# Wage Diﬀerentials And Structure Research Paper

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At a point in time in a particular economy there will be a distribution of wage rates (average total compensation per hour) across all economically active members of the population. This distribution of wages is referred to as the wage structure of the economy. The value of the wage rate of each member of the labor force will depend systematically on a set of observable characteristics of that person as well as on other characteristics that are not observed. This relation between wages and worker characteristics as well as the distribution of worker characteristics determines the wage structure of the economy. The average wage of a person with a particular characteristic relative to the wage of a person with a diﬀerent characteristic (e.g., the wage of a worker in Paris relative to one in Lyon), all other observed and unobserved characteristics held constant (ceteris paribus), is called a wage diﬀerential. This research paper discusses the eﬀects of diﬀerent worker characteristics on wage structure.

## 1. Earnings And Wages

There are several diﬀerent ways of deﬁning the wage rate, and the appropriateness of any particular deﬁnition depends on the questions in which one is interested. Table 1 shows the distribution of average hourly gross (pretax) wage rates of a random sample of 4,300 full-time workers in the United States in 1995. In principle, one would like to include nonwage compensation (employer contributions for fringe beneﬁts and social insurance programs), but such data usually must be collected from employers rather than from individuals. A worker at the 10th percentile of the distribution earned \$6.07 per hour, which means that 10 percent of workers earned less than this amount. One way to summarize the wage structure is to compare the average wage in the highest quintile (from the 80th percentile up) to the average wage in the lowest quintile (from the 20th percentile down). These estimated averages for the US in 1995 were, respectively, \$33.15 and \$5.84, a ratio of 5.7.

An alternative to the use of hourly wage rates is the use of average weekly, monthly, or annual earnings of individuals. Total earnings per year for an individual are by deﬁnition equal to the average wage times hours per year. Data on individual incomes rather than hourly wages are often more readily available in most countries. An example of this is reported in Table 2 in which the ratio of the average annual income of workers in the top quintile to that in the lowest quintile is reported for a selection of countries. The study from which this study was taken includes data for 108 diﬀerent countries. The dispersion of incomes within a country generally is higher than the dispersion of wages becauseannual hours tend to be higher for persons with higher wage rates. Notice that for the US the ratio of the highest to the lowest quintile in terms of income is 8.5 compared to 5.7 for the wage rates of full-time workers.

Table 2 shows that there is substantial variation among countries in the dispersion of incomes—as there would be if the data referred to hourly wages rather than annual incomes. A few facts are illustrated by these data. First, there tends to be substantially less dispersion in individual wages and incomes within industrialized countries than in the developing countries. Second, there is much greater dispersion of incomes in the US than in other industrialized countries. Third, the degree of wage and income dispersion in the formerly socialist countries is relatively low.

## 2. The Determinants Of Individual Wages

The hourly wage rate (W ) of any individual worker in a particular economy at a moment in time will, in principle, depend on a set of observable variables (such as that person’s level of completed schooling) as well as on a set of factors that generally are not observed (such as the individual’s innate ability, a characteristic that is diﬃcult to measure and usually not obtained in a census-type surveys). Let X represent all the variables determining wages that are observed and U represent all the unobserved determinants. We can then specify what economists call an earnings function in which the value of W for each individual depends on X and U according to

where ε is a random error term (pure ‘luck’) that is unrelated to the values of X and U.

β is a vector of coeﬃcients representing the eﬀects of each of the observable variables on wages and γ a vector of coeﬃcients representing the eﬀects of the unobserved variables. If, for example, we thought that there were only two observable determinants of W, years of completed schooling (S) and age (A), βX might be speciﬁed as β1 S + β2 A, and the average eﬀect of an additional year of schooling on W would be β1 .

In practice most estimated earnings functions feature the replacement of the numerical value of W with its natural logarithm. This means that a unit increase in the value of a particular X variable causes W to increase proportionately by the coeﬃcient on that variable. In the case of years of schooling discussed above, with the semilogarithmic form β1 represents (δW/δ)/W rather than ∆W / ∆S if W is entered in numerical form.

From the earnings function given by Eqn. (1) it is clear that the wage structure, the distribution of W across the working population, depends on both the joint distributions of X and U (as well as the distribution of ε) and the parameters β and γ. Wage diﬀerentials, the ceteris paribus diﬀerence between the average wages of individuals with one characteristic versus another, are determined by the β parameters.

The various determinants of individual wages, both potentially observable and unobserved, can be classiﬁed into ﬁve groups. These include:

(a) skill characteristics, (b) job location,

(c) job characteristics,

(d) discrimination/nepotism, and

(e) rents.

We will discuss the variables within these groups in turn.

### 2.1 Skill Characteristics

Generally, it is presumed that in most societies more skilled workers are more productive and that they earn higher wages. Two fairly crude but readily observable variables relating to skill of each worker are their years of schooling and potential labor market experience. Some microdata sets allow a more detailed speciﬁcation of education (what subjects were studied, how many resources were allocated to each year of schooling, etc.) and experience (actual vs. potential years, amount of on-the-job-training, etc.), but this sort of detail is rare.

An important source of diﬀerences in skill and productivity diﬀerences among individuals is variations in unobserved ability and motivation. Although a few surveys have included the scores on simple IQ tests, these factors are either largely or completely ignored, that is, they are considered U rather than X variables. This illustrates a general problem associated with the estimation of earnings functions. The true model is given by Eqn. (1) above, but the researcher is only able to estimate W as a function of observed variables, that is

where e now represents variation in W that cannot be explained by the observed variables. We know that for most empirical earnings functions e is very important, for the fraction of the variation in W jointly explained by the observable variables is usually fairly small— between 25 and 35 percent (see Juhn et al. 1993).

There is thus a large potential for empirical estimates of the eﬀects on W of any individual observed variable to be biased upward or downward due to the correlation of that variable with unobserved variables. In the very simple model above in which schooling and age are the only observed variables, we want to estimate the ‘true’ eﬀect of S on W from the model W= β1 S + β2 A + γU +ε, but we are forced because of data limitations to estimate W = b1 S + b2 A + e. The use of b as an estimate of the true eﬀect β1 is in general subject to speciﬁcation error which arises if S is correlated with γU (holding A constant). It seems reasonable to suppose that persons with relatively high levels of intelligence and/or motivation (a) will tend to have higher wage rates (i.e., γU > 0) and (b) be more likely to have relatively high schooling levels. This would suggest that b1 would be an upward-biased estimate of β1 . Interestingly, however, the consensus of the mass of research into this question (see the review by Card 1999) is that conventional estimates of the eﬀect of schooling on wages are probably not signiﬁcantly biased in an upward direction.

Another feature of empirical earnings functions is that their coeﬃcients may change over time. This is especially true for coeﬃcients concerning skill variables. For example, in the US the relative hourly wage of 30-year old male workers with a bachelor’s degree (16 years of schooling) to those with just a high school degree (12 years of schooling) fell from 1.18 in 1973 to 1.11 in 1979, but it then rose during the 1980s to a value 1.41 in 1989 (see Bound and Johnson 1992, Table 1). Why these changes in relative wages occurred (in the US and in other countries with relatively ﬂexible wage determination systems such as Canada and Britain) has received a great deal of attention from economists, but the answer is still a matter of controversy.

### 2.2 Job Location

A second set of observable variables that are usually included in empirical earnings functions are dummy (one zero) variables describing the location of the worker within the country. Typically the locational variables represent the size of the area in which the person lives (whether or not, for example, it is a metropolitan area with a population in excess of a million) and indicators of residence in particular areas. For example, in a hypothetical study of the determinants of wages in the Great Britain, one would include a large city dummy variable (Llarge) and separate dummy variables for persons employed in Greater London (Llondon), other parts of Southern England (Lsouth), and Scotland (Lscot). This speciﬁcation would be represented as W = b1Llarge + b2 Llondon + b3 Lsouth + b4 Lscot +…with the other observable determinants of wages (the X’s in Eqn. (2)) included. The estimated coeﬃcient b in this earnings function would represent the average ceteris paribus wage diﬀerential between a person working in London and another working in a large city in Northern England. If, as is generally the preferred approach, W is entered as a natural logarithm, the estimated coeﬃcient b would reﬂect the approximate proportionate wage diﬀerential associated with employment in London.

What is the economic interpretation of coeﬃcients on location of employment? First, because of higher land prices, it is generally more expensive to live in areas with a highly concentrated population. In order for real wages (nominal wages divided by the price level) to be equal across areas, observed wages must be appropriately higher in expensive areas. This would apply especially to very large cities within individual countries—London, Paris, New York, Tokyo, etc.

A second reason for the existence of wage diﬀerentials by job location is the preferences of workers concerning the characteristics of diﬀerent areas. For example, living in a large urban area involves greater stress and poorer air quality than living in a rural area, so, holding the cost of living constant, the typical worker might have to be paid a compensating wage diﬀerential to work in the large urban area. Similarly, some regions have better weather and other amenities (like public services) than others, and one would expect that wages would be higher in the more desirable than in the less desirable areas in order for potential migrants to be indiﬀerent between diﬀerent areas. For the US, the estimated eﬀect on wages of an area having sunshine 80 percent of the time vs. only 30 percent is, as simple economic theory would predict, a reduction of about 7 percent (Blomquist et al. 1988).

This, of course, presumes that all (or most) workers in the economy have the same preferences for the amenities of diﬀerent areas. To the extent that preferences diﬀer across the population—some people prefer rural areas (warm weather) to large cities (cold), others the opposite—predictions concerning compensating wage diﬀerentials become somewhat less clear.

A ﬁnal reason for the existence of wage diﬀerentials across locations is the eﬀect of changes in the structure of labor demand. Suppose, referring to the example above, that there was for some reason a major boom in Scotland that caused the demand for labor there to increase permanently by 50 percent. It is unlikely that there would be an immediate large migration of workers from England to Scotland, so wages in Scotland would be bid up signiﬁcantly. The earnings function for Great Britain based on data collected after the demand shift would yield an estimated coeﬃcient bscot that would now be positive. How rapidly the Scottish/English relative wage would return to one (the value of bscot to return to approximately zero) depends on how long it takes for a portion of the British population to relocate to Scotland.

### 2.3 Job Characteristics

In addition to the location of employment, an important set of determinants of wage rates is the attributes of the job held by each individual worker. We can arbitrarily deﬁne each job attribute (the set of which we will call A) as a bad—the degree to which it is physically onerous, monotonous, a threat to the worker’s health and safety, has low social status, etc. It would be expected that higher values of the elements of A would require a compensating diﬀerential. Put diﬀerently, holding all other (observed and unobserved) determinants of wages constant, the market equilibrium wage of each job would be higher for ‘bad’ jobs (those with high values of A) than for ‘good’ jobs (those with low values of A). Thus, for the speciﬁcation W = b1 A1 + b2 A2 + … , where the Ais are numerical representations of bad characteristics (like the injury rate of the job), we would expect to estimate positive bis.

There are numerous examples of the operation of compensating diﬀerentials. (For an excellent introduction to the topic, see Chapter 8 of Ehrenberg and Smith 2000.) On the other hand, there are many instances in which the estimated eﬀects of certain job attributes tend to be zero or have the ‘wrong’ sign (from the point of view of the theory) (see Brown 1980 for a refreshingly honest discussion of these problems).

An important set of applications of estimates of job amenities on wages is to the question of the economic value of life. If one of the As (say A1 ) is the rate of accidental death associated with the occupation of the worker, then one can infer from the estimated value of δW/δA1 how much individuals value—apart from the opportunity to earn and consume—place on the continuation of their lives. This information can, in principle, be used to do cost beneﬁt analyses of programs to reduce risks to life and health.

An example of wage diﬀerentials associated with diﬀerences in job characteristics is given in Table 3. These results illustrate some of the diﬃculties in the interpretation of the eﬀect of job attributes. The sample refers to individuals working full-time in the US in 1995 who had received a Ph.D. in science or humanities. The regression equation relates the annual salary of each respondent to years since receipt of the doctorate, gender, race, and region as well as the ﬁeld of receipt of the Ph.D. and the current type of employment.

The range of ﬁeld eﬀects (with economics equal to 100) is from 73 for humanities to 105 for specialists in computer science. This means that, holding gender, race, years of experience, type of employment, and region constant, the computer /humanities relative salary is 1.44. There are also substantial compensation diﬀerences across employer types. For example, Ph.D.s employed in the for-proﬁt business sector earn, ceteris paribus, 29 percent more than those in tenure track academic positions.

There are various explanations of why relative compensation diﬀerentials of this magnitude exist—in this case among sets of individuals who have the same quantity of education. First, these diﬀerentials may reﬂect compensating diﬀerentials in the sense that some ﬁelds (economics, for example) are intrinsically boring relative to other ﬁelds (like humanities) and require higher monetary rewards in order to induce persons to study them. Some of the relative compensation levels by employer type—for example, the business/academia comparison—most likely reﬂect premiums that are necessary to get Ph.D.s to work in jobs that are perceived to be less rewarding in a nonﬁnancial sense.

A second potential explanation of diﬀerentials of this sort is that they reﬂect, in part, average ability diﬀerences of the individuals who are in each ﬁeld or employment type. This is especially relevant for comparisons of employment type in which there is partial sorting on the basis of ability. For example, the compensation diﬀerence between academics in tenure track positions and those in both nontenure track positions and lower education (secondary schools and 2-year colleges) is very likely to reﬂect practices by which the ‘better’ Ph.D.s are granted tenure.

A third explanation of these compensation diﬀerentials is that some of them reﬂect temporary market factors, and there is a presumption that the high relative compensation of the computer science ﬁeld in Table 3 is an example of this. This phenomenon is illustrated theoretically in Fig. 1. The demand for a particular type of labor is assumed to increase such that the demand curve shifts from D` to D“. In the short run the supply curve, SSR, is quite inelastic, reﬂecting the fact that the pool of persons qualiﬁed to work in this market is ﬁxed. (In the case of computer scientists, some additional labor can be obtained from people not on the labor force or from closely related ﬁelds, but these possibilities are limited.) Thus, the short-run eﬀect of an increase in the demand for this type of labor is to increase its relative compensation level. In the long run the supply of labor to this market is very or completely elastic, for new entrants to the labor force can choose to train for this type of work. (In the case of computer specialists, young persons are induced to get Ph.D.s in that ﬁeld rather than in mathematics or physics.) Over time, therefore, the relative compensation level in this market would be expected to return to its initial equilibrium value, C`, rather than stay at its temporary value, C“ in Fig. 1.

Analysis of wage diﬀerentials of various sorts can proceed along the above lines. A major example of this is the analysis of average compensation across industries. An example of this is Table 4 in which average monthly salaries across broad industrial groups are reported for six rather diverse countries. Wages in agriculture, trade, hotels and restaurants, and personal services tend to be relatively low; wages in mining, utilities, and ﬁnance tend to be relatively high. Some of these diﬀerentials reﬂect quality and compositional diﬀerences (that are not adjusted for in the table). But some of the diﬀerentials reﬂect diﬀerences in the amenities associated with work in the particular industries.

### 2.4 Gender And Ethnicity

A set of observable variables that are generally included in earnings functions are the demographic characteristics of the workers—his/her gender, race, or ethnicity. For example, the inclusion of a one/zero dummy variable for women as one of the Xs in Eqns. (1) and (2) is very common. For the theoretically complete model given by Eqn. (1), which includes all observed and unobserved inﬂuences on wage rates, the interpretation of the (presumably negative) coeﬃcient on women must be in terms of some sort of labor market discrimination against women. Why else would otherwise identical workers receive lower compensation? The same conclusion applies to conclusions concerning potential dummy variables on race and ethnicity for earnings functions in probably every country in the world (blacks in the US, French speakers in Quebec, Arabs in France, natives of Greenland in Copenhagen, etc.).

The problem with attributing the negative eﬀects of gender and certain racial and ethnic distinctions entirely to labor market discrimination is that we are only able to estimate the model for which we have data, Eqn. (2) rather than the theoretically complete Eqn. (1) above. Thus, there is the possibility that the negative coeﬃcients on gender and ethnicity reﬂect, wholly or in part, diﬀerences in the average value of omitted variables rather than some form of direct labor market discrimination. Further, it is necessary to know exactly what is the cause of an observed wage diﬀerential if a society decides it wants to eliminate this diﬀerential (see Altonji and Blank 1999 for an extensive discussion of these issues).

### 2.5 Rents

Most of the above discussion proceeded as if wages are determined in markets that are similar in process to the markets for melons and equities. The fact that the commodities involved in labor markets are human beings requires that this ‘model’ be modiﬁed to some extent. Indeed, a set of institutions has emerged to provide modiﬁcation of the outcomes that would follow from the unfettered equilibrium of the labor market. Among these institutions is trade unionism, which has, over time and across societies, taken several forms. Government policy—both directly through legislation determining wages and indirectly through its role as employer—also aﬀects the wage structure.

At one level the existence of institutions such as trade unions creates another wage diﬀerential in which to be interested. In terms of Eqns. (1) and (2), being a union member or working in which wage rates are determined by a collective bargaining contract means that a worker could earn a higher wage than another worker who is not so situated. In this case, W = β1 U + … is the complete wage equation, including all observed and unobserved variables, where U equals one with union representation and equals zero otherwise. We do not, of course, observe everything about the workers and his job, so we estimate the equivalent of Eqn. (2), W = b1 U + …

How good the estimator b1 is of the ‘true’ eﬀect of unionism β1 depends, as in the estimation of other wage diﬀerentials, on the correlation of the omitted determinants of wages with U. In the US, the consensus estimate of the average eﬀect of unionism on wages is about 15 percent (see Lewis 1986).

A more important eﬀect of unionism and government policy is their inﬂuence on other wage diﬀerentials. Much of the above discussion of the structure of wages and of wage diﬀerentials reﬂected the implicit assumption that relative wages are, at least in the long run, free to adjust to their market-clearing levels. This assumption is all right for the analysis of labor markets in the US, Japan, and (during the past 20 years) the United Kingdom, but there are serious problems associated with its application to most other industrialized countries in which bargaining coverage is over 75 percent (vs. 18 percent in the US and 22 percent in Japan in the early 1990s). To the extent that union and/or government policy attempts to prevent increases in the dispersion of earnings, wage diﬀerentials will not behave as neatly as the elementary theory suggests. Instead, wage structures will be subject to a great deal of inertia, and they will adjust at best very slowly to shocks in demand.

That the wage structure is slow to change is not per se a bad thing. Indeed, I would join most economists in agreeing that stability of the distribution of income is a good thing. The problem with such policies, however, is that they often lead to heavy unemployment of those groups whose relative wages are protected.

Bibliography:

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4. Brown C 1980 Equalizing diﬀerences in the labor market. Quarterly Journal of Economics 94: 113–34
5. Card D 1999 The causal eﬀect of education on earnings. In: Ashenfelter O, Card D (eds.) Handbook of Labor Economics, Vol. 3A. Elsevier Science, Amsterdam, pp. 1801–63
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