Cheating with Models
- American Economic Review: Insights (Forthcoming)
Beliefs 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.
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