Discussion paper
DP14100 Cheating with (recursive) models
To what extent can misspecified models generate false estimated correlations? We focus on models that take the form of a recursive system of linear regression equations. Each equation is fitted to minimize the sum of squared errors against an arbitrarily large sample. We characterize the maximal pairwise correlation that this procedure 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.
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