Markov chains are mathematical models that describe a sequence of future events based on a set of probabilities defined by previous events. They are a useful statistical tool to understand complex systems and how they evolve with time.
In a proof of concept we demonstrated how Markov chains can be deployed to predict trends in the Rwandan school system, using EICV-5 attendance data as a starting point. Our results suggest that the secondary school population will almost double in the next four years, and that primary school enrollment rates will remain stable. The 2019 Rwanda Education Statistics published by MINEDUC show that our Markov chains model is on the right track.
Or at least it was, until COVID-19.
We don’t need a statistical model to tell us that the pandemic is having and will have a lasting impact on education systems worldwide. But we can update our Markov chains model to account for the shock of the pandemic and see its effects on the predictions.
Modelling the shock of a pandemic
We assume that COVID-19 will affect dropout, repetition and enrollment rates in primary and secondary education through three pathways:
- By impacting the socio-economic environment of pupils
- By making all pupils older compared to a scenario where COVID-19 did not occur (because school closures kept some kids from joining school)
- By creating circumstances that affect learning (through school closures, disruptions due to COVID-19 and the shortening of the academic calendar).
The third pathway on learning cannot be analyzed using EICV-5 data, but we can model the first two.
We find that COVID-19 is estimated to increase overall dropout rates compared to a non-COVID scenario in the school year of 2020/2021. We anticipate that P5, P6, and S3 will be the most affected grades and that pupils 13 years and older will be at a higher risk of dropping out. These two trends were already predicted by our original Markov chains model. The shock of COVID-19 amplifies dropout rates.
We also predict that pupils from the richest wealth quintiles will be impacted the least by the shock. We do not detect clear differences between predictions for boys and girls.
The shutdown of schools is expected to increase enrollment at Primary 1 from an estimated 550,000 pupils in 2020 in a non-COVID scenario to 770,000 pupils in 2021 due to an increase in the number of students who will become eligible to begin primary education. There will essentially be a double-cohort in Primary 1: students that were enrolled in primary 1 when schools were shut (just a few months into the school year), combined with new students that are turning 7 and are eligible to enroll. Our model predicts that the higher enrollment in P1 will have a long-term impact on the structure of the education system as this larger cohort will increase enrollment in every subsequent grade that they transition into. This will put extra pressure on resources, specifically on the grade which the 2020 P1 cohort moves to every year as well.
- Overall enrollment is estimated to increase compared to a non-COVID setting but our model suggests that values will converge to pre-COVID levels by 2025. This is because the increase in Primary 1 enrollment will cancel out the increase in the dropout rate.
- Secondary enrollment is expected to decrease compared to a non-COVID scenario driven by higher dropout rates in the transition from primary to secondary school. Secondary enrollment was poised to increase rapidly in the non-COVID scenario, but we anticipate that enrollment rates will instead stagnate for the next five years due to the effect of COVID-19.
Primary enrollment is expected to increase due to higher enrollment at the Primary 1 level.
Our hope is that these insights will support policy-makers to better target both interventions to limit dropout when schools re-open, and investments in teaching and infrastructure resources. Laterite will be looking to further test and fine-tune its modelling capabilities, including bringing predictions and scenario-testing down to the school level.
This blog post is a contribution from Zia Khan, Research Analyst at Laterite Rwanda, and Dimitri Stoelinga, Managing Partner of Laterite.
|Markov chains are statistical models that describe a sequence of future events based on a set of probabilities defined by previous events. For example, two students enrolled in Secondary 1 in 2018 will have different chances of progressing, dropping out or repeating according to their gender, age, socio-economic background and past academic performance. This means that in 2019 the students may be classmates again in Secondary 2, or one of them might stay in Secondary 1. These new parameters will again influence their new transition probabilities in 2020. By scaling up the Markov chain from the individuals to the school population, it’s possible to estimate the number of students enrolled per grade per year in Rwanda.|