How Does Your Kindergarten Classroom Affect Your Earnings?
How Does Your Kindergarten Classroom Affect Your Earnings? Evidence from Project STAR Raj Chetty, Harvard John N. Friedman, Harvard Nathaniel Hilger, Harvard Emmanuel Saez, UC Berkeley Diane Schanzenbach, Northwestern Danny Yagan, Harvard May 2011 Introduction What are the long-term impacts of early childhood education? Limited evidence because few datasets link information on childhood education with adult outcomes We link data from the STAR experiment to U.S. tax records to analyze how class assignment in grades K-3 affects adult outcomes Project STAR Background Student/Teacher Achievement Ratio (STAR) experiment: Conducted from 1985 to 1989 in Tennessee One cohort of 11,571 children in grades K-3 at 79 schools Most children born in 1979-80 graduate high school in 1998 Students and teachers randomized into classrooms within schools Class size differs: small (15 students) or large (22
students) Classes also differ in teachers and peers Project STAR Background Large literature on STAR shows that class size, teacher quality, and peer quality have causal impacts on scores Students in small classes have 5 percentile point (0.2 sd) higher test scores in K-3 (Krueger 1999) But test score gains fade out to 1-2 percentiles by grade 8 Similar fade out effects observed in other early childhood interventions (e.g. Currie and Thomas 1995, Deming 2009) Do early test score gains translate into impacts on adult outcomes? United States Tax Data Dataset covers full U.S. population from 1996-2008 Approximately 90% of working age adults file tax returns Third-party reports yield data on many outcomes even for non-filers Employer and wage earnings from W-2 forms College attendance from 1098-T forms 95% of STAR records were linked to tax data Table 1: Summary Statistics STAR Sample (1)
U.S. 1979-80 cohort (2) Mean Wage Earnings (2005-07) $15,912 $20,500 Zero Wage Earnings (2005-07) 13.9% 15.6% Attended College in 2000 (age 20) 26.4% 34.7% Attended College by age 27 45.5% 57.1% $48,010
$65,660 Mean Parents Income (1996-98) Outline 1. Test scores and adult outcomes in the cross-section 2. Impacts of observable classroom characteristics 3. Impacts of unobservable classroom characteristics 4. Fade-out, re-emergence, and non-cognitive skills 5. Cost-benefit analysis Part 1: Cross-Sectional Correlations Begin by correlating KG test scores with adult outcomes Useful to benchmark estimates from randomized interventions Estimate both raw correlations and OLS regressions with controls: - quartic in parental household income interacted with marital status - mother age at childs birth - parents 401K contributions, home ownership - childs gender, free lunch status, race, and age Test score: percentile score on Kindergarten Stanford Achievement Test (math + reading) What is a kindergarten test? Instructions: Ill say a word to you. Listen for the ending sound.
You circle the picture that starts with the same sound. cup Figure 1a: Wage Earnings vs. KG Test Score Mean Wage Earnings from Age 25-27 $25K $20K $15K R = 0.05 $10K 0 20 40 60 KG Test Score Percentile 80
100 Test Scores and Earnings in the Cross-Section Dependent Var.: KG Test Percentile Wage Earnings (1) (2) (3) (4) $132 ($12.2) $93.8 ($11.6) $90.0 ($8.65) $97.7 ($8.47) Parental Income Percentile
Entry Grade $146 ($8.15) KG KG All All Class Fixed Effects x x x Student Controls x x x Parent Controls
x x Adjusted R2 0.05 0.17 0.17 0.16 Observations 5,621 5,621 9,939 9,939 Figure 1b: College Attendance Rates vs. KG Test Score Attended College before Age 27
80% 60% 40% 20% 0% 0 20 40 60 KG Test Score Percentile 80 100 An Earnings-Based Index of College Quality We construct an index of college quality using tax data Tuition paid to any higher ed. institution (Title IV) automatically generates a 1098-T form linking student and institution
Calculate average wage earnings (from W-2s) by college For those who do not attend college, define college quality index as mean earnings for those not in college in 1999 An Earnings-Based Index of College Quality US News Ranking College Mean Earnings at age 28 1 2 3 4 5 Harvard Princeton Yale Cal Tech MIT $79,643 6
7 8 9 10 . 121 122 123 124 125 Stanford U Penn Columbia U Chicago Duke $75,570 Arizona St. Catholic U MI Tech U Buffalo U San Fran $46,390 College Quality vs. KG Test Score
Earnings-Based College Quality Index $28K $26K $24K $22K $20K $18K 0 20 40 60 KG Test Score Percentile 80 100 Owned a Home by Age 27
Home Ownership vs. KG Test Score 40% 30% 20% 0 20 40 60 KG Test Score Percentile 80 100 Retirement Savings vs. KG Test Score Made a 401(k) Contribution by Age 27 45%
40% 35% 30% 25% 20% 0 20 40 60 KG Test Score Percentile 80 100 Marriage by Age 27 vs. KG Test Score 55% Married by Age 27
50% 45% 40% 35% 30% 25% 0 20 40 60 KG Test Score Percentile 80 100 Lived Outside TN before Age 27 Cross-State Mobility vs. KG Test Score
35% 30% 25% 20% 0 20 40 60 KG Test Score Percentile 80 100 Percent College Graduates in ZIP code vs. KG Test Score Percent College Graduates in 2008 ZIP 22% 20%
18% 16% 14% 0 20 40 60 KG Test Score Percentile 80 100 Part 2: Validity of the STAR Experimental Design Validity of experimental analysis rests on two assumptions: Assumption 1: Randomization All pre-determined variables (e.g. parent characteristics) are balanced across classrooms Assumption 2: No Differential Attrition 95% match rate little attrition here
No evidence of differences in match rates across classrooms No evidence of differences in death rates across classrooms Part 3: Class Size Impacts Regress outcomes on dummy for small class assignment (intent to treat) with school fixed effects Analyze impacts on four outcomes: 1. College attendance 2. College quality index 3. Mean earnings (ages 25-27) 4. Standardized (SD = 1) summary index of other outcomes: Index = 401K + Home Owner + Married + Moved out of TN + Pct. College Grads. in Zip Figure 2a: Effect of Class Size on College Attendance by Year Percent Attending College 30% 25% 20% 15%
10% 2000 2002 2004 Year Large Class Small Class 2006 Frequency Figure 2b: College Earnings Quality by Class Size $20K $30K $40K $50K Earnings-Based Index of College Quality Large Class
Small Class Figure 2c: Effect of Class Size on Wage Earnings by Year $18K $16K Wage Earnings $14K $12K $10K $8K $6K 2000 2002 2004 Year Large Class Small Class
2006 Table 5: Impacts of Class Size on Adult Outcomes Dependent College In 2000 Var.: (1) College Quality Wage Earnings (2) (3) Summary Index (4) Small Class 2.02% (1.10%) $119 ($97) $4 ($327) 5.06%
(2.16%) Observations 10,992 10,992 10,992 10,992 Mean of Dep. Var. 26.4% $27,115 $15,912 0.00 Note: All specifications control for school-by-entry-grade effects. Part 3: Teacher/Peer Effects Students randomly assigned to classes that differ in teacher and peer quality Do teachers/peers affect adult outcomes? First test: does random assignment to a more experienced
KG teacher improve adult outcomes? Not necessarily causal effect of raising teacher experience per se Experienced teachers may also differ on other dimensions such as dedication to teaching Figure 3a: Effect of Teacher Experience on Test Scores KG Test Score Percentile 56 54 52 50 48 0 5 10 15 Kindergarten Teacher Experience (Years)
20 Figure 3b: Effect of Teacher Experience on Earnings Mean Wage Earnings, 2005-2007 $19K $18K $17K $16K 0 5 10 15 Kindergarten Teacher Experience (Years) 20 Figure 3c: Effect of Teacher Experience on Earnings by Year $20K
$1104 $18K Wage Earnings $16K $14K $12K $10K $8K 2000 2002 2004 2006 Year Teacher Experience <=10 Years Teacher Experience > 10 Years Table 6: Observable Teacher vs. Peer Effects Dependent Var.: Test Score (1)
(2) Teacher with >10 Years Experience 3.18% (1.26%) $1093 ($546) Teacher has post-BA deg. -0.85% (1.15%) -$261 ($449) Wage Earnings (3) % Black Classmates -$1,757 ($2,692) % Female Classmates
-$67.5 ($1,539) % Free-Lunch Classmates -$285 ($1,731) Classmates Mean Age -$25.8 ($1,359) Classmates Mean Pred. Score (4) -$23.3 ($93.7) Entry Grade KG KG All
All Observations 5,601 6,005 10,992 10,992 Note: All specifications control for school fixed effects and class size, as well as student and parent demographics. Part 4: Unobservable Class Effects Many elements of teacher and peer quality (e.g. clarity of instruction, enthusiasm) are not observable Well known problem in literature on teacher effects Test for class effects on adult outcomes using analysis of variance Is there significant intra-class correlation in students outcomes? This class effect includes effect of teachers, peers, and any class-level shocks such as noise outside classroom Formally, we are testing for clustering of outcomes by (randomly assigned) classroom A Model of Class Effects Test scores and earnings for individual i in class c:
s ic z c a ic y ic z c z Yc a ic v ic zc = class-level intervention (e.g. better teaching) that affects scores and earnings zYc = intervention that affects earnings but not scores A Model of Class Effects Test scores and earnings for individual i in class c: s ic z c a ic y ic z c z Yc a ic v ic zc = class-level intervention (e.g. better teaching) that affects scores and earnings zYc = intervention that affects earnings but not scores aic = academic ability ic = earnings ability orthogonal to academic ability A Model of Class Effects Test scores and earnings for individual i in class c: s ic z c a ic y ic z c z Yc a ic v ic zc = class-level intervention (e.g. better teaching) that affects scores and earnings zYc = intervention that affects earnings but not scores aic = academic ability
ic = earnings ability orthogonal to academic ability = impacts of interventions on earnings = covariance of class effects on scores and earnings A Model of Class Effects Test scores and earnings for individual i in class c: s ic z c a ic y ic z c z Yc a ic v ic Thus far, we have estimateddirectly by using observable zs that affect test scores (e.g. teacher experience) How can we estimate and when class-level interventions are unobserved? Strategy 1: Analysis of Variance Test for class effects on earnings () using ANOVA Do earnings vary across classes by more than what would be predicted by random variation in student abilities? Two steps: [Fixed effects] Test for significance of class fixed effects [Random effects] Estimate class-level SD of outcomes assuming normally distributed class effects Table 7: Analysis of Variance: Kindergarten Class Effects Dependent Var.: Grade Grade
K Scores 8 Scores (1) (2) Wage Earnings (3) (4) (5) (6) P-value of F-Test on KG Class Fixed Effects 0.000 0.419 0.047 0.026 0.020 0.042 SD of Class Effects
(RE estimate) 8.77% 0.000% $1,497 $1,520 $1,703 $1,454 x x x x x Demographic Controls Large Classes Only x
Observable Class Chars. Observations x 5,621 4,448 6,025 6,025 Note: All specifications control for school fixed effects and class size. 4,208 5,983 Strategy 2: Covariance of Class Effects on Scores and Earnings ANOVA does not tell us whether class effects on scores are correlated with class effects on earnings () Do class-level interventions that raise test scores also improve adult outcomes? Turn to a second strategy to measure covariance between class effects on scores and earnings () What is the correlation of class effects on scores and class effects on earnings? Derive estimator for and prove it is unbiased in paper;
give a heuristic explanation here Peer-Score Measure of Class Quality Average end-of-year test scores in class relative to school sc is a (noisy) measure of class effect on scores: sc zc 1 I I j 1 a jc Motivates regression of the form: y ic a b M s c ic Own-observation bias: with finite class size, EbM 0 even if bM =0 Smart kid raises average class score and has high earnings Analogous to bias in 2SLS estimate with weak instruments Peer-Score Measure of Class Quality
Regression specification: y ic a b LM s c i ic This regression does not estimate peer effects because we are using end-of-year test scores Class quality sc-i captures teacher quality + class-level shocks Good teachers raise peers end of year scores Class quality sc-i varies randomly within schools Can test whether classes that generate test score gains also generate earnings gains Peer-Score Measure of Class Quality Regression specification: y ic a b LM s c i ic Three remaining sources of bias in bLM 1. Mechanical: Peers below-avg. you are above avg. (Guryan, Kroft, Notowidigdo 2009). Solution: define intercept using leaveout mean 2. Attenuation: sc-i is a noisy measure of class quality 3. Reflection: with peer effects, smart kid raises peers scores and earns a lot, driving up bLM Figure 4a: Effect of Early Childhood Class Quality on Own Score 70 Own Test Score Percentile
65 60 55 50 45 40 -20 -10 0 10 Class Quality (End-of-Year Peer Scores) 20 Figure 4c: Effect of Early Childhood Class Quality on Earnings Mean Wage Earnings, 2005-2007 $17.0K $16.5K
$16.0K $15.5K $15.0K $14.5K -20 -10 0 10 Class Quality (End-of-Year Peer Scores) 20 Figure 5a: Effect of Class Quality on Earnings by Year $18K $875 Wage Earnings $16K $14K
$12K $10K $8K 2000 2002 Below-Average Class Quality Year 2004 2006 Above-Average Class Quality Table 8a: Impacts of Class Quality on Earnings Dependent Variable: Class Quality (peer scores) Entry Grade Wage Earnings ($)
(1) (2) (3) (4) 50.61 (17.45) 61.31 (20.21) 53.44 (24.84) 47.70 (18.63) All All KG Grade 1 6,025
4,934 Observable class chars. Observations x 10,959 10,859 NOTE--All regressions control for student and parent demographics and school-by-entry-grade fixed effects. Table 8b: Impacts of Class Quality on Other Adult Outcomes Dependent Variable: College in 2000 College by Age 27 College Quality Summary Index
(0.053) (4.573) (0.098) Observations 10,959 10,959 10,959 10,959 NOTE--All regressions control for student and parent demographics and school-by-entry-grade fixed effects. Bounding Reflection Bias Small impact of KG class quality on subsequent test scores places a tight upper bound on reflection bias Smart kids score high on all tests (test scores highly autocorrelated) To have large reflection bias, smart kid must raise peer scores a lot Large correlation between peer scores and own score in later grades We formalize this intuition in a linear-in-means model and
derive a bound on the degree of reflection bias Observed correlation between KG peer scores and 8th grade score places an upper bound on reflection bias of 20% Figure 6a: Fadeout of Class Effects Effect of 1 SD of Class Quality on Test Scores by Grade 10 Test Score Percentile 8 6 4 2 0 0 2 4 6 8
Grade 1 SD Class Quality Effect on Test Scores 95% CI E Figure 6b: Fadeout of Class Effects Effect of 1 SD of Class Quality on Earnings $1000 Wage Earnings $800 $600 $400 $200 $0 0 2 4
6 8 Grade 1 SD Class Quality Effect on Wage Earnings 95% CI E Fade-out and Re-emergence: The Role of NonCognitive Skills Why do effects of kindergarten class fade out and reemerge? One explanation: non-cognitive skills (Heckman 2000) Data on non-cognitive measures (effort, initiative, disruption) collected for random subset of STAR students in 4th and 8th grade Please consider the behavior of Jim Smith over the last 2-3 months. Circle the number that indicates how often the child exhibits the behavior. #1. Acts restless, is often unable to sit still #2. Annoys or interferes with peers work SomeNever times Always 1 2
3 4 5 1 2 3 4 5 Convert mean non-cog score to percentile scale as above Mean Wage Earnings vs. Grade 4 Non-Cognitive Percentile Mean Wages Earnings, 2005-2007 $25K $20K $15K $10K 0 20
scores) Observations Grade 4 Scores 1,360 1,254 4,023 1,671 (5) (6) 0.064 0.128 (0.041) (0.054) 4,448 1,780 Fade-out and Re-emergence: The Role of NonCognitive Skills Non-cognitive skills provide a simple explanation of our findings High quality KG teachers raise KG test scores partly through good classroom management Good classroom management instills social skills
Social skills not directly measured in standardized tests but have returns in the labor market Rapid fadeout in math and reading tests after KG But significant earnings gains from better KG class Part 6: Cost-Benefit Analysis Assume: 3% real discount rate, constant percent income gains, income follows average US income profile, constant effects of class quality 1. One SD increase in KG class quality for a single year Total NPV earnings gain for class of 20 students of $782K 2. 33% reduction in class size $4K-$189K per class (very imprecisely estimated) 3. One SD improvement in teacher quality $170-$214K per class th th School Quality and Income Inequality Intergenerational income correlation of around 0.3 (Solon 1999) How much of this can be explained by the fact that higher income families have access to better public schools? In STAR data, each $10K of parents income increases class quality in each grade by 0.7% of a SD Use our estimates of effect of class quality on childs
earnings and assume constant class-quality effects across grades Roughly 1/3 of intergenerational income transmission runs Part 2: Validity of the STAR Experiment Design Threat #1: Failure of Randomization Prior studies had few baseline measures, limiting ability to evaluate randomization protocol (Schanzenbach 2006) We test for balance across class types with an expanded set of parent/sibling characteristics in two ways: 1. Do characteristics vary across small vs. large class types? 2. Do characteristics vary across classrooms within schools? Table 2: Randomization Tests Dependent Variable: Wage Earnings (%) (1) Small Class (%) (2) Teacher Exp. Class Effects (%) p-value (3)
(4) Parents Income ($1,000s) 65.47 (6.634) [9.87] -0.003 (0.015) [-0.231] -0.001 (0.002) [-0.509] 0.848 Mothers Age at STAR Birth 53.96 (24.95) [2.162] 0.029 (0.076) [0.384]
(0.864) [-0.261] 0.236 (0.111) [2.129] 0.502 Student Black -620.8 (492.0) [-1.262] 0.204 (1.449) [0.141] 0.432 (0.207) [2.089] 0.995 p-Value of F Test 0.000
0.261 0.190 Observations 10,992 10,992 10,914 Note: Regressions include school-by-entry-grade fixed effects. Validity of the STAR Experiment Design Threat #2: Selective Attrition Much less attrition than in prior studies of STAR because we follow 95% of the sample Test for selective attrition through two channels: 1. Does match rate vary across treatment groups? 2. Does death rate vary across treatment groups (Muennig et al. 2010)? Table 3: Tests for Selective Attrition Dependent Variable: Small Class
p Value on F test on Class Effects Matched (%) (%) (1) (2) -0.019 (0.467) 0.079 (0.407) -0.010 (0.286) -0.006 (0.286) 0.951 0.888 0.388 0.382 Demographic Controls
Mean of dep. Var. Observations Deceased (%) (%) (3) (4) x x 95.0 95.0 1.70 1.70 11,571 11,571 10,992 10,992
Correlation between Earnings at Age and Age + 6 Appendix Table 1: Correlation of Earnings Over the Life Cycle .8 .6 .4 .2 0 20 30 40 Age 50 Table 6: Observable Teacher vs. Peer Effects Dependent Var.: Test Score (1)
Wage Test Score Earnings (2) (3) Wage Earnings (4) Teacher with >10 Years Experience 3.18% (1.26%) $1093 ($546) 1.61% (1.21%) -$536 ($619) Teacher has post-BA deg. -0.85% (1.15%) -$261
($449) 0.95% (0.90%) -$359 ($500) (5) % Black Classmates -$1,757 ($2,692) % Female Classmates -$67.5 ($1,539) % Free-Lunch Classmates -$285 ($1,731) Classmates Mean Age -$25.8 ($1,359)
Classmates Mean Pred. Score (6) -$23.3 ($93.7) Entry Grade KG KG Observations 5,601 6,005 Grade 1 Grade 1 4,270 4,909 All All
10,992 10,992 Note: All specifications control for school fixed effects and class size, as well as student and parent demographics.
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