ECON 123A Code and Code Output Questionnaire

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ECON 123A: ECONOMETRICS I
Homework 3
(Due: November 16 Tuesday at 3 pm, Pacific Time)
This assignment is worth 20 points in total. It is composed of 2 parts:
Part 1 – Multiple Choice (15 points, 3 attempts, no time limit)
There will be 15 multiple choices. Each question is worth 1 point.
Part 2 – Code and Code Output (5 points, unlimited attempts, no time limit)
You need to present both code and code output for each question in order to receive full 10
points. Upload your code under
Assignments – Homework 3 (Upload Your Code Here) . I accept html, word, or pdf
file.
Problem 5.23
The file cocaine contains 56 observations on variables related to sales of cocaine powder in
northeastern California over the period 1984–1991. The data are a subset of those used in the
study Caulkins, J. P. and R.Padman (1993), “Quantity Discounts and Quality Premia for Illicit
Drugs,” Journal of the American Statistical Association, 88, 748–757. The variables are:
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:
PRICE = ?1 + ?2 QUANT + ?3 QUAL + ?4 TREND + e (Equation1)
Question 1: What signs would you expect on the coefficients ? 2 , ? 3 and ? 4 ?
Question 2: Estimate the regression model stated in Equation 1.(round to 4 decimals)
Question 3: What proportion of variation in cocaine price is explained jointly by variation in
quantity, quality, and time? (round to 2 decimals)
Question 4: It is claimed that the greater 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.
Question 5: Carry out the hypothesis test at 95%, and state your conclusion. (round to 3
decimals)
Question 6: What is the average annual change in the cocaine price? Can you suggest why
price might be changing in this direction? (round to 4 decimals)
Problem 6.28
Using time-series data on five different countries, Atkinson and Leigh18 investigate the impact of
the marginal tax rate paid by high-income earners on the level of inequality. A subset of their
data can be found in the file inequality . For this problem, use data on Australia only.
Considers these regression models:
SHARE = ?1 + ?2TAX + e (Equation2)
SHARE = ?1 + ?2 TAX + ?3 YEAR + ?4 YEAR2 + e (Equation3)
SHARE = ?1 + ?2 TAX + ?3 YEAR + ?4 YEAR2 + ?5 GWTH + e (Equation4)
Question 7: Estimate Equation 2 , where SHARE is the percentage income share of the top 1%
of incomes, and TAX is the median marginal tax rate (as a percentage) paid on wages by the top
1% of income earners. (round to 4 decimals)
Question 8: Interpret your estimate for ? 2 . (round to 4 decimals)
Quesiton 9: It is generally recognized that inequality was high prior to the great depression,
then declined during the depression and World War II, increasing again toward the end of the
sample period. To capture this effect, estimate Equation 3 with a quadratic trend, where YEAR is
defined as 1 = 1921, 2 = 1922, …, 80 = 2000. (Generate variable YEAR2 = YEAR2). (round to 4
decimals)
Question 10: Interpret the estimate for ?2 . Has adding the trend changed the effect of the
marginal tax rate? (round to 4 decimals)
Question 11: Can the change in this estimate, or lack of it, be explained by the correlations
between TAX and YEAR and TAX and YEAR2? (round to 4 decimals)
Question 12: Conduct joint hypothesis testing for the coefficients in Equation 3, where H0: all
coefficients are zero, H1: at least one of the coefficients is zero. Find the F statistic and state
your conclusion. (round to 2 decimals)
Question 13: Add the growth rate (GWTH) and estimate Equation 4. What’s your estimated
equation? (round to 4 decimals)
Question 14: Interpret the estimated coefficient ?2 for TAX. (round to 4 decimals)
Question 15: Using the results in Question 13, estimate the year when SHARE will be smallest?
(For this question, use original coefficients first. Then round to the nearest integer in the end.)

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