What is your average friend worth? Analysing friendship behaviour can help us better understand spillover effects when evaluating education policy
The tutor learning initiative in Victoria
In light of the current lockdown measures, teachers were required to adapt their learning to online platforms to compensate for the fact that students were unable to attend school physically. These platforms do not provide the same level of engagement as conventional teaching methods, and required students to self-motivate without the supervision, support, and encouragement conducive within a physical learning environment. The barriers introduced by remote learning have evidently impacted learning outcomes with students learning at only 50 – 75% of their usual pace.
The persistent gap in quality of education provided by public and private schools has only been aggravated in remote learning environments. Students that attend private schools have access to a higher quality of education and generally have better learning outcomes. A switch to online learning has impaired learning at public schools more than private schools due to their limited access to mainly technological resources required to engineer this shift effectively.
As shown within the following plot provided by Grattan Institute, disadvantaged students with specific needs were impacted even further, with their pre-existing problems amplified during the switch to remote learning. Students with limited English proficiency who already presented struggles in a physical learning environment were further hindered by the lower levels of engagement and attention from teachers. This should also be highlighted for disadvantaged student groups e.g., those from low socioeconomic backgrounds, living with pre-existing mental health conditions and/or present in unstable home environments who are most significantly impacted by this change and therefore urgently require assistance.
Figure 1: Source – Grattan Analysis
Evaluating the costs and benefits from education policy
Recently, the Victorian government invested $250m into the tutor learning initiative dedicated to help over 200,000 disadvantaged students catch up in their learning. $209.6 million of the Victorian investment was allocated to government schools to attract and employ 3500 tutors across the 2021 school year. $30 million was invested to employ 600 tutors at non-government schools. 
The costs of the program are straightforward to consider, however, it’s difficult to estimate the economic benefits in real time. The direct benefits of the program are being evaluated using the change in assessment data for participating students and their education plans. This initiative will better equip students for future learning and participation in the workforce, which will increase the productivity of human capital and increase GDP. By modelling the predicted increase in future wages, an estimate can be produced for the predicted increase in GSP for every $ invested. Does this estimate truly represent the gains from this policy?
Direct measures only account for the direct change in teaching outcomes for the students participating in the tutoring services. The actual benefit is greater than what’s being estimated. This can be explained using peer effects in education.  Students share knowledge from the tutor services with their friends, which increases their educational outcomes and indirectly increases the GDP. Let’s analyze the localized effect by considering the direct transmission of knowledge between friendship groups.
Games on networks
Most students study for their subjects within their friendship groups. On the theoretical drawing board, games on networks can be used to quantify the economic value from these study groups. Our economic utility for a given level of effort is based on:
- What we learn (α) –determined by characteristics such as ability, for example: a high ability student may learn more from a subject given the same level of effort.
- Opportunity cost (κ) of studying – how much do we value our leisure, are we really enjoying g the 5th re-run of the big bang theory
- Deviating (Φ) from the social norm.
This can be represented using the following quadratic equation:
Let’s consider a simple illustrative example:
Say we have 4 friends in our study group, which can be represented using the following network:
Without considering the network effect, each student would trade off what they learn against the opportunity cost of studying to determine their optimal level of effort. An initial evaluation would conclude it’s optimal for all 4 students to put in a different level of effort into education.
However, since friendship groups often hang out together, the optimal amount of effort to spend studying also depends on how much effort their friends put in. Armengol et. al. has shown that with perfect information everyone will put in as much effort as the average friend in their study group. Students who initially exert high effort will converge down, while students who initially exert less effort will converge up towards their ‘social norm’, so all friends study and enjoy leisure together.
Do we really know the social norm?
Often, we don’t know what the ‘social norm’ is. We infer this information depending on what we perceive from the people around us. Are our friends as smart as they come across? do they enjoy watching Netflix (or are they just trying to keep up with the latest tea)? and how much do we really care about converging to the social norm?
To investigate this, suppose we all start with an initial assumption of what we think is cool (based on our first impression) and with time, based on our observations, we update our beliefs. This behaviour can be modelled by extending the initial game to account for imperfect information in the parameters that determine these values. We find that there is an optimal level of information we should know about our friends to maximise the amount of utility we get from our study group.
Linking back to the education policy to recover from a pandemic, by better understanding how students derive value from their subject we can decompose the spillover effects of our education policy, which are often larger than the direct benefit we observe. By carefully crafting policy around incentives, we can cater towards students who think they are too 2kool4skool.
Author Description: Emad is an economics honours student at Monash University, interested in the application of social network theory to public policy. While running student clubs and start-ups, Emad finds himself overanalysing every social situation.
 Azevedo, R. (2005). “Using Hypermedia as a Metacognitive Tool for Enhancing Student Learning? The Role of Self-Regulated Learning”. Educational Psychologist 40.4, pp. 199–209. https://doi.org/10.1207/s15326985ep4004_2.
 Evidence for Learning (2020a). COVID-19 home-supported learning: Global evidence review. https://www.evidenceforlearning.org.au/covid-19- home-supported-learning/global-evidence-review/.
 The Hon Daniel Andrews (2020). “Thousands of tutors to bring students up to speed”. Victoria State Government (Press Release). https://www.premier.vic.gov.au/thousands-tutors-bring-students-speed
 Sacerdote, B (2011). “Peer effects in education: How they might work, how big are they and how much do we know thus far?” In: Hanushek, E.A., Machin, S., Woessmann, L. (Eds.) Handbook of Economics of Education, vol.3 pp. 249 – 277
 Jackson, M. O. and Y. Zenou (2015). Games on Networks. Handbook of Game Theory with Economic Applications, Elsevier B.V. 4: 95-163.
 CalvÓ-Armengol, A., et al. (2009). “Peer Effects and Social Networks in Education.” Review of Economic Studies 76(4): 1239-1267.
 Iqbal. (2021). “What is your average friend worth; Incomplete information in network games.” Working paper