Assignment: ECONOMIC AND FINANCIAL MODELLING
Objectives:
By the time you finish this practical session, you should be able to:
• Run a multiple regression using STATA
• Use output to conduct hypothesis testing with individual coefficients
• Use output to calculate a confidence interval
• Use output to conduct a joint hypothesis
PROBLEM FOR PRACTICAL EXERCISE 2
The file IllicitDrugs.xlsx contains 56 observations on variables related to sales of cocaine powder in different regions of northeastern California in the United States for over the period 1984-1991. The data area subset of those used in the study Caulkins, J.P. and R.Padman (1003), "Quantity Discounts and Quality Premia for Illicit Drugs," Journal of the American Statistical Association, 88, 748-757.
The variables are as described in the data file:
Obs: 56 sales of cocaine
price = price per gram in dollars for a cocaine sale,
quant = number of grams of cocaine in a given sale,
qual = quality of the cocaine expressed as percentage purity,
trend = a time variable with 1984 = 1 up to 1991 = 8.
Consider the regression model:
Model 1.
PART 1:
• What signs do you expect on the coefficients, and?
(Hint: Given an explanation on how each variable will affect the price of cocaine. If a rise in the variable will lead to a rise in the price of cocaine, the expected sign should be positive (). If a rise in the variable will lead to a drop in the price of cocaine and vice versa, the sign should be negative ().)
• Use STATA to estimate the equation.
Below are the results of a regression based on a smaller sample.
Report the results in the same way as above, using the figures from your STATA output. This is how you need to report regression results in the future. You will need to include the standard errors (s.e.) of the intercept and coefficients, sample size (), R-squared (), adjusted R-squared (), Probability of t- statistics, F-statistic () and Probability of F-Statistic ().
• Based on the results, what proportion of variation in cocaine price is explained jointly by variation in quantity, quality and time?
• What is the average annual change in the cocaine price? Can you suggest why price might be changing in this direction?
PART 2
• It is claimed that the number of sales, the higher the risk of getting caught. Thus, sellers are willing to accept a lower price if they can make sales in larger quantities. Set up and that would be appropriate to test this hypothesis. Carry out the hypothesis test.
• Some researchers argue that quantity is the main driver of price not quality. Law enforcement would like to know whether quality does have a significant effect on the price. Carry out the hypothesis test.
• What are the variables that have a significant effect on price? Use 5% as the level of significance.
• Set up the using the F-test to test whether quantity, quality and time are jointly significant in explaining price. Write the, . Use probability of the F-statistic from the STATA output. Do you reject or not reject the null hypothesis?
• Testing that the residuals are normally distributed. Specify the Null and the Alternative Hypothesis. What test will you use? Specify the test and the decision Rule. Conclusion.
• A researcher would like to know whether estimating the model based on quantity alone would make it significantly different from the original model. Use the STATA command no 5-6 and report the results like in part b. Calculate the F-statistic accounting for the restriction.
STATA COMMANDS FOR PRACTICAL EXERCISE 2
Enter the commands as shown on the third column below to the command pane of your STATA screen.
Remember to press the Enter button on your keyboard at the end of each line.
|
COMMAND NO
|
PROCESS
|
STATA COMMAND
|
|
1
|
Regression for the original model
|
regress price quant qual trend
|
|
2
|
Get residuals from the original model
|
predict eo, residuals
|
|
3
|
Obtain detailed summary statistics of residuals
|
summarize e2, detail
|
|
4
|
Hypothesis testing that the residuals are normally distributed
|
Sktest e2
|
|
5
|
Regression for the restricted model
|
regress price quant
|
|
6
|
Get residuals from the restricted model
|
predict er, residuals
|
Attachment:- Illicit-Drugs.rar