uppose a wine seller has 1000 different wines on offer and decides to are asked to assess the effect of advertising on wine sales, and are given

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question 3 In this problem we will decompose a naive comparison of averages into a treatment
effect and selection bias. Suppose a wine seller has 1000 different wines on offer and decides to
advertise half of them. We are asked to assess the effect of advertising on wine sales, and are given
last month's sales figures.
a) Explain in words why the 'naive' comparison of sales figures may not be informative of the ATE,
ATT or ATU.
b) What do you need to assume about selection bias for the comparison of sales figures to be
informative of the ATE, ATT and ATU? Also write your answer in terms of conditional expectations.
c) Can the naive comparison equal the ATE even with selection bias? Explain.
d) Assume average sales for advertised wines were $600, whereas non-advertised wines were $800.
Assume also that the selection bias in o is -$300 and the selection bias in y, is -$400. Complete
the table below and explain your answers. (Note: Half of wines are advertised).
Not Advertised Advertised Total
Sales with advertising
$600
Sales without advertising
$800
Difference
Transcribed Image Text:Question 3 In this problem we will decompose a naive comparison of averages into a treatment effect and selection bias. Suppose a wine seller has 1000 different wines on offer and decides to advertise half of them. We are asked to assess the effect of advertising on wine sales, and are given last month's sales figures. a) Explain in words why the 'naive' comparison of sales figures may not be informative of the ATE, ATT or ATU. b) What do you need to assume about selection bias for the comparison of sales figures to be informative of the ATE, ATT and ATU? Also write your answer in terms of conditional expectations. c) Can the naive comparison equal the ATE even with selection bias? Explain. d) Assume average sales for advertised wines were $600, whereas non-advertised wines were $800. Assume also that the selection bias in o is -$300 and the selection bias in y, is -$400. Complete the table below and explain your answers. (Note: Half of wines are advertised). Not Advertised Advertised Total Sales with advertising $600 Sales without advertising $800 Difference
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