The equation below estimates the demand for alcoholic beverages in the United Ki

Question

The equation below estimates the demand for alcoholic beverages in the United Kingdom using annual data for 20 years (n=20). The estimated equation takes the following form (t-statistics in parenthesis):


Qt = - .014 - .354X2t + .0018X3t + .357X4t + .0059X5t
(1.16) (2.86) (3.39) (2.47) (1.73)
Where:
Q = the annual change in alcohol consumption
X2 = the annual change in the price of alcoholic drinks
X3 = the annual change in disposable income
X4 = the annual change in the number of licensed premises/adult population
X5 = the annual change in advertising expenditure on alcoholic drinks per adult


a. Are the estimated signs of the regression coefficients consistent with economic theory (ie. just common sense)? Explain.
b. Explain what each of the estimated coefficients means that is interpret the results. Explain.
c. Are each of the estimated coefficients statistically significant at the 5% level of significance? Explain Completely.
d. Interpret the coefficient of determination, R2.

I need to learn how to do this, so a breakdown of the work, equations used and whatever else you can offer would be great! Thanks!

Explanation / Answer

The equation below estimates the demand for alcoholic beverages in the United Kingdom using annual data for 20 years (n=20). The estimated equation takes the following form (t-statistics in parenthesis):


Qt = - .014 - .354X2t + .0018X3t + .357X4t + .0059X5t
(1.16) (2.86) (3.39) (2.47) (1.73)
Where:
Q = the annual change in alcohol consumption
X2 = the annual change in the price of alcoholic drinks
X3 = the annual change in disposable income
X4 = the annual change in the number of licensed premises/adult population
X5 = the annual change in advertising expenditure on alcoholic drinks per adult


a. Are the estimated signs of the regression coefficients consistent with economic theory (ie. just common sense)? Explain.

The coefficient for the annual change in price of alcoholic drinks, X2 is negative which is consistent with the law of demand. As the price of alcoholic drinks increase, the demand or the consumption of the good falls.

Alcohol can be assumed to be a normal good, i.e. as income increases, the consumption of the good also increases. Here the sign of the coefficient, X3, is positive and hence consistent with economic theory.

Economic theory suggests that greater the availability of the good and easier the access to it, greater will be its consumption. Here, the ease of access and availability as measured by X4 is positive and hence consistent with the theory.

Similarly, economic theory suggests that greater the advertising expenditure on the good, greater the consumption of it. In the given model, X5 which measures the annual change in advertising expenditure on alcoholic drinks per adult is positive.

b. Explain what each of the estimated coefficients means that is interpret the results. Explain.

For an unit change annually in the price of alcoholic drinks, the annual consumption of alcohol on average reduces by 0.354 units.

For an unit change annually in disposable income, the annual consumption of alcohol on average increases by 0.018 units.

For an unit change annually in the number of licensed premises/adult population, the annual consumption of alcohol on average increases by 0.357 units.

For an unit change annually in the advertising expenditure on alcoholic drinks per adult, the annual consumption of alcohol on average increases by 0.0059 units.

c. Are each of the estimated coefficients statistically significant at the 5% level of significance? Explain Completely.

At 5% level of significance and with 15 degrees of freedom (degrees of freedom are given by the total number of observations less the number of coefficients in the model, i.e. =20-5=15), the absolute critical value of the t statistic (to determine the significance of each coefficient we use the t statistic to test the null hypothesis that the coefficient is zero and the alternative hypothesis that the coefficient is not zero) is approximately 2.13. If the t statistic of the coefficient exceeds the critical t value then the null hypothesis is accepted, that is the coefficient is statistically insignificant (since the coefficient of the variable is zero, it has no influence on the dependent variable and hence statistically insignificant).

In the given model, the t value of X2, X3 and X4 exceed 2.13 and hence they are statistically insignificant. However the coefficient for X5 is statistically significant.

d. Interpret the coefficient of determination, R^2.

The coefficient of determination (R^2) measures the proportion of variation in the dependent variable, i.e. annual change in alcohol consumption explained by the independent variables (or right hand side factors).

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