A small company sells medical supplies to hospitals. Management wants to assess the efficacy of the company’s advertising, and an analyst has produced the following three regressions:
salesi = -516.4+ 2.47 advertisingi+ 1.86 bonusi +ei
salesi = -156.5+ 2.77 advertisingi +ui
bonusi = 193.5 +0.16 advertisingi +vi
where salesi are sales in location i (in $1,000), advertisingi is spending on advertising (in $ 100), and bonusi is the amount of bonuses paid to sales people in location i (in $ 100).
(a) Why is the coefficient on advertising different in the first two regressions? Show how the coefficient in the second regression relates to the one in the first using the information provided.
(b) Is either of the regressions likely to provide a good indication of the causal effect of advertising spending on sales? Why or why not?