Thursday, October 26, 2006

Are Children Giffen Goods: An Economic Puzzle

Suppose someone invents an inexpensive and reliable way in which parents can choose the gender of their offspring. From the economic standpoint, this represents an increase in quality—you get a child of your preferred gender instead of a fifty-fifty chance—at no significant increase in cost. Increased quality at constant cost corresponds to decreased cost at constant quality; you are now getting more for your money. Lowering the cost of something increases the quantity demanded.

Do you conclude that, as a result of the new invention, the birth rate goes up? If not, why not? Are children Giffen goods?

Hint: I am fond of the sort of mathematical puzzle which consists of a proof of something obviously false, for example that two equals one; the puzzle is finding the mistake in the proof.

At 10:23 PM, October 26, 2006,  Mark said...

It's not clear to me what would happen to the birth rate. I found myself initially thinking the birth rate would go down, but I think this is because the framing of the question put a particular kind of parent in my head. High income, wants their life to stay "just so" even after the kid. This sort of parent is more likely to only want to have one child, so it mistakenly led me to believe the effect of the sex-selector would be to decrease birth rate. But on considered re-evaluation, I don't think that's necessarily so.

At 12:23 AM, October 27, 2006,  Berna said...

I think the birthrate would go down. Today, some parents have more children than they'd have if they could choose the sex of their children. For example,if a couple really want a girl and a boy, and they get two boys or two girls, they might have another child, hoping it will be of the other sex. If they could choose the sex, that couple would have only two children instead of three.

At 1:31 AM, October 27, 2006,  David Friedman said...

Berna makes an entirely plausible argument for why the birthrate might go down.

But that leaves the puzzle. What is the flaw in my argument to show it must go up? Is it that children are a Giffen good--something you buy less of when it gets cheaper? That's logically possible but not, I think, plausible. Is there a better simple answer?

At 4:52 AM, October 27, 2006,  adam said...

First of all, it's not the case that the cost of having children goes down with sex selector technology (SST). Rather, the cost of having a child of a given sex goes down. SST would not affect the cost of having a child at all for parents who don't care about the sex of their children.

Currently, a side effect (and a cost) of having a child of a specific sex is a chance having more children of the other sex, thus increasing the birth rate. This side effect would be eliminated with SST. So let's do a thought experiment, and say we can quantify the cost of having a child at \$100,000 per child. For simplicity, we'll assume that that number is constant no matter how many children a couple has. Without SST, the average number of children that a couple must have to have a child of a specific sex is 2 (=sum n/2**n, for n from 1 to infinity). Let's say that the government passes a law setting the price of SST at the same \$100,000. Then the cost of having a child of a specific sex will remain the same as it is now, but the birthrate will go down, because parents who want a child of a specific sex will use the technology, pay the same cost, but without the side effect of having more children. So the lowered birthrate that would be an effect of SST is not related to the cost of having a child of a specific sex, because the birthrate would decrease even if the cost of having a child of a specific sex remained constant. Thus, the decreased birth rate is not evidence that children are a Giffen good.

David, did you have a specific solution in mind, and am I anywhere close?

At 4:58 AM, October 27, 2006,  Andy said...

Is the flaw that the argument hasn't distinguished between total value and marginal value?

Parents will stop having children when the marginal value of an extra child falls below the cost of the extra child. However, although sex selection will increase the total value of a litter of children, that tells us nothing about the point at which the marginal value falls below the cost.

So, to put numbers to Berna's example, litters of 1, 2 and 3 children may have total (expected) values of 20, 30 and 35, respectively without sex selection, and 35, 40 and 41 with sex selection. The marginal values of the 1st, 2nd and 3rd children are thus 20, 10 and 5 in the first case and 35, 5 and 1 in the second.

If the cost per child is, say, 7, then a couple will have 2 children without sex selection (MV(2) = 10 > 7, but MV(3) = 5 < 7), but only one child with sex selection (MV(1) = 35 > 7, but MV(2) = 5 < 7).

If, however the cost per child is, say, 25, then the couple will have no children in the first instance and one child in the second.

So, whether sex selection results in increased or decreased fertility will depend on the details.

In neither case are children necessarily Giffen goods. Provided that the total cost is a small proportion of total income, so that the value is unaffected by expenditure, in each case lowering the cost per child increases the number of children a couple can have before MV falls below cost per child.

At 5:26 AM, October 27, 2006,  paul said...

I would think of the problem more like trying to maximize the return on my portfolio of offspring. The return would consist of likelihood of passing on my genes and quality of the relationship during my lifetime. So things like lower child mortality rates should reduce number of offspring. Increases in wealth could lower the birth rate if the quality of relationship increases faster than lower cost of child rearing. Given that the ability to spend a lot of time with a child is a severely limiting factor (at least for now), utility for a high quality per child dominates more children.

I know this isn’t a proof but I think this explains my motivations.

At 7:07 AM, October 27, 2006,  markm said...

Children aren't a Giffen good. What do you call a good where one wants so much, but definitely no more, and there is limited ability to substitute? That is, a boy may substitute for a girl, or vice versa, but some people won't be satisfied, and the only substitutes for your own children are a very limited supply of adoptable children, or pets.

I knew a couple who had five boys, and the noisiest house I've ever been in, before she gave up on getting a girl. With sex-selection, they would have stopped at two or three. That was quite a while ago (her boys will be middle-aged now), so both the targeted family size and the point where people would give up on getting the desired gender are probably lower, but I do know someone who decided to have a third child because the first two were boys. (#3 was a girl, and definitely the last one.)

I'm not sure how many people would decide to have just one (girl or boy) if it was possible to specify which one, but wouldn't risk getting the wrong gender. There's no one who would admit to thinking that way in my conservative Midwestern small town, but I can't guess as to how the numbers would balance out over the country.

At 7:08 AM, October 27, 2006,  jose carlos said...

Imagine a couple that has already five children, but all of them are girls. When they got married they wanted to have two kids, a boy and a girl, but because the boy didn't come with the second pregnancy, with the third and so on. They kept their quest to get a boy.

So, if this couple had the possibility to choose their children's gender, they, probably, would not have five or more but two kids!

The japanese and spanish crown can't be hold by a female. Japan solved their problem with a recently born boy, in Spain princess Letizia is pregnant and hoping to give birth to a male, who, i guess, like in the japanese case, would not "exist" if the gender of a child was decided by parents or by the government.

At 7:09 AM, October 27, 2006,  markm said...

Correction: What do you call a good where one wants so much, but definitely no more, and there is limited ability to substitute and virtually no trade?

At 9:10 AM, October 27, 2006,  Mark said...

Got it now, thanks to Berna.

For some people, "children" are actually two different normal goods which only weakly substitute for one another. You put in an order, and you randomly get one of the two goods.

At 11:55 AM, October 27, 2006,  David Friedman said...

Several people saw why the argument was wrong. I don't think anyone put the fallacy in quite the terms I would, although Adam came close.

The error in my original post is the definition of quantity. I'm treating it as if the quantity axis measures number of children. But for some parents, the relevant quantity is number of children of the desired sex (or some weighted average of children of the desired and the undesired sex). By that measure quantity goes up--but since children of the unwanted sex are no longer a side effect of producing children of the wanted sex, number of children might go down.

For a clearer example, suppose we are told that the producers of light bulbs have increased the quality of their packages of bulbs while holding the price constant. Do we buy more packages? Not necessarily--the "quality" increase might be that the packages now have three bulbs instead of two, and it is light bulbs, not packages, that are the relevant quantity dimension. Similarly in my case, except that the "package" goes from .5 desired + .5 undesired to 1 desired.

I think it's an interesting puzzle because, in doing economics, we normally don't think about ambiguities in what belongs on the quantity axis of a diagram.

At 12:54 PM, October 27, 2006,  Mark said...

The "different goods" model strikes me as more apt than the "quantity" explanation.

Hypothetically say the only way to get fruit is to put in an order for "1 fruit," and you randomly get an apple or an orange.

If we were suddenly change that delivery system so that you could specify the type of fruit, we might see total fruit demand go down.

Under the old system, those people who only wanted an apple, or who really wanted at least one of each, might decide to just keep ordering until they got the set they wanted or until they were unwilling to risk more unwanted fruit being delivered.

Under the new system, they order only what they want, so total "fruit" ordered by such people goes down.

At 12:25 AM, October 28, 2006,  Anonymous said...

'Increased quality at constant cost corresponds to decreased cost at constant quality'

No it doesn't - whilst the quality may increase at the same cost, this doesn't mean that the cost of the previous quality decreases. The price doesn't fall, and therefore the number of children being born doesn't rise.

At 10:37 AM, October 28, 2006,  Matt Brubeck said...

If, many more people chose boys than girls, then the birthrate would drop dramatically in the second generation (when there are fewer women around to bear children).

At 6:29 PM, October 28, 2006,  Anthony said...

The only way I could see the birthdate going up is if there are large numbers of parents whose preference to not have a boy (or two boys) is stronger than their preference to have many girls, but who would prefer many girls to few girls. Given the ability to avoid having boys, those parents might choose to have more children than they might otherwise. (Of course, the genders are reversible here. I also take it as given that people who would prefer many children are far less likely to engage in sex-selection abortion than those who prefer fewer children.)

At 9:02 AM, November 02, 2006,  Anonymous said...

Its helpful to use more precise labeling. Lets call a child of the unwanted gender a BRAT and a child of the desired gender an ANGEL. With SST, we have reduced the cost of having an ANGEL. Obviously, the number of ANGELS would increase, while the number of BRATS would decrease. Would the increase in ANGELS be greater than the decrease in BRATS? We don't have enough info to answer that question.