The secret recipe for making friends

September 22, 2020

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It is the spring of 2021. A vaccine for Covid-19 has been distributed and life is getting back to normal. The weather is improving and it is the so-called first ‘Rokjesdag’. The perfect day to hit the terrace with your friends. You are enjoying a drink with your friends, while reminiscing all the good times you had together before the pandemic. You mention that it is quite remarkable that even though you could not really spend time together, you still kept in contact with each other. One of your friends responds that it is only logical, that is where you are friends for! You agree, but you wonder how you became friends in the first place.



It is a bit of a far-fetched story however, you have probably thought about this question yourself. In the past few years, you have surrounded yourself with a group of friends with whom you spend your time. You got to know them during school, sports, or on the job, and for some reason, you grew fond of each other. But do you remember how it all started? What sparked your friendship? There are a lot of theories about how friendships come into existence, many of which are based on sociometric techniques such as survey data. However, in real life, friendships are based on individual choices. Therefore, it could be interesting to look at it using an ‘individual behaviour’ approach, for example by using a proven econometric method. This article will look into the econometric method to better understand social pair forming, to uncover the secrets of becoming friends.


Law of attraction

Over the years a lot of theories about friendship have been proposed in psychology and sociology. You may have heard the saying “birds of a feather flock together”, which describes one of the most well-known theories. This saying is based on Byrne (1971) in which people had to complete a survey about their personal characteristics. Thereafter, they were shown descriptions of a range of different people. When asked how the subjects felt towards the descriptions, it was found that those with similar characteristics to the subject were rated as more amiable. This and many other theories on friendship have been found by conducting controlled experiments. This gives the possibility to really test the hypothesis at hand. However, it does not give much insight into the explanatory power of a factor or the interaction between multiple factors. Therefore, a mathematical model could be interesting.


Omitted variable bias

On the other hand, gaining more insight into friendship formation could also be beneficial for economic models. Take for example the concept of ‘ability bias’. Many people will know the example of the wage equation, where you estimate the wage based on the level of schooling. When you leave out the unobserved ability from this equation, this will result in an upwardly biased estimate for the returns from schooling. In other words, people with the highest ability will opt for a high level of education, and thus a higher wage will partly be caused by being more able in the first place. Suppose now that friendships are based on ability, so people with similar abilities will become friends more easily. Then friends could cause a positive effect on academic productivity. That will in return mean that a higher wage will partly be caused by friends, and excluding that from the model will cause even more omitted variable bias.

friendship and ability


The friendship model

Hence, for sociology as well as an economic point of view, it is beneficial to be able to model friendship. In particular, we could be interested in the effect of similarities in the formation of friendships without conducting a survey. However, to establish such a model one will encounter a couple of difficulties. Firstly, we note that one time period is not enough to infer any information about friendships. Secondly, it could be that some people tend to make friends more than other people. This could be caused by individual-specific unobservable attributes, which are in fact correlated with observable predictors of friendship. To accommodate these problems the proven econometric method mentioned above comes into play.


The unobserved effects model

In microeconometric theory, one can encounter the unobserved effects regression model. In these models, one uses panel data, which is a longitudinal data set that follows the same individuals, firms, or countries, etc. over time. So this model can cope with the fact that we need multiple time periods. In addition, this model is able to capture fixed effects. These are time-invariant characteristic, unique for each individual. So, we can conclude that using an unobserved effects model a model for friendship could be composed.


Implementing the model

As you probably expected, such a model has been composed. In Foster (2005) a linear probability model is proposed as follows:

    \[\text{Friend}_{ij} = X_{i}\beta + X_j\delta + X_ij\gamma + v_i + u_j + \varepsilon_{ij}\]

Here \text{Friend}_{ij} is the probability that two individuals achieved friendship, X_i and X_j contain observable characteristics of individual i and j respectively, X_{ij} contains information on how close i and j along certain scales and v_i and v_j capture the fixed effects for student i and j. This model has been used to gain insight into the formation of friendships between students entering the housing system of the University of Maryland (UM).


Finding friends in Maryland

In this research, the housing system of UM was considered. Students that enter the university are randomly assigned to a room in one of the 37 dorms. Each of these dorms consists of a number of floors and each floor consists of a number of wings. After the first semester and after each semester after that students are able to request where and with whom they want to live. Hence, a group of students might attempt to get assigned to the same location. Students start their university life surrounded by random people. Later on, they are able to choose certain ones to accompany them as they continue.



After creating a viable data set, the \text{Friend}_{ij} variable is set to 1 if students i and j live in the same wing, and 0 otherwise. Then information on demographics such as race, gender, home address, and high school achievements are collected for both students (X_i and X_j) and the variables measuring similarities are constructed (X_{ij}). It is then found that social similarities are far more important than similarities in academic aptitude. The area you originated from or the year you finished high school has a far greater influence on the formation of friendships than high school achievements. However, most striking is that the factor that influences friendships the most is the location where he or she is assigned to in his or her first semester.



It can be very interesting to model the formation of friendships, to uncover the underlying mechanics. This holds for sociology as well as the economic sector. Indeed, research is done into the matter for example Foster (2005). As one would expect it is found that friendships are partly based on social similarities as well as similar abilities. However, the greatest influences are found to be factors that are outside the control of the individual (room assignment in this case).
So to return to our story. You will probably have found your friends by sheer luck. Maybe you would have had a completely different group of friends if you went to a different school or sports club. However, you would certainly have made friends there too! Keep this in mind when starting a new chapter in your life: Indulge in the “Get to know your fellow …” activities, because by sheer luck you can make friends of a lifetime!

Dit artikel is geschreven door Jochem Hak
Jochem Hak

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