Even correctly specified and well-estimated regression models can mislead

Area of Science:

• Econometrics
• Causal Inference
• Statistical Modeling

Background:

• Regression models are widely used to infer causal relationships from observational data.
• A common assumption is that predictor variables can be held constant to isolate causal effects.
• However, the validity of this assumption in real-world scenarios is often questionable.

Purpose of the Study:

• To critically examine the possibility of drawing causal conclusions from observational data using regression models.
• To demonstrate the limitations of even perfect regression models in establishing causality.
• To highlight the complexities in interpreting causal effects when predictor variables are held constant.

Main Methods:

• A thought experiment is employed to illustrate the challenges in causal inference.
• The study analyzes the implications of assuming constant predictor variables within regression models.
• The historical case of road safety research on the effects of speed is used as an example.

Main Results:

• Even with perfect models and ample data, incorrect causal conclusions can arise.
• The core issue lies in the assumption that other predictor variables remain unchanged when one is altered.
• This assumption may be impossible to fulfill or may necessitate unmodeled real-world changes.

Conclusions:

• Interpreting regression models for causal inference requires careful consideration of the real-world consequences of holding predictor variables constant.
• The assumption of ceteris paribus (all other things being equal) in regression analysis can be problematic when applied to observational data.
• The study underscores the need for caution when drawing causal claims from single-equation regression models, particularly in fields like road safety research.