Experimental Design
Our primary specification estimates the impact of the offer to enroll in Elevating Families or intention-to-treat (ITT) effects of the program on outcomes. The basic specification is
yi = βTreatmenti + γyi0 + αs(i) + εi (1)
where yi is an outcome for enrolled participant i, Treatmenti indicates whether participant i was randomly assigned to the treatment group, yi0 is the outcome of participant i at baseline, and αs(i) are strata fixed effects (i.e., randomization-pair indicators). Within each randomization block, we plan to randomize between pairs of parents that are sequentially matched on employment status, reported income, months worked in the past 12 months, and household income at baseline. The coefficient of interest – β – estimates the average difference in outcomes between treatment and control groups, controlling for baseline outcome levels. This is our preferred specification provided that treatment and control groups do not meaningfully differ (by chance) in observable baseline characteristics.
We will also estimate treatment effects conditional on control vector Xi′ to account for any sampling variation in the composition of treatment and control groups:
yi =βTreatmenti +Xi′δ+γyi0 +αs(i) +εi (2)
Xi′ includes household-level controls that will be selected from the following variables collected in the baseline survey: gender, educational attainment, age, race, ethnicity, home language, parental status, marital status, disability status, employment status, employment history, household income, individual earnings, individual weekly hours worked, and felony arrest history. As described in Chetty et al. (2018), we will select baseline covariates using “the state-of-art approach to penalize overfitting such as LASSO (at present) or the preferred machine learning approach for covariate selection available at the time the analysis is done”.
In addition to the reduced-form estimates obtained by Equations 1 and 2, we are also interested in estimating the causal impact of the program on those who received it, or treatment-on-treated (TOT) effects. To this end, we will instrument for different measures of program take-up using treatment status. Using 2SLS, we will estimate the system:
yi = βDi + γy0i + X′iδ + δs(i) + ϵi (3)
Di = πTreatmenti + ηy0i + X′iν + ζs(i) + υi (4)
where Di is a measure of program enrollment and/or engagement. These exact engagement measure will depend on the data that are collected by CCNN. Similar to Engle et al. (2022), we would ideally measure enrollment as the participant having completed a bridge assessment and set at least one goal with their mentor. Similarly, engagement could be measured as the fraction of months the participant was marked as “actively engaged” throughout the two-year program period. Under reasonable assumptions, β^Di captures the causal impact of engagement with the program on outcome yi. Note that this parameter equals the intent-to-treat parameter (β^ITT ) divided by the regression-adjusted take-up rate (π).
Citations and Footnotes:
Engle, L., Katz, L., & Tebes, J. (2022). Pre-Analysis Plan for “Supporting Pathways Out of Poverty: A Randomized Evaluation of AMP Up Boston”
Chetty, R., S. DeLuca, L. F. Katz, and C. Palmer (2018). Creating moves to opportunity in seattle and king county randomized controlled trial pre-analysis plan.
This approach relies on the assumption that there was no average effect of being offered program enrollment on those who did not take up the program and that the control group was not affected by losing the lottery.