Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 7

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. 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) = 1log(avgprc) + 10 + 11mont + 12tuest + 13wedt + 14thurst + 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 wave2 and wave3 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 wave2 and wave3 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, Ût1. Add a single lag, Ût-1,1 in estimating the demand equation by 2SLS. Remember, use Ût-1,1as 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
The file FISH.RAW contains 97 daily price and quantity observations on fish prices at the Fulton Fish Market in New York City. Use the variable log(avgprc) as the dependent variable.
(i) Regress log(avgprc) on four daily dummy variables, with Friday as the base.
Include a linear time trend. Is there evidence that price varies systematically within a week
(ii) Now, add the variables wave2 and wave3, which are measures of wave heights over the past several days. Are these variables individually significant Describe a mechanism by which stormy seas would increase the price of fish.
(iii) What happened to the time trend when wave2 and wave3 were added to the regression What must be going on
(iv) Explain why all explanatory variables in the regression are safely assumed to be strictly exogenous.
(v) Test the errors for AR(1) serial correlation.
(vi) Obtain the Newey-West standard errors using four lags. What happens to the t statistics on wave2 and wave3 Did you expect a bigger or smaller change compared with the usual OLS t statistics
(vii) Now, obtain the Prais-Winsten estimates for the model estimated in part (ii).
Are wave2 and wave3 jointly statistically significant