Developing a Model Pre-K Program: Lessons Learned from the ...
The Moderating Effect of Neighborhood Disadvantage on Preschool Effectiveness: Evidence from Tennessee F. Alvin Pearman, II Peabody Research Institute Vanderbilt University March 2, 2017 SREE 2017 Annual Meeting
Motivation • The experimental evidence for the long-term positive effects of preschool exposure comes from a small set of interventions implemented in confined geographical areas. • States looking to expand access to prekindergarten for large segments of their child population will need to accommodate children living in varying types of neighborhoods • Little is known about whether children’s residential environments matter for how children engage and respond to preschool interventions.
Why might neighborhoods matter for Pre-K effects? What is the counterfactual condition? Neighborhood environments vary in terms of… •Opportunity structures (Aber, Morris, & Raver 2012) •Stress inducements (Hostinar & Gunner 2013; SchaeferMcDaniel, & Ramsey 2010)
•Information networks (Aber, Morris, & Raver 2012) •Behavioral patterns (Van Ewijk & Sleegers 2010) •Environmental contaminants (Zhang et al. 2013)
Neighborhood Disadvantage (see Sampson, Sharkey, & Raudenbush
& 2008; Wodtke 2016)
• Principal component derived from 6 neighborhood characteristics: •Poverty •Unemployment •Welfare receipt •Female-headed households •Education (percent of residents age 25 or older without a high school diploma), •Occupational structure (percent of residents age 25 or older in managerial or professional occupations) Subsequent analyses divide neighborhood disadvantage into quintiles based on the TN distribution of the composite disadvantage index. All variables gathered from 2008-12 ACS.
Research Question Do the effects of attending Pre-K on children’s 3rd grade achievement vary by the amount of disadvantage in children’s home neighborhood at baseline?
Sample Full TNVPK Sample 84% of full sample provided valid street addresses at baseline that could be geocoded (n = 2521). 362 children missing valid TCAP scores in 3rd Grade. Final analytic sample: 2,159.
Analytic Method: 2-Stage Least Squares First stage(s): Regress treatment-on-treated indicator (TOT) and the interaction between TOT and neighborhood disadvantage (ND), respectively, on intent-to-treat indicator (ITT) and an interaction between ITT and ND. Second stage: Predicted values from the first-stage equation(s) are then used in place of the original endogenous measures of TOT and TOT/ND interaction in the second stage equation to predict children’s 3rd grade achievement. The IV estimates mitigate bias and produce consistent estimates of whether the effects of attending Pre-K on children’s 3rd grade achievement vary by neighborhood disadvantage.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Analytic Method: 2-Stage Least Squares First stage equations. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Second stage equation.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Child i’s 3rd grade math or reading score, respectively, standardized to have a mean of 0 and standard deviation of 1.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
The effect of attending Pre-K on children’s achievement if children lived in the least disadvantaged neighborhoods. (This variable is instrumented.)
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
The effect of living in a more disadvantaged neighborhood compared to a less disadvantaged neighborhood on children’s 3rd grade achievement if children did not attend Pre-K.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
The incremental effect of Pre-K associated with living in a more- compared to a less-disadvantaged neighborhood. (This interaction is instrumented).
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Vector of controls variables that include gender, race, English language background, age, immigrant status, cohort, urbanicity, and the percentage of residents who are black and Hispanic, respectively.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Randomization pool fixed effect
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Standard error clustered at neighborhood level
TCAP-Reading
TCAP-Reading
Attending PreK and living in the least disadvantaged neighborhoods in TN produces a strong negative effect on children’s thirdgrade reading achievement.
TCAP-Reading
Neighborhood disadvantage has a depressive effect on children’s achievement in the absence of PreK.
TCAP-Reading
The effect of PreK on children’s 3rd grade reading achievement becomes less negative as neighborhood disadvantage increases.
TCAP-Reading
The effect of attending PreK is over 1 Standard Deviation higher for children living in the most disadvantaged neighborhoods in TN compared to the least disadvantaged.
Results: TCAP-Math
Results: TCAP-Math
Attending PreK and living in the least disadvantaged neighborhoods in TN produces a strong negative effect on children’s thirdgrade math achievement.
Results: TCAP-Math
This study finds mixed evidence that exposure to a disadvantaged neighborhood in the absence of PreK affects children’s 3rd grade math achievement.
Results: TCAP-Math
This study finds limited evidence that the effect of PreK on children’s 3rd grade math achievement varied by neighborhood disadvantage.
What about a continuous measure of neighborhood disadvantage?
What about a continuous measure of neighborhood disadvantage?
What about a continuous measure of neighborhood disadvantage?
In terms of 3rd grade reading achievement, children living in the most disadvantaged neighborhoods benefitted the most from attending Pre-K.
What about a continuous measure of neighborhood disadvantage?
What about a continuous measure of neighborhood disadvantage?
This study finds no evidence that neighborhood disadvantage moderates the effects of Pre-K on math achievement.
How does the TNVPK sample compare to poor children across TN in terms of exposure to disadvantaged neighborhoods?
Returning to the Research Question... Do the effects of attending Pre-K on children’s 3rd grade achievement vary by the amount of disadvantage in the children’s home neighborhood at baseline? Answer: Yes for reading. Mostly no for math.
Conclusions Low-income children living in the least disadvantaged neighborhoods in TN experienced negative effects from Pre-K exposure on 3rd grade math and reading. The effect of attending PreK on low-income children’s third grade reading achievement is over 1 SD higher for children living in the most disadvantaged neighborhoods compared to the least. Fewer highly-disadvantaged neighborhoods were represented in the sample than would otherwise have been expected had the sample been randomly drawn from the population of low-income children in Tennessee who were of preschool age.
Potential Policy Implications • Increase the representation of children from highly-disadvantaged neighborhoods in preschool classrooms. 1. Concentrate Pre-K classrooms in highly-disadvantaged neighborhoods to attract children who would presumably benefit most. 2. Create better access channels for children living in highlydisadvantaged neighborhoods to attend preschool in other neighborhoods. • Targeting advertising & recruitment • Transportation hubs • Enrollment “Caps & Floors”
Thank you.
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Motivation • The experimental evidence for the long-term positive effects of preschool exposure comes from a small set of interventions implemented in confined geographical areas. • States looking to expand access to prekindergarten for large segments of their child population will need to accommodate children living in varying types of neighborhoods • Little is known about whether children’s residential environments matter for how children engage and respond to preschool interventions.
Why might neighborhoods matter for Pre-K effects? What is the counterfactual condition? Neighborhood environments vary in terms of… •Opportunity structures (Aber, Morris, & Raver 2012) •Stress inducements (Hostinar & Gunner 2013; SchaeferMcDaniel, & Ramsey 2010)
•Information networks (Aber, Morris, & Raver 2012) •Behavioral patterns (Van Ewijk & Sleegers 2010) •Environmental contaminants (Zhang et al. 2013)
Neighborhood Disadvantage (see Sampson, Sharkey, & Raudenbush
& 2008; Wodtke 2016)
• Principal component derived from 6 neighborhood characteristics: •Poverty •Unemployment •Welfare receipt •Female-headed households •Education (percent of residents age 25 or older without a high school diploma), •Occupational structure (percent of residents age 25 or older in managerial or professional occupations) Subsequent analyses divide neighborhood disadvantage into quintiles based on the TN distribution of the composite disadvantage index. All variables gathered from 2008-12 ACS.
Research Question Do the effects of attending Pre-K on children’s 3rd grade achievement vary by the amount of disadvantage in children’s home neighborhood at baseline?
Sample Full TNVPK Sample 84% of full sample provided valid street addresses at baseline that could be geocoded (n = 2521). 362 children missing valid TCAP scores in 3rd Grade. Final analytic sample: 2,159.
Analytic Method: 2-Stage Least Squares First stage(s): Regress treatment-on-treated indicator (TOT) and the interaction between TOT and neighborhood disadvantage (ND), respectively, on intent-to-treat indicator (ITT) and an interaction between ITT and ND. Second stage: Predicted values from the first-stage equation(s) are then used in place of the original endogenous measures of TOT and TOT/ND interaction in the second stage equation to predict children’s 3rd grade achievement. The IV estimates mitigate bias and produce consistent estimates of whether the effects of attending Pre-K on children’s 3rd grade achievement vary by neighborhood disadvantage.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Analytic Method: 2-Stage Least Squares First stage equations. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Second stage equation.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Child i’s 3rd grade math or reading score, respectively, standardized to have a mean of 0 and standard deviation of 1.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
The effect of attending Pre-K on children’s achievement if children lived in the least disadvantaged neighborhoods. (This variable is instrumented.)
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
The effect of living in a more disadvantaged neighborhood compared to a less disadvantaged neighborhood on children’s 3rd grade achievement if children did not attend Pre-K.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
The incremental effect of Pre-K associated with living in a more- compared to a less-disadvantaged neighborhood. (This interaction is instrumented).
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Vector of controls variables that include gender, race, English language background, age, immigrant status, cohort, urbanicity, and the percentage of residents who are black and Hispanic, respectively.
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Randomization pool fixed effect
Analytic Method: 2-Stage Least Squares
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑎𝑎: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑏𝑏: 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽1 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 + 𝛽𝛽2 × 𝐼𝐼𝐼𝐼𝐼𝐼𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽3 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2: 𝑦𝑦𝑖𝑖 = 𝛽𝛽0 + 𝛽𝛽̂1 × 𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝛽𝛽2 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 +𝛽𝛽̂3 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖 × 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖 + 𝛽𝛽4 × 𝜃𝜃 + 𝛾𝛾 + 𝜀𝜀𝑖𝑖
Standard error clustered at neighborhood level
TCAP-Reading
TCAP-Reading
Attending PreK and living in the least disadvantaged neighborhoods in TN produces a strong negative effect on children’s thirdgrade reading achievement.
TCAP-Reading
Neighborhood disadvantage has a depressive effect on children’s achievement in the absence of PreK.
TCAP-Reading
The effect of PreK on children’s 3rd grade reading achievement becomes less negative as neighborhood disadvantage increases.
TCAP-Reading
The effect of attending PreK is over 1 Standard Deviation higher for children living in the most disadvantaged neighborhoods in TN compared to the least disadvantaged.
Results: TCAP-Math
Results: TCAP-Math
Attending PreK and living in the least disadvantaged neighborhoods in TN produces a strong negative effect on children’s thirdgrade math achievement.
Results: TCAP-Math
This study finds mixed evidence that exposure to a disadvantaged neighborhood in the absence of PreK affects children’s 3rd grade math achievement.
Results: TCAP-Math
This study finds limited evidence that the effect of PreK on children’s 3rd grade math achievement varied by neighborhood disadvantage.
What about a continuous measure of neighborhood disadvantage?
What about a continuous measure of neighborhood disadvantage?
What about a continuous measure of neighborhood disadvantage?
In terms of 3rd grade reading achievement, children living in the most disadvantaged neighborhoods benefitted the most from attending Pre-K.
What about a continuous measure of neighborhood disadvantage?
What about a continuous measure of neighborhood disadvantage?
This study finds no evidence that neighborhood disadvantage moderates the effects of Pre-K on math achievement.
How does the TNVPK sample compare to poor children across TN in terms of exposure to disadvantaged neighborhoods?
Returning to the Research Question... Do the effects of attending Pre-K on children’s 3rd grade achievement vary by the amount of disadvantage in the children’s home neighborhood at baseline? Answer: Yes for reading. Mostly no for math.
Conclusions Low-income children living in the least disadvantaged neighborhoods in TN experienced negative effects from Pre-K exposure on 3rd grade math and reading. The effect of attending PreK on low-income children’s third grade reading achievement is over 1 SD higher for children living in the most disadvantaged neighborhoods compared to the least. Fewer highly-disadvantaged neighborhoods were represented in the sample than would otherwise have been expected had the sample been randomly drawn from the population of low-income children in Tennessee who were of preschool age.
Potential Policy Implications • Increase the representation of children from highly-disadvantaged neighborhoods in preschool classrooms. 1. Concentrate Pre-K classrooms in highly-disadvantaged neighborhoods to attract children who would presumably benefit most. 2. Create better access channels for children living in highlydisadvantaged neighborhoods to attend preschool in other neighborhoods. • Targeting advertising & recruitment • Transportation hubs • Enrollment “Caps & Floors”
Thank you.
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