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.

翻译：我们研究了宏观经济调查预测响应平均值随调查受访者数量增加时的特性。此类平均值可视为预测的"投资组合"。我们在以下两种环境中刻画了多样化收益随投资组合规模（调查受访者数量）变化的速度与模式：(1)基于美国专业预测者调查真实数据的关键现实环境；(2)基于等相关预测误差理论模型的环境。我们通过提出并比较多种直接与基于模型的"群体规模特征图"展开研究，这些图表总结了$k$个预测平均值（$k$为参与平均的预测数量）的预测性能随$k$变化的规律。随后，我们通过最小化直接特征图与模型特征图之间的差异来选择模型参数，从而估计增长与通胀预测误差的等相关模型。结果表明该模型对增长和通胀均具有近乎完美的拟合度，我们通过解析证明：在极弱条件下，当模型参数处于特定配置时，直接特征图与拟合的等相关模型特征图完全一致。该参数配置直接推导出直接特征图的解析闭式估计量，因此等相关性最终成为便捷计算直接特征图的工具，而非产生独立特征图的独立"模型"。无论如何，我们发现调查多样化对通胀预测的收益高于增长预测，且当纳入5-10位代表性预测者时，收益已基本达到饱和。