ECON2206 - Book Publisher - Regression Models - Gauss-Markov Assumptions - Econometrics Assessment Answer

Assessment Task:

ECON2206 Gauss-Markov Assumptions - Econometrics Assessment Answer

Description

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. Use OLS to estimate equation (1). Report ˆα0 and ˆα2 Assume that the Gauss-Markov assumptions hold and interpret these parameters.

2. 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 can assume that all Gauss-Markov assumptions hold when interpreting the estimates (Answer in less than 60 words for each parameter you interpret)

3. Using the estimates from question 2. provide a prediction of how much an English non-fiction book of 200 pages should sell.

4. Perform a statistical test to determine whether equation (1) suffers from heteroskedasticity. What is the result of this test (use 5% significance level)?

5. Assume that V ar(U|length, fiction, English) = σ 2 × (length/500) where U 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).

6. 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? 

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