Monday, April 03, 2006

Are black ghetto kids at the bottom of the work food-chain? Poor Americans and competition with immigrants

Mickey Kaus claims that the only way to to help out poor Americans, especially poor black Americans, is to create a tight labor market: low unemployment drives up demand for labor, and wages, high enough to start a family and give the disadvantaged a real stake in society. (Kaus dismisses the EITC and universal health care.) His theory:
A tight labor market is especially important for young black men because they tend to be at the end of the employment queue. You have to let employers run through all the groups they prefer--and illegal immigrants are one of them--before they will reach out to ghetto kids. That's the sociological reality. If we let in lots of unskilled immigrants, however deserving, they will jump ahead in the queue.
If there is truly a perception that (i) there are fairly homogeneous subpopulations in America, and that (ii) each individual in a given subpopulation has a fairly well-defined productivity given by his subpopulation, and that (iii) even illegal immigrants are above ghetto-folk in this productivity ranking, then inner city youth are in dire straits indeed. If this is true, then there is basically no way to assist poor inner-city black Americans except by changing the basic social facts on the ground--by training these disadvantaged folks to be more employable, and simultaneously by changing perceptions about them. On Kaus's hypothesis, trickle-down just doesn't work (until the unemployment rate hits unsustainably low levels).

One way to test this hypothesis would be to compare how ghetto residents' unemployment changes with the aggregate national unemployment level. Recall that ghetto unemployment is astronomical: roughly 72% of poor black young men are either out of work or incarcerated. We can take this number to be, in effect a measure of the tragedy of "full unemployment." If this number does not vary with the national unemployment rate (unless the national rate drops very low and employers are "forced" to dip into the ghetto pool) then Kaus is on strong ground. If the ghetto rate varies in some proportion with the national rate, then the different pools of laborers are perceived as being at least slightly (a) internally inhomogeneous and (b) partially overlapping in perceived productivity. That is, the most productive ghetto resident is (perceived as) more productive than, for example, the least productive illegal immigrant. In that case, a national economy which is growing overall can indeed trickle down to the poorest American citizens, and one might suppose that admitting immigrants would be consistent with helping the disadvantaged. (Through, for example, incentive effects that push ghetto residents to be more productive.)

Beneath the fold is a suggested way to mathematically model this question of ghetto vs. national unemployment and whether poor blacks are discretely at the bottom of the food chain. That is the only way to test the Kaus hypothesis. One could model this as follows. Consider the distribution for various subpopulations of numerosity as a function of productivity, so that number of people is the ordinate, and monetary value per hour is the abscissa. Of course the productivities will range somewhere on the order of the minimum wage, and the numerosities will be measured in millions of people who are economically employable at that productivity.

Let's take the distributions to be three gaussians g_i, {i=1,2,3} with means m_i and standard deviations s_i. Say that i=1 is ghetto blacks, i=2 is illegal immigrants, and i=3 is some boring non-minority lower-middle class America. We assume, with Kaus, that m_1 and m_2 are less than m_3. We'll need to normalize g_i to their respective percentages of the total population.

The unemployment rate u% sets the minimum productivity p which is employed, p_min(u). p_min(u) for a given u% is set by integral(sum(g_i)) from infinite productivity down until we reach a given productivity where the area is equal to 1-u%. (Determining u% from g requires inversion.) Then we ask what the value of 1-integral(g_1) from p_min(u) to infinity is; that is, what the ghetto unemployment rate is. Assuming that the non-minority lower-middle class American pool is sufficiently distinct (highly productive) from 1 and 2, one would then play around with m_1, m_2, s_1, and s_2 to try to reproduce empirical data from NBER or Dept of Labor or wherever. Of course this requires minimizing errors, and so a calculus of variations is required for m, s. One is basically assuming that cultural facts remain constant and the unemployment rate is sampled, resulting in some determination of black unemployment as a function of total unemployment.

When this is finished, if m_1 is less than m_2, and s_1 and s_2 are both less than |m_2-m_1|, then blacks indeed can only be helped by a tight labor market. Otherwise, the best blacks will be picked off by the national market, and the ghetto will be at least somewhat intertwined with the overall economy.

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