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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