the variation in accident probabilities justwith indicators of the individuals’ gender (male equal to 1, female equal to zero) delivers aResidual Sum of Squares of about 78% of the Total Sum of Squares, could you tell me a roughestimate of the R-squared and explain its meaning?e) If to the conjectured regression introduced in d) I add a measure of whether the personwears a seal-belt when driving, would you expect the coefficient on gender to increase ordecrease? (For simplicity assume the coefficient on gender in the simple regression waspositive) Why? How is this related to the concept of Omitted Variable Bias?

Sample Solution