Worked case · Chapter 4, Signals, Disclosure, and Persuasion · p. 158 · sources checked 9 November 2026

Bank stress tests as a committed information policy

what does a published test buy the supervisor, at whose expense, and how much of it depends on the test's binding?

The network

leader, commits first an object of the game player Model S5. A reading of the mapping table, drawn by the site. Hover a node or an arrow; the arrows in words:

Supervisor → Published test commits the design binds with probability ρ
The bank → Published test signal the state drives the result
Published test → Creditors signal design and reported result
Supervisor → Published test acts may revise the report when the design does not bind
Creditors → The bank acts fund or not

The mapping

The six fields of the model card, as the book fills them in for this situation.

Field	In the case
1 Decision-makers	the supervisor, which designs, runs and reports the test; the bank's creditors and counterparties, who decide whether to keep funding it. One bank and one representative creditor in the model; dozens of banks and many creditors in fact
2 Time	the test is designed and published before its results are known; the results are reported; then funding decisions follow. One period in the model; an annual cycle in fact
3 Information	the bank's health is the state; the published test is the experiment; creditors see the design and the reported result. In fact the supervisor holds supervisory data on each bank before it designs the scenarios
4 Commitment	the probability $ρ$ that the published test binds as published. The rule's calendar, comment requirement and materiality threshold are what would make revision costly; the mapping from those provisions to $ρ$ is R, and none of their numbers is used as a parameter
5 Payoffs	creditors gain from funding a sound bank and lose from funding a weak one; the regulator values a funded sound bank at $1$ and a funded weak bank at $w$ . The sign of $w$ is the regulator's aim: $w > 0$ if it prefers a weak bank funded to a run on it, $w < 0$ if it prefers market discipline
6 Strategies	pass/ fail tests with chosen pass rates for sound and weak banks; the regulator's report when it can revise; the creditors' threshold rule

What the mathematics licenses.

Six statements about the model; the mapping to supervisory practice is a reconstruction R, and no statement is an estimate of any test's effect.

A designed test funds some weak banks, and creditors pay for it. At the base values the regulator's best test passes every sound bank and a quarter of the weak ones; a pass leaves creditors exactly at their threshold. The regulator obtains $\frac{5}{12}$ , against $\frac{1}{3}$ from full disclosure and $0$ from none; creditors obtain $0$ — what they would get without any test — against $\frac{1}{3}$ under full disclosure (Proposition 4.15 (p. 178)(a),(b),(e); Figure 4.6 (p. 163)a). The stability gain over no disclosure, that no sound bank faces a run, is delivered by full disclosure as well; what the designed test adds is funding for weak banks, with probability $\frac{1}{6}$ D [Proposition 4.15 (p. 178)(e)].

The regulator's aim decides whether commitment matters. If the regulator prefers a weak bank to face its creditors ( $w < 0$ ), full disclosure is its unique best test and it would report truthfully even without commitment: commitment is worth exactly nothing. Only when it prefers weak banks funded ( $w > 0$ ) does its unbound word become worthless, and commitment is then worth the whole value of the test, $\frac{3}{8}$ , $\frac{5}{12}$ and $\frac{1}{2}$ at $w = \frac{1}{4}, \frac{1}{2}, 1$ (Table 4.1 (p. 161)b; Proposition 4.15 (p. 178)(c)). Read in the model, a commitment to an information policy is valuable to a regulator exactly to the extent that its interests in the outcome differ from those of the market reading the test D [Table 4.1 (p. 161)b]. The reading cuts both ways and should be used with care: it does not say that any regulator that commits has lenient aims, only that commitment buys nothing for one that does not.

Commitment matters most to a sceptical, but not hopeless, market. The value of commitment rises in proportion to the prior up to the creditors' threshold, $\frac{5}{48}$ at a prior of $\frac{1}{12}$ and $\frac{5}{8}$ at $\frac{1}{2}$ , and vanishes at and above it, where no test is needed (Table 4.1 (p. 161)a). Creditors gain nothing from the designed test at any prior below the threshold D [Table 4.1 (p. 161)a].

Credibility is a threshold, not a dial. If the published test binds only with probability $ρ$ , and otherwise the regulator reports after seeing the state, the regulator loses nothing as long as $ρ \geq \frac{3}{4}$ , and everything below: the test then persuades nobody (Proposition 4.15 (p. 178)(d); Figure 4.6 (p. 163)b). The threshold is higher the more sceptical the market: $\frac{21}{22}$ at a prior of $\frac{1}{12}$ , $\frac{1}{2}$ at a prior of $\frac{1}{2}$ D [Table 4.1 (p. 161)a].

A less credible test must be harsher. Above the threshold, the binding part of the test must pass fewer weak banks to offset the passes the revising regulator would report: a quarter at $ρ = 1$ , $\frac{1}{6}$ at $ρ = \frac{9}{10}$ , $\frac{1}{10}$ at $ρ = \frac{5}{6}$ , none at $ρ = \frac{3}{4}$ . A supervisor whose results may be revised needs a stricter published procedure to be believed to the same degree D [Proposition 4.15 (p. 178)(d)].

Publication of a procedure and publication of results are different commitments. Publishing models, scenarios and a calendar, with comment required before material changes, fixes the experiment (field 4) and in the model raises $ρ$ ; non-material changes and scenario adjustments for incoming data are the provisions through which revision remains possible. Publishing bank-level results without a pass/ fail threshold, as in the European exercise, concerns field 3: it passes on more of what the test found, and in Model S5 moves towards full disclosure of the test's information, which is full disclosure of the bank's health only to the extent that the test itself is informative R.

Where the mapping breaks.

Supervisory tests are not pass/ fail: their results are projected capital ratios, published bank by bank, and they act on banks mainly through capital requirements, which the model omits: the bank's own response, raising capital or cutting distributions, is a move the model does not contain. The supervisor does not design the test in ignorance of the state; it holds supervisory data on each bank, so the design can depend on what it knows, which moves the problem towards Model S2. Creditors are many and their decisions interact: a run is a coordination problem, and with many receivers information design becomes a problem of coordination that a single threshold does not capture. Banks are tested together and their health is correlated, so a test is also a statement about the system. Banks that know the models can adapt their portfolios to them, which turns the tested party into a player. Revision in the rule is not a coin toss: it is permitted under stated conditions (non-materiality, incoming data) that a strategic designer would use selectively, which calls for credibility that depends on the state, as in the general analysis of Lipnowski et al. (2022). Averaging two years of results makes the requirement depend on past tests, a dynamic link the one-period model omits. And the supervisor is a board that votes, not a single player with a known $w$ .

In the book

The full case runs through six steps: The situation, as documented; The model card; What the mathematics licenses; Where the mapping breaks; What one would have to measure; Sources. The numbers in step 3 are certified in the chapter's engine room, and the sources in step 6 are listed with the day they were read. The site shows the model mapping (step 2), what the mathematics licenses (step 3) and where the mapping breaks (step 4); the full case is on p. 158 of the book.