Modelling growth in student achievement is a significant challenge in the field of education. Understanding how interventions or experiences such as part-time work can influence this growth is also important. Traditional methods like difference-in-differences are effective for estimating causal effects from longitudinal data. Meanwhile, Bayesian non-parametric methods have recently become popular for estimating causal effects from single time point observational studies. However, there remains a scarcity of methods capable of combining the strengths of these two approaches to flexibly estimate heterogeneous causal effects from longitudinal data. Motivated by two waves of data from the High School Longitudinal Study, the NCES' most recent longitudinal study which tracks a representative sample of over 20,000 students in the US, our study introduces a longitudinal extension of Bayesian Causal Forests. This model allows for the flexible identification of both individual growth in mathematical ability and the effects of participation in part-time work. Simulation studies demonstrate the predictive performance and reliable uncertainty quantification of the proposed model. Results reveal the negative impact of part time work for most students, but hint at potential benefits for those students with an initially low sense of school belonging. Clear signs of a widening achievement gap between students with high and low academic achievement are also identified. Potential policy implications are discussed, along with promising areas for future research.

翻译：学生学业成就增长的建模是教育领域的一项重大挑战。理解干预措施或经历（如兼职工作）如何影响这一增长同样至关重要。传统方法如双重差分法能有效估计纵向数据中的因果效应。与此同时，贝叶斯非参数方法近年来在单时间点观察性研究的因果效应估计中日益流行。然而，目前仍缺乏能够结合这两种方法优势、灵活估计纵向数据中异质性因果效应的研究方法。基于美国国家教育统计中心最新纵向研究——跟踪超过20,000名美国学生代表性样本的高中纵向研究的两轮数据，本研究提出了贝叶斯因果森林的纵向扩展模型。该模型能够灵活识别数学能力的个体增长规律及参与兼职工作的影响效应。模拟研究证明了所提模型具备良好的预测性能和可靠的不确定性量化能力。研究结果显示兼职工作对大多数学生产生负面影响，但对学校归属感初始水平较低的学生可能存在潜在益处。同时研究明确发现了高学业成就与低学业成就学生之间不断扩大的成绩差距。本文进一步讨论了潜在的政策启示以及未来研究的前景方向。