Empirical Application

The Pioneer Schools Program (PSP): Education Reform in Morocco

Study Design Overview

Our empirical strategy uses a matched-pair difference-in-differences (DiD) design to estimate the intent-to-treat effect of the Pioneer Schools Program (PSP).

Conceptually:

  1. Build a credible school-level counterfactual with matching.
  2. Track baseline-to-endline changes in PSP and comparison schools.
  3. Estimate treatment effects from within-pair differences over time.

This design was implemented on two program waves (Cohort 1 and Cohort 2), with school pairs formed before impact estimation.

How We Constructed Matched School Pairs

Step 1: Build the school-level candidate database

We start from an administrative school-level dataset covering public primary schools (8,034 schools), with a high-dimensional set of candidate predictors (248 variables).

Step 2: Use post-double-selection LASSO (PDSLASSO) for variable selection

To avoid arbitrary manual covariate selection, we run two LASSO models at the school level:

  1. Outcome-selection equation:
  • Baseline outcome as dependent variable.
  • All candidate school predictors as controls.
  1. Treatment-selection equation:
  • PSP treatment indicator as dependent variable.
  • Same set of candidate predictors as controls.

The final matching covariate set is the union of variables selected by these two LASSO models. In our implementation, this procedure selected 16 variables from the original 248 candidates.

Step 3: Match schools using calibrated Mahalanobis distance

Using the LASSO-selected variables, we match non-PSP schools to PSP schools with an iterative, calibrated Mahalanobis-distance procedure.

The calibration loop:

  1. Run matching with a candidate caliper.
  2. Check post-match diagnostics:
  • Common support.
  • Covariate balance (e.g., standardized differences).
  • Distributional similarity between treated and comparison schools.
  1. Tighten calipers iteratively (descending sequence) until acceptable balance is achieved.

This produced matched school pairs that were closer and more comparable than the initial uncalibrated match attempts.

Difference-in-Differences Estimation on Matched Pairs

After pair formation, treatment effects are estimated with a student-level matched-pair DiD specification.

Estimating Equation (paper notation)

Using paper notation, the regression is:

\[ Y_{igsjt} = \beta\,(TREAT_{sj}\times POST_t) + \gamma\,(X_{igsj}\times POST_t) + \phi\,(\zeta_j\times \vartheta_g\times POST_t) + \alpha_{igsj} + \varepsilon_{igsjt} \]

where:

  • \(Y_{igsjt}\) is outcome \(Y\) for student \(i\), grade \(g\), school \(s\), matched pair \(j\), period \(t\).
  • \(TREAT_{sj}\) indicates PSP assignment for school \(s\) in pair \(j\).
  • \(POST_t\) indicates endline period.
  • \(X_{igsj}\) are baseline student and school controls.
  • \(\zeta_j\times\vartheta_g\times POST_t\) are grade-by-matched-pair-by-post interactions.
  • \(\beta\) is the intent-to-treat effect of PSP.

Standard errors are clustered at the matched-pair level, consistent with the pairing-based assignment structure.

Why this helps identification

  • Matching improves pre-treatment comparability (selection on observables).
  • DiD differences out pair-invariant unobservables and common shocks.
  • Pair-by-grade-by-post structure allows flexible local trends within matched pair contexts.

LASSO Inside the DiD Specification

The DiD model includes many candidate interaction controls. To avoid overfitting while keeping relevant heterogeneity, we implement post-double-selection LASSO in the analysis stage.

Paper-aligned implementation steps:

  1. For each student, compute baseline-to-endline test score change.
  2. Residualize this change by subtracting the comparison group grade-by-matched-pair mean.
  3. Run PDSLASSO on the residualized outcome with the candidate control set.
  4. Include selected \(X_{igsj}\times POST_t\) interactions in the final DiD equation.

This mirrors the paper’s approach: machine-learning selection is used to discipline a high-dimensional control space, while treatment effects are estimated in the final matched-pair DiD regression.

Controls Used in Selection

The candidate set includes baseline student-level variables (e.g., demographics, baseline score measures, social safety net status) and baseline school-level variables (e.g., school average test scores, region, average class size, student-teacher ratio), plus interactions as specified in the paper’s high-dimensional design.

Replication Workflow

For readers reproducing the PSP approach:

  1. Prepare baseline school-level data and treatment flag.
  2. Run PDSLASSO (outcome model + treatment model).
  3. Take union of selected controls.
  4. Match schools via Mahalanobis distance with iterative caliper tuning.
  5. Validate common support and balance before analysis.
  6. Estimate the matched-pair DiD equation in paper notation with pair-level clustered standard errors.
  7. Use post-double-selection LASSO to select high-dimensional interaction controls for \(X_{igsj}\times POST_t\).
  8. Report pair-clustered inference and adjusted p-values as in the paper’s reporting framework.

Contribution

The contribution of this design is not a single estimator, but a design pipeline:

  • machine-learning-assisted covariate screening,
  • transparent pair construction with balance diagnostics,
  • and DiD estimation within matched school comparisons.

This makes the counterfactual more credible than either naive DiD without pairing or naive matching without time differencing.

References