17.3 Marginal Effects Interpretation
The interpretation of marginal effects differs depending on whether \(X\) is continuous or discrete:
Variable Type | Definition of Marginal Effect |
---|---|
Continuous | The derivative \(\frac{\partial E[Y|X]}{\partial X}\) represents an infinitesimal change in \(X\). |
Discrete | The change in \(E[Y|X]\) when \(X\) increases by one unit (also called an incremental effect). |
For example, in a binary variable case (e.g., a dummy variable for gender), the marginal effect is:
\[ E[Y|X=1] - E[Y|X=0]. \]
which quantifies the expected change in \(Y\) when switching from \(X = 0\) to \(X = 1\).