The Groucho Effect of Uncertain Standards

Rick Harbaugh

John W. Maxwell

Beatrice Roussillon

Problem of uncertain standards

• Disclosure literature assumes that consumers know what the standard is for a label or other quality certificate

• But often there is considerable uncertainty

• Is the standard for a label tough? Or easy?

• If I see a “good” firm adopt a label, I will have a different impression of the standard for the label than if I see a “bad” firm adopt a label

I won’t belong to any organization that would have me as a member – Groucho Marx

• Consumers face a dual inference problem– Uncertainty over firm quality– And uncertain over label standard

• Groucho Effect:– Meeting the standard diminishes the standard itself– Stronger if consumer has bad prior impression of quality

• Reverse Groucho Effect:– Failing to meet the standard enhances it– Stronger if consumer has good prior impression of quality

Implications of Groucho Effects due to uncertain standards• Meeting standard is still good news, but not as good

– Could be that the product is high quality– Or that standard is pretty low

• Not meeting standard is still bad news, but not as bad– Could be that the product was low quality– Or that standard was pretty high

• Uncertainty over standard implies:– Disclosure of meeting standard “less likely”– Non-disclosure “more likely”– ….

The Model

• Two players: firm and consumer• Consumer pays expected quality of good• Firm payoff is expected quality minus disclosure costs c

if disclose• Firm knows own quality q and standard s• Consumer knows only distributions:

q ~F(.) on [0,1], s ~ G(.) on [0,1]• Look for pure strategy Perfect Bayesian Equilibria

– Disclosure equilibrium: consumer expects firm to disclose if it can (adopt label)

– Nondisclosure equilibrium: consumer expect firm to not disclose even if it can (don’t adopt label)

Expected quality in disclosure equilibrium• If Standard is known to be s=s’:

• If Standard is uncertain:

Eq|q s 0

1 s

1qdFqdGs

0

1 s

1dFqdGs

Eq|q s 0

1 0

sqdFqdGs

0

1 0

sdFqdGs

Eq|q s s1qdFq

s1dFq

Eq|q s 0

sqdFq

0

sdFq

The Groucho Effect

I.I.D uniformdistributionsof q and s

If standard is s=1/2then meeting standard shifts expectation to 3/4. But if standard is uncertain expectation rises only to 2/3

The Reverse Groucho Effect

I.I.D uniformdistributionsof q and s

If standard is s=1/2 then not meeting standard shifts expectation to 1/4. But if standard is uncertain expectation falls only to 1/3

Disclosure equilibrium

• Net gain from disclosure greater than cost

• Due to GE and RGE, the net gain is always higher if standard is uncertain

• In uniform example (2/3-1/3)=1/3 vs (3/4-1/4)=1/2

• Proposition: The expected range of costs supporting a disclosure equilibrium is always higher if the standard is certain rather than uncertain.

Eq|q s Eq|q s c

Nondisclosure equilibrium

• Gain from disclosure less than cost

• Note that the firm is not penalized for nondisclosure in the nondisclosure equilibrium

• And that unexpected disclosure is treated as good news

• In uniform example gain is (2/3-1/2)=1/6 vs (3/4-1/2)=1/4

• Proposition: The expected range of costs supporting a nondisclosure equilibrium is always smaller if the standard is certain rather than uncertain.

Eq|q s Eq c

Multiple equilibria

• Equilibrium condition for disclosure

• Equilibrium condition for non-disclosure

• Since an equilibrium must exist

• Multiple equilibria if

Eq|q s Eq|q s c

Eq|q s Eq c

Eq|q s Eq

Eq|q s Eq c Eq|q s Eq|q s

Informativeness of disclosure

• Uniform example• MSE of consumer estimate of quality if s=1/2:

• MSE of consumer estimate of quality if s uncertain:

• Proposition 3: In the disclosure eq., MSE of consumer estimates of quality is higher if standard is uncertain.

The Role of Firm Quality

Proposition: (Reverse) Groucho effect is larger for a firm that consumers expect to be bad (good)

Groucho Effect makes it hard for bad firms to prove quality by disclosing label

Reverse Groucho Effect makes it less damaging for good firms to not show label

D= Disclosure regionN= Nondisclosure region

fx; 1 x for 0

1 1 x for 0

Very different than with certain standard

Multiple labels (new)

• Now suppose that there are N different labels with iid standards

• Consumer sees that a firm has a label – only proves that it met the weakest standard

• So problem same as before but replace G(s) with lowest order statistic GN:N(s)

• Qualitative results didn’t depend on exact G so still hold• Getting a label is even less attractive for firms that are

expected to have low quality• Disclosure equilibrium is even less informative than if

standards were certain

Nondisclosure region expands

Results of increasing N are generally opposite than when standards are certain!

In limit, Disclosure only region disappears with uncertain standards,Nondisclosure only region disappears with certain standards

Asymmetric “focal” equilibria

• With multiple labels might meet more than one • [Disclose more than one? – Each label is costly and as N

increases marginal benefit of each label falls] • Above results assume that firms choose which label to

disclose based on which has toughest standard (or easiest – doesn’t matter)

• Suppose consumers believe that a firm will try to disclose one label in particular even if it is not easy or tough based on firm’s private information

• Then adopting this label is pretty good news – like N=1 case

• For N>1 such a “focal” equilibrium is always more informative than symmetric equilibria

“Spoiling” vs “Legitimizing” a standard

• N=1: If a bad firm attains a standard, Groucho effect is strong

• N=1: If a good firm attains a standard, Groucho effect is weaker

• N>1: Suppose firm discloses toughest standard that it met– Bad firm – probably still a weak standard– Good firm – probably a tough standard

• Sequencing implications:– If a bad firm discloses a standard first, good firms reluctant to

adopt same standard– But if a good firm discloses a standard first, bad firms want to

adopt same standard

Conclusions and Policy Implications

• Double cost from uncertainty – less disclosure and more noisy disclosure when occurs

• Important role for information provision about standards

• Role for “look for the label” campaigns since there are regions of multiple equilibria

• When there are multiple labels, such campaigns can focus on one particular label and have big impact

• When there are multiple labels, start with good firms to legitimize the label