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arxiv: 2606.30040 · v1 · pith:OM5OHJO6new · submitted 2026-06-29 · 💰 econ.EM

The Shape of Macroeconomic Beliefs

Giovanni Angelini This is my paper

Pith reviewed 2026-06-30 03:32 UTC · model grok-4.3

classification 💰 econ.EM
keywords prediction marketsinflation riskdistributional expectationsCPIKalshi contractsforecast surprisestail probabilitiesmacroeconomic beliefs
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The pith

Prediction markets recover distributions of short-run inflation beliefs missed by point forecasts.

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

The paper constructs high-frequency probability distributions for CPI and core CPI using prices from Kalshi prediction markets. These distributions show that market means track consensus but that uncertainty and upper-tail probabilities respond to past forecast surprises. Positive lagged surprises raise the chance assigned to inflation above 0.3 percent by 4.7 percentage points per tenth of a point, after controlling for current consensus. Readers would care if these markets supply timely information on inflation risk that standard forecasts overlook.

Core claim

The central claim is that prediction-market prices can be turned into probability mass functions over inflation outcomes that contain real-time information about uncertainty and tail risks. Lagged Reuters Poll surprises do not shift the market mean away from consensus but do increase implied uncertainty and the probability of high inflation outcomes. In validation, the upper-tail probabilities forecast actual high-inflation episodes even when the mean is near consensus.

What carries the argument

The conversion of adjacent threshold contract prices on Kalshi into a probability mass function over possible inflation outcomes.

If this is right

  • Lagged surprises increase market-implied uncertainty about inflation.
  • Positive lagged surprises raise the probability assigned to high-inflation outcomes.
  • Upper-tail probabilities from the market predict realizations of high inflation.
  • The distributional signal provides information beyond the market mean or consensus point forecast.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the approach generalizes, similar distributions could be recovered for other macroeconomic variables traded on prediction platforms.
  • Policy makers could monitor these markets for early signals of shifting inflation risk.
  • Extensions might test whether the same patterns hold for longer-horizon inflation expectations.

Load-bearing premise

The conversion of adjacent Kalshi threshold contract prices into a probability mass function over inflation outcomes accurately recovers the market's true belief distribution without material liquidity premia, transaction costs, or other pricing frictions.

What would settle it

A failure of the Kalshi upper-tail probabilities to predict high-inflation realizations in out-of-sample releases, particularly in cases where the implied mean matches the consensus forecast.

Figures

Figures reproduced from arXiv: 2606.30040 by Giovanni Angelini.

Figure 1
Figure 1. Figure 1: Market-implied distribution of CPI beliefs before release [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Market-implied inflation beliefs before release [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Kalshi-implied mean versus realized inflation at one hour [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Reuters surprises and the shape of market-implied inflation beliefs [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Upper-tail beliefs after recent inflation deviations [PITH_FULL_IMAGE:figures/full_fig_p030_5.png] view at source ↗
read the original abstract

Macroeconomic expectations are usually observed through point forecasts or through asset prices whose mapping into beliefs is model-dependent. This paper uses prediction-market prices to recover high-frequency distributions of short-run macroeconomic beliefs. We construct a panel of Kalshi-implied distributions for CPI and core CPI releases by converting adjacent threshold contracts into probability mass over inflation outcomes. The data reveal market-implied means, uncertainty, and upper-tail probabilities from 30 days to one hour before each release. The market-implied mean contains meaningful forecast information, especially for headline CPI, but the main signal is distributional. Lagged Reuters Poll surprises do not predict systematic deviations of Kalshi means from the current Reuters consensus. By contrast, large lagged surprises are associated with higher implied uncertainty, and positive lagged surprises raise the probability assigned to fixed high-inflation outcomes. In the baseline specification with variable-by-horizon fixed effects, a 0.1 percentage point positive lagged surprise raises the probability of monthly inflation above 0.3 percent by about 4.7 percentage points, even after controlling for the current consensus forecast. In release-level validation tests, Kalshi upper-tail probabilities also predict the realization of high-inflation states, including episodes in which the market-implied mean remains close to the Reuters consensus. The evidence suggests that prediction markets can provide real-time information about inflation risk that is missed by point forecasts.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper constructs high-frequency implied probability distributions for CPI and core CPI releases by converting prices of adjacent Kalshi threshold contracts into discrete probability mass functions. It reports that lagged Reuters poll surprises do not shift the market-implied mean relative to the current consensus but do increase implied uncertainty and raise the probability mass on upper-tail outcomes; in the baseline specification a 0.1 pp positive lagged surprise raises the probability of inflation above 0.3 percent by 4.7 pp after controlling for the consensus forecast. Release-level tests show these upper-tail probabilities also predict realized high-inflation states.

Significance. If the results hold, the work supplies a new source of real-time distributional beliefs about short-run macroeconomic variables that is not model-dependent in the usual sense and that appears to contain information about inflation risk missed by point forecasts. The panel structure at horizons from 30 days to one hour before release is a distinctive feature with potential value for studies of expectation updating.

major comments (2)
  1. [Data construction] Data construction paragraph (abstract and methods): the mapping from adjacent Kalshi threshold contract prices to a PMF over inflation bins is presented without reported checks for liquidity premia, bid-ask spreads, or inventory effects, particularly in the upper-tail contracts that define the >0.3 percent bin. Because this mapping supplies the dependent variable for the headline regression, any systematic pricing friction correlated with lagged surprises would directly affect the 4.7 pp coefficient.
  2. [Baseline specification] Baseline specification (results section): the regression with variable-by-horizon fixed effects reports a 4.7 pp response of P(inflation > 0.3 percent) to a 0.1 pp lagged surprise. It is not stated whether the standard errors incorporate the fact that the outcome is a generated regressor derived from noisy contract prices, nor whether the result is robust to alternative ways of allocating probability mass between adjacent thresholds.
minor comments (2)
  1. The abstract refers to 'release-level validation tests' but does not list the exact specifications, sample restrictions, or number of high-inflation episodes examined.
  2. Notation for the probability mass function and the exact thresholds used to define the upper-tail bin should be stated explicitly in the main text rather than only in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on data construction and inference. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Data construction] Data construction paragraph (abstract and methods): the mapping from adjacent Kalshi threshold contract prices to a PMF over inflation bins is presented without reported checks for liquidity premia, bid-ask spreads, or inventory effects, particularly in the upper-tail contracts that define the >0.3 percent bin. Because this mapping supplies the dependent variable for the headline regression, any systematic pricing friction correlated with lagged surprises would directly affect the 4.7 pp coefficient.

    Authors: We agree that explicit checks for liquidity premia, bid-ask spreads, and inventory effects are warranted given that the PMF is the source of the dependent variable. The revised manuscript will add a robustness subsection that (i) reports average bid-ask spreads by horizon and contract, (ii) re-estimates the main specification using mid prices, and (iii) restricts the sample to contracts with above-median trading volume. We will also discuss the possibility of inventory effects in thin upper-tail markets and note that the headline coefficient remains stable under these checks. revision: yes

  2. Referee: [Baseline specification] Baseline specification (results section): the regression with variable-by-horizon fixed effects reports a 4.7 pp response of P(inflation > 0.3 percent) to a 0.1 pp lagged surprise. It is not stated whether the standard errors incorporate the fact that the outcome is a generated regressor derived from noisy contract prices, nor whether the result is robust to alternative ways of allocating probability mass between adjacent thresholds.

    Authors: We acknowledge that the outcome is a generated regressor and that the current draft does not address the resulting inference issues or alternative PMF constructions. The revision will (i) implement a bootstrap that resamples contract prices before constructing the PMFs and (ii) report the main result under two alternative mass-allocation rules (uniform within bins and linear interpolation). These additions will confirm whether the 4.7 pp coefficient and its significance are robust. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical construction and regressions are externally falsifiable

full rationale

The paper performs data construction by converting adjacent Kalshi threshold contract prices into a discrete PMF over inflation bins, followed by panel regressions of implied moments and tail probabilities on lagged surprises (with controls for consensus forecasts and fixed effects). No equations, ansatzes, or uniqueness claims are present that reduce by construction to fitted inputs or prior self-citations. The PMF conversion is an identifying assumption about risk-neutral pricing, but the resulting regression coefficients are testable against realized inflation outcomes and can be replicated or falsified with independent data. No load-bearing self-citation chains or self-definitional steps appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that prediction-market prices map directly to beliefs.

pith-pipeline@v0.9.1-grok · 5760 in / 1097 out tokens · 41649 ms · 2026-06-30T03:32:26.789489+00:00 · methodology

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Reference graph

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