This manuscript has been reproduced from the microfilm master UMI films the text directly from the original or copy submitted Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer
The quality of this reproduction is dependent upon the quality of the copy submitted Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction
In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted Also, if unauthorized copyright material had to be removed, a note will indicate the deletion
Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps
ProQuest Information and Learning
300 North Zeeb Road, Ann Arbor, MI 48106-1346 USA 800-521-0600
®
Trang 3RETURNS TO EDUCATIONAL SIGNALS
by
Steffen Habermalz
A Dissertation Submitted in Partial Fulfillment of the
Requirement for the Degree of
Doctor of Philosophy
in Economics
at
The University of Wisconsin-Milwaukee
Trang 4UMI Number: 3075467
®
UMI
UMI Microform 3075467
Copyright 2003 by ProQuest Information and Learning Company All rights reserved This microform edition is protected against
unauthorized copying under Title 17, United States Code
ProQuest Information and Learning Company 300 North Zeeb Road
Trang 5RETURNS TO EDUCATIONAL SIGNALS
by
Steffen Habermalz
A Dissertation Submitted in Partial Fulfillment of the
Requirement for the Degree of
Doctor of Philosophy
in Economics
at
The University of Wisconsin-Milwaukee May 2002
KL ấ Hay _—⁄ 4⁄2
Professr t John S Heywood Date
5/18/02
Graduate School Afproval Date
Trang 6ABSTRACT
SEQUENTIAL REVEALING OF INFORMATION AND THE RETURNS TO EDUCATIONAL SIGNALS
by
Steffen Habermalz
The University of Wisconsin-Milwaukee, 2002
Under Supervision of Professor John S Heywood
Recent work proposes that returns to educational degrees decline with work experience as emplovers directly observe employees’ abilities Yer, these models use simple, two-period (before and after) revelation of ability This paper employs a multi-period model
in which workers are matched with jobs according to their educational degree (signal) and
which takes into account the quality of the job match (e.g is the worker over/under qualified for the job?) It is assumed that information is revealed sequennally (e.g the most underpaid workers reveal their true ability first, the second most underpaid second, etc.) The
main result is that, while the general outcome of the two -period model is preserved, returns
to educational signals for many workers show an increase in the early stage of the model before eventually declining Using data from the 1979 -98 waves of the National Longitudinal Survey of Youth 1979 and a constructed panel data set trom the Current Population Survey a model is estimated in which diploma effects (returns to educational signals) are allowed to vary over time (experience) in a non-linear fashion The empirical analysis confirms the hypothesis that returns to educational signals increase over a substanual part of a person”s work life
Trang 8
To my family for bankrolling me To Catherine
Trang 9to
Introduction ccsccesssssessecesesesesecscsscessoceneuscessecncassnceescsecusutscseeessressesnsssecesereeesesnesnesnens 1 7 The Revealing Process 10
3.1 Firm Wages ố 14
3.2 Wages to educatlonal SigTl3Ìs «sung 31111111111 srre 18 3.3 Above median pTOUDS sex HH TH HH0 111 xrkrre 19 :h¬—.- — 19 3.3.2 Stage HHÍ CR1 KH TH nh Tnhh ru 21
3.3.4 STAĐC uc HH HH TT HH KH TH Tnhh nhe 23
3.4 Wages to Signals below and including the median proup 24
BAL Stage Uc 24
3.5 Returns to Educadonal SignialèĐ -s- ôch tre re, 25 3.5.1 Returns to cducauonal signals within Stagc Ì 26 3.5.2 Returns to educational signals between Stage [ and Stage ID 27 3.6 Šimulaton of the Rcturns to cducatdonal signs -5-5-c-cc-cc«- 27 FEempirical Results and Data ccssesssssssssessssssessesseeessescesseceecseeesssesssssssessssssecssceeess 32 4.1 Review of Empirical ÍLIt€TATUFC con t2 reree 33
nơ -— 35 >> —.—— ,ƠỎ 36
Trang 105
4.3 be 1)120A0r1 Cố 39
4.3.1 Regressions with potential €XD€TICTICC .SẶ cà ntererkerxrereee 41 4.3.2 NLSY79 Regressions with actuaÌ €XP€TICnCC - o7 ccccerrreere 45 4.3.3 Public-Private Repression - 56 4.4 Robustness “Testingg - << H1 1e ke 58 4.4.1 Fixed Effects, Random Effects and Spline (OLS) Regressions 58 44.2 MXcdian repT€SSIOT ìĂ on HH ng rrrrrrrrrrrke 60 4.4.3 Human Capital vs Sipgnaling cscseeerererererererrrererree 64 4.5 [ˆurthcr Tfcsting - «se ca cành tt HH HH nh re 67 4.5.1 Distrbuuon of Abiliry Within Degree Groups -cc-c 67 4.5.2 Increasing Variance of Wages over TĨme -c«-cceereererereer 68 0941 10 73
Trang 11Table 1: Descriptive Statistics for both SampÌ€s - «cscece nhe 38 Table 2: Pooled OLS-Reyression with potential Experience (CPS and NLSY79 data) 42 Table 3: Means of potential experience by race gender, diploma <cscc<c- 43 Table 4: Diploma* Effects by race and gender (pot Exp.) -cccecccrrree.reer 43 Table 5: Pooled OLS-Regression with actual Experiencc (NLSW 79 -adjusted) 46 Table 6: Àlcans of actual cxperlence by race gender and dipÌoma -. c ccee 49 Table 7: Diploma E=tfects by race and gender (actual expcrlenCc) . -cccc-ccee 49 Table 8: Public-Private Comparison (both đata s€tS) .- - s5 57 Table 9: Fixed/Random Effects and Sphùne Regression co 59 Table 10: Least Absolute Deviations (Median) regression for the NLSY79 sample 62 Table 11: Diploma Effects* by race and gender 0 seecessceerseseseeesesneseseseseseessseseesseseseneeens 63 Table 12: OLS regression with eduCation -ecxp€TI€TCC InItCTACUIONS 27s sesererree 65
Table 13: Correlation matrix for Interactons betwecn cducatdon and the Àssociate/Bachelor
degree and actual experience and actual experlence squared ce xcerx 65 Table 14: Distribution of AFQT-Scores by degree .ccecscscesesssessssecsceesesessesserceseseeseesssessesaes 68 Table 15: Distribution of Time in Labor Market by Degree eee ceeeecsesnenseeeeseeeseees 69
Trang 12LIST OF FIGURES
Figure I: Relocatlon of workers in a 4x4x4 modÌ -. -5 s-scc<cecrscrexerexrerrkreeesrsrervee 13 Figure 2: Revealing/Detection process for a 6x6xĨ modicÌ . - 5< s+cceecexeerreersree 13 Figure 3: Revealing/Detection and Changes in Firm \W'ages .cccrrrrrreeerrreee 17
Figure 4: Stages in the Revealing/Detection Process .::ccsssessssesssssecescssecseeacsseeseeneeseneeesneces 20
Figure 5: Diploma Effects over time (all) 0 sccsesescssessscsesesessssesessssescssesessesesscsnsssesceessesencaeaees 51 Figure 6: Diploma Effects over time (White males) :cssessesssessesessesesessesssscssssserseneseeneneseesene 52 Figure 7: Diploma Effects over ume (White Females) .ecsssessssessssssesrcssscsssensencnsencecneneneeeees 53 Figure 8: Diploma Effects over time (Black Males) scsesscssssssssesesecsesesessessssssensasessseseacacaees 54 Figure 9: Diploma Effects over time (Black Perm aÌCS) 7< c+ càng re rree 55 Figure 10: Standard Deviation of Real Hourly Wages by Time Spent in Labor Market for
High School diplomas scsecssesecesseseesessscesssssssecessscsseeteeneseneecsesesasenssenesesseneeeessesseseeeceeeeneoss 70 Figure 11: Standard Deviaton of Real Hourly Wages by Time Spent in Labor Market for
Associate/Bachclor €BT€S sành HH TH HH0 Hà nành He cgrờ 71 Figure 12: Standard Devianon of Real Hourly Wages by Time Spent in Labor Market for Profcssional IDe€BrCS cong 114711111 Terrrkrerrke 72
Trang 141 Introduction
Ever since the contributions of Spence (1973) and Arrow (1973) there has been
considerable work in the human capital versus signaling debate The theory of human capital as laid out by Becker (1964) and Mincer (1962) claims that education (and job training) add directly to a person’s productivity and that innate ability is merely a foundation to build on This approach has received widespread attention over the last 30 year and the empirical literature investigating the effect of schooling on carnings is very large '
Within the signaling (or screening) framework developed by Spence and _ his
followers, additional years of education have (in the extreme version of the theory) no effect
on a individual’s productivity In the Spencian framework education serves as a signal of innate productivity to alleviate the informational asymmetry about the true productivity of a worker between the emplover and the employee It therefore solves the information problem introduced by Akerlof (1971) The crucial assumpton within the signaling framework is that the cost of acquiring education is negauvely correlated with innate productivity tor the
individual such that the more productive individuals will acquire more education Therefore,
the amount of education an individual acquires can be used as a signal of the individual's innate ability Due to the lack of better informatuon on prospective employees, employers use these educational signals to predict the true productivity of workers in the hiring process
Trang 16that a group purchasing a signal contains workers of all types and education is the only signaling device, the process results in non-optmal matching in the first period In the second (and last) period the true producavity of the new employees is revealed At this point mismatched workers are reassigned to appropriate jobs and the matching is optimal The main feature of this process is that the average productivity of all workers improves from period one to period two Belman and Heywood calculate the return to an educational signal in each period to demonstrate theoretically (and empirically) that the return to an educational signal attenuates over time The intuition behind their result is that there is improved matching in the second period but since higher level signals have less "room" to improve, the returns to educational signals declines '
However, the question of how and when workers’ true productivities are revealed is not given any attention The model changes from a period in which nothing is known to a period in which there is perfect information about workers’ true producuivities Instead, this paper presents a model with a multi-period setting that allows modeling the productivity revealing process explicitly Following Belman and Heywood (1997) information in the first period is impertect but symmetric which implies that neither the worker not the ¢ mployer has knowledge of the worker’s true productivity From period two onward the informational structure of the model changes Workers become privately aware of their true producuvity Information becomes asymmetric between employers and employees beca use employers are still excluded from the knowledge of the true productivity of their workforce From that moment onward workers behave in two ways It is assumed that workers are utility
Trang 17the wage they are being paid A rational worker wants to eliminated the impact of the producuvity constraint
On the other hand, there are workers that do not have the abiliry chat the job requires and are thus better off than in a world with perfect information The rational response of those workers is to do everything possible to not to be detected
Employers are assumed to be profit maximizers It turns out that they behave quite differendy towards to two groups Surely, it is not in their best interest to waste resources on finding out who the “underpaid” workers are since their output is exactly what the firm wants Thus, employers need only be concerned with detecting the “overpaid” workers with true productivides less than the job requirement
This approach offers a departure from the employer -learning hypothesis (Farber and Gibbons [1996], Altonji and Pierret [1998, 2001]) in nwo ways First, as in Belman and Heywood (1997) the productivity of workers is assumed to increase over time with better matches Second, it is assumed that both employers and emplovees learn over time and react optimally to their findings Since emplovees are ut ility maximizers it is assumed that a worker with sub par performance has to be detected by the employer in order to give up his favorable position On the other hand, a worker that finds out that she is underpaid will reveal her true productivity as soon as she can in order to increase her earnings *
Trang 18the results of the mainstream human capital model Both are able to generate the aforementioned tme path The results of the theoretical model are therefore tested within a narrower framework, the literature on sheepskin effects Using the 1979-1998 waves of the National Longitudinal Survey of Youth 1979 (NLSY79) and a synthetic panel from the 1979 - 1998 Current Population Survey (CPS) the main hypothesis of the theoretical model is confirmed within that framework Returns to educational signals (sheepskins) show a concave pattern over time The regression results also suggest that the returns to an educational signal increase for a substantial part of an employee’s work life
The contributon of this paper to the literature ts twotold First, it is shown that in signaling/job matching framework with productivity constraints the returns to educational signal tollow a concave pattern over time This is an interesting result because it leads to the conclusion that it is not possible to reject the signaling hypothesis just on the grounds of the time pattern of the returns to educational signals Second, it suggests a rational way in which employees and employers interact
It should be mentioned how this paper differs from other attempts to analyze skills mismatches between jobs and workers, especially from the literature on “over -education’”” This body of literature analyzes the consequence of an educational mismatch The effect of over-education on wages is not well established While some studies have found positive
returns to the years of over-education, the paper of Groot/Maasen van den Brink (2000)
Trang 19human capital (education) determines producuvity, it is exactly the difference between true producuvitw and the amount of education an individual acquires that is analy zed here Thus, there is a distinct difference between the two approaches of investigating the effect of skills mismatches
Section two gives a briet descripuon of the model Section three describes the new process that governs the revealing/detection of the workers true productivides and develops the model accordingly The model will then be simulated Section four describes both data sets, contains the empirical results and compares them to earlier studics Various specifications of the models are run to test for the robustness of the results The section also contains a look at the time path of sheepskin effects when differentiated by whether the employee works in the private or the government sector of the economy Furthermore, the secuon evaluates the results in light of the human capital/signaling discussion and test some of the assumpuons of the theoretical model empirically Section five concludes and suggests
Trang 20„8
2 The model
Assume N ordered worker types consisting of equal numbers of workers, T,, i= 1,2,3 N with productivites v, i= 1,2,3 N There also are N firm types, ¢,, = 1,2,3 N The job match determines the productivity of each worker A worker matched with a job c, has maximum productvity v, even though his true productivity might be higher His productivity is constrained by the job match Workers who are assigned to a job t, and have
productivity v,, with 1>j, realize producuvity v,
Fach worker purchases an ordered educational signal S,, i=1,2,3 N The model
does not explicitly model the process in which agents acquire educational signals However,
it seems reasonable to assume that the acquisition of signal originates from a Spencian process in which agents observe their own productvity with noise and base the decisions about educational signals on unbiased estimates of their own productivity This process would result in signaling groups that potenually contain workers of all twpes and whose heterogeneity depends on the sampling distributon of the estimator used by the agents Section 4.5.1 addresses this issue and finds that there is considerable heterogencity in terms of ability amongst purchasers of a given educational signal
Trang 21information The magnitude of @ depends on the ability of individuals to esamate their true producuvity For simplicity I assume that workers who purchase a signal and are not of the corresponding productivity are represented in equal proportions in each signaling group Thus the share of workers of any given productivity in a signaling group S, that is not of true
(| ễŒ
productivity v, is (ina) N-|
The model has N periods In period 1 the firm j's profit maximizing choice is to hire workers that purchased the signal S, Theretore the first period wage in firm j 1s equal to the expected productivity of the group that purchased the signal S
y-l
(1) wil =Œ-v, +a) Gy (N - j)-¥, tà for all
The first term on the nght side of equation | represents the share of workers who purchased the educational signal S, and are of the truc producuvity v, The second term ts an average ot the productivities of the remaining N-1 signal groups, some of which are constrained by the job match The first term inside the parenthesis shows the workers that
are of higher productivity than j but are constrained by the job match The second term
Trang 22In the last period in which all true productivities are revealed and all matches are
perfect the wage to Signal S, is’
(2) S'=a@-v ;ũ-=®#) $v
The first term represents the share of signaling group S, that are of true productivity v, and are working in firm j The second term summarizes all other workers that belong to signaling group S, but are of either higher or lower productivity than v, They have all been assigned to their optimal firm and earn wages equal to the respective marginal products
Both (1) and (2) do not change when moving to a multi-period setting The following
Trang 233 The Revealing Process
In the analysis employers are assumed to be profit maximizers and emplovees are assumed to behave according to utility maximization In the periods atter the hiring is completed both employers and employees try to improve their position It ts assumed that in the first period workers are assigned into the jobs according to their educational signals, i.e firms with jobs that require productivity v, will hire workers with signals equal to S Since the group that purchased educational signal S contains workers of all true productivities there will be perfect matches, undermatched workers (workers have higher productivity than the job requires) or overmatched workers (workers have lower producnvities than the job requires)
The employees that are constrained by the job match (undermatched) have an incentive to move on to another job and try to reveal their true productivity Employers have an incentive to “weed”? out underachievers and are thus trving to detect those employees that have a lower productivity than the job requires (overmatched) This means that, from the first period forward, employers have to try to gather information on who the sub par performing workers are On the other hand, workers who are constrained by the job match have to find ways of distinguishing themselves from the other workers
Trang 24Il so depends on either (or both) of the following: the ame at which they realize thar they are underpaid and the means they possess to credibly reveal their productivity Ít is argued here that both abilities rest on the deviation of their truce productivity from the productivity required by the job This implies that the workers that are most “‘displaced” learn about their true productivity carlier and/or can credibly signal this disparity to the employer It should be noted that this does not keep two individuals who possess different educational signals from revealing their true productivity in the same period
Consider two examples First we look at the group ot workers that is the most undermatched Imagine tor example a world with four firms, F @=1 4, ordered according to the producuvity of their jobs and four types of workers, v, 0 0 =1 4, ordered according to their true producuvity In period two the workers who are v, and ended up working in F, are the most undermatched because the productivity constraint imposed by the job match has the greatest effect This group is assumed to have the greatest incentive to reveal their true productivity In period nwo they do just that In other words period two begins whenever enough time has clapsed for the worker to be able to reveal his true productivity.”
Trang 25Conunuing with the four-firm-example above, workers with true productivity v , will, of course, go on to work for firm F,.’ Simultaneously workers that are of true productivity v, and purchased educational signal S, four are detected in firm F , They are shipped to firm F, In essence the two firms exchange workers At the end of the second period there will be no workers in firm F, that are of true productivity v, and no workers in firm F, who are of true productivity v,."" Figure | illustrates this process Empirical evidence on job matching supports the proposed mechanism Bartel/Borjas (1981) and Mincer(1986, Part A) find that the wages of quitters (underpaid in the model) usually increase and that the wages of workers who get laid off (detected) usually decrease
Trang 2613 Figure 1: Relocation of workers in a 4x4x4 model
<$ FIRM 1 <— FIRM 2
workers with workers with
true productivity true productivity
four one
FIRM 3
Vy FIRM 1! |Ì———>
Figure 2: Revealing/ Detection process for a 6x6x6 model
Revealing Detection period ; ¬
worker type in firm] worker type in firm
1 no revealing no detection 2 6 1 6 3 6 2 2 6 3 5 ] I 5 4 6 3 3 6 4 5 2 2 5 4 4 1 1 4 5 6 4 4 6 5 5 3 3 5 5 4 2 2 4 5 3 1 1 3
6 all revealed all detected
Trang 273.1 Firm Wages
The revealing/detection process obviously has the potenual to alter tirm wages In period one, without any information other than the educational signal, tirms of type F , will hire the workers with educational signal S, and pay a wage equal to the expected productivity of the workers This is the case because the employers do not know the true productivity of the workers Thus the firms must maximize expected productivity For example, in the simple 4x4x4 case the wage in firm one and four would be
(I—ø)
(3) wF!' =a@-v, rT + +)
(4) wF" =-v,+Ú =5) 0 xạ +)
The first term on the right hand side in both equations shows the share of workers that signaled S, and actually is of true productivity v, The second term captures the workers that signaled S, and whose true productivity is not equal to v, Note that the job productivity constraint is binding for all workers in the wage equation for firm F, that are not of true productivity v, On the other hand no worker that is of true productivity less than v, is
constrained in firm F ,
In period two, as described above, the revealing/detection process will cause workers with true productivity v, to migrate from firm F, to firm F, and workers with truc
Trang 28G wE“°=ø-v+U=#)„ ,-#) 3 3 (v, +¥;)
The first component of the wage of firm one in period two are the workers that signaled productivity one and are of true productivity one The second are the workers that signaled producuvity S, but whose true productivity is v, that were detected in the second period by the process described above The remaining component is comprised of workers that signaled productivity S, and that are of true productivity v, or v, By analogy the period nwo wage in firm F, ts:
M2) +=) ¢, +)
(6) wFi =a-v,
3 3
Since the revealing/detecting process does not affect firms two and three in the
second period, their respective wages stay on their first period level
A special feature of this model is that due to the job productivity constraints the
revealing/ detection process does not alter the wages of all firms involved '' For example,
firm one loses workers of true productivity v, that go on to work for firm F, and acquires worker of true productivity v, from firm F, However, due to the job productivity constraint, both groups have the same productivity (=v ,) while working in firm F, Thus, although firm one acquired new workers with lower true productivity the wage does nor change
The situation is different for firm F, in period rwo Ít gets workers with trục productivity v, and releases workers with true productivity v, Clearly, the wage for workers in firm four will go up As a result there are two equations for firm wages in the model In general, the wages for firms whose wages are still unaffected by the revealing/detection
Trang 29_ -l
(7) WF) =v, - mì (v, -v,), for J<N-r+l ¡ml
The wages for the firms who gain from the revealing/detecting process follow: (8) wFi sy -—& F (v,—v,) for j>N-t+l
TỶ ey N=n)
The intuition behind this formula is that the wage of a worker in firm F, depends on the producnvity of the optimal worker v, (first term) and is negatively affected by ditferences in true producavity between the opumal group and all other twpes of workers that are retained by the firm at a parucular stage of the model [t is a compositional affect on the firm level
Trang 313.2 Wages to educational Signals
Note that in period one the wages to the educational signals are equal to the firm wages because all members of a particular signaling group S, are in firm F,, thus
(9) wF°' =w§ˆ'
From period two on wages to educational signals are changing in response to the
revealing/detection process Again resorting to the 4x4x4 example we used earlier, the
period two wage to the educational signal S, is
(0 wS!* =a@-w, 2M) 3 Mo) 3 + (I - a) 3
The first term on the right hand side captures the share of the group with the educational signal S, that is actually of true productivity v, These workers are still in firm F, in the second period and carn the firm F, wage The second term represents the share of workers who signaled S, and whose true productivity is v, They revealed in the second period, migrated to firm F, and thus earn the firm F, wage The last two terms correspond to the unrevealed workers in firm one that have signaled S, and are of true productivity v, and Vv; respectively
By the same reasoning the wages paid to members of the group with educational signal S, are:
(I-a) (i-q@) |, +ũ-#),
(1) WS sar-w, +, + wy
The members of the two remaining signaling groups have not yet changed firms, which is why their wages paid to signals in period two are equal to the firm wages in period
Trang 3219
Equation 10 and 11 show that changes to the wage to an educational signal have two sources First, the wage to the educational signal changes because of changes in firm wages." The second source of change is a compositional effect It pertains to the fact that the level of the wage to the educational signal will change if members of the signaling group change firms, holding constant the level of the firm wages
There are up to five distinct stages in the revealing/detection process that a particular educational signaling group can pass through over ume Equation 11, tor example, shows the wage to an educational signal in the second revealing/detection stage when workers start revealing (or being detected) at all The different stages will be categorized
according to two criteria First, a distinction will be made according to their relative position
towards the median educational signaling group Second, we will label wages to educational signals depending on what stage in the revealing process they are in Stage | is the stage in which the wage to an educational signal has not changed yet It is the same for all groups Figure + shows all stages in a 15x15x15 model
3.3 Above median groups
After stage Il, above the median signaling groups can experience 4 distinct stages
within the revealing/detection process before they enter the last period in which all information is present
3.3.1 Stage II
Trang 34and earn lower wages The signaling group’s composition in terms of firm wages changes and affects the wage to the educational signal negatively For example, in the 4x4x4 model of equation 11 workers with true productivity v, that belong to signaling group S, will be detected and will work in firm F, from then on This means that the wage to the educational signal S,, wS, will now be composed of firm four and firm one wages The signaling group 1s collecting firm wages from below For the general NxNxN case equation [1 can be written
as
(12 wS) = wF; - — “SWF —: r)
7 r=]
for M—r+l< /<2-(N-—r+l) and 7/3!
The second term on the right hand side partially reflects the compositional effect on the wage to the educational signal It depicts the influence of members migrating from firm F, to firm of lower order which weighs negatively on the wage to the signal S, and also reflects differences in firm wages Note that in stage II member of signaling group S, migrate exclusively to firms whose wages have not changed yet
3.3.2 Stage II
Trang 3513 w§;,=wF; = Sứ; - wF')+ “SW - wF')
rl I2 r3
for j>MN—r+land j>r
The first term on the right hand side simply reflects the wage of firm F, The terms inside the parenthesis shows the compositional effect and the effect of other firms wages on the wage to the signal S The first term depicts the negative effect on the wage to the signal S, of workers who migrate to firms whose wages have not changed vet The second term does the same for workers who migrated to firms involved in the revealing/detection
process
3.3.3 Stage IT”
Stage IV marks the first stage in which the wage to a signal S, is affected by both the detection and the revealing process Before stage [V the compositional and wage etfect on the wage to the Signal Sj (second term on the right hand side of equation 12 and 13) was exclusively dependent on the difference between wages in firm F, and wages of firms of lower order However, if enough time has passed and the wage to the signal in question is sufficiently different from the higher order signal, workers that signal S, and are of trục productivity higher than v, will migrate to firms of higher order This has a positive effect on
the wage to the educational signal S, In the 10° period in a 15x15x15 model, tor example,
Trang 3623
(4 w§,=wF, _ảT “SWr; - wF')+ > (wr — wF')
t=l 1=/+C{ÁÑÝ rely
tor M]—r+l< j<t
The term in the parenthesis shows the compositional effect on the wage to the signal S, The first term depicts the negative effect on the wage to the educational signal that stems from the presence of workers that work at lower order firms The second term captures the positive effect of the workers that migrate to higher order firms and carn higher wages
3.3 Stage V
The difference between stages [V and V is the same as between stages II and IH Workers with signal S, keep on migrating to firms of lower order, which from this stage on can have wages that cither have changed due to the revealing/detection process or have not Equation 15 depicts this
(15) wS, =wF -—* tr —wF' )+ “Sor —wF )+ ¥ (oF — wF')
7 rl t2N-re2 rapt N-rel)
for 2-(M—r+l)< j<r
Again the first term on the right hand side is the wage in firm F, (wage effect) and the terms in the parenthesis retlect the compositional effect on the wage to the educational signal S The first two terms inside the brackets reflect the negative effect of having worker work for tirms of lower order with unchanged wages (first) or changed wages (second) The last term in the brackets depicts the positive compositional effect of having workers work in
6
Trang 373.4 Wages to Signals below and including the median group
Wages to signals below and including the median group follow a very similar pattern to the wages to signals above the median group However, there are two main differences First, the compositional effect will start out to be positive since workers migrate to higher order firms It will include a negative effect later on when both the revealing and the detection process affect the wage to the signal Second, there is no comparable stage three for wages to signals in this setting This stems from the fact that all workers that are detected migrate to tirms of higher order whose firm wages are already affected by the revealing/detection process and therefore have changed Thus, until the wage to the signal is
affected by both revealing and detection, we don’t have to distinguish between members of a
signaling group migraung to firms whose wages has changed and firms whose wages have
not
3.4.1 Stage I
In this stage the only source of variation comes from the compositional and wage effect and thus leads to an unambiguous increase in the wage to the educational signal S
Equation 16 captures this
_ N
(16) w§; =wF ~— Xe > (we: - wF')
aye N—r4lt
for j<tand jSN-r+l
Trang 3825
positive since it sums up the differences of the wages in firm F, and wages of firms of higher order
Stages IV and V are the same as for the above median groups Figure 4 summarizes the different stages of the revealing/detection process graphically and shows that a wage to an educational signal doesn’t have to pass through all possible stages
3.5 Returns to Educational Signals
In this section the returns to an educational signal are examined Returns to an educational signal are detined as the difference in the wages of two adjacent educational signaling groups at a given point in ume
Return to educational Signal S, at ume t
(19 RS) =wS) -wS),
As the last section showed, a wage to the signal can pass through muluple stages depending on the particular signaling group Therefore the return to an educational signal can be calculated between the following groups
e Within Stage |
° Between Stage I and Staye II ° Within Stage II
° Between Stage III] and Stage II (only for above median educational signals)
° Within Stage HI (only for above median educational signals)
° Between Stage IV and Stage IL (only for above median educational signals) ° Between Stage V and Stage HI (only for above median educational signals)
Trang 39° Within Stage V
° Returns when everything is revealed
No single return to an educational signal passes through all of the above stages Therefore we will focus on the first two (above median) returns to an educational signal as an important subset of all possible returns to educational signals We will do so for the following reasons First, all returns to educational signals pass through those stages Second, as it turns out in the ensuing simulation of the model, the returns to educational signals in these stages are most important in answering the question whether returns to educational signals decline over time As it turns out, the simulation will show increasing returns to above median educational signals between the first two stages Third, since the simulation shows a monotonously declining pattern for the returns to educational signals for below the median signals we will focus on returns to above median educational signals We will continue in the following way After we specify the returns to an educational signal within Stage [ in detail, we will focus on the change of this return upon its transiuon to Stage II 3.5.1 Returns to educational signals within Stage |
During this first stage of the model the included signaling groups have wages to their respective educational signals equal to the firm wages they work in Thus, the return to an
+ + * - = ~ 1
educational signal is merely the difference between the firm wages of two adjacent firms." _ -1
Trang 4027 Equation 20 shows that the return to the educational signal S, depends on the differences in true productivities of the two groups involved, the share of workers that signaled their true productivity (@) and the number of groups in the model (N)
3.5.2 Returns to educational signals between Stage I and Stage II
_ 2 -ON-1el) i-l inl
(21) RS’ = within Stage I return + s ol — ` ` Ñ —YN )-YO, -v,,)
l r=l K=rp-cXN
r1 m=l
The interesting feature of this return to an educational signal is, as the simulation will show, that the second term on the right hand side of equation 21 is positive An intuitive explanation will be given after the mathematical proof in the next section of the paper This means that for the above median groups the returns to educational signals actually increases between stages I and II
3.6 Simulation of the Returns to educational signals
As a next step the model was simulated using a 15x15x15 framework The simulation
was run qwice Once with a parameter value for alpha, the share of workers that purchase