Is it Better to Average Probabilities or Quantiles?

31 Pages Posted: 25 May 2012 Last revised: 29 Sep 2012

Kenneth C. Lichtendahl Jr.

University of Virginia - Darden School of Business

Yael Grushka-Cockayne

University of Virginia - Darden School of Business

Robert L. Winkler

Duke University - Fuqua School of Business

Date Written: March 27, 2012

Abstract

We consider two ways to aggregate expert opinions using simple averages: averaging probabilities and averaging quantiles. We examine analytical properties of these forecasts and compare their ability to harness the wisdom of the crowd. In terms of location, the two average forecasts have the same mean. The average quantile forecast is always sharper: it has lower variance than the average probability forecast. Even when the average probability forecast is overconfident, the shape of the average quantile forecast still offers the possibility of a better forecast. Using probability forecasts for GDP growth and inflation from the Survey of Professional Forecasters, we present evidence that both when the average probability forecast is overconfident and when it is underconfident, it is outperformed by the average quantile forecast. Our results show that averaging quantiles is a viable alternative and indicate some conditions under which it is likely to be more useful than averaging probabilities.

Keywords: probability forecasts, quantile forecasts, expert combination, linear opinion pooling

JEL Classification: C10, C53, E17

Suggested Citation

Lichtendahl, Kenneth C. and Grushka-Cockayne, Yael and Winkler, Robert L., Is it Better to Average Probabilities or Quantiles? (March 27, 2012). Darden Business School Working Paper No. 2066806. Available at SSRN: https://ssrn.com/abstract=2066806 or http://dx.doi.org/10.2139/ssrn.2066806

Kenneth C. Lichtendahl Jr.

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States

Yael Grushka-Cockayne (Contact Author)

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States

Robert L. Winkler

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

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