Use the data set in FISH.RAW, which comes from Graddy (1995), to do this exercise. The data set is also used in Computer Exercise C12.9. Now, we will use it to estimate a demand function for fish.
(i) Assume that the demand equation can be written, in equilibrium for each time period, as
log(totqtyt) = α1log(avgprct) + β10 + β11mont + β12tuest + β13wedt + β14thurst + ut1,
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) The 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 wavet and wave3t as IVs for log{avgprct) in estimating the demand equation?
(iii) Regress log(avgprct) on the day-of-the-week dummies and the two wave measures. Are wave2t and wave3t jointly significant? What is the p-value of the test?
(iv) Now, estimate the demand equation by 2SLS. What is the 95% confidence interval for the price elasticity of demand? Is the estimated elasticity reasonable?
(v) Obtain the 2SLS residuals, t1. Add a single lag, t-1,1, in estimating the demand equation by 2SLS. Remember, use t-1,1, as its own instrument. Is there evidence of AR( 1) serial correlation in the demand equation errors?
(vi) Given that the supply equation evidently depends on the wave variables, what two assumptions would we need to make in order to estimate the price elasticity of supply?
(vii) In the reduced form equation for log(avgprct), are the day-of-the-week dummies jointly significant? What do you conclude about being able to estimate the supply elasticity?