Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Use the data set in FISH, which comes from Graddy $(1995),$ to do this exercise. The data set is also used in Computer Exercise $\mathrm{C} 9$ in Chapter $12 .$ 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$\begin{aligned} \log \left(\text {totqty}_{t}\right)=& \alpha_{1} \log \left(\text {avgprc}_{t}\right)+\beta_{10}+\beta_{11} m o n_{t}+\beta_{12} t u e s_{t} \\ &+\beta_{13} w e d_{t}+\beta_{14} t h u r s_{t}+u_{t 1} \end{aligned}$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 estimate the demand-equation parameters consistently?(ii) The variables wave $2_{t}$ and wave $3_{t}$ are measures of ocean wave heights over the past several days. What two assumptions do we need to make in order to use wave $2_{t}$ and wave $3_{t}$ as IVs for $\log \left(avgprc_{t}\right)$ in estimating the demand equation?(iii) Regress $\log \left(avgprc_{t}\right)$ on the day-of-the-week dummies and the two wave measures. Are wave $2_{t}$ and wave $3_{t}$ jointly significant? What is the $p$ -value of the test?(iv) Now, estimate the demand equation by 2 $\mathrm{SLS.}$ What is the 95$\%$ confidence interval for the price elasticity of demand? Is the estimated elasticity reasonable?(v) Obtain the 2 SLS residuals, $\hat{u}_{t 1} .$ Add a single lag, $\hat{u}_{t-1,1}$ in estimating the demand equation by 2SLS. Remember, use $\hat{u}_{t-1,1}$ as its own instrument. Is there evidence of $\mathrm{AR}(1)$ 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 $\log \left(avgprc_{t}\right)$, are the day-of-the-week dummies jointly significant? What do you conclude about being able to estimate the supply elasticity?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

(i) we need one exogenous variable to appear in the supply equation (ii) 2 assumptions: 2 vars must exclude from the demand equation and at least one of them appears in the supply equation (iii) (iv) see video (v) strong evidence of serial correlation (vi) assume weekday dummies do not appear in the supply equation (vii) no, we can't without more information

No Related Courses

Chapter 16

Simultaneous Equations Models

No Related Subtopics

13:51

The file FISH contains 97 …

part one. To estimate the demand equation, we need at least one exhaustion is variable that appears in their supply equation part to you. For the two variables Wave to T. And wave three T. To be valid instruments for the lock of average price. We need to assumptions First, these two can be excluded from the demand equation. Yeah. This may not be entirely reasonable as wave heights are determined partly by weather. Yeah. And the demand at a local fish market could also depend on whether the second assumption at least One of wave two and wave three appears in the supply equation. There is evidence of this in part three, as the two variables are jointly significant in the reduced form for lock of average price, Part three, these are the L. L. S. estimates of the reduced form. The lock of irish price depends on weekday dummies, we have monday, Tuesday Wednesday thursday. The two explanatory variables are the main ones are wave two and weigh three. There are 97 observations and our square is .3. We test the not hypothesis. The coefficient of way to equals the coefficient of way three. All together equal zero With an f statistic of 19.1 and AP value roughly zero. We are able to retract the null hypothesis and we conclude that two variables wave t way to and weigh three are yeah, George, lee pictures very significant. Mhm. Uh huh. In part four we will estimate the demand function by two stage least square. This is what we get. Mhm. So total quantity in lug has a negative relationship with average price and with monday Tuesday Wednesday dummies, total quantity has a positive relationship with her stay dummy. Again we use 97 observations and our square is .193. The demand elasticity is the coefficient of a lot of average price. This one The 95 confidence interval for the demand elasticity is about -1.47 two minus point 17 at this point When is 1.47 to -17. The point estimate point -12 seems reasonable. Mm hmm. A 10% increase in price reduces quantity demanded. Yeah. Bye. 8.2 percent. Part five. We find a strong you find strong evidence of positive serial correlation because we estimate the coefficient of you IT -1 to be point two 94 with a centered barrel of .103. Yeah. So we could fix this problem by estimating a new we west centered errol for the two stage least square instead of the usual standard error. Hard 6th. To estimate the supply elasticity, we would have to assume that the weekday dummies do not appear in the supply equation. Yeah, yeah. But yeah, they do appear in the demand equation. Part three Shows. Is that, yeah, there are weekday effects in the demand function, but we cannot know about the supply function. Part seven. In the estimation of the reduced forum for log of average price In part three, the weekday dummies are jointly insignificant. The value of the f statistic is .53 very small and the p value is .71. This means some of these dummies could show up in the demand equation, but they canceled out in a way that they do not affect the equilibrium price Once we've two and wave three are in the equation, so we can't estimate the supply equation without more information.

View More Answers From This Book

Find Another Textbook