Which sector becomes a profitable occupation depends on the initial occupational composition of the community. When the distribution of skill in the two sectors is similar and the positive correlation in skill is weak, both sectors benefit from a positive selectivity bias—the average skill level in both sectors is higher than the population average. If the skill correlation is high enough, then this latter behavior causes the smaller sector to suffer from a negative selection bias -- the average skill level here is lower than the population average.
Typically, the sector with the highest variance becomes the preferred sector, but when the correlation in skills is sufficiently high, full clustering in the sector with low variance is possible. Likewise, agents with less talent in both professions prefer to hide in the smaller sector. The only exception is when a sector average is invariant to shifts in the indifference line.
Solution to the Single Period Problem
This generates enough downward pressure on the mean in sector Y for a stable corner solution (L3 and L4) to exist. Indeed, for sufficiently high levels of correlation, the corner solution is the only stable equilibrium (L4). To understand why a stable corner solution can exist, consider the case of identical skill distributions in both sectors with perfect positive correlation.
When the older generation mostly belonged to sector X, more weight was given to individual than average talent for those who chose sector X (and vice versa for those who chose Y). Since all agents are equally talented in both sectors (due to perfect positive correlation), those with above-average skills would choose X. Suppose there is an equilibrium in which all agents with skills below some critical level, say η, choose Y and the rest go to X.
A perfect positive correlation implies two properties of any such equilibrium: the average skill level in X would be above η and the average skill level in sector Y would be below η. Given these facts about sector assets, the frontier agent strictly prefers sector X; switching from Y to X increases its status -- from the average in sector Y to η among the elderly in sector X and from η to the average in sector X among the elderly in sector Y. Thus, the frontier agent always prefers sector X, resulting in of all in sector X as the only equilibrium.
A question that follows logically is that of the continuation of such an extreme grouping in a sector in the long term.
Steady State
Analytic Steady States
As mentioned earlier, the rather high positive correlation in skill implies that if a large proportion of highly skilled agents chooses one of the two sectors, it significantly lowers the average skill level in the other sector. When this causes a very sharp drop in average skill in the other sector, it results in extreme clustering in the sector that is initially larger. Note that conclusion 1 holds even when the mean in the low-variance sector is below that of the high-variance sector.
The intuition for this result is as follows: If the entire population is in the low-variance sector, people who are highly skilled in that sector do not want to move because their skill is recognized by a large audience. The answer lies in the inferences that would be made about them if they were to move. For the reasons just mentioned, everyone knows that highly skilled individuals in the low-variance sector will not switch sectors.
If the positive correlation in the endowments is sufficiently high (as defined in Proposition 2), this implies that its expected endowment in the high-variance sector is also relatively low. However, because the other sector has a higher variance, relatively low capital in that sector is worse than relatively low capital in the low-variance sector. The reason why extreme clustering is not possible in the high-variance sector is most easily discovered in the case of bounded endowments.
Even though the rest of the population assumes she has the lowest possible endowment in that sector, her status is still greater than what she received in the high variance sector. Furthermore, while individuals in a society may all be caught in such a "low" equilibrium trap, it is unlikely that they would all end up in the higher skill sector, despite the desire to be valued.
Numerical Simulations
Additionally, for each steady state Table 1 contains the share of the population in sector X and the average skill level in each sector. Figures III through V show the fraction of the population in sector X as a function of the fraction in that sector in the previous generation. The sector with medium or greater variance is the largest sector in the steady state and has the most status associated with it, i.e.
Second, we maintain identical marginal distributions in the two sectors, but allow for positive correlation in skills across sectors. The introduction of a positive correlation in skills results in systematic (and symmetrical) overallocation in one of the two sectors, with the degree of misallocation increasing with the strength of the correlation. As seen in the top panel of Table 1, the degree of positive correlation must be quite large before the misallocation effect is noticeable.
The model can explain why changes in marginal distributions should amplify the effect of a positive correlation on skill. In particular, when the marginal distributions are identical and the correlation in endowments is weak, most agents have a distinct absolute advantage in one of the two sectors. The finding that a negative correlation in skill reduces the rate of misattribution is in contrast to some previous results in the literature.
Jovanovic assumes that skills are perfectly observable in the low-variance sector and unobservable in the high-variance sector. However, when the marginal distributions are different, one of the sectors is larger when the correlation in endowments is zero.
Policy Implications
The presence of a large sector increases (decreases) the size of the absolute advantage needed for highly endowed (poorly endowed) people to stay in the smaller (larger) sector. In other words, the presence of a large sector creates an integrated stage in which the highly endowed can be seen and a hiding place, the smaller sector, for poorly endowed individuals. Returning to Figure III, the transition paths show that at steady state, a community is overrepresented in the sector to which it was historically (or initially) predisposed.
An alternative approach to changing this relationship is to collectively shift the focus of the current residents. A good example of this latter kind is the impact of Eugene Lang's scholarship guarantee experiment, which he offered to an entire class of sixth-grade boys in Harlem, New York.27 Six years later, 40 of the 51 boys had done well enough to could attend college without Lang's financial assistance. Alternatively, programs that devote large amounts of resources to education in the housing projects may be dead weight until a more positive environment is created where educational achievement is encouraged and valued by the reference group.
Similarly, policies that provide merit-based (isolated) incentives to people living in low-educated communities may not be very effective in improving performance. Thus, isolation and lack of appreciation of one's performance in the reference group may reduce the incentive effects of merit premiums enough to result in choices that go against comparative advantage. At the same time, cost subsidies and scholarships can have a greater significance in changing individual choices in a society if it is already in an internal equilibrium.
In the context of the policy debate on measures to improve the educational attainment of disadvantaged minorities in the United States, we believe we recognize this. Thus, while individual communities may underinvest in education, society as a whole is likely to overinvest in education (the only remaining stable situation).
Other Issues
In particular, when analyzing the economy as a whole, wage effects would prevent the economy from moving to a stable boundary condition. There are additional factors that affect one's position in a community, many of which are interesting to study in their own right. Banerjee, Abhijit and Andrew Newman, "Occupational Choice and the Process of Economic Development." The Journal of Political Economy Volume 101, Number 2 (April.
Heckman, James, and Guilherme Sedlacek, "Heterogeneity, Aggregation, and Market Wage Functions: An Empirical Model of Self-Selection in the Labor Market." The Journal of Political Economy Volume 93, Issue 6 (December.
Appendix
- Proof of Lemma 1
- Lemma 2
- Proof of Proposition 2
- Proof of Corollary 1
Therefore, as *0 y increases, the average*0 allocation in sector Y increases in size at an increasing rate (unless ρ =Y 0) with the same sign as ρY. Thus, the average endowment in sector Y is negative and decreases at an increasing rate if σXY σY2 <−1 m and positive and increases at an increasing rate if σXY σY2 >−1 m. In contrast to sector Y, as y increases, the average endowment in sector X is 0* which decreases in size at a decreasing rate (unless ρ =X 0) with the opposite sign to ρX.
Thus, the average endowment in sector X is negative and increases at a decreasing rate if m< σXY σ2X and positive and decreases at a decreasing rate if m> σXY σX2. However, as the correlation increases, the slope of the line increases, eventually becoming positive (when ρY is negative, i.e., m−1<σXY σY2). In this case there are two solutions, the fixed point depicted in the graph (line B) and the limiting point of y equal to plus infinity.0 However, the limiting point is unstable.
As the correlation becomes even stronger, the slope of the function will exceed one, as illustrated by line C. Finally, for correlations0 close enough to one, the function never falls below the forty-five degree line and the only solution is the limiting point of y equal to plus infinity which is stable.0. However, for the series of correlations corresponding to line C, there are two stable equilibria: one in the interior and the other with the entire population in one sector.
From Proposition 1, we know that extreme clustering in maternity is a single period equilibrium if and only if the slope of the RHS of (3-1) is greater than one. The loss in total employed skills and the proportion of the population in both sector X and incorrectly allocated to each sector, assuming a bivariate normal distribution of skills.
The Loss in Total Employed Skill and the Fraction of the Population in both Sector X and Misallocated to Each Sector, Assuming a Bivariate Normal Distribution of Skills
Indifference Line Dividing Sectors X and Y
The fraction of the current population that wants sector X as a function of the fraction actually in sector X.
The Fraction of the Current Population Desiring Sector X as a Function of the Fraction Actually in Sector X
Single Period Solutions: Equal Means and Variances in the Two Sectors
Single Period Solutions: Endowments Are Uncorrelated with Equal Variances (Differences in Sector Means Are Given in Standard Deviations)
Single Period Solutions: Equal Means and Zero Covariance Between the Sectors
