Special education services are designed to provide tailored support for students with diverse learning needs, with the expectation of improving academic achievement. This study examines the causal effect of special education services on fifth-grade mathematics performance using data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K). To address confounding, we employ both traditional and modern causal inference methods. First, propensity score matching (PSM) is implemented to create balanced treatment and control groups. Complementarily, three machine learning-based approaches—Bayesian Additive Regression Trees (BART), Causal Forests (CF), and Double Machine Learning (DML)—are applied to flexibly capture nonlinear relationships and treatment heterogeneity. Across all methods, we find consistently negative average treatment effects, with PSM and DML estimating stronger impacts, while BART and CF reveal moderately negative but significant effects. Importantly, machine learning models uncover substantial individual variation, indicating that while many students experience adverse outcomes, some benefit from targeted interventions. Variable importance analysis highlights early academic ability, socioeconomic background, and parental expectations as key predictors of later achievement, suggesting that observed disadvantages largely predate special education assignment. These findings underscore the methodological value of combining traditional and machine learning approaches for causal inference and carry important policy implications for designing equitable, preventive, and individualized educational interventions.
References
[1]
Rubin, D.B. (1974) Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies. Journal of Educational Psychology, 66, 688-701. https://doi.org/10.1037/h0037350
[2]
Holland, P.W. (1986) Statistics and Causal Inference. Journal of the American Statistical Association, 81, 945-960. https://doi.org/10.1080/01621459.1986.10478354
[3]
Rubin, D.B. (1986) Comment: Which Ifs Have Causal Answers. Journal of the American Statistical Association, 81, 961-962. https://doi.org/10.1080/01621459.1986.10478355
[4]
Imbens, G.W. and Rubin, D.B. (2015) Causal Inference for Statistics, Social, and Biomedical Sciences. Cambridge University Press. https://doi.org/10.1017/cbo9781139025751
[5]
Spirtes, P., Glymour, C. and Scheines, R. (2001) Causation, Prediction, and Search. 2nd Edition, The MIT Press. https://doi.org/10.7551/mitpress/1754.001.0001
[6]
Belloni, A., Chernozhukov, V., Fernandez-Val, I. and Hansen, C. (2017) Program Evaluation and Causal Inference with High-Dimensional Data. Econometrica, 85, 233-298. https://doi.org/10.3982/ecta12723
[7]
Fan, J., Han, F. and Liu, H. (2014) Challenges of Big Data Analysis. National Science Review, 1, 293-314. https://doi.org/10.1093/nsr/nwt032
[8]
Filzmoser, P. and Nordhausen, K. (2020) Robust Linear Regression for High-Dimensional Data: An Overview. WIREs Computational Statistics, 13, e1524. https://doi.org/10.1002/wics.1524
[9]
Kleinberg, J., Ludwig, J., Mullainathan, S. and Obermeyer, Z. (2015) Prediction Policy Problems. American Economic Review, 105, 491-495. https://doi.org/10.1257/aer.p20151023
[10]
Rose, S. (2016) A Machine Learning Framework for Plan Payment Risk Adjustment. Health Services Research, 51, 2358-2374. https://doi.org/10.1111/1475-6773.12464
[11]
Ryll, L. and Seidens, S. (2019) Evaluating the Performance of Machine Learning Algorithms in Financial Market Forecasting: A Comprehensive Survey. arXiv: 1906.07786.
[12]
McConnell, K.J. and Lindner, S. (2019) Estimating Treatment Effects with Machine Learning. Health Services Research, 54, 1273-1282. https://doi.org/10.1111/1475-6773.13212
[13]
Opper, I.M. (2020) Using Machine Learning Techniques to Improving Average Treatment Effect Estimates in Small-Scale Randomized Controlled Trials. RAND.
[14]
Lake, B.M., Ullman, T.D., Tenenbaum, J.B. and Gershman, S.J. (2016) Building Machines That Learn and Think Like People. Behavioral and Brain Sciences, 40, e253. https://doi.org/10.1017/s0140525x16001837
[15]
Sagawa, S., Raghunathan, A., Koh, P.W. and Liang, P. (2020) An Investigation of Why Overparameterization Exacerbates Spurious Correlations. International Conference on Machine Learning, 13-18 July 2020, 8346-8356.
[16]
Salahuddin, Z., Woodruff, H.C., Chatterjee, A. and Lambin, P. (2022) Transparency of Deep Neural Networks for Medical Image Analysis: A Review of Interpretability Methods. Computers in Biology and Medicine, 140, Article ID: 105111. https://doi.org/10.1016/j.compbiomed.2021.105111
[17]
Pearl, J. (2009) Causality. 2nd Edition, Cambridge University Press. https://doi.org/10.1017/cbo9780511803161
[18]
Feuerriegel, S., Frauen, D., Melnychuk, V., Schweisthal, J., Hess, K., Curth, A., et al. (2024) Causal Machine Learning for Predicting Treatment Outcomes. Nature Medicine, 30, 958-968. https://doi.org/10.1038/s41591-024-02902-1
[19]
Hill, J.L. (2011) Bayesian Nonparametric Modeling for Causal Inference. Journal of Computational and Graphical Statistics, 20, 217-240. https://doi.org/10.1198/jcgs.2010.08162
[20]
Stanovich, K.E. (2009) Matthew Effects in Reading: Some Consequences of Individual Differences in the Acquisition of Literacy. Journal of Education, 189, 23-55. https://doi.org/10.1177/0022057409189001-204
[21]
Sanchez, P., Voisey, J.P., Xia, T., Watson, H.I., O’Neil, A.Q. and Tsaftaris, S.A. (2022) Causal Machine Learning for Healthcare and Precision Medicine. Royal Society Open Science, 9, Article ID: 220638. https://doi.org/10.1098/rsos.220638
[22]
Kuzmanovic, M., Frauen, D., Hatt, T. and Feuerriegel, S. (2024) Causal Machine Learning for Cost-Effective Allocation of Development Aid. Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Barcelona, 25-29 August 2024, 5283-5294. https://doi.org/10.1145/3637528.3671551
[23]
Hwang, N. (2024) Label to Help: The Effects of Special Education on Student Outcomes. EdWorkingPaper No. 24-939. Annenberg Institute for School Reform at Brown University.
[24]
Hornby, G. and Kauffman, J.M. (2024) Inclusive Education, Intellectual Disabilities and the Demise of Full Inclusion. Journal of Intelligence, 12, Article 20. https://doi.org/10.3390/jintelligence12020020
[25]
Stark, K., Koslouski, J.B., Vadhan, J. and Vega, M. (2024) The Future Is Inclusive: An Invitation for Interdisciplinary Collaboration between Social Emotional Learning and Special Education Researchers. Social and Emotional Learning: Research, Practice, and Policy, 3, Article ID: 100043. https://doi.org/10.1016/j.sel.2024.100043
[26]
Dell’Anna, S., Entrich, S.R. and Banks, J. (2025) Assessing the Outcomes of Students with Special Educational Needs in Inclusive Education: A Comparative Study of Germany, Ireland, and Italy. PROSPECTS. https://doi.org/10.1007/s11125-025-09730-2
[27]
Rosenbaum, P.R. and Rubin, D.B. (1983) The Central Role of the Propensity Score in Observational Studies for Causal Effects. Biometrika, 70, 41-55. https://doi.org/10.1093/biomet/70.1.41
[28]
Chipman, H.A., George, E.I. and McCulloch, R.E. (2010) BART: Bayesian Additive Regression Trees. The Annals of Applied Statistics, 4, 266-298. https://doi.org/10.1214/09-aoas285
[29]
Wager, S. and Athey, S. (2018) Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests. Journal of the American Statistical Association, 113, 1228-1242. https://doi.org/10.1080/01621459.2017.1319839
[30]
Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018) Double/Debiased Machine Learning for Treatment and Structural Parameters. The Econometrics Journal, 21, C1-C68.
[31]
Winship, C. and Radbill, L. (1994) Sampling Weights and Regression Analysis. Sociological Methods & Research, 23, 230-257. https://doi.org/10.1177/0049124194023002004
[32]
Solon, G., Haider, S.J. and Wooldridge, J.M. (2015) What Are We Weighting For? Journal of Human Resources, 50, 301-316. https://doi.org/10.3368/jhr.50.2.301
[33]
Breiman, L. (2001) Random Forests. Machine Learning, 45, 5-32. https://doi.org/10.1023/a:1010933404324
