Online Resource

Preparing Students for College and Careers: The Causal Role of Algebra II

Research in Higher Education

Authors’ Names and Affiliations Removed

Electronic Supplementary Material for Revision Submitted for Consideration for the 2013 Research in Higher Education Annual Forum Issue

Online Resource 1a.Algebra II Effects: College GPA (NELS)

Freshman GPA / Sophomore GPA / Cumulative GPA
Naive Model / Control Function / Naive Model / Control Function / Naive Model / Control Function
Algebra II / 0.165*** / 0.703** / 0.0438*** / 0.342** / 0.110*** / 0.834***
(0.0207) / (0.267) / (0.00946) / (0.104) / (0.0150) / (0.200)
Male / -0.141*** / -0.153*** / -0.0343*** / -0.0437*** / -0.0729*** / -0.0956***
(0.0194) / (0.0209) / (0.00744) / (0.00785) / (0.0126) / (0.0132)
Asian / 0.0484 / -0.00636 / 0.000472 / -0.0349 / 0.00708 / -0.0744*
(0.0368) / (0.0466) / (0.0139) / (0.0188) / (0.0197) / (0.0298)
Hispanic / -0.149*** / -0.133*** / -0.0359* / -0.0316* / -0.0389 / -0.0272
(0.0328) / (0.0332) / (0.0156) / (0.0158) / (0.0252) / (0.0257)
Black / -0.224*** / -0.202*** / -0.0965*** / -0.0925*** / -0.151*** / -0.147***
(0.0359) / (0.0365) / (0.0162) / (0.0167) / (0.0264) / (0.0265)
Native / -0.467*** / -0.412*** / -0.0375 / -0.00996 / -0.0996 / -0.0313
(0.0924) / (0.0949) / (0.0612) / (0.0621) / (0.0979) / (0.0996)
High school GPA / 0.000826* / 0.000840* / 0.000131 / 0.000207 / 0.000157 / 0.000349
(0.000405) / (0.000384) / (0.000139) / (0.000145) / (0.000208) / (0.000219)
Freshmen GPA / 0.885*** / 0.884*** / 0.699*** / 0.697***
(0.00629) / (0.00646) / (0.00996) / (0.0101)
SES / 0.112*** / 0.0420 / 0.0342*** / -0.00370 / 0.0797*** / -0.0119
(0.0127) / (0.0361) / (0.00512) / (0.0137) / (0.00832) / (0.0264)
Algebra II residual / -0.537* / -0.300** / -0.728***
(0.268) / (0.105) / (0.200)
N / 6397 / 6220 / 6397 / 6220 / 6397 / 6220
Note: Ordinary least squares estimates are reported. Standard errors are in parentheses.
* p<0.05; ** p<0.01; *** p<0.001

Online Resource 1b.Algebra II Effects: Initial Annual Earnings & Annual Earnings Change

NELS / ELS
Initial Annual Earnings / Annual Earnings Change / Initial Annual Earnings / Annual Earnings Change
Naive Model / Control Function / Naive Model / Control Function / Naive Model / Control Function / Naive Model / Control Function
Algebra II / 14.31 / -3254.6 / 1925.9* / 9452.2* / 227.8 / -954.2 / 1015.7* / -6397.3
(410.9) / (1975.6) / (963.1) / (4484.1) / (355.3) / (2995.6) / (511.3) / (4327.9)
Male / 3555.4*** / 3603.0*** / 6513.5*** / 6856.3*** / 3407.8*** / 3471.8*** / 1322.4** / 1102.0
(361.6) / (371.8) / (717.5) / (707.9) / (331.5) / (363.7) / (491.0) / (568.3)
Asian / -679.6 / -343.3 / -1665.0 / -2315.3 / -1420.6* / -1284.6 / -911.7 / 325.9
(1082.0) / (1121.8) / (1970.4) / (2044.1) / (668.6) / (789.6) / (1198.3) / (1381.7)
Hispanic / -269.0 / -233.4 / -1961.4 / -2092.5* / -870.9* / -658.2 / 165.5 / 1172.1
(644.2) / (674.4) / (1010.3) / (1059.1) / (441.9) / (493.8) / (636.6) / (845.3)
Black / -3033.2*** / -2725.5*** / -1816.7 / -2409.9* / -1464.0** / -1158.5 / -307.2 / 1028.6
(625.4) / (668.5) / (1002.5) / (1098.5) / (504.5) / (771.9) / (887.3) / (1178.6)
Native / 491.5 / 823.9 / -2345.5 / -3008.5 / -2208.1* / -2111.9* / -655.3 / -319.8
(1336.2) / (1344.7) / (3652.4) / (3707.1) / (926.3) / (933.3) / (2578.7) / (2604.2)
Reading & math composite score / -85.73*** / -34.86 / 79.54 / -15.79 / -35.09 / -14.83 / -51.57 / 89.75
(22.39) / (39.97) / (49.08) / (75.73) / (19.00) / (55.08) / (27.27) / (81.08)
SES / 95.83 / 144.5 / 1641.1** / 1252.8* / 538.5 / 587.9 / -287.8 / -56.77
(279.1) / (291.2) / (586.0) / (602.8) / (286.9) / (349.7) / (488.2) / (552.6)
Work during high school / 1151.5** / 1226.1** / 251.7 / -406.5 / 1416.8*** / 1506.8*** / 429.1 / 370.8
(377.3) / (387.5) / (713.5) / (725.4) / (383.8) / (392.5) / (510.3) / (523.2)
Algebra II residual / 1408.1 / -3187.8 / 535.9 / 3487.1
(817.2) / (1753.5) / (1360.8) / (2031.2)
N / 2265 / 2179 / 2148 / 2065 / 3911 / 3728 / 2496 / 2373
Note: Ordinary least squares estimates are reported. Standard errors are in parentheses.
* p<0.05; ** p<0.01; *** p<0.001

Online Resource 2a.Algebra II Effects: Retention & Graduation

NELS / ELS
Persistence to Sophomore Yr / Persistence to Junior Yr / College Graduation / Persistence to Sophomore Yr / Persistence to Junior Yr
Naive Model / Control Function / Naive Model / Control Function / Naive Model / Control Function / Naive Model / Control Function / Naive Model / Control Function
Algebra II / 0.104*** / 0.290*** / 0.140*** / 0.498*** / 0.167*** / 0.560*** / 0.111*** / 0.0809 / 0.115*** / 0.204
(0.00829) / (0.0766) / (0.0102) / (0.0992) / (0.0116) / (0.109) / (0.00973) / (0.173) / (0.0105) / (0.198)
Male / -0.00597 / -0.0136 / -0.00747 / -0.0201 / -0.0258* / -0.0392*** / -0.0238** / -0.0247** / -0.0312*** / -0.0309***
(0.00889) / (0.00955) / (0.0102) / (0.0107) / (0.0110) / (0.0113) / (0.00744) / (0.00776) / (0.00778) / (0.00819)
Asian / 0.0623** / 0.0491* / 0.127*** / 0.103*** / 0.0849*** / 0.0626** / 0.0677*** / 0.0693*** / 0.0707*** / 0.0661***
(0.0195) / (0.0200) / (0.0228) / (0.0238) / (0.0199) / (0.0208) / (0.0157) / (0.0188) / (0.0160) / (0.0198)
Hispanic / 0.0223 / 0.0319* / 0.0298 / 0.0445* / -0.0512** / -0.0349 / -0.0112 / -0.0115 / -0.0221 / -0.0214
(0.0137) / (0.0142) / (0.0168) / (0.0177) / (0.0182) / (0.0190) / (0.0121) / (0.0124) / (0.0124) / (0.0127)
Black / 0.00782 / 0.0159 / 0.0311 / 0.0457* / 0.00421 / 0.0134 / -0.0370** / -0.0369** / -0.0456*** / -0.0432***
(0.0145) / (0.0149) / (0.0177) / (0.0184) / (0.0210) / (0.0213) / (0.0118) / (0.0121) / (0.0124) / (0.0128)
Native / -0.0452 / -0.0259 / -0.0237 / 0.0132 / -0.0955 / -0.0608 / -0.0329 / -0.0381 / -0.0277 / -0.0123
(0.0351) / (0.0362) / (0.0544) / (0.0562) / (0.0905) / (0.0925) / (0.0456) / (0.0572) / (0.0492) / (0.0630)
SES / 0.0777*** / 0.0575*** / 0.121*** / 0.0840*** / 0.167*** / 0.129*** / 0.0656*** / 0.0689*** / 0.0672*** / 0.0629***
(0.00573) / (0.0105) / (0.00683) / (0.0127) / (0.00714) / (0.0128) / (0.00587) / (0.0124) / (0.00609) / (0.0142)
Freshman GPA / 0.0688*** / 0.0504*** / 0.117*** / 0.0850*** / 0.223*** / 0.188*** / 0.000417** / 0.000429* / 0.000427** / 0.000403*
(0.00621) / (0.0101) / (0.00715) / (0.0116) / (0.00750) / (0.0118) / (0.000150) / (0.000167) / (0.000153) / (0.000175)
Algebra II residual / -0.0864* / -0.165*** / -0.177*** / 0.0294 / -0.0901
(0.0358) / (0.0461) / (0.0492) / (0.173) / (0.198)
N / 6716 / 6542 / 6716 / 6542 / 6716 / 6542 / 7492 / 7219 / 7492 / 7219
Note: Marginal probability estimates are reported. Standard errors are in parentheses.
* p<0.05; ** p<0.01; *** p<0.001

Online Resource 2b.Algebra II Effects: Maintaining Occupational Prestige

NELS / ELS
Naive Model / Control Function / Naive Model / Control Function
Algebra II / 0.0260 / 0.0639 / -0.0394* / -0.0660
(0.0152) / (0.0618) / (0.0174) / (0.154)
Male / 0.0246 / 0.0240 / 0.107*** / 0.106***
(0.0130) / (0.0134) / (0.0165) / (0.0175)
Asian / 0.0186 / 0.0102 / -0.0863* / -0.0853
(0.0413) / (0.0427) / (0.0409) / (0.0472)
Hispanic / 0.0168 / 0.0127 / -0.0661** / -0.0641*
(0.0193) / (0.0196) / (0.0227) / (0.0276)
Black / 0.0278 / 0.0233 / -0.122*** / -0.116**
(0.0218) / (0.0228) / (0.0242) / (0.0358)
Native / 0.0814* / 0.0755* / -0.165* / -0.162*
(0.0370) / (0.0383) / (0.0698) / (0.0700)
Reading & math composite score / -0.000307 / -0.00105 / -0.00248* / -0.00188
(0.000807) / (0.00134) / (0.00105) / (0.00292)
SES / 0.0114 / 0.0109 / -0.0327* / -0.0306
(0.0111) / (0.0115) / (0.0143) / (0.0174)
Work during high school / 0.00408 / 0.00188 / 0.00631 / 0.00660
(0.0130) / (0.0136) / (0.0178) / (0.0182)
Occupational prestige / -0.186*** / -0.185*** / -0.0452*** / -0.0477***
(0.0130) / (0.0133) / (0.00934) / (0.00981)
Algebra II residual / -0.0152 / 0.0128
(0.0241) / (0.0725)
N / 2043 / 1968 / 3596 / 3417
Note: Marginal probability estimates are reported. Standard errors are in parentheses.
* p<0.05; ** p<0.01; *** p<0.001

Online Resource 3a.Instrumental Variables in NELS: Final Test Statistics

Model / Endogeneity Test / Overid Test / 1st Stage F-Test / Weak ID Test
H0: Alg2 Exogenous / H0: Excluded IVs Valid / and (p-value) / H0: Alg2 Unidentified
Rule of Thumb >10 / (Critical Values)
College Outcomes
Freshman GPA / Reject at (p = 0.044) / N/A / 14.78 (p=.0001) / 28.14 (16.38; 8.96)
Sophomore GPA / Reject at (p = 0.004) / N/A / 13.39 (p=0.003) / 28.29 (16.38; 8.96)
Cumulative GPA / Reject at (p = 0.0000) / N/A / 25.71 (p=0.0000) / 32.48 (16.38; 8.96)
Graduation / Reject at (p = 0.0002) / N/A / 9.58 (p=0.0020) / 14.86 (16.38; 8.96)
Persist to Year 2 / Reject at (p = 0.0067) / N/A / 9.58 (p=0.0020) / 14.86 (16.38; 8.96)
Persist to Year 3 / Reject at (p = 0.0000) / N/A / 9.58 (p=0.0020) / 14.86 (16.38; 8.96)
Persist to Year 4 / Reject at (p = 0.0012) / N/A / 9.58 (p=0.0020) / 14.86 (16.38; 8.96)
Career Outcomes
Initial Wage / Reject at (p = 0.0052) / N/A / 17.7 (p=0.0000) / 17.70 (16.38; 8.96)
Full Sample
Initial Wage / Reject at (p = 0.0055) / N/A / 9.6 (p=0.0020) / 9.60 (16.38; 8.96)
w/o "Gappers" (NELS only)
Wage Change / Reject at (p = 0.0003) / N/A / 8.9 (p=0.0029) / 8.90 (16.38; 8.96)
w/o "Gappers" (NELS only)
Maintain Prestige / Reject at (p = 0.0185) / N/A / 11.21 (p=0.0008) / 11.21 (16.38; 8.96)
w/o "Gappers" (NELS only)
Note:
Same 1st Stage Specification Used on Persistence/Graduation Models.
The "Weak ID Test" is the Kleibergon-Paaprk Wald F-test, appropriate when cluster-robust standard errors employed.
Critical values reported for Kleibergon-Paap test are the (10%; 15%) maximal IV size values.
Single IV used in NELS data so no overid tests conducted.

Online Resource 3b.Instrumental Variables in ELS: Final Test Statistics

Model / Endogeneity Test / Overid Test / 1st Stage F-Test / Weak ID Test
H0: Alg2 Exogenous / H0: Excluded IVs Valid / and (p-value) / H0: Alg2 Unidentified
Rule of Thumb >10 / (Critical Values)
College Outcomes
Freshman GPA / Fail to Reject (p=0.7742) / Fail to Reject (p = 0.8376) / 16.22 / 29.19 (19.93; 11.59)
Persist to Year 2 / Fail to Reject (p = 0.8395) / Fail to Reject ( p = 0.3563) / 8.05 (p= 0.0003) / 11.68 (19.93; 11.59)
Persist to Year 3 / Fail to Reject (p = 0.4268) / Fail to Reject (p = 0.5056) / 8.05 (p= 0.0003) / 11.68 (19.93; 11.59)
Career Outcomes
Initial Wage / Fail to Reject at (p = 0.1705) / NA / 20.31 (p=0.0000) / 20.31 (16.38; 8.96)
Wage Change / Fail to Reject at (p=0.8087) / N/A / 11.18 (p=0.0008) / 11.19 (16.38; 8.96)
Maintain Prestige / Fail to Reject at (p=0.9587) / N/A / 20.11 (p=0.0000) / 20.11 (16.38; 8.96)
Note:
Same 1st Stage Specification Used on Persistence/Graduation Models.
The "Weak ID Test" is the Kleibergon-Paaprk Wald F-test, appropriate when cluster-robust standard errors employed.
Critical values reported for Kleibergon-Paap test are the (10%; 15%) maximal IV size values.
Single IV used in NELS data so no overid tests conducted.

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