Even correctly specified and well-estimated regression models can mislead

Abstract

It should be possible to draw causal conclusions from happenstance data. However, there are many well-known reasons for doubting the causal interpretation of single equation regression models based on such data. Still, hope springs eternal. The hope is founded on the belief that if the function linking the response variable to the predictor variables was known and its parameters estimated from plentiful data then one could predict what change in the response variable is caused by a change in a predictor variable. But what if this foundational belief was incorrect?I use a thought experiment to show even perfect models can lead to incorrect conclusions. The problem is that to say what change in the response variable is caused by a change in a predictor variable one must assume that all the other predictor variables remain unchanged. This may not be possible or may require changes to reality that are outside of the model, changes that almost certainly will not exist. To interpret the estimated model equation correctly one must trace all real-world consequences of holding the predictor variables constant. This is not easy to do. The history of regression-based research about the road safety effect of speed supports my case.