Harmonious relations

All of us have had teachers who we can recall decades later. Many of us have struggled with a concept right up until the right teacher at the right time comes with the right explanation that makes the pieces fall into place. Teachers can have a profound effect on their students, both through the knowledge they share and the sparks of inspiration they provide.

This effect is especially true in creative fields, where promising new talents are shaped and motivated by established figures. In a newly published paper, Karol Jan Borowiecki, Maria Marchenko and I examine the specific case of music composers. Throughout history, composers have learnt from other composers. In this setting, the teacher–student dynamic involves an individual relationship between the expert practitioner and the novice.

Our analysis is enabled by a novel dataset that covers several centuries of teacher–student pairs. Our data include 17,433 composers, who together form 36,927 unique teacher–student pairs. (Any given composer may be a student of multiple composers, and may also be a teacher of multiple composers.) We measure quality transmission between composers using the length of biographies recorded in Grove Music Online — a professionally edited encyclopaedia of music. All else being equal, a longer biography of an individual composer implies a higher ‘quality’.

We find a significant correlation between teacher quality and student quality. Moreover, we find this effect is persistent over successive generations: that is, from teacher to student to student’s student and so on. The effect of quality transmission is amplified by similarities between teacher and student: for example, whether they come from the same country. 

My very dear master

One does not need to be a music aficionado to recognise several of the names who appear in our dataset. Beethoven, Bach, Haydn, Mozart and Tchaikovsky are among the composers we capture — all of whom are within the top tier as far as biography lengths go.

Among slightly lesser-known names are some powerful stories, which help motivate our analysis. Consider Franz Liszt, a prominent Hungarian composer during the nineteenth century. Liszt studied under the Austrian composer, Carl Czerny (himself a student of Beethoven). Czerny recognised a remarkable talent in Liszt, writing of his pupil that ‘never before had I had so eager, talented, or industrious a student’.

Liszt was likewise impressed by — and grateful to — his teacher. As Liszt’s career advanced, he wrote to Czerny to credit his ‘master’ for his success:

Liszt’s letter to Czerny highlights — in perhaps unusually effusive terms — the contribution an experienced teacher makes to a student’s career. And while the Czerny–Liszt pair is one of tens of thousands in our dataset, we find that their relationship is more than a ‘one-hit wonder’ among music composers.

As the figure below illustrates, there is a significant correlation between teacher quality and student quality. Given that students can have multiple teachers, we measure teacher effects in two ways. The left-hand panel of the figure shows the average effect of each student’s teachers (as measured by their biography word counts). The right-hand panel charts the maximum effect given by the highest quality teacher for each student. Regardless of which effect we are looking at, we find that a 1 per cent increase in the length of the average/maximum teacher’s biography is associated with an average 0.1 per cent increase in the length of a student’s biography.

Hitting the right note

Correlation is not causation, of course. Multiple factors could play a role in influencing the observed positive relationship between teacher quality and student quality. For one thing, not all composers become teachers; on average, teachers have longer biographies than non-teacher composers. But even when we zoom in specifically on teachers, we find that the longer their biographies are, the greater the number of students they teach on average.

Furthermore, when we look at all our teacher–student pairs from the perspective of students, there is a significant positive relationship between the length of teachers’ biographies and the likelihood of a recorded student ending up with a biography in Grove.

In our primary analysis (summarised in the table below), we regress teacher quality on student quality while controlling for a range of other factors that might influence quality transmission. In particular, teachers and students are not randomly paired, hence we control for time periods and places of birth and death. We also control for the number of teachers a student has. Even after accounting for these factors, there remains a strong and significant positive effect of teacher quality on student quality.

The lingering echoes of quality

Our dataset also allows us to examine the persistence of quality transmission across multiple generations of students: that is, from teacher to student, to student’s student, to student’s student’s student and so on. As one example (illustrated below), the longest generational chain we identify spans 21 generations and includes 10,321 individual composers (including Liszt and Czerny).

A key finding from our analysis is that quality transmission persists across several generations. While the effect unsurprisingly diminishes from generation to generation, we find a positive effect of teacher quality on up to the eighth generation of student when controlling for teacher fixed effects. That is, a high quality teacher matters not only for the direct student, but also has cascading effects as that teacher’s knowledge and skills are passed on.

While we find evidence of quality transmission among music composers, less clear are the precise mechanisms at play. Our data do not allow us to determine precisely what quality-related attributes teachers pass on to their students. One channel is skills-related: students learn more from more accomplished teachers. But a range of other possibilities are relevant to consider, such as reputational effects from being associated with a top composer, and better access to influential networks. We offer no definitive conclusions here, though we note that the effects of teacher quality are not exclusively driven by the top tier of composers.

Our results provide relevant insights for understanding the determinants of creativity, and provide a distinct perspective on broader questions of teacher quality and educational attainment. But perhaps the most important message is for aspiring composers: find yourself a good teacher. Quality matters.