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arxiv: 1907.07425 · v1 · pith:TQKAHWIHnew · submitted 2019-07-17 · 💱 q-fin.GN · econ.TH· physics.soc-ph

Confidence Collapse in a Multi-Household, Self-Reflexive DSGE Model

Federico Guglielmo Morelli , Michael Benzaquen , Marco Tarzia , Jean-Philippe Bouchaud This is my paper

Pith reviewed 2026-05-24 20:09 UTC · model grok-4.3

classification 💱 q-fin.GN econ.THphysics.soc-ph
keywords DSGE modelself-reflexive feedbackhousehold confidenceeconomic crisescrisis probabilitymonetary policynarrativesrisk premium
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The pith

A minimal self-reflexive DSGE model produces economic crises whose probability depends exponentially on its parameters.

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

The paper constructs a multi-household DSGE model where individual households adjust their consumption based on past aggregate consumption through a confidence channel. This feedback generates several distinct regimes of economic output, including stable growth, short recessions, and sudden collapses from mild triggers. The key finding is that the likelihood of crises rises exponentially with changes in model parameters. This exponential sensitivity implies that financial markets cannot accurately price the risk premium for such events. The authors suggest that shaping economic narratives becomes a relevant tool for monetary policy to influence confidence.

Core claim

In this multi-household, self-reflexive DSGE model, past aggregate consumption directly modulates the confidence and thus the consumption propensity of individual households. This minimal mechanism produces a range of realistic dynamics: persistently high output, high output with volatility and brief deep recessions, or alternating high and low output states where small downturns can trigger steep declines via confidence collapse. The probability of entering a crisis state depends exponentially on the model's parameters.

What carries the argument

The self-reflexive feedback loop in which past aggregate consumption impacts individual household confidence and consumption propensity.

If this is right

  • Various parameter values lead to qualitatively different output dynamics, from stable to crisis-prone.
  • Crisis probability is an exponential function of the parameters.
  • Markets cannot efficiently price the risk premium due to this exponential dependence.
  • Narratives can act as a monetary policy instrument to steer the economy.

Where Pith is reading between the lines

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

  • Small policy-induced shifts in parameters might dramatically alter crisis likelihood.
  • Similar self-reflexive mechanisms could be explored in other macroeconomic models to test robustness.
  • Empirical calibration using consumption and survey data on confidence could validate the exponential scaling.

Load-bearing premise

Past aggregate consumption directly impacts the confidence and consumption propensity of individual households in a setup that produces the reported output dynamics.

What would settle it

Empirical data showing that crisis frequencies do not scale exponentially with measurable proxies for the model's parameters, or that aggregate consumption does not influence household confidence as assumed.

Figures

Figures reproduced from arXiv: 1907.07425 by Federico Guglielmo Morelli, Jean-Philippe Bouchaud, Marco Tarzia, Michael Benzaquen.

Figure 1
Figure 1. Figure 1: Numerical simulation of the model for increasing values of the confidence threshold c0 and for fixed values of θ = 5, σ = 0.6 and η = 0.5. Top graphs: temporal trajectories of the log output xt := log ct with a horizontal dot-dashed red line located at x0 and dashed black lines at x>,<; Bottom graphs: (log-)probability distribution p(x) of the output, with the corresponding positions of x0 and x>,<. From l… view at source ↗
Figure 2
Figure 2. Figure 2: Left: Phase diagram of the model, with analytically determined boundaries. Phase A: High Output, No Crises; Phase B+: High Output with Short-Lived Re￾cessions; Phase C: Long-Lived Booms & Recessions; Phase B−: Phase B−: Low Output with Short-Lived Spikes. The colour level encodes the distance ratio (c> −c ∗ )/(c ∗ −c<). This ratio is large in the yellow region, small in the blue region and equal to one alo… view at source ↗
Figure 3
Figure 3. Figure 3: Plot of log T(c> → c<) (left row) and log T(c< → c>) (right row) vs σ −2 for different values c0, and η = 0 (top graphs) and η = 0.5 (bottom row). The value of c0 increases with the points tonality becoming darker. The linear dependence confirms the validity of Eq. (16). The inset shows the corresponding barriers W as a function of c0. For η = 0, we plot the continuous time prediction Eq. (20) with ε = 1 (… view at source ↗
read the original abstract

We investigate a multi-household DSGE model in which past aggregate consumption impacts the confidence, and therefore consumption propensity, of individual households. We find that such a minimal setup is extremely rich, and leads to a variety of realistic output dynamics: high output with no crises; high output with increased volatility and deep, short lived recessions; alternation of high and low output states where relatively mild drop in economic conditions can lead to a temporary confidence collapse and steep decline in economic activity. The crisis probability depends exponentially on the parameters of the model, which means that markets cannot efficiently price the associated risk premium. We conclude by stressing that within our framework, {\it narratives} become an important monetary policy tool, that can help steering the economy back on track.

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 / 1 minor

Summary. The manuscript investigates a multi-househousehold DSGE model in which past aggregate consumption impacts the confidence and therefore the consumption propensity of individual households. This minimal self-reflexive setup is reported to generate a variety of realistic output dynamics, including stable high output without crises, high output with increased volatility and short recessions, and alternation between high and low output states in which mild downturns trigger temporary confidence collapses and steep declines. The central claim is that crisis probability depends exponentially on the model parameters, implying that markets cannot efficiently price the associated risk premium. The authors conclude that narratives become an important monetary policy tool for steering the economy.

Significance. If the exponential dependence of crisis probability on parameters is established by explicit derivation or exhaustive parameter sweeps, the result would strengthen the case for behavioral feedback mechanisms in DSGE models and would carry direct implications for tail-risk pricing and the scope of conventional monetary policy. The suggestion that narratives can serve as a policy instrument is a distinctive policy-oriented implication that, if formalized, could open new lines of research on communication effects within reflexive models.

major comments (2)
  1. [Abstract] Abstract: the claim that 'the crisis probability depends exponentially on the parameters of the model' is presented without any supporting equation, closed-form derivation, simulation protocol, or parameter sweep, so it is impossible to determine whether the exponential form is a derived property or an artifact of the chosen functional specification.
  2. [Abstract] Abstract: the model is described as 'minimal' yet no equations, state variables, or aggregation rules are supplied, preventing evaluation of whether the reported variety of output regimes follows from the self-reflexive consumption-confidence link or requires additional ad-hoc assumptions.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'self-reflexive DSGE model' is introduced without a concise definition or reference to the precise feedback channel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed comments on the abstract. We address each point below and will revise the abstract accordingly to improve clarity while preserving its concise nature.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'the crisis probability depends exponentially on the parameters of the model' is presented without any supporting equation, closed-form derivation, simulation protocol, or parameter sweep, so it is impossible to determine whether the exponential form is a derived property or an artifact of the chosen functional specification.

    Authors: The abstract summarizes a result established in the full manuscript via extensive numerical simulations and parameter sweeps (detailed in Section 4), rather than a closed-form derivation. The exponential dependence emerges from the self-reflexive feedback and is not an artifact of the functional form chosen for confidence updating. To address the concern, we will revise the abstract to briefly indicate that the claim is supported by simulation protocols and sweeps reported in the main text. revision: yes

  2. Referee: [Abstract] Abstract: the model is described as 'minimal' yet no equations, state variables, or aggregation rules are supplied, preventing evaluation of whether the reported variety of output regimes follows from the self-reflexive consumption-confidence link or requires additional ad-hoc assumptions.

    Authors: The abstract is intentionally high-level. The full model specification—including the equations governing individual household consumption propensity, the state variables (past aggregate consumption as the confidence input), and the aggregation from heterogeneous households to macro outcomes—is provided in Section 2 of the manuscript. The variety of regimes arises directly from the minimal self-reflexive link without additional ad-hoc elements. We will revise the abstract to include a short reference to the model section or a one-sentence outline of the setup. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The provided abstract and context contain no equations, derivations, parameter-fitting procedures, or self-citations. Claims such as exponential dependence of crisis probability on parameters are stated as model outputs without any visible chain that could reduce to fitted inputs or self-referential definitions. No load-bearing steps are present to inspect, so the derivation cannot be shown to collapse by construction.

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 an unspecified functional form linking aggregate consumption to individual confidence.

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