Public Subsidies to Private Schools Do Make a Difference for Achievement in Mathematics: Longitudinal Evidence from Canada
Bibliographic record
Abstract
Selection into private schools is the principal cause of bias when estimating the effect of private schooling on academic achievement. By exploiting the generous public subsidizing of private high schools in the province of Québec, the second most populous province in Canada, we identify the causal impact of attendance in a private high school on achievement in mathematics. Because the supply of highly subsidized spaces is much higher at the high school level than at the grade school level, 60% of transitions from the public to private sector occur at the end of grade school, we assume that these transitions are exogenous with respect to changes in transitory unobserved variables affecting math scores conditional on variables such as changes in income and child fixed effects. Using data from Statistics Canada’s National Longitudinal Survey on Children and Youth (NLSCY), we estimate the effect of attending a private high school on the percentile rank and a standardized math test score with different models (child fixed-effect, random-effect and a pooled OLS) and restricted samples to control for the degree of selection. The results, interpreted as a treatment on the treated effect show that the effect of changing schools, from a public grade school to a private high school, increases the percentile rank of the math score between 5 and 10 points and by between .13 to .35 of a standard deviation depending on the specifications and samples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.008 |
| Science and technology studies | 0.004 | 0.002 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".