ECON2206: Introductory Econometrics

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ECON2206: Introductory Econometrics
Problem Set 2

Assignment instructions

  • You must submit your work via the Turnitin link on Moodle. Typed answers are preferred, but neatly and readable hand-written answers are also accepted.
  • This assignment will be marked for the course assessment and will be worth 5% of your final mark. You must include a screen-shot of Stata do-file commands estimating the equations 1, 2, and 3 to your answers. Failure to do so will result in a zero mark for the computing questions.
  • Name, student number, course title, tutorial group number and tutor’s name should be clearly included in the submission. Your answers including the Stata do-file should not exceed 6 pages. The Assignment is based on the material covered inboth lectures and tutorials up to the end of Week 10.
  • The assignment is INDIVIDUAL work. You may discuss the assignment with your peers, but you must submit YOUR OWN answers.
  • If the answer requires some mathematical calculation show the steps, don’t just report the final results.
  • This assignment has a total of 5 points awarded.
A book publisher is interested in what makes a book successful. In order to answer this question the publisher provides you with a dataset of books they have published in the last 5 years (PS2.dta). For each book this dataset contains information on the number of thousands of books sold (sales), the length of the book in number of pages (length), if the book was originally written in english (english = 1 if it was originally written in english, english = 0 otherwise) and whether the book is fiction or non-fiction (fiction = 1 if the book is fiction, fiction = 0 if the book is non-fiction).

In order to analyze the data you first estimate the following population regression models:

Sales = α0 + α1length + α2fiction + α3english + U, (1)

1. (1 point) Imagine that you don’t believe that equation (1) is the correct population regression model. Instead you think that the correct population regression model should take into account that the length of a book affects sales by a different amount depending on if the book was originally written in English and if the book is fiction. Estimate this regression using OLS and interpret all the estimates (you must include a screen-shot of Stata do-file commands estimating the equation). You can assume that all Gauss-Markov assumptions hold when interpreting the estimates (Answer in less than 60 words for each parameter you interpret)

2. (1 point) Using the estimates from question 1, provide a prediction of how much an English non-fiction book of 200 pages should sell.

3. (1 point) Perform a statistical test to determine whether equation (1) suffers from heteroskedasticity . What is the result of this test (use 5% significance level)? (you must include a screen-shot of Stata do-file commands estimating the equation)

4. (1 point) Assume that V ar(U|length, f iction, english) = σ 2 ×(length/500) whereU is the error term of equation (1). Use this information to estimate equation (1) using Weighted Least Squares (in STATA if you need to perform a regression of y on x where you don’t want to include the constant you can write the following: reg y x, nocons) (you must include a screen-shot of Stata do-file commands estimating the equation).

5. (1 point) The book publisher tells you that the length of a book may have been measured with some error. They assure you that while the errors are quite frequent they are completely at random. Do you expect that ˆα1 you estimated in question 1. to be biased? In which direction you expect the bias to go? (Answer in less than 80 words)

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