Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On the Wisdom of Crowds (of Economists)

Francis X. Diebold, Aaron Mora, Minchul Shin

Abstract

We study the properties of macroeconomic survey forecast response averages as the number of survey respondents grows. Such averages are ``portfolios" of forecasts. We characterize the speed and pattern of the gains from diversification as a function of portfolio size (the number of survey respondents) in both (1) the key real-world data-based environment of the U.S. Survey of Professional Forecasters, and (2) the theoretical model-based environment of equicorrelated forecast errors. We proceed by proposing and comparing various direct and model-based ``crowd size signature plots", which summarize the forecasting performance of $k$-average forecasts as a function of $k$, where $k$ is the number of forecasts in the average. We then estimate the equicorrelation model for growth and inflation forecast errors by choosing model parameters to minimize the divergence between direct and model-based signature plots. The results indicate near-perfect equicorrelation model fit for both growth and inflation, which we explicate by showing analytically that, under very weak conditions, the direct and fitted equicorrelation model-based signature plots are identical at a particular model parameter configuration. That parameter configuration immediately suggests an analytic closed-form estimator for the direct signature plot, so that equicorrelation ultimately emerges as a device for convenient calculation of direct signature plots, rather than a separate ``model" producing separate signature plots. In any event we find that the gains from survey diversification are greater for inflation forecasts than for growth forecasts, and that they are largely exhausted with inclusion of 5-10 representative forecasters.

On the Wisdom of Crowds (of Economists)

Abstract

We study the properties of macroeconomic survey forecast response averages as the number of survey respondents grows. Such averages are ``portfolios" of forecasts. We characterize the speed and pattern of the gains from diversification as a function of portfolio size (the number of survey respondents) in both (1) the key real-world data-based environment of the U.S. Survey of Professional Forecasters, and (2) the theoretical model-based environment of equicorrelated forecast errors. We proceed by proposing and comparing various direct and model-based ``crowd size signature plots", which summarize the forecasting performance of -average forecasts as a function of , where is the number of forecasts in the average. We then estimate the equicorrelation model for growth and inflation forecast errors by choosing model parameters to minimize the divergence between direct and model-based signature plots. The results indicate near-perfect equicorrelation model fit for both growth and inflation, which we explicate by showing analytically that, under very weak conditions, the direct and fitted equicorrelation model-based signature plots are identical at a particular model parameter configuration. That parameter configuration immediately suggests an analytic closed-form estimator for the direct signature plot, so that equicorrelation ultimately emerges as a device for convenient calculation of direct signature plots, rather than a separate ``model" producing separate signature plots. In any event we find that the gains from survey diversification are greater for inflation forecasts than for growth forecasts, and that they are largely exhausted with inclusion of 5-10 representative forecasters.

Paper Structure

This paper contains 12 sections, 2 theorems, 72 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction and Basic Framework
  2. Related Literature.
  3. Direct SPF Crowd Size Signature Plots
  4. Model-Based SPF Crowd Size Signature Plots
  5. Population Results Under Equicorrelation
  6. Estimating the Equicorrelation Model
  7. Calculating the Solution
  8. Understanding the Near-Perfect Equicorrelation Fit
  9. On the Assessment of Equicorrelation Model Fit
  10. Summary, Conclusions, and Directions for Future Research
  11. Data Definitions and Sources
  12. Optimal Combining Weights Under Weak Equicorrelation

Key Result

Theorem 1

Let $e_{t}$ be any covariance stationary $N \times 1$ vector with mean zero and covariance matrix $\Sigma$, given by and define the population $k$-average $MSE$, where $g_{k}$ represents any subset of $e_t$ of size $k$ ($k \in [1, N]$). Then and where

Figures (10)

  • Figure 1: SPF Participation
  • Figure 2: Direct $\widehat{MSE}^{avg}_{R,NT}(k)$ Crowd Size Signature Plots
  • Figure 3: Direct $\widehat{DMSE}^{avg}_{R,NT}(k)$ Crowd Size Signature Plots
  • Figure 4: Direct $\widehat{F}^{avg}_{R,NT}(k)$ Crowd Size Signature Plots
  • Figure 5: Theoretical Equicorrelation $MSE^{avg}_{R,N \infty}(k; \rho)$ Crowd Size Signature Plots
  • ...and 5 more figures

Theorems & Definitions (20)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8
  • Remark 9
  • Remark 10
  • ...and 10 more