Cheating with (Recursive) Models

41 Pages Posted: 15 Nov 2019 Last revised: 2 Dec 2019

See all articles by Kfir Eliaz

Kfir Eliaz

Tel Aviv University

Rani Spiegler

Tel Aviv University

Yair Weiss

Hebrew University of Jerusalem

Date Written: November 2019

Abstract

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.

Suggested Citation

Eliaz, Kfir and Spiegler, Rani and Weiss, Yair, Cheating with (Recursive) Models (November 2019). CEPR Discussion Paper No. DP14100. Available at SSRN: https://ssrn.com/abstract=3486251

Kfir Eliaz (Contact Author)

Tel Aviv University ( email )

Ramat Aviv
Tel-Aviv, 6997801
Israel

Rani Spiegler

Tel Aviv University ( email )

Yair Weiss

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, IL Jerusalem 91905
Israel

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