Signalling (economics)

Last updated

In contract theory, signalling (or signaling; see spelling differences) is the idea that one party (termed the agent) credibly conveys some information about itself to another party (the principal). For example, in Michael Spence's job-market signalling model, (potential) employees send a signal about their ability level to the employer by acquiring education credentials. The informational value of the credential comes from the fact that the employer believes the credential is positively correlated with having greater ability and difficult for low ability employees to obtain. Thus the credential enables the employer to reliably distinguish low ability workers from high ability workers.

In economics, contract theory studies how economic actors can and do construct contractual arrangements, generally in the presence of asymmetric information. Because of its connections with both agency and incentives, contract theory is often categorized within a field known as Law and economics. One prominent application of it is the design of optimal schemes of managerial compensation. In the field of economics, the first formal treatment of this topic was given by Kenneth Arrow in the 1960s. In 2016, Oliver Hart and Bengt R. Holmström both received the Nobel Memorial Prize in Economic Sciences for their work on contract theory, covering many topics from CEO pay to privatizations.

In commercial law, a principal is a person, legal or natural, who authorizes an agent to act to create one or more legal relationships with a third party. This branch of law is called agency and relies on the common law proposition qui facit per alium, facit per se.

Michael Spence American economist

Andrew Michael Spence is a Canadian American economist and recipient of the 2001 Nobel Memorial Prize in Economic Sciences, along with George Akerlof and Joseph E. Stiglitz, for their work on the dynamics of information flows and market development.

Contents

Although signalling theory was initially developed by Michael Spence based on observed knowledge gaps between organisations and prospective employees, [1] its intuitive nature led it to be adapted to many other domains, such as Human Resource Management, business, and financial markets. [2]

Introductory questions

Signalling took root in the idea of asymmetric information (a deviation from perfect information), which says that in some economic transactions, inequalities in access to information upset the normal market for the exchange of goods and services. In his seminal 1973 article, Michael Spence proposed that two parties could get around the problem of asymmetric information by having one party send a signal that would reveal some piece of relevant information to the other party. [1] That party would then interpret the signal and adjust her purchasing behaviour accordingly—usually by offering a higher price than if she had not received the signal. There are, of course, many problems that these parties would immediately run into.

Perfect information

In economics, perfect information is a feature of perfect competition. With perfect information in a market, all consumers and producers have perfect and instantaneous knowledge of all market prices, their own utility, and own cost functions.

Job-market signalling

In the job market, potential employees seek to sell their services to employers for some wage, or price. Generally, employers are willing to pay higher wages to employ better workers. While the individual may know his or her own level of ability, the hiring firm is not (usually) able to observe such an intangible trait—thus there is an asymmetry of information between the two parties. Education credentials can be used as a signal to the firm, indicating a certain level of ability that the individual may possess; thereby narrowing the informational gap. This is beneficial to both parties as long as the signal indicates a desirable attribute—a signal such as a criminal record may not be so desirable.

Wage Reimbursement paid by an employer to an employee

A wage is monetary compensation paid by an employer to an employee in exchange for work done. Payment may be calculated as a fixed amount for each task completed, or at an hourly or daily rate, or based on an easily measured quantity of work done.

Price quantity of payment or compensation given by one party to another in return for goods or services

A price is the quantity of payment or compensation given by one party to another in return for one unit of goods or services.. A price is influenced by both production costs and demand for the product. A price may be determined by a monopolist or may be imposed on the firm by market conditions.

A credential is an attestation of qualification, competence, or authority issued to an individual by a third party with a relevant or de facto authority or assumed competence to do so.

Spence 1973 "Job Market Signaling" paper

Assumptions and groundwork

Michael Spence considers hiring as a type of investment under uncertainty, [1] analogous to buying a lottery ticket, and refers to the attributes of an applicant which are observable to the employer as indices. Of these, attributes which the applicant can manipulate are termed signals.[ clarification needed ] Applicant age is thus an index, but is not a signal since it does not change at the discretion of the applicant.

The employer is supposed to have conditional probability assessments of productive capacity, based on previous experience of the market, for each combination of indices and signals.[ clarification needed ] The employer updates those assessments upon observing each employee's characteristics.

In probability theory, conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A | B), or sometimes PB(A) or P(A / B). For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person has a cold, then they are much more likely to be coughing. The conditional probability of coughing by the unwell might be 75%, then: P(Cough) = 5%; P(Cough | Sick) = 75%

Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event, which can change as new information is gathered, rather than a fixed value based upon frequency or propensity. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event. This differs from a number of other interpretations of probability, such as the frequentist interpretation that views probability as the limit of the relative frequency of an event after a large number of trials.

The paper is concerned with a risk-neutral employer. The offered wage is the expected marginal product. Signals may be acquired by sustaining signalling costs (monetary and not). If everyone invests in the signal in the exactly the same way, then the signal can't be used as discriminatory, therefore a critical assumption is made: the costs of signalling are negatively correlated with productivity. This situation as described is a feedback loop: the employer updates his beliefs upon new market information and updates the wage schedule, applicants react by signalling, and recruitment takes place.

Michael Spence studies the signalling equilibrium that may result from such a situation. He began his 1973 model with an hypothetical example: [1] suppose that there are two types of employees—good and bad—and that employers are willing to pay a higher wage to the good type than the bad type. Spence assumes that for employers, there's no real way to tell in advance which employees will be of the good or bad type.

Bad employees aren't upset about this, because they get a free ride from the hard work of the good employees. But good employees know that they deserve to be paid more for their higher productivity, so they desire to invest in the signal—in this case, some amount of education. But he does make one key assumption: good-type employees pay less for one unit of education than bad-type employees. The cost he refers to is not necessarily the cost of tuition and living expenses, sometimes called out of pocket expenses, as one could make the argument that higher ability persons tend to enroll in "better" (i.e. more expensive) institutions. Rather, the cost Spence is referring to is the opportunity cost. This is a combination of 'costs', monetary and otherwise, including psychological, time, effort and so on. Of key importance to the value of the signal is the differing cost structure between "good" and "bad" workers. The cost of obtaining identical credentials is strictly lower for the "good" employee than it is for the "bad" employee.

The differing cost structure need not preclude "bad" workers from obtaining the credential. All that is necessary for the signal to have value (informational or otherwise) is that the group with the signal is positively correlated with the previously unobservable group of "good" workers. In general, the degree to which a signal is thought to be correlated to unknown or unobservable attributes is directly related to its value.

The result

Spence discovered that even if education did not contribute anything to an employee's productivity, it could still have value to both the employer and employee. If the appropriate cost/benefit structure exists (or is created), "good" employees will buy more education in order to signal their higher productivity.

The increase in wages associated with obtaining a higher credential is sometimes referred to as the “sheepskin effect”, [3] since “sheepskin” informally denotes a diploma. It is important to note that this is not the same as the returns from an additional year of education. The "sheepskin" effect is actually the wage increase above what would normally be attributed to the extra year of education. This can be observed empirically in the wage differences between 'drop-outs' vs. 'completers' with an equal number of years of education. It is also important that one does not equate the fact that higher wages are paid to more educated individuals entirely to signalling or the 'sheepskin' effects. In reality education serves many different purposes to individuals and society as a whole. Only when all of these aspects, as well as all the many factors affecting wages, are controlled for, does the effect of the "sheepskin" approach its true value. Empirical studies of signalling indicate it as a statistically significant determinant of wages, however it is one of a host of other attributes—age, sex, and geography are examples of other important factors.

The model

To illustrate his argument, Spence imagines, for simplicity, two productively distinct groups in a population facing one employer. The signal under consideration is education, measured by an index y and is subject to individual choice. Education costs are both monetary and psychic. The data can be summarized as:

Data of the Model
GroupMarginal ProductProportion of populationCost of education level y
I1y
II2y/2

Suppose that the employer believes that there is a level of education y* below which productivity is 1 and above which productivity is 2. His offered wage schedule W(y) will be:

Working with these hypotheses Spence shows that:

  1. There is no rational reason for someone choosing a different level of education from 0 or y*.
  2. Group I sets y=0 if 1>2-y*, that is if the return for not investing in education is higher than investing in education.
  3. Group II sets y=y* if 2-y*/2>1, that is the return for investing in education is higher than not investing in education.
  4. Therefore, putting the previous two inequalities together, if 1<y*<2, then the employer initial beliefs are confirmed.
  5. There are infinite equilibrium values of y* belonging to the interval [1,2], but they are not equivalent from the welfare point of view. The higher y* the worse off is Group II, while Group I is unaffected.
  6. If no signaling takes place each person is paid his unconditional expected marginal product . Therefore, Group I is worse off when signaling is present.

In conclusion, even if education has no real contribution to the marginal product of the worker, the combination of the beliefs of the employer and the presence of signalling transforms the education level y* in a prerequisite for the higher paying job. It may appear to an external observer that education has raised the marginal product of labor, without this necessarily being true.

Another model

For a signal to be effective, certain conditions must be true. In equilibrium the cost of obtaining the credential must be lower for high productivity workers and act as a signal to the employer such that they will pay a higher wage.

Simple signalling framework.PNG

In this model it is optimal for the higher ability person to obtain the credential (the observable signal) but not for the lower ability individual. The table shows the outcome of low ability person l and high ability person h with and without signal S*:

Summary of the outcome for l and h with and without S*
PersonWithout SignalWith SignalWill the person obtain the signal S*?
lWoW* - C'(l)No, because Wo > W* - C'(l)
hWoW* - C'(h)Yes, because Wo < W* - C'(h)

The structure is as follows: There are two individuals with differing ability (productivity) levels.

The premise for the model is that a person of high ability (h) has a lower cost for obtaining a given level of education than does a person of lower ability (l). Cost can be in terms of monetary, such as tuition, or psychological, stress incurred to obtain the credential.

For the individual:

Person(credential) - Person(no credential) Cost(credential) Obtain credential
Person(credential) - Person(no credential)< Cost(credential) Do not obtain credential

Thus, if both individuals act rationally it is optimal for person h to obtain S* but not for person l so long as the following conditions are satisfied.

Edit: note that this is incorrect with the example as graphed. Both 'l' and 'h' have lower costs than W* at the education level. Also, Person(credential) and Person(no credential) are not clear.

Edit: note that this is ok as for low type "l": , and thus low type will choose Do not obtain credential.

Edit: For there to be a separating equilibrium the high type 'h' must also check their outside option; do they want to choose the net pay in the separating equilibrium (calculated above) over the net pay in the pooling equilibrium. Thus we also need to test that: Otherwise high type 'h' will choose Do not obtain credential of the pooling equilibrium.

For the employers:

Person(credential)=E(Productivity | Cost(credential) Person(credential) - Person(no credential))
Person(no credential)=E(Productivity | Cost(credential)> Person(credential) - Person(no credential))

In equilibrium, in order for the signalling model to hold, the employer must recognize the signal and pay the corresponding wage and this will result in the workers self-sorting into the two groups. One can see that the cost/benefit structure for a signal to be effective must fall within certain bounds or else the system will fail. [4]

IPOs

Leland and Pyle (1977) analyse the role of signals within the process of IPO. The authors show how companies with good future perspectives and higher possibilities of success ("good companies") should always send clear signals to the market when going public (e.g. the owner should keep control of a significant percentage of the company). To be reliable, the signal must be too costly to be imitated by "bad companies". If no signal is sent to the market, asymmetric information will result in adverse selection in the IPO market.

Brands

Waldfogel and Chen (2006) [5] demonstrate the importance of brands in signalling quality in online marketplaces.

eBay Motors' Price Premium

Signalling has been studied and proposed as a means to address asymmetric information in markets for Lemons. [6] Recently, signalling theory has been applied in used cars market such as eBay Motors. For example, Lewis (2011) [7] examines the role of information access and shows that the voluntary disclosure of private information increases the prices of used cars on eBay. Further, Dimoka et al. (2012) [8] analyzed data from eBay Motors on the role of signals to mitigate product uncertainty. Extending the information asymmetry literature in consumer behavior literature from the agent (seller) to the product, authors theorized and validated the nature and dimensions of product uncertainty, which is distinct from, yet shaped by, seller uncertainty. Authors also found information signals (diagnostic product descriptions and third-party product assurances) to reduce product uncertainty, which negatively affect price premiums (relative to the book values) of the used cars in online used cars markets.

Outside options

Most signalling models are plagued by a multiplicity of possible equilibrium outcomes. [9] In a study published in the Journal of Economic Theory , a signalling model has been proposed that has a unique equilibrium outcome. [10] In the principal-agent model it is argued that an agent will choose a large (observable) investment level when he has a strong outside option. Yet, an agent with a weak outside option might try to bluff by also choosing a large investment, in order to make the principal believe that the agent has a strong outside option (so that the principal will make a better contract offer to the agent). Hence, when an agent has private information about his outside option, signalling may mitigate the hold-up problem.

(Self-)signalling and gambling

Signalling influences bettors in domains that are relevant to their identity or commitments. When betting on or against a group, belief, or ideal, such as a favorite sports team or politician, the choice of bet (i.e., for or against) sends a signal to the bettor about his or her identity. Betting on the outcome seems to send a reaffirming signal to the bettor about her identity, whereas betting against the outcome seems to send a signal to the bettor that the outcome is less important than before. As a result, bettors are reluctant to bet against such identity-relevant outcomes, even when bets against identity-relevant outcomes are more favorable than bets on identity relevant outcomes. When presented real gambles of equal expected value (ev = $7.50) on the 2000 US Presidential election, for example, both supporters of George W. Bush and Al Gore were more likely to bet their candidate to win (74%) the election than to lose the election (26%). As further evidence, more than 45% of N.C.A.A. basketball and hockey fans turned down a free chance to earn $5 if their team lost its upcoming game. [11]

See also

Related Research Articles

Labour economics seeks to understand the functioning and dynamics of the markets for wage labour.

Minimum wage lowest wage which can be paid legally in a state for working

A minimum wage is the lowest remuneration that employers can legally pay their workers. Equivalently, it is the price floor below which workers may not sell their labor. Although minimum wage laws are in effect in many jurisdictions, differences of opinion exist about the benefits and drawbacks of a minimum wage. Supporters of the minimum wage say it increases the standard of living of workers, reduces poverty, reduces inequality, and boosts morale. In contrast, opponents of the minimum wage say it increases poverty, increases unemployment and is damaging to businesses, because excessively high minimum wages require businesses to raise the prices of their product or service to accommodate the extra expense of paying a higher wage and some low-wage workers "will be unable to find work...[and] will be pushed into the ranks of the unemployed."

Human capital is the stock of knowledge, habits, social and personality attributes, including creativity, embodied in the ability to perform labor so as to produce economic value. Human capital theory is closely associated with the study of human resources management as found in the practice of business administration and macroeconomics. The original idea of human capital can be traced back at least to Adam Smith in the 18th century. The modern theory was popularized by Gary Becker, an economist and Nobel Laureate from the University of Chicago, Jacob Mincer, and Theodore Schultz. As a result of his conceptualization and modeling work using Human Capital as a key factor, the Nobel Prize for Economics, 2018, was awarded (jointly) to Paul Romer who founded the modern innovation-driven approach to understanding economic growth.

The Phillips curve is a single-equation econometric model, named after William Phillips, describing a historical inverse relationship between rates of unemployment and corresponding rates of rises in wages that result within an economy. Stated simply, decreased unemployment, in an economy will correlate with higher rates of wage rises. Phillips did not himself state there was any relationship between employment and inflation, this notion was a trivial deduction from his statistical findings. Samuelson and Solow made the connection explicit and subsequently Milton Friedman and Edmund Phelps put the theoretical structure in place. In so doing, Friedman was to successfully predict the imminent collapse of Phillips' a-theoretic correlation.

In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. This asymmetry creates an imbalance of power in transactions, which can sometimes cause the transactions to go awry, a kind of market failure in the worst case. Examples of this problem are adverse selection, moral hazard, and monopolies of knowledge.

Employment is a relationship between two parties, usually based on a contract where work is paid for, where one party, which may be a corporation, for profit, not-for-profit organization, co-operative or other entity is the employer and the other is the employee. Employees work in return for payment, which may be in the form of an hourly wage, by piecework or an annual salary, depending on the type of work an employee does or which sector she or he is working in. Employees in some fields or sectors may receive gratuities, bonus payment or stock options. In some types of employment, employees may receive benefits in addition to payment. Benefits can include health insurance, housing, disability insurance or use of a gym. Employment is typically governed by employment laws, regulations or legal contracts.

Underemployment

Underemployment is the under-use of a worker due to a job that does not use the worker's skills, or is part time, or leaves the worker idle. Examples include holding a part-time job despite desiring full-time work, and overqualification, where the employee has education, experience, or skills beyond the requirements of the job.

An incentive is a contingent motivator. Traditional incentives are extrinsic motivators which reward actions to yield a desired outcome. The effectiveness of traditional incentives has changed as the needs of Western society have evolved. While the traditional incentive model is effective when there is a defined procedure and goal for a task, Western society started to require a higher volume of critical thinkers, so the traditional model became less effective. Institutions are now following a trend in implementing strategies that rely on intrinsic motivations rather than the extrinsic motivations that the traditional incentives foster.

In labor economics, the efficiency wage hypothesis argues that wages, at least in some markets, form in a way that is not market-clearing. Specifically, it points to the incentive for managers to pay their employees more than the market-clearing wage in order to increase their productivity or efficiency, or reduce costs associated with turnover, in industries where the costs of replacing labor are high. This increased labor productivity and/or decreased costs pay for the higher wages.

Signaling game

In game theory, a signaling game is a simple type of a dynamic Bayesian game.

Information economics or the economics of information is a branch of microeconomic theory that studies how information and information systems affect an economy and economic decisions. Information has special characteristics: It is easy to create but hard to trust. It is easy to spread but hard to control. It influences many decisions. These special characteristics complicate many standard economic theories.

Employment discrimination is a form of discrimination based on race, gender, religion, national origin, physical or mental disability, age, sexual orientation, and gender identity by employers. Earnings differentials or occupational differentiation—where differences in pay come from differences in qualifications or responsibilities—should not be confused with employment discrimination. Discrimination can be intended and involve disparate treatment of a group or be unintended, yet create disparate impact for a group.

The intuitive criterion is a technique for equilibrium refinement in signaling games. It aims to reduce possible outcome scenarios by first restricting the type group to types of agents who could obtain higher utility levels by deviating to off-the-equilibrium messages and second by considering in this sub-set of types the types for which the off-the-equilibrium message is not equilibrium dominated.

Involuntary unemployment occurs when a person is willing to work at the prevailing wage yet is unemployed. Involuntary unemployment is distinguished from voluntary unemployment, where workers choose not to work because their reservation wage is higher than the prevailing wage. In an economy with involuntary unemployment there is a surplus of labor at the current real wage. Involuntary unemployment cannot be represented with a basic supply and demand model at a competitive equilibrium: All workers on the labor supply curve above the market wage would voluntarily choose not to work, and all those below the market wage would be employed. Given the basic supply and demand model, involuntarily unemployed workers lie somewhere off of the labor supply curve. Economists have several theories explaining the possibility of involuntary unemployment including implicit contract theory, disequilibrium theory, staggered wage setting, and efficiency wages.

In economics, a monopsony is a market structure in which a single buyer substantially controls the market as the major purchaser of goods and services offered by many would-be sellers. In the microeconomic theory of monopsony, a single entity is assumed to have market power over sellers as the only purchaser of a good or service, much in the same manner that a monopolist can influence the price for its buyers in a monopoly, in which only one seller faces many buyers.

In macroeconomics, rigidities are real prices and wages that fail to adjust to the level indicated by equilibrium or if something holds one price or wage fixed to a relative value of another. Real rigidities can be distinguished from nominal rigidities, rigidities that do not adjust because prices can be sticky and fail to change value even as the underlying factors that determine prices fluctuate. Real rigidities, along with nominal, are a key part of new Keynesian economics. Economic models with real rigidities lead to nominal shocks having a large impact on the economy.

Labor discrimination as defined by Kenneth Arrow is “the valuation in the market place of personal characteristics of the worker that are unrelated to worker productivity”. It can be thus understood as the differentiation of workers based on characteristics such as color, race, origin, gender etc. that can be classified as factors that do not have a role in determining his or her productivity. There are multiple dimensions that need to be considered when discussing such discrimination. The most obvious is that the group discriminated against is paid less for identical jobs. This is known as wage discrimination and is the most prevalent form of discrimination. The attempt to combat such a form of discrimination can be seen in increasing equal pay legislation in different countries. Examples of this are the Equal Pay Act (1970), Sex Discrimination Act (1975), and Employment Protection Act (1975), but the effectiveness of such legislation is subject to much debate. Secondly, that the level of unemployment for the disadvantaged group in general is higher than that of other groups that do not face such discrimination. Thirdly, there is discrimination based on the kind of jobs that they have access to, the discriminated group given preference for repetitive and menial tasks.This is known as employment discrimination, where an individual is excluded from a job that is worked on by a person with equal productivity. When this happens, the disadvantaged group is employed for a job he or she is over-qualified for, simply because the group does not have access to better paying jobs in par to their counterparts and are denied opportunities of recruitment and promotion. A general misconception prevails that discrimination is only practiced by the employer. This is not true. In addition to employer discrimination, customer discrimination can also exist in the market. Customers may prefer to transact with only a certain kind of people.

In labour economics, Shapiro–Stiglitz theory of efficiency wages is an economic theory of wages and unemployment in labour market equilibrium. It provides a technical description of why wages are unlikely to fall and how involuntary unemployment appears. This theory was first developed by Carl Shapiro and Joseph Stiglitz.

Credentialism and educational inflation are any of a number of related processes involving increased demands for formal educational qualifications, and the devaluation of these qualifications. In Western society, there have been increasing requirements for formal qualifications or certification for jobs, a process called credentialism that is not easily differentiated from professionalization. This process has, in turn, led to credential inflation, the process of inflation of the minimum credentials required for a given job and the simultaneous devaluation of the value of diplomas and degrees. These trends are also associated with grade inflation, a tendency to award progressively higher academic grades for work that would have received lower grades in the past. In countries in the Middle East, where the rulers have traditionally used public sector jobs as a form of political appeasement for the middle classes, this has resulted in many youth seeking university degrees that are only suited for work in public sector roles, making them unqualified for private sector roles.

References

  1. 1 2 3 4 Michael Spence (1973). "Job Market Signaling". Quarterly Journal of Economics . 87 (3): 355–374. doi:10.2307/1882010. JSTOR   1882010.
  2. Connelly, B. L.; Certo, S. T.; Ireland, R. D.; Reutzel, C. R. (2011). "Signaling theory: A review and assessment". Journal of Management. 37 (1): 39–67. doi:10.1177/0149206310388419.
  3. Hungerford, Thomas; Solon, Gary (1987). "Sheepskin Effects in the Returns to Education". Review of Economics and Statistics . 69 (1): 175–177. doi:10.2307/1937919. JSTOR   1937919.
  4. http://economics.mit.edu/files/552
  5. Waldfogel, Joel; Chen, L (2006). "Does Information Undermine Brand? Information Intermediary Use and Preference for Branded Web Retailers". Journal of Industrial Economics. 54 (4): 425–449. CiteSeerX   10.1.1.201.155 . doi:10.1111/j.1467-6451.2006.00295.x.
  6. Akerlof, G. A. (1970). The market for" lemons": Quality uncertainty and the market mechanism. The Quarterly Journal of Economics, 488-500.
  7. Lewis, Gregory (2011). "Asymmetric Information, Adverse Selection and Online Disclosure: The Case of eBay Motors". American Economic Review. 101 (4): 1535–1546. CiteSeerX   10.1.1.232.8552 . doi:10.1257/aer.101.4.1535.
  8. Dimoka, Angelika; Hong, Yili; Pavlou, Paul (2012). "On Product Uncertainty in Online Markets: Theory and Evidence". MIS Quarterly. 36 (2): 395–426. doi:10.2307/41703461. JSTOR   41703461.
  9. Fudenberg, Drew; Tirole, Jean (1991). Game Theory. MIT Press.
  10. Goldlücke, Susanne; Schmitz, Patrick W. (2014). "Investments as signals of outside options". Journal of Economic Theory. 150: 683–708. doi:10.1016/j.jet.2013.12.001.
  11. Morewedge, Carey K.; Tang, Simone; Larrick, Richard P. (2016-10-12). "Betting Your Favorite to Win: Costly Reluctance to Hedge Desired Outcomes". Management Science. 64 (3): 997–1014. doi:10.1287/mnsc.2016.2656. ISSN   0025-1909.

Further reading