Cheating with Models
AbstractBeliefs and decisions are often based on confronting models with data. What is the largest "fake" correlation that a misspecified model can generate, even when it passes an elementary misspecification test? We study an "analyst" who fits a model, represented by a directed acyclic graph, to an objective (multivariate) Gaussian distribution. We characterize the maximal estimated pairwise correlation for generic Gaussian objective distributions, subject to the constraint that the estimated model preserves the marginal distribution of any individual variable. As the number of model variables grows, the estimated correlation can become arbitrarily close to one regardless of the objective correlation.
CitationEliaz, Kfir, Ran Spiegler, and Yair Weiss. 2021. "Cheating with Models." American Economic Review: Insights, 3 (4): 417-34. DOI: 10.1257/aeri.20200635
- C13 Estimation: General
- C46 Specific Distributions; Specific Statistics
- C51 Model Construction and Estimation
- D83 Search; Learning; Information and Knowledge; Communication; Belief; Unawareness