Chapter 12: 74E (page 756)

Buy-side vs. sell-side analysts’ earnings forecasts. Refer to the Financial Analysts Journal (July/August 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86 (p. 112). The Harvard Business School professors used regression to model the relative optimism (y) of the analysts’ 3-month horizon forecasts. One of the independent variables used to model forecast optimism was the dummy variable x = {1 if the analyst worked for a buy-side firm, 0 if the analyst worked for a sell-side firm}.
a) Write the equation of the model for E(y) as a function of type of firm.
b) Interpret the value of $β_{0}$ in the model, part a.
c) The professors write that the value of $β_{1}$ in the model, part a, “represents the mean difference in relative forecast optimism between buy-side and sell-side analysts.” Do you agree?
d) The professors also argue that “if buy-side analysts make less optimistic forecasts than their sell-side counterparts, the [estimated value of $β_{1}$ ] will be negative.” Do you agree?

Short Answer

Expert verified

a) A dummy variable model with one qualitative independent variable can be written as $E (y) = β_{0} + β_{1} x_{1}$ where $x_{1}$ represents the type of firm.

b) $β_{0}$ represents the value of relative optimism (y) at the base level which here is if the analysts worked for a sell-side firm. $β_{1}$ represents the changes in the value of relative optimism (y) due to analysts working in the buy-side firms.

c) The value of $β_{1}$ represents the mean difference in relative forecast optimism between buy-side and sell-side analysts. The base-level here is analyst representing sell-side firms hence for x₁= 1 the coefficient for buy-side firms will be ( $β_{0} + β_{1}$ ). Therefore, $β_{1}$ essentially represents the mean difference between the two levels.

d) If buy-side analysts, make less optimistic forecasts than the sell-side analysts then the mean difference between the $β_{0}$ and $β_{1}$ will be less and the value of $β_{1}$ will be negative.

Step by step solution

Dummy variable model

A dummy variable model with one qualitative independent variable can be written as $E (y) = β_{0} + β_{1} x_{1}$ where $x_{1}$ represents the type of firm.

Interpretation of β

_{$β_{0}$}represents the value of relative optimism (y) at the base level which here is if the analysts worked for a sell-side firm

_{$β_{1}$}represents the changes in the value of relative optimism (y) due to analysts working in the buy-side firms.

Interpretation of β1

The value of $β_{1}$ represents the mean difference in relative forecast optimism between buy-side and sell-side analysts. The base-level here is analyst representing sell-side firms hence for x₁= 1the coefficient for buy-side firms will be ( $β_{0} + β_{1}$ ). Therefore, $β_{1}$ essentially represents the mean difference between the two levels.

Analysis of β1

If buy-side analysts, make less optimistic forecasts than the sell-side analysts then the mean difference between the $β_{0}$ and $β_{1}$ will be less and the value of $β_{1}$ will be negative