Births Revisited: Births, Population and Per Capita Income

Well, after my last post I finally got around to calculating another measure of the birth rate – births per capita.  Total births are a useful aggregate but the measure does not adjust for population size.  There are other fertility measures out there such as births per woman aged 15 to 44 years but per capita births is a nice intuitive measure that adjusts for population size and can be readily compared to other numbers – such as per capita income. Moreover, it was easy to calculate.

When per capita births are considered for Canada (Figure 1), the Depression era sees a drop in births and is then followed by a rising birth rate - a baby boom.  (The data sources are described in my previous post). However, when per capita births are used, the birth rate starts to rise in 1937 and peaks in the mid-1940s and then starts to decline.  Interestingly enough, even this series shows a slight rebound in the birth rate since about the year 2000.

 

Figure 2 plots per capita births against real per capita GNP/GDP (in 1981 dollars) for the period 1921 to 2010 and then takes a LOWESS smooth of the relationship.  There is a bit of an inverted J-curve here.  As per capita income increases, per capita births at first increase and then begin to drop sharply.  The overall relationship is negative and babies eventually become an inferior good if income rises high enough. Babies in Canada became an inferior good right about the point when real per capita GNP in 1981 dollars hit about $5,000 annually which happened in the 1940s.

 

Indeed, a log-log linear regression of per capita births on real per capita GNP gets you a coefficient estimate of -0.45, which is negative income elasticity.  A 1 percent increase in real per capita income causes per capita births to drop by almost half of one percent.  The linear regression estimate (t-statistics in brackets) was:

Log of Per Capita Births = 0.133(0.50) - 0.453(-15.65)*Log of Real Per Capita GNP

and with an adjusted r-squared of 0.73. Given that real per capita income in this regression explains almost three quarters of the variation in per capita births and that the post war baby boom is usually seen as starting in the late 1940s - about the same time having children becomes an inferior good - I think that the post-war baby boom is the residual in this regression equation.  Or, we may need to rethink when the baby boom actually occurred.  On a per capita birth basis, the birth rate satarts rising in 1937 so the baby boom may have been underway a decade earlier than usually ascribed.  This first phase was a response to the front end of the J-curve - a positive relationship between income and children.  Rising income after the abyss of the Depression led to people having more children.   The second phase of the boom after 1947 actually coincided with a negative income elasticity of demand for children and therefore can be viewed as driven by extraordinary factors that countered the effect of a rising income. 

Comments

[marcel]

Or, we may need to rethink when the baby boom actually occurred. On a per capita birth basis, the birth rate satarts rising in 1937 so the baby boom may have been underway a decade earlier than usually ascribed.

So, by the late '40s, there were enough children not yet into puberty (but counted in the per capita denominator), and not yet having children of their own, to bring down the per capita birthrate? I think there is a reason that demographers focus on the fertility rate (with women, 15-44, in the denominator) rather than the per capita birth rate.

[blink]

Like marcel, I think more specific demographic data would be more convincing. Even so, I think the relationship is likely overstated in the data because of expectations. One expects a "bust" during the depression as parents who expect their financial prospects to improve delay having children. Thus a "boom" simply due to the business cycle.

Separately, I think it is unfair to call babies "inferior goods". Yes, I see the income elasticity, but the "price" and "quality" of children is endogenous. This simply shows that parents are "trading up" -- one "luxury" model kid for two barely-fed rug rats.

[Livio Di Matteo]

Marcel/Blink:
Per capita birth rate is definitely a crude measure. I suppose it would be interesting if such limited data could get a handle on the quantity/quality issue. For example, real GDP per birth over time might be a way of measuring how more resources per child are now available - a quality of children measure. Another point is that the declining per capita birth rate starting in the early 1950s could also be partly driven by the higher amounts of immigration into Canada in the immediate post-war era.

[J.V. Dubois]

Very interesting stuff. However if you are on to the long-term measures, I think the best possible way to do is to do the stats as birth rate per cohort. The big problem with other measures is that it does not count with delayed births due to the facts such as:

- Temporary adverse phenomena, such as recessions. This is what happened to Sweden in 90ies crisis. It almost seemed as if births fell from 2 childs per woman to 1,5. But there was a sharp rebound and small "baby boom" in late 90ties and early oughts to make up for this temporary depression induced fall in fertility rate.
- Long-term phenomena such as increase of participation of women in labor force or tertiary education prior to giving birth. There was overall trend of delaying births by almost a decade

But if we assume that a cohorts of women 44 years old and older are done with reproduction, you can make the comparisons much more easily.

[Ryan]

Let's not forget the role and increased access to birth control. If population increases steadily, the per capita birthrate should obviously also decrease. But doesn't that just make the mid-80s and early-00s increases in the numbers all the more interesting?

I presume we're not looking for a perfect statistical model here, but rather using statistics as a tool to discover some interesting trends and theorize some implications. There's nothing so egregious about the per-capita birthrate that would invalidate any of Matteos's theoretical musings.

I think you've uncovered some very interesting things here.

[JW Mason]

You are regressing two nonstationary series. You can't do that - the results are meaningless. All you are seeing is the upward trend in GDP and the downward trend in birth rates. You've shown nothing about their relationship.

Seriously, you can get to be an economist these days without knowing about unit roots?

[Livio Di Matteo]

JW:
Well, I suppose I could test for unit roots and then estimate co-integrating relationships but given the span of the data as well as the quality of the data (remember I have two different birth series here) I'm not sure if the power of the tests would be sufficient to shed that much more light on the relationship. There is definitely the possibility of a spurious relationship between birth rate and per capita income but there are also other variables left out here that might be involved in the relationship.

[JW Mason]

It's not that you could, it's that you have to. If this data won't help you answer the question once you do that, then it just won't help you answer the question, full stop.

Anyway it's pretty obvious the series are nonstationary. Take any two series where the trend is large -- any two at all -- and you will find a highly significant relationship between them such that one "explains" much of the variation in the other. It's meaningless.

[Livio Di Matteo]

Well, I guess you got me there JW. That is why I'm glad I do most of my empirical work with micro-data!

[Julian Janssen]

I just posted a new blog post on Professor Arthur Laffer's op-ed in the Wall Street Journal and mentioned Nick Rowe's post on Milton Friedman's Thermostat.

http://socialmacro.blogspot.com/2012/08/laffernomics-strikes-again.html