Estimating causal relationships from data is one of the fundamental endeavors of researchers. Ideally, we could conduct a controlled experiment to estimate causal relations. However, conducting a controlled experiment may be infeasible. For example, education researchers cannot randomize education attainment and they must learn from observational data.
In the absence of experimental data, we construct models to capture the relevant features of the causal relationship we have an interest in, using observational data. Models are successful if the features we did not include can be ignored without affecting our ability to ascertain the causal relationship we are interested in. Sometimes, however, ignoring some features of reality results in models that yield relationships that cannot be interpreted causally. In a regression framework, depending on our discipline or our research question, we give a different name to this phenomenon: endogeneity, omitted confounders, omitted variable bias, simultaneity bias, selection bias, etc.
Below I show how we can understand many of these problems in a unified regression framework and use simulated data to illustrate how they affect estimation and inference. Read more…