Friday, 29 January 2010

Explaining the cross-sectional variation

Sinclair Davidson is a bit puzzled by cross sectional variation in the paper I noted a few days ago. The paper suggests that stigmatization of pre-marital sex had a lot to do with the costs of raising children out of wedlock and the incidence of those costs; since churches are no longer largely liable for the costs of the orphanarium, mainline protestant church prohibitions on premarital sex have declined over time. Davidson then is puzzled by the current cross sectional variation, where the incidence of premarital sex and out of wedlock births are higher for the lower deciles, who potentially have to pay a greater proportion of income to raise an out-of-wedlock child.

I'd argue to the contrary. Think of the game as follows. At time t, you choose whether to engage in premarital sex. If so, there's probability p of an unwanted pregnancy. The female bears those costs with certainty; the male, only probabilistically. At time t+1, you marry, and there's a chance of getting a high quality or a low quality spouse. If you're in a high decile, you're more likely to get a high quality spouse. If you have a prior child (or child support payment encumbrances) from time t, you're less likely to get a high quality spouse. If your chances of getting a high quality spouse at time t+1 are sufficiently low (because you're low decile), then the lifetime costs of having an out of wedlock birth at time t are lower. Cross-sectional variation explained!


  1. Eric thanks for that.
    I'm puzzled by this line in the conclusion
    "Parents at the lower end of the social economic scale would have less incentive to engage in such practice" [socialising their daughters].
    Bearing in mind that grandparents also bear costs of child rearing, especially if born out of wedlock and by your argument stood to benefit if they could trade up the social scale by securing a 'better' marriage for their daughter.

  2. Parents at the top end of the scale would see their chances of high quality grandkids (because of high quality spousal match for the daughter) drop considerably while those at the bottom would see a smaller drop in the probability. So the expected costs are lower at the bottom end. No? Sure, the benefits of hitting lotto are higher, but the odds are tiny.