The previous plate showed how equally able workers may earn different wages because the work asks different things of them: danger, dirt, insecurity, the burdens for which a compensating difference is paid. This plate takes up the harder case, the wage that follows the worker's identity even when the contribution is the same. The question cuts into the promise that has accompanied the wage from the beginning of this volume. If the price of an hour measures what the hour produces, two equally productive hours ought to command the same price. Yet an employer may dislike the person who supplies one of them, or may infer less about that person's capacity from the information available. These are different ways for identity to enter the bargain. The first places a private surcharge on employing someone; the second changes the employer's forecast of what that someone will produce. Competition bears differently on each. To ask whether the market will punish discrimination is therefore already to ask which discrimination the market contains.
Gary Becker gave prejudice a place inside price theory by treating it as a taste for which someone would pay. The employer with a taste for discrimination behaves as though a worker's wage carried a surcharge visible only to him. In an invented example, two applicants will each produce twenty units of revenue per hour, and each asks for sixteen. The employer attaches a psychic cost of three to employing one applicant because of her group. The money cost of either hire is still sixteen; the cost as he experiences it is sixteen for one and nineteen for the other. He can indulge his preference by choosing the favored worker, or demand that the other accept thirteen to offset the three-unit aversion. This arithmetic gives prejudice a price. It does not establish that the worker will accept the discount, that every employer has the same aversion, or that the market wage gap equals this particular employer's three. Those depend on the alternatives open to both sides of the bargain.
The prospect of buying equal work more cheaply is what puts competitive pressure on the discriminating employer. If excluded workers can be hired at thirteen while equally productive favored workers cost sixteen, a rival willing to employ them has a three-unit saving. Expansion by such employers increases demand for the underpaid workers and can bid their wages upward. The employer who insists upon paying more for the same contribution must finance that preference from somewhere. The force is real, but its reach depends on entry, expansion, access to the relevant skills and capital, and how much labor the less prejudiced employers can profitably absorb. A market with one tolerant employer need not pay as though every employer were tolerant. Nor does the most hostile employer alone determine the wage. The distribution of demand matters: who is willing to hire the next worker, at what rate, and with what capacity to take another. The attractive proposition is a mechanism of erosion, with conditions under which it can operate.
The prejudice of customers and fellow workers can turn the employer's saving into a more complicated calculation. A customer who refuses to buy from a member of the disfavored group can reduce the receipts of an otherwise indifferent firm; a coworker who demands extra pay to work beside her can increase its costs. The proprietor may then discriminate while pursuing money profits, transmitting another person's taste through the wage. There may still be gains from reorganizing work, finding other customers or entering another market, but those opportunities have to exist and be large enough. Becker himself made the persistence of employee and customer discrimination central to the long-run qualification. The distinction between a productive contribution and the revenue prejudice allows that contribution to earn also becomes essential. If the customer's aversion lowers a worker's sales, describing the resulting wage as equal to revenue product accounts for the receipts. The aversion that reduced those receipts remains part of the explanation. A prejudice can enter the measured value of the work before it enters the pay slip.
Statistical discrimination begins with a different difficulty: the employer must pay for productivity before being able to see it. Schooling, experience, an interview and a test are evidence, each more or less informative about the work to come. If group membership contains additional predictive information, a profit-seeking employer may use it alongside those individual signs. The forecast can then differ between two people whose eventual contributions will prove equal. The important words are predictive information. A false stereotype is not made accurate by being entered in a calculation, and a belief that leads firms systematically to overpay one set of workers can create an opportunity for a better-informed rival. The statistical account acquires its distinctive force where the conditional prediction is accurate under the available information, even though it does not identify every individual correctly. In that setting an employer may lose money by discarding information, while a worker loses the opportunity to be judged by a capacity she actually possesses. Forecast accuracy and individual justice have become separate questions.
A deliberately invented forecast makes the separation visible. Suppose individual productivity varies normally around group means of twenty and sixteen, and an unbiased test measures it with independent normal noise. Give both groups the same productivity variance and a test-error variance equal to it. The best conditional prediction then puts half its weight on the test and half on the group mean. Two applicants both scoring twenty-two receive predictions of twenty-one and nineteen. They can in fact be equally productive; the employer cannot read that fact directly from their scores. Even averaging over the test noise for workers whose true productivity is twenty-two leaves the same two expected offers in this model. Yet each group's average predicted productivity equals its own average actual productivity. The unequal treatment of equally productive individuals and a discrepancy between group-average pay and group-average product are distinct propositions. The first exists in the illustration; the second does not. Neither group mean says anything about innate capacity, and neither is a finding about an actual population.
A less reliable signal, by itself, produces a different pattern from a lower group mean. Hold both means at twenty in a second invented example, but let the employer put three-quarters of the weight on one group's test and one-quarter on the other's. At a score of twenty-four, the predictions are twenty-three and twenty-one; at sixteen, they are seventeen and nineteen. Greater uncertainty pulls an estimate toward the common mean. It discounts the strong signal and cushions the weak one. With risk-neutral payment equal to these forecasts, differing precision alone therefore does not establish a uniform penalty or lower average pay for the less precisely measured group. Additional conditions, such as selection into a particular job or a cost attached to uncertainty, can change the outcome; they have to be specified. The distinction matters because a phrase as plausible as “employers know less about this group” can conceal several models with different predictions. An explanation of a persistent wage disadvantage must do more than name an information gap.
The more troubling possibility is that employers' expectations help produce the differences they subsequently observe. A worker deciding whether to acquire a costly skill considers the chance that it will earn access to better work. If the employer requires a particularly strong signal from her group, the extra investment may have too little prospect of changing the assignment. Fewer workers then invest, leaving the employer with a less qualified applicant pool and an apparently confirmed belief. Stephen Coate and Glenn Loury make this circle explicit in a model where groups begin with the same distribution of investment costs, employers observe noisy signals, and pay within each task is the same for both groups. Disadvantage operates through access to the better task. Under conditions permitting multiple self-confirming equilibria, identical initial opportunities for investment can lead to different investment and assignment outcomes. The qualification matters: making a standard harder does not always lower investment, and the model does not say that every difference must reproduce itself. It shows how a forecast can be accurate about a world that the forecast itself helped make.
Those mechanisms also explain why measuring discrimination requires more care than subtracting two average wages. An observed gap can reflect differences in work, measured skills, unmeasured skills, access to jobs and treatment within them. Controlling for a characteristic answers a conditional question: how does pay differ among workers with the same recorded characteristic? If earlier exclusion helped determine who reached an occupation, holding occupation fixed removes that pathway from the comparison. If employers see a productive difference that the researcher cannot see, leaving it unmeasured can make the residual gap look like unequal treatment. Both difficulties can arise in the same data. A remainder after adjustment is consequently neither a complete measure of discrimination nor an alibi for the pathways that were adjusted away. The theoretical distinctions sharpen the empirical task. The question is which treatment changed, for whom, with what information held fixed, and at which point in the route from acquiring a skill to being paid to use it.
A correspondence experiment can isolate one such point by changing the name on an application while randomly assigning the same pool of résumés. Marianne Bertrand and Sendhil Mullainathan sent fictitious applications to help-wanted advertisements in Boston and Chicago. In their 2004 paper, applications assigned White-sounding names received callbacks at a rate of 9.65 percent, against 6.45 percent for those assigned African-American-sounding names: a difference of 3.20 percentage points, or about fifty percent relative to the lower rate. Random assignment makes that difference attributable to the name manipulation in the experiment. The applicants were fictitious; their actual productivity was not measured and held equal. The outcome was an invitation to an interview, with neither the eventual hiring decision nor an offered wage observed. Names can also convey more than one association. The experiment provides direct evidence about a gate through which applicants had to pass, while its interpretation remains tied to the signal changed and the response counted. That bounded result is substantial enough without turning a callback gap into a wage estimate.
The same callback result cannot, on its own, decide between a taste and an inference. An employer can reject an application because of an aversion or because of what its name leads him to expect; both can reduce the chance of a reply. Bertrand and Mullainathan use other patterns in their experiment to press the models further, including the response to improved credentials, and find difficulties for simple versions of both accounts. This is the point at which the theory earns its keep. A mechanism should explain how treatment changes when information improves, when a decision is exposed to competition, or when the party whose prejudice matters is removed from the encounter. A model that accommodates every possible result after the fact has supplied little discipline. The wage following identity is the phenomenon to explain. Whether a particular explanation fits depends on its additional predictions and on evidence capable of separating them.
The remedy likewise depends on where identity enters the bargain. Opening access to employers can enlarge the market for excluded workers; improving a credible individual signal can reduce reliance on group information; changing access to training or better assignments can alter the investment incentives that sustain a self-confirming difference. Each addresses a distinct obstruction. Concealing a group label may remove one channel while leaving other signals available, and a signal's greater precision may help workers whose capacities had been underestimated while exposing those previously overestimated. These are consequences to trace, rather than reasons to regard the existing arrangement as settled. The worker's claim to fair treatment also cannot be reduced to the employer's interest in a cheaper prediction. A rule can be accurate on average and still impose a burden on an individual because of the history of others. The economic account makes the conflict visible; it does not choose the principle by which that burden should be allocated.
The wage can follow a prejudice, or a prediction. The question is what makes either one costly to keep.
Return, then, to the two equally productive workers with whom the plate began. Their unequal pay may contain an employer's aversion, a customer's preference, a forecast made with imperfect information, or the effects of an earlier decision about who could acquire and demonstrate a skill. Competition can make some of these practices costly and can transmit others. A sufficiently informative individual record can dissolve a prediction based on a group; a self-confirming pattern of assignment can obstruct the record from being made. The hopeful part of the argument is the opportunity to hire equal work on better terms. The difficult part is establishing that the opportunity is available, visible and usable by someone with reason to take it. Between the two lies the worker whose contribution exceeds the wage her identity commands. The price of her hour is carrying more than a measure of its product. It is carrying the terms on which the market will allow that product to be recognized. The argument remains open.