The Economics of Child Development
Should you enroll your kids to Kumon at age 4 or 16?
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A little foreword from Toby. This article at a glance, might seem completely unrelated to economics or investments in the traditional financial market sense. But in truth, your child (or future child if you wish to have one) will most likely be your biggest investment. Education, travels for experience, sports, music and most importantly, your time spent for a quality interaction to impart your wisdom and values. So doing it right, or as best as you could, matters.
While Shania is not an expert nor a professional in child development, this post is meant to be interpreted as a form of sharing on what literature she’s been reading pertinent to economics of child development and translating it to more relatable and easier to understand terms for every day people like you and me. There will be a bit of math, but it is meant to illustrate a point better with mostly intuitive explanations.
Side note, if you find this post valuable and you’d like to step forward to contribute to the blog as a guest poster, email me. I would be happy to learn from you!
Introduction
I am inspired to write this post for 2 reasons. First, I am doing research related to this field and so I have to read related materials. Second, I am entering the age where soon I will be getting married and have children, and so these matters become important.
So what am I writing about? My questions are simple:
Is someone’s “smartness” genetic or buildable?
If my kids are born “not so smart”, should I do something about it or just accept it? Or maybe find his/her other hidden talent?
When I have kids in the future, should I keep working / hire a nanny / send my kids to childcare?
Do I need to send my kids to lots of different tuition (extra-curricular stuff) like my parents did for me? Or should I just let them play, have fun, and have a great childhood?
Should I focus a lot on academic achievement when they are young?
What is the best way to raise a kid — should I work extremely hard so that I can earn a lot of money to send them to expensive school (or maybe even go overseas) and hire expensive teachers? Or should I focus on spending a lot of time with my kids, playing with them, reading with them, going to museums and parks, etc etc?
At the end of the day, I was also reflecting on my childhood and what my parents did to me. I guess I am pretty lucky as I would think that I had a pretty good childhood.
I naturally don’t mind studying and even grow to enjoy them. I do well academically in school. My hobbies were what parents deem to be good hobbies. I like reading and playing music. My parents send me to lots of tuition — English, Mandarin, Abacus, Piano, Violin, Ballet — and I don’t hate them.
But my brother’s case was different. My brother did not like studying nor reading. He was also forced to go to tuition, albeit a much smaller number — he only had to attend English, Mandarin, school supplementary session (or what we call bimbel, where students do their school homework and prepares for school exams). He came in second last in school, would find every possible reasons to skip tuition, and was more interested in playing Play Station.
So if you are a parent with 2 kids — a Shania and a Shanio (a fake name for my real brother) — you may wonder, what should you do? Should you force Shanio to go to all these tuition? If he has been coming second last in school, should you give up all hope in him?
Here’s some of the lessons we can learn from the field of Economics.
The Economics of Child Development
What? Economics and child development? How are they related?
Getting into this may be the topic of an article in itself, but here’s the short answer.
Yes, the field of Economics is not just about GDP or interest rate or the stock market. Economics is about studying how people make decisions and trying to infer causation. So how Economics relate to child development is like this: how do parents make decisions on how much time and money to spend on their kids? And how much do parental time and money investments matter in the development of the child, with any possibility of the importance of the time in which these investments are made?
Most of this article will be summarising the findings of several prominent papers in the Economics of Child Development — Cunha and Heckman (2007); Cunha and Heckman (2008); Cunha, Heckman and Schennah (2010); Todd and Wolpin (2007) — with the main reference being the Cunha and Heckman (2007) paper.
A Simple Model
We can think about a child’s cognitive ability (or intelligence) as an output. If you put in different types and different amount of input, you will get a certain amount of output.
An analogy is like cooking. If you put in some chicken, garlic, rice, egg, and soy sauce into the pan, you get chicken fried rice. If you change the chicken to prawn, you get prawn fried rice.
Now there is also an element of the chef. If you get the chef of Bakmi GM to cook, you’ll get a pretty solid plate of fried rice. But if you ask Toby to cook, you’ll need to pray hard not to gulp down 10 tables of Norit after.
So you can think about a child’s cognitive ability as an output that requires input (both the type, quality and quantity matters).
To put this into mathematical language:
In the equation above,
represents the cognitive ability of a child at time t,
represents the parents’ characteristics (such as IQ, education, etc),
represents the investments that parents make for their child (which can include multiple things such as how many books they buy, how often they read with their child, how often they bring their child to the park, how much money they spend on school, etc), and…
represents the cognitive ability production function.
So you can think of the left hand side as the output, and the terms in the right hand side as the input. As for the function f at time t, is the chef that will convert the input into the output. In this case if you are a parent, you are that chef that puts in work, time and money into your child so that they will be of a certain state at time t+1, a.k.a in the future.
The equation above is trying to map how a child’s cognitive ability in the next period is a function of the parents’ characteristics, the child’s cognitive ability in the previous period, as well as the investments the parents make in the previous period. All of this also depends on the technology (or the chef) responsible for converting the inputs into the output.
We can then play around a little bit. If you think that the child’s ability at age 10 is affected by his ability at age 9; and the ability at age 9 is affected by his ability at age 8; and we continue; we’ll soon notice that at the end of the day, his ability at any period depends on his ability at age 1. Just doing some notational change, I can re-write equation (1) above to:
Now, the exact form of equation above is unknown, that is, I don’t exactly know how the input is converted into output and how much input is needed to produce a unit of output.
In simpler terms intuitively, I don’t know if I want to produce a child as smart as Albert Einstein, what exactly I need to give him as an input — books? toys? tuition? play station? — and I don’t know how much of each input I need to supply — 2 books a month? 1 car toy a year? 3 math tuition sessions a week?
But I can have several hypothesis of how my input to my child today translates to the output of my child tomorrow. So I’d like to introduce 2 features into equation (2), which are the notion of
(i) substitutability/complementarity, and
(ii) self-productivity.
Don’t worry if this does not make sense now.
Substitutability vs Complementarity: Should I put in effort when the child is small or when he/she is older?
Substitutability or complementarity seeks to understand whether the investments I make when the child is very young (say 4-6 years old) is a substitute or a complement for the investments when the child is older (say 7-10 years old). For instance, if I want my child to be good at math (the output is high math ability) and I am considering sending him to Kumon (investments), should I send him to Kumon when he is young or when he is older, or both?
If investments exhibit substitutability pattern, it means that if I fail to supply high amount of investments when the child is young, I can still make up for this when the child is older. Therefore it does not matter when I send the child to Kumon. If you are also considering financial planning, maybe it makes sense for me to save all of my salary when the child is still young, then use this money to invest and generate returns. In future, I’ll have more money to send my kids to more extra-curricular or supplementary tuition.
On the other hand, if investments exhibit complementarity pattern, it means that if I have invested in my child when he is young, this investments would generate even more return when I invest again when he is older. Formally, this relates to the fact that skills produced at one stage raise the productivity of investment at subsequent stages. That means if I have sent my child to Kumon when he is young, I should continue putting effort to harness his math skills when he is older (I should continue sending him to Kumon or any other math lessons). On the flipside, if I did not send my child to Kumon when he is young and he has shown to be bad at Math since young, then it is not the most economically efficient to try making up for his poor Math skills when he is older.
Now, what does that data show?
Empirical studies have shown that investments seem to be complementary. A study by Currie and Thomas (1995) shows that a pre-school program that aims to improve cognitive ability to minority and disadvantaged groups experienced initial improvement, but without follow-up intervention, these individuals return to disadvantaged environments.
The takeaway for us? Paying proper attention and investing in your children when they are still young is critical, and this should be continued even as they grow older.
Is there a period where it is most important to invest properly in my kids?
Now comes the question of returns to investments. It’s almost like investing in any other monetary instruments or in the stock market. Suppose you have the option of buying a government bond and earn a return of 5% annually, or you can invest in Indonesian equity by using Recompound’s service and earn a return of 15% annually — anyone would know to choose Recompound right?
Now comes the element of time. Suppose you have 2 options of stocks to buy — a pharmaceutical company (say Kimia Farma (KAEF)) or an instant noodles producing company (say Indonesia’s national pride Indofood (INDF)). If you invest in February 2020, one year later, you would make a returns of 870% from KAEF and about 0% returns from INDF. But if you invest in May 2024, by June 2025, you would have earned 37% from INDF and lost 29% from KAEF.
The above example highlights the point of sensitive period. Sensitive period of a child’s development refers to the period in which an investment generates the highest return compared to any other period. For instance, if the sensitive period of a child’s math ability is at age 4, this means that if you spend IDR200,000/month on Kumon tuition at age 4, your child’s math ability would be developed the most compared to attending the tuition at age 10.
What does the data show?
The study by Cunha and Heckman (2008) finds that there is a different sensitive period for the development of children’s cognitive and non-cognitive (measures of temperament, social development, behavior problems and self-confidence) skills. The authors find that the sensitive period for parental investments in the development of cognitive skills is at younger age — that is, the transition from ages 6-7 to ages 8-9. Meanwhile, the sensitive period for the development of non-cognitive skills is at a slightly older age — the transition from age 8-9 to 10-11.
The takeaway for us? If you want to develop the cognitive ability of your child, start as early as age 6-7 At the same time, do not neglect the non-cognitive development of your child and pay greatest attention to non-cognitive development at around age 8-9.
My child is not doing well in primary school. Is he a hopeless case?
Now we’re going into the topics of self-productivity.
Self productivity means that skills acquired in one period persist into future periods. For instance, if your child exhibit plays the piano very well at age 4, you’d expect them to continue being very good at music even at age 5, 6, 7 and onwards. This musical ability will not just disappear one year later. This also can mean that skills are self-reinforcing and cross fertilising. Self-reinforcing skills mean that one’s stock of skills at one period also contributes to the development of skills in the next period. Intuitively this makes sense, a child that plays a grade 4 piano at age 5 can play a grade 5 piano at age 6 because they have the pre-requisites of playing a grade 5 piano.
Cross-fertilising skills capture the idea that skills in one area may help the development of skills in another area. For instance, playing piano really well might help a child develop mathematical skills.
What does the data show?
Again, the study by Cunha and Heckman (2008) shows that there is strong self-reinforcement in children’s cognitive and non-cognitive skills. This is quite intuitive because the better a child gets at a certain skill at an earlier age, the better that child would be at that skill at a later age if that skill is continuously honed.
More interestingly, when we consider cross-fertilisation, it is found that non-cognitive skill contributes to the development of cognitive skills, but not the opposite direction.
The interesting bit is because “soft” skills, ability to empathise, socialise, etc that are not formally taught in schools actually mattered to the development of cognitive skills that require more of an analytical mind such as math and engineering.
So how important is it for me to invest in my child?
Combining the features of
(i) complementarity/substitutability and
(ii) self-productivity,
we can then introduce the third feature, which is (iii) the multiplier effect of parental investments
The multiplier effect maps the relationship of early investment not only in directly developing the skills of the child on period 1 and then through self-productivity, the skills in period 2, period 3, and so on. It also captures the effect through increasing the returns of investment in period 2.
To simplify this example, suppose there are only 2 periods: period 1 is when the child is young (say age 4-10) and period 2 is when the child is an adolescent (age 11-17). Suppose that by age 18, the child turns into an adult and his skills is denoted by the term
Then we can construct the equation below that denotes the function, input (your investments to your child), and output (the child’s skills) at a period of time.
So how do we comprehend the multiplier effect?
The multiplier effect is illustrated in the flowchart above.
I_1 acts as an input and affects theta_2 directly (second box),
which then serves as an input for the production of theta_3 (last box on the most right).
This shows how I_1 affects theta_3 through the channel of self productivity.
At the same time,
I_1 also acts as an input that affects theta_2 directly.
But remember that there is a dynamic complementarity component in the production of ability.
Higher theta_2 makes the returns of I_2 higher, and so increases theta_3.
Well this, my friends, are perhaps why we see child prodigies. It is not through one-off investments that are made by the parents at the early or the later stage of a child’s life. But it is through consistent investments that is being made throughout the lifetime of the child that seems to enable the multiplier effect to take place.
The takeaway of all this?
Non disputable: Investment in your children matters (best if done consistently throughout their childhood).
Pay attention not only on their cognitive skills, but also on their non-cognitive skills.
Data suggests that it is good to invest in a child’s cognitive skills as early as possible, and this investment should be continued as they grow.
Data suggests that investing in the development of a child’s non-cognitive skills, particularly when they enter the age of 8-9. This not only benefits their non-cognitive development, but will also help them build their cognitive skills.
Raising a child is not easy, but from what I’ve heard, it’s a meaningful journey.
And just like investing with Recompound (I myself am a client), it is full of ups and downs and it requires a lot of patience.
But hopefully, if done right, the returns will be well worth the investment. Good luck ❤️
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