20.9 Conclusion

Prediction and Estimation/Causal Inference serve distinctly different roles in data analysis:

• Prediction: The emphasis is on predictive accuracy. The final model $\hat{f}$ may have uninterpretable parameters (e.g., deep neural networks) yet excel at forecasting $Y$. Bias in parameter estimates is not necessarily problematic if it reduces variance and improves out-of-sample performance.

• Estimation/Causal Inference: The emphasis is on obtaining consistent and unbiased estimates of parameters ($\beta$, or a treatment effect $\tau$). We impose stronger assumptions about data collection and the relationship between $X$ and $\varepsilon$. The success criterion is whether $\hat{\beta}\approx\beta_0$ in a formal sense, with valid confidence intervals and robust identification strategies.

Key Takeaway:

• If your question is “How do I predict $Y$ for new $X$ as accurately as possible?”, you prioritize prediction.

• If your question is “How does changing $X$ (or assigning treatment $D$) affect $Y$ in a causal sense?”, you focus on estimation with a fully developed identification strategy.