the signaling value of a high school diploma - damon clark€¦ · the signaling value of a high...
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The Signaling Value of a High School Diploma∗
Paco MartorellRAND
Damon ClarkCornell University, NBER, IZA
January 26, 2012
Abstract
This paper distinguishes between the human capital and signaling the-ories by estimating the earnings return to a high school diploma. Unlikemost indicators of education (e.g., a year of school), a diploma is essen-tially a piece of paper hence by itself cannot affect productivity. Anyearnings return to holding a diploma must therefore reflect the diploma’ssignaling value. Using regression discontinuity methods to compare theearnings of workers that barely passed and barely failed high school exitexams - standardized tests that students must pass to earn a high schooldiploma - we find little evidence of diploma signaling effects.
∗For useful discussions, we thank Kelly Bedard, Ken Chay, Mike Geruso, Marco Man-acorda, Rob McMillan, Devah Pager, Craig Riddell and, especially, David Lee. For help-ful comments and suggestions, we thank seminar participants at Bristol University, BrownUniversity, Columbia University, the Florida Department of Education, Harvard University,London School of Economics, Northwestern University, Pompeu Fabra, Princeton University,RAND, Rutgers University, University of Toronto, UC Davis, UC Irvine, UC Santa Barbara,University of Florida, the SOLE 2010 conference, the NBER 2010 Summer Institute and theSouthern California Conference of Applied Microeconomics (Claremont McKenna College).Clark thanks the Florida Department of Education for generously supplying the Florida dataused in this paper and for providing invaluable information on the relevant institutions. Muchof this work was completed while Clark was visiting the Industrial Relations Section at Prince-ton University. We thank Marion Aouad and Yu Xue for excellent research assistance. Fi-nancial support was generously provided by the U.S. Department of Education (under grantR305R060096). The opinions expressed in this paper are ours, and do not necessarily reflectthe views of the Florida Department of Education, the Texas Department of Education or theU.S. Department of Education.
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Figure 1: Last-chance exam scores and diploma receiptFL
OR
IDA 0
.51
1.5
-100 -50 0 50
Density of last-chance scores
0.2
.4.6
.81
-100 -50 0 50
Diploma receipt and last-chance scores
TEX
AS
Notes: Graphs based on the last-chance samples. See Table 1 and text. For Texas, dots are cell means. For Florida, dots are averages of bins defined over two test scores ( .[-2,-1], [0,1], ). Lines are fourth-order polynomials fitted separately on either side of the passing threshold.
01
23
45
6
-30 -25 -20 -15 -10 -5 0 5 10 15
Density of last-chance scores
0.2
.4.6
.81
-30 -25 -20 -15 -10 -5 0 5 10 15
Diploma receipt and last-chance scores
Figure 2: Descriptive statisticsFL
OR
IDA
01
2
-200 -150 -100 -50 0 50 100 150 200
Distribution of initial scores (full and last-chance samples)0
.2.4
.6.8
1
-200 -150 -100 -50 0 50 100 150 200
Complete 12th grade and initial scores (full sample)
0.2
.4.6
.81
-200 -150 -100 -50 0 50 100 150 200
Diploma receipt and initial scores (full sample)
Notes: Graphs based on the full samples and the last-chance samples. See Table 1 and text. For Texas, dots are cell means. For Florida, dots are averages of bins defined over five exam scores ( .[-5,-1], [0,4], ) The scores on the X-axis are the minimum scores achieved on the initial exam for the subsample with scores on both subtests (see Table 1 for the relevant descriptive statistics).
TEX
AS
01
23
45
-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15
Distribution of initial scores (full and last-chance samples)
0.2
.4.6
.81
-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15
Complete 12th grade and initial scores (full sample)
0.2
.4.6
.81
-40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15
Diploma receipt and initial scores (full sample)
Figure 3: Earnings by last-chance exam scoresFL
OR
IDA
3000
7000
-100 -50 0 50
Year 1
4000
8000
-100 -50 0 50
Year 2
5000
9000
-100 -50 0 50
Year 3
5000
1000
0
-100 -50 0 50
Year 4
5000
1000
0
-100 -50 0 50
Year 5
5000
1000
0-100 -50 0 50
Year 6
Notes: Graphs based on the last-chance samples. See Table 1 and text. For Texas, dots are cell means. For Florida, dots are averages of bins defined over two test scores ( .[-2,-1], [0,1], ). Lines are fourth-order polynomials fitted separately on either side of the passing threshold. For Texas, "Year 2" exlcuded to conserve
TEX
AS
3500
6000
-30 -25 -20 -15 -10 -5 0 5 10 15
Year 1
6000
1000
0
-30 -25 -20 -15 -10 -5 0 5 10 15
Year 3
6000
1200
0
-30 -25 -20 -15 -10 -5 0 5 10 15
Year 4
6000
1200
0
-30 -25 -20 -15 -10 -5 0 5 10 15
Year 5
6000
1400
0
-30 -25 -20 -15 -10 -5 0 5 10 15
Year 6
8000
1600
0
-30 -25 -20 -15 -10 -5 0 5 10 15
Year 7
Figure 4: Earnings effects by subgroup and year after last-chance exam (X-axis)FL
OR
IDA
-20
20
1 2 3 4 5 6
Main
-202
0
1 2 3 4 5 6
Male
-20
20
1 2 3 4 5 6
Female
-20
20
1 2 3 4 5 6
White
-20
20
1 2 3 4 5 6
Nonwhite
Notes: Graphs based on last-chance samples. See Table 1 and text. The solid lines connect 2SLS estimates of the diploma effect on earnings in each year after last-chance exam (i.e., the estimates reported in the final column of Table 4). The dashed lines connect points equal to these estimates plus and minus two times the associated standard errors. Estimates are expressed as a percentage of mean earnings in that year among individuals with an last-chance exam score of -1.
TEX
AS
-20
020
1 2 3 4 5 6 7
Main
-20
020
1 2 3 4 5 6 7
Male
-20
020
1 2 3 4 5 6 7
Female
-20
020
1 2 3 4 5 6 7
White
-20
020
1 2 3 4 5 6 7
Nonwhite
Figure 5: Probability of earnings being in particular groupFL
OR
IDA
-.05
.05
0 1 2 3 4 5 6 7 8 9
Year 1
-.05
.05
0 1 2 3 4 5 6 7 8 9
Year 2
-.05
.05
0 1 2 3 4 5 6 7 8 9
Year 3
-.05
.05
0 1 2 3 4 5 6 7 8 9
Year 4
-.05
.05
0 1 2 3 4 5 6 7 8 9
Year 5
-.05.
050 1 2 3 4 5 6 7 8 9
Year 6
Notes: Graphs based on the last-chance samples. See Table 1 and text. Solid and dashed lines represent 2SLS estimates and associated confidence intervals, as in Figure 4. Group 0 corresponds to zero earnings. Groups 1-9 are equal-sized cuts of the conditional-on-positive earnings distribution. In Florida, the fractions with zero earnings in years 1 through 6 are 0.271, 0.280, 0.308, 0.324, 0.348 and 0.377. In Texas, the fractions with zero earnings are 0.2 in years 1-4, 0.21 in years 5-6, and 0.22 in year 7. For Texas, "Year 2" excluded to conserve space.
TEX
AS
-.1.1
0 1 2 3 4 5 6 7 8 9
Year 1
-.1.1
0 1 2 3 4 5 6 7 8 9
Year 3
-.1.1
0 1 2 3 4 5 6 7 8 9
Year 4
-.1.1
0 1 2 3 4 5 6 7 8 9
Year 5
-.1.1
0 1 2 3 4 5 6 7 8 9
Year 6
-.1.1
0 1 2 3 4 5 6 7 8 9
Year 7
Appendix Figure 1: Routes to a diploma for students that fail the last-chance examFL
OR
IDA 0
.2.4
.6.8
1
-100 -50 0
High School Diploma (HSD)
0.2
.4.6
.81
-100 -50 0
Special Education (SE)
0.2
.4.6
.81
-100 -50 0
SE=1: HSD (solid), Passed after LCE (dash)
0.2
.4.6
.81
-100 -50 0
SE=0: HSD (solid), Passed after LCE (dash)
TEX
AS
Notes: Florida graphs based on last-chance sample. Texas graphs based on last-chance sample excluding the final (10th grade in 1995) cohort. The final cohort is excluded because the testing data for the 1997-98 year are incomplete (this is the year after this cohort's last-chance exam). See Table 1 and text. Dots and lines as in Figure 1. Bottom-left (bottom-right) graph refers to those (not) classified as special education. "LCE" refers to last-chance exam.
0.2
.4.6
.81
-30 -25 -20 -15 -10 -5 0
High School Diploma (HSD)
0.2
.4.6
.81
-30 -25 -20 -15 -10 -5 0
Special Education (SE)
0.2
.4.6
.81
-30 -25 -20 -15 -10 -5 0
SE=1: HSD (solid), Passed after LCE (dash)
0.2
.4.6
.81
-30 -25 -20 -15 -10 -5 0
SE=0: HSD (solid), Passed after LCE (dash)
Appendix Figure 2: Local linear estimates relative to preferred estimates (dashed line)FL
OR
IDA
-10
10
0 10 20 30 40 50
Year 1
-10
10
0 10 20 30 40 50
Year 2
-10
10
0 10 20 30 40 50
Year 3
-10
10
0 10 20 30 40 50
Year 4
-101
0
0 10 20 30 40 50
Year 5
-101
00 10 20 30 40 50
Year 6
TEX
AS
Notes: Graphs based on last-chance samples. See Table 1 and text. The solid lines connects reduced-form estimates (dashed lines +/- two standard errors) for the symmetric bandwidth defined by the point at the x-axis (e.g., the estimates corresponding to x=10 are based on exam scores in the [-10,10] interval. The dashed horizontal line is the preferred reduced-form estimate (i.e., the estimate in column (5) of Table 4). For Texas, "Year 2" excluded to conserve space.
-50
5
5 10 15 20 25 30
Year 1
-50
5
5 10 15 20 25 30
Year 3
-50
5
5 10 15 20 25 30
Year 4
-50
5
5 10 15 20 25 30
Year 5
-50
5
5 10 15 20 25 30
Year 6
-50
5
5 10 15 20 25 30
Year 7
Appendix Figure 3-F: Postsecondary outcomes in Florida
Appendix Figure 3-T: Postsecondary outcomes in Texas
Notes: Graphs based on the 2000 cohort of the last-chance sample. See Table 1 and text. Dots are averages of bins defined over two test scores ( .[-2,-1], [0,1], ). Lines are fourth-order polynomials fitted separately on either side of the passing threshold. The lines refer to the number of semesters enrolled in community colleges (CC) and the state university system (SUS) after the last-chance exam. For this cohort we observe post-secondary information for four years after the last-chance exam.
Enroll Yr 1 Enroll Yr 2
01
23
-100 -50 0 50
Semesters in CC(solid) and SUS(dash)
Note: Graphs based on the last-chance sample. See Table 1 and text. Dots are exam score cell averages. Lines are fourth-order polynomials fitted separately on either side of the passing threshold. Estimated discontinuities (using a fully-interacted quadratic in the test score) are: 0.086 (se=0.010) for enrolled in college in Year 1, 0.005 (se=0.010) for enrolled in college in Year 2, 0.332 (se=0.677) for total college academic credits, and -0.062 (se=0.005) for receive GED degree. We observe post-secondary information for these cohorts for seven years after the last-chance exam. 2SLS estimates of diploma impacts on these outcomes would be roughly 2.5 times as large.
0.1
.2.3
.4.5
-30 -25 -20 -15 -10 -5 0 5 10 15
Enroll Yr. 1
0.1
.2.3
.4.5
-30 -25 -20 -15 -10 -5 0 5 10 15
Enroll Yr. 2
05
1015
2025
-30 -25 -20 -15 -10 -5 0 5 10 15
College Academic Credits
0.0
4.0
8.1
2
-30 -25 -20 -15 -10 -5 0 5 10 15
Receive GED
Appendix Figure 4-F: Industry shares in Florida: full sample (Y) v last-chance sample (X)
Professional, technical & scientificPublic AdminstrationConstruction
Wholesale tradeTransportation & warehousing
Unclassified
Accomodation & food services
Health care & social assistance
Administration, etcRetail trade
0.0
5.1
.15
.2
0 .05 .1 .15 .2
Two-digit industry
Full service restaurantsProfessional employer orgns
Unclassified
.06
.09 Six-digit industry
Notes: Graphs based on 2000 cohort (full sample and last-chance sample) with positive earnings in the first quarter of Year 6 (after the last-chance exam). See Table 1 and text. Industry refers to industry of main employer in first quarter of sixth year after the last-chance exam. Industries defined using NAICS 2002 classification. "Adiminstration, etc" in top panel is "Administrative and Support and Waste Management and Remediation Services".
Temporary help services
Warehouse clubs and supercenters
General medical and surgical hospitals
Limited service restaurants
General warehousing and storage
0.0
3
0 .03 .06 .09
Table 1: Descriptive statistics
Full sampleAll Fail Pass
Sample size 600,462 51,626 39,723 11,903 Coeff SEDemographics: Male 0.487 0.442 0.440 0.449 -0.019 0.015
Black 0.210 0.444 0.461 0.387 -0.010 0.015Hispanic 0.202 0.267 0.265 0.272 0.005 0.013
Free or reduced price lunch 0.279 0.479 0.497 0.421 -0.025 0.015Limited english proficient 0.187 0.337 0.346 0.305 -0.010 0.014
Special education 0.089 0.204 0.226 0.131 -0.004 0.010At grade level (initial attempt) 0.761 0.681 0.667 0.726 -0.023 0.015
Cohort 1 (grade 10 in 2000) 0.220 0.181 0.168 0.225 -0.013 0.012Cohort 2 (grade 10 in 2001) 0.240 0.270 0.248 0.343 0.010 0.014Cohort 3 (grade 10 in 2002) 0.265 0.258 0.261 0.250 -0.003 0.013Cohort 4 (grade 10 in 2000) 0.275 0.291 0.324 0.182 0.006 0.012
Initial exam: Took All Sections 0.976 0.976 0.976 0.974 0.004 0.004Reading (mean,sd) 7.7 (56.1) -54.9 (40.2) -60.2 (40.6) -37.3 (33.3) -0.434 1.015
Math(mean,sd) 23.3 (46.4) -24.3 (38.3) -27.9 (39.8) -12.2 (29.9) 0.819 0.926Pass (%) 0.570 0 0 0
Total exam attempts in HS: 1.723 4.422 4.498 4.168 0.009 0.0394Predicted earnings 28,548 28,140 27,357 30,754 -62.814 300.838
Full sample
All Fail PassSample size 777,892 37,571 23,242 14,329 Coeff SEDemographics: Male 0.487 0.421 0.416 0.430 -0.020 0.012
Black 0.117 0.246 0.256 0.230 -0.003 0.010Hispanic 0.289 0.478 0.505 0.434 -0.001 0.012
Free or reduced price lunch 0.213 0.409 0.442 0.354 -0.004 0.012Limited english proficient 0.040 0.147 0.177 0.099 -0.011 0.008
Special education 0.034 0.034 0.040 0.024 -0.006 0.004At grade level (initial attempt) 0.770 0.541 0.494 0.617 -0.031 0.012Cohort 1 (grade 11 fall 1991) 0.177 0.356 0.296 0.453 -0.006 0.011Cohort 2 (grade 11 fall 1992) 0.174 0.156 0.179 0.120 0.006 0.009
Cohort 3 (grade 10 spring 1993) 0.214 0.185 0.189 0.179 -0.017 0.009Cohort 4 (grade 10 spring 1994) 0.211 0.157 0.180 0.120 0.009 0.008
Initial exam: Took All Sections 0.949 0.956 0.956 0.955 -0.004 0.005Reading (mean,sd) 0.9 (11.7) -14.9 (7.9) -16.4 (7.7) -12.4 (7.4) 0.021 0.021
Math(mean,sd) 3.8 (7.5) -5.7 (6.8) -7 (6.9) -3.7 (6.2) -0.005 0.021Pass (%) 0.514 0 0 0
Total exam attempts in HS: 2.050 5.727 5.830 5.559 -0.008 0.030Predicted earnings Year 1-7 70,438.2 66,305.5 64,984.6 68,448.2 -323.194 328.563
TEXAS
Notes: See text for further description of full and last-chance samples. Last two columns report the estimated coefficients (and robust standard errors) on a "pass" dummy variable in regressions of these variables on the pass dummy and a third-order polynomial (Florida) or second-order polynomial (Texas) in the last-chance exam scores (interacted with the pass dummy). The final row refers to the fitted values from a regression of cumulative earnings in the six years (Florida) or seven years (Texas) after the last-chance exam on all of the demographics in the first panel, initial reading and math scores (missing values set to zero) and dummies for which sections were taken as part of the last-chance exam. This is the standard set of covariates used in the paper.
Last-chance sampleDiscFLORIDA
Last-chance sampleDisc
Table 2: Regression-based estimates of the signaling value of a diploma
(1) (2) (3) (4) (5)
Diploma 2,694.7 2,687.2 2,686.4 3,297.4 2,119.2(226.1) (177.6) (196.7) (476.0) (438.8)
Demographics X XTest score XN 56,900 56,900 17,780 5,462 5,338Mean w/o HSD 17,627.8 17,627.8 15,979.9 18,873.1 18,729.9Diploma effect (%) 15.3 15.2 16.8 17.5 11.3
(1) (2) (3) (4) (5)
Diploma 4731.5 4129.2 3139.5 3975.6 3188.4(56.5) (55.4) (99.1) (275.2) (275.0)
Demographics X XTest score XN 432,222 432,222 180,972 47,777 47,777Mean w/o HSD 21,790.8 21,790.8 21,248.0 26,620.5 26,620.5Diploma effect (%) 21.7 18.9 14.8 14.9 12.0
White male only
Notes: Tables based on full samples. See Table 1 and text. First row reports estimates (second row reports robust standard errors) of the estimated coefficient on diploma receipt in regressions of earnings in the last year of the observation window (Florida: Year 6; Texas: Year 7) on diploma receipt and various controls. All models use only observations with positive earnings in every quarter of the relevant year. Estimates in columns (3)-(5) based on the subset of the full sample that complete twelfth grade and did not enroll in college. See text for further explanation. Demographic controls include sex, race and cohort dummies. Test score controls are scores on the initial attempt (with dummies for missing scores on a particular subject). The second-to-final row reports mean earnings among the subset of the relevant sample that did not earn a diploma. The final row reports the coefficient estimates as a percentage of this mean.
FLORIDA
Full sample Completed grade 12, no collegeTEXAS
Full sample Completed grade 12, no college
White male only
Table 3: Impact of passing the last-chance exam on the probability of earning a diploma
Poly-1 Poly-2 Poly-3 Poly-4 Poly-3+X
Pass 0.553 0.529 0.510 0.507 0.509(0.007) (0.010) (0.011) (0.012) (0.011)
Pass 0.548 0.519 0.498 0.495 0.499(0.008) (0.010) (0.011) (0.012) (0.011)
Pass 0.546 0.518 0.499 0.497 0.500(0.008) (0.009) (0.010) (0.011) (0.011)
Pass 0.545 0.484 0.481 0.475 0.486(0.007) (0.009) (0.012) (0.016) (0.009)
Pass 0.480 0.420 0.425 0.424 0.422(0.007) (0.009) (0.012) (0.016) (0.009)
Pass 0.472 0.415 0.419 0.417 0.417(0.007) (0.009) (0.012) (0.016) (0.009)
Pass 0.468 0.412 0.416 0.414 0.414(0.007) (0.009) (0.012) (0.016) (0.009)
Notes: Tables based on last-chance samples. See Table 1 and text. Cells report estimates (robust standard errors in parentheses) of the impact of passing the last-chance exam on diploma receipt. The column headings denote different exam score polynomials controlled for in these regressions (all interacted with a dummy for passing the exam). The final column presents estimates based on models that also control for covariates (see notes to Table 1).
Receive diploma within 1 year of last-chance exam (N=51,626)
Receive diploma within 2 years of last-chance exam (N=51,626)
Receive diploma within 1 year of last-chance exam (N=37,571)
Receive diploma within 2 years of last-chance exam (N=37,571)
Receive diploma within 3 years of last-chance exam (N=37,571)
FLORIDA
TEXAS
Receive diploma by end of summer of 12th grade (N=51,626)
Poly-1 Poly-2 Poly-3 Poly-4 Poly-2+X
Receive diploma before summer of 12th grade (N=37,571)
Table 4: Discontinuity-based estimates of the signaling value of a diploma
2SLS EstimatesPoly-1 Poly-2 Poly-3 Poly-4 Poly-3+X Poly-3+X
Pass/HSD -67.034 -51.506 -150.871 -221.647 -185.882 -372.115(80.506) (108.186) (127.240) (161.074) (134.172) (268.375)
Pass/HSD 24.142 -23.875 -257.322 -297.754 -286.701 -573.942(125.113) (183.936) (236.948) (278.897) (244.167) (488.308)
Pass/HSD 109.846 -52.121 -207.064 -74.161 -226.233 -452.893(157.231) (218.532) (276.025) (313.988) (283.406) (567.829)
Pass/HSD 107.069 -31.508 -164.844 10.325 -171.655 -338.086(184.994) (252.647) (306.313) (390.729) (324.031) (641.525)
Pass/HSD -327.268 -57.347 541.643 312.821 584.694 1186.428(449.648) (412.541) (420.181) (818.350) (436.215) (873.667)
Pass/HSD -860.494 -1105.003 -94.648 -270.329 -128.648 -256.265(595.864) (541.511) (505.279) (875.930) (493.726) (977.195)
Pass/HSD -46.998 -86.262 -103.401 -107.586 -123.873 -247.600(139.297) (170.221) (207.096) (267.951) (205.946) (411.829)
2SLS EstimatesPoly-1 Poly-2 Poly-3 Poly-4 Poly-2+X Poly-2+X
Pass/HSD -58.123 -26.765 -182.352 -209.524 -32.158 -77.126(100.732) (137.460) (173.737) (213.061) (134.500) (322.555)
Pass/HSD -2.754 39.427 -13.575 9.288 45.121 108.216(124.204) (169.980) (214.785) (263.331) (166.052) (398.262)
Pass/HSD 90.018 104.963 107.692 225.174 124.022 297.450(145.977) (197.152) (249.164) (303.060) (192.712) (462.258)
Pass/HSD 52.544 221.979 262.838 294.673 264.822 635.141(163.874) (219.469) (277.211) (336.630) (214.116) (513.727)
Pass/HSD -4.912 47.124 136.804 268.807 117.635 282.132(177.934) (240.035) (304.451) (373.857) (234.006) (561.234)
Pass/HSD 6.889 -52.730 -189.176 -80.987 34.183 81.983(198.010) (267.447) (337.067) (413.798) (260.499) (624.763)
Pass/HSD -24.726 -147.900 -192.856 16.023 -43.741 -104.906(213.279) (288.282) (361.694) (443.843) (280.866) (673.651)
Pass/HSD 8.420 26.585 -10.089 74.779 72.840 174.698133.399 180.113 227.229 277.775 174.074 417.501
Year 6 (Mean at score=-1: 9,794.0; N=9,336)
Reduced-Form Estimates
Year 1 (Mean at score=-1: 5,451.2; N=51,626)
Year 2 (Mean at score=-1: 7,267.1; N=51,626)
Year 3 (Mean at score=-1: 7,454.7; N=51,626)
Year 4 (Mean at score=-1: 8,389.5; N=36,604)
FLORIDA
Years pooled (Mean at score=-1: 8005.7; N=224,086, N(cluster)=51,626)
Years pooled (Mean at score=-1: 9580.2; N=262,997, N(cluster)=37,571)
Year 6 (Mean at score=-1: 12,355.1; N=37,571)
Year 7 (Mean at score=-1: 12,879.0; N=37,571)
Year 5 (Mean at score=-1: 8,653.5; N=23,268)
Notes: Estimates based on same samples/models as those reported in Table 3. Individuals with zero earnings included in these regressions. The bottom row reports estimates from models in which year-specific data are stacked and standard errors are clustered at the individual level.
Reduced-Form EstimatesTEXAS
Year 1 (Mean at score=-1: 5,529.2; N=37,571)
Year 2 (Mean at score=-1: 7,107.6; N=37,571)
Year 3(Mean at score=-1: 8,381.8; N=37,571)
Year 4 (Mean at score=-1: 9,783.4; N=37,571)
Year 5 (Mean at score=-1: 11,025.4; N=37,571)
Table 5: Restricted and combined estimates of the signaling value of a diploma
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Pooled
Unrestricted Coeff -372.11 -573.94 -452.89 -338.09 1186.43 -256.26 -247.60SE (268.37) (488.31) (567.83) (641.53) (873.67) (977.19) (411.83)Ub on CI 3.02 5.54 9.16 11.26 33.90 17.34 7.20
Restricted Coeff -76.69 -0.16 118.96 287.25 -304.66 -2254.7 -74.77SE (218.56) (272.41) (316.09) (375.86) (818.97) (1120.20) (283.47)Ub on CI 6.61 7.49 10.08 12.38 15.41 -0.15 6.15p-value 0.42 0.09 0.23 0.4 0.61 0.45 0.37
Unrestricted Coeff -77.13 108.22 297.45 635.14 282.13 81.98 -104.91 174.70SE (322.55) (398.26) (462.26) (513.73) (561.23) (624.76) (673.65) (417.50)Ub on CI 10.27 12.73 14.58 16.99 12.74 10.78 9.65 10.54
Restricted Coeff -57.06 78.29 338.22 305.66 169.70 -10.28 -92.53 104.57SE (258.82) (318.37) (375.04) (420.34) (453.53) (509.19) (551.39) (339.72)Ub on CI 8.33 10.06 12.98 11.72 9.77 8.16 7.84 8.18p-value 0.99 0.99 0.69 0.18 0.77 0.68 0.91 0.54
Unrestricted Coeff -251.442 -164.286 -1.61969 254.8875 546.2927 -16.1617 -39.34SE (206.30) (308.63) (358.49) (401.00) (472.20) (526.38) (293.19)Ub on CI 2.94 6.32 8.93 11.44 14.43 8.93 6.23
Restricted Coeff -68.5189 32.99776 210.0232 295.4299 58.36799 -394.618 -1.16SE (166.99) (206.98) (241.70) (280.18) (396.76) (463.55) (217.65)Ub on CI 4.84 6.21 8.84 9.50 8.14 4.47 5.02
FLORIDA
TEXAS
FLORIDA & TEXAS COMBINED
Notes: Tables based on last-chance samples. The “unrestricted” estimates are reproduced from Table 4. The “restricted” estimates are the ratio of reduced-form to first-stage estimates, where these are estimated separately, using separate specifications (standard errors calculated using the delta method). The first-stage specification uses a polynomial that is fully-interacted with the pass dummy. The reduced-form specification uses a polynomial that is not interacted with the pass dummy. The “Florida and Texas combined” estimates are weighted averages of the corresponding state-specific estimates. The associated standard errors are a function of the weights and the state-specific variance estimates. The weight on the Florida estimate is the Texas variance estimate as a proportion of the summed variance estimates.
Appendix Table 1: Regression-based estimates of the signaling value of a diploma: by ability
All Group 1 Group 2 Group 3 Group 4 Group 5 Group 6<-31 [-31,-2) [-2,18) [18,36) [36,56) >=56
HS diploma 2,687.22 1,025.73 2,025.35 1,962.70 1,808.08 2,562.86 3,142.76(177.64) (376.80) (241.85) (312.62) (352.15) (412.67) (640.02)
N 56,900 7559 9510 9495 10038 10029 8885Mean w/o diploma 17,627.8 17,106.9 17,039.6 18,177.5 18,800.4 18,618.7 19,757.6Diploma effect (%) 15.2 6.0 11.9 10.8 9.6 13.8 15.9
HS diploma 2,686.44 1,126.65 2,231.49 2,786.91 2,415.95 3,688.69 4,096.02(196.69) (310.78) (385.14) (598.35) (728.73) (960.22) (1748.06)
N 17,780 3780 4017 3296 2839 2082 1300Mean w/o diploma 16,979.9 16,781.2 16,852.7 17,487.5 17,971.4 17,853.0 20,356.8Diploma effect (%) 15.8 6.7 13.2 15.9 13.4 20.7 20.1
All Group 1 Group 2 Group 3 Group 4 Group 5 Group 6<-12 [-12,-5) [-5,1) [1,5) [5,9) >=9
HS diploma 4129.2 1944.1 1871.1 2287.7 2607.6 3383.2 3042.5(55.4) (85.1) (109.3) (129.6) (169.4) (204.7) (281.8)
N 432,222 71,182 65,697 77,309 64,200 72,366 62,779Mean w/o diploma 21,790.8 19,218.8 21,530.2 22,906.5 24,314.0 25,538.4 28,715.7Diploma effect (%) 18.9 10.1 8.7 10.0 10.7 13.2 10.6
HS diploma 3139.5 1414.8 1659.7 1825.8 2485.2 3176.3 3444.6(99.1) (129.4) (172.8) (231.1) (319.1) (422.7) (701.1)
N 180,972 37,394 40,323 41,801 30,307 26,841 20,584Mean w/o diploma 21,248.0 19,119.0 21,391.4 23,047.4 24,151.0 25,377.8 28,200.5Diploma effect (%) 14.8 7.4 7.8 7.9 10.3 12.5 12.2Notes: Table based on full samples. See Table 1 and text for more details. Bottom panel based on subset of full panel that complete twelfth grade and do not enroll in college. See text for more details. The cells report estimates (robust standard errors in parentheses) from models identical to those underlying Table 2 (see notes to Table 2 for more details). The first columns use all observations, hence estimates are identical to those reported in columns (2) and (3) of Table 2. The next six columns report estimates from models restricted to observations from six groups corresponding to 6-tiles of the minimum score on the initial exam (only observations with non-missing scores for all initial-attempt subjects included). The column headings describe the relevant score cutoffs. The second-to-final row reports mean earnings among the subset of the relevant sample that did not earn a diploma. The final row reports the coefficient estimates as a percentage of this mean.
Full Sample
Completed grade 12, no college
FLORIDA
TEXAS
Full sample
Completed grade 12, no college