Does Universal Preschool Hit the Target?: Program Access and Preschool Impacts

Elizabeth U. Cascio

doi:10.3368/jhr.58.3.0220-10728R1

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Figure 1
Trends in Public Preschool Enrollment Rates and Pre-K Funding: 1968–2015
Notes: Data on public preschool enrollment rates by age are three-year moving averages calculated from the 1968–2016October Current Population Survey School Enrollment supplements (Flood et al. 2015). Head Start enrollment rates divide Head Start enrollments reported by the Head Start Bureau by cohort size estimates based on annual (as of July 1) national age-specific population estimates from the Census Bureau. State funding dates were constructed from program narratives published by the National Institute for Early Education Research (Barnett et al. 2017).
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Figure 2
Pre-K Access and Quality Standards by State: 2005–2006
Source: Data are from Barnett et al. (2006).
Notes: Dot sizes represent the size of the state’s four-year-old population. The quality standards checklist has ten points, one for each of ten program standards: one point for comprehensive early learning standards, four points for teacher training and credentialing requirements (teacher has BA, specialized training in pre-K, assistant teacher has child development associate degree or equivalent, at least 15 hours of in service training annually), two points for staffing ratios (maximum class size no larger than 20, staff-to-child ratio 1:10 or better), two points for comprehensive services (vision, hearing, health, and one support service, at least one meal provided), and one point for a site visit requirement. To qualify as “treated,” a state must have had in 2005–2006 a statewide kindergarten entry cutoff birth date that did not fall in the middle of a month and a pre-K enrollment differential favoring four-year-olds (over three-year-olds) of at least eight percentage points. “Universal” treatment states are ones that met these criteria and had no eligibility requirements beyond age; “targeted” treatment states are ones that met these criteria and had additional eligibility requirements based on family income or other risk factors. (See Online Appendix Table 1.) Comparison states did not surpass the pre-K enrollment threshold to be a treatment state but did have a statewide kindergarten entry cutoff birth date that did not fall in the middle of a month. Not all comparison states are represented in the figure, as some did not have pre-K programs in 2005–2006. (See Online Appendix Table 2.)
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Figure 3
Pre-K Attendance and Test Scores by Age and Program Type
Source: Author’s calculations from the ECLS-B.
Notes: Sample is restricted to respondents with nonmissing values of key variables resident in one of the analysis states at Wave 3 (2005–2006), born within four months after and eight months before that state’s cutoff birth date for kindergarten entry, and assessed during 2005–2006. Panel A corresponds to pre-K attendance in 2005–2006; Panel B corresponds to average standardized reading and math scores in 2005–2006. Subpanel 1 of each panel plots average values of the dependent variable by age relative to the minimum age for kindergarten entry (two-month bins) by state type; see Online Appendix Tables 1 and 2. The dots in Subpanel 2 of each panel represent the coefficients on interactions between a treatment dummy and a series of dummies for age relative to the minimum age for kindergarten entry (two-month bins) from a regression that allows for direct effects of each of these (sets of) variables in addition to month × year of assessment dummies and state fixed effects. The interaction with the dummy for missing eligibility by one to two months is omitted for identification. Capped vertical lines represent 90 percent confidence intervals, with standard errors clustered on state × month of birth.
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Figure 4
Eligibility Effects on Pre-K Attendance and Test Scores, by Program Type and Socioeconomic Status Quintile
Source: Author’s calculations from the ECLS-B.
Notes: Sample is restricted to respondents with non-missing values of key variables resident in one of the analysis states at Wave 3 (2005–2006), born within four months after and eight months before that state’s cutoff birth date for kindergarten entry, and assessed during 2005–2006. Each dot in each panel represents an estimate of θ in Model 1 restricting attention to children in states with universal or targeted programs (in both cases relative to the same group of comparison states) in the designated quintile of the ECLS-B index for socioeconomic status (SES). The SES index is measured contemporaneously with outcomes and is derived from a factor analysis of parental education, parental occupation, and family income. The underlying regression also includes indicators for month × year of assessment and the demographic and background characteristics listed in Table 1, Panel B. The capped vertical lines represent 90 percent confidence intervals, with standard errors clustered on state × month of birth.
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Figure 5
Pre-K Eligibility and Test Scores by Age, Program Type, and Poverty Status
Source: Data are from the ECLS-B.
Notes: Sample is restricted to respondents with non-missing values of key variables resident in one of the analysis states at Wave 3 (2005–2006), born within four months after and eight months before that state’s cutoff birth date for kindergarten entry, and assessed during 2005–2006. The dependent variable in each panel is average standardized reading and math scores during Wave 3, when respondents were four years of age. Panel A corresponds to respondents who were eligible for free or reduced-price lunch in 2005–2006; Panel B corresponds to respondents who were not. Subpanel 1 of each panel plots the average standardized test score by age relative to the minimum age for kindergarten entry (two-month bins) by state type; see Online Appendix Tables 1 and 2. The dots in Subpanel 2 of each panel represent the coefficients on interactions between a treatment dummy and a series of dummies for age relative to the minimum age for kindergarten entry (two-month bins) from a regression that allows for direct effects of each of these (sets of) variables in addition to month × year of assessment dummies and state fixed effects. The interaction with the dummy for missing eligibility by one to two months is omitted for identification. Capped vertical lines represent 90 percent confidence intervals, with standard errors clustered on state × month of birth.

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Table 1

Descriptive Statistics and Balance Tests on Key Variables, by Program Type: Full Sample

	Universal		Targeted		Universal–Targeted
	Ineligible Mean [SD] (1)	DD Coeff. (SE) (2)	Ineligible Mean [SD] (3)	DD Coeff. (SE) (4)	DDD Coeff. (SE) (5)
Panel A: Treatment Variable
Prekindergarten^{^a}	0.052	0.211 (0.047)	0.091	0.114 (0.033)	0.097 (0.048)
Panel B: Background Characteristics
Age in months^{^a}	48.525 [3.160]	−0.099 (0.060)	48.235 [3.316]	−0.093 (0.051)	−0.006 (0.055)
Female	0.463	0.078 (0.046)	0.521	−0.007 (0.044)	0.085 (0.047)
Black non-Hispanic	0.206	0.042 (0.033)	0.201	0.026 (0.029)	0.015 (0.035)
Hispanic	0.196	−0.034 (0.039)	0.255	−0.021 (0.033)	−0.014 (0.036)
Low birth weight	0.074	0.022 (0.014)	0.079	0.015 (0.012)	0.007 (0.014)
Maternal education ≤ HS^{^a}	0.445	0.022 (0.042)	0.468	−0.031 (0.045)	0.053 (0.042)
Both biological parents in HH^{^a}	0.704	−0.052 (0.038)	0.692	0.045 (0.035)	−0.097 (0.041)
Not English at home^{^a}	0.152	−0.010 (0.031)	0.160	−0.008 (0.026)	−0.002 (0.030)
Family income ≤ 185% FPL^{^a}	0.473	−0.092 (0.043)	0.451	−0.064 (0.043)	−0.028 (0.045)
Panel C: p-Value: Joint Test
All background characteristics		0.01		0.17	0.26
Excluding poverty		0.32		0.40	0.27
Observations^{^b}	300	3,400	400	3,950	7,350

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” “Direct Child Assessments,” and “Early Care and Education Providers” (collection at 48 months).
Notes: Odd-numbered columns give means for respondents in treatment states ineligible for pre-K in 2005–2006 [standard deviations for nonbinary variables]. Even-numbered columns give DD coefficients (standard errors) on the interaction between a dummy for being eligible for pre-K in 2005–2006 and a dummy for residing in a treatment state (elig × treat) from a separate regression that also includes dummies for state of residence, month × year of assessment, and month age five relative to the state kindergarten entry cutoff birth date in 2006–2007. See Online Appendix Tables 1 and 2 for lists of universal, targeted, and comparison states. A child is eligible for kindergarten in 2006–2007 if they turned age five in time to start kindergarten in fall 2006, given their date of birth and the kindergarten entry age regulations in effect in 2006–2007 reported by Barnett et al. (2007). Sample is limited to children who turn age five between four months after and eight months before the cutoff date and who were assessed during the 2005–2006 school year. Means and regressions are weighted by longitudinal sampling weights, and standard errors (in parentheses) are clustered on state × month of birth.
↵^aMeasured at preschool age (Wave 3), or in 2005–2006.
↵^bRounded to the nearest 50, per IES guidelines.

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Table 2

Impacts of State-Funded Pre-K on Preschool-Age Test Scores

	Pre-K	Test Score (Average Reading and Math)
	First-Stage (1)	Ineligible Mean (2)	RF (ITT) (3)	IV (TOT) (4)	OLS (5)
Panel A: Universal (N = 3,400)
No additional controls	0.211 (0.047)	−0.183	0.144 (0.081)	0.682 (0.389)	−0.168 (0.057)
With additional controls^{^a}	0.211 (0.047)		0.120 (0.065)	0.569 (0.315)	−0.069 (0.048)
Panel B: Targeted (N = 3,950)
No additional controls	0.114 (0.033)	−0.235	−0.009 (0.069)	−0.076 (0.594)	−0.232 (0.049)
With additional controls^{^a}	0.118 (0.034)		−0.044 (0.060)	−0.373 (0.513)	−0.093 (0.042)
Panel C: p-Value on Universal–Targeted Difference (N = 7,350)
No additional controls	0.045		0.071	0.185	0.227
With additional controls^{^a}	0.057		0.012	0.046	0.609

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” “Direct Child Assessments,” and “Early Care and Education Providers” (collection at 48 months).
Notes: The first-stage and RF (ITT) [reduced-form (intent-to-treat)] columns in Panels A and B give coefficients on the interaction between a dummy for being eligible for kindergarten in 2006–2007 and a dummy for being in a treated state (elig × treat). (See text or Online Appendix Tables 1 and 2 for definition of universal, targeted, and comparison states.) The IV (TOT) [instrumental variables (treatment-on-treated)] and OLS columns in Panels A and B give coefficients on pre-K attendance (prek), in the first case instrumenting with elig × treat using TSLS. All coefficients are from separate regressions that also include dummies for state of residence, month × year of assessment, and month age five relative to the state kindergarten entry cutoff birth date in 2006–2007. Regressions are weighted by longitudinal sampling weights, and standard errors (in parentheses) are clustered on state × month of birth.
↵^aAdditional controls include all demographic and background characteristics in Table 1, Panel B: age at assessment, dummies for female, Hispanic, Black non-Hispanic, low birth weight, not English at home, mom has high school degree or less, both biological parents in household, and low-income.

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Table 3

Impacts of State-Funded Pre-K on Preschool-Age Test Scores, by Poverty Status

	Pre-K	Test Score (Average Reading and Math)
	First-Stage (1)	Ineligible Mean (2)	RF (ITT) (3)	IV (TOT) (4)	OLS (5)
Panel A: Universal
Low-income (N = 1,550)	0.226 (0.062)	−0.572	0.263 (0.107)	1.160 (0.544)	−0.037 (0.055)
Not low-income (N = 1,850)	0.189 (0.047)	0.165	0.007 (0.102)	0.038 (0.530)	−0.079 (0.077)
p-value on difference	0.550		0.118	0.191	0.635
Panel B: Targeted
Low-income (N = 1,750)	0.223 (0.051)	−0.497	−0.018 (0.102)	−0.082 (0.450)	−0.015 (0.051)
Not low-income (N = 2,200)	0.037 (0.037)	−0.018	−0.066 (0.080)	no f.s.	−0.174 (0.079)
p-value on difference	0.002		0.732		0.107
Panel C: p-Value on Universal–Targeted Difference
Low-income	0.996		0.02	0.032	0.728
Not low-income	0.001		0.461	n.a.	0.255

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” “Direct Child Assessments,” and “Early Care and Education Providers” (collection at 48 months).
Notes: A child is considered low-income if their (preschool-age or 2005–2006) family income is at or below 185 percent FPL, the threshold for eligibility for reduced-price lunch and the modal income eligibility criterion for the targeted programs under study. The first-stage and RF (ITT) columns in Panels A and B give coefficients on the interaction between a dummy for being eligible for kindergarten in 2006–2007 and a dummy for being in a treated state (elig × treat). The IV (TOT) and OLS columns in Panels A and B give coefficients on pre-K attendance (prek), in the first case instrumenting with elig × treat using TSLS.All coefficients are from separate regressions that also include dummies for state of residence, month × year of assessment, and month age five relative to the state kindergarten entry cutoff birth date in 2006–2007, and all demographic and background characteristics listed in Table 1, Panel B except the low-income indicator. Regressions are weighted by longitudinal sampling weights, and standard errors (in parentheses) are clustered on state × month of birth. “no f.s.” means “no first-stage.” “n.a.” means “not applicable.”

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Table 4

Sensitivity of Estimated Effects of Pre-K to the Choice of Outcome

	Pre-K	Test Scores
	First-Stage (1)	RF (ITT) (2)	IV (TOT) (3)	OLS (4)
Panel A: Baseline
Universal (N = 3,400)	0.211 (0.047)	0.120 (0.065)	0.569 (0.315)	−0.069 (0.048)
Targeted (N = 3,950)	0.118 (0.034)	−0.044 (0.060)	−0.373 (0.513)	−0.093 (0.042)
p-value on difference	0.057	0.012	0.046	0.609
Panel B: Reading Score Only
Universal (N = 3,400)	0.211 (0.047)	0.135 (0.064)	0.639 (0.328)	−0.036 (0.047)
Targeted (N = 3,950)	0.118 (0.034)	−0.037 (0.067)	−0.314 (0.564)	−0.100 (0.045)
p-value on difference	0.057	0.007	0.054	0.214
Panel C: Math Score Only
Universal (N = 3,400)	0.211 (0.047)	0.106 (0.082)	0.500 (0.378)	−0.102 (0.058)
Targeted (N = 3,950)	0.118 (0.034)	−0.051 (0.067)	−0.432 (0.587)	−0.087 (0.047)
p-value on difference	0.057	0.061	0.102	0.786
Panel D: Mental Score (age 2)^{^a}
Universal (N = 3,350)	0.211 (0.046)	0.005 (0.069)	0.023 (0.326)	−0.062 (0.051)
Targeted (N = 3,950)	0.115 (0.034)	0.035 (0.068)	0.299 (0.610)	−0.081 (0.051)
p-value on difference	0.049	0.613	0.556	0.643
Panel E: = 1 If Parent Reports Not Ready for K (Age 4)
Universal (N = 3,400)	0.207 (0.047)	−0.091 (0.046)	−0.440 (0.231)	0.003 (0.025)
Targeted (N = 3,950)	0.114 (0.033)	−0.036 (0.036)	−0.315 (0.343)	−0.021 (0.023)
p-value on difference	0.053	0.261	0.712	0.327

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” “Direct Child Assessments,” and “Early Care and Education Providers” (collection at 48 months).
Notes: The first-stage and RF (ITT) columns give coefficients on the interaction between a dummy for being eligible for kindergarten in 2006–2007 and a dummy for being in a treatment state (elig × treat). The IV (TOT) and OLS columns give coefficients on pre-K attendance (prek), in the first case instrumenting with elig × treat using TSLS. All coefficients are from separate regressions that also include dummies for state of residence, month × year of assessment, and month age five relative to the state kindergarten entry cutoff birth date in 2006–2007, and all demographic and background characteristics listed in Table 1, Panel B. Regressions are weighted by longitudinal sampling weights, and standard errors (in parentheses) are clustered on state × month of birth.
↵^aAdditional controls include age at assessment and dummies for month × year of assessment in Wave 2 of the ECLS-B, and panel weights incorporate observation in Wave 2.

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Table 5

Sensitivity of Estimated Effects of Pre-K on Test Scores to Estimation Sample

	Pre-K	Test Scores
	First-Stage (1)	RF (ITT) (2)	IV (TOT) (3)	OLS (4)
Panel A: Baseline
Universal (N = 3,400)	0.211 (0.047)	0.120 (0.065)	0.569 (0.315)	−0.069 (0.048)
Targeted (N = 3,950)	0.118 (0.034)	−0.044 (0.060)	−0.373 (0.513)	−0.093 (0.042)
p-value on difference	0.057	0.012	0.046	0.609
Panel B: Sample ±4 Months from Threshold^{^a}
Universal (N = 2,000)	0.226 (0.054)	0.203 (0.075)	0.900 (0.350)	−0.050 (0.071)
Targeted (N = 2,350)	0.129 (0.039)	0.042 (0.068)	0.321 (0.527)	−0.067 (0.056)
p-value on difference	0.091	0.024	0.197	0.808
Panel C: Identification ± 4 Months from Threshold^{^b}
Universal (N = 3,400)	0.218 (0.055)	0.220 (0.074)	1.007 (0.377)	−0.066 (0.047)
Targeted (N = 3,950)	0.143 (0.039)	0.040 (0.070)	0.278 (0.488)	−0.092 (0.042)
p-value on difference	0.191	0.015	0.104	0.587
Panel D: Expanded Sample (+ Middle-of-Month Cutoffs)^{^c}
Universal (N = 3,450)	0.212 (0.045)	0.127 (0.065)	0.600 (0.314)	−0.046 (0.048)
Targeted (N = 4,250)	0.118 (0.032)	−0.020 (0.059)	−0.170 (0.503)	−0.089 (0.040)
p-value on difference	0.042	0.022	0.089	0.379
Panel E: Restricted Sample (Aug. 31/Sept. 1 Cutoffs)^{^d}
Universal (N = 1,800)	0.267 (0.054)	0.150 (0.085)	0.561 (0.311)	−0.086 (0.072)
Targeted (N = 1,850)	0.192 (0.037)	−0.038 (0.076)	−0.201 (0.397)	−0.095 (0.061)
p-value on difference	0.173	0.010	0.023	0.908

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent-Guardian Interviews,” “Direct Child Assessments,” and “Early Care and Education Providers” (collection at 48 months).
Notes: See note to Table 4.
↵^aSample further limited to respondents with birthdays within four months of the cutoff birth date for kindergarten entry in their Wave 3 state of residence.
↵^bInteractions between treat and indicators for birth four to five months and six to seven months after cutoff included.
↵^cSample expanded to include respondents residing in treatment states with middle-of-month cutoffs (targeted: AR, NC; universal: ME) not born in the cutoff birth date month.
↵^dSample limited to treatment and comparison states with Aug. 31 or Sept. 1 cutoffs (Online Appendix Tables 1 and 2).

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Table 6

Impacts on Alternative Care Arrangements, by State Program Type: Low-Income Children

	Pre-K	Alternatives
	First-Stage (1)	Head Start (2)	Other Center-Based Care (3)	Any Formal (2+3) (4)	Informal Nonparental Care (5)	Parental Care (6)	Any Informal (5 + 6) (7)
Panel A: Ineligible Means
Universal	0.08	0.22	0.21	0.43	0.18	0.31	0.49
Targeted	0.11	0.21	0.10	0.32	0.18	0.40	0.57
Panel B: Reduced-Form, Coeff. (SE) on dig × treat_s
Universal (N= 1,550)	0.226 (0.062)	−0.079 (0.070)	−0.022 (0.058)	−0.102 (0.088)	−0.033 (0.047)	−0.092 (0.072)	−0.125 (0.068)
Targeted (N= 1,750)	0.223 (0.051)	−0.082 (0.063)	0.016 (0.051)	−0.066 (0.069)	−0.038 (0.045)	−0.120 (0.059)	−0.158 (0.060)
p-value on diff.	0.966	0.968	0.483	0.711	0.924	0.700	0.647
Panel C: Instrumental Variables, Coeff. (SE) on prek_is
Universal (N= 1,550)	n.a.	−0.349 (0.274)	−0.099 (0.242)	−0.448 (0.317)	−0.146 (0.203)	−0.406 (0.327)	−0.552 (0.317)
Targeted (N= 1,750)	n.a.	−0.368 (0.244)	0.073 (0.227)	−0.295 (0.273)	−0.168 (0.196)	−0.537 (0.268)	−0.705 (0.273)
p-value on diff.	n.a.	0.948	0.459	0.660	0.914	0.704	0.660

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” “Direct Child Assessments,” and “Early Care and Education Providers” (collection at 48 months).
Notes: A child is considered low-income if their (preschool-age or 2005–2006) family income is at or below 185 percent FPL, the threshold for eligibility for reduced-price lunch and the modal income eligibility criterion for the targeted programs under study. RF coefficients in Panel B are on the interaction between a dummy for being eligible for kindergarten in 2006–2007 and a dummy for being in a heated state (elig × treat”). IV coefficients in Panel C are on pre-K attendance (prék), estimated by instrumenting with elig × treat using TSLS. All coefficients are from separate regressions that also include dummies for state of residence, month × year of assessment, and month age five relative to the state kindergarten entry cutoff birth date in 2006–2007, and all demographic and background characteristics listed in Table 1, Panel B except the low-income indicator. Regressions are weighted by longitudinal sampling weights, and standard errors (in parentheses) are clustered on state × month of birth, “n.a.” means “not applicable.”

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Table 7

Robustness of the Universal-Targeted Difference in Age Four Test Estimates to Adjusting for Other Sources of State Heterogeneity

	Full Sample			Low-Income
	Test Scores		Characteristic	Test Scores		Characteristic
	RF (ITT) (1)	IV (TOT) (2)	RF (3)	RF (ITT) (4)	IV (TOT) (5)	RF (6)
Baseline	0.164 (0.065)	0.942 (0.473)	n.a.	0.281 (0.120)	1.241 (0.580)	n.a.
Panel A: Heterogeneity by Class Size Requirements
Class size standards	0.135 (0.071)	1.154 (0.521)	0.125 (0.067)	0.231 (0.114)	1.196 (0.590)	0.214 (0.108)
Panel B: Heterogeneity by Individual Background Characteristics
Female	0.162 (0.065)	1.090 (0.498)	0.088 (0.063)	0.279 (0.120)	1.235 (0.576)	0.062 (0.095)
Black non-Hispanic	0.163 (0.065)	0.994 (0.485)	0.121 (0.091)	0.282 (0.121)	1.248 (0.576)	0.200 (0.114)
Hispanic	0.154 (0.066)	0.907 (0.530)	0.023 (0.086)	0.267 (0.120)	1.190 (0.600)	−0.058 (0.113)
Low birth weight	0.164 (0.065)	0.952 (0.479)	0.022 (0.083)	0.281 (0.120)	1.243 (0.578)	0.102 (0.097)
Maternal education ≤ HS	0.160 (0.065)	1.313 (0.662)	0.172 (0.074)	0.277 (0.121)	1.233 (0.567)	0.200 (0.103)
Both biological parents in HH	0.157 (0.065)	0.674 (0.449)	−0.143 (0.072)	0.276 (0.119)	1.228 (0.579)	−0.059 (0.096)
Not English at home	0.165 (0.065)	1.010 (0.493)	0.119 (0.089)	0.282 (0.120)	1.255 (0.577)	0.111 (0.114)
Family income ≤ 185% FPL	0.168 (0.067)	1.314 (0.691)	0.116 (0.072)	n.a.	n.a.	n.a.
All characteristics	0.143 (0.066)	1.104 (0.703)	n.s.	0.256 (0.119)	1.198 (0.598)	n.s.

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” “Direct Child Assessments,” and “Early Care and Education Providers” (collection at 48 months).
Notes: A child is considered low-income if their (preschool-age or 2005–2006) family income is at or below 185 percent FPL. RF (ITT) columns give the difference in RF (ITT) coefficients on elig × treat between universal and targeted states. IV (TOT) columns give the difference in IV (TOT) coefficients on prek (instrumented with elig × treat using TSLS) between universal and targeted states. The RF column shows the coefficient on elig× treat × characteristic from the same model that produced the RF (ITT) coefficients. All regressions include dummies for state of residence, month × year of assessment, and month age five relative to the state kindergarten entry cutoff birth date in 2006–2007, and all demographic and background characteristics listed in Table 1, Panel B (except the low-income indicator in Columns 4–6), with separate control coefficients for the universal and targeted estimation samples. Regressions are weighted by longitudinal sampling weights, and standard errors (in parentheses) are clustered on state ×month of birth, “n.a.” means “not applicable.” “n.s.” means “not shown.”

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Table 8

Impacts of Universal Public Kindergarten on Kindergarten Age Test Scores, Overall and by Poverty Status

	Public K	Test Score (Average Reading and Math)
	First-Stage (1)	RF (ITT) (2)	IV (TOT) (3)	OLS (4)
Panel A: Full Sample (N = 2,400)
All states	0.657 (0.036)	0.376 (0.084)	0.573 (0.132)	0.250 (0.064)
Panel B: Low-Income (N = 1,050)
All states	0.778 (0.050)	0.440 (0.144)	0.566 (0.182)	0.458 (0.107)
Panel C: Not Low-Income (N = 1,300)
All states	0.557 (0.049)	0.332 (0.095)	0.597 (0.180)	0.110 (0.073)

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort(ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” (collection at 48 months), “Direct Child Assessments,” “Early Care and Education Providers,” and “School Questionnaires” (collection at kindergarten entry).
Notes: A child is considered low-income if their (preschool-age or 2005–2006) family income is at or below 185 percent FPL, the threshold for eligibility for reduced-price lunch. The first-stage and RF (ITT) columns in Panels A and B give coefficients on a dummy for being eligible for kindergarten in 2006–2007 (elig). The IV (TOT) and OLS columns in Panels A and B give coefficients on public kindergarten attendance, in the first case instrumenting with elig using TSLS. All coefficients are from separate regressions that also include as controls dummies for state of (Wave 4) residence and month × year of (Wave 4) assessment, a linear term in month age five relative to the state kindergarten entry cutoff birth date in 2006–2007, an interaction between that linear term and elig, and all demographic and background characteristics listed in Table 1, Panel B (except the low-income dummy in Panels B and C). Regressions are weighted by longitudinal sampling weights, and standard errors (in parentheses) are clustered on state × month of birth. Sample is limited to the subset of the original estimation sample born within four months after and four months before the minimum kindergarten entry age in their Wave 4 state of residence.

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Table 9

Cost-Benefit Analysis under Alternative Assumptions

	Universal K (1)	Uni. Pre-K (2)	Tar. Pre-K (3)	p: Uni. = Tar. (4)
Panel A: Benefit-to-Cost
1. Program outlays = per-pupil K-12 spending
Cost = program outlays	1.98 (0.45)	1.39 (0.77)	−0.18 (1.03)	0.16
	[0.03]	[0.61]	[0.25]
Cost = net program outlays	2.96 (0.68)	1.85 (1.02)	−0.24 (1.32)	0.15
	[0.00]	[0.41]	[0.35]
2. Program outlays = p.p. Head Start spending
Cost = program outlays	n.a.	2.17 (1.20)	−0.27 (1.50)	0.14
		[0.33]	[0.40]
Cost = net program outlays	n.a.	3.52 (1.94)	−0.40 (2.20)	0.12
		[0.20]	[0.52]
Panel B: Marginal Value of Public Funds (MVPF)
1. Program outlays = per-pupil K-12 spending	3.94 (1.63)	1.96 (1.39)	−0.24 (0.99)	0.14
	[0.07]	[0.49]	[0.21]
2. Program outlays = p.p. Head Start spending	n.a.	4.27 (4.19)	−0.39 (1.58)	0.25
		[0.43]	[0.38]

Source: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Birth Cohort (ECLS-B) of children born in calendar year 2001, “Children’s Birth Certificates” (collection at nine months), “Parent–Guardian Interviews,” (collection at 48 months), “Direct Child Assessments,” “Early Care and Education Providers,” and “School Questionnaires” (collection at kindergarten entry).
Notes: Benefit-to-cost ratios and the MVPF calculated under two assumptions: per-pupil program outlays are equal to per-pupil K–12 spending (an upper bound for pre-K programs) and per-pupil program outlays are to per-pupil Head Start spending. For the benefit-to-cost ratio, benefits are calculated by multiplying the preferred IVestimates of the per-pupil attendance impact on test scores (with additional controls, low-income subsample in the case of targeted pre-K) by the predicted effect of a one standard deviation increase in early life test scores on lifetime earnings; net costs subtract fiscal savings from substitution from Head Start and from other private center-based care. For the MVPF, the beneficiary’s marginal willingness to pay sums predicted earnings impacts net-of-taxes and the transfer to parents from substitution from other private center-based care; net government costs subtract the fiscal externalities from substitution from Head Start and predicted tax revenues from per-pupil program outlays. Throughout, I assume a one standard deviation increase in test scores yields a 10 percent increase in earnings, that targeted pre-K attendees have lifetime earnings approximately 80 percent of those for the average child, and that the PDVof lifetime earnings at age 12 is on average $522,000 (in 2010 dollars, from Chetty et al., 2011). I also assume a discount rate of 3 percent to calculate PDVs of lifetime earnings at age five (Column 1) and age four (Columns 2–3), a tax rate of 20 percent, and a per-pupil annual price of private center-based care equal to approximately $5,000, based on Laughlin (2013) calculations from the Survey of Income and Program Participation. Per-pupil K–12 and Head Start spending is from Barnett et al. (2006) and corresponds to the 2005–2006 for the relevant states. Standard errors (in parentheses) are calculated using the delta method; p-values in brackets test of whether the ratio is equal to one.