Signaling

Signaling of Hidden Quality in Health Care

Signalling (spelt signaling in American usage) happens when the better-informed side of a health care transaction takes a visible, costly step so that the other side can infer something it cannot check directly, such as a hospital's clinical quality or a clinician's skill. The step works only if it would cost a lower-quality provider too much to copy, so that taking it separates one type from another. Patients, insurers and commissioners usually know far less about quality than providers do, so voluntary accreditation, specialist certification and advertised rankings are common in health care, and whether each one informs or merely absorbs resources depends on how its cost differs between types. The wider body of models and refinements is set out under signalling theory, and the uninformed party's mirror-image tool is screening.

Hidden quality and the problem a signal solves

Health care is a textbook case of information asymmetry. Arrow, in his 1963 paper on the welfare economics of medical care, observed that the customer cannot test the product before consuming it, and that there is an element of trust in the relation. When buyers cannot tell high quality from low, they pay for average quality, and the providers whose quality is above average are underpaid relative to their value. The Royal Swedish Academy's scientific background to the 2001 economics prize notes that a labour market in which employers cannot tell high from low productivity might collapse into one where only low-productivity workers are hired at a low wage, the counterpart of Akerlof's market where only lemons remain, which is the adverse selection problem.

Spence's answer was that informed parties may act to escape the average. The same background defines signalling as observable actions taken by economic agents to convince the opposite party of the value or quality of their products, and it states the condition that makes such actions work, namely that signalling can succeed only if the signalling cost differs sufficiently among the senders. In his Nobel lecture Spence said the signal distinguishes types because its cost is negatively correlated with the unseen characteristic the receiver values.

How a signal changes the receiver's beliefs

A signal is useful to the receiver only through what it does to beliefs. A purchaser deciding which hospitals to contract with starts from a prior view of the share of high-quality providers and revises it after seeing whether a hospital holds the signal. The revision follows Bayes' theorem.

$$\mu(H \mid s) = \frac{P(s \mid H)\,\pi}{P(s \mid H)\,\pi + P(s \mid L)\,(1 - \pi)}$$

where $\mu(H \mid s)$ is the receiver's posterior probability that the sender is of high-quality type $H$ after observing signal $s$, $\pi$ is the prior probability of type $H$, the prior probability of low-quality type $L$ is one minus $\pi$, and $P(s \mid H)$ and $P(s \mid L)$ are the probabilities that each type sends the signal.

If every type sends the signal with the same probability, the posterior equals the prior and the signal carries no information, which is a pooling outcome. If only type $H$ sends it, the posterior is one for senders and zero for non-senders, which is a separating outcome. Spence stressed in his lecture that in equilibrium the receivers' beliefs must be self-confirming, since beliefs set the rewards to signalling, the rewards set who signals, and who signals is what the receivers then observe. That circularity allows several equilibria in the same market, including one in which nobody signals, so a model has to state which one it uses.

Conditions for a separating signal

The separating case can be written as two incentive compatibility conditions. Suppose a receiver pays $V_H$ to a sender believed to be high quality and $V_L$ to one believed to be low quality, and a signal of intensity $s$ costs $c_H s$ for type $H$ and $c_L s$ for type $L$, with $c_H < c_L$.

$$V_H - c_H s^{*} \ge V_L \qquad \text{and} \qquad V_H - c_L s^{*} \le V_L$$

where $s^{*}$ is the level of the signal that the receiver treats as proof of high quality, $V_H$ and $V_L$ are the payments to senders believed to be high and low quality, and $c_H$ and $c_L$ are each type's cost per unit of signal. The first condition says the high-quality type gains from signalling, and the second says the low-quality type does not gain from imitating. Rearranged, the two conditions bound the standard.

$$\frac{V_H - V_L}{c_L} \le s^{*} \le \frac{V_H - V_L}{c_H}$$

where $V_H - V_L$ is the reward for being recognised as high quality, the lower limit is the level at which imitation stops paying, and the upper limit is the most a high-quality sender would spend.

The assumption that a unit of signal is cheaper for the better type is closely related to what the Nobel background calls Mirrlees's single-crossing condition, often referred to as the Mirrlees-Spence condition. Absent further conditions any standard inside the range is an equilibrium, and Spence identified the least-cost one, in which the high type acquires only the minimum signal needed to stand apart, as the socially most efficient.

Signalling devices in health care

Many health care institutions act partly as signals. Arrow described three ways a society can meet the demand for guaranteed quality, namely licensing that excludes the unqualified, certification or labelling without compulsory exclusion, and doing nothing. He gave medical-board examinations for specialists as certification done by non-governmental agencies. Licensing is imposed on everyone who wants to practise, so it restricts entry rather than signalling, whereas voluntary certification is chosen by the informed party and fits Spence's idea closely.

Dranove and Jin, reviewing quality disclosure and certification, give health examples. A hospital may report that most of its medical staff are board certified, and an industry may set up a certification agency such as the Joint Commission on the Accreditation of Healthcare Organizations. They note that many insurers refuse to reimburse services at hospitals without the credential, which turns accreditation into a condition of payment as well as a signal. Credentialing of individual clinicians plays a similar role for insurer networks. They call it unclear whether a brand is a bond sunk to signal quality or an aid to recall, and observe that warranties for hospital care are almost unheard of. The Nobel background adds that consumers may read prices and advertising as quality signals, with equilibria in which only high-quality firms find costly advertising worthwhile.

Worked example with two hospital types and an accreditation standard

All figures in this example are illustrative. A purchaser contracts with hospitals of two types. Care at a high-quality hospital is worth GBP 10.0 million a year to the purchaser and care at a low-quality hospital GBP 8.0 million. The purchaser cannot see quality directly but can see how many optional levels of a voluntary accreditation standard a hospital has passed. Each level costs a high-quality hospital GBP 0.4 million and a low-quality hospital GBP 1.0 million, which must build processes it lacks. Accreditation does not change quality.

1. Pooled payment. With half the hospitals of each type and no signal, the purchaser pays expected value, 0.5 × 8.0 + 0.5 × 10.0 = GBP 9.0 million to every hospital.

2. Range of separating standards. The reward for recognition is 10.0 − 8.0 = GBP 2.0 million. Imitation does not pay for a low-quality hospital once the standard is at least 2.0 / 1.0 = 2 levels, and signalling pays for a high-quality hospital up to 2.0 / 0.4 = 5 levels. Any standard between 2 and 5 levels can sustain separation.

3. Least-cost separation. At 2 levels a low-quality hospital that imitated would get 10.0 − 2 × 1.0 = GBP 8.0 million, no better than staying out, so a standard a fraction above 2 makes imitation strictly unprofitable. A high-quality hospital spends 2 × 0.4 = GBP 0.8 million and nets 10.0 − 0.8 = GBP 9.2 million, while a low-quality hospital nets GBP 8.0 million.

4. Who gains. High-quality hospitals gain GBP 0.2 million each against pooling and low-quality hospitals lose GBP 1.0 million. The average net payment falls to 0.5 × 9.2 + 0.5 × 8.0 = GBP 8.6 million, and the gap of 0.5 × 0.8 = GBP 0.4 million is the average spend on a signal that adds no quality.

5. A larger high-quality share. If only 30% of hospitals are low quality, the pooled payment is 0.3 × 8.0 + 0.7 × 10.0 = GBP 9.4 million. That exceeds the GBP 9.2 million a high-quality hospital nets under separation, so both types would be better off pooled.

6. A noisy signal. Suppose instead that idiosyncratic costs mean 90% of high-quality and 20% of low-quality hospitals hold the accreditation, with a prior of 0.5. Then 0.9 × 0.5 + 0.2 × 0.5 = 0.55 of hospitals are accredited, and the posterior for an accredited hospital is 0.45 / 0.55 = 0.818, so expected value is 0.818 × 10.0 + 0.182 × 8.0 = GBP 9.64 million. For a non-accredited hospital the posterior is 0.05 / 0.45 = 0.111 and expected value is GBP 8.22 million. The weighted average, 0.55 × 9.64 + 0.45 × 8.22, returns the GBP 9.0 million pooled value.

Steps 4 and 5 follow a general rule for this set-up. The high-quality type prefers least-cost separation to pooling only when the share of low-quality senders exceeds the cost ratio $c_H / c_L$, here 0.4.

$$V_H - c_H \frac{V_H - V_L}{c_L} > V_H - \lambda (V_H - V_L) \iff \lambda > \frac{c_H}{c_L}$$

where $\lambda$ is the share of low-quality senders, the right-hand side of the first inequality is the pooled payment, and other symbols are as above. Spence's lecture example, with signal costs in the ratio of one half, reaches the same conclusion, that a Pareto-preferred pooling equilibrium exists when the low type is less than half the population. Step 6 is closer to what a purchaser reading accreditation status faces.

Signals, disclosure and screening compared

Signalling is easily confused with disclosure and with screening. Where quality can be verified, a provider can simply disclose it. Dranove and Jin summarise the unravelling result of Grossman and Milgrom, in which costless, verifiable disclosure leads every seller except the worst to disclose, because rational consumers treat silence as lowest quality. When disclosure is costly only sellers above a quality threshold disclose, and they remark that hospitals highly ranked by rating services often advertise their rankings while average hospitals remain silent. Choosing to publicise a ranking then works much like a signal, even though the ranking itself is verified information. Trial results submitted to a health technology assessment body belong on the disclosure side, since the assessor examines the evidence itself.

Screening reverses the initiative, with the uninformed party offering a menu, such as plans that trade a lower premium for a higher deductible, and letting choices reveal type. In signalling the informed party moves first and the receiver only interprets, so the analysis turns on the receiver's beliefs.

Use in economic evaluation and policy

Signalling seldom enters a cost-effectiveness model directly, but it matters when an appraisal values a quality-information scheme. In Spence's simple model, investment in a signal dissipates resources without improving productivity, and the separating equilibria are inefficient. A pure signal therefore transfers income between provider types and uses real resources, and an appraisal of a voluntary accreditation or certification scheme should count provider compliance costs alongside any gain in how well patients and providers are matched. The Nobel background notes that incentives to acquire the signal are stronger when it also raises productivity, and a standard that improves care is partly an input to quality of care, so its effect on outcomes has to be measured rather than assumed.

Limitations and common misreadings

Most misreadings come from treating any credential as a signal, or any signal as informative.

1. Assuming a credential separates types. A step that every provider can take at similar cost informs no one, because credibility needs cost to differ sufficiently by type.
2. Treating signalling cost as a benefit. In a pure signal the spending is a deadweight cost, as step 4 showed, even if the high type gains.
3. Ignoring receivers. Dranove and Jin note that most consumers are unaware of hospital report cards, and that patients may believe their own providers are above average without disclosure, so silence may not be read as low quality.
4. Forgetting selection. Where a signal or report rests on measured outcomes, providers can improve the figure by choosing patients, a form of cream skimming that imperfect risk adjustment does not remove.

Sources

• Arrow KJ. Uncertainty and the welfare economics of medical care. American Economic Review. 1963;53(5):941-973.
• Dranove D, Jin GZ. Quality disclosure and certification: theory and practice. Journal of Economic Literature. 2010;48(4):935-963. Also NBER Working Paper 15644, January 2010. https://www.nber.org/system/files/working_papers/w15644/w15644.pdf
• Royal Swedish Academy of Sciences. Markets with asymmetric information. Scientific background on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 2001. 10 October 2001. https://www.nobelprize.org/uploads/2018/06/advanced-economicsciences2001.pdf
• Spence M. Signaling in retrospect and the informational structure of markets. American Economic Review. 2002;92(3):434-459. Prize lecture, 8 December 2001. https://www.nobelprize.org/uploads/2018/06/spence-lecture.pdf