6313-001TakeHomeSP23.pdf

ECON 6313-001 Spring 2023 Take-Home Project Professor C. Brown 02-08-23 Answer all questions. The project is due. Please submit your answers in Word (PDF also acceptable). Do NOT submit Excel files. Charts should be copied and pasted from Excel to Word. This project is worth sixty (60) points. Submit your work in-class on Wednesday, February 15. The Excel file necessary to complete this project is attached (also available at the MANAGERIAL ECON SP23 course shell). 1. This question is worth 50 points—2 points each, except for subparts (a) and (i), which are

worth 6 points each, and subpart (j), which is worth 10 points. Use the file “Data for Question 1.” This file contains 145 monthly observations (2006-1 to 2018-1) on the following variables: SUV: Sales of new sport utility vehicles in the U.S. (seasonally adjusted, in millions of dollars). U: The civilian unemployment rate. Gas: Average price per gallon of unleaded gasoline. SP: Standard and Poor’s Index of 500 stock prices with dividend reinvestment, monthly average. a) Use regression to estimate the following model specification. Report the results of the

regression—that is, report your estimates of β0 , β1 , β2, and β3.

𝑆𝑈𝑉𝑡 = 𝛽0 + 𝛽1𝐺𝑎𝑠𝑡 + 𝛽2𝑈𝑡 + 𝛽3𝑆𝑃𝑡

b) Are the signs of the (estimated) coefficients consistent with your (prior) expectations? Explain.

c) Suppose that the unemployment rate (U) is projected to decline by 0.2 percentage points next month. Based on the equation you have estimated, what is the predicted effect on SUV in the next month, holding all other factors constant? Be precise.

d) Can the following null hypothesis be rejected at the 0.01 significance level? Explain.

𝐻0: 𝛽2 = 0

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e) Use the equation you estimated above to obtain a fitted value of SUV for 2008-7.

Compute (and report) the ratio of the in-sample forecast error (𝑆𝑈𝑉𝑡 − 𝑆𝑈�̂�𝑡) for this month to the standard error of the regression (SE). Provide an interpretation of this ratio.

f) Prepare a chart (not table or spreadsheet) illustrating actual and fitted values of SUV for the period 2006-4 to 2018-1.

g) Report the value of R2 and provide a (precise) interpretation.

h) Set up an F-test. Can you reject null hypothesis at the 1 percent (.01) significance level?

i) Use the data contained in “Forecast” of your spreadsheet to forecast the value of SUV for 2023-02 t 2023-06. Report your results.

j) Estimate the following regression specification:

𝑙𝑛𝑆𝑈𝑉𝑡 = 𝛽0 + 𝛽1𝑙𝑛𝐺𝑎𝑠𝑡 + 𝛽2𝑙𝑛𝑈𝑡 + 𝛽3𝑙𝑛𝑆𝑃𝑡 Is the demand fo𝑟 𝑆𝑈𝑉𝑠 elastic with respect to gas prices? 𝑃𝑙𝑒𝑎𝑠𝑒 𝑒𝑥𝑝𝑙𝑎𝑖𝑛.

2. This question is worth 10 points. Answer the following questions. a) See the diagram above that depicts the demand for non-diet soft drinks. Assume the

current price of soft drinks is $3.58 per 12-pack. Compute point elasticity of demand at the current price. Are soft drink companies maximizing profits from the sale of soft drinks? Explain.

b) Soft drink consumption is blamed for health problems such as childhood obesity and diabetes. Several states (including Arkansas) impose a soft drink tax, justified by public

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health concerns. Suppose a soft drink tax is imposed that raises the price of soft drinks (from the current price of $3.50) by 8 percent. How successful would the tax be in reducing soft drink consumption? Would it make a difference if the pre-tax price were $4.89 per 12-pack?

c) Which figures stated below is likely to represent each of the following. Give the reasons for your choice in each case.

a. Income elasticity of demand for low price cuts of meat; b. Income elasticity of demand for Apple iPads; c. Price elasticity of demand for gasoline

-1.6 -0.1 +4.3

d) When the price of Good X is $27, the quantity-demanded of Good Y is 1,200 units. When the price of Good X falls to $23 (the price of good Y unchanged), the quantity-demanded of Good Y falls to 800 units. Compute cross-price elasticity of demand between Goods X and Y. Are Goods X and Y substitutes, or complements? Explain.