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1 Introduction

The relationship between education and earnings has long intrigued economists and in recent years two contrasting views have emerged. The theory of human capital holds that education directly augments individual productivity and, therefore, earnings (Schultz, 1961; Mincer, 1974; Becker, 1975). By forgoing current earnings and acquiring, or more precisely, investing in, education, individuals can improve the quality of their labour services in such a way as to raise their future market value. Human capital, according to this view, is akin to physical capital, the acquisition of which entails a present cost but a future benefit. Thus education may be regarded as an investment good, and should be acquired until the point at which the marginal productivity gain equals the marginal opportunity cost.

There is, however, an alternative line of thought. The 'sorting' hypothesis attests that education also 'signals' or 'screens' intrinsic productivity (Spence, 1973; Arrow, 1973; Stiglitz, 1975).1 Higher levels of education are associated with higher earnings, not because they raise productivity, but because they certify that the worker is a good bet for smart work. The intuition for this is straightforward. Educated workers are not a random sample. They tend, for example, to have lower propensities to quit or to be absent. They are also less likely to smoke, to drink or to use illicit drugs. Such attributes are attractive to firms, but are not readily observed at the time of hiring. It could be the case, then, that firms take into account this aspect of education when hiring workers, anticipating that graduates, for example, may be both more productive and less likely to absent. Following this line of thought, one might expect workers to anticipate the way firms hire when making their education decisions. For example, students may choose a particular course to 'signal' their desirable, but unobservable, attributes to potential employers. And firms, in turn, may insist on certain educational attainments when hiring to help them 'screen' potential applicants. By such signalling and screening, education is able to 'sort' workers according to their unobserved attributes.2

The debate over education and productivity is often presented as an 'either/or' question: education either raises productivity or it does not. Such views are stereotypical and even the most vociferous proponents of sorting would concede the productivity-augmenting power of education. More-

over, the observed correlation between education and earnings renders the debate largely redundant at an individual level. Regardless of whether schooling sorts or augments productivity, it certainly enhances lifetime earnings and, as such, represents a good investment for individual workers (Psacharopoulos, 1994). Whether or not schooling is a good investment for society is less clear. If its only purpose is to sort prospective workers then questions arise as to the appropriateness of investing in the expansion and/or qualitative upgrading of schooling: does it really need three years of undergraduate education to sort young adults effectively?3 Such an issue is particularly pertinent in the present UK educational climate; the current expansion of student numbers is suggestive of productivity-augmenting sympathies, whilst the recent moves to student-centred funding would appear to indicate prima facie sorting leanings.4

The plan of this chapter is as follows: section 2 examines the background to sorting, focusing on the problems caused by asymmetric information; section 3 outlines the basic signalling model of education, while section 4 explores the ways in which firms may use education to sort potential applicants; section 5 reviews the empirical evidence regarding sorting and section 6 concludes.

2 Asymmetric information and the market for lemons

The need for sorting arises when information is asymmetric. Employers, for example, may be unable to observe an applicant's intrinsic productivity, and cannot rely on workers' pronouncements regarding their own attributes since all workers would claim to be highly able. More generally, the same problem can arise in any buyer-seller situation when goods can be differentiated in terms of quality and, without an effective sorting mechanism, the problems can be insurmountable.

If it is impossible to observe the quality of a particular good at the time of purchase, even if buyers do eventually learn of average quality, goods will be traded at a price reflecting this average. Moreover price will adjust until buyers' beliefs about this average quality are confirmed ex post. Such markets will tend to exhibit two undesirable characteristics: (a) sellers may attempt to lower cost by lowering quality; (b) if sellers cannot 'shave' quality, the sellers of high-quality products, with higher opportunity costs, may prefer to withdraw from the market. Average quality may thus fall below that in a world of complete information and adverse selection problems arise. This problem was highlighted by Akerlof (1970) who showed that the process would continue until only the lowest quality 'lemons' were traded on the market. Akerlof used the example of a second-hand car market and focused on a key information asymmetry: the owner of a used car is better informed about its quality than a potential buyer. Indeed the buyer may be unable to discern whether the car is a low-quality 'lemon' or a high-quality 'peach'.

If buyers are unable to observe the quality of a particular used car, then peaches and lemons will trade at a single price reflecting the average quality of cars on the market. The more lemons on the market, the lower the average quality and the lower the market price for all cars - good and bad. Faced with such a situation the owners of good cars may find it unattractive to sell their cars and may withdraw from the market. If there is a distribution of quality then we might envisage the owner of the highest-quality car withdrawing from the market, followed by the owner of the second-best car, and so on. It is feasible that the market may unravel completely, or that the market will move to an equilibrium in which only cars below a certain quality threshold are traded.

The key points of Akerlof's model can be ascertained in the following stylized example: Assume for simplicity a second-hand car market in which there are just two types of car, good quality cars (i.e. peaches) and bad quality cars (i.e. lemons). The reservations values to potential buyers and sellers are as follows:

Seller 2500 1000

Assume also that it is known that there are three times as many bad cars as good cars on the market, (i.e. Nb = 3Ng), that each potential seller wants to sell one used car only, and each potential buyer wants to buy one used car only, and that all the bargaining power lies with sellers, so that at any trade it will be the buyers' reservation value that holds.

Symmetric information

Assume first that there is symmetric information amongst buyers and sellers. In this case the market should operate without problem. Firstly, if quality is known perfectly by both buyers and sellers then equilibrium will be characterized by the following prices:

That is, the market separates to allow trade of both good and bad cars at the buyers' reservation prices of £3000 and £2000 respectively. If quality is unknown by everybody then buyers and sellers will consider expected average quality in their calculation of 'bid' prices:

pd = (l) Pd + (4) Pd = (4) £3000 + (3) £2000 = £2250. (2.3)

The offered 'supply' price, ps, is thus a weighted average of the supply price for good pg) and bad (psb) cars. Following our assumption that the buyers' reservation price holds, the market will clear atp* = £2250. Problems arise, however, if only one side of the market is aware of the true quality of the cars.

Asymmetric information

It is reasonable to assume that sellers will have acquired some knowledge regarding the true quality of the car they are selling. Such information, however, is unlikely to be known by prospective buyers. Assume now that only sellers are able to observe quality. There will be no trade at all at any p < £1000, since at these prices even owners of 'lemons' are not prepared to sell. Owners of lemons would be willing to sell if p > £1000, but no 'peaches' will appear on the market until p > £2500. Therefore buyers will assume that any car offered for sale at a price £1000 < p < £2500 is a lemon, and so they will only be willing to pay a maximum of pd = £2000. Such a price would be acceptable to sellers of lemons, and so lemons will trade for pb = £2000. If p > £2500 then all sellers are willing to put their cars on the market and so there would be a 75 per cent chance of a car being a lemon and therefore buyers would be prepared to offer at most pd=£2250, which would be unacceptable to sellers of peaches. Since buyers would be aware of this, they would (quickly) revise their offer down to pd = £2000. Indeed there will be no demand at all at any p > £2000 because there will be no demand at any p > £2250, whilst at any p < £2500 demand only starts at p < £2000 since buyers assume that the car is a lemon. Such an equilibrium is obviously inefficient; further gains from trade are theoretically possible (i.e. between buyers and sellers of peaches). But such gains cannot be made because buyers do not know if they are getting a lemon.

The root of the market failure in Akerlof's model lies in the dual role being performed by the market price; it determines the average quality of cars offered for sale and then equilibrates this supply with market demand. We thus have one instrument aiming at two targets. Is there no way that such a failure can be salvaged? In terms of the second-hand car market, it would make sense for the owners of good cars to acquire independent, third party verification as to the quality of their car. Indeed this is what is actually offered in the second-hand car market by reputable organizations such as the Royal Automobile Club (RAC) and the Automobile Association (AA) in the UK, and the American Automobile Association (AAA) in the USA. Such organizations are effectively certifying quality, in much the same way, advocates of the sorting hypothesis would claim, as do universities.

3 Job market signalling

Extending the Akerlof model to the labour market, we can envisage two types of worker, 'good' and 'bad', where these are intrinsically productive qualities known only to the worker. If firms cannot spot the difference between good and bad workers, we might have an equilibrium in which only 'lemons' are traded: the competitive wage will necessarily reflect average quality and as such may fall below the reservation wages of the 'good' workers. We do not, however, see this occurring in real world labour markets: highly able individuals do work. The question is why, and there are perhaps two answers: first, buyers (i.e. firms) learn; second, firms and workers act to screen and signal particular productivities.

The first discussion of the role of information and search was initiated by Stigler (1962), who examined more closely the decision-making process of individuals as part of their job search under imperfect information. These and similar ideas were translated into a notion of signalling by Spence (1973), who concentrated on the job market and the role of signalling in transmitting the personal characteristics of an individual.

Essentially, the side to a transaction that has superior information will try to do something to indicate the quality of the good on offer, e.g. used car warranties. Such indicators will act as signals of quality. In terms of the labour market, it follows that 'good' workers might attempt to signal their quality to firms, hoping, by so doing, to increase their marginal products. This was the basis for the study by Spence (1973). If a seller of a high-quality product could find some activity that was less costly for him than the seller of a low-quality product, it might pay him to undertake (i.e. signal) the activity as an indication of high quality. Moreover, even if buyers (i.e. firms) were not aware of the underlying costs of the activity, they would quickly learn that the signal was associated with higher quality and therefore would be prepared to pay a premium price for it. And providing that the marginal cost of some activity was lower for sellers of high quality then an equilibrium would emerge in which quality would be perfectly inferred by buyers from the level of activity undertaken by sellers.

The basic idea

Assume a market situation in which signallers are relatively numerous and in the market sufficiently infrequently not to acquire reputations. Consider further the hiring decision of the firm as a process of investment under uncertainty. The employer is unaware of the productive capability of the worker at the time of hiring. We thus have a situation of (a) investment, since it takes time for the firm to learn an individual's productive capability; and (b) uncertainty, since this capability is not known to the firm beforehand.

Now, although the firm cannot directly observe productivity, it can observe a plethora of personal data in the form of observable characteristics and attributes. That is: signals, observable characteristics attached to the individual and under the individual's control; and indices, observable, unalterable characteristics.

Some time after hiring, the firm will learn an individual's productive capabilities and, on the basis of previous experience in the market, will have conditional probability assessments over productive capacity given various combinations of signals and indices. At any point in time, when confronted by an individual applicant with certain observable characteristics, the firm's subjective 'lottery' with which it is confronted when making this investment decision is defined by these conditional probability distributions over productivity given the new data. Ignoring risk (i.e. assuming risk neutrality) the firm will have an expected marginal product for an individual for each configuration of signals and indices that it confronts. And, assuming a competitive atomistic market, these marginal products will be reflected in wages.

We can envisage the nature of the hiring process in terms of the feedback loop illustrated in Figure 2.1. An equilibrium occurs where any part of the loop repeats itself; for example, the employer's conditional probabilistic

Employers' conditional probabilistic beliefs

Offered wages as a function of signals and indices

Hiring: Observation of relationship between marginal products and signalling

Signalling decisions by applicants; maximization of returns net of signalling costs

Signalling costs

Signalling costs

Figure 2.1

beliefs are not changed from one period to the next because they are not disconfirmed by the data.

Although individuals can do little about their indices, they can alter their signals, even if at some cost to themselves. Education is a classic example.

A formal model

Consider the following stylized model. There are two groups of individuals (Group I and Group II) with marginal products equal to 1 and 2, respectively. The population comprises a proportion q (1 - q) of Group I (II) individuals. Group II individuals are not only more productive than Group I individuals, but they can also acquire a particular signal, y, at a lower cost. Assume for simplicity that the cost to Group I (II) of acquiring y units of the signal is equal to y (y/2). In what follows we will interpret y in terms of education. Finally we assume that firms are competitive and pay workers a wage equal to their marginal product. The data of our model are summarized below.

Individual Marginal Proportion in Cost of acquiring group product population education signal y

To locate an equilibrium we proceed by attempting to ascertain a set of self-confirming conditional probabilistic beliefs on the part of employers. Assume, for example, that an employer's beliefs are as follows.

That is, if an individual has fewer than y* units of education, he is a Group I individual, and he is a Group II individual otherwise. Such conditional beliefs imply the wage schedule set out in Figure 2.2.

Given the offered wage schedule, members of each group will select optimal levels of education. Consider a person who is considering acquiring y < y*. It is apparent that such an individual will acquire y = 0 because education is costly and, given the employer's beliefs, there are no benefits to increasing y until he reaches y*. Conversely an individual who is considering acquiring y > y* will in fact acquire only y = y* since further increases in y would merely incur costs with no additional benefits. Thus individuals will only set either y = 0 or y = y*. An equilibrium will therefore require all Group I individuals setting y = 0 and all Group II individuals setting y = y*. The options available to each group are set out in Figure 2.3.

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