I'm trolling Elizabeth Breunig. Because she said that "Human capital is one of the more odious terms in the capitalist lexicon". And I like the term "human capital", because I think it helps us think more clearly about investment in training and education.
Are new-born babies "human capital"? My first thought was that they possess no human capital, because they haven't invested in learning anything yet, so it was an abuse of the concept to say that babies are human capital.
Then I remembered "Lark Rise to Candleford", (HT Frances), a memoir of 19th century girlhood in a poor English village. Only one couple in the village had any savings. They were saving for their pension. They were the only childless couple in the village. All the other couples had children, who were costly to feed and clothe, but would support them when they were too old and sick to work. Their children were their pension plans.
At the individual level it might no longer be true that we expect our own children to support us in our retirement. But at the aggregate level it is still true. If nobody has any children, who will produce the goods and services we will consume when we are retired? Unless we can store consumption goods, or invest in building robots that don't need human labour to produce goods.
Think about a OverLapping Generations model with three generations: kids, parents, and grandparents. Only the parents work.
There is a Cobb-Douglas technology in which labour L and non-human capital K produce output, which can be either consumed C or invested I in creating more non-human capital.
C + I = La Kb where a+b=1 and dK/dt = I – dK where d is the depreciation rate, usual stuff.
A Barro-Ricardo version of the model assumes intergenerational altruism, where each individual maximises the sum of the utilities of all three generations. But dynasties are selfish, in the sense that individuals care only about themselves, their own kids, and their own parents.
If all dynasties are identical, the competitive equilibrium will duplicate the social planner's problem. You would not need to introduce Samuelsonian "money" into the model to ensure dynamic efficiency, because retired grandparents will support and be supported by their middle-aged children anyway, with gifts flowing in either direction, depending on the parameters in the model. There are no externalities between dynasties.
What happens if we relax the assumption of intergenerational altruism?
If the whole population stops having kids, because they don't care for their kids, and they know their kids won't care for them, they are in a collective pickle. They can still invest in non-human capital for their retirement, but there won't be any middle-aged workers to add their labour to that capital. So the rate of return on their investment will be minus the depreciation rate d. And that is the most favourable assumption, because I am assuming the investment process is fully reversible, so that machines can be converted back into consumption goods at zero cost.
That is an extreme case, of course, and a population like that will die out anyway. But it illustrates the point that there is an externality. My having kids will increase the labour supply when I am retired, which will increase the rate of return on my investment in non-human capital. But I can't force my kids to work with my machines; they will work with your machines too, and raise the rate of return on your investment. And if the population is large, almost none of the benefits will flow to me. Those who are selfish would agree to a social compact where they will all have more kids to work on each others' machines when they are retired, to raise each others' rate of return on their investment in non-human capital.
Are they treating their own kids as a means to an end? Yes. And in part, it was ever thus, in the age before pension plans. And it's still true today, in aggregate. My kids are part of your pension plan, and your kids are part of my pension plan.
But (I think this is true in the model) those who are Barro-Ricardian, and who want to have kids anyway, and can have kids anyway, might not care about them others who don't have kids. And they will die out anyway. But it's tough on the people who can't have kids, for whatever reason, if nobody else does.
I'm not 100% sure I've got my head fully around this idea yet. But don't say I'm odious for thinking about these things. They matter for human welfare, and they might matter a lot. And we need to think about them clearly.
[Update. If we add a fixed stock of land to the model, as perhaps we should, then the population level matters too. Without land, and with constant returns to scale, only the population growth rate matters.]
Worthwhile Canadian Initiative 
Ugh, really sorry about the typos. In the above it should be “one of those will depend only on exogenous demographics” (and not on saving rate)
Eric,
L and K are in the production function, they are not the production function. Y(T,K,L), where Y is output. If you generalize the idea of a “production function” though then with capital accumulation you could say that capital is produced with a production function which has old capital and old labor (and saving rare and depreciation) as arguments. Likewise if you go Malthusian, then new labor can be said to be “produced” with old capital and old labor.
The feedback from “other stuff” to endogenous technology T, is a subject of study in some models. In “learning by doing” models, technology depends on old capital. In Boserupian/Malthusian models, technology depends on old capital and old labor (and how closely to “subsistence income” these put you). In Michael Kremer’s model, technology depends on the level of population. Etc. But to consider all these things, its useful to first work out just a baseline simple model.
” If I have more kids that increases the future R/W ratio, so it helps those who earn R and hurts those who earn W.”
The thing that makes the whole thing efficient in a OLG model is exactly the fact that those who earn R and those who earn W are the same people (in the aggregate) just at different points in their life. Young people work and get w, which they use for consumption and to acquire capital/land, so last generations fertility hurts them. But then they grow up and own capital/land and that same fertility helps them. The only thing you can do in terms of welfare is to force the initial, generation 0 to have fewer kids which makes all subsequent generations better off. But there’s no way to compensate that initial generation, so such a policy is not Pareto efficient.
Malthus == miserable, but efficient economy.
Since notsneaky brought C+I = L+K up again and lent it some credibility, I’ll post some more underinformed stuff:
So the robots simplification of the economy seems to be inaccurate … Does this matter? To me what’s interesting is that our economy is becoming more like the robots one and less like the model. Even if our incentives are still very like the incentives in the model, I want to know if a small but persistent erosion of those incentives can cause weird things to happen.
Or perhaps a better way to think about it is that the cost of creating one more unit of labor productivity through educating a human may be decreasing relative to the cost of creating a new human. So the production function can always stay multiplicative but generations can still decrease the population rationally. But I think the model requires these extra productive humans to consume just as much more at some point in their own retirement as their education allows them to produce?
@Nick Rowe:
Max, Nick: “Imports are real benefits and exports are real
costs. Trade deficits directly improve our standard of
living.” (temporarily till you repay by a current account surplus he should add.) Like Nick, it’s one thing that I try to make my students understand. Not esy to make them understanfd that a CA surplus is not “agood thing” but a debt payment…They listen too much to the commentariat. It doesn’t help when sometimes, StatCan get a GDP number out and add “this will be revised downward as Import data will be available”. This mlead them to think that imports are bad.
Business students are taught that exports pay for imports, which is true in the financial sense, not the economic sense.Anyone who reads european sources will always see references about “the need to earn foreigh exchange” or “dollar shortage ” of the 40’s-70’s.
The more advanced may read about “those imports are ok because they are investment goods”. No. Importing consumption goods are ok if they liberate resources for your own production of investment goods. It’s the investment as such that is ok.
Germany do not understand how their “proof-of-their-virtuous-and-behavior” current account surplus is detrimental to their living standard.
I always tell students the fallacy of the “oil (or whatever)imports cost us $X billions, money that could stay here and create jobs instead of abroad.” Making them understand that foreign goods are a gift (especially if you pay with your own fiat money) goes again their common sense and what they hear politicians and journos say daily.
I also tell them the day I finally truly understood that. It was during an International Economics cours. For years I had been going through the motions of comparative advantages. One day, I had a flash during the class. I finally saw how imports save you the ressources necessary for exports. They thought I was having a kind of seizure…
Babies as human capital? Oh, Brave New World. Or the antebellum South.
Jacques René Giguère: “I always tell students the fallacy of the “oil (or whatever)imports cost us $X billions, money that could stay here and create jobs instead of abroad.”
Back in stagflation days there was the following story: Petrodollars went to Middle Eastern countries which, having no developed banking system of their own, sent them back to New York City banks, which then lent them at high interest rates to Latin American countries with poor credit ratings instead of lending them within the US, to Oklahoma farmers, for instance. Thus the US did not receive the benefit of increased money in circulation from the inflation caused by high oil prices.
Is that just nonsense?
Thanks.
Min: but those countries had to buy US goods.So the circuit is closed.Otherwise the Saudis are paid in monkey currency. So a competent CB should merely print money and give it to the oil producers. They didn’t because the were concerned about “fighting inflation.” They didn’t understood that, at least temporarily, it was a real increase in the price of oil, a real not a monetary phenomenon. They raised interest rates, compounding the problem.
Adjustment problems arise however:
1) the mechanism isn’t instantaneous. When the US consumers reduce their buying of let’s say housing, there is a time lag before the Saudis order jet fighters.
2) the PSST is disturbed. People employed in the “housing” industry are not immediately and may not be forever employable and employed in the jet fighters sector.
Hope it’s ok but busy and writing fast…
Thanks, Jacques René. 🙂