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 have
insured their cars in New York State. The insurance company (Letís call is Patakazo Inc.)
gives us a set of demographic and socio-economic variables, among them the probability that
each 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 the
average value of the cars insured by the same company is $23,000, what is the average
premium paid by New Yorkers insured with Patakazo if we assume the insurance company
makes zero economic profits.
b) Can you write an econometric model that tries to explain using a set of variables the
accident probabilities provided by the insurance company
c) Spell out which variables do you think belong in your econometric model and what do you
think would be the sign of their coefficients if we were to use OLS to estimate the model.
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d) If I told you that a regression that tries to explain the variation in accident probabilities just
with indicators of the individualsí gender (male equal to 1, female equal to zero) delivers a
Residual Sum of Squares of about 78% of the Total Sum of Squares, could you tell me a rough
estimate of the R-squared and explain its meaning?
e) If to the conjectured regression introduced in d) I add a measure of whether the person
wears a seal-belt when driving, would you expect the coefficient on gender to increase or
decrease? (For simplicity assume the coefficient on gender in the simple regression was
positive) Why? How is this related to the concept of Omitted Variable Bias?
Sample Solution
