<p>Separate life in four intervals (ignoring senior age): young children $(1)$, teenagers-youngs$(2)$, young productive adults $(3)$, middle-age productive adults $(4)$. </p>

<p>If we follow the argument, as a young productive adult the individual will have </p>

<p>$$H_1\cdot(1+g_1)^2 \tag{1}$$</p>

<p>of human capital</p>

<p>What we currently do results in </p>

<p>$$H_1\cdot(1+g_1)^2+H_2\cdot (1+g_{1,2}) \tag{2}$$</p>

<p>Where $H_i$ is the value of investment on young children $(1)$ and teenagers-young $(2)$ respectively, $g_1$ is the inherent growth of human capital invested in young children when mixed with life experience, and $g_{1,2}$ is the corresponging growth rate of that part of investment in human capital installed in teenagers-youngs.</p>

<p>if $F()$ is a production function, and ignoring discounting, the argument in terms of "return per unit of investment" would get a first-step validation if we had</p>

<p>$$\frac {F\left[H_1\cdot(1+g_1)^2\right]}{H_1} &gt; \frac {F\left[H_1\cdot(1+g_1)^2+H_2\cdot (1+g_{1,2})\right]}{H_1+H_2}$$</p>

<p>and manipulating,</p>

<p>$$\frac {F_1}{H_1} &gt; \frac {F_{1,2}-F_1}{H_2}$$</p>

<p>i.e. if, on average, output per unit of initial investment is larger than <em>additional</em> output per <em>additional</em> unit of investment.</p>

<p>Drawing from my experience in participating in production activities, the marginal product of human capital <em>is not everywhere diminishing</em>. There is a range where it is <em>increasing</em>.</p>

<p>Also I expect that $g_{1,2}&gt;g_1$ at least for certain ranges : "automatic compounding" <em>accelerates</em>, since a higher level of human capital tends to rip more benefits from the same life experience. Or so I have noticed casually for some decades now.</p>

<p>So to me, the issue is mute theoretically: we should go into <em>measuring</em> these things (I have not read the link, maybe it does measure).</p>

CC BY-SA 3.0
2015-11-24T18:47:34.193Z
Would you please explain your notation? ($H_1$, $g_1$)
Giskard
CC BY-SA 3.0
2015-11-24T19:21:47.830Z
@denesp  Just did.
Alecos Papadopoulos
CC BY-SA 3.0
2015-11-24T22:31:07.927Z
Thank you! And why is $(1+g_1)$ squared? (In two equations even. The second one is suspect.) Is the difference between growth not already implied by the difference between $g_1$ and $g_{1,2}$? Also it seems to me that once you treat $H$ as the cost of investment and another time as the resulting value.
Giskard
CC BY-SA 3.0
2015-11-24T23:09:36.320Z
@denesp Becuase $H_1$ is invested when "young child" so by the time you reach "young productive adult", two periods have passed, and it has compounded twice.$H_2$  is invested when "teenager-young" so by the time you reach "young productive adult" it has only compounded once, at possible different growth rate, as I muse in my post.
Alecos Papadopoulos
CC BY-SA 3.0
2015-11-25T08:04:28.700Z
But why is it not $H_1 \cdot (1 + g_1) \cdot (1 + g_{1,2})$? Young children are between ages 3-10 for seven years and between ages 10-17 for seven years, while not young children start at between ages 10-17? I stop with the knitpicking.
Giskard
CC BY-SA 3.0
2015-11-25T10:17:25.967Z
@denesp Because if you have invested "only" $H_1$ it compounds at rate $g_1$. But if, on top of that you invest an additional $H_2$, then $H_2$ compounds at rate $g_{1,2}$, which is possibly different.
Alecos Papadopoulos
CC BY-SA 3.0
2015-11-24T16:55:31.150Z
2015-11-24T19:21:23.567Z
2015-11-24T19:21:23.567Z
Alecos Papadopoulos
<p>You ask for studies which I don't have, but I can think of a few reasons:</p>

<ul>
<li><p><strong>Diminishing returns</strong> - if a child has a decent home and parental support you can give them a good education at reasonable cost. To get a child from a broken home to the same point requires much more intervention - and cost.</p></li>
<li><p><strong>Moral hazard</strong> - there are many hard-working families just above the breadline. The parents go to great lengths to ensure their children have a decent home. It may be that they get no support for all this effort - but if they simply stop making an effort, the child then gets massive support from school.</p></li>
<li><p><strong>Need for high achievers</strong> - for society to achieve (cure cancer, explore space, win wars, etc.) there is a need for high achievers. If the education system focuses entirely on getting under-achieving children up to average, this comes at the cost of high achievers.</p></li>
</ul>

<p>I'm from the UK, where there is an extensive welfare system and extra investment in education in deprived areas, called the <a href="https://www.gov.uk/guidance/pupil-premium-information-for-schools-and-alternative-provision-settings" rel="nofollow">Pupil premium</a>. Although, not nearly as much as suggested by the paper you reference. </p>

<p>Many people do not support the pupil premium. There is a large "squeezed middle" in the UK, not poor enough for extra support, not rich enough for private schools, and this group sees extra support for deprived areas as unfair.</p>

CC BY-SA 3.0
2015-11-24T18:46:02.573Z
It is not clear whether what you describe is indeed diminishing returns. The costs are certainly high in the situation described, but perhaps the increase in this child's intellect will be much greater than that of child's with good background being supported with the same sum of money. I would argue that if the parents support the child the school is relegated into a marginal role.
Giskard
CC BY-SA 3.0
2015-11-24T21:10:22.500Z
@denesp - What I was getting at is: say we can reach 80% of children for cost x. At 2x we can reach 95%, 3x gets 98% and the last couple of percent are extremely hard to reach. I see what you mean about the gains for individual children though, that will offset the effect I was thinking of.
paj28
CC BY-SA 3.0
2015-11-24T11:58:46.190Z
2015-11-24T14:58:09.130Z
2015-11-24T14:58:09.130Z
paj28
<p>Famous labor economist James Heckman made the argument that given money for investing into educating people, we should invest into young children, and pretty much only that age group, because they have the most periods of time to compound human capital over time, and arguably get the most benefit from it. </p>

<p><a href="http://jenni.uchicago.edu/papers/Heckman_Masterov_RAE_2007_v29_n3.pdf" rel="nofollow">http://jenni.uchicago.edu/papers/Heckman_Masterov_RAE_2007_v29_n3.pdf</a></p>

<p>Obviously it's a pretty strong argument, and I was wondering what sort of research in the literature you might find important that takes the stance against this sort of idea. My intuition tells me that we'd want to smooth investment into all sorts of age groups of people for some sort of externality reason.</p>

<reference-request><human-capital>
Human Capital and Investment into Children
Kitsune Cavalry
# Human Capital and Investment into Children

(Asked by: username_0 on 2015-11-24)

Famous labor economist James Heckman made the argument that given money for investing into educating people, we should invest into young children, and pretty much only that age group, because they have the most periods of time to compound human capital over time, and arguably get the most benefit from it.

<http://jenni.uchicago.edu/papers/Heckman_Masterov_RAE_2007_v29_n3.pdf>

Obviously it's a pretty strong argument, and I was wondering what sort of research in the literature you might find important that takes the stance against this sort of idea. My intuition tells me that we'd want to smooth investment into all sorts of age groups of people for some sort of externality reason.

**Tags:** reference-request, human-capital


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## 2 answers

### Answer by username_1 on 2015-11-24. Score: 1 | Accepted answer

Separate life in four intervals (ignoring senior age): young children $(1)$, teenagers-youngs$(2)$, young productive adults $(3)$, middle-age productive adults $(4)$.

If we follow the argument, as a young productive adult the individual will have

$$H\_1\cdot(1+g\_1)^2 \tag{1}$$

of human capital

What we currently do results in

$$H\_1\cdot(1+g\_1)^2+H\_2\cdot (1+g\_{1,2}) \tag{2}$$

Where $H\_i$ is the value of investment on young children $(1)$ and teenagers-young $(2)$ respectively, $g\_1$ is the inherent growth of human capital invested in young children when mixed with life experience, and $g\_{1,2}$ is the corresponging growth rate of that part of investment in human capital installed in teenagers-youngs.

if $F()$ is a production function, and ignoring discounting, the argument in terms of "return per unit of investment" would get a first-step validation if we had

$$\frac {F\left[H\_1\cdot(1+g\_1)^2\right]}{H\_1} > \frac {F\left[H\_1\cdot(1+g\_1)^2+H\_2\cdot (1+g\_{1,2})\right]}{H\_1+H\_2}$$

and manipulating,

$$\frac {F\_1}{H\_1} > \frac {F\_{1,2}-F\_1}{H\_2}$$

i.e. if, on average, output per unit of initial investment is larger than *additional* output per *additional* unit of investment.

Drawing from my experience in participating in production activities, the marginal product of human capital *is not everywhere diminishing*. There is a range where it is *increasing*.

Also I expect that $g\_{1,2}>g\_1$ at least for certain ranges : "automatic compounding" *accelerates*, since a higher level of human capital tends to rip more benefits from the same life experience. Or so I have noticed casually for some decades now.

So to me, the issue is mute theoretically: we should go into *measuring* these things (I have not read the link, maybe it does measure).

> **Comments:**
> **username_2**: Would you please explain your notation? ($H_1$, $g_1$)  
> **username_1**: @denesp  Just did.  
> **username_2**: Thank you! And why is $(1+g_1)$ squared? (In two equations even. The second one is suspect.) Is the difference between growth not already implied by the difference between $g_1$ and $g_{1,2}$? Also it seems to me that once you treat $H$ as the cost of investment and another time as the resulting value.  
> **username_1**: @denesp Becuase $H_1$ is invested when "young child" so by the time you reach "young productive adult", two periods have passed, and it has compounded twice.$H_2$  is invested when "teenager-young" so by the time you reach "young productive adult" it has only compounded once, at possible different growth rate, as I muse in my post.  
> **username_2**: But why is it not $H_1 \cdot (1 + g_1) \cdot (1 + g_{1,2})$? Young children are between ages 3-10 for seven years and between ages 10-17 for seven years, while not young children start at between ages 10-17? I stop with the knitpicking.  
> **username_1**: @denesp Because if you have invested "only" $H_1$ it compounds at rate $g_1$. But if, on top of that you invest an additional $H_2$, then $H_2$ compounds at rate $g_{1,2}$, which is possibly different.  

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### Answer by username_3 on 2015-11-24. Score: 1

You ask for studies which I don't have, but I can think of a few reasons:

* **Diminishing returns** - if a child has a decent home and parental support you can give them a good education at reasonable cost. To get a child from a broken home to the same point requires much more intervention - and cost.
* **Moral hazard** - there are many hard-working families just above the breadline. The parents go to great lengths to ensure their children have a decent home. It may be that they get no support for all this effort - but if they simply stop making an effort, the child then gets massive support from school.
* **Need for high achievers** - for society to achieve (cure cancer, explore space, win wars, etc.) there is a need for high achievers. If the education system focuses entirely on getting under-achieving children up to average, this comes at the cost of high achievers.

I'm from the UK, where there is an extensive welfare system and extra investment in education in deprived areas, called the [Pupil premium](https://www.gov.uk/guidance/pupil-premium-information-for-schools-and-alternative-provision-settings). Although, not nearly as much as suggested by the paper you reference.

Many people do not support the pupil premium. There is a large "squeezed middle" in the UK, not poor enough for extra support, not rich enough for private schools, and this group sees extra support for deprived areas as unfair.

> **Comments:**
> **username_2**: It is not clear whether what you describe is indeed diminishing returns. The costs are certainly high in the situation described, but perhaps the increase in this child's intellect will be much greater than that of child's with good background being supported with the same sum of money. I would argue that if the parents support the child the school is relegated into a marginal role.  
> **username_3**: @denesp - What I was getting at is: say we can reach 80% of children for cost x. At 2x we can reach 95%, 3x gets 98% and the last couple of percent are extremely hard to reach. I see what you mean about the gains for individual children though, that will offset the effect I was thinking of.  

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