ECON 483: Forecasting

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Empirical homework 2

The data for the homework assignment is available in EasyReg space delimited text format (*) and as an Excel CSV file (**). These data files contains the following variables for 300 companies in a particular year:

• Y = Stock return
• X(1) = Sales growth
• X(2) = Profit growth
• X(3) = Dummy sales growth > 0 (=1 if X(1)>0, =0 if not)
• X(4) = Dummy sales growth < 0 (=1 if X(1)<0, =0 if not)

1. Regress Y on X(1), X(2), X(3), X(4) and a constant 1. Thus, [try to] estimate the model

   Y = b₁X(1) + b₂X(2) + b₃X(3) + b₄X(4) + b₅ + U.

   Explain what happens and why it happens.

2. Regress Y on X(1), X(2), X(3) and X(4) without a constant 1. Thus, estimate the model

   Y = b₁X(1) + b₂X(2) + b₃X(3) + b₄X(4) + U,

   using all available data. Forecast Y for company 300.

3. Regress Y on X(1), X(2), X(3) and a constant 1. Thus, estimate the model

   Y = b₁X(1) + b₂X(2) + b₃X(3) + b₄ + U

   using all available data. Forecast Y for company 300.

   • Explain why the estimates of the slope coefficients b₁ and b₂ are the same in models (2) and (3).

   • How are the estimates of the slope coefficients b₃ and b₄ in model (2) related to the estimated slope coefficient b₃ and intercept b₄ in model (3), and why?

   • Explain why the forecasts of Y for company 300 are equal in these two cases.

   • You may assume that in model (3) the model errors U are independent normally N[0,s²] distributed. Given this assumption, construct the 90% confidence interval of the actual but unknown value of Y for company 300.

   • Test at the 5% significance level the following hypotheses for model (3):
     • b₁ = 0 against b₁ ¹ 0.

     • b₂ = 1 against b₂> 1.

     • b₂ = 2b₁, using the Wald test option in EasyReg.

     • b₂ = 2b₁ = 2b₃, using the Wald test option in EasyReg.

   • Describe in words how you would conduct the Wald test in the latter case if the point-and-click Wald test option were not available.

(*) Click on the link, and save the file as a text file (*.TXT) on your hard disk via the "Save as .." option of your web browser.

(**) If you use Internet Explorer and you click on the link the file will be automatically imported in Excel. Then use the "Save as .." option of Excel to save the file on your hard disk. Netscape and Mozilla Firefox will display the file as a text file. Therefore, if you use Netscape or Mozilla Firefox follow the procedure under (*).