Tutorial 5: Stata Application of Simultaneous Equation Models The University of Queensland
ECON7360
Instructor: Rigissa Megalokonomou
Problem I: The Deterrent Effects of Smoking on Income
Use the data in smoke.dta for the following questions. A model to estimate the effects of smoking on annual income (perhaps through lost work days due to illness, or productivity effects) is provided by:
ln(income) = β0 + β1cigs + β2educ + β3age + β4age2 + u1 (1) where cigs is number of cigarettes smoked per day, on average.
(i) Load smoke.dta data and describe the data.
(ii) Run OLS regression for (1). How do you interpret β1?
To reflect the fact that cigarette consumption might be jointly determined with income, a demand for cigarettes equation is:
cigs = γ0 + γ1ln(income) + γ2educ + γ3age + β4age2 + γ5ln(cigpric) + γ6restaurn + u2 (2)
where cigpric is the price of a pack of cigarettes (in cents) and restaurn is a binary variable equal to 1 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 (1) is identified?
(iv) Use equation (2), get rid of the endogenous variables from the RHS and express
cigs as a function of exogenous variables only. Estimate this model for cigs using OLS. Are ln(cigpric) and restaurn significant in this equation? Perform an F − test.
(v) Now estimate the income equation (1) by 2SLS. Compare β1 from 2SLS to that from OLS.
(vi) Do you think that cigarette prices and restaurant smoking restrictions are exoge- nous in the income equation?
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Problem II: Demand and Supply for fish
Use the data in fish.dta for the following questions.
Background Graddy (1995) collected data on a market for whiting (a kind of fish) at the Fulton Fish Market in New York City. For each of 111 days, she collected observations on the price and quantity of whiting sold, along with some other variables. (So here, i indexes the market on different days.) A key additional variable she collected was a measure of offshore weather. The idea is that variation in offshore weather affects the supply of fish, but not demand. (Graddy, K., (1995), Testing for Imperfect Competition in the Fulton Fish Market”, RAND Journal of Economics.) We are primarily interested in estimating the demand for fish.
(i) Assume that the demand equation can be written, in equilibrium for each time period, as
ln(totqtyt) = α1ln(avgprct) + β10 + β11mont + β11tuet + β11wedt + β11thurt + ut1 (3)
so that demand is allowed to differ across days of the week. Treating the price variable as endogenous, what additional information do we need to consistently estimate the demand- equation parameters?
(ii) Variables wave2t and wave3t are measures of ocean wave heights over the past several days. What two assumptions do we need to make in order to use wave2t and wave3t as IVs for ln(avgprct) in estimating the demand equation?
(iii) Derive a reasonable supply equation for ln(avgprct). Use the supply, get rid of the endogenous variable on the RHS and then estimate this equation using OLS. Are wave2t and wave3t jointly significant? What is the p-value of the test?
(iv) Now estimate demand equation using 2SLS. What is the 95% confidence interval for the price elasticity of demand? Is the estimated elasticity reasonable?
(v) Given that the supply equation evidently depends on the wave variables, what two assumption would we need to make in order to estimate the price elasticity of supply?
(vi) Let’s assume that we are thinking of using the day-of-the-week dummies as excluded variables (they do not affect supply) to identify the supply equation. Do these dummies af- fect demand? Are the day-of-the-week dummy variables jointly significant? What do you conclude about being able to estimate the supply elasticity?
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