  To what extent can agents with misspecified subjective models predict false
correlations? We study an "analyst" who utilizes models that take the form of a
recursive system of linear regression equations. The analyst fits each equation
to minimize the sum of squared errors against an arbitrarily large sample. We
characterize the maximal pairwise correlation that the analyst can predict
given a generic objective covariance matrix, subject to the constraint that the
estimated model does not distort the mean and variance of individual variables.
We show that as the number of variables in the model grows, the false pairwise
correlation can become arbitrarily close to one, regardless of the true
correlation.
