The Conditional Expectation Function represents the expected value of an outcome variable, given specific values of one or more conditioning variables. In causal inference, this function serves as a fundamental tool for understanding the relationship between a potential cause and its effect. For example, one might use this function to estimate the expected crop yield given different levels of fertilizer application. The resulting function maps fertilizer levels to expected yield, providing insight into their association.
Understanding and estimating this function is crucial for identifying and quantifying causal effects. By carefully considering the variables that influence both the potential cause and the outcome, researchers can use statistical methods to isolate the specific impact of the cause on the effect. Historically, this approach has been instrumental in fields ranging from econometrics and epidemiology to social science and public policy, providing a framework for making informed decisions based on evidence.