Senior Honor Thesis: A Survey of the Signaling Theory€¦ · Since Spence proposed his seminal...

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Senior Honor Thesis: A Survey of the Signaling Theory I-Hsiang Robert Chang May 20, 2008 Thesis Advisor: Shachar Kariv 1

Transcript of Senior Honor Thesis: A Survey of the Signaling Theory€¦ · Since Spence proposed his seminal...

Page 1: Senior Honor Thesis: A Survey of the Signaling Theory€¦ · Since Spence proposed his seminal work: Job Market Signaling in 1973, there has been a plethora of economics literature

Senior Honor Thesis: A Survey of the

Signaling Theory

I-Hsiang Robert Chang

May 20, 2008

Thesis Advisor: Shachar Kariv

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Introduction

Since Spence proposed his seminal work: Job Market Signaling in 1973, therehas been a plethora of economics literature discussing the effects of signalingin job markets. Furthermore, many extensions of the Spence’s model havebeen developed, including topics as: Multidimensional Signaling, Counter-signaling, and many others. It is impressive and perhaps daunting thatmany economists are devoting their work in this fascinating area

Organization In this thesis, I will briefly discuss how education has con-verged as a major subject in economics, how it was formally formulated,and how it is related to game theory and signaling. In the subsequent sec-tion, I will formally introduce Spence’s signaling model in education, andmore importantly, discuss the intuition and insight we can learn from themodel. In the third section of this paper, I will superficially introduce oneof the important extensions in signaling–Counter-signaling. Finally in thelast section, I will conduct a small empirical exercise, and test some of theimplications drawn from the original signaling model.

A Remark My original intention was to discuss signaling in educationfrom a strict point of view via game theory. But I have come to the real-ization1 that this is somewhat difficult, if not short-sighted. The topic ofsignaling encompasses a wide range of economics disciplines from informa-tion economics, labor economics to game theory, and many of their toolsare used concurrently for analysis. As a result, before I delve into the the-ory of signaling, I believe it is the most appropriate to discuss how thistopic(education and signaling) has emerged in economics, and why it is im-portant to consider it in these contexts. In the end, I hope to provide a moreintegral point of view to my readers, particularly for undergraduate read-ers who are interested in learning signaling in the context of an economicframework.

1This realization came from the fact that I have consistently diverged to papers thataddressed labor economics or information economics, and not necessarily game theory. Iam thankful that I have done so, for the completeness and integrity in this subject matter.

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Background

Some Statistics In 1960, only 41 percent of American adults graduatedfrom high school and only 8 percent of American adults had a universityaccredited degree. By 1998, 82 percent of the American adults had at leasthigh school degrees, and 24 percent had college degrees. On Jan. 8, 2002,President Bush signed the landmark No Child Left Behind Act (NCLB) inhope that all children in the U.S can learn in a better environment; Federal,state and local expenditures on education have continued to rise in thelast decade; in recent years, competition for college admission has becomeincreasingly intense. Unquestionably, education is one of the most importantpriorities to many people. But why? Why is education so important foralmost all of us?

Perhaps one might ridicule me for asking such a simple question–Theanswer cannot be more simple: education (for the majority of people) leadsto jobs, which provides financial support and ultimately a comfortable andsatisfying life. It is a means for us to achieve the life that we want, and itis unquestionable that education serves this purpose. I would not disagreewith the above statement. However, from the perspective of economics, Iwould like to study the aggregate effects of education on our society from astructural point of view. More importantly, we also want to investigate howexactly education can help us to achieve these goals from an informationalcontext.

Where it all began Nowadays, education is a rather popular subject inthe field of economics, not only because it arises quite frequently in manyof the public policy issues, but also because datasets and statistics relatedto education are easily accessible. Interestingly, despite its current popu-larity in economics, educational attainment was once (and not surprisingly)considered as a subject exclusive to sociology rather than in economics.

Becker and Human Captial Theory Certainly, many propositions con-cerning educational issues were raised by sociologists; but analyzing andfurther quantifying the effects of education was a rather difficult task. Itwas not until Becker (An exceptional Economist as well as a sociologist)that sociological issues (i.e. racial discrimination, crime, and family orga-nizations ) were first introduced and analyzed in the context of economics.In 1964, Becker proposed the human capital theory, in which he believedindividuals make choices of investing in human capital based on rational

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benefits and costs. In addition, he also argued that education is the key fac-tor that increases one’s productivity, and therefore, one’s wage. His modelswere controversial at the time, but slowly became the paradigm model thatexplained education attainment and its association to economics growth.

The Mincerian Model In addition to Becker, Mincer, in his ground-breaking work, Schooling, Experience and Earnings, explained (from a mi-cro, individual point of view) the possible connections between earningpower and schooling using earning function. Though with many sim-plifying assumptions, the Mincerian Model has proved to be robust whenapplied to datasets and statistics in many different settings–even in thepresent complicated, tumultuous labor markets.2

Spence’s Signaling Model In the 1970’s, a series of propositions amongthe works of Akerlof, Stigler, Spence and others, have gained increasingnotice. Their works deal with the impacts of information transfer in themarket. Particularly, they have argued that information asymmetry is afundamental problem that could affect the equilibrium outcome of a market.In 1973, Spence explained (in his seminal paper, Job Market Signaling)how education can potentially serve as a device to differentiate among thedifferent qualities of potential employees.

Spence’s methodology of explaining education attainment was rather dif-ferent from the ones we discussed above, but his theory does seem intuitivelyand mathematically convincing. Since then, Economics use these two main-stream theories to explain education and its associations with wage and pro-ductivity. However, it is rather difficult to conclude exactly which theoryhas better explanatory power for reality. In the following paragraphs, I willbriefly discuss the similarities and differences of the two models. Interestedreaders can be guided for further readings on these topics.

Signaling V.S Human Captial Theory The most notable feature ofboth theories is that they assume the labor market is heterogeneous. Hetero-geneity among labors means that potential employees have different abilities,attributes and characteristics at the very personal level. More importantly,the equilibrium wages are determined partially by these characteristics. As

2While Becker was awarded the Noble Prize in 1992, Mincer never recieved the samerecognition. But both have been considered as two of the most important contributors tothe field of labor economics.

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a result, instead of having a constant wage in the market, the equilibriumwage should be a function that maps variations of workers to monetarypayoffs. In additional, both theories assume (the standard framework) thata worker obtains education up to the point where the marginal increase inwage equals to the marginal cost of education attainment. Finally, both the-ories concluded that workers with higher abilities may obtain, on average,more education than less capable agents, which leads to higher wage.

While the two models have similar observations for the overall structureof the labor markets, they diverge drastically when it comes to the func-tionality of education. The human capital theory describes education asa channel for individual growth; a gateway to increase one’s productivitiesand skills. On the other hand, Spence’s model argues that education is adevice that allows individuals to reveal their unobservable characteristics.Undoubtedly, this divergence in explanation is significant. If education is ameans to accumulate human capital, many labor economists and macroe-conomists argue that it should be one of the primary sources in explainingeconomics growth. However, if education serves primarily as a screening de-vice for employers, it is only obtained so that we could exploit informationasymmetry.

Supports This is a rather delicate point, and how we can test the validityof these two theories is difficult to justify. There have been many papersthat use empirical approaches or quasi-experiments to resolve the debates.Methods include: tracking the rate in which employers learn about the pro-ductivities of the workers (Altonji,Pierret [1997]); Kroch and Sjoblom [1994],argue that if education is a signal, the essence of the signal should be ”dis-tilled in the position of an individual in the distribution of education for hiscohort”. As a result, by estimating the earning function that includes bothabsolute and relative measures of education, one could distinguish betweenthe two hypothesis.

In addition, there are other papers that favor signaling theory. Tyler,Murnane and Willett [2000] in their paper, test whether the General Ed-ucational Development certificate (GED) raises the subsequent earnings ofrecipients. Their strategy was rather ingenious: They exploited the fact thatGED passing standards differ by U.S state. For example, some test takerswith low scores could have passed in Texas but not in New York. However,they argued, if the GED reflects one’s true productivity, then supposedly

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individuals with GED would receive higher wage than the one who doesn’t.Since TMW knew ex-ante the score of each individual, they compared thewage differentials among people who passed and failed the GED, given thatthey received the same score. In other words, because the differences instandard of passing the GED, their quasi-experiment effectively randomizethe GED ’signal’ assigned to individuals. The result was encouraging for thesignaling model, and they concluded that there was a large signaling effectof GED attainment.

Summary To summarize, there has been much literature discussing thetwo explanations, but many of them can only support one instead of dis-proving the other. Many econometric methods have continued to be appliedin quasi-experiments, and the level of signaling effects varies, depending onthe industry, sample studies and other unobservable factors. In my per-sonal and humble point of view, I believe that both theories explain whythat education could have caused differences in wages, but the existence andfunctionality of education is less apparent. Furthermore, I would argue thatboth theories may sometimes have more explanatory power than the other,but it largely depends on the context in which we are discussing.

Why focus on signaling? In particular, I want to assert the claim3

that the signaling effects of education perhaps explain more accurately wagevariations for new college graduates. Since most students spend the majorityof their time in academic work, it is logical to believe that employers evaluateapplicants more heavily on their academic credentials such as school nameand G.P.A. On the other hand, as one gets more experience in the industry,it is expected that the effects of signaling of school names and grades shoulddeteriorate. From this point and on, I will focus exclusively on signalingtheory instead of human capital theory for two reasons:

• It was my original intention to discuss signaling and its developments,particularly in its applications in job market, and I will not furtherdiscuss or compare the similarities and differences of the two theories.

• Followed by the claim above, I believe signaling is more apparent fornewly graduates. Since my empirical tests and samples are drawn fromthis year’s graduating seniors at UC Berkeley, I felt signaling to be amore appropriate tool to use.

3An empirical study will follow in the subsequent sections to support my claim.

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The Original Signaling Model

Some Examples So far, we have restricted our attention to the context ofeducation and job markets. However, readers should be aware that signalingbehaviors are pervasive, and can be observed in biological systems, socialactivities and business practices. For example, male animals often developphysical features that are biological handicaps; well functioning firms areoften involve in charity works that do not necessarily gain revenue; somestudents ask difficult questions that are not required for the course duringProfessors’ office hours. Why are animals and human beings pursuing theseseemly wasteful activities? Is there an underlying explanation that coulddecode these behaviors?

Definition Signaling seems to be the paradigm answer so far. To definesignaling formally: signaling is an activity that arises when asymmetric in-formation affects the interactions of two parties. Particularly, the sender[s],in order to convey his private information, sends a signal[s] to the receiver.Upon receiving the signal[s], the receiver[s] uses it in order to infer the un-observable characteristics of the sender[s]. In our examples, male animalsdemonstrate how biologically superior they are relative to the others sincethey can afford to be handicaped while others cannot; well functioning firmsdonate to charity, not only to show magnanimity, but also to demonstratethat they have excess finance for other activities. Students similarly askdifficult questions in order to impress to the professors that he/she is on topof things. There are many other real life examples, but many of them sharethe same structure.

Properties of Signaling games In a signaling situation, there are twoimportant properties. First, the signals sent by the sender must be affordableto the sender; or that expected payoffs induced by the inference from signals(if the receiver infer correctly about senders’ intention) should be greaterthan the cost of transmitting the signals. Secondly, signals must be tooexpensive for some particular party. In our examples, biological inferioranimals would rather not to have the handicap feature on their body, poorfunctioning firms would rather focus on their own financial operations, andmediocre students would rather focus on what is being covered in class. Inthis way, the signals become especially important because it automaticallydifferentiates the different types without revealing the unobservables.

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Furthermore, from the receivers’ point of view, it is important that theiranticipations of the sender’ actions to be consistent with the actual actions ofthe senders, such criterion is called ”self confirming”. After all, if one formsincorrect beliefs, they should adjust their beliefs in time. I.e. The profes-sor would eventually realize that students who ask advanced questions areperhaps intellectually more equipped than the other students, even thoughprofessor cannot differentiate different types of students in the beginning ofthe semester.

This property makes the argument circular: the receiver holds some sub-jective beliefs about the sender. The sender, who knows such subjectivities,sends out his/her signals in order to help the receiver adjust and updatebeliefs. Once the receiver has adjusted their beliefs based on the signals, anew cycle begins (seller would again, based on the subjectivities of sellers,inform the receiver of the new information using signals). At this point, itis perhaps the most clear to explain the concept using a generic example.

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Example

Assumptions

1. Assume there is a firm and two types of workers, H (High) and L (Low)type distributed with probability BH and BL respectively.

2. The workers have productivities rH and rL respectively.

3. Assume that each worker can receive some education level at e > 0.but education does not contribute to their productivity, norto the revenue of the firm.

4. The firm’s profit is Π = r − w where w is the wage

5. Assume that the firm does not observe the type of the workers, thisleads to information asymmetry in the job market.

6. Finally, we assume that type is negatively correlated with the θH ≤θL. It is more costly for the Low type to obtain education.

Timeline Now, the timeline of the Job matching process is as follow, thefirm has some ex-ante beliefs about the type of the worker conditional on thelevel of education. Denoted it β(θi|e), ∀ i. Given the beliefs, the workers willselect their level of education. After observing the education level, the firmwill propose a wage schedule w(e) in which the workers can decide whetherto accept or not.

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Equilibrium

Equilibrium Definition Before we can solve the model, let us definewhat an equilibrium is. In our context,4an equilibrium is a Triple 〈e∗H , e∗L, β(θi|e)〉which represent a pair of education levels and an equilibrium belief systems.Furthermore, e∗H and e∗L are obtained through worker’s utility maximizationbehavior (i.e. There are no profitable deviation of e’s which provide worker ahigher payoff). Finally, the belief system must satisfied according to Baye’sRule. In addition, the out of equilibrium Beliefs are no restricted.5

In this model, I will restricted my attentions on Pure Nash Equilibrium,and ignore the possibility of Mixed Strategy Nash Equilibrium. There aretwo types of Pure Nash Equilibrium, namely, Separating Equilibriumand Pooling Equilibrium. I will start my analysis with the SeparatingEquilibrium.

Separating Equilibrium A Separating equilibrium is a Sequential Equi-librium where each type of worker selects different levels of education atequilibrium: eH 6=eL. Particularly, we define a specific equilibrium beliefsystem: β(θL|eL) = 1 and β(θH |eH) = 1. Note that this belief baysianconsistent.

Procedure

• We first assume that the firm holds some Equilibrium Beliefs : β(θL|eL) =1 and β(θH |eH) = 1.

• Given those beleifs, workers find the optimal level of education attain-ment.

• We then check whether these beliefs are consistent with the choice ofthe workers.

4I am adapting the equilibrium definition that better suited our context, it is no thetechnical definition.

5The out of equilibrium is something that is important in shaping the decisions ofthe workers, they take into account what would have happened outside of equilibrium.These threats and imaginary scenarios is the crucial force that makes the workers stay atequilibrium. We will discuss further about refinement in later sections.

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Consider the Low Type

Low type worker selecte∗L =argmaxe {β(θH |e)rH+(1− β(θH |e))rL - θLeInstead of taking the F.O.C of the utility function of L type, we break downthe optimization problem into different scenarios:

• Select e∗L as equilibrium ⇒w = 0rH + 1rL - θLe∗L = rL − θLe

∗L (1)6

• Select e∗H as equilibrium ⇒w = 1rH + 0rL - θLe∗H = rH − θLe

∗H (2)7

• Select some e 6=e∗L,e∗H ⇒ w = β(θH |e)rH+(1− β(θH |e))rL-θLe.8

Assume out of equilibrium belief is such that any deviation fromthe equilibrium is from L type.9 Then the w=rL-θLe (3)

Note that, for e∗L to be an equilibrium education, we need (1)≥ (2) and (1) ≥(3).from(1) ≥ (3),we learn that rL-θLe ≥rL−θLe

∗L ⇒e∗L ≤e for all e. ⇒ e∗L

= 0.

Consider the High Type

Similarly, productive worker select e∗H = argmaxe { β(θH |e)rH+(1−β(θH |e))rL-θLe. Again, instead of taking the F.O.C, we consider the discrete cases:

Select e∗H as equilibrium ⇒w = 1rH + 0rL - θLe∗H = rH − θLe

∗H (4)

Select e∗L = 0 as equilibrium ⇒w = 0rH + 1r∗L - θLe∗L = rL (5)

Select some e 6=e∗L,e∗H ⇒w = β(θH |e)rH+(1− β(θH |e))rL-θLe.

Assume out of equilibrium belief is such that any deviation fromthe equilibrium is from L type. Then the w = rL-θLe (6)

6Note that β(θH |e) is 0 because the firm believe at equilibrium, the person who selecte∗L cannot be high type, so the probability for him/her to be H is 0. Similarly, the workeris for certain a L Type

7Note that β(θH |e) is 1 because the firm believe at equilibrium, the person who selecte∗H cannot be low type, so the probability for him/her to be H is 1. Similarly, the workeris for certain not a L Type

8Now, it is important here that we assume some kind of out of equilibrium belief,otherwise the worker cannot effectively optimizes his/her utility.

9We will discuss later why we choose this particular out of equilibrium beliefs

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For eH to be an equilibrium, we require (4) ≥ (5) and (4) ≥ (6) ⇒(4) ≥ (5) ≥ (6)⇒ rH θHe

∗H ≥ rL > rL − θLe.

Finally, from(1) ≥ (2) and (4) ≥ (5),we obtain a bound for the valueof e: eH ∈ [( rH -rL)/θL , (rH − rL)/θH ]

The Set of Separating Equilibria As a result, we conclude that thereexists a set of Separating Equilibria such that:

eL =0 , eH ∈ [( rH -rL)/θL , (rH−rL)/θH ] and a belief function β(θH |eH) =1, β(θL|eL) = 0, and β(θH |e 6= eL, eH) = 0, given the assumption that anydeviations comes from the L type.

Discussions

First of all, let us observe that it is only worthwhile for the high type topursue education. Recall the first two properties we discussed earlier aboutsignaling, we require that the signal (which is education in our case) to beaffordable to the high type but too costly for the low type.

Low Type We solve our model by considering the possible deviations foreach type. For the L type, it is too costly for them to obtain the level ofeducation that firms expect a high type to have. In other words, the gainsfrom pretending to be a high type is much less than the cost incurred fromthe additional education. As a result, it is impossible for the low type tomimic the signals and behaviors of the high type. Furthermore, since the lowtype decided not to mimic the high type, and education is purely wastefulin our set up, the best thing for low to do is to not obtain education. Thisreasoning leads to our conclusion that the equilibrium education for the Lowtype has to be 0.

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High Type If we considered all possible profitable deviations for the hightype, we realize that it is suboptimal to pursue any non-equilibrium level ofeducation. As a result, if the high deviate, he might be able to save somecosts from education, but he will be treated as a low type and thereforereceive a lower wage. Here, the cost does not come from education, but thecost from what the high type could have originally obtained (i.e. rH - rL).

Consistency Finally, it is worth noting that the firm’s belief are self-confirming–while the firm believes that only the high type would choose ahigh level of education, and L type would not, the actual actions of eachtype of workers reflect these beliefs.

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Pooling Equilibrium

A Pooling equilibrium is a Sequential Equilibrium in which each worker,regardless of his/her type, selects the same level of education at equilib-rium: eH = eL. In this context, the firm cannot effectively differenti-ate the workers, therefore its equilibrium belief must follows the A prioripopulation distribution. Namely, β(θH |eH) = βH and β(θL|eL) = βL andw(eH) = w(eL) = βLrL + βHrH = r.Like before, out of equilibrium belief is such that any deviates comes fromthe low type.

Consider the Low type

• At equilibrium eL = e, w = r − θLe.(7)10Suppose there is a deviation,then w =rL-θLe (8)

So we conclude that we need (7) ≥ (8) for the equilibrium to hold⇒βH(rH−rL)/θL ≥ e.

Consider the High type

•• At equilibrium eH = e, w = r − θH e.(9)Suppose there is a deviation,then w =rL-θHe (10)

We conclude that we need (9) ≥ (10) for the equilibrium to hold⇒βH(rH−rL)/θH ≥ e. As a result, from (7), (8), (9), we observe that βH(rH −rL)/θH ≥βH(rH − rL)/θL ≥ e⇒ e ∈ [0, βH(rH − rL)/θL].

The Set of Equilibria

There exists a Set of Pooling equlibria with:{(eH , eL)|eH = eL = e, e ∈ [0, βH(rH − rL)/θL]

10Here, since the firm cannot differentiate the workers, the best thing to do is give outthe expected wage according to the distribution of the population

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Discussion continue

Belief System and the Set of Equilibria Again, I want to emphasizethat the above example is only one possible separating equilibrium, theremay exist many other equilibriums in which the belief functions are different.As a belief functions adjust accordingly, it will also affect each worker’soptimization problem, hence their optimal level of education.

The reason why we implemented the out of equilibrium that any deviationcomes from Low type is that this belief particularly magnifies the differencebetween the Low and the High. For the High, any deviation would be con-sidered as low, so it is best for the High to stay at a high level of education.On the other hand, this has less effect on the Low, since it is already notprofitable in the first place. This belief enforces the Set of separating equi-libria for us. But remember, they are only used for demonstration purposesonly.

In fact, one of the problems with the signaling model is that it has toomany equilibria, and the model gives very low predictive power about theactual behaviors of agents. There have been many refinement proposed innarrowing the set of equilibria, including: The intuitive criterion, theinformed principle problem, and the D1 refinement, but I will notget into the detail discussion of refinements for now. 11

A Remark In a separating equilibrium, the more capable will obtain moreeducation, and this difference in schooling will be precisely the signal thatallows firms to infer the hidden types of workers. More importantly, thesedifferences in education will be reflected in wage differentials. i.e. The hightype receives higher wage than the low type.

Semi-Pooling Equilibrium One can show (if allow mixed strategieswhere L type mixed between eL and eH), there exists a set of Semi-PoolingEquilibrium which lies just between the Set of Separating and Pooling equi-libria. However, this result is true in general.

11The above mathematical formulation was reference from Osborne, An introductionto Game Theory page 340; Kariv, lectures notes from Economics 104: advance microe-conomics and David Sraer, lecture notes from Economics 103: Information economics;Autor, discussion and presentation in his labor economics course at MIT

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• Extensions: Counter-Signaling

There are many extensions of the original signaling Model, particularlyin the extensions of the state space: Multidimensional Signaling, ContinumType Model, among many others. Most of the papers are technically chal-lenging to read for the undergraduate student. Therefore, I have decided toexclude them from this section12. However, I have encountered a paper byFeltovich, Harbaugh and To [2002], who published a paper in the RANDJournal about a theory called Counter-signaling. Their explanations wereclear and intuitive; the mathematical formulation was also acceptable. Mostimportantly, counter-signaling theory is quite fascinating. As a result, I havedecided to include this topic in my thesis.

Motivation We have already discussed, in a traditional separating equi-librium, high types will send out a signal that is otherwise too costly for thelow types in order to differentiate themselves. As opposed to the traditionalframework, Feltovich, Harbaugh and To [2002], propose an extension of thetraditional model, call counter-signaling.

Counter-signaling refers to situations in which the best type decides notto signal in order to express their confidence. Let us again consider somereal life examples. Capable students answer easy and somewhat challengingquestions that the teacher proposes, but very good students would ratheranswer very hard questions that mediocre students cannot answer. As aresult, like bad students who do not know how to answer the question, thevery good ones remain silent as well. The most skillful people are often muchmore humble than people who have ordinary skills, and might sometimes alsobe perceived as the incapables. Good products offer a period of warranty, buttruly great products do not offer warranties because their products will breakwith a very small probability. These are common phenomenon of behaviors,where the very good ones hides themselves from showing off. Similarly,we would like to develop tools to analyze these behaviors, and Feltovich,Harbaugh and To [2002] had proposed the theory of counter-signaling toanswer this question, with some simplifications.

Set up To formally describe the conditions in which counter-signaling canhold, let us continue using the framework of a job market. Assume there are

12Interested reader can be guided to papers: Multidimensional Signaling, by MartineQuinzii, Jean-Charles Rochet. Evolutionary Learning in Signalling Games,by Hans Jor-gen Jacobsen, Mogens Jensen and Birgitte Sloth.

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three type of workers, L (Low), M (Medium) and H (High) type. Type isagain private information to the workers, and the type is negatively corre-lated with the cost. The firm, as before, can only infer these characteristicsfrom workers’ attributes or signals. The extension from this model, however,is that there also exists an additional noise/information that the firm coulduse for inference. Without lost of generality, one can think of the additionalnoise as the second signal, except with some special properties. We assumethat this special noise almost surely reveals the Low and the High type cor-rectly, but sends a mixed signal for the Medium type (The Medium typecan sometimes be perceived as Low or High, depending on the underlyingprobability distribution). One real life example of such noise would be theletters of recommendation. It is likely that Low types with minimal workingexperience would almost surely receive a bad recommendation, while Hightypes who have extensive working experiences would almost surely to receivea good recommendation. Finally, the Medium type might receive a good orbad recommendation, depending on their performances and recommender’sperceptions.

Intuitions While the ability to send signals differentiates the senders fromthe Low type, it can also reveal the sender’s insecurity. Since there is a rea-sonable chance that the extra information will not differentiate the mediumfrom the low, the medium would want to signal to show that they are notthe low ones. On the other hand, high types expect to have a much favorablesupports from the extra information, so instead of differentiating themselvesfrom the low, they are more concern about differentiating themselves fromthe medium type. Since the medium is already signaling, the very goodtypes would rather counter-signal. In other word, by pooling with the be-haviors of the low type, the high types show a sign of confidence that themedium type cannot otherwise imitate. However, the high types need notto be afraid of being label as low, thanks to the favorable extra information.

Stylized Example Formal formulation can be found in Feltovich, Har-baugh and To [2002]. Therefore, I would like to give only a stylized examplethat demonstrates the intuitions of counter-signaling. Assume once againwe are in the job market context. Grades serve as a signal in this environ-ment, and we assume that the medium and high types always receive goodgrades. On the other hand, low types always obtain bad grades. Lying istoo costly for the low type because he/she might get caught. The cost ofrevealing grades for medium and high type is free.

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In addition to grades, each applicant is required to send a reference letterto their potential employee. Assume that the high types expect to receivegood recommendations, and that a low types expect to receive bad recom-mendations. Lastly, we assume that the medium types receive good or badrecommendations with equal probability.

Reasoning What should be the optimal actions of the interviewee? With-out the recommendation, the answer seems trivial: medium and high typeswould reveal their grade in no cost, while low types prefer not to reveal theirgrades because their bad grades might hurt their chances of getting the po-sitions. However, if we include the recommendation, the answer seems moresubtle. Consider the employer’s belief such that only medium types wouldreveal their grades. The medium type can reveal his/her grade and be per-ceived as a medium type, or else he/she could choose not to reveal the grade.However, if the low type are considerably unproductive relative to the Mand the H, the medium would rather reveal themselves from betting on thepossibility of being perceived as high. On the other hand, the High types donot worry about being perceived as the lows because of the additional letter.As a result, the high types would rather not signal in order to differentiatethemselves from the medium.

Numerical example A numerical example may help illuminate this case.Assume that productivity is 400, 700, and 900 for Lows, Mediums, andHighs respectively, and that Lows and Highs are equally prevalent in thepopulation. Given the interviewer’s beliefs, Mediums can choose to receiveeither 700 by mentioning their grades or (400+900)/2 = 650 by deviatingfrom the equilibrium and mimicking the Lows and Highs. Meanwhile, Highsare perfectly separated from Lows so they receive 900 by countersignallingversus only 700 by deviating and looking like a Medium. Finally, as long aslying about grades costs Lows at least 300, Lows do not gain from mimickingthe Mediums, so a countersignalling equilibrium exists.13

Comparison with the Traditional Model

Shortfalls Counter-signaling is, for conspicuous reasons, more difficult forthe players to really execute. Some have questioned whether players aresophisticated enough to perform the reasoning provided in the theory, andmany believe that it is perhaps difficult even for the high type to have such

13The Numerical section is quoted from Feltovich, Harbaugh and To[2002]

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confidence. Since in general, human beings are risk averse, and thereforewould use other, less radical means to ensure the revelation of their type.

In additional, many have believed that the context of counter-signalingtheory is rather narrow, and is not easily relaxed. Its unique structuremakes the mathematical model simpler, but it loses its predictive power. Inreal life, there are perhaps a continuum of types, and the recursive logic thatcounter-signaling implemented might seem helpless in that regard, and play-ers might not have the deductive abilities. In addition, it might be difficultto find the ideal noisy information with such special properties. Complica-tions might arise when there are additional signals.14

Summary Nevertheless, Counter-signaling has described the intuitivedynamics of when high types are surprisingly humble. Several comparisonscan be made from the traditional games and the counter-signaling model.Quoted from Feltovich, Harbaugh and To:

• Whereas signaling equilibria can be inefficient because of excessivesignalling, countersignalling equilibria may be inefficient because ofinadequate signalling.

• While signalling equilibria can play an informational role in increasingthe efficiency of receiver estimates of type, countersignalling equilibriamay lower the efficiency of these estimates.

• while higher costs tend to reduce signalling in a signalling model, alimited increase in costs can lead to more signalling in a countersig-nalling

Final Remark There are some interesting works that apply the theoryof counter-signaling to real life situations. A further paper by Harbaughand To explain that sometimes it is not the best strategy to reveal one’sgood news or good attributes. Similar to the spirit of the counter-signalingmodel, they argued that it is only the anxious type that is eager to revealtheir good characteristics. In real life, very good products often receive morecredibility through word of mouth than the company self-advertising. Evenin relationships, a man has a higher chance in dating the girl if it is the girl’s

14Feltovich, Harbaugh and To have conducted a laboratory experiment, and the resultssomehow diverged from the theory’s prediction, though high types seem to counter-signalmore as the game progresses. The detail result can be found in the same paper.

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friends who praise him instead of self-promoting by the man alone. I wasparticularly impressed by the Quasi-experiment they implemented. Namely,they investigated Professors from various ranked departments within theUC system, and have found that professors who are involved with the Ph.Denvironment de-emphasize their titles. On the other hand, professors fromlower ranked programs with less Ph.D’s around tend to emphasize their titlesmore. Interested readers can be guided to False Modesty, by Harbaugh, To[2007].

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Empirical Test

The objective of this section is to investigate empirical verification ofsignaling effects in the labor markets. Particularly, I investigated whetherGPA and working/internships experiences can serve as a signal for new grad-uates. Finally, I investigated whether signaling effects contribute to wagedifferentials.

Comments Before I jump into the analysis, I would like to share brieflyhow I decided to focus on new graduates. As one might imagine, signalingeffects might be apparent in some particular industry, such as Account-ing industry, Actuarial industry, and the financial industry. One commoncharacteristic of these industries is that they all encourage post graduationeducation and attainment of certifications. In the Accounting and finan-cial industry, CPA (Certified Public Account) and CFA (CharteredFinancial Analyst) have become the norm. Similarly in the actuarial in-dustry, there is a strong correlations between the number of actuarial examspassed and the level of compensation.15. Furthermore, there are so calledBrand Names among these industry.16 As a result, it is expected that onewho has multiple certifications and who works for a brand name companywould on average, earn more because of signaling effects.

Sweeney, and Bame-Aldred, in their paper, Signaling in the AccountantLabor Market had already investigated the signaling effects in the Account-ing industry. Their results was intuitive: Participants in the accountantlabor market with a masters degree commanded a wage premium; partic-ipants in the accountant labor market with CPA certification commandeda wage premium; participants in the accountant labor market with Big 4experience commanded a wage premium. And finally, length of tenure witha Big 4 firm positively affected the Big 4 premium in the accountant la-bor market. Certainly, these four claims can be equally explained using thehuman capital theory, particularly the last one.

Among other motivations, this paper motivated me to pursue a similarresearch, but on the actuarial industry. I spent a considerable time commu-

15One such data are available through D.W Simpson, an actuarial recruiting firm.http://dwsimpson.com/salary.html

16The Big 4 Accounting Firms, Merrill Lynch, Goldman Sachs, and Citigroup for Fi-nance industry. Towers Perrin, Watson Wyatt for the actuarial industry are examples ofthe ”‘brand names”.

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nicating with several actuarial consultants from Towers Perrin and WatsonWyatt, and had collected some sample data from them. However, many con-sultants felt reluctant to provide their information. (Since my survey askedthem about their compensation, which are rather commercially sensitive, asthe consultants claimed). Later, I learned that actuary salary surveys havebeen a relatively difficult task to conduct, even within the industry itself.After communicating with the HR department in Towers Perrin, I decidedto abandon my data set.

In the subsequent month, I decided to focus on signaling effects on newgraduates, because surveys are relatively easy to be distributed, and muchof the student information is not commercially sensitive.

Data Collection

I have contacted the majority of the undergraduate advisors from each de-partment, in different colleges. I have contacted College of Letters andScience, College of Engineering, College of Environmental Design, as well asCollege of natural resources. It was difficult to contact the School of Busi-ness, since they do not seem to have major advisors (They further breakdown their students into different concentrations).17Among the different ma-jors, EECS, English, Public Health and Economics were the most active inresponding and supporting the distribution of my research.18

Survey For the department which allowed me to use their listserv as achannel to distribute surveys, each student received an e-mail from the de-partment listserv with a URL to the survey. Each student then filled out theset of questions that I proposed19. Questions included: Gender, GPA, work-ing experiences, number of internships, number of hours spent in academicsand work experience.

Summary Statistics 165 students answered and completed the survey.All information is confidentially held and is used for academic research pur-

17Majors include: Philosophy, Psychology, Political Science, Public Health, Sociology,Economics, EECS, Civil Engineering, Industrial Engineering, Mechanical Engineering,Material Science and Engineering, Architecture, and Urban Planning.

18This might have caused sample selection bias, but I will later control them usingeconometrics

19The survey will be append in the appendix.

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poses only. In order to avoid sample selection bias, I did not inform theseniors about the context or the purpose of this survey.20

The following is the summary statistics of my sample population.

20However, some departments are unwilling to use their listserv to send out my surveys.As a result, there are higher percentage of samples from departments in which they agreedto send my surveys. I tried controlling this bias by conducting simple random samplingof seniors from UC Berkeley Directory in order to counter overweighting any particulardepartment.

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The majority of the students are 21 and 22 (There are three outliers atages 34, 39, and 61). The student samples have relatively high GPAs, (56percent have 3.5 or above). The distribution for the number of hours spenton academics is quite spread out. Job offers and their related industries arequite diverse, ranging from business, NPO, to education.21. 68 percent ofthe sample population is female, and 32 percent are male. Many studentshave multiple internships or part-time work experiences. Finally, the salarydistribution ranges from as low as 28,000 to as high as 110,000.

21Due to sample restrictions, I have labeled the industries using numbers instead.1=Business, 2=Education, 3=Engineering, 4=Health, 5=Mass Communication and Me-dia, 6=Graduate School, 7=NPO, 8=Research positions, 9=Others, 10=Service

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Hypothesis

As I mentioned earlier before, I believe signaling effects are more preva-lent among new college graduates, because most of them do not have ex-tensive working experience. As a result, firms would more heavily valueschool credentials and academic performance. However, the way employersscreen new graduates is well-known among prospective employees, and manystudents would seek to present the best of themselves by any means.

In the United States, the process of college recruiting is conducted throughseveral different channels: job fairs, on-campus recruiting events, companypresentations, and resume screening. Among these activities, resume screen-ing seems to be an important method that allows students to create positive?initial impressions to the firms. Interestingly, the format of resumes (in theU.S.) is quite open ended. More importantly, it is to the discretion of theapplicants to decide whether GPA should be listed on the resume. SinceGPA and internship experiences are important screening standards, I claimthe following hypothesis:

• High GPA students would especially emphasize their grades by puttingGPA on the resume.

• Low GPA students would de-emphasize the importance of GPA by notlisting their GPA on the resume.

Furthermore, it seems to me that applicants with extensive internshipexperience or part-time working experience would also prefer to mentionmore about their working experience rather than their GPA, especially whenthey have low GPA. On the other hand, students with very good GPAsbut very poor working experience would want to emphasize their academicperformances rather than the other. As a result, I want to test the following:

• Students with extensive working experiences and bad GPA would oftenchoose not to list their GPA, and mention more about their workingexperiences.

• Students who has good academic credentials but with little working ex-perience would emphasize especially about their GPA

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Table 1: No Show V.S ShowType Average GPA Average Internship experiences Average part time hours Average study hours Average Salary

No Show 3.251 1.183 8.785 16.244 57277.77Show 3.546 1.185 8.921 19.773 59807.69

Table 2: Good working experiences + Low GPAAverage GPA Average Internship experiences Average part time hours Average study hours Average Salary

3.2865 3.4 18.6 15.6 46666.66667

Table 3: High GPA + poor working experiencesAverage GPA Average Internship experiences Average part time hours Average study hours Average Salary

3.795 0.285714286 0.714285714 22.35714286 53000

No Show V.S Show The difference of GPA between shows and no showsis 0.295, a rather significant difference. It perhaps suggests that higherGPA students tend to signal their grades, but it is still unclear at thisstage. The difference in internship experience is very small, 0.00015. Inaddition, students who showed their GPA worked 0.135 hours more thanthe no shows, and also studied 3.528 hours more than no shows. Finally,students who showed their GPA have on average 2529.915 more salary indollar value.

Profiles with Extensive working experiences but with low GPAAmong the samples, there are ten students who have more than 3 internshipsin the past four years, and are currently working more than 15 hours perweek22 as part-time workers. The average GPA of this group is 3.286. Thereare five people in this group whose GPA is below 3.3, and only one individualputs his GPA(2.9) on his/her resume. In addition, all students from thiscategory are joining the industry in the next year.

Profiles with very high GPA but with poor working experiencesAmong the samples, there are fourteen students who have GPAs higher than3.7, less than 1 internship experience, and five or less part time workinghours. The average number of internship is 0.287, the average number ofpart time working hours is 0.71 hours per week. The average GPA is 3.795.Finally, only 28.5 percent of this population did not list their GPA on theirresume.

22By the regulation of College of Letters and Science, student who work 15 to 19 hoursper week can take 10 units at minimum, 20 to 29 hours per week corresponds to 8 minimumunits. Finally 30 or above hours per week corresponds with 6 minimum units.

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Hypothesis Testing

Originally, I tried to compare the number of students who put their GPAon the resumes, given that the students come from either a High GPA orLow GPA group. Nevertheless, I have realized that conducting hypothesistesting on this random variable (The number of students who show theirGPA) is rather difficult, because it is a binary variable. This implies thateven when the sample size is large, the distribution of the random variablewould never converge to a normal distribution. As a result, I have decided todo the opposite. Namely, fixing two groups (The group who show their GPAV.S the ones who do not), I compare whether there is a significant differencebetween the GPAs23. 24The shortfall of this methodology, however, is thatI am not directly testing whether H type is trying to signal to differentiatethemselves from the low. Instead, I try to indirectly verify that indeedpeople who signal often have higher GPA’s.

Set up Suppose we have two separate population: X and Y, where Xrepresent the samples who do not show their GPA on the resume,and Y are the sample students who do. Define two sequences where{X1, X2, . . . X49} and {Y1, Y2, . . . Y108} represent the sequences of stu-dents’ sample GPA. Finally, denote X and Y to the sample averageGPA from each group respectively.Then our objective test is a onesided test such that:

H0 : X > Y ; H1 : X ≤ Y

As mentioned above, by the Central Limit Theorem, the distri-bution of students’ GPA will converge to the Normal as n goes to ∞.However, the true mean µX and µY , as well as the true variance σX

and σY25 are all unknown. Follow the standard econometric approach,

we want to compute the t-statistic. Finally, at 5 percent significancelevel, we reject H0 if T ≥ t0.05,n+m−2. and not reject H0 otherwise.

23I assume that anyone with a GPA lower than 2 will not be able to sustain theiracademic status in Berkeley(which is the policy). As a result, it is reasonable to thinkthat GPA has a distribution between 2 and 4 that center around 3. Suppose one imaginesthere are infinitely many increments, then this distribution resembles the infinite tails ofa normal distribution at 2 and 4

24I am using the Central Limit Theroem to assume that the distribution of GPA wouldconverge to Normal as the sample size goes to ∞

25IMPORTANT, I assume the two unkown variances are the same for simplicity

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However, in order to compute the t-statistic, we need to use a samplemean and sample standard error. After some calculations, We obtainedX = 3.251 Y = 3.546. S2

X = 0.382 S2Y = 0.014. Since T (t statis-

tic)= [X - Y - (µX-µY ) ] / S2p(1/n+ 1/m) where S2

P is the pooled

estimator26 of the common variance27, our t-statistic is (-4.970 whichis much larger than 1.645=t0.05,156. Finally, the p value is very small:0.001. Therefore, we reject the hypothesis that X > Y .

If we switch our test to H0 : Y > X ; H1 : Y ≤ X, then we cannotreject the test, since the p value is 0.99. In other word, it seemsconsistent that people who show their GPAs on their resumes are theones who tend to have higher GPA.

Discussion Again, the ideal test would be to investigate whetherthere exists a systematic difference between the behavior of a highGPA and a low GPA candidate (In our experiment, this difference isbeing reflected by the number of people who show their GPA in eachrespective group). However, such numbers would never have a normaldistribution. As a result, I cannot apply hypothesis testing since I donot know the underlying distribution for this random variable. How-ever, I decided to do the opposite. By fixing the two groups (ShowsV.S No Shows), I tried to see if there is a systematic difference betweenGPAs. The result was intuitive, and that people in the Show grouptend to have higher GPA. This result does not imply signaling effect,but it indirectly verifies that there is some divergence of behaviors be-tween the high and the low (resembling the separating equilibrium).

Table 4: Summary StatisticsNull Hypothesis Alternative Hypothesis t statistic P value Conclusion

H0 : X > Y H1 : X ≤ Y -4.970 0.001 Null is rejectedH0 : Y > X H1 : Y ≤ X -4.970 0.999 Null cannot be rejected

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26The formula for pooled estimator is ignored27I have made the assumptions that two groups have the same population variance.28Certainly, there could be factors (other than signaling) that attribute to this phe-

nomenon. Possible explanations might be that people who shows GPAs are also the ones

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Regression on Wage Differentials

An important insight from the signaling model is that the high typedifferentiate themselves from the low type by taking an action that istoo costly for the low. In terms, high types are rewarded for this signal,and on average receive higher wage. I wanted to test the hypothesis(using a linear regression) that students who signal indeed received onaverage, a higher wage. In order to do this, we must fix all potentialcharacteristics that might contribute to wage variations.

There are many attributes that could contribute to wage differentials.I have chosen six attributes that I believe to be the most important,especially for newly graduates.

1. Age: People with older age might have more opportunities togain more job experience, which is associated with wage.

2. Gender: Gender might causes wage differentials, but to whichgender it is unclear.

3. GPA: higher GPA conveys higher working ethnics, and mightcontributes to students’ overall profiles.

4. Internship experiences: Internship experiences should also bean important factor, since firm used them to evaluate relativeexperiences among individuals.

5. Part time working hours: Similarly, people who work parttime, especially with longer hours, might have more on job expe-riences.

6. Academic study hours: Study durations might be correlatedwith GPA, so I included it in order to avoid omitted variable bias.

To summarize, the regression equation should look like:

who have more self-confidence, which might leads to better performance; or people whoshows GPAs because it is required for a particular industry. These possibilities can befurther tested in more detail econometric exercises.

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Wage = β0 + β1(Age) + β2(Gender) + β3(GPA) + β4(Internship) +β5(PartT ime) + β6(Academic) + β7(Show)

After running the regression, we get the following coefficients:

Wage = −18023.938 + 2967.083(Age) + 22256.974(Gender) −4567.713(GPA)+4445.331(Internship)+2.457(Partime)+140.659(Academics)+8976.817(Show)

Discussion All the coefficients seem intuitive, except for β3(GPA).For the ones that make sense: An additional year of age would in-crease the wage by 2967.0833 dollars; An additional internship experi-ence could increase the wage by 4445.331 dollars. Working part-timecan also increase the wage by 2.457 dollars. Additional time spent onacademics might attribute additional 140.659 dollars.

It was quite surprising for me to learn that gender actually playsa big role. One possible explanation is that the sample population isbiased. Since about 23 percent of the samples are English majors, andabout 21 percent of the student population are EECS majors, the twodominated groups might have affected the overall representation of ourpopulation. It is plausible to believe that many of the students from theEnglish department could be female, and many of the students from theEECS department are male. Male students majoring in EECS tend tomake more, on average, than many other majors, because of Berkeley’s

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proximity to the Silicon Valley.29 Such effects might be exacerbatedwhen the proportions of the two majors are large.30. Certainly, thismight not be the only explanation, and there might be other omittedvariable bias that I have not considered.

Counter-intuitively, GPA is negatively correlated with wage. Onepossible explanation is the inclusion of sample students who are at-tending graduate school (29.7 Percent). This group of students hasthe highest average GPA (3.573), but none of them are entering thework force next year. There are a fair amount of students enteringthe work force next year with high GPA (32/100). However, an evenhigher percentage, 42.8 percent of the people (30/70) have GPAs lowerthan 3.3. As a result, the exclusion of prospective graduate studentsmight attribute to the negative coefficient of GPA.

Finally, one can observe that by showing the GPA, one increases thesalary by 8976.817. However, the regression is not claiming that onewould always get a bonus for showing GPA. Rather, it informs us ofthe possibility that if someone signals his/her good GPA, there maybe potential rewards. This coefficient is consistent with the signalingprediction.

Refinement I believe refinements for this regression can be made inthe future. In fact, there are some data in which I collected, but did notuse. For example, I have not control the relative difficulties among ma-jors, since there is not such ranking. In addition, industry might haveparticular effects on wage. For example, one might imagine that startup engineers might make more (on average) than a start up NPO’s. Inaddition, we could further break down our existing data. For example,for the internship experiences category, we might break it down to spe-cific firms, and record if any of the applicants have worked at a brandname firm. There are many refinements that can be made. And thisexperiment is only the initial step.

29I am not claiming that Female makes less than Male on average.30According to the career center, the average salary of 2007 EECS major is 67,394 while

the average salary of 2007 English major is 35,120

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Conclusion

In this thesis, we have surveyed the topic of education in the context ofsignaling. First, I introduced how education had emerged as a majortopic in Economics. By comparing the Human Capital Theory and theTheory of Signaling, I motivate readers to understand education in abroader context. Furthermore, I have drawn comparisons between thetwo, and explained why I want to focus particularly on Signaling. In thelater section, I introduced formally the signaling model. Particularly, Ihave introduced the standard approach to solving this type of problem,and have concluded the conditions in which separating and poolingequilibrium can be sustained. In the subsequent section, I discussed theextensions of signaling games–counter-signaling, and how it relates tothe original model. Finally, I introduced an empirical section in whichI investigated potential signaling effects among the new graduates.

By introducing topics in this sequence, I wish to provide, especiallyto the undergraduate students who are interested in signaling and gametheory, a brief survey of the theory, yet with some level of sophistica-tion.31

31I want to thank Shacar Kariv, who was supportive of my thesis when I first proposedthe idea of writing a thesis on game theory. In addition, I want to thank Emily Wu, whohelped me to distribute the surveys. Also thanks to Cathy Hwang, who gave me someimportant advice on my thesis. I would also like to thank Tim Kwan for proofreading mythesis. Thank you all!

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Appendix

Survey

1. Are you a graduating senior who is planning to join the workforces in the next academic calendar year?1.Yes, I have recieved a full time offer and will be working nextyear2.Yes, and I am still in the process of job finding3.No4.Others (i.e. Grad school, taking a year off..etc)

2. What industry will you be working in after graduation?1. Business: Consulting, Finance, Accounting, Marketing2. Engineering: Electrical, Civil, Industrial, Mechnical, Chemi-cal, Nuclear3. Health Industry: Hosptial, Clinics4. Service5. Mass communication: Magazine, Media, Movies6. Non Profit Organizations7. Research: Lab, biomedical tech, economics research8. Education9. Others10. N/A (i.e. Graduate School, taking a year off...etc).

3. What is your Age and Gender? (e.g. Male/21)

4. If you have been offered a full time position, What is your ex-pected Salary for next year? (Skip if not applicable)

5. What is your Major? and What is your Cumulative GPA? (e.g.Economics/3.0)

6. How many internship experiences have you had during your col-lege years? Please specify a numerical value. (e.g. 3)

7. Do you work part time during regular semesters? If yes, Pleasespecify the number of hours you work PER WEEK? (e.g. 15)(skip if not applicable)

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8. Approximately, how many hours do you spend on academics workper week (excluding attending lectures, discussions and office hours)?(e.g. 20)

9. Did you list your GPA on your resume or CV?1. Yes2. No

10. Do you think GPA is an important indicator for the employerswhen evaluating a new college graduates? Do you think GPAis less important as one gets more experiences in the industries?Please elaborate in a sentence or two.

[end of survey]

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References

1. name title journal where

2. Spence, M. ”Job Market Signaling.”. The Quarterly Journal of Eco-nomics, Vol. 87, No. 3, (Aug., 1973), pp. 355-374

3. Feltovich, Harbaugh, To. ”Too cool for school? Signaling and Coun-tersignaling”. RAND Journal of Economics Vol. 33, No. 4, Winter2002 pp. 630V64

4. Harbaugh, To. ”False Modesty: When Disclosing Good News LooksBad”. In progress Paper.

5. Becker, G. Human Capital. University of Chicago Press, December31, 1975. ISBN-10: 0226041093

6. Daley, B and Green, B. ”Market Signaling with Grades”. StanfordGradate School of Business. In progress Paper.

7. Kroch, E and Sjoblom, K. ”Schooling as Human Capital or a Signal:Some Evidence”. The Journal of Human Resources, Vol. 29, No. 1,(Winter, 1994), pp. 156-180.

8. Helliwell, J and Putnam, R. ”Education and School Capital”. EasternEconomic Journal, Vol. 33, No. 1, Winter 2007.

9. Layard, R and Psacharopoulos, R. ”The Screening Hypothesis and theReturns to Education”.The Journal of Political Economy, Vol. 82, No.5, (Sep. - Oct., 1974), pp. 985-998.

10. Albrecht, J. and Ours, J. ”Using Employer Hiring Behavior to Test theEducational Signaling Hypothesis.”. Scand. J. of Economics 108(3),361V372, 2006.

11. Tyler, J. ”Economics Benefits of the GED: Lessons From Recent Re-search”. Review of Educational Research, Vol. 73, No.3, 369-403(2003).

12. Selected Notes from Autor, D (MIT, Graduate Labor Economics Sem-inar). Kariv, S. (UC Berkeley, Econ 104: Advanced Microeconomics).Sraer, D. (UC Berkeley, Math 103: Mathematical Economics)

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