## 16.3 Causation versus Prediction

Understanding the relationship between causation and prediction is crucial in statistical modeling.

Let $$Y$$ be an outcome variable dependent on $$X$$, and our aim is to manipulate $$X$$ to maximize a payoff function $$\pi(X, Y)$$ . The decision on $$X$$ hinges on:

\begin{aligned} \frac{d\pi(X, Y)}{d X} &= \frac{\partial \pi}{\partial X} (Y) + \frac{\partial \pi}{\partial Y} \frac{\partial Y}{\partial X} \\ &= \frac{\partial \pi}{\partial X} \text{(Prediction)} + \frac{\partial \pi}{\partial Y} \text{(Causation)} \end{aligned}

Empirical work is essential for estimating the derivatives in this equation:

• $$\frac{\partial Y}{\partial X}$$ is required for causal inference to determine $$X$$’s effect on $$Y$$,

• $$\frac{\partial \pi}{\partial X}$$ is required for prediction of $$Y$$.

(SICSS 2018 - Sendhil Mullainathan’s presentation slide)

### References

Kleinberg, Jon, Jens Ludwig, Sendhil Mullainathan, and Ziad Obermeyer. 2015. “Prediction Policy Problems.” American Economic Review 105 (5): 491–95.