ECONOMIC AND FINANCIAL MODELLING PRACTICAL SESSION - MULTIPLE REGRESSION AND HYPOTHESIS TESTING

Topics covered:

• Multiple Regression Analysis - Estimation
• Multiple Regression Analysis - Inference

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 -

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.

PRICE= β₁+ β₂ QUANT+ β₃ QUAL+ β₄ TREND+e

PART 1:

a. What signs do you expect on the coefficients β₂, β₃ and β₄?

(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 (-).)

b. Use STATA to estimate the equation.

Below are the results of a regression based on a smaller sample.

PRICE = 88.13602-0.0750812QUANT+ 0.8863771QUAL-17.50298TREND

s.e. (10.36773) (0.0124203) (0.2977204) (8.033694)

N=18

R² = 0.7379

R ¯²= 0.6817

F_(3,14) = 13.14

Prob > F = 0.0002

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 (N), R-squared (R²), adjusted R-squared (R ¯²), Probability of t- statistics, F-statistic (F) and Probability of F-Statistic (Prob > F).

c. Based on the results, what proportion of variation in cocaine price is explained jointly by variation in quantity, quality and time?

d. What is the average annual change in the cocaine price? Can you suggest why price might be changing in this direction?

PART 2 -

a. 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 H₀ and H₁ that would be appropriate to test this hypothesis. Carry out the hypothesis test.

b. 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.

c. What are the variables that have a significant effect on price? Use 5% as the level of significance.

d. Set up the using the F-test to test whether quantity, quality and time are jointly significant in explaining price. Write the H₀, H₁. Use probability of the F-statistic from the STATA output. Do you reject or not reject the null hypothesis?

e. 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.

f. 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.

Attachment:- Assignment Files.rar