Linear-in-Means Peer Externalities Model

Picture this

Think of a team relay race where swapping a fast runner onto Team A makes Team A faster but makes Team B equally slower, leaving the combined average time of all runners completely unchanged. Unless the swap somehow inspires individual runners to run faster on their own regardless of who runs next to them, overall race performance remains identical.

What the evidence says

The theoretical framework demonstrates that under linear-in-means peer assumptions, student re-sorting does not alter aggregate population test scores ($\bar{Y} = \beta_0 \bar{X} + \beta_1 \bar{X}$); individual gains are strictly offset by losses to non-participants unless $\beta_2 > 0$.

Who was studied

Theoretical general equilibrium model applied to secondary education populations in urban school districts.

How

Mathematical nesting model specifying student outcomes as $Y_i = \beta_0 X_i + \beta_1 \bar{X}_s + \beta_2 P + \epsilon_i$, where $\beta_1$ isolates redistributive peer effects and $\beta_2$ isolates direct productive effects.

What to do

Incorporate a direct productive coefficient alongside baseline peer averages when evaluating the aggregate social welfare impact of school choice policies.

From the source

"Under the hypothesis that $\beta_2>0$ and $\beta_1=0$ vouchers work purely through a productive effect and the benefit to participants will be equal to the social benefit."

Are Educational Vouchers Only Redistributive?

Tags

• peer effects
• welfare economics
• general equilibrium