Question

From the data for 46 states in the United States for 1992, Baltagi obtained the following regression results:

                                              LogC=  4.3- 1.34 log P +0.17 log Y

                                                    Se=(0.91)  (0.32)       (0.20)                                    R²=0.27

Where C= cigarette consumption, Packs per year

              P= real price per pack

              Y= real disposable income per capita

1. What is the elasticity of demand for cigarettes with respect to price? Is it statistically significant?
2. What is the income elasticity of demand for cigarettes? Is it statistically significant?
3. What is the overall significance of the regression? Which test do you use?  

Answer 1

Answer:-

Given That:-

From the data for 46 states in the United States for 1992, Baltagi obtained the following regression results:

                                              LogC=  4.3- 1.34 log P +0.17 log Y

                                               Se = (0.91)  (0.32)       (0.20) R²=0.27

Where C= cigarette consumption, Packs per year

              P= real price per pack

              Y= real disposable income per capita

Given,

Summarized the equations given in the problem;

From the data for 46 states in the United States for 1992, Baltagi obtained the following regression results:

                                              LogC=  4.3- 1.34 log P +0.17 log Y

Se=(0.91)  (0.32)       (0.20) R²=0.27

Where C= cigarette consumption, Packs per year

              P= real price per pack

              Y= real disposable income per capita

a. What is the elasticity of demand for cigarettes with respect to price? Is it statistically significant?

The elasticity of demand for cigarettes with respect to price is -1.34

2 + is not statistically different from 1

2 + is statistically different from 1

Let the loss be alpha = 5%

Test statistic = (-1.34 - 1)/0.32

= - 7.3125

t - critical value = 2.015368

Here 't' value is not in the critical values.

So we reject

Thus we conclude that it is statistically different from 1.

b. What is the income elasticity of demand for cigarettes? Is it statistically significant?

The elasticity of demand for cigarettes with respect to income is 0.17.

:  2 + is not statistically different from 0

2 + is statistically different from 0.

Let the loss be = 5%

Test Statistic = (0.17)/0.20

= 0.85

t - critical value = 2.015368

Here 't' value is not is the critical values

so we reject .

Thus we conclude that is statistically different from 0.

c. What is the overall significance of the regression? Which test do you use?  

i.e, 27% of variations in the variable cigarrete consumption can be explained by the independent variables price and Income.

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