Use SMOKE.RAW for this exercise.
(i) A model to estimate the effects of smoking on annual income (perhaps through lost work days due to illness, or productivity effects) is
log{income) = β0 + β1cigs + β2educ + β3age + β4age2 + u1,
where cigs is number of cigarettes smoked per day, on average. How do you interpret β1?
(ii) To reflect the fact that cigarette consumption might be jointly determined with income, a demand for cigarettes equation is
cigs = γ0 + γ1 log(income) + γ2educ + γ3age + γ4age2 + γ5log(cigpric) + γ6estaurn + u2,
where cigpric is the price of a pack of cigarettes (in cents), and restaurn is a binary variable equal to unity if the person lives in a state with restaurant smoking restrictions. Assuming these are exogenous to the individual, what signs would you expect for γ5 and γ6?
(iii) Under what assumption is the income equation from part (i) identified?
(iv) Estimate the income equation by OLS and discuss the estimate of β1.
(v) Estimate the reduced form for cigs. (Recall that this entails regressing cigs on all exogenous variables.) Are log{cigpric) and restaurn significant in the reduced form?
(vi) Now, estimate the income equation by 2SLS. Discuss how the estimate of B compares with the OLS estimate.
(vii) Do you think that cigarette prices and restaurant smoking restrictions are exogenous in the income equation?