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Cognitive and non-cognitive efficiency gaps between private and public schools in the Latin America region-a hybrid DEA and machine learning approach based on PISA 2022

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Private schools in Latin America turn resources into learning more efficiently than public schools, the paper estimates.

desk verdict The first post-pandemic regional private-public school efficiency benchmark for LAC, but the headline 0.10 gap is not identified as stated because the DEA frontiers are estimated separately by school type and never compared on a common technology. read the letter →

arxiv 2509.25353 v2 pith:FJQVDEW2 submitted 2025-09-29 econ.GN q-fin.EC

Marcos Delprato This is my paper · ORCID
classification econ.GNq-fin.EC
keywords schoolefficiencyprivateandpublicschoolsdataenvelopmentanalysisinterpretablemachinelearningSHAPLatinAmericaPISA2022
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to measure whether private secondary schools in Latin America use their resources more efficiently than public schools, and to identify what pushes a school toward the top of the efficiency ladder. Using PISA 2022 data on 2,034 schools in nine countries, it estimates output-oriented Data Envelopment Analysis frontiers separately for each school type, for both cognitive outcomes (math, reading, science) and a non-cognitive well-being index. The headline result is a bias-corrected cognitive efficiency score of 0.865 for private schools versus 0.768 for public schools—a gap of nearly 0.10—and a non-cognitive gap of 0.045 (0.685 versus 0.640), with tighter dispersion among private schools. The second stage uses gradient-boosted trees and SHAP values to rank 42 possible drivers of high efficiency. A sympathetic reader would care because, if the gap is real, public schools could raise cognitive output by roughly a quarter without additional inputs, and the paper points to concrete levers such as school climate, repetition, and pandemic-era homework barriers.

What carries the argument

The carrying machinery is output-oriented Data Envelopment Analysis (DEA) under variable returns to scale—a nonparametric linear-programming method that builds a best-practice frontier from the observed schools and scores each school by how far it falls short of the maximum output attainable from its inputs—run separately for private and public schools and for cognitive and non-cognitive outputs, with 2,000-repetition bootstrap bias correction. Efficiency is then converted into a binary indicator (above or below the regional mean) and modelled with gradient-boosted trees, an ensemble of decision trees that captures nonlinearities and interactions, with SHAP values used to rank and sign the contribution of 42 student-, school-, and COVID-related covariates. The DEA scores carry the efficiency claim; the SHAP analysis carries the attribution of which factors separate high- from low-efficiency schools.

What would settle it

Re-estimate the DEA with all schools pooled into one frontier and move average family SES from the input set to a non-discretionary environment variable. If the bias-corrected cognitive efficiency gap between private and public schools drops below roughly 0.05 or reverses, the reported gap is an artifact of the modeling choice; if it stays near 0.10, the paper's central claim is supported.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is a private-school efficiency advantage that holds across the whole distribution, not just at the mean. Bias-corrected technical efficiency for cognitive outputs is 0.865 for private schools and 0.768 for public schools; for the non-cognitive output it is 0.685 versus 0.640. Stochastic dominance tests accept first- and second-order dominance of private over public efficiency profiles, meaning an education planner who values higher efficiency and lower between-school dispersion would prefer the private-school profile. Within the region the cognitive gap is positive in every country, ranging from about 0.08 to 0.11, while non-cognitive gaps are positive in all nine countries though not statistically significant in four. The interpretable-machine-learning stage shows that high-efficiency private schools are characterized by more books and computers at home, little student paid work, and high school autonomy, while low-efficiency public schools are marked by poor climate, high repetition and truancy, intense paid work, few books, and COVID-era homework barriers. The paper also reports a positive correlation between cognitive and non-cognitive efficiency that is stronger for public schools.

Load-bearing premise

The load-bearing premise is that a school's average family wealth is an input the school can control and that private and public schools each have their own production technology; if either premise fails, the estimated efficiency gap is a modeling artifact.

Editorial extensions

If this is right

  • Public schools' average cognitive efficiency of 0.768 implies they could increase learning outcomes by about 23 percent while holding inputs constant, if the frontier estimate is correct.
  • Because private schools also dominate in non-cognitive efficiency by 0.045, the private advantage is not confined to test scores; it extends to the well-being/soft-skills output measured in PISA.
  • Lower dispersion in private-school efficiency (IQR 0.083 versus 0.117 for cognitive outcomes) means the private advantage is not driven by a few outliers; the whole distribution is shifted and compressed.
  • The SHAP ranking suggests different policy levers for the two sectors: in private schools the high-efficiency profile is tied to home educational resources and autonomy, while in public schools the low-efficiency profile is tied to repetition, truancy, paid work, and poor climate.
  • The positive correlation between cognitive and non-cognitive efficiency, stronger for public schools, implies that policies improving soft skills could also help close the cognitive efficiency gap.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's separate-frontier design leaves open whether a single pooled technology would shrink the 0.10 cognitive gap; testing that specification directly would show how much of the gap is genuine production efficiency rather than sector-specific technology.
  • Because the PISA soft-skills score is a school average over self-reported personality domains, the non-cognitive gap may reflect reporting or composition; disaggregating the index by domain would test whether the private advantage is uniform across traits like empathy, perseverance, and emotional control.
  • The cross-sectional design cannot establish that autonomy, books, or homework support cause efficiency; a pilot that transfers the high-efficiency private-school profile to public schools and tracks cognitive and non-cognitive efficiency would be the natural test of the paper's policy story.
  • Future waves of PISA or a value-added panel of schools could separate the persistent efficiency gap from selection into private schooling, since the current data contain only one cross-section.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. Using PISA 2022 data on 2,034 schools in nine Latin American countries, the paper estimates school-level technical efficiency separately for private and public schools, with cognitive outputs (math, reading, science) and a non-cognitive output (a soft-skills composite), via output-oriented VRS Data Envelopment Analysis with bootstrap bias correction. It reports a mean bias-corrected efficiency gap of about 0.10 in cognitive efficiency (0.865 vs. 0.768) and 0.045 in non-cognitive efficiency (0.685 vs. 0.640), with lower dispersion among private schools, and interprets these as private-sector technical superiority. In a second stage, the paper dichotomizes efficiency at the regional mean and uses gradient-boosted trees with SHAP values to rank 42 school and student covariates associated with high efficiency, profiling the highest-efficiency private school and the lowest-efficiency public school. The paper claims to be the first post-pandemic regional LAC study of school-type efficiency gaps and to extend DEA-plus-interpretable-ML to cross-country education efficiency.

Significance. If the headline gap withstands specification scrutiny, the paper would supply timely regional evidence on private-public school efficiency after the pandemic, and its combination of DEA with SHAP-based second-stage explanations is a useful addition to the emerging DEA-ML literature. The analysis is careful in several respects that deserve credit: bias-corrected radial efficiency with bootstrap confidence intervals, a robustness check for outliers (Appendix C), stochastic dominance comparisons, and detailed tables reporting country-level efficiency scores. The central empirical claim, however, rests on two untested specification choices: separate production frontiers for private and public schools, and the treatment of average family SES as a school input. Because the estimated gap is defined as the difference between each sector's distance to its own frontier, it is not yet established that the gap reflects a real technological or managerial advantage rather than a mechanical consequence of sample size, frontier estimation noise, or the SES-as-input assumption.

major comments (4)
  1. [Section 4.1 and Section 5.1] The main private-public efficiency gap is computed from four separate VRS DEA frontiers, one per school type and outcome, without any test of whether private and public schools operate under a common technology. With separate frontiers, the reported gap of 0.10 (cognitive) and 0.045 (non-cognitive) measures each sector's average distance to its own estimated best practice; under a common technology, different sample sizes (1,584 public vs. 486 private) and finite-sample noise can alone produce a mechanical gap, while if the technologies genuinely differ, the scalar gap does not identify which technology is more productive. Please add a pooled-frontier re-estimation or a formal test of technology equality (for example, a bootstrap test of the equality of the two frontiers, or a meta-frontier analysis with a technology gap ratio) and report whether the gap persists in that specification.
  2. [Section 3.1 and Table 1] Average family SES is included as one of the four DEA inputs, and the summary statistics show a 1.12 difference in SES between private and public schools. If SES is an environmental or non-discretionary factor rather than a school-controlled resource, then treating it as a regular input can bias the efficiency scores in favor of high-SES private schools, because the frontier can 'explain' higher outputs by the more favorable student mix. The paper should report a robustness analysis that either omits SES from the input set or treats it as an external/non-discretionary variable; without this, the headline 0.10 cognitive gap remains dependent on a contestable modeling assumption.
  3. [Section 3 and Tables 3-4] There is a numerical inconsistency in the reported sample sizes. Section 3 states that the working sample contains 2,034 schools, of which 1,548 are public and 486 are private, but Tables 3 and 4 report N = 1,584 public schools and the country-level public-school rows sum to 1,584, giving a total of 2,070. Please reconcile these numbers and clarify which sample is used for the DEA estimation and which is used for the second-stage analysis; if 36 additional schools enter the DEA sample, the estimates and standard errors would need to be re-checked.
  4. [Section 5.1.1 and Table 5] The stochastic dominance tests are reported with p-values of 1.0000 and 0.9450 for the first-order tests, and the null hypothesis is written as 'bθ_private ⪯_s bθ_public'. As written, acceptance of this null does not transparently establish that private schools dominate public schools; the notation is ambiguous about whether '⪯' orders the CDFs (so private CDF below public CDF means private dominance) or orders the efficiency levels. Please restate the null in terms of the cumulative distribution functions and explain whether a failure to reject in these tests is being treated as affirmative evidence in favor of private dominance, since failure to reject a null is not normally evidence for it.
minor comments (5)
  1. [Title, Abstract, Introduction] There are several typographical errors, including 'INLATIN AMERICA—ACOMBINEDDEAAND', '˘interpreable' in Section 4.2, and 'loosing around lost around 0.9-1.1 years' in the Introduction; these should be corrected throughout.
  2. [Section 4.1 and Note 5] The VRS-versus-CRS tests are said to be 'available from the author upon request'; for a central modeling choice, the tests and their p-values should be reported in the appendix or a table rather than left to request.
  3. [Section 4.2 and Figure 3] The binary dependent variable is defined as efficiency above the regional mean, separately within each school type, so the second-stage results describe predictors of being above the sector-specific average, not predictors of reaching an absolute efficiency standard. This should be stated more explicitly in the text, and the SHAP-based comparisons between private and public schools should be interpreted accordingly.
  4. [Appendix C and Table C1] The outlier robustness check is a welcome addition, but the country-level proportional differences in Table C1 are large in some cases (e.g., -9.53% for Dominican Republic non-cognitive private efficiency and +3.01% for Chile), so the statement that the estimates 'are not as different' should be softened or the country-level outlier sensitivity should be discussed directly.
  5. [Tables 3 and 4 notes] Table 3 notes state that all private-public differences are statistically significant at 10%, while the text and Figure 1c report that four non-cognitive country gaps are not statistically significant; the table notes should be aligned with the reported significance pattern.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: DEA scores are computed from observed inputs/outputs; the gap is a descriptive comparison, not a fitted prediction.

full rationale

The core derivation is self-contained. DEA scores are computed by solving the output-oriented VRS linear program (Eq. 2) using observed school-level outputs (PISA cognitive scores; soft-skills index) and inputs (family SES, school infrastructure indices, inverse student-teacher ratio) for each school type separately. The headline private-public gap is the difference of the sample means of these bias-corrected nonparametric scores (Tables 3 and 4); no equation defines a parameter in terms of the gap and then reuses that parameter to produce the gap. The second-stage ML models use a binary transformation of the same DEA scores (equal to one if the score exceeds the regional mean for that school type) as the dependent variable and 42 covariates as predictors. This is a standard two-stage descriptive design: the SHAP attributions explain the fitted model, but the fitted model is not used to construct the DEA scores, nor is any DEA input parameter fitted to the gap. The paper's self-citations (Delprato and Antequera 2021a, 2021b, 2025; Delprato 2025) are prior published empirical studies cited for context and comparison; no load-bearing uniqueness theorem or ansatz is imported from them. The separate-frontier comparison may be sensitive to the assumption that private and public schools have distinct technologies and that family SES is a controllable input, but that is a modelling and identification concern, not a circular reduction: the comparison does not define its conclusion into its inputs. I therefore find no significant circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the DEA input-output specification, the separate-frontier assumption, and the factor-analytic construction of the non-cognitive outcome. No entirely new theoretical entities are postulated; the free parameters listed are modeling and tuning choices in the empirical pipeline.

free parameters (4)
  • Outlier detection order-alpha values = 95.33 (public, cognitive), 75.98 (private, cognitive), 89.39 (public, non-cognitive), 21.77 (private, non-cognitive)
    Used in Appendix C to identify super-efficient schools; the alpha values are chosen from discontinuity points in the data and affect the robustness comparison, not the main estimates.
  • GBT hyperparameters per model = e.g., cognitive private: estimators=100, subsample=0.7, depth=5, learning rate=0.1; see Table A1 for all four models
    Selected by grid search with 5-fold cross-validation; these parameters shape the SHAP importance rankings in Figures 3 and 4.
  • Regional-mean efficiency threshold = sample mean of the corresponding DEA efficiency distribution (not reported numerically)
    Defines the binary dependent variable in the second-stage ML; alternative thresholds (e.g., terciles) could alter the driver rankings.
  • Non-cognitive factor loadings
    The non-cognitive output is built by factor analysis of seven personality domains (Note 3); loadings are estimated from the data but not reported, and they are not free parameters in the sense of fitting the target result, but they do affect the measurement of the non-cognitive outcome.
assumptions (5)
  • standard math Education production technology has convexity, free disposability, and variable returns to scale (VRS).
    DEA frontier estimation relies on these axioms; VRS was tested and accepted against CRS, but the test results are not shown (Section 4.1, Eq. 2).
  • domain assumption School-level averages of student characteristics adequately represent the school's production inputs and outputs.
    The analysis aggregates student data to school-level means (Section 3), implicitly assuming that within-school distribution and interactions do not affect efficiency measurement.
  • domain assumption Private and public schools operate under different production frontiers.
    Separate DEA models are estimated by school type (Section 4.1); no statistical test that the technologies differ is reported, yet the efficiency gap is interpreted as a between-type comparison.
  • domain assumption Family SES and school infrastructure are legitimate DEA inputs, not environmental factors.
    The model treats average family wealth and infrastructure as inputs that schools transform into outputs (Section 3.1, Table 1); if SES is an exogenous environmental variable, the efficiency scores are biased measures.
  • domain assumption PISA 2022 school and student samples are representative within each country and measurement error in the constructed indices is negligible.
    The analysis uses PISA data directly; no sampling weights are mentioned in the DEA or ML stages, and no correction for measurement error in school averages or factor scores is discussed (Section 3).

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Pith. "Pith review of Cognitive and non-cognitive efficiency gaps between private and public schools in the Latin America region-a hybrid DEA and machine learning approach based on PISA 2022." pith.science (2026). https://pith.science/paper/FJQVDEW2

@misc{pith2026250925353,
  author       = {Pith},
  title        = {Pith review of: Cognitive and non-cognitive efficiency gaps between private and public schools in the Latin America region-a hybrid DEA and machine learning approach based on PISA 2022},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FJQVDEW2}},
  note         = {Machine review of arXiv:2509.25353}
}
read the original abstract

Latin America's education systems are fragmented and segregated, with substantial differences by school type. The concept of school efficiency (the ability of school to produce the maximum level of outputs given available resources) is policy relevant due to scarcity of resources in the region. Knowing whether private and public schools are making an efficient use of resources --and which are the leading drivers of efficiency-- is critical, even more so after the learning crisis brought by the COVID-19 pandemic. In this paper, relying on data of 2,034 schools and nine Latin American countries from PISA 2022, I offer new evidence on school efficiency (both on cognitive and non-cognitive dimensions) using Data Envelopment Analysis (DEA) by school type and, then, I estimate efficiency leading determinants through interpretable machine learning methods (IML). This hybrid DEA-IML approach allows to accommodate the issue of big data (jointly assessing several determinants of school efficiency). I find a cognitive efficiency gap of nearly 0.10 favouring private schools and of 0.045 for non-cognitive outcomes, and with a lower heterogeneity in private than public schools. For cognitive efficiency, leading determinants for the chance of a private school of being highly efficient are higher stock of books and PCs at home, lack of engagement in paid work and school's high autonomy; whereas low-efficient public schools are shaped by poor school climate, large rates of repetition, truancy and intensity of paid work, few books at home and increasing barriers for homework during the pandemic.

Figures

Figures reproduced from arXiv: 2509.25353 by the authors.

Figure 1
Figure 1. DEA estimated efficiency scores by school type and scatter of cognitive and non-cognitive outcomes [PITH_FULL_IMAGE:figures/full_fig_p017_1.png] view at source ↗
Figure 2
Figure 2. Cumulative density functions of efficiency scores by school type [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Comparison of determinants of school efficiency [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Covariates specific SHAP values for private schools with highest values contributions and public schools with [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.