This page brings together lecture notes on selected topics in economic theory, econometrics, and causal inference, prepared by Professor Moisés A. Resende Filho, Department of Economics, University of Brasília (UnB).
These notes examine confounder bias through a graphical and algebraic decomposition in a linear structural model. They show how omitting a confounder leaves an open backdoor path between the explanatory variable and the outcome. As a result, the OLS estimator converges to a population regression coefficient that generally differs from the structural causal effect. The graphical representation identifies the source of the bias, while the algebra provides an explicit decomposition of its magnitude and sign.
These notes examine collider bias through a graphical and algebraic decomposition in a linear structural model. They show how conditioning on a collider opens an otherwise blocked noncausal path between the explanatory variable and the outcome. Consequently, the OLS estimator from a regression that includes the collider as a control converges to a population coefficient that generally differs from the structural causal effect. The graphical representation identifies the collider as a bad control, while the algebra quantifies the resulting bias.