by Filip Palda
The difference from the case where equalizing differences were possible would be that in the sorting, the effort to lobby would chew up or “dissipate” resources through the competitive lottery to find a job or hire a worker. Without the wage differential the simple process of achieving an equilibrium solely through matching would call for a huge and wasteful expenditure of resources on lobbying.
Here is a hint of the wisdom of spatial analysis. In tied-sales, any sort of government attempt to control prices may have unexpected and unpleasant consequences. This is not an indictment of government but rather the reverse. Intelligent intervention requires an appreciation for the subtleties of markets, and in these, spatial analysis abounds.
Racism and the dissipation of wealth
IN THE CASE of the gold mine, workers have preferences for certain employers that go beyond the wages paid. We can also see this play of preferences at work in the case of racial discrimination. When racism is at work the employer prefers a type of worker that has nothing to do with that worker’s productivity but rather with the worker’s race. What emerges from this toxic brew of hatred is a wage premium for the favored racial group. But racism in the market sort of meets its match at the margin when the wage premium starts making some employers with a lower taste for the favored group consider the attractiveness of hiring equally productive members of the despised group. As in the case of mines, an equalizing difference in wages emerges that sorts favored workers with employers who have a strong taste for them, and despised workers with employers who don’t mind them so much.
Here, as with miners toiling in environments contaminated by cyanide, the wage premium allows everyone to find work quite easily but in a segregated setting. Yet racial discrimination is a bad thing, just as is cyanide pollution. What if we pass a law saying that everyone must be paid the same wage? Now companies with a taste for racism cannot use a premium to attract favored workers and firms that previously were not racist have no financial reason to hire members of the despised group. But racism has not disappeared. The racist group may use informal means, such as lobbying favored workers to join their firm. And non-racist companies may now hire members of the favored group because there is no wage discount to entice them to prefer members of the despised group. This may force members of the despised group themselves to actively lobby non-racist companies to hire them.
The result of all this lobbying may result in the depressing outcome that the same old segregation emerges. In addition to which no one will be better off than before. Racist companies will have dissipated in lobbying expenses the premium they once paid favored workers, and despised workers will have expended the windfall from the new equal wage they are earning on efforts to gain employment.
This example shows that space and tied-sales have the makings of a curse. Remedies we apply may work against our best intentions. Hope may lie in education and research that reduce the dimension of these spaces by cleansing hatred from the heart and pollution from the workplace.
The curse of dimensionality
IF YOU THOUGHT space was a curse in one dimension, such as racism or pollution, imagine how bad its effects can be when both employees and employers have a list of demands for the other.
In deciding where to work, a teacher will not just care about salary but also about the quality of the school’s students and its amenities. Schools care how well a teacher educates. This may depend not just on his or her abilities as vouched for by testimonials and degrees earned but also on the types of students he or she will be teaching. How well that teacher interacts with a particular school’s students will depend on his or her age, ethnicity, sex, and potentially many other factors which may only be of particular interest to that school, such as perhaps a tolerance for lack of discipline.
Rosen explained the problem as follows: “While teachers may have well defined preferences for schools and students of various characteristics, it is also true that schools may well have distinct preference for various types of teachers and their attributes. The matching problem is therefore more complicated ...” (1986, 664). To clear this market, there must be a separate wage premium, or “equalizing difference” for each possible combination of dimensions which matter to teachers and schools. The simplest case is that of predominantly black or white schools in the US and the salaries they pay to black or white teachers. There are four possible wage situations here. White teachers and white schools may have a preference for each other, yet there may be too few white teachers to fill all the posts so black teachers with a preference for black schools may have to be attracted by a wage premium. This drives up wages in black schools which must fill their need for teachers, so some white teachers on the margin of indifference between teaching in black or white schools may be attracted away from white schools. In the end, both black and white schools will have mixes of black and white teachers, and any teacher of one race will have to be paid a different premium to teach in a school of different race. The degree of mixing may be quite limited if teachers interact poorly with students of different race and have strong preferences for teaching students of their own race. Of course the same problem was evident in the case of racism in hiring decisions, but there was “only” the racial preference of the employer to contend with.
When racial considerations by both employers and employees must be considered, the conundrum of clearing the market swells. Wage premiums may have to be large in order to clear the teaching market. These may kill off schools and leave teachers unemployed as the racial factors involved in the tied-sale may be so varied that there is no market clearing price for teachers of one race in schools of another race.
Such is the curse of dimensionality in space. As more features figure in the tied-sale, wages progressively lose their ability to make markets clear. That means personal characteristics become the only features that matter regarding where you work and whom you wish to work for. The price of such indulgence of preferences can be foregone productivity, as people who could be a productive asset in one business are blocked by prejudice. Our preferences balkanize us instead of uniting us.
As we can see, space is an unwelcome relative in the family of economic concepts. It can make nonsense of the most reasonable propositions. It can also lead to surprising conclusions about government policies that show contemporary economic sages in a diminished light.
Curving economic space
ONE SUCH SURPRISING application arises in the labor market. Some jobs are about more than just wages. Workers are not simply selling their labor. They are also buying certain desirable on-the-job amenities such as child-care, comfortable parking, and cafeteria services. They “purchase” these amenities by providing employers with desirable qualifications and perhaps by accepting a wage that is below what they contribute to the company’s profits. The sales are “tied” because they are an inseparable part of working in the chosen firm.
One of the most studied aspects of tied labor market transactions is the value of on-the-job training for young, low-wage workers. In pre-industrial times apprentices valued this training so much that they paid their employers for the privilege of working the seven years it took to become certified in a trade. Even the young James Watt, later the inventor of the modern steam engine, trudged all over Scotland and England in a desperate attempt to find someone willing to train him in the trade of scientific tool-making. Today schools have assumed the task of teaching trades. Yet one can still detect an echo of this process in medicine, last of the surviving secretive medieval trade-protection organizations. Interns work like serfs in the expectation of princely salaries to follow.
Apprentices and budding physicians are not the only ones who benefit from on-the-job training. The same can be said of young, low-wage workers. Firms may be willing to take them on and train them up provided that they can be compensated for their efforts. Young workers will compete for jobs that teach general skills by offering their services at a wage sufficiently low to compensate employers for the
learning experience. Finnis Welch wrote that “since workers can take the benefits of training with them when they leave for other employment, firms may have little incentive to offer training. But they can offer on-the-job training in exchange for lower wages” (1978, 31-32).
The reason such training is of necessity to a tied-sale is that not everything can be learned in the classroom. Sherwin Rosen explains that “It is a common observation that most specific job skills are learned from work activities themselves. Formal schooling complements these investments, both by setting down a body of general knowledge and principles for students as well as teaching them how to learn. But even in the case of professional training there is no perfect substitute for apprenticeship and for work experience itself” (1986, 677). There is no educational substitute for elbow grease.
Into this discussion, add the minimum wage. Few people, even few economists, associate this seemingly humanitarian government policy with worker training. Yet a bit of reflection clarifies that in the tied-sales environment of the workplace the minimum wage may rob workers of the chance to learn job skills that could raise them out of poverty. As Sherwin Rosen has explained,
An effective minimum wage puts a distinct ceiling on the worker’s ability to pay for on-the-job training, and this constraint is more binding the lower the worker’s productivity … Minimum wage legislation not only denies on-the-job training opportunities for those who are displaced from employment, but also constrains young workers’ access and opportunity to those work environments with intensive training and learning components (1986, 680).
The logic is that when the minimum wage rises it creates among workers an excess demand for on-the-job training. At current levels of training the minimum wage effectively reduces what workers must implicitly pay through an equalizing difference in their remuneration. With this excess demand, firms can to some degree “curve” characteristic space by reducing the amount of training their jobs offer. With sufficient flexibility to curve this space, the supply of workers equilibrates with the demand by businesses. Put less technically, if government mandates that you be paid a great deal to do a job which is basically a form of education and stepping stone for other jobs then you can expect that many outsiders will try to compete for your position. These competitors may be willing to accept less on-the-job training than are you. Companies will oblige them and you will be obliged also to accept less on-the-job training.
This complicated view of labor markets may help to explain a finding that crops up now and then. Minimum wages do not seem to lower employment in some cases. According to Economics 101 when the price of something rises people demand less of it. If you raise the wage, the price of labor, employers should demand less of it. But some serious examination of real-life data shows that this is not so in some cases. Which is not to say that the minimum wage has no effect on equilibrium in labor markets. What it means, as seen through the lens of Rosen’s model, is that we must realize that the employer has a certain degree of control over the job characteristic which is being implicitly purchased, namely training. This control allows firms to clear markets with fixed minimum wages by lowering training. Conventional economic theory argues that such markets will not clear because the minimum wage should create a surplus of workers. The tied-sales view of the labor market suggests that the action lies elsewhere. Minimum wages have unfortunate consequences where they are least expected. They reduce on-the-job training for the young.
Married in space
WHERE YOU FIT as a person in characteristics space is a central determinant of whom you will marry. In a marriage each partner is simultaneously providing the other with positive and negative features while receiving in return positive and negative features from the other. If the features do not balance, the marriage may not take place unless some residual cash payment is made to equalize the remaining differences.
In the distant past in Western countries, and in some countries today, if in addition to housekeeping, a woman had good breeding potential she could command a “bride price”. This cash exchange would compensate her family for the genetic bonus of having produced a daughter deemed to be fertile. The letters between Lorenzo de Medici and his mother in the 15th century speak of potential brides as being “comely”, having good hair, teeth, posture, and thus being worthy of sharing in the family fortune in exchange for producing heirs. Inversely, women deemed less desirable would have to compensate the groom with a dowry. The equalizing cash difference in these cases helps to clear the “marriage market”. This type of market leads to a segregation of highly fertile women with men who have a strong preference for such unions and the ability to pay for them. Less fertile women pair off with older men or men with less economic potential. Just as in the labor market for mines, the equalizing difference allows some accommodation between unequally matched people who nonetheless are not too far off in what they are seeking from each other. The factor of accommodation is the equalizing cash difference.
Looking at marriage in this light may seem antiquated but alerts us to the unexpected consequences of government intervention in this most intimate of markets. Until the 1950s, divorce was difficult to obtain in Western countries. Opponents of divorce believed it would lead to the downfall of the family. The economics of space predicted otherwise. Suppose the liberalization of divorce law tempts the wife to leave the union because over time she has grown dissatisfied with the initial matching and the bride price her parents negotiated for her. Under threat of divorce the wife may insist that the husband change his ways. This means bending his characteristics space by perhaps slimming his belly, or taking anger management classes. If he finds himself too set in his ways to curve space, he may compensate the wife with extra money for her family or for her personal needs and desires. Thus liberal divorce law may not lead to the breakdown of the family, but rather to a redistribution of resources within it. We can only understand this possibility by looking at marriage as a spatial matching problem resolved by the addition of an equalizing cash payment to make up for unequally matched characteristics.
This economic view of marriage is complementary to the romantic view. A tenet of romance is that the characteristics of the person should be of secondary importance. What matters is the person inside. Romance is a meeting of spirits. Seen from an economic perspective the spiritual dimension is supposed to fill the gap left by an awkward matching of beauty and beast. Yet when you take an equalizing cash payment out of the calculation, beauty and beast may remain single. The gap in physical and mental characteristics may be so large that qualities of spirit are not able to bridge the gap between partners. That is the economic view based on the immutability of who we are. Perhaps the staggering sums people invest in transforming their bodies through exercise, steroids, and surgical interventions, and the rise of the cult of mental and spiritual self-improvement are attempts to bend characteristics space in an effort to attain true spiritual union between partners. These expenditures may be seen as a reaction to the collapse of the age-old marriage market in which all such disparities could be overcome through simple cash payments.
The final frontier
I BEGAN WITH a story so kindly allow me to end with one. In 1963 Martin Luther King gave his famous “I have a dream” speech in which he said “The marvelous new militancy which has engulfed the Negro community must not lead us to distrust of all white people, for many of our white brothers, as evidenced by their presence here today, have come to realize that their destiny is tied up with our destiny. They have come to realize that their freedom is inextricably bound to our freedom. We cannot walk alone. And as we walk, we must make the pledge that we shall march ahead. We cannot turn back.”
King’s speech actually came at a time when African-Americans had improved their lot steadily since WWII by moving from southern states, where the spirit of discrimination was strong, to northern states where it was weaker. Many occupations were segregated, but that was changing as migration allowed for a better match
of “tied-sales” between minority employees and employers who did not mind hiring minorities. To complete the match, labor markets adjusted salaries in such a way that a wage premium or “equalizing difference” was being paid to whites. Discrimination existed even in Northern states. There was only so much that migration could do to narrow the discriminating wage premium.
King and other social reformers can be seen as wishing to eliminate and thus in a sense “untie” the racial component from labor market exchanges through a campaign of education and persuasion. Their approach to tied-sales may depart from the neutral stance that economists try to adopt concerning people’s preferences, but King had the right idea. Changing preferences is one of several ways to overcome the matching problem in markets with tied-sales. King’s vision can be seen as a sort of psychological technology which eliminates counter-productive criteria for matching, thereby making exchanges easier to conclude.
A complementary approach is to physically untie criteria from the match. This does not mean altering preferences but rather coming up with some means of physically separating elements in the tied-sale from each other. This is clearly difficult if you have a taste for hiring a particular racial group. But it is feasible in the case of a parent wishing to work at a business that has a daycare. If daycare can be subcontracted to a separate business economically and thus removed from the employment contract it no longer becomes a factor that might thwart a match between employers and employee.