Wednesday, May 20, 2009

The Incidence of Women's Progress -- Technical Version

In the New York Times Economix blog today, I discussed recent empirical findings that women have lost in relative happiness even while their labor market outcomes improved. The purpose of this post is to interpret this finding with more technical notation than I did in NYT.

The 1970s through the 1990s are notable because (economists have repeatedly measured that) women worked more in the marketplace, both in absolute terms and relative to men. I am not aware of any evidence that women consumed significantly more relative to men.

The major reason for working in the market place is to enhance one's own consumption or the consumption of one's family. The major reason for not working is, well, working is EFFORT. The evidence compiled on the women's labor market clearly shows that women put forth much more time effort in the marketplace than they once did. Absent good evidence on their consumption, I have to say that it is very likely that women did not have their individual consumption increase as much as their market effort did.

Previous studies have attempted to partly rebut this point by saying that women have ENTIRELY offset their extra market time and effort with less non-market time and effort. There was an offset, but not 100%.

Professor Yona Rubinstein and I have published a theory of why women supply more human capital to the marketplace now than they used to -- the increase in the return to skill. The increase in the return to skill does not necessarily make people happier on average (not that unskilled people had their wages fall). But it does change COMPARATIVE advantage and therefore the identity of the people who will put forth the effort.

Consider this simple model: all Americans are in one family and consume the same amount c. But time and effort is individual, with person i working ni. Each individual's personal happiness is u(c) - vi(ni), where u and v are increasing functions. Moreover, v for men is such that the efficiency supply of effort for men is less elastic.

Now change comparative advantage in a way that raises aggregate output. Consumption rises for everyone, and that by itself makes everyone happier.

It is efficient to increase the effort of some people and perhaps efficient to decrease the effort of others. The people who work more are (individually) LOSING happiness relative to those who decreased their effort [Kydland and Prescott made this point in a published paper once -- I forget the citation].

As Professor Rubinstein and I explained, between 1970 and 1990 comparative advantage changed in the direction of causing high skilled women to work more in the marketplace. Low-skilled women's market work did not fall to offset this, so the average woman was working more. Thus, to the extent the one family model is correct, women will lose happiness relative to men.

The one-family model has been criticized -- one obvious thing is that consumption is not the same for all people. But, given that women and men so often live together in reality, the one-family model illustrates the reality that the incidence of effort can be quantitatively different than the incidence of consumption, so that the people working most in the marketplace are not necessarily the happiest.

No comments: