Marginal effect
Marginal effect is the change in a predicted outcome when one explanatory variable rises by one unit while all other variables are held constant.
Also known asincremental effect · partial effect
FrameworkOrdinary least squares (OLS)
See it move
The infographic is a formula card presenting the marginal effect in a multiple regression: Δŷ = β̂ⱼ × Δxⱼ, where Δxⱼ is a one-unit change in regressor j and all other regressors are held fixed. In a linear model the marginal effect equals the constant slope β̂ⱼ — a schooling coefficient of 85 means one additional year of education adds €85 per month to predicted earnings, holding experience unchanged. In a log–level specification the marginal effect equals β̂ⱼ × y and varies with the current level of y, so the functional form must always be stated alongside the coefficient value.
The formula
Variables
- OLS slope estimate for regressor Xⱼ
- Change in the predicted value of the outcome
- One-unit increase in explanatory variable Xⱼ
In a standard linear regression the marginal effect is constant across all observations and equals the OLS slope coefficient.
Check yourself
A regression of monthly apartment rent (€) on rooms and distance from the city centre yields: Rent = 620 + 38 × Rooms + 15 × Distance. A student interprets the coefficient 38 as 'the average effect of having one more room, across all apartments in the sample.' What is precisely correct about this interpretation?