Tobit I and Tobit II models
Say we are interested in explaining the size in $ of insurance claims for fire damage (di) and have information on both buildings and owners of the buildings that have suffered fire damage (Xi). We have data from an insurance company on all buildings insured, i.e. on buildings with no fire damage and those with fire damage. a.) If we are not worried about the subset of buildings with fire damage as being a selected sample, we can use a Tobit I model to estimate the impact of the di variables on both the probability of fire damage, the con- ditional (on damage being postive) expectation of the value of the damage, and on the expected value of the damage. Write down the tobit I model specification including the observation rules and the assumptions made. Then write down expressions for P[di = 0], E[dildi > 0) and E[di]. Explain the steps in your working. Now find the marginal effects of a continuous variable, Lik on both P[di = 0] and E[di]. b.) Why might we prefer to model this using a Tobit Il model instead? Give at least one specific examples. c.) Write down the Tobit II model specification including the observation rules and the assumptions made. Here we are modelling both the value of the fire damage (di) and the probability of a fire (firei) Describe in detail how we would model the relationship between di and X; using both the MLE and the Heckman two-step approaches d.) Why do we want the variables that explain fire; to be a superset of the variables that explain d;? Use equations to aid your answer. Use a diagram too. Say we are interested in explaining the size in $ of insurance claims for fire damage (di) and have information on both buildings and owners of the buildings that have suffered fire damage (Xi). We have data from an insurance company on all buildings insured, i.e. on buildings with no fire damage and those with fire damage. a.) If we are not worried about the subset of buildings with fire damage as being a selected sample, we can use a Tobit I model to estimate the impact of the di variables on both the probability of fire damage, the con- ditional (on damage being postive) expectation of the value of the damage, and on the expected value of the damage. Write down the tobit I model specification including the observation rules and the assumptions made. Then write down expressions for P[di = 0], E[dildi > 0) and E[di]. Explain the steps in your working. Now find the marginal effects of a continuous variable, Lik on both P[di = 0] and E[di]. b.) Why might we prefer to model this using a Tobit Il model instead? Give at least one specific examples. c.) Write down the Tobit II model specification including the observation rules and the assumptions made. Here we are modelling both the value of the fire damage (di) and the probability of a fire (firei) Describe in detail how we would model the relationship between di and X; using both the MLE and the Heckman two-step approaches d.) Why do we want the variables that explain fire; to be a superset of the variables that explain d;? Use equations to aid your answer. Use a diagram too
