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 \(X = 1\).

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