Estimator of What? A Note on Teaching Regressions in Introductory Econometrics

The most widely used textbooks today conflate three distinct population parameters: the population regression function (PRF), the conditional expectation function (CEF), and the causal effect. They also incorrectly suggest, and sometimes state, that the Conditional Mean Zero assumption implies causal interpretation of regression coefficients. I highlight these issues and show that by incorporating new notation these limitations can easily be overcome.