The marginal effect is formally derived from the derivative of the function describing the relationship between variables. For instance, if Y = f(X) expresses the relationship between output Y and input X, the marginal effect of X on Y is represented as dY/dX. In discrete choice models such as logistic regression, the marginal effect is computed from the estimated coefficients and the predicted probabilities, reflecting how an additional unit of a predictor changes the probability of a given outcome.
An advantage of the marginal effect is that it provides a localized, point‑specific measure of sensitivity. This is useful for policy analysis where one needs to evaluate the impact of small policy changes, like a 1 percent tax cut or a 1‑unit increase in education spending. In contrast, the average effect—often inferred from the slope of a linear regression—captures a global relationship but may mask nonlinearities and variable‐dependent variations.
Marginal effects are widely used in cost‑benefit analysis, welfare economics, and environmental economics to assess the incremental cost or benefit of activities such as pollution abatement or resource extraction. They also appear in bidding strategies in auction theory, where a player’s marginal utility guides incremental bid adjustments.
However, the marginal effect is not without limitations. It depends on the origin of measurement and can vary dramatically across the range of values of the independent variable if the relationship is nonlinear. Furthermore, in non‑linear models the marginal effect can be a function of other variables, making interpretation context‑dependent. Care must also be taken in translating marginal changes in theory to practical policy, as implementation lag and behavioral responses may alter the realized effect.