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What Do Students Know about Wages? Evidence from a Survey of Undergraduates Author(s): Julian R. Betts Reviewed work(s): Source: The Journal of Human Resources, Vol. 31, No. 1 (Winter, 1996), pp. 27-56 Published by: University of Wisconsin Press Stable URL: http://www.jstor.org/stable/146042 . Accessed: 08/12/2011 03:52 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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What Do Students Know About Wages? Evidence from a Survey of Undergraduates Julian R. Betts

ABSTRACT The paper uses a survey to examine undergraduates' knowledge of salaries by type of education. Students' beliefs varied systematically with their year of study and personal background. The median student made (estimated) absolute errors of approximately 20 percent, but the mean signed error was only -6 percent. Regression analysis revealed links between students' knowledge of the labor market, and year of study, proximity of the occupation to the student's own field and parents' income. Over half of learning occurred during the fourth year. Logit analyses of students' use of information sources supported this conclusion. Implications for human capital theory are considered.

I. Introduction How do people choose whetherto attendcollege? Once in college, how do they choose a field? Despite the pivotal importanceof educationin labor economics, we know surprisinglylittle about how people make these decisions aboutschooling. Ourignoranceis reflectedby the fact that manyempiricalmodels of earningsstill treat education as an exogenous regressor. A centraltenet of humancapitaltheory is that people choose the optimallevel and type of schooling based in part on the market returns to education. This raises the question of whether people do in fact have an accurateperceptionof the role that education plays in the determinationof earnings. The author would like to thank Dan Black, George Borjas, Laurel McFarland, Richard Murnane, Herbert Smith and two anonymous referees for helpful comments, and Fred Koerber, Catherine Moore, Nima Patel, Phong Trinh, Vadim Vorobyov, and Jay Wrightfor excellent research assistance. He is also indebted to UCSD for research support. The data used in this article can be obtained beginning in August 1996 through July 1999 from the author: Department of Economics, University of California, San Diego, La Jolla, California 92093-0508. [Submitted November 1993; accepted February 1995] THE JOURNAL

OF HUMAN

RESOURCES

* XXXI * 1

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The Journalof HumanResources Similarly,we know little about how young workers form expectations about the future returns to different levels of schooling. In a series of publications, Freeman(1971, 1975a, 1975b, 1976a, 1976b)appliedthe cobweb model, with its inefficientenrollmentresponse to wage shocks, to enrollmentin numerousfields.1 Morerecently, other researchershave arguedthat if workersformrationalexpectations aboutfutureearningsin differentfields, then observedvolatilityin college enrollmentmay in fact reflect highly efficientsupplyresponsesto shocks in labor demand. Examples include Siow (1984) and Zarkin(1983, 1985), who find that the rational and adaptive expectations models fit the data about equally well, despite their radically different policy implications. The rational expectations models assume that workers at time t forecast future earningsbased on vtI the currentinformationset. It is plausiblethatthis informationset will includepresent salaries by field and degree.2Thus one indirectway to assess the credibilityof the rationalexpectations formulationis to study the accuracyof each student's set of informationabout currentwages. A third question concerns when students acquire informationabout wages. One would expect the marginalvalue of informationto be greatest in the early years of study, before sunk costs createdby study in field-specificcourses make it costly for a studentto switch fields. Thus most learningaboutthe labormarket would occur duringthe first year or two of study. On the other hand, if much of the informationwhich studentsacquireaboutthe labormarketcomes not through any explicit choice by the studentsto invest in information,but throughinformal exchanges with students, faculty, and others, then fourth-yearstudents might have an automaticinformationaladvantageover freshmen. A fourth importantquestion is whether students, as they specialize in fields, also specialize in the informationwhich they gatheraboutthe labormarket,again due to sunk costs which make a change of fields more costly as the student progresses. Such a findingwould help explain why large differencesin relative wages between differentfields can persist over time.3 A fifthreason why it is importantto understandwhat informationpeople gather about the labor market stems from work by Manski (1993), who argues that if there is heterogeneity in the way in which students form expectations, two identificationprobleihsbecome muchmoredifficultto control.First, it is impossible to model a person's choice of educationaccuratelyif the mechanismthrough which the personforms expectationsis unknown.Second, it becomes muchmore 1. For somewhat skeptical views of the ability of Freeman'scobweb model to capture enrollment dynamics,see Blaug(1976,pp. 833-36) andSmith(1986).FreemanandHansen(1983)updateFreeman's work and show that his models predictedenrollmenttrendsthroughthe early 1980squite well. 2. Siow (1984)makes precisely this assumption.Zarkin(1985)makes similarassumptions:he assumes that prospectiveteachers have accurateknowledgeof the currentvalues of most of the variablesdeterminingthe currentteacherwage, and, in the case of otherdeterminingvariables,thatthe prospective teachers have perfect foresight about their future values. The predictionsof the cobweb model, in contrast,rely on studentsmakingdecisions based on currentor recent wages only, measuredwith or withouterror. 3. See Altonji(1993)for an interestingstudy of the extent to which studentsmakesequentialdecisions aboutwhetherto attendcollege, and once there, what field in whichto major,andwhetherto dropout, based on uncertaintiesrelatedto labormarketreturns,personaltastes, and abilities.

JulianR. Betts difficultto control for self-selection of people into college if studentsdifferin the way in which they forecast earnings. An indirect method of gaugingthe importance of this problemis to measure the extent to which knowledgeof the labor marketis homogeneous among students. We are left with a series of interestingquestions. Is there a high degree of variationin wage beliefs among students, and if so, what determinesthese differences? Do studentshave accurateknowledgeof wages and relativewages? When does investment in informationabout the labor marketoccur, in the early years of college study when students must declare a major,or only later?Do students invest only in labor marketinformationspecific to theircurrentfield?Whatinformation sources do students use to learn about labor marketopportunities? This paper reports the results of a survey of undergraduatesat a public fouryear college which is designedto explorethese issues.4The next section describes the survey. Section III informallydiscusses a model of educationalchoice, which has implicationsfor how students invest in informationabout the labor market. Section IV analyzes the variationsin wage beliefs amongstudents, and the determinants thereof. Section V econometricallymodels the student characteristics contributingto lower errors, Section VI examines the informationsources which students use, and Section VII concludes.

II. Descriptionof the Survey A survey of 1,269undergraduateswas carriedout across all undergraduatefaculties at the University of California,San Diego. Students were selected by a samplingof classes designed to locate students in each faculty and year of study. Engineers were oversampled due to the abundantinformation sources concerning engineers' salaries. The survey, which required about ten minutesof students'time, was carriedout over a periodof four monthsbeginning in November 1992. Table Al at the end of the paper describes the sample. After obtaining informationon personal and family background,the survey ascertainedwhich sources of informationstudentshad used to find out aboutjob prospects for graduatesin various fields. The survey asked students three types of questions about earningsat the nationallevel. 1) Startingsalaries. These questions were asked for workers with a bachelor's degree in chemical, electrical, mechanical,or civil engineering(that is, four separate questions), a master's degree or Ph.D. in chemical and electrical engineering (four separate questions), bachelor's degrees in chemistryand psychology, and for a person with an MBA precededby a technical degree (science and engineering)and a person with an MBA preceded by a nontechnicaldegree. 4. Some readersmay questionthe usefulnessof subjectivesurvey data to answerthese questions. But the more conventionalsurveys used by laboreconomistswhich examinepeople's choices, as opposed to beliefs, can shed no light on the informationwhich people use. See Manski(1993)for a forceful argumentin favor of using subjectivedata in orderto analyzeeducationaldecisions.

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The Journalof HumanResources 2) Average salariesfor engineersby theirhighestdegreeand years of experience. These first two sets of questions asked for students' estimates of salaries at the time of the survey. 3) Average earnings in 1990 of "workers aged 25-34 years, workingfulltime" with a "high school diplomaonly" and those with a "bachelor's degree."5 For the exact wordingof the questions, and informationon responserates, see the appendix. Students' estimates of starting salaries were comparedwith data on starting salaries reportedin the September 1992edition of the College PlacementCouncil's Salary Survey, which reports national average starting salaries based on reportsof 24,519 salaryoffers from 433 campusplacementoffices throughoutthe United States, between September1991and August 1992. Estimatesof errorsin students'beliefs about engineers' salariesby engineers'years of experiencewere calculated using national average salaries reported in Appendix B of the May 1992 edition of the Professional Engineer Income and Salary Survey (National

Society of ProfessionalEngineers1992).This surveyis based on 10,069responses to the January1992mailingby the National Society of ProfessionalEngineersto its members, and represents a 21.8 percent response rate. Estimated errors in students'beliefs about wages in 1990of young workerswith a bachelor'sdegree and those with only a high school diplomawere calculatedusing weighted data from the March 1991CurrentPopulationSurvey.

III. An Informal Model of Educational Choice We can shed some light on the value of labor marketinformation to college students by consideringhow students choose their majorin college.6 Over time, students obtain new information.Relative wages of graduateswith differentdegrees change. Also, the student almost surely learns more about his or her abilities and interests duringthe college years, which reduces or changes the student's set of likely majors.One might model this as increasingdispersion in the student's beliefs about the expected utility of enteringdifferentfields as he or she progresses in college. Some students will act on new labor market informationor new informationabout their suitabilityto variousfields by changing majors while in college. But note that changingone's majorhas increasing costs over time due to the sunk costs in courses taken in the originalfield. This leads to several results. First, the value of informationabout the labor marketmay be greatest in the earliest years of study, since as the student progresses, sunk costs and the increasingdispersion of beliefs about field-specific abilities make switchinginto higher-payingfields less likely. On the other hand, 5. These questionsaskedfor estimatesof wages in 1990ratherthanthe currentyearin orderto facilitate comparisonbetween the students'responses and actualwages calculatedfor the most recent year for which CurrentPopulationSurveydata were availableat the time of the study. 6. A formalizationof this modelis availablefromthe author.

JulianR. Betts students, findinginformationcostly, may decide to invest in informationonly at a later stage of study, after their beliefs about their suitabilityto variousoccupations have evolved to the point where they have virtuallyruled out many fields of study. By waitingfor one or more years beforelearningaboutthe labormarket, students would reduce the total cost of gatheringinformationabout earnings. Thus there are countervailingforces which makeit uncertainwhetherinformation acquisitionshould occur most intensively in the early or later years of study. Second, it can be shown that a student will invest more in informationabout his or her current field of study and closely related fields, since the costs of switchingto largely unrelatedfields are high. Third, the discountingof future earningssuggests that accurateknowledgeof wages of inexperiencedworkersis more valuablethan accurateknowledgeabout earningsof highly experiencedworkers. All three of these predictionscan be tested informallyby examiningthe types of labor marketinformationwhich students at differentstages of college gather.

IV. Variationsin Students'Beliefs about Wages Table 1 describesthe distributionof students'beliefs aboutsalaries for each question asked. It displays the 10th, 50th, and 90th percentile wage beliefs, along with the standarddeviation and the standarddeviationdivided by the mean. The standarddeviation divided by the mean is on average 0.28. The ratio of the 90th to the 10thpercentilesalaryestimatesis typicallyjust under2.0. By both these measures, the variation appears to be particularlylarge for students' beliefs about the salariesof engineerswith 15 or more years of experience. The questionnaireexplicitly asked students to estimate average salaries at the nationallevel in the currentyear, ratherthan estimates of their own salaries. In other words, the students were makingestimates of average salaries ratherthan their own expected salaries in given fields. Thus it seems fair to conclude that the observed differences in responses reflect substantialvariationin students' informationabout average nationalsalaries in each field. Figure 1 displays the mean, 10th, and 90th percentileestimates of annualsalaries. The figureincludes data for startingsalariesfor each field/degreecombination, as well as earningsof workers aged 25-34 who have a high school diploma only or a bachelor's degree. The figurealso shows estimated "true" salariesfor each question. We postpone discussion of this latter variableuntil the next section. The figure illustrates that wage beliefs are far from uniform. Figures 2 through4 illustratestudents' beliefs about salariesfor engineersby their highest degree and years of experience, with each data point centered on the midpoint of the range of experience in question.7These figures indicate that students do realize that wage profiles are positively sloped. They also show a large variation in students' estimates, particularlyat the upper end of the experience profile. 7. There is no point on the graphfor Ph.D.'s in engineeringwith 0-2 years' experiencebecause the salarysurvey did not reportthis figure,apparentlydue to the paucityof respondentsin this range.

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Table 1 The Distribution of Students' Estimates of Wages, by Field, Degree, and Experience Percentiles

Young workers, by degree High school only, ages 25-34, 1990 Bachelor's degree, ages 25-34, 1990 Starting salaries, by degree Psychology Chemistry Civil engineering Electrical engineering Mechanical engineering MBA, + nontechnical first degree Chemical engineering Master, chemical engineering Master, electrical engineering MBA, plus technical first degree Ph.D., chemical engineering Ph.D., electrical engineering Engineers' salaries by years of experience Bachelor's, experience = 0-2 Bachelor's, experience = 5-9 Bachelor's, experience = 15-19 Bachelor's, experience = 25-29 Master's, experience = 0-2 Master's, experience = 5-9 Master's, experience = 15-19 Master's, experience = 25-29 Ph.D., experience = 5-9 Ph.D., experience = 15-19 Ph.D., experience = 25-29

StandardDev

plO

p50

p90

$12,000 $22,000

$19,000 $30,000

$26,000 $40,000

$6,015 $7,764

$20,000 $22,000 $24,000 $25,000 $25,000 $24,000 $24,000 $30,000 $30,000 $28,000 $36,000 $35,000

$26,000 $28,000 $30,000 $32,000 $32,000 $32,000 $32,000 $40,000 $39,000 $36,000 $48,000 $48,000

$38,000 $40,000 $44,000 $40,500 $42,000 $46,000 $44,000 $56,000 $53,000 $52,000 $70,000 $70,000

$8,471 $8,003 $9,753 $7,510 $8,843 $9,517 $8,563 $11,233 $10,282 $10,696 $14,830 $14,059

$22,000 $28,000 $34,000 $38,000 $28,000 $34,000 $40,000 $45,000 $39,000 $45,000 $50,000

$30,000 $36,000 $45,000 $50,000 $35,000 $45,000 $54,000 $65,000 $52,750 $65,000

$38,000 $49,000 $60,000 $75,000 $50,000 $60,000 $75,000 $90,000 $75,000 $90,000 $120,000

$6,727 $8,433 $11,830 $16,323 $8,583 $10,872 $14,986 $20,945 $15,320 $21,652 $31,784 Average:

$77,750

Thousand 0 C.'C

00

0h 0 00,

00

Bachelor's Psychology

OQ (DC

High School, ages 25-34 Bachelor's Chemistry Bachelor's Civil Engineering a-;L

Bachelor's, ages 25-34

OI

aCCyC O

CL CD

^(

@

I

I

Bachelor's MechanicalEngineering

I

MBA, non-technicalBachelor's I

Bachelor's Chem. Engineering

Master'sChem. Engineering Master's ElectricalEngineering MBA, technical Bachelor's c S

0

I

Bachelor's ElectricalEngineering

-Q

'O

I GE

I

Ph.D. Chem. Engineering Ph.D. ElectricalEngineering

34

The Journalof HumanResources 80 70 60

r

50 - ^-

l 40

_

20 10

0

5

10

15

20

25

30

Years of Experience (Mean of Interval) -*

'True'

Wage

plO

p90

-

- - Mean Guess

Figure 2 Earnings of Engineers with Bachelor's Degrees by Years of Experience: Mean, 10th and 90th Percentile of Students' Estimates and Estimated True Value

Economic theory predicts that occupationalchoice should depend on relative salaries,ratherthanon the absolutelevel of salariesin any one occupation.Thus, it may be that a large degree of variationin beliefs about salariesin a given field or for a given level of education may mask quite uniformbeliefs about relative salaries,in that some studentsconsistentlyoverestimateor underestimatesalaries in all fields or for all levels of education.Accordingly,11relativestartingsalaries were calculatedbased on the questions in the middlepanel of Table 1, using the startingsalaryfor a bachelor'sdegree in chemistryas the numeraire.The average of the standarddeviation divided by the mean for these relative salaries was

JulianR. Betts 90 T 80 + 70 + 2

I

Du -.1r

o

0

o

50

Q_

co

c 40 -

-

>-o/

0

30 -?F- 30 20 + 10 + 0 5

0

10

15

20

25

30

Years of Experience (Mean of Interval) -

'True'

Wage

plO

p90

- - Mean

Guess

Figure3 Earnings of Engineers with Master's Degrees by Yearsof Experience:Mean, 10th and 90th Percentile of Students' Estimates, and Estimated True Value

0.23, comparedto 0.27 for the 11 correspondingsalaries. The same measure of dispersionfor the ratio of wages of young college-educatedworkers relative to high-school-educatedworkers was 0.27, roughly midway between the 0.25 and 0.31 recorded for the individualwage estimates. Thus, there is some evidence that there is less variationamong students in estimates of relative salaries than in their estimates of absolute salaries, but the evidence is ratherweak. To test whether there were any systematic links between wage beliefs and studenttraits, a series of regressionsfor wage beliefs was performed.The regressions includethe student's self-reportedgradepoint average(GPA),which serves

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The Journal of Human Resources

130 120 110 100 90 80 o

70 -

I

60

o

50

40 30 20 10

5

10

15

25

20

30

Years of Experience (Mean of Interval) *

'True' Wage

pO-

p90

-

-

Mean Guess

Figure 4 Earnings of Engineers with Ph.D. Degrees by Years of Experience: Mean, 10th and 90th Percentile of Students' Estimates, and Estimated True Value

as a roughproxy for ability, to controlfor the possibilitythat more able students learn more about wages than less able students. Other personal characteristics include binary variables for sex and race and one for whether the student is a foreign student in the country on a temporaryvisa. In addition, students from families with higher socioeconomic status might obtain different information about the marketfor college-educatedlabor. Thus the regressionsinclude three dummyvariablesfor parents'income, with studentswhose parentshave incomes above $75,000servingas the excluded group.Also includedare dummyvariables indicatingwhether the student's mother or father acquired any postsecondary

JulianR. Betts education, and whetherthe fatheror motherstudiedin the same majordiscipline (for example, engineering,science, etc.) as the wage question at hand.8 Columns 1 and 2 of Table 2 model students' beliefs about salaries in 1990for full-time workers aged 25-34 with a high school degree only and a bachelor's degree respectively. Although the personal traits of the students have little explanatorypower overall, several significantpatterns do emerge.9Students who are in the upper years of study tend to make lower estimates for both salaries, but the effect is much more noticeable for estimates of salaries of those with a college degree. Asian students gave significantlylower estimates of salaries for highschool graduates,while black studentsandforeignstudentsgave significantly higher estimates of earnings of college graduates.College attendanceby a student's parents appearedto have no strong effect on either wage estimate.'0 One of the most interestingpatterns is that students whose parents' income was less than $50,000tended to make significantlylower estimatesof earningsof college graduatesthan did students in the excluded group, which was students whose parents'income exceeded $75,000.This findinglends supportto the model of Streufert(1991),which arguesthat young people formbeliefs aboutthe returns to education by observing workers in their neighborhood.To the extent that families segregatethemselves by income, studentsin low-incomeneighborhoods should systematicallyunderestimatethe returnsto education. The next section will reinforce this conclusion by showing that these students also make larger errorswhen estimatingthe salariesof young workerswith a bachelor'sdegree.11 Smith and Powell (1990) present interestingresults from a survey of 388 students at two universities. They asked studentsto predictearningsof both graduates fromtheirown college andtheirhigh school peers who did not attendcollege, for one and ten years in the future. Just as in the regressions reported here, women's estimates of earningsof high school graduatestended to be lower than those of men. Also, as in the present results, there was no statisticallysignificant differencebetween men's and women's expectationsfor earningsof college graduates as a whole. But the latter result does not appear to hold in the present sample when students were asked about earningsof college-educatedworkersin specific fields, as will become clear below.12 8. For questionsaskingaboutengineers'salaries,these last dummyvariableswere set to 1 if the given parent'sfinalfield of study was engineering.Similarly,the indicatorwas set to 1 for the wage questions involvingchemistry,psychology,and MBA's if the finalparentalfieldof studywas science, humanities/ social sciences, or business respectively. 9. The OLS regressionsin this table and latertables use Whiteheteroskedastic-robust t-statistics. 10. The one exception to this last statementwas that studentswhose fathers attendedcollege made significantlylower estimates of the salariesof young workerswith a bachelor'sdegree. This result is similarto that of Smithand Powell (1990).Theirinterpretationis that, holdingfamily incomeconstant, a studentwith a more highly educatedfatherwill underestimatethe returnsto college. 11. I thanka refereefor bringingthe paperby Streufertto my attention. 12. Perhapsthe most interestingfindingby Smith and Powell (1990)is that althoughmen and women made highly similarforecasts for the earningsof college graduates,when asked to predicttheir own earningsmen had a muchhighertendencyto inflatethis figurerelativeto theirestimatefor theircollege peers than did women. Unfortunately,the questions in the present survey referredonly to national averages,andnot own expectations,so thatI cannotattemptto replicatetheirfindingof "self-enhanced" earningsforecasts amongmen.

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The Journalof HumanResources Column 3 models students' estimates of the college wage premium(college salaries divided by high school salaries). Again, fourth-yearstudents made significantlylower estimates of this relative salary than freshmen. The other main findingis that female and black students made significantlyhigherthan average estimates of the returnsto college. Column4 presents the results from a regressionin which all the startingsalary questions are pooled, a dummyvariableis added for each wage question, and a random effect for each student is added to account for randomdifferences in estimates between students. The results of this regressionsupportthe findingin regression #2 that students in their third and fourth year make estimates of salariesfor young college graduateswhich are significantlylower thanthose made by freshmen, on the order of $2,000 to $4,000 per year. Another similaritywith the regressionin Column2 is that studentsfrompoorerfamiliesmakesignificantly lower estimates of the startingsalaries of college graduates.As for personaland family background,the most importantinfluences on wage estimates were the indicatorsfor female and Hispanic students, with both effects being positive. Regression #4 includes two variableswhich indicatewhetherthe studentwas in the same broad discipline and/or the same specific field as the wage question at hand. The firstvariable,"Given majordiscipline," was set to 1 if the student's major field was engineering, science, or social science and the wage question involved engineering,chemisiry, or psychology respectively. The dummy variable was also set to 1 for the questions about salaries of MBA's if the student's finalexpected degree was an MBA. The latterindicatorvariable,"Given specific field," is set to 1 if, for instance, an observationgives a civil engineeringstudent's estimateof the startingsalaryfor a workerwith a civil engineeringdegree. These variablesare useful because they indicatewhetherstudentsspecializewhen gathering informationabout the labor market.No clear patternemergedfor students who were in the same major discipline as the given wage question. But those studentsenrolled in the given field made significantlyhigherestimates of starting salariesthan other students, on the order of $2,000. This findingcan be interpretedin two ways. If occupationalchoice depends on wage information,one would expect that those in a given field would have better informationabout their chosen field. Alternatively, a person may have chosen a given field because they overestimateearningsin that field. To distinguish between these explanations,we need to estimate the errors made by students. The next section will present evidence that in fact students in the given field, althoughthey make significantlyhigherestimatesof startingsalariesin their own field, in fact make smallererrorsthan studentsoutside the field. This finding reducesthe plausibilityof the second explanationabove. In truth,studentsappear to underestimatewages in fields outside their own. In another regression (not shown) the same randomeffects specificationwas run on students' estimates of engineers' salaries by degree level and years of experience. (For a summaryof these responses, see the bottom panel of Table 1.) The only regressorswhich were statisticallysignificantat conventionallevels were the family income dummies, which suggested that students from poorer families made significantlylower estimates of these salaries. Surprisingly,students did not vary significantlyby year of study in their estimatesof the salaries

JulianR. Betts of these workers. Engineeringstudentsmadehigherestimatesthanthose students outside the field, but the effect was only marginallysignificant. To summarize,these results suggest that studentsdo specializeto some extent in the type of labor market informationwhich they gather, and that moreadvanced-studentsmake significantlylower estimatesof startingsalariesfor workers with various college degrees than do freshmen. Demographiccharacteristics also seem to capture some of the underlyingvariationin students' beliefs about the labor market. We now measure and analyze the errorsin students' beliefs about wages.

V. Accuracy of Students' Perceptions This section of the paperestimateserrorsin students'assessments of salariesusing three data sources for the "true" salaries:the CurrentPopulation Survey for overall salaries by degree, the College PlacementCouncil survey for startingsalaries, and the Professional EngineerIncome and Salary Survey. The CurrentPopulationSurvey is arguablythe most accurate annual source of data on earningsby age and level of education available, so that the estimatederrors in students'perceptionsof salariesof young workerswith a high school or college degree are likely to be quite accurate. But the other two surveys do not use a purely random sample of workers. Thus the estimates of errors based on these latter data sources may be subject to error, and must be interpretedwith care. Figure 1 displays the mean estimate of annual salaries for young or inexperienced workersplottedwith the "true" values, estimatedfromthe aforementioned sources. The figuredemonstratesthat on average students make very good estimates of current salaries of young workers. In particular,the average guess of the premiumearnedby college graduatesrelativeto those with only a high school diplomain 1990for the age group25-34 is quite accurate(57.8 percentcompared to 50.9 percent in reality).13 Figures 2, 3, and 4 depict the estimated actual wage profiles and the mean estimatedwage profilefor bachelor's, master's, and Ph.D. degrees in engineering respectively. A clear and striking pattern emerges from the figures. Students' knowledge of salaries of younger workers is quite good, but becomes progressively worse as the experience of the workerin questionincreases. In particular, the students greatly underestimatedthe slope of the wage profile for engineers with bachelor's and master's degrees. This findingaccords with the predictions of the informalmodel discussed above.14 For all of the wage questions listed in Table 1, the mean percentageerrorwas -5.8 percent. Althoughthe mean errorswere quite small, at least for questions about the earningsof young workers, these simple means conceal sizable varia13. This findingis similarto that of Smith and Powell (1990), who found that students'forecasts of futureearningsof high school and college graduateswere quite close to values in 1985as reportedby the Bureauof the Census. 14. An alternativeexplanationmight be that many students do not realize that engineers often are promotedinto management,which acts to increasethe slope of engineers'earningsprofile.

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Table 2 Models for Students' Beliefs Concerning Wages and Relative Wages of Young Workers, by Type o

Variable Constant Student's year of study Two Three Four GPA Female Hispanic Black Asian Foreign

High School Diploma, Ages 25-34

Bachelor's Degree, Ages 25-34

19.867 (11.87)

35.131 (17.66)

-0.1149 (-0.20) - 1.3678 (-2.47) -0.5756 (-1.13) 0.3988 (0.88) - 0.7007 (-1.89) 0.9961 (1.50) 0.3161 (0.17) - 1.1463 (-2.79) 2.4828 (1.85)

(-2.40) - 2.7550 (-3.76) - 3.7718 (-5.79) -0.2976 (-0.57) 0.1211 (0.24) 1.3224 (1.56) 4.5421 (2.08) -0.9591 (-1.76) 2.3767 (2.42)

- 1.6853

College W Gain (#2

1.79 (15.01

- 0.07 (-1.79) - 0.03 (-0.63) -0.190 (-5.18) -0.034 (-1.07) 0.07 (2.22 0.00 (0.14 0.26 (2.03 0.05 (1.61 - 0.03 (-0.50)

Given majordiscipline Given specific field Parents'income <$30,000 $30,000-$50,000 $50,000-$75,000 Father attended college

-1.2207 (-1.94) -0.4219 (-0.83) -0.4938 (- 1.10) -0.6543

(-1.33) Mother attended college

Fatherstudiedgiven discipline

-0.2537

(-0.58)

-2.0776 (-2.64) -1.6976 (-2.65) -0.5134 (-0.90) - 1.2596

(-1.96) 0.1991

0. (0. -0.0 (-1.24 0. (0.

-0.00

(-0.21

0.0

(0.35)

(1.

0.0568 0.0442 1,067 1,067

0.0 0.0 1,0 1,0

Motherstudiedgiven discipline R-squared AdjustedR-squared Observations Numberof individuals

0.0329 0.0201 1,067 1,067

Note: Column#4 pools all the questionsabout startingsalaries,addingdummyvariablesfor each questionand a randomeff use OLS.

42

The Journalof HumanResources tions in the accuracyof the students'beliefs. The medianof the absolutepercentage errors is a better measure of the errors typically made than is the mean of the signed errors.The averageof these mediansacross all wage questionsshown in Table 1 is 19.6 percent, comparedto -5.8 percent for the raw mean. Furthermore,not one student accurately ranked all 14 earnings levels. But perhaps a fairer test is to examine the proportionof students correctly ranking fourjobs with quitehighlydispersedsalaries:jobs of those with an MBApreceded by a science or engineeringbachelor'sdegree, and bachelor'sdegreesin mechanical engineering,chemistry,and psychology. If all studentshad guessed randomly due to a lack of information,we would expect just 4.2 percent [that is, (100 percent)/4!]to have answered correctly. If all students had possessed complete information,then 100percent shouldhave answeredaccurately.Of 1,163students who answeredthe questions, 26.3 percent rankedthese salariescorrectly. Thus, students do know something about salaries, but they fall far short of having complete information.15 What determinesstudents' errors in perception?To answer this question, we now econometricallymodel the students' errors. See Table 3. It is not useful to make the signed error the dependent variable, since a positive coefficient on regressor x could indicate that a higher value of x is associated with a higher positive error, a smallernegative error, or both.16Thereforethe following series of regressionsexamines the absolute value of errors,in orderto determinewhat factors influencethe actual size of errorsin absoluteterms. The dependentvariable is the log of the absolute value of the percentagewage error:17 ln

(west

-

wtrue) wtrue

x

1o00

The basic regressionuses the same set of wage questions and regressorsused to model wage beliefs in Table 2. The firsttwo columnsmodel absolute errorsin 15. As mentionedin the previoussection, largeabsoluteerrorsin students'beliefs abouta given salary may conceal relativelysmallerrorsin theirestimatesof relative salaries.This does not appearto be the case, though.Whenall of the salariesin the top two panelsof Table 1 were convertedto relativesalaries using the salaryof those with a bachelor'sdegree in chemistryas the numeraire,estimatesof relative errorswere quite similar,but were slightlyhigherin 11 of 13 cases. Usingthe startingsalaryfor a Ph.D. in electricalengineeringas numeraireproducedsimilarresults. 16. Considerthe followingexample to see why modelingsigned errorsis not useful. Supposewomen are equallydividedinto those makinga - 1 percenterroror a + 2 percenterror,while men are equally dividedinto those makinga - 50 percenterrorand a + 50 percenterror.Regressionof signederrorson a dummyfor male would give a negative coefficient,incorrectlyimplyingthat the typical man made smallererrorsthanthe typicalwoman.In contrast,if we use the absoluteerroras the dependentvariable, then the coefficienton the male dummywould be positive, indicating(correctly)that the typicalmale makeslargererrors. 17. The log absoluteerroris used as the dependentvariablesince the absolutevalues themselvesare positive, whichwouldhave renderedthe normalityassumptionused for inferencein OLS highlyuntenable. Comparisonof the log likelihoodvalues for both linearand log versionsof the dependentvariable (afteradjustingfor the Jacobianterm)showedthe log specificationto be superiorin almostall regressions involvingstartingsalaries,and for five of 11regressionsin TableA2. Estimatesusingthe linearabsolute percentageerrors,which are availablefromthe authoron request, show highlysimilarresultsto those outlinedbelow. Anotheradvantageof the log specification,of course, is that it lessens the influenceof outliers.

JulianR. Betts students' estimates of 1990 salaries of young full-timeworkerswho have a high school diplomaonly or a bachelor's degree respectively. Since the "true" values for these salarieswere calculatedusing the most reliabledata source of the three used-the CurrentPopulationSurvey-it is for these questionsthat we can have most confidencethat we are accuratelymeasuringerrorsin students' beliefs. For both wage questions, students' errors tend to decline with year of study. But the differences become significantonly between fourth-yearand first-year students' errors in estimatingthe earningsof high school graduates.This result suggests continuallearningabout the labor market.18 A second notablefindingis that studentsfrompoorerfamiliesmadesignificantly largererrors estimatingsalaries of college graduates.The results in Table 2 indicate that this differencestems from studentsfrompoorerfamiliesunderestimating the earningsof college graduates.The findingof a negative correlationbetween students' errors and parents' income has at least three possible interpretations. The firstis that higherfamilyincome itself buys betterinformation.Second, since lower income is often associated with retirementor families in which only one parent works, it may be that a workingparent provides a child with a valuable window into the workplace.Third,the aforementionedmodel by Streufert(1991) of geographicsortingof families by income may explainthe result: childrenfrom poorer neighborhoodsmay underestimatethe returnsto college due to a lack of information. Column3 models log absolute errors in students' estimates of the earningsof young college graduatesrelative to the earningsof young high school graduates. This regression reveals that fourth-yearstudents appear to make significantly smallererrors than freshmen, which we interpretas anothersign of learning.19 Column 4 models the estimated log absolute error in all startingsalary questions. A randomeffect is addedto accountfor repeatedobservationsfor students, and dummy variablesare added for each question.20 The effect of year of study is highlysimilarto that in the regressionsin Columns 1-3, but the coefficients are far more significant.Absolute errorsdecrease monotonically with year of study, with well over half of learning occurring among fourth-yearstudents. The conclusion that most learningabout the labor market occurs late in the student's college career runs against the predictions of the informalmodel discussed earlier, but as noted there, is consistent with the idea that students wait until they have learnedabout their abilitiesbefore investingin 18. One referee suggested that once a student has started college, she will have no furtheruse for investingin informationaboutthe earningsof highschoolgraduates.The resultsheresuggestthatcollege students do in fact learn more about the earningsof high school graduatesas they progressthrough college. One possible explanationis that many of the informationsources which studentsuse, such as newspaperarticles,often reportearningsfor college graduatesalongsidethosefor less educatedworkers. In other words, it may not be entirelypossible to unbundleinformationacquisition. 19. To test whethera few particularlylarge wage errorswere influencingthese three regressions,the methodproposedby Kraskeret al. (1983)was used to removeinfluentialobservations,after which the regressionswere repeated. No importantchanges resulted, except that the coefficienton the dummy variablefor blacks became unidentifieddue to the small sampleof blacks in the data set. 20. An nR2test for exclusionof the dummyvariablesrejectedthe nullwith a p-valueless than0.000005. Regressionswithout the randomeffect for individualsproducedhighly similarcoefficients,but the tstatisticswere in generalhigher.

43

Table 3

Models of (Estimated)Log Absolute Percentage Errorsin Students'Beliefs about Earningsand R

Variable

Constant Student's year of study Two Three Four GPA Female Hispanic Black Asian Foreign

High School Diploma, Ages 25-34

Bachelor's Degree, Ages 25-34

College Gain (#2

2.7374 (10.68)

2.7432 (9.49)

2.6 (9.0

-0.0345 (-0.41) 0.0347 (0.41) -0.2308 (-2.70) 0.0043 (0.06) -0.0045 (-0.07) 0.1579 (1.57) 0.3695 (1.39) 0.0890 (1.25) -0.1728 (-1.11)

0.0008 (0.01) - 0.0811 (-0.81) -0.1451 (-1.47) - 0.0988 (-1.25) 0.0364 (0.50) -0.0877 (-0.75) - 0.2501 (-0.63) - 0.0908 (-1.17) - 0.0077 (-0.06)

- 0.0 (-0.65 -0.09 (-0.82 -0.28 (-2.69 -0.11 (-1.34 0.1 (1.6 0.1 (1.2 0.5 (1.4 0.0 (0.3 - 0.0 (-0.22

Given majordiscipline Given specific field Parents'income <$30,000 $30,000-$50,000 $50,000-$75,000 Fatherattendedcollege Motherattendedcollege

0.0697 (0.68) 0.0305 (0.39) 0.0913 (1.20) 0.0629 (0.75) -0.0843 (-1.21)

0.2364 (2.29) 0.1869 (2.13) -0.0103 (-0.12) 0.1398 (1.44) 0.0067 (0.08)

0.1 (1.0 0.0 (0.5 0.0 (1.0 0.1 (1.4 0.1 (1.1

0.0203 0.0072 1,067 1,067

0.0140 0.0008 1,067 1,067

0.0 0.0 1,0 1,0

Father studiedgiven discipline Motherstudiedgiven discipline R-squared AdjustedR-squared Observations Numberof individuals LM (nR2)test for exclusion of (year) (given field) interactions (p-value) Note: See notes to Table 2.

46

The Journalof HumanResources information.Also, as one referee pointed out, those fourth-yearstudents who alreadyhad ajob offer at the time of the survey(in late fall andearlywinter)could have learnedabout earnings,at least in their own area, directlyfrom employers. Studentswho are in the same "majordiscipline"as the occupationin question make significantlylower errors, by about 8.7 log points, while those who are in the specific discipline make even smallererrors, with a furtherreductionin the averageerrorby 11.2 log points. Takentogether,the implicationis that a student in the specificfield, such as chemicalengineering,on averagemakeserrorswhich are only 0.82 as large as students outside of engineeringaltogether.21 The informalmodel suggested that students might increasinglyspecialize in informationacquisitionas they progressthroughcollege, since the costs of transferringto other fields rise. The bottom of the table reportsresults of tests for the exclusion of two interactionterms between the year of study and the dummy variablesfor the studentbeing in the given field and the given area. The restrictions were easily retained, so that the data do not give evidence of an increase in specializationas students progress. Somewhat surprisingly,the coefficients on the measuresof parentaleducation are not significant,althoughthere is evidence that studentswhose motherstudied in the given field made significantlysmallererrors. Finally, students with higher GPAs appearto make significantlylower errors when estimatingstartingsalaries. It is not clear whether GPA may be acting as an ability proxy in this model.22 The theoreticaldiscussion in Section III suggestedthat studentswill be more willingto invest in informationabout startingsalariesthanaboutsalariesof highly experienced workers, due to the discountingof future income. The figures discussed earlierindicatethat this hypothesisis correct. Moreformally,regressions in Table A2 in the appendix model estimated errors in students' beliefs about current salaries of engineers by years of experience.23The regressions suggest

21 In other words, instead of makinga 10 percenterror,an engineermightmake an errorof 0.82 (10 percent)or 8.2 percent. 22. As a test of robustness,the modelsin Table3 were reestimatedusingthe proportionalerrorssquared ratherthan the log of the absolute values of the errors. For the regressionsin Columns 1 and 3, no coefficientcrossed frombeing significant(thatis, t I > 1.96)to insignificantor vice versa. In regression #2, the coefficienton the dummyfor studentsin theirfourthyear of studybecamenegativeand significant at the 5 percentlevel, while the familyincomevariablesbecameinsignificant.In the pooledregression, the only crucialchangewas that the dummiesfor whetherthe studentwas in the specificfield or majordisciplinebecameinsignificantlydifferentfromzero. However,it becameapparentthatthe squaring of the errorshad createdoutlierproblemswhichcontributedto the latterchanges.Thusobservations were deleted if the squarederrorwas greaterthan 0.5. (This correspondsto percentageerrorsgreater than 70.7 percent.) In the remainingsample, containing97 percent of the originalobservations,the dummyfor study in the majordisciplinebecame significant(t = -3.10) and the dummyfor study in the given field became moderatelysignificant(t = - 1.77) again. Thus the overall patternssuch as specializationby field and learningover time appearquite robustto the choice of dependentvariable. 23. The responserate on these questionswas 77-78 percent,comparedto 93-97 percentfor the questions on startingsalaries.One reasonfor the dropin responserate may simplybe that these questions appearedat the end of the survey. But two of the studentswho did not fill out these questions on engineers'salariesby years of experienceindicatedon the formthatthey had "no idea" whatthe wage profileslooked like.

JulianR. Betts that studentsinvest more in informationabout startingwages than they do about wages of highly experienced workers. The regressions show that students learn about the labor marketover time, and that engineeringstudents do know more about salaries of engineers. But these relations break down when students are asked about salaries of engineers with 15-19 and 25-29 years of experience, where no patternof learningor specializationis discernible. In summary, although our estimates of students' errors in wage beliefs are based on our own possibly biased estimates of the "true" values, the results providemostly intuitiveresults. In particular,studentsdo specializein the acquisition of labor marketinformation,even at an early date of study. Second, they learn more about the labor market as they progress. Third, the discussion of theory in Section III impliedthat students will invest more in informationabout the earningsof youngerworkersthan older workers, due to discountingof future income. This idea gains support from errors in the students' estimates of the earningsof engineersby years of experience.

VI. InformationSourcesUsed by Students Whilethe above analysisproves that observablestudentcharacteristics are associated with students' beliefs about the labor market, it does not provide any direct evidence about why certainstudents are better informed.For instance, why do fourth-yearstudentsseem to know more aboutthe labormarket than their younger colleagues? Does it reflect active search for informationor merely learningby osmosis which automaticallyoccurs over time? To this end, the survey asked students to indicate which informationsources they had used to "find out aboutjob prospects of graduatesin various fields." The distributionof responses by year of study appearsin Figure 5.24 As the figure shows, by far the most commonlyused source of informationis newspapers and magazines. Surprisinglyfew students report consultingprofessors, graduatestudents, or salary surveys for information. In all but one case there is a large increase in the proportionof studentsusing each informationsource in the fourth year of study. This pattern is especially strongfor use of the campus CareerServices Center. It appearsthat this Center is not used by a majorityof students until their fourth year of study, implying that the Center serves less to help studentschoose a field than it does to provide informationaboutjobs to those who are about to graduate. In orderto model the determinantsof the use of each of these eight information sources more formally, while controllingfor possible collinearitybetween year of study and other studenttraits, logit models were estimatedfor each source of information. Table A-3 in the appendix shows the estimated coefficients, tstatistics, and, in squarebracketsbelow the t-statistics, the dPIdX values calcu-

24. Students were specifically asked whether they had consulted the Salary Survey of the College PlacementCouncil both because this survey is readily availableat the campusplacementcenter and because it was used above to calculateerrorsin students'estimatesof startingsalaries.

47

The Journalof HumanResources

48

Professors

Otherprofessionals

0 C 'EZ c Uk cC c

Other undergraduates

a

4w

Papers + magazines

"Salary Survey," CPC

Othersurveys

Percent of Students Using Given Source * Fourth YearU0ThirdYear MSecond YearElFirst YearI Figure5 Students' Use of Various Information Sources by Year of Study

lated at the means. The table shows that senior undergraduatesare significantly morelikely to have used the CareerServices Centerandto have consultedprofessors, graduatestudents,and otherundergraduates.Asian studentswere less likely to have talked to professors or other professionals about the labor market, but

morelikely to have consultedpapers,magazines,andthe CareerServices Center. Students from families with lower incomes were less likely to have consulted

JulianR. Betts professorsor otherprofessionals.Finally,the variablesmeasuringparents'education in general had little effect.25 Thus, this section sheds some light on the reasons for the significantcorrelations observedearlierbetween errorsin wage estimatesandpersonalbackground. But, given that in manycases the logits successfullypredictonly about60 percent of the responses, there is much that remainsto be learnedabout how, for example, more senior students hone their knowledgeof wages.26

VII. Summary and Conclusion The above results provide answers to many of the questions set out in the introduction.First, students do have diverse beliefs about the labor market,as is shown in Section IV. These differencesin beliefs are systematically linked to personaltraits such as year and field of study. Second, estimates of students' median absolute errors in wage beliefs were typically about 20 percent. But the mean of the estimated raw errors was very small, averaging only about -6 percent, as some students overestimated the salary in a given job while others underestimatedit. Third, two implications of the informal model were borne out by the data. Students specialized in acquiringinformationabout earningsof workers in their own major discipline and subfield. This finding suggests the presence of sunk costs relatedto field-specifichumancapital. The second implicationof the model was that students should find it more worthwhileto invest in informationabout earnings of young workers, due to discounting. The results support this hypothesis. Third, the regression results indicate that fourth-yearstudents knew significantly more about salary levels than first year students. On averageover half of the learningbetween the first and fourthyear of study occurredin the finalyear. This conclusion is supportedby logit analyses of the determinantsof the use of specific sources of labor marketinformation,such as the campusplacementcenter, which showed a significantincrease in usage of a broad arrayof information sources during the fourth year of study. In contrast, the informal model had predictedthat students might find it most worthwhileto invest in labor market informationat an earlierstage. Possible explanationsfor the discrepancyinclude postponementof research into the labor marketuntil the student has narrowed down the list of potentialfields of study (due to the cost of information),and the automatic learning which occurs when fourth-yearstudents begin to apply for jobs. 25. Repetitionof the logit regressionswithout the dummiesfor parents'field(s)of specializationhad little effect on the results, leaving the significanceof the two dummiesfor college attendanceby the parentslittle changed. 26. As anotherway of seeing this point, consider the fact that when the regressionsin Table 3 were repeated with dummy variablesfor use of each source of informationas additionalregressors, the coefficientsand t-statisticson the otherregressorswere littlechanged.(However,interpretation of these regressionsis difficult,given the obvious endogeneityof the information-source variables.)

49

50

The Journalof HumanResources The finding that students differ significantlyin their beliefs about wages in differentfields deserves furthercomment. It implies that studentswill also form diverse expectations of future returnsto education in various fields. As shown by Manski(1993),in such a world conventionalmethodsof estimatingthe returns to schooling are likely to be biased.27 Indeed, the above findingsraise doubts about the assumptionmade in some rationalexpectations versions of the humancapitalmodel that studentsforecast future wages based on accurate knowledgeof currentwages. Informationis far from complete. For instance, only 26 percent of studentsaccuratelyrankedfour jobs by starting salary, compared to 4 percent in the case of purely random guessing and 100 percent in the case of perfect information.It is unlikely that these errors reflect measurementerroralone: the regressionanalysis found systematic differencesin wage errorsbetween students suggestive of, for instance, learningover time. Two other branchesof researchpoint in the same direction.The Government AccountingOffice (1990)reviews a series of paperswhich findlargegaps in what high school students and their parents know about postsecondaryfinancialaid and college costs, and suggests that this lack of informationmay preventfamilies from makingfully rationaleducationaldecisions. Similarly,Leonard(1982)uses data from an annual survey of employers'wage expectations, and in most cases stronglyrejects the hypothesis of rationalexpectations. But taken as a whole, the above findingsstronglysupportthe assumptionmade by humancapitaltheory that workersacquireinformationaboutearningsby level of education in order to choose their optimallevel of education. Informationis not perfect, but a process of learningover time is clearly discernible. The findingsof this study suggest that it would be worthwhilefor economists to study the acquisitionof labormarketinformationin a panelformat.A repeated survey of young workers over several years could yield importantnew insights into how people learn about the labormarketand the ways in which this learning informstheir subsequentdecisions about education.

Appendix 1 Description of Survey Instrument

The survey begins with 16 backgroundquestionsin multiplechoice format,which is followed by a section asking studentsto estimate salariesin various fields. For the questions on startingsalaries students were given a list of 44 salaries in increments of $2,000, that is, "14 16 . . . 100," and were asked to circle the

appropriatesalary for the given occupationand level of educationin each case. This list of salaries was used in order to minimize "roundingerror," that is, roughestimates such as $30,000, $40,000, etc. In addition,the survey stated "If your estimate lies in between two of the printed numbers, insert an arrow in 27. Manskialso shows that even if all studentshave identicalinformation,inferencecan still be biased in the case in which the researcher misspecifies the information set.

JulianR. Betts between, e.g. indicate an estimate of $25,000 by writing '22 24 J 26.' If your estimate lies outside the limits printedbelow, please write in your estimate by hand. Please make an estimate for all of the following, even if you are unsure." The exact wording for the questions on startingsalaries was "Below, please circle your estimate of the national average for annual starting salaries (in thou-

sands of dollars)of graduatesin the indicatedfields and degree levels duringthis year." (Emphasisis as in the survey form). The overall response rate on these questions was 94.4 percent. Similarwording was used for the questions about annual salaries in 1990 of workersaged 25-34 by highest degree. The response rate for these questionswas 96.9 percent. For these two questions, students were asked to estimate earnings in 1990,because at the time of the survey 1990was the most recent year for which data from the March CurrentPopulationSurvey were availablefor purposes of comparison.

For all of these questions described above, there was some evidence of "roundingerror," although students on the whole provided fairly precise estimates. For instance, 25.1 percent of estimates were exact multiplesof $10,000, and 77.4 percent of estimates were multiples of $2,000. (Recall that the scale written on the survey form displayed salaries in even incrementsof $2,000.) For the questions about salaries of engineers by level of educationand years of experience, the instructions read: "The table below classifies engineers by their highest degree and their years of work experience since their final degree. In each box, please write your best estimate of the currentANNUAL SALARY of the given type of engineer." The overall response rate for these questionswas 77.2 percent. Of these, 35.4 percent consisted of estimates which were exact multiplesof $10,000.

51

52

The Journalof HumanResources Table Al Characteristics of Students in the Sample (n = 1,269)

Variable Year of study One Two Three Four Missing Field of study Engineering Science Humanities Social sciences Missing Sex Male Female Missing Race

23.64% 30.26% 21.91% 23.88% 0.32% 46.65% 21.20% 8.43% 22.46% 1.26% 69.66% 29.94% 0.39%

White

57.84%

Hispanic Black Asian

8.12% 1.10% 26.40%

Other

Missing Foreign student Yes

No Missing Motherattended college Yes No Missing Father attended college Yes No Missing Family income

5.75%

0.79% 5.75%

93.30% 0.95% 67.14% 32.39% 0.47% 77.46% 20.88% 1.65%

<$30,000

13.95%

$30,000-$50,000 $50,000-$75,000 >$75,000 Missing

21.83% 21.59% 39.72% 2.92%

Table A2 Regressions of (Estimated) Log Absolute Percentage Errors in Students' Estimates of Salaries of E Degree and Years of Experience Bachelor'sDegree 0-2 Student'syear of study Two Three Four GPA Student'smajordiscipline Engineering Science Humanities R-squared AdjustedR-squared Numberof observations

5-9

15-19

-0.0116 (-0.10) -0.0368 (-0.29) -0.2389 (-1.93) -0.0089 (-0.10)

0.0034 -0.0077 (0.03) (-0.12) -0.1939 -0.0234 (-1.76) (-0.37) -0.1265 0.0057 (-1.24) (0.10) 0.0249 0.0322 (0.30) (0.71)

-0.3535 (-3.55) -0.0408 (-0.35) 0.1845 (1.21) 0.0582 0.0299 858

-0.2018 (-2.26) -0.0529 (-0.50) 0.0498 (0.35) 0.0437 0.0147 849

0.0175 (0.32) 0.0460 (0.71) 0.0893 (0.93) 0.0645 0.0359 845

Master'sDegree 25-29

0-2

5-9

15-19

25-29

-0.0024 (-0.03) -0.0772 (-0.95) -0.0134 (-0.17) 0.0377 (0.69)

-0.1092 (-0.75) -0.1263 (-0.85) -0.3644 (-2.46) -0.0973 (-0.93)

-0.0557 (-0.60) -0.3019 (-3.04) -0.2872 (-2.99) -0.0383 (-0.54)

0.1128 (1.25) -0.0045 (-0.05) 0.0743 (0.80) 0.0385 (0.59)

0.0227 (0.24) -0.0917 (-0.88) -0.0164 (-0.16) 0.0477 (0.78)

0.1322 (1.53) 0.1823 (1.79) 0.2182 (1.59) 0.0678 0.0394 846

0.0683 (0.70) 0.1750 (1.61) 0.0318 (0.17) 0.0562 0.0274 844

0.0539 -0.3305 -0.3075 (0.72) (-2.50) (-3.68) 0.1623 0.0110 -0.0654 (1.88) (0.07) (-0.68) 0.0360 -0.2275 -0.2004 (-1.05) (0.26) (-1.33) 0.0595 0.0446 0.0684 0.0309 0.0158 0.0400 847 854 848

Note: Otherregressorsnot shown are a constant,dummyvariablesfor female, black, Hispanic,Asian, and foreignstudents,e ents' finalfield of study, two dummyvariablesfor whetherthe parentsattendedcollege, and three dummyvariablesindicating in parentheses.

Table A3 Logit Analyses of the Determinants of Students' Use of Various Sources of Information about Job

InformationSource #1

#2

#3

#4

#5

#6

Student's year of study

Two Three Four GPA Parents'income <$30,000 $30,000-$50,000 $50,000-$75,000

0.4801 (2.25) [0.09] 0.4928 (2.17) [0.10] 0.9073 (4.13) [0.18] 0.0455 (0.29) [0.01] -0.5420 (-2.06) [-0.11] -0.2754 (- 1.44) [-0.05] -0.1265 (-0.69) [-0.02]

0.3766 0.1196 -0.1357 (-0.74) (0.65) (1.78) [0.07] [0.03] [-0.03] 0.2728 -0.0036 0.0402 (-0.02) (0.21) (1.19) [0.00] [0.01] [0.05] 0.6070 0.2546 0.6180 (2.81) (3.13) (1.32) [0.14] [0.12] [0.06] -0.4788 -0.1587 -0.0544 (- 1.10) (- 3.29) (-0.34) [-0.01] [-0.11] [-0.04] -0.4395 (-1.92) [-0.11] -0.3602 (-2.09) [-0.09] -0.2301 (-1.38) [ - 0.06]

-0.0871 (-0.34) [-0.02] -0.0035 (-0.02) [0.00] 0.3084 (1.71) [0.06]

-0.2931 (-1.27) [-0.07] -0.0309 (-0.18) [-0.01] 0.0849 (0.51) [0.02]

-0.0391 (-0.21) [-0.01] 0.0688 (0.34) [0.02] 0.3294 (1.64) [0.08] -0.1637 (- 1.11) [-0.04]

-0.3 (-1.0 [-0.0 -0.1 (-0.3 [-0.0 0. (1. [0. -0.0 (-0.1 [0.

-0.0722 0. (-0.31) (1. [-0.02] [0. -0.0753 0. (-0.43) (1. [0. [-0.02] 0.2276 -0.2 (1.30) (-0.8 [0.05] [-0.0

Student'smajordiscipline Engineering Science Humanities Parents'college attendance Fatherattended

0.7411 (3.82) [0.15] 0.6676 (2.97) [0.13] 0.8000 (2.92) [0.16]

0.1847 -0.1854 (1.11) (-1.02) [0.041 [-0.04] 0.2729 0.0473 (1.40) (0.22) [0.07] [0.01] 0.2729 0.2162 (1.10) (0.81) [0.07] [0.04]

-0.0785 0.1263 0.1775 (-0.31) (0.56) (0.70) [0.03] [0.04] [-0.02] Motherattended 0.3374 -0.2167 -0.1885 (-1.18) (1.67) (-0.95) [-0.05] [-0.04] [0.07] 0.0510 0.0345 0.0322 R-squared Fractionof predictionscorrect 0.5716 0.7166 0.7138 Numberof observations 1,069 1,069 1,069

-0.1266 (-0.76) [-0.03]

-0.0103 (-0.05) [0.00] -0.2648 (-1.06) [-0.06] 0.2865 (1.26) [0.07] 0.1434 (0.78) [0.03] 0.0427 0.5828 1,069

0.1445 0. (0.85) (0 [0 [0.03] -0.0086 0. (0 (-0.04) [0 [0.00] 0.1054 -0.6 (-1.2 (0.42) [-0.0 [0.02]

0.1306 0. (0.56) (0 [0.03] [0 0.3709 0. (1.96) (0 [0.08][0.08] [0 0.0342 0. 0.6239 0. 1,069 1,0

Note: Dependentvariableis a dummyset to 1 if studentused given sourceof information.The parentheses( ) indicatet-statis values evaluatedat the means. For a list of other regressorsnot shownin the table, see Table 3. Informationsources: #1: Professors.#2: Otherprofessionalsin the given field. #3: Graduatestudents.#4: Otherundergrad zines. #6: SalarySurvey,College PlacementCouncil.#7: Othersurveys. #8: CareerServicesCenter.

56

The Journal of Human Resources

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