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.