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Forecasting with Feedback

T0 review · 0 major / 3 minor · reviewed 2026-05-24 · grok-4.3

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Pith's one-line read Forecasts can be optimally biased under quadratic loss when they shape policy and the forecaster cannot predict the exact policy response.

desk verdict The paper shows that uncertainty about the policymaker's reaction function can produce optimal forecast bias under quadratic loss via a feedback channel. read the letter →

arxiv 2308.15062 v4 submitted 2023-08-29 econ.TH econ.EM

Robert P. Lieli , Augusto Nieto-Barthaburu This is my paper
classification econ.THecon.EM
keywords forecastbiaspolicyfeedbackquadraticlossrationalityinflationforecastsGreenbookendogenousoutcomes
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper shows that forecasts used to guide policy decisions can rationally exhibit bias even when the forecaster minimizes quadratic loss, provided the policy actions alter the target variable and the forecaster is uncertain about the policy reaction. This setup creates an endogenous feedback loop in which the forecast influences the outcome it is trying to predict. A sympathetic reader would care because the result supplies a rational explanation for systematic forecast errors, such as those seen in inflation data, without needing to invoke irrationality or asymmetric loss functions. The finding directly questions the validity of standard rationality tests that ignore policy feedback.

What carries the argument

The uncertain policy reaction function, which turns the forecast into an input that endogenously shifts the target variable and thereby requires the forecaster to solve a fixed-point problem under incomplete information about the reaction.

What would settle it

If the policymaker's reaction rule is known with certainty, the optimal forecast under quadratic loss must be unbiased; any persistent bias observed in such a controlled setting would falsify the claim that uncertainty about the reaction is what produces the bias.

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Extended reading notes

Core claim

When a forecast informs policy actions that affect the realization of the forecasted variable itself, and the forecaster does not know the policymaker's exact reaction function, the forecast that minimizes expected quadratic loss is biased. The bias arises because the forecaster must account for the uncertain mapping from forecast to policy to outcome. The authors motivate the setup with stylized facts from Greenbook inflation forecasts and conclude that policy feedback undermines conventional tests of forecast rationality.

Load-bearing premise

The forecaster does not know exactly how the policymaker will respond to the forecast.

Editorial extensions

If this is right

  • Systematic forecast bias can be rational even under symmetric quadratic loss.
  • Standard tests of forecast rationality will tend to reject rationality when policy feedback is present.
  • The bias disappears once the forecaster learns the precise policy reaction rule.
  • Observed biases in inflation forecasts, such as those in the Greenbook, can be consistent with rational behavior.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same feedback logic could generate rational bias in non-policy domains whenever a forecast triggers actions that alter the forecasted quantity.
  • Making policy reaction rules more transparent would reduce the scope for this form of rational bias.
  • Empirical work could compare forecast bias before and after periods when policy rules became more predictable.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The paper claims that forecasts can be optimally biased under quadratic loss when they influence policy actions that feed back into the target variable, provided the forecaster is uncertain about the policymaker's reaction function. This is motivated by stylized facts from Greenbook inflation forecasts and implies that standard rationality tests may be misspecified in the presence of policy feedback.

Significance. If the derivation holds, the result supplies a rational, quadratic-loss explanation for observed forecast biases without requiring asymmetric loss or irrationality. It identifies a distinct channel (uncertainty over the policy mapping) that alters the first-order condition relative to the usual conditional-expectation benchmark and therefore has direct implications for how forecast rationality is tested in macroeconomic applications.

minor comments (3)
  1. [Abstract] Abstract: the stylized facts motivating the theory are referenced but not enumerated; a one-sentence summary of the key Greenbook patterns would make the link to the model immediate for readers.
  2. The complementary case (known reaction rule yields unbiased forecast) is noted but could be stated as a formal proposition or corollary to sharpen the boundary of the result.
  3. Notation for the forecaster's belief over the policy reaction function is introduced informally; an explicit definition early in the model section would aid traceability of the first-order condition.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the supportive summary, significance assessment, and recommendation of minor revision. The referee accurately captures the paper's core result on optimal bias under quadratic loss when forecasts affect policy and the forecaster is uncertain about the reaction function.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in theoretical derivation

full rationale

The paper advances a theoretical argument that uncertainty about the policymaker's reaction function alters the forecaster's optimization problem under quadratic loss, yielding optimal bias. This follows directly from the stated setup without any reduction to fitted parameters, self-definitional loops, or load-bearing self-citations. The abstract explicitly notes the complementary case (known reaction rule implies unbiased forecast), confirming the derivation is self-contained and falsifiable against external benchmarks rather than constructed from its own inputs.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The argument rests on standard domain assumptions in forecasting theory plus the novel modeling choice of uncertainty about the policy reaction; no free parameters or invented entities are mentioned in the abstract.

assumptions (3)
  • domain assumption Forecasters minimize expected quadratic loss
    Standard maintained assumption in tests of forecast rationality referenced in the abstract.
  • domain assumption Policy actions taken on the basis of the forecast affect the realized value of the target variable
    Core premise required for the feedback channel to operate.
  • ad hoc to paper The forecaster does not know the exact mapping from forecast to policy action
    The abstract states this uncertainty is the condition under which bias becomes optimal.

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Cite this review

Pith. "Pith review of Forecasting with Feedback." pith.science (2026). https://pith.science/paper/2308.15062

@misc{pith2026230815062,
  author       = {Pith},
  title        = {Pith review of: Forecasting with Feedback},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2308.15062}},
  note         = {Machine review of arXiv:2308.15062}
}
read the original abstract

Systematically biased forecasts are typically interpreted as evidence of forecasters' irrationality and/or asymmetric loss. In this paper we propose an alternative explanation: when forecasts inform policy decisions, and the resulting actions affect the realisation of the forecast target itself, forecasts may be optimally biased even under quadratic loss. The result arises in environments in which the forecaster is uncertain about the policymaker's reaction to the forecast, which is presumably the case in most applications. We motivate our theory by reviewing some stylised properties of Greenbook inflation forecasts. Our results point out that the presence of policy feedback poses a challenge to traditional tests of forecast rationality.

Figures

Figures reproduced from arXiv: 2308.15062 by the authors.

Figure 1
Figure 1. Properties of GB inflation forecasts: evolution of bias (left) and MZ-slope (right) [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. The MZ slope of the equilibrium forecast as a function of [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. The MZ slope of the equilibrium forecast as a function of [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The model’s timeline and influence diagram [PITH_FULL_IMAGE:figures/full_fig_p028_4.png]

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Reference graph

Works this paper leans on

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Reviewed May 24, 2026 · model on record in the stance chip above.