Combining Forecasts from Multiple Experts for Multiple Variables

We propose a new method for combining point forecasts from multiple experts across multiple variables to improve inference about an unknown variable. Traditional aggregation methods combine forecasts for each variable separately (we refer to these methods as separate inference methods). However, in practice, each expert frequently provides a forecast for each variable across multiple variables. Because forecast errors can be correlated across the variables, the decision maker may additionally benefit from pooling forecasts for the other variables (we refer to our proposed method as pooled inference). Our model assumes that the forecast error arises from multiple sources of randomness, including a variable-specific factor, an expert-specific factor, a common factor, and idiosyncratic noise. When the covariance structure of the forecast errors is known, we show that the pooled inference is structurally equivalent to the separate inference but with reduced idiosyncratic noise, thereby allowing for more effective weighting of experts’ forecasts. When the covariance structure is unknown, we derive the optimal form for the consensus forecast under the pooled inference, which can be easily implemented. Our empirical analysis demonstrates that the pooled inference can outperform widely used separate inference methods in some forecasting environments. Additionally, even when pooling a large number of variables—necessitating the handling of high-dimensional covariance matrices—the pooled inference remains computationally manageable.

This paper was accepted by Manel Baucells, behavioral economics and decision analysis.

Funding: The research of Z. Chen and L. Zhao is supported by Start-Up Grants from the National University of Singapore [Grants A-0003854-00-00 and A-0003853-00-00, respectively].

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.06161.