Question

4. Question 4: Consider the following equation for U.S. per capita consumption of beef: CB--330.3+ 49.1InY, 0.34 PB,+0.33 PRP 15.4 D (se 7.4 t-6.6) (se-0.13 -2.6) (se-0.12 t-2.7) (se-4.1 -3.7) RP = 0.7 N 28 DW = 0.94 where CB. the annual per capita pounds of beef consumed in the U.S. in year t, In Yǐ : the log of per capita disposable real income in the U.S. in year t, PBt Ξ , PRI average annualized real wholesale price of pork in year t (in cents per pound) average annualized real wholesale price of beef in year t (in cents per pound) a dummy variable equal to 1 for vears in which there was a "health scare" about the dangers of red meat, 0 otherwise. (a) Develop and test your own hypotheses with respect to the individual estimated slope (b) Calculate the elasticities of CB with respect to Y and PB respectively. Explain the (c) What econometric problems appear to be present in this equation? Support your answer coefficients. obtained numbers.

Answer 1

Solution :-

Given data :

Consider the following equation for U.S. per capita consumption of beef:

$\hat{CB_t}=-330.3+\underset{se=7.4,t=6.6}{49.1}lnY_t-\underset{se=0.13,t=-2.6}{0.34}PB_t+\underset{se=0.12,t=2.7}{0.33}PRP_t-\underset{se=4.1,t=-3.7}{15.4}$

$\hat{R}^2=0.7$

N = 28

DW = 0.94

(a) Develop and test your own hypotheses with respect to the individual estimated slope coefficients.

Here consider the critical t-value. i.e, $t_{\alpha /2,df}$

Here, $\alpha =0.05$

and df = N - p ( p= number of regression coefficient ( including constant ) = 5 )

df = 28 - 5

df = 23

Then, $t_{\alpha /2,df}=t_{0.05/2,23}$

  $t_{\alpha /2,df}=t_{0.025,23}$

  $t_{\alpha /2,df}=2.069$

Here the critical t-value. i.e, $t_{\alpha /2,df}=2.069$   is less than the absolute value( neglect -ve symbol ) of the t of each predictor, so each of the predictor $lnY_t$, $PB_t$, $PRP_t$ and  $D_t$ is significant in the given multiple linear regression.

(c) What econometric problems appear to be present in this equation? Support your answer.

$\Rightarrow$ Since the $PB_t$ and $D_t$, have negative sign so it has negative effect on the ward or reaction variable $\hat{ CB_t }$.

$\Rightarrow$ Also, $lnY_t$ and $PRP_t$ have positive sign so it has positive effect on the ward or reaction variable $\hat{ CB_t }$.

Note :-

As HOMEWORKLIB RULES rule, i have little bit doubt about the 'bit-b'. so i didn't answered the 'bit-b'. If you want that bit also please upload that bit as another question. please don't give thumbs down.

Thank you.