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The calculus of dissent: Bias and diversity in FOMC projections


Economic projections by the Federal Open Market Committee (FOMC) were very inaccurate in the years during and after the Great Recession. Relying on a model of collective prediction that weighs the “wisdom of crowds” against shared biases, we examine GDP forecast errors in a panel dataset of FOMC projections from 1992 through 2016. Consistent with the model, we find that diversity of projections reduces collective error, while shared bias magnifies collective error. Collective error is associated strongly with errors by the Federal Reserve Board staff. The benefits of diversity often are statistically significant, especially for projections with terms longer than 1 year.

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Fig. 1

Sources: a Based on FOMC \(SEP\), b adapted from FRB Greenbook (p. I-20), actual rates from FRED

Fig. 2

Sources: a based on FOMC \(SEP\), b adapted from FRB Greenbook (p. I-27), actual rates from FRED

Fig. 3
Fig. 4
Fig. 5


  1. Krause (1996) identifies different voting patterns between the FRB Governors and the regional Federal Reserve bank presidents. Eichler and Lähner (2014) find that FOMC members with experience at regional banks focus more on inflation stabilization, while those from the FRB favor output stabilization.

  2. Landemore (2012, p. 1) notes that the idea of collective wisdom dates back to the time of Aristotle. Surowiecki (2004) proposes several types of crowd-sourced wisdom and identifies elements that lead to the success or failure of collective wisdom. Page (2007) provides a mathematical formalization, while Page (2014) discusses the sources and benefits of predictive diversity. Hong and Page (2004, p. 16385) find that “[g]roups of diverse problem solvers can outperform groups of high-ability problem solvers.” Budescu and Chen (2014) argue that the wisdom of crowds can be used to improve central bank forecasting.

  3. See, for example, Ellison and Sargent (2012), Ellis and Liu (2013), El-Shagi et al. (2014), Sheng (2015), and Binder and Wetzel (2018).

  4. See Havrilesky and Gildea (1995), Eichler and Lähner (2014), Smales and Apergis (2016), and Bennani et al. (2018).

  5. Orphanides and Wieland (2008) find that FOMC decisions are more closely related to the FOMC’s own projections than to recent economic conditions. Sheng (2015) finds that variation in FOMC forecasts is affected by economic conditions in the Federal Reserve districts.

  6. For discussions of more recent political influence on Fed policy, see Selgin (2020), Boettke et al. (2021), Cachanosky et al. (2021), and Jordan and Luther (2020).

  7. See

  8. See the FRB staff Greenbook (September 2008, p. I-26).

  9. See the FRB staff Greenbook (December 2008, p. I-25).

  10. For now, we discuss the case of predicting a single value X. For our empirical analysis in Sect. 5, predictions are made for values of \(X_t\) at some future time t.

  11. Quadratic loss functions are commonly assumed in the evaluation of monetary policy.

  12. The mathematical derivation is provided in Appendix A. For further discussion of the diversity prediction theorem, see Page (2007) and Hong and Page (2012).

  13. Despite its widespread popularity, however, the authors argue that The Calculus has had limited impact on academic research outside the field of public choice or on the US political process.

  14. Available online at

  15. Available online at

  16. Romer (2010) provides a similar dataset back to 1978 but acknowledges (p. 952) that data prior to 1992 are incomplete and sometimes reveal discrepancies between the data available from the FRB and those published in the MPRs. Marquez and Kalfa (2021) update and extend Romer’s analysis using a dataset of MPRs and SEPs similar to the one used in this paper.

  17. Available online at

  18. Available online at

  19. Available online at

  20. Like Romer and Romer (2004), we find that results from regressions estimated by ordinary least squares (OLS) with robust standard errors are similar to those of our base-case WLS regressions.

  21. For example, the forecast for the current year is the lag for the forecast 1 year ahead. The forecast 1 year ahead is the lag for the forecast 2 years ahead, and the forecast 2 years ahead is the lag for the forecast 3 years ahead. Forecasts for the current year are dropped since no lags are available.

  22. Available at

  23. See, for example, Eichler and Lähner (2014) and Smales and Apergis (2016).

  24. For potential output, we rely on the percentage change in real potential GDP from the prior year available from FRED. The results relying on SEP data are similar using a constant rate of potential output such as the long-run average from 1960–2018 of \(y^*=3.1\%\) or the average over our sample period of \(y^*=2.6\%\). Future studies might explore other deviations from trend such as difference from the non-accelerating inflation rate of unemployment (NAIRU).


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For helpful comments and suggestions, the author thanks Carola Binder, Maxwell Hampton, Amelia Janaskie, Leo Krasnozhon, Alexander Schaefer, David Schatz, seminar participants at Texas Tech University, the Public Choice Society annual conference, and the AIER Sound Money Program annual conference.

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Correspondence to Thomas L. Hogan.

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The author has no related interests to disclose and received no grants or funding for this project. All data used in this study are publicly available from the Federal Reserve Board of Governors and the Federal Reserve Banks of Philadelphia and St. Louis.

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Appendix A. Applying the diversity prediction theorem to FOMC projections

Appendix A. Applying the diversity prediction theorem to FOMC projections

Assume agents want to predict the true value of some variable \(X\). Let \(x_{im}\) be independent predictions of \(X\) by individual \(i\) at meeting \(m\). Let \(s_m\) be the mean prediction of \(i\) individuals at meeting \(m\).

$$\begin{aligned} s_m = \frac{1}{k}\sum _{i=1}^k x_{im} \end{aligned}$$

Let \(c\) be the mean of \(s_m\) over \(m\) meetings.

$$\begin{aligned} c = \frac{1}{n}\sum _{m=1}^n s_m \end{aligned}$$

Let collective error be the squared difference between the collective error and the target value \((c-X)^2\). We use the diversity prediction theorem (DPT) to solve for collective error in terms of meeting diversity, the squared difference between individual and collective predictions at each FOMC meeting \((s_m-c)^2\), and meeting error, the squared difference between the mean meeting prediction and the actual value \((s_M-X)^2\). We begin by expanding the polynomial of collective error, inserting an additional square of collective error \((c^2-c^2)\), and then rearranging the terms.

$$\begin{aligned} (c-X)^2&= c^2-2cX+X^2 \end{aligned}$$
$$\begin{aligned}&= c^2-2cX+X^2 +(c^2-c^2) \end{aligned}$$
$$\begin{aligned}&= 2c^2-c^2-2cX+X^2 \end{aligned}$$

Since \(c\) is the mean of \(s_m\) as shown in equation 17, we can replace two of the \(c\) variables with the mean of \(s_m\). We then insert a square of the mean of \(s_m\) minus itself. We then rearrange the terms into groups of \(X\) and \(c\).

$$\begin{aligned} (c-X)^2&= 2s_m c-c^2-2s_m X+X^2 \end{aligned}$$
$$\begin{aligned}&= 2s_m c-c^2-2s_m X+X^2+\bigg [\frac{1}{n}\sum _{m=1}^n(s_m^2-s_m^2)\bigg ] \end{aligned}$$
$$\begin{aligned}&= \bigg [\frac{1}{n}\sum _{m=1}^n(s_m^2)\bigg ]-2s_m X+X^2-\bigg [\frac{1}{n}\sum _{m=1}^n(s_m^2)\bigg ]+2s_m c-c^2 \end{aligned}$$

Since \(X\) and \(c\) are constant in \(m\), these terms can be moved inside a single summation.

$$\begin{aligned} (c - X)^2 =\frac{1}{n}\sum _{m=1}^n\bigg [(s_m^2-2s_m X+X^2)-(s_m^2-2s_m c+c^2)\bigg ] \end{aligned}$$

Factoring the polynomials gives us the DPT used in Eq. 1.

$$\begin{aligned} (c - X)^2 =\frac{1}{n}\mathop {\sum }_{m=1}^n \bigg [-(s_m-c)^2+(s_m-X)^2\bigg ] \end{aligned}$$

Since \(s_m\) is the mean of individual predictions per meeting, we can follow the same process of the DPT to expand into components of meeting diversity, the squared difference between individual predictions and the mean meeting prediction \((x_{im}-s_m)^2\), and the individual error, the squared difference between individual predictions and actual values \((x_{im}-X)^2\).

$$\begin{aligned} (s_m-X)^2&= s_m^2-2s_m X+X^2 \end{aligned}$$
$$\begin{aligned}&= s_m^2-2s_m X+X^2 +(s_m^2-s_m^2) \end{aligned}$$
$$\begin{aligned}&= 2s_m^2-s_m^2-2s_m X+X^2 \end{aligned}$$
$$\begin{aligned}&= 2x_{im} s_m-s_m^2-2x_{im} X+X^2 \end{aligned}$$
$$\begin{aligned}&= 2x_{im} s_m-s_m^2-2s_{im} X+X^2+\bigg [\frac{1}{k}\sum _{i=1}^k(x_{im}^2-x_{im}^2)\bigg ] \end{aligned}$$
$$\begin{aligned}&= \bigg [\frac{1}{k}\sum _{i=1}^k(x_{im}^2)\bigg ]-2x_{im} X+X^2-\bigg [\frac{1}{k}\sum _{i=1}^k(x_{im}^2)\bigg ]+2x_{im} s_m-s_m^2 \end{aligned}$$
$$\begin{aligned}&= \frac{1}{k}\sum _{i=1}^k\bigg [(x_{im}^2-2x_{im} X+X^2)-(x_{im}^2-2x_{im} s_m+s_m^2)\bigg ]\end{aligned}$$
$$\begin{aligned}&= \frac{1}{k}\mathop {\sum }_{i=1}^k \bigg [-(x_{im}-s_m)^2+(x_{im}-X)^2\bigg ] \end{aligned}$$

Inserting Eqs. 33 into 25 gives us Eq. 34. Collective error \((c-X)^2\) equals the mean of individual errors \((x_{im}-X)^2\) less group diversity \((s_m-c)^2\) and mean meeting diversity \((x_{im}-s_m)^2\).

$$\begin{aligned} (c - X)^2 = \frac{1}{n}\mathop {\sum }_{m=1}^n \bigg [-(s_m-c)^2+\frac{1}{k}\sum _{i=1}^{k}\bigg (-(x_{im}-s_m)^2+(x_{im}-X)^2\bigg ) \bigg ] \end{aligned}$$

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Hogan, T.L. The calculus of dissent: Bias and diversity in FOMC projections. Public Choice 191, 105–135 (2022).

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  • Federal Reserve
  • Forecasting
  • Committee decisions
  • Wisdom of crowds

JEL Classification

  • D71
  • D73
  • E37
  • E47
  • E58