Abstract:
To what extent can misspecified subjective models distort 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 an objective empirical distribution. We characterize the maximal pairwise correlation that the analyst’s model 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 estimated pairwise correlation can become arbitrarily large, regardless of the objective correlation.