Assignment 1: Understanding the role of Econometrics

Write a small essay (1 page?45 lines max.) with your views on David Hendry's "Econometrics: alchemy or science?"

Assignment 2: Running your first regression in Gretl

• Look in the Internet for a data set of two variables x and y that you think they might be related: (that is, y ? f(x) )
• Download the econometric program Gretl
• Read gretl's primer
• Carry out a single regression of y on x ( y = f (x) + u )
• Interpret your results.

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Assignment 3a: Estimating a SLRM (Single Linear Regression Model)

Data file h-Editorial-en contains 40 quarterly observations from four variables ^(*):

• S (book Sales in thousands of euros),
• P (average Price in euros),
• C (average price of the Competition in euros) and
• A (Advertising expenditure in euros)

as follows:

You must load/open the data file into Gretl in the usual way:

File ? Open data ? User file? or +? h-Editorial-en.xls

and do the following?

3a.1 Regress Sales on Price only:

S_t = ?₀ + ?₁ P_t + u_t

1. What sign do you expect for ?₁?
2. Plot a scatter graph of S against P and comment
3. Run the OLS regression: do the results agree with your expectations?
4. Interpret the estimated coefficients
5. Show that the regression line crosses the point of averages (X^?,Y^?)
6. What is the value of the coefficient of determination? Interpret this value.

3a.2 Regress Sales on Advertising expenditure only:

S_t = ?₀ + ?₂ A_t + u_t

• Repeat the process in 3a.1 above for this model, and interpret the results, etc.
  1. ?
  2. ?

Assignment 3b: Estimating & Testing a GLRM (General Linear Regression Model)

S_t = ?₀ + ?₁ P_t + ?₂ A_t + ?₃ C_t + u_t

1. Repeat the process described in Assignment 3a for the full GLR Model, and interpret the results, etc.
   1. ?
   2. ?
2. Compare the results obtained to those from the previous SLR Models. Are they the same? Why?
3. Obtain an estimate for the variance of the error term
4. Obtain the Variance-covariance matrix of the OLS estimators
5. Table of observed values, fitted vales and residuals
6. Estimate the variances of the estimators of the coefficients ?₁ and ?₂
7. Estimate the covariance of ?^{^}₁ and ?^{^}₂
8. Plot of Sales observations against fitted values
9. Plot of OLS residuals
10. Obtain their frequency distribution. Do they appear Normally distributed?
11. Plot of residuals against Price

Assignment 3c: Testing of hypothesis in a GLRM

In the same model as in Assignment 3b above:

1. Test for the individual significance of all variables.
2. Perform an overall significance test of the whole regression.
3. Test the hypothesis ?₁ + ?₂ = ?₃.

Assignment 3d: Prediction with the GLRM

In the same model as in Assignment 3b and 3c above:

1. Let us suppose that since the last recorded date neither our prices nor those of the competition have changed but our advertising expenditure has been cut by 10%. What consequences would that have on our sales?
2. Part of the board believe that the firm can still keep the previous target of 425000 ? in sales for this book. Do you agree with that opinion? (Hint: construct a suitable confidence interval).

Assignment 4a: Qualitative information in the GLRM (seasonal effects)

In the same model as in Assignments 3b to 3d above, consider the possibility that book sales may increase significantly during the Summer:

1. Modify the model to take this qualitative information into account. Describe in detail the suggested modifications.
2. What signs do you expect for the new coefficients (if any)?
3. Interpret all the coefficients in your new model.
4. Run the OLS regression: do the results agree with your expectations?
5. Test whether book sales do actually increase during the Summer.

Assignment 4b: Qualitative information in the GLRM (transversal effects)

Given the characteristics of the book the firm wants to consider the possibility that Women tend to read more than Men. In order to study how this may affect book sales the firm's sales director asks you to design a survey to collect the relevant information from a sample of 500 of their readers:

1. What variables would you include in the survey? Describe in detail the suggested quantitative as well as qualitative variables.
2. Write down a GLRM that takes all the relevant information into account.
3. Interpret all the coefficients in your new model.
4. What signs do you expect for the coefficients in the model?
5. What if Women do read more than Men but only during the Summer? Modify your survey accordingly and write down the appropriate linear regression model.
6. What if Women's marginal propensity to consume books (i.e. read) is higher than that of Men? Include new variable(s) to take into account this possibility.

Note:

^(*)As in Alonso, Fernández & Gallastegui's book Econometría, pp. 14 & 42. Appendix B of this book, p.383, shows full resolution of many questions related to this course that are illustrated with this data set.