Normalization and instrumental variables in demand-supply equilibria: a graphical identification approach

This note studies graphical identification in the canonical competitive demand-supply model. Using Pearl’s (Citation2009) latent projection with explicit demand and supply shocks, it derives acyclic directed mixed graph representations that accommodate equilibrium determination while preserving standard econometric assumptions. The key point is that graphical identification is query-dependent: the same equilibrium system can imply different ADMGs depending on the normalization used to pose the structural question. Pearl’s (Citation2012) instrumental-variables theorem identifies the structural effect represented by the selected directed edge; normalization determines which economic parameter that edge denotes. Under demand-side normalization, the theorem identifies the demand slope; under supply-side normalization, it identifies the inverse supply slope. Standard IV estimands arise as special cases. An extension with instruments that have side effects shows how graphical separation diagnoses exclusion violations, identifies conditioning variables that restore validity, and yields a closed-form bias decomposition when side effects are ignored.