Thresholds in Education

Malcolm Gladwell suggests in his celebrated book “Outlier” that the key to success lies in investing 10,000 hours in practising and perfecting a pertinent task. Does that mean that 10,000 hours guarantees success in your profession? Skill is a perquisite for success in most profession, yet that is not all it takes.

Malcolm Gladwell focusses only on the “outliers” in the society. It is obvious that practising a relevant skill for 10,000 hours is just one part of the success matrix. The outliers are likely to be individuals with exceptional innate abilities. The sample that Malcolm Gladwell studies consists of individuals that already have certain innate abilities and have gone on to invest 10,000 hours to hone a particular skill to perfection. Malcolm does, however, make an useful point of about the effect of thresholds in skill formation that we explore here in the wider context of education.

Across the world, there is a considerable debate on whether the quality of education matters, i.e., to what extent does a good teacher have an positive impact on the student’s future life? The fadeout effect has always puzzled the economist, i.e., the impact of good quality education in kindergarten fades out as the student’s grade drop to average level. The Project STAR, a well known education experiment in Tennessee randomly assigned students to kindergarten classes. This allowed Chetty et. al. (2010) to identify the impact that being in a “good class” had on a student. Students from some kindergarten classes did better than others but this effect on student’s educational performance faded out by high school. What is surprising is that the initial positive effect revisits the student in later years. Students that did better in kindergarten were more likely to go to college, less likely to become single parents, more likely to save for retirement and earn more.

What is striking is the impact initial education in kindergarten had on seemingly unrelated aspects of the student’s later life. Of course, the exact channel through which early education impacts later life is not clear from the study.

Heckman and Cunha (2007) summarise decades of empirical work on education. Their story suggests that thresholds are relevant in a very specific way. Formal education consists of acquiring a series of skills that can be mapped on an inverted pyramid. There is certain hierarchy of skills, i.e., acquiring a particular skills allows one to acquire a range of further skills. More specifically, certain primary skills facilitate the acquisition of intermediate skills. Learning how to write or do basic math could be one of those primary skills. Similarly, these intermediate skills allow the students to acquire more advanced skills. Heckman and Cunha (2007) also make the point that the level of a primary skill increases the marginal returns on effort in acquiring a related advanced skill. Put another way, the cost of acquiring a certain expertise on a new skills gets lower if you have mastered the previous skill. That is, the more skilled a child is at reading and writing, the easier it is for her to learn history, geography and physics. In Tennessee, students that were put in better kindergarten classes presumably acquired primary skills that allowed them to attain better outcomes in later life. Some of these could have been direct effect in terms of lifetime income where as others could have been indirect effect like lower likelihood of being a single parent.

This paints a rather depressing picture. Children who get a good quality early education get far ahead of children who miss out on early education. Further, it is almost impossible to catch up once there is gap in a child’s education. Further, at a day to day level, the education systems need to be designed to plug the skill gaps so that children are able to acquire more advanced skills. One critical gap could have a disproportionate effect on a child’s ability to acquire skill in future, which a flexible education system would immediately plug. This is where good schooling and home environment becomes critical. A high human capital parent may be more effective in both recognising a critical skill gap in their child and ensuring that it gets plugged by hook or crook. Thus, low human capital parents and under-performing schools are a combination that fatally damages a child’s future from which there is no escape. If a society aspires to provide social mobility to its citizens, then it needs to address this problem head on. Of course, the problem even the richest societies face is that under-peroforming schools are often found in neighbourhood where the average human capital level tends to be low. Hence, these neighbourhoods find themselves caught in a vicious trap, where human capital acquisition remains low from one generation to another.

Malcolm Gladwell suggests that the critical threshold is 10,000 hours of learning a particular skill. Of course, Malcolm Gladwell has a very specific issue in mind. The point he makes about thresholds applies generally to any skills an individual acquires. Heckman-Cunha‘s story of smaller inter-connected skill thresholds is more likely representation of reality. Ensuring that each child gets the best possible chance in life is very resource intensive, which is expensive even for the richest nations in the world. Given the enormity of the problem, it is not surprising that education policy and its role in inter-generational mobility is still being hotly debated in even the most developed of nations of world.


Education and threshold effects

According to Malcolm Gladwell, to make it big you have to put in 10,000 hours. This is irrespective of any profession. It is a bold claim and has got me wondering. Can anyone put in 10,000 hours and expect to succeed. Or does it depend on certain other factors as well. And if so, what are these other factors?

First of all, it should be clear that Malcolm Gladwell seems to be reporting what he has observed from looking at the lives of the people who have succeeded. He is not counting the people who put in the 10,000 hours and did not make it. These are the invisible people who are difficult to find. Further, he is presumably talking about highly skilled people with sufficient human capital. After all, it would be very difficult to imagine that an unskilled worker can make it big by putting in 10,000 hours. There are hundreds of millions of unskilled workers across the globe that have put in 10,000 hours and yet remain poorly paid with no significant chance of progress in sight. If we were to believe the premise, the relevant question is what are the prerequisites that need to fulfilled before 10,000 hours start counting.

Lets think of this in the context of the debate on whether the quality of education counts. Does a good teacher have a positive impact on the students. The fadeout effect has always puzzled the economist. The impact of good quality education in kindergarten fades out as the student’s grade drop to average level. Chetty et. al. (2010) look at this using data of 12,000 children from a well know Tennessee education experiment Project STAR which randomly assigned students to kindergarten classes. Some classes did better than others but this effect disappeared by the high school. Surprisingly, the initial positive effect revisits in later years. Students that did better in kindergarten were more likely to go to college, less likely to become single parents, more likely to save for retirement and earn more.

The study does illuminate the contribution that educators and schooling environment makes. What it does not tell us how it affects it. Does it give each person a step up jump or does it increase the amount a person can extract from a given set of fortuitous circumstances. It also leaves me wondering if there are threshold effects. To put it more specifically, does the income increase with quality of education through at level effect or does it have an affect through various interaction terms. Further, are these effects continuously increasing in the quality of education or are there thresholds beyond which earning jumps suddenly.

These questions are very important from a policy perspective. If there are threshold effects, then providing education that does not reach the threshold is infructuous. This maybe a the story of a lot of education. It may also explain why systematically poorer people across the opt out of education. The returns to education do depend on other factors like health, public goods, infrastructure, economic activity and credit markets. These are factors that are all inter-connected and conspire together to provide an environment where the returns from education are high or low. This in turn determines whether markets can be used to deliver education or not. If returns are very high and people have an ability to pay, then the schooling can provided through the market. People would pay for the schooling in anticipation of high future earnings. People would be able to pay either if they (or their parents) have sufficient wealth or people can borrow against their future earnings. When the factors conspire to keep the earnings from education low, the state (government) needs to take the burden of education. Education here maybe helpful socially because of its external effects but individuals may not have the incentive to acquire education. This in turns leads to the vicious circle which keeps areas poor persistently as people do not have the incentive to acquire education and economic activity is limited due to low average level of education in the area.

One cannot think about education without thinking about it in terms of quantum as well as its interaction with other factors in the local economy. These links are complicated and it is not surprising that even though there is a large literature that shows education’s impact in micro studies, its impact in macro studies is yet to be discovered.

Raj Chetty, John Friedman, Nathaniel Hilger, Emmanuel Saez, Diane Schanzenbach and Danny Yagan (2010). How Does Your Kindergarten Classroom Affect Your Earnings? Evidence from Project STAR.