Fat Tail Notes · Part 16 · V10-P4 revisited
Last week this series argued that a backstop builds the tail it truncates: once leveraged accounts believe the policy will cap their losses, leverage rises, and the same shock lands on bigger books. A real academic paper is now arguing the opposite — and it is not a blog post, it is IMF-published research. Gideon Bornstein and Guido Lorenzoni's Moral Hazard Misconceptions: The Case of the Greenspan Put (2018) makes the case that the fear of the Fed put is, in their words, a misconception: under optimal discretionary intervention, borrowing rises but overborrowing disappears, and ex-post intervention becomes a substitute for ex-ante regulation.
My first reaction after reading it was to concede. My second reaction was that this is not a dispute about who is right. It is a dispute about which moment of the loss distribution you are willing to optimize. And the third, most uncomfortable finding: our own Part 15 contained a data error in two of its mean figures. This post fixes that too, because if you want readers to trust your tail numbers, you correct your center numbers in public.
1. What the paper actually says
The model is a three-period economy with a levered agent (B) who holds the risky asset, financed by debt from a patient saver (A), with sticky prices and an aggregate-demand externality. The mechanism runs through the labor wedge: a larger debt stock worsens recessions because debt payments transfer resources from high-propensity borrowers to low-propensity lenders, dragging down output exactly when output is already too low.
The paper compares three monetary regimes:
- Inertial: the central bank sets the interest rate before seeing the shock. The shock is uninsured, the aggregate-demand externality is live, and there is overborrowing — a marginal welfare loss from debt (dW/dD < 0). This is the textbook case for macroprudential regulation.
- Proactive: the central bank sets rates state-by-state after seeing the shock. With log preferences, it can fully stabilize asset prices and output — the Greenspan put at maximum potency. Borrowing goes up (Proposition 2), but overborrowing goes to zero (Proposition 3): dW/dD = 0, so a borrowing tax buys nothing.
- Output targeting: commits to the flexible-price allocation; coincides with the proactive regime in the log case.
The headline: more borrowing, less overborrowing. The put does not create the inefficiency that regulation exists to fix, so ex-post intervention and ex-ante macroprudential policy are substitutes. Moral hazard as conventionally feared is a misconception.
2. The knife-edge they concede
The full-results version is narrower than the headline, and the paper says so itself. The perfect-stabilization result is a knife-edge that requires log utility — an elasticity of intertemporal substitution of exactly one, where income and substitution effects cancel. Section 5 shows what happens away from that edge: once preferences are general CRRA, the central bank faces a tradeoff between output stabilization and financial stability, and the insurance motive pushes it to stabilize asset prices beyond what output targeting requires.
That is the telling part. In their own Section 5.2, the moment the central bank goes beyond output-gap targeting to prop up asset prices — the actual behavior people mean by "the put" — monetary policy and macroprudential policy become complements, and the optimal borrowing tax is larger in the proactive regime than in the output-targeting regime. The conventional moral-hazard result comes back. What the paper really shows is not "moral hazard is a misconception" but "moral hazard disappears exactly on the log-utility knife-edge where the put is a perfect insurance contract."
There is a second, quieter assumption running through the whole paper: welfare is always evaluated as expected utility, E[V^A + βV^B]. Every proposition is about the mean of the welfare distribution. Nothing in the model — not one equation — looks at the lower tail of the outcome distribution as a separate object.
3. What our code says, on both accounts
Here is the trap we built to show. Our Monte Carlo (2,000 paths, seed 20260921) lets leverage be either exogenous (λ = 1.0) or policy-endogenous (λ drawn from a distribution with mean above 1 — the world the backstop creates). The same 2,000 shocks, two different worlds:
| scenario | mean | p10 | p1 | worst |
|---|---|---|---|---|
| no backstop, λ=1.0 (exogenous) | -34.1% | -41.0% | -43.9% | -49.0% |
| backstop, λ=1.0 (exogenous) | -21.3% | -23.2% | -24.8% | -31.1% |
| backstop, λ ~ N(1.35, 0.25) | -24.5% | -27.5% | -29.4% | -31.3% |
| backstop, λ ~ N(1.5, 0.30) | -25.5% | -28.4% | -30.4% | -31.7% |
| backstop, λ ~ N(1.75, 0.35) | -26.9% | -29.5% | -31.1% | -33.2% |
Now read the same table through each paper's lens.
Bornstein-Lorenzoni's lens — the mean. The backstop rescues the mean by 12.8 points (-34.1% → -21.3%). Endogenous leverage eats 5.6 of those points back (-21.3% → -26.9% at λ~1.75), 44% of the mean rescue. By a mean-welfare standard, the policy is doing its job: it improves the average outcome massively, and the erosion, while real, is a second-order correction to a first-order rescue.
Our lens — the tail. The backstop's p1 rescue is 19.1 points (-43.9% → -24.8%) — the tail is where the policy's value is concentrated. Endogenous leverage eats 6.3 points of that tail (-24.8% → -31.1%), 33% of the p1 rescue, and shifts p10 from -23.2% to -29.5%. The rescue is not canceled, but the deepest outcomes the policy promises to prevent are precisely the ones drifting back toward the no-policy world.
Same shocks, same policy, two defensible accounts. The disagreement is not in the mechanism — both accounts agree leverage responds to the put. The disagreement is in the objective function: expected welfare has no tail. Tail risk has no average.
4. Which measure is right? It depends on the cost of the tail.
Here is the honest version of the argument. If the social cost of a crisis is proportional to the mean loss, Bornstein and Lorenzoni are right — the backstop is a clean win and the moral-hazard complaint is a distraction. But crisis costs are not proportional. A -25% drawdown and a -31% drawdown do not cost society in the same units: the second one crosses into forced selling cascades, dealer gamma flips, liquidity gaps, policy-space exhaustion, and the political aftershocks that turn a market event into a regulatory one. The cost function is convex in the loss, and convexity is exactly what expected utility with representative agents averages away.
Two doctors see the same patient. Doctor A prescribes the painkiller because mean pain over the year falls from 7 to 4. Doctor B objects that the worst day — the day the patient overexerts because the painkiller masks the injury — went from 9 to 10. Both are reporting the same data. The patient's choice is which number the treatment is supposed to optimize. A central bank that only reports the mean is Doctor A reporting only the mean.
5. Their paper actually licenses our setup
The most useful sentence in Moral Hazard Misconceptions is the one that limits its own headline: complementarity — the return of moral hazard — appears "if the monetary authority goes over and above a simple objective of reducing the output gap." Our Part 12-15 series models exactly that kind of intervention: a backstop, an explicit asset-price floor and liquidity guarantee, not a Taylor rule. We are not on their log-utility knife-edge where the put is a perfect insurance contract; we are in the regime their Section 5.2 shows to be the complementary one, where the put stabilizes asset prices beyond output targeting and the borrowing tax is more valuable, not less.
Which is why the two literatures converge on the same policy conclusion from opposite directions. Boissay and Uhlig's Reserves and the Buyer of Last Resort (NBER w35548) calls it the market-backstop principle: make the backstop state-contingent and pair it with liquidity requirements that tax the behavior the backstop insures. Our Part 15 ended at the same place by simulation: ambiguity stops the front-run, but only a leverage rule stops the subsidy.
6. Correction and judgment
Correction. In the Part 15 Monte Carlo table, two mean figures were wrong: the no-backstop mean should be -34.1% (published as -42.3%) and the exogenous-backstop mean should be -21.3% (published as -24.6%). All p10, p1, and worst figures were correct. The corrected means change one sentence of that post's argument: the mean does move under endogenous leverage (-21.3% → -24.5% → -25.5% → -26.9%), it just moves less than the tail, and the rescue's value is concentrated in the tail either way. The stronger, corrected claim: the backstop's value lives in the tail, and the tail is also where the leverage it induces does the most damage.
Judgment. For the retail investor, the academic argument over moral hazard is not the thing to resolve. Two facts survive it. First, in mean terms, interventions do hold the market up — the rescue is real, and betting against it is a fool's trade. Second, in tail terms, the same intervention is accumulating the leverage that will make the next floor deeper — the rescue is expensive, and it is priced in the distribution's tail, not its headline. A put is not permission to be naked; it is time to put on the underwear.
Code: crash_simulator_v10/policy_moral_hazard.py (V10-P4), self-test and Monte Carlo included. Deterministic, 402 lines, no external dependencies. Correction committed alongside this post.
Paper: Bornstein & Lorenzoni, "Moral Hazard Misconceptions: The Case of the Greenspan Put" — gideon-bornstein.com/papers/Moral_Hazard_Greenspan_Put.pdf
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Drafted with AI assistance; facts, figures, and errors are the author's own.
Photo by Dave Hoefler on Unsplash
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