Question

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${\beta }_0$in the model, part a.

c) The professors write that the value of${\beta }_1$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${\beta }_1$] will be negative.” Do you agree?

Short answer

a) A dummy variable model with one qualitative independent variable can be written as $E\left(y\right)={\beta }_0+{\beta }_1{x}_1$where $x_1$represents the type of firm.

b) ${\beta }_0$represents the value of relative optimism (y) at the base level which here is if the analysts worked for a sell-side firm. ${\beta }_1$represents the changes in the value of relative optimism (y) due to analysts working in the buy-side firms.

c) The value of ${\beta }_1$ 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 (${\beta }_0+{\beta }_1$). Therefore, ${\beta }_1$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${\beta }_0$ and ${\beta }_1$will be less and the value of ${\beta }_1$will be negative.

Step-by-step solution

Dummy variable model

A dummy variable model with one qualitative independent variable can be written as $E\left(y\right)={\beta }_0+{\beta }_1{x}_1$where $x_1$represents the type of firm.

Interpretation of β

_{${\beta }_0$}represents the value of relative optimism (y) at the base level which here is if the analysts worked for a sell-side firm

_{${\beta }_1$}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 ${\beta }_1$ 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 (${\beta }_0+{\beta }_1$ ). Therefore,${\beta }_1$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${\beta }_0$and ${\beta }_1$will be less and the value of ${\beta }_1$will be negative