Pay Dispersion, Information, and Returns to Search in a Professional Labour Market

The Review of Economic Studies, Ltd.

Pay Dispersion, Information, and Returns to Search in a Professional Labour MarketAuthor(s): David MetcalfSource: The Review of Economic Studies, Vol. 40, No. 4 (Oct., 1973), pp. 491-505Published by: Oxford University PressStable URL: http://www.jstor.org/stable/2296583 .

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Pay Dispersion, Information, and

Returns to Search in a Professional

Labour Market12 DAVID METCALF

London School of Economics

Stigler [15] states that the number of potential employers available to an individual with most sorts of specialized training will be in the thousands. Under such circumstances, the worker will never be able to " become informed on the prospective earnings which would be obtained from every one of these potential employers at any given time, let alone keep this information up to date" (p. 94). Wage dispersion will result and searching in the labour market will yield progressively higher expected maximum wages. The purpose of this paper is to examine wage dispersion and the expected benefits of search for new entrants to the UK university teachers labour market.

The analysis of wage dispersion, search, and information in the labour market is "much complicated by the lack of homogeneity of the workers (and, to a much lesser extent, of non wage conditions of employment) " [15, p. 94]. Further, " differences in quality of workers cast a deep shadow over all measures of pure dispersion " [15, p. 101]. Previous empirical studies [7, 15] made only a token attempt to surmount this problem. One novel feature of this analysis is that it attempts to eliminate that part of the observed wage dispersion due to non-homogeneity of labour and to locational advantages. This modification produces powerful results.

Some relevant features of the labour market are briefly discussed in Section I. Section II examines the data source. The underlying model of the salary determination process, together with a brief discussion of the regression results, is given in Section III. Section IV examines dispersion in pay and Section V analyses the gains from search and tests a number of hypotheses as to which individuals are likely to search the most. Concluding remarks are presented in Section VI. An appendix contains the full regression results.

I. THE LABOUR MARKET The peculiarities of the academic labour market are discussed elsewhere [9]. However, three features are particularly relevant to the analysis of information and search.

(i) Uniform salary scales exist and are common to all universities except Oxford and Cambridge.

(ii) It has been demonstrated [9] that interfaculty differences in labour market pressure exist in this market. Whilst the salary scales do provide some flexibility to enable universities to begin to accommodate interfaculty variations in labour market pressure,

1 First version received December 1971; final version received April 1973 (Eds.). 2 An earlier version of this paper was presented in the Labour and Human Capital section of the

Econometrics Society Meetings, New Orleans, December 1971. I am greatly indebted to Meghnad Desai, Harry Johnson, Kenneth Wallis, an editor of this Review and an anonymous referee all of whose comments measurably improved the content of this paper. It is a pleasure to also acknowledge the research assistance provided by Robin Harrison and Kristine Jensen of the Economics Research Division in LSE.

491



492 REVIEW OF ECONOMIC STUDIES

the evidence suggested that faculties facing recruitment and retention difficulties have adjusted their hiring and retention standards. This is an important cause of heterogeneity of labour in this labour market. Further, within any subject, certain university types might comprise non-competing groups. Specifically, prestigious institutions (within any subject) may not be drawing on the same pool of recruits as non-prestigious institutions.

(iii) The number of employing institutions is relatively small. There are less than fifty universities and no university teaches all subjects.

Features (i) and (iii) yield the intuitive prediction that within any subject the wage dispersion will be relatively small for individuals of approximately homogeneous quality.

II. THE SAMPLE

The data used here are derived from a sample survey of all recruits to (and applications for) university teaching posts in 12 subjects in 21 university institutions during session 1968/69.' The data were collected for purposes other than analysing the economics of information and search but are, fortuitously, nearly perfect for such an analysis. Very few posts were in the senior grades. We therefore concentrate here entirely on the lecturer grade. Five of the twelve subjects covered (Civil Engineering, Chemical Engineering, Statistics, English and French) had less than twenty posts vacant (in the 21 university institutions overall). These subjects are therefore excluded from this analysis. This paper focuses on wage dispersion, search and information in the following subjects: Physics, Chemistry, Mathe- matics, Economics, Sociology, Law and History.

Stigler argued implicitly that the ideal sample with which to examine pure wage dispersion needs the following characteristics. First, homogeneous labour is necessary. Our sample consists of heterogeneous labour, but we are able to correct for some part of this heterogeneity. Second, it must be possible to make allowance for the non-wage elements of the various jobs. We are dealing with a homogeneous profession. Individuals in each subject, and therefore in the whole sample, work in universities. Whilst it is not sensible to allege that this is equivalent to identical absolute or proportionate non- monetary elements for all individuals, intuitively it is likely that the non-wage attractions of university teaching to individuals within a subject (e.g. Economics) will be less diverse than if we were comparing non-wage attractions to economists working in universities, civil service, and business. Rather, the important variable non-wage element in this sample is location within the university sector. We are able to control for this. Third, the sample should refer to an extended geographical market. This sample covers the whole of Britain. The main defect of the sample is that we have no evidence on offers received by individual employees. We only have, for each individual, his pay in the post he accepts. Some (or most) individuals will have applied for more than one post, and received more than one offer. Recapitulating, the wage dispersion examined here refers to actual salaries paid to 1968/69 recruits in the lecturer grade in 7 subjects in 21 university institutions.2

III. SALARY DETERMINATION

Before examining the dispersion in pay and the returns to search it is necessary to describe the elements of a model of the salary determination process. Although the thrust of this paper is not towards explaining observed salaries via regression analysis, such analysis is undertaken both to enable us to correct the dispersion in salaries for heterogeneity of

1 Full details of the sample and results are given in [6]. 2 The discussion in Section IV of wage dispersion by sex and age also utilizes data from a more com-

prehensive survey of university teachers (a one-in-ten sample covering 3300 individuals) undertaken in November 1969.



METCALF PAY DISPERSION 493

labour and universities and because it is of intrinsic methodological interest to spell out the underlying labour market model.'

The model proposed is:

Sjk =f,(X,; X2, ..., Xm)

Sjk ==f2(Xl; X2, ...,Xm),

which states that salary offered (S?) to and salary demanded (SD) by individual i in subject j at university k are a function of a number of independent variables (X's). Not all independent variables will appear in both equations. Observed salaries are

Sjk if SIJk > SDjk)

This model contains three important features. First the unit of observation is the individual. Second the market clearing mechanism is an inequality; the observed salary will be the salary offered provided that the salary offered is equal to or greater than the salary the individual demands. Therefore, third, if SVk< D then the individual will not be hired and there will be no observed salary; because we are dealing with individual data and the clearing mechanism is an inequality, the salary demand function is completely unidentifiable. All data points lie along the salary offered curve except in the very special case where Sgk = Sik. It is therefore a structural equation, not a reduced form equation, that is estimated. Shifts in the salary demand function simply determine how much of the salary offered curve is observed. The market clearing mechanism (equation (3)) reflects the outcome of the bargaining position between the employer and employee in this market; because the clearing mechanism is an inequality the normal " Marshallian cross " identification problem does not occur here.2

It is hypothesized3 that:

S.k = bo + b, Subjectj + b2 Universityk + b3 (Number of applicationsjk" kSNumber of jobsJk

(Ab4 bility and +Highest Ag +Previous + Ujk b4 Motivationi Degree Occupationi Jk

Subjects. Relative labour market tightness varies across the non-competing groups (subjects) comprising the university sector. The uniform salary scale for the lecturer grade applies across subjects and universities. Subjects facing an excess demand for labour will tend to appoint an individual at a higher point on the common salary scale or relax their hiring standards. In either case this will result in a higher salary per efficiency unit than is offered in subjects facing no recruitment difficulties.4

1 Numerous so-called earnings functions exist in the literature, i.e. earnings of a sample of individuals are regressed on their own attributes and others, e.g. those of the industry in which they work. Blaug [4] surveys some of these studies. To this author's knowledge not one such study has set up the model in terms of the underlying labour demand and labour supply equations. This severely limits the true implica- tions that can be drawn from the findings of such studies.

2 If data on the dynamics of the adjustment process were available it would be possible under some circumstances to observe SD. If S? was revised following a low S?_ 1, etc., SD would eventually be observed. However, this sequence will only occur for those recruits the employer really desires to hire; for such individuals if SD>5S the dynamic adjustment induces the specical case SD= SO. Note that such data on the bargaining process is never available in published form.

3 The estimated salary determination model is only a stepping stone to the later analysis of this paper; therefore the hypotheses concerning the factors that influence salary offered are not presented in detail here. Readers interested in such detail are referred to [17]. For the same reason the full results of the regression analysis are presented in the Appendix and not in the text. A limitation of the regression analysis should be noted: with the exception of a few observations the dependent variable takes on a value equal to one of the fourteen points on the then incremental lecturer scale. The fact that the dependent variable is of limited values and not continuous induces heteroscedasticity.

4 The relative strengths of equity and efficiency considerations in salary determination in this labour market, the extent to which hiring standards vary across subjects and other devices which universities can use to overcome an excess demand for labour in a particular subject, are fully discussed in [9].




Universityk. Certain universities, for example those that are prestigious or locationally advantaged, are likely, ceteris paribus, to offer lower starting salaries than other universities.

Number of applicantsjklNumber of Jobsjk. This variable is included in the salary offered equation to allow for interaction between subject and university. An excess demand for labour in a particular subject (university) may not occur across all universities (subjects).

Individual Attributes. Universities will tend to offer a relatively high starting salary to individuals who are able and/or highly motivated and who possess a higher degree in the expectation that they will be more productive teachers and researchers than less qualified individuals. Quality of first degree is the proxy used for ability and motivation. Further, in so far as universities use equity as well as efficiency as a principle in salary determination they will tend to offer older individuals a higher starting salary than younger individuals. To the extent that age is a proxy for experience, equity and efficiency considerations pull in the same direction. We also hypothesize that universities will, ceteris paribus, tend to offer higher salaries to individuals with relevant previous labour market experience. Therefore previous occupation is included as an explanatory variable.

The model was tested by Multiple Classification Analysis, a form of regression analysis using dummy variables. Each variable (e.g. highest degree) is split into a number of categories (no higher degree, masters/diploma, doctorate) and each category is represented by a dummy variable.' The full results of the regression are presented in Table A.1 in the Appendix. All the variables in the model are statistically significantly related to salary. The formulation of the model in which the dependent variable enters linearly was preferred over one where it enters in logs for reasons outlined in the Appendix.

It may be noted in passing that the evidence in Table A.1 indicates that whilst age is certainly the dominant influence on salary (age alone explains 63 per cent of the variation in salary) the influence of the other variables is not quantitatively trivial. This contrasts with the findings of the National Board for Prices and Income [10], especially pp. 40-41, who state that " interdepartmental as well as inter-subject group salary differences are very small once age has been discounted ". For example, the regression results reported in Table A.1 indicate that, ceteris paribus, recruits' starting salaries in Law departments were ?286 higher than those of Historians.2 Similarly, holders of first-class honours degrees were paid well over ?100 more than holders of other first degrees and individuals whose highest degree was a doctorate were similarly rewarded as compared with individuals with Masters or no higher degree. The NBPI did not allow for the fact that very small observed inter-subject differences in starting salaries after allowing only for age are consistent with much larger subject differentials when hiring standards are also controlled for.

IV. SALARY DISPERSION

The dispersion of salary within each subject is shown together with the mean salary in Table I. Column (2) gives the number of individuals in each subject; column (3) indicates the number of employing institutions. For example, 33 Physicists were hired by 13 institutions. The mean salary and coefficient of variation (standard deviation x 100/mean) for each subject is given in column (4). The coefficient of variation indicates the dispersion in salary within each subject. It ranges from 13-4 to 33-8. This figure is high in comparison to the results of Stigler and Holtman. Stigler [15, p. 95] found that the coefficient of variation of wage offers to college graduates in Engineering, Accountants,

1 Age could be entered in the regression equation as a continuous variable. Breaking it down into a number of categories, each represented by a dummy variable, has the advantage that the influence of age on salary is made more sensitive. As all the explanatory variables are broken down into categories, each represented by a dummy, the regression is equivalent to an analysis of variance; see Suits [16] for a fuller discussion on representing continuous variables by dummies.

2 These differentials probably understate actual subject differentials because individuals in faculties with the greatest relative excess demand for labour also have a higher probability of gaining a post in the senior grades (i.e. above lecturer) and only the lecturer grade is examined here. This point is pursued below.




Salesmen and General Business never exceeded 10-0 per cent. Holtman [7, p. 101] found the coefficient of variation of starting salaries of teachers in Massachusetts was 4-6 per cent. Given the attributes of the labour market discussed in Section I which, ceteris paribus, will tend to lessen salary dispersion in this labour market, how may we account for this surprising extent of salary dispersion?

One important cause of the salary dispersion is non-homogeneity of labour. Within any subject there are at least four elements making for this labour heterogeneity, First, individuals differ with respect to age. The regression analysis demonstrated unambiguously that salary rises with age and experience. Second, individuals differ with respect to ability

TABLE I Mean salary and salary dispersion by subject

(4) Corrected for variation

Subject Number of Number of Uncorrected in (i) age, (ii) first degree (5) Corrected for individuals institutions observations held, and (iv) previous d e variation in

appointment

(1) I (2) (3) (4) (5) (6)

Mean salaries (?) Chemistry 20 11 1617 1305 1271 Mathematics 50 18 1732 1436 1413 Physics 33 13 1813 1359 1357 Economics 52 14 1747 1511 1495 Sociology 32 13 1713 1414 1414 Law 28 12 1652 1618 1567 History 21 11 1435 1306 1305

Coefficient of variation (per cent)

Chemistry 20 11 20-1 14 0 13-3 Mathematics 50 18 23-5 17-2 16-4 Physics 33 13 22-1 18-4 18-7 Economics 52 14 27-9 17-5 16-9 Sociology 32 13 33-8 26-7 25-3 Law 28 12 26-9 20-2 20K1 History 21 11 13-4 11.2 10.9

Source. Derived from data discussed in Section II.

and motivation. Third, individuals have not all had identical amounts of formal training. Fourth, individuals differ with respect to previous experience. We expect, ceteris paribus, lecturers who are older, more able and/or more highly motivated, who have had a long period of formal training and who have had relevant labour market experience to be paid more than those who are young, less able and/or less motivated, who have had a short period of formal training and no experience. Quality of first degree is a tolerable proxy for ability and motivation. Highest degree held is similarly adequate to represent formal training.' Previous occupation reflects experience. The net effect of age, quality of first degree, level of highest degree and previous occupation on the pay of these individuals (after controlling for subject and university type) was estimated by the regression analysis reported in the Appendix. It is therefore possible to eliminate that part of the wage dispersion attributable to those four variables. The correction method is as follows: within each subject the pay of each individual is adjusted to make it what it would be if

1 A minor problem, completely ignored here, is that some individuals recruited from non-student occupations might have trained for their Masters or Doctorate whilst employed. They will therefore not have forgone the same amount of earnings which a postgraduate student forgoes, and the prediction that, ceteris paribus, the higher the degree, the higher the pay, is less strong.




that individual was identical to all other individuals with respect to age, first degree, higher degree and previous occupation. The synthetic homogeneous individual was chosen to be aged 25, with an upper second-class honours degree with no higher degree, and whose previous occupation was working in a UK university.' These particular attributes were chosen because in each instance they formed the largest category when the observations were defined by age, first-degree quality, highest degree and previous occupation respectively. That is, more individuals were aged 25 than any other; more individuals had II(i)'s than any other first degree class; more individuals had no higher degree than a Diploma/ Masters or a Doctorate; more individuals were previously working in a UK university than were students or working elsewhere.

TABLE II Corrections for labour heterogeneity and locational advantage

Age ? First ? Highest ? Previous ? University ? degree degree appointment type

21 186 I -74 Doctorate -130 Student 107 Oxbridge 414 22 195 11(i) or II 0 Diploma or -14 Working at 0 London -53

Masters UK university 23 153 Other 29 Scotland -138 24 66 None 0 Other -86 Wales -8 25 0 Old Civic 0 26 -63 Young Civic - 9 27 -138 New 2 28 -296 Ex CAT -23 29 -600 30 - 399 31 -621 32 - 879 33 -767 34 -563 35 -748 37 -474 38 -1165 39 -1236 40 -890

Source. Calculated from Table A.1.

The actual corrections made for each individual are given in Table II. Say an individual (within any subject) was aged 32 with an " other " first degree, a Ph.D., and was previously a student and his actual salary was ?2500. Now his corrected salary is ?2500 -879 + 29- 130+ 107. Thus ?873 of his salary was due to his specific attributes compared with those of our synthetic individual. He earned ?879 more because he was older and ?130 more because he possessed a Ph.D. These amounts were therefore subtracted from his actual salary. He earned ?29 less than our synthetic individual because he possessed only an other first degree and ?107 less because he was previously a student. These amounts were added to his actual salary. These corrections were made for each individual in the sample.

The result of these corrections, as predicted, was to reduce the wage dispersion within each subject substantially. The coefficients of variation calculated from the corrected salary distributions within each subject are presented in column (5) of Table I. They are in each case substantially lower than the coefficients of variation presented in column (4) which were calculated from uncorrected data.

In an attempt to explain some part of the remaining wage dispersion, a correction was made to the salary of each individual according to the type of university in which he

1 Note, this leaves in for now any wage dispersion attributable to the pleasantness of working in a particular location. This cause of wage dispersion is corrected for subsequently.




worked. It is commonly asserted that some institutions have to pay more than other institutions to recruit a given individual. As universities as a whole receive around three- quarters of their finance from the UGC, [10, p. 34], they are unlikely to be able to pay wildly differing amounts; but nevertheless to work in a Young Civic university may not, for example, bestow the same status as working in Oxbridge and an individual may have to be compensated for this lack of status. The corrections made are given in Table II. The " base " university type is Old Civic, because it is the university type in which the largest number of individuals in our sample were employed. The regression analysis showed, for example, that as compared with working in an Old Civic university the net effect of working in an ex-CAT was plus ?23. This amount was therefore subtracted from his (" homogeneous labour") salary.'

Surprisingly, this correction has little impact in explaining any of the remaining salary dispersion. The new coefficients of variation (Table I, column 6) are, with one exception, never more than one percentage point smaller than those which take no account of this influence on wages. Indeed, in the case of Physics this correction causes salary dispersion to rise fractionally. It is difficult to account for this result: it is not, of course, attributable to certain institutions lowering their hiring standards rather than paying more-for the impact of age, degree quality and years of formal training and previous experience have already been eliminated.2 It simply suggests that the assertion that locational advantage is an important determinant of the dispersion in university salaries is unfounded.3

V. INFORMATION Additional causes of wage dispersion Thus far we have considered two causes of salary dispersion: heterogeneity of universities and of labour. However, substantial wage dispersion still exists. Stigler [15] points out that some wage dispersion will always exist and cites three reasons for this. First, wage dispersion will exist because of changes in jobs due to changes in workers' tastes and abilities and employers' identities. Second, if a market has appreciable geographic extent transportation costs inhibit search and this adds to the minimum of dispersion caused by the first reason. These causes of wage dispersion are unlikely to exert strong influence in this particular labour market. There are relatively few employers and they do not go bankrupt or merge. New entry is controlled by the government. Whilst the ex-CAT's did enter the market as employers in 1966 they are of course subject to the uniform salary scales. These scales also mitigate the impact of the wide geographic market on wage dispersions.

Third, wage dispersion results from fluctuations in supply and demand conditions: "The information of the worker (and employer) now becomes obsolete with time: there will be changes in the level of wages and in the relative wage rates of different employers (and workers) which call for additional search. The more rapidly ' the ' equilibrium wage rate changes, the smaller the returns from search and hence the smaller the amount of search that will be undertaken-and the larger the resulting wage dispersion" (p. 97).

Fluctuations in demand and supply are clearly relevant in explaining inter-subject differences in the extent of wage dispersion. Reference to Table I column 6 shows that wage dispersion is greatest in Sociology, the subject which (in terms of the staff numbers

I Not all types of university are equally prestigious in all subjects. Interaction between subject and university type was allowed for by including the number of applications/number of posts variable (although a previous test for interaction between subject and university type, using the algorithm interaction detector method (see Sonquist and Morgan [14]) had found no evidence of such interaction). Note also that the salaries for iniversity type London exclude the London allowance.

2 This is not to deny, of course, that a particular university may pay relatively high salaries to give it a superior selection of candidates than other universities.

3 Note that if we werediscussing thedispersion of university teachers'supplementaryearnings, correction for university type would lessen the dispersion; individuals at Oxbridge and London earn substantially higher supplementary earnings than other individuals, see [6].




since 1964) expanded the most and was in 1969 in a relatively tight labour market. Con- versely, the subjects where wage dispersion is smallest, Chemistry and History have expanded least, and were in relatively loose labour markets [9].

Table III presents the rankings of each subject with respect to wage dispersion (col. 2), and a proxy for expansion (col. 3). The full relationships between wage dispersion and expansion were tested by calculating the Spearman rank correlation coefficient (ru) between the two variables. As predicted a significant positive relationship exists between wage dispersion and expansion (r- = + 0.73): the higher the rate of expansion (i.e. shift in demand for staff), the more disturbed is " the " equilibrium wage, the lower the return to search and the higher the wage dispersion.

TABLE III Subject ranks by wage dispersion and expansion

Subject Wage Su bject dispersion Expansion

(1) (2) (3) Sociology 1 1 Law 2 4 Physics 3 5 Economics 4 3 Mathematics 5 2 Chemistry 6 6 History 7 7

Note. A rank of 1 indicates the most wage dispersion and highest expansion. Source. Col. (2) from Table I, column 6

Col. (3) from UGC Statistics of Education, Vol. 6, Table 27. Result. r8 = +073: t = 2 37 which is significant at the 5 per cent level.

Returns from search by workers The dispersion of wages gives a payoff to searching for a higher wage. Our purpose now is to measure these benefits of search. To do so we apply our data to Stigler's formulation of this problem. Stigler's model is a prior theory of search. In his model (i) the worker must decide prior to searching how many searches he will undertake, (ii) the offers remain open to the searcher for an infinite time. Whilst this static model does not provide a totally accurate description of the search process in this labour market, it is probably more realistic than the alternative model developed by Gronau [5].1

In Gronau's model the worker searches sequentially, but if he does not accept a job offer instantaneously, that offer expires. Gronau states that his model " assumes in effect that the search process has no memory. Every offer expires as soon as it is made; the worker has no alternative job offers to fall back on, and his asking wage in each period is, therefore, unaffected by past offers " (p. 292). In any event, both models yield similar predictions (see Klinov-Malul [8]). Further, Nelson [I1] suggests that the monetary value of the gains from incremental searching are similar for the prior and sequential models. Like Nelson we confine our analysis to the prior decision model. We work, of course, with the corrected salary distributions. This is because the benefits from search are attributable to pure wage dispersion and not to labour heterogeneity.

If the wage offers are normally distributed the expected maximum wage offer an individual will encounter in a given number of searches is approximately 2

wm = 0-65n 037 + w, .. (i) 1 Gronau's work, like that of some other studies which consider information in the labour market-

for example, Alchian, Holt, Mortenson and Phelps, presented in Phelps [12]-is addressed to the problem of providing the microeconomic foundations for the Phillips curve.

2 See Stigler [15, p. 97J for the derivation of this expression. It is an approximation (for 3< n <20) to the mean maximum observation from a normal population in random samples of size n.




where wm is the expected maximum wage offer, Tv is the average wage, n is the number of searches and iw is the standard deviation. It follows that the marginal wage gain from additional search is the increase in the expected maximum wage (Awm) when the number of searches is increased by one.'

The gain from search may extend over more than one year. The total gain depends on the length of employment and the correlation between starting salaries and future salaries. The longer the period of employment and the higher the correlation the larger is the payoff to search. Ignoring the possibility that the individual might die over the duration of employment, if the wage differentials were fixed the marginal income gain from search would be the capitalized value of the marginal annual wage gain. This is given by the formula:

A\wm. j(I + ) ...(ii) i( + i)t where Awm is the marginal annual wage gain, i is the rate of discount and t is the duration of employment. Although this formula is unlikely to be useful for long time periods (because, clearly, it is unlikely that wage differentials will remain constant) it may give

TABLE IV Marginal wage gains from search (?)

searchesf Chemistry Mathematics Physics Economics Sociology Law History

(A) Marginal wage gains 4 17-1 25-1 27-3 27-8 39.3 35.7 20-8 6 12-8 18-8 20-4 20-7 29-3 26-6 15-5

10 9 2 13-5 14-7 14-9 21-1 19-2 11 1

(B) Marginal wage gains capitalized for 3 years with i = 6 per cent 4 45.7 67-1 73 0 74-3 105-1 95 4 55 6 6 34-2 50.3 54 5 55 3 78-3 71-1 41*4

10 24-6 36-1 39 3 39-8 56 4 51-3 29-7

(C) Marginal wage gains capitalized for 6 years with i = 6 per cent 4 84 5 124-0 134-8 137-3 194-1 176-3 102-7 6 63-2 92-9 100-8 102-2 144-7 131-4 76-6

10 45 4 66 7 72-6 73.6 104 2 94-8 54 8

Note. (A) is calculated by subtracting w,, (3rd search) from wm (4th search) etc., (B) and (C) are calculated from equation (ii), i = discount rate.

tolerably accurate estimates for short periods. This is particularly true in this labour market where the quasi-automatic progression up the incremental salary scale ensures that a wage differential established at the beginning of the employment period will hold for a number of years. However, it would be silly to estimate the capitalized value of Awm for time periods longer than around six years because an individual may take a post at a well-regarded low-paying university in the knowledge that this increases the probability that he will get a senior (well-paying) position at another university.

The magnitude of the benefits of search in the university teachers' labour market is shown in Table IV. The marginal wage gain is between ?9-2 and ?39-3, depending on

1 Stigler [15, p. 97] differentiates equation (i) to arrive at aWmIfn = 0-24uw/n 63 as the marginal wage gain from additional search. This is a mistake because the number of searches is not a continuous differ- entiable variable; rather differences between the wm for successive numbers of search give the correct value of the marginal gains from additional search. The discrepancy between the two methods is small in absolute amounts. Refer to Table IV. The difference method of calculating the marginal wage gain gives a return to the 4th and 10th search in Chemistry of ?1741 and ?9-2 respectively. The corresponding figures using the differential suggested by Stigler are ?15-7 and ?E88.




subject and number of searches. Table IV also provides the capital values of the marginal wage gains from additional search, assuming that the discount rate is 6 per cent and that the initial gains extend over either 3 or 6 years. Given the quasi-automatic progression along the salary scales it is likely that the wage differential established at time of appointment will persist for 3 and probably 6 years.

The magnitude of the benefits from search in this labour market may be compared with Holtman's results. Holtman studied the teachers' labour market in Massachusetts. He found that " with a mean wage of $3,596 and a standard deviation of $165 .. . the capitalized value of 5 searches would be $38 for an employment duration of 3 years and $71 for an employment duration of 6 years, using a 5 per cent rate of interest " [7, p. 102]. The salary dispersions within each subject (measured by the coefficient of variation, see Table I) are all greater than those in Holtman's study, and the benefits from search are correspondingly greater. For example, the capitalized value of the marginal wage gains from the fourth search in Economics (the subject in the middle of the rankings by salary dispersion), with i = 6 per cent and t = 6, are ?137 or 9-2 per cent of the mean annual salary of ?1495 (Table I, col. 6). In contrast, the Holtman result reported above, with n = 5, i = 5 per cent, t = 6, gives a gain from search of less than 2 per cent of mean salary. Clearly, the payoff to search in the British university teachers' labour market is greater than that for " new " teachers in Massachusetts. Nevertheless, the absolute amounts involved are relatively small. In all but one instance the marginal wage gains from additional search (section A of Table IV) are less than one-third of one (discrete) increment on the lecturers' scale (then ?115). However, the aggregated marginal gain from the second and third searches (not reported here) approximate one increment in five of the seven subjects. Thus whilst it may not be sensible to accept the first offer received, extensive search does not yield a large return. In particular it would certainly appear irrational to postpone taking a job now in the hope of an improved offer in a year's time as an individual is then competing with the new cohort of potential recruits and may receive no wage offer.

Thus far, we have fleshed-out empirically what Stigler demonstrated theoretically, namely " that the gains from search are larger the longer the prospective period of employment " [15, p. 98]. Stigler goes on to say " When search is more extensive, however, the dispersion of maximum wage rates will be smaller-the lowest wage offers will more often be rejected for known better offers. So the realised dispersion of wage rates should be smaller the longer the prospective period of employment." A number of empirical tests of this implication are possible. The most obvious is to examine wage dispersion by sex. Women typically expect to stay in the labour force a shorter period than men do, so among homogeneous groups of men and women we should expect that the latter have large wage dispersions. Unfortunately, our data do not distinguish the sex of the recruit. However, data derived from the one-in-ten sample of university teachers covering 3300 individuals across all grades provides us with a measure of wage dispersion by sex. The ratio of the inter-quartile range: median is 0 54 for the male salary distribution and 0-62 for females.' These figures are calculated from salary distributions uncorrected for labour heterogeneity. This result provides particularly interesting support for the hypothesis as relatively few females hold senior posts. We reason as follows. Senior posts are high paying. A maximum of 35 per cent of the total university staff can hold senior posts. Therefore, the larger the proportion of either male or female staff holding such posts the greater, ceteris paribus, will be the dispersion in the wage distributions of that sex. On these (institutional) grounds we should therefore expect the salary dispersion of the male teachers to be greater than that of the females. In fact we find the reverse, demonstrating the dominance of the economic factors over the institutional ones in determining salary dispersion.

1 Calculated from November 1969 Survey Results, Tables 9c (355) and llc (363). The full results of this survey are lodged in the HERU library, LSE.




Second, we expect dispersion to be smaller for younger persons than for older persons.' Young persons will make more extensive search than old persons because of their longer prospective employment period. This expectation is tested as follows. Table II gave the corrections undertaken to overcome labour heterogeneity and locational advantages. For each individual we now add back the " age-effect ". Thus, for each subject, the salary distributions are heterogeneous with respect to age, but homogeneous with respect to first- degree quality, higher degree, previous occupation and location. We then estimate the dispersion of salary for each five-year age group within each subject. The results are presented in Table V. They provide striking confirmation of the hypothesis that wage dispersion rises with age. Within each subject the coefficient of variation was estimated for each five-year age group having five or more observations. Unfortunately, with'two exceptions, this limits the test of the hypothesis to the youngest age groups for each subject. In every case but one the wage dispersion is greater for the 26-30 age group than the preceding age group.2 For example, Sociology has an equal number of observations in each age bracket (12) and the coefficient of variation of the pay distribution of the 26-30 age group is three times that of the < 25 age group.3

Dispersion rises with age for a number of reasons. First, young teachers make more extensive search than older teachers. Second, differences in ability of recruits becomes better known as they become older. We have corrected for this factor in part by eliminating that wage dispersion attributable to heterogeneity in first degree quality. However, this variable may not be an adequate proxy for (e.g.) teaching ability or ability to undertake unsupervised research.4 Note, of course, that any increased dispersion due to better recognition of differences in ability (the search for information on the quality of workers) is to be counted as a reduction in the dispersion of earnings of homogeneous workers.5

1 This is the expectation of both Stigler [15] and the early work of Becker [2]. Recently, however, Becker [3, p. 66] has stated " dispersion in wage rates among younger persons generally exceeds the dispersion amongst older persons partly because the former have had less time to accumulate information about the labour market ". The factual basis of the first part of that statement is not given and the second part ignores the length of time people expect to be in the labour force.

2 It is, of course, not sensible to aggregate two or more five-year age groups to get five or more observations because the regression results show that pay rises with age. Therefore, ceteris paribus, wage dispersion would automatically be larger for a ten-year age bracket than for a five-year age bracket.

3 Calculations from the results of the one-in-ten sample survey also show clearly that salary dispersion rises with age. Note, however, that these figures are uncorrected for labour heterogeneity. Further, one explanation of the rise in dispersion with age is that relatively few young persons are in the senior grades (i.e. above lecturer), whilst not all older persons are in the senior grades.

Age Salary Income [(Q3-Q1)/Q2]

< 24 0-21 0 24 25-29 0-27 0-29 30-34 0-21 0-27 35-39 0-26 0-31 40-44 0-31 037 45-49 0-36 0-38 50-54 0 40 0-42 55-59 0-42 0 40 60+ 0 34 0 34

Source. Calculated from November 1969 Survey Results, Tables 9D (356) and lID (364). Income equals university salary plus supplementary earnings.

4 One important quality indicator, publications record, is omitted. Initially all individuals are homogeneous in this quality but diverge through time.

5 Assuming differences in ability do become better known as an individual gets older, it is possible that the amount of dispersion in this labour market has been understated. The more able individuals may be appointed to the (high paying) senior grades, which are not included in this analysis. We must repeat, however, that if appointment to the senior grades is a function of ability this is equivalent to a reduction in the dispersion of earnings for homogeneous individuals.

E-40/4




Third, older staff have made different amounts of on-the-job investment in training, which serves to increase their dispersion of abilities. We have, via the previous occupation variable, been able to correct for part of this element in labour heterogeneity which causes wage dispersion independent of that caused by ignorance. Finally, late entrants to a subject, whilst relatively old may receive a relatively low salary.

TABLE V Mean earnings and dispersion of earnings by subject anid age

Subject Number of Mean Standard Coefficient of Age observations (?) deviation (?) variation (%)

Chemistry ?25 5 1334 132 9 9

26-30 11 1471 206 14-0

Mathematics <25 19 1396 126 1 9 0 26-30 24 1640 306 18-6

Physics <25 5 1337 76 5-7

26-30 20 1612 220 13 6 31-35 8 1949 400 20-6

Economics < 25 23 1366 154 11-2

26-30 17 1765 284 16-1 31-35 8 2135 375 17-6

Sociology <25 12 1320 102 7-7

26-30 12 1631 363 22.3

Law <25 15 1395 125 8'9

26-30 10 1756 378 21 5

History <25 12 1322 104 7.9

26-30 8 1532 274 17-9

VI. SUMMARY

This paper has applied Stigler's theory of search and information to a specific labour market: recruits to UK university teaching. It advances the earlier work on information in the labour market by correcting for that part of wage dispersion resulting from labour heterogeneity. Certain specific features of the labour market, such as uniform salary scales and a relatively small number of easily identifiable employers reduce search costs compared with those in the private sector. It was therefore hypothesized, particularly after eliminating labour heterogeneity, thAt wage dispersion in this labour market would be small relative to that found in other studies. This specific hypothesis was not confirmed. The reasons for this result await further work on this subject; specifically, it is possible -that wage dispersion in the private sector in the UK is substantially greater than that found in this labour market. However, the other predictions were strikingly confirmed-wage dispersion is substantially reduced after correction for labour heterogeneity. The dispersion is positively associated with supply and demand fluctuations and age, and is higher for women than men.




REFERENCES

[1] Andrews, F., Morgan, J. and Sonquist, J. Multiple Classification Analysis: a Report on a Computer Program for Multiple Regression Analysis Using Categorical Predictors (Ann Arbor, Survey Research Centre, 1967).

[2] Becker, G. Human Capital (Columbia University Press, New York, 1964).

[3] Becker, G. Economic Theory (Knopf, New York, 1972).

[4] Blaug, M. An Introduction to the Economics of Education (Penguin, 1970).

[5] Gronau, R. "Information and Frictional Unemployment", American Economic Review, 61, No. 3 (1971).

[6] Higher Education Research Unit. Economic and Social Aspect of University Teaching, LSE, Mimeo (January 1971).

[7] Holtman, A. " Teacher Salaries and the Economic Benefit of Search ", Journal of Human Resources (1969).

[8] Klinov-Malul, R. " Labour Mobility ", HERU, WP/35, LSE, Mimeo (June 1970).

[9] Metcalf, D. " Some Aspect of the UK University Teachers' Labour Market ", Paper 11 in M. Parkin (ed.), Essays in Positive Economics: Proceedings of the 1972 A UTE Conference (Longmans, 1973).

[10] National Board for Prices and Incomes. Standing Reference on the Pay of University Teachers in Great Britain, First Report, Report No. 98, Cmnd. 3866 (1968).

[11] Nelson, P. " Information and Consumer Behaviour ", Journal of Political Economy, 78, No. 2 (March/April 1970).

[12] Phelps, E. Microeconomic Foundations of Employment and Inflation Theory (Norton, New York, 1970).

[13] Sargan, D. " Wages and Prices in the UK: A Study in Econometric Methodology " in Hart, P., Mills, G. and Whitaker, J. (eds.), Econometric Analysis for Economic Planning: Sixteenth Symposium of Colston Research Society (London, Butter- worth's, 1964).

[14] Sonquist, J. and Morgan, J. "Problems in the Analysis of Survey Data and a Proposal ", Journal of American Statistical Association, 58 (June 1963).

[15] Stigler, G. " Information in the Labour Market ", Journal of Political Economy, Supplement, 70 (1962).

[16] Suits, D. " Use of Dummy Variables in Regression Equations ", Journal of American Statistical Association, 52 (December 1957).

[17] Williams, G. et al. The UK Academic Labour Market: Some Essays (North Holland, 1973).

APPENDIX

The complete results of the salary determination model are presented in Table A. 1. The model was estimated by multiple classification analysis, a form of regression analysis using dummy variables. Column (4) describes the effect upon salary of each variable working alone. Column (5) gives the effect of each variable when the effect of all other variables in the equation has been taken into account. The " gross " and " net " effects thus simply correspond to the simple and multiple regression coefficients of conventional




TABLE A.1 Regression of university salary on six sets of explanatory variables

Variable Category Distribution Gross effect Net effect

per cent ? ?

(1) (2) (3) (4) (5)

Subject Chemistry 8-1 -81 -36 Mathematics 21 3 34 -12 Physics 14 0 116 -43 Economics 22 1 50 58 Sociology 13-6 15 -20 Law 11.9 -45 129 History 8 9 -277 -157

E2 = 0-05 /2 = 0-03 F6,147 = 3-35**

University type Oxbridge 2-6 -111 -437 London 21-7 44 29 Scotland 7-7 20 115 Wales 3 0 -80 -15 Old Civic 26-8 6 -23 Young Civic 15-3 -136 -15 New 19-6 32 25 Ex-CAT 3-4 209 -4

E2 = 0 03 /2 0-03 F7,147= 3.41**

Number of applicants/ 0-5 6-4 144 -35 number of vacant posts 6-10 42-1 3 25

11-15 26-0 70 3 16-20 11.9 -77 -140

20 13-6 -143 58 E2 = 0-03 /2 = 0 02

F4,147 = 2.92*

Class of first degree I 37.4 -5 48 11(i) or II 56-6 19 -26 Other 6-0 -142 -55

E2 = 001 /32 0.01 F2.147 = 365*

Highest degree held Doctorate 31P5 204 87 Master or Diploma 25-5 1 -29 Other 43 0 -150 -43

E2 = 011 /32 = 002 F2,147 =854**

Age 21 1 7 -429 -407 22 3-8 -432 -417 23 4-7 -364 -375 24 119 -345 -288 25 16 6 -256 -222 26 10 6 -186 -159 27 10 2 -52 -84 28 10-2 68 74 29 4-7 339 378 30 7-7 261 177 31 5-1 411 399 32 2-6 673 657 33 2-6 680 545 34 1-3 386 341 35 1-0 692 526 37 1-0 520 252 38 1P3 829 943 39 0-5 922 1014 40 3 0 725 668

E2 = 0-63 /2 = 0-55 F18,147 = 22-22**




TABLE A.1-continued

Variable Category Distribution Gross effect Net effect

per cent ? ?

(1) (2) (3) (4) (5)

Previous appointment Student 36-6 -287 -90 Working at UK university 37 4 119 17

Other 26 0 233 103 E2 = 0 25 =2 _ 0.03

F2,147 = 10 82**

R2 = 0 744. Number in sample 235. Mean salary ?1698. Standard deviation ?444. ** Significant at 1 per cent level; * Significant at 5 per cent level.

regression analysis. Note that the regression coefficient (column 5) indicates the influence ,of each category of each variable on salary, ceteris paribus, as a deviation from the grand mean salary of the whole sample (?1698).

E2 and /2 correspond to simple and partial correlation coefficients: 2 gives the proportion of the variance in salary explained by each variable operating alone; /32 is the proportional reduction in the residual variation after the effect of the other variables has been taken into account. All the explanatory variables are significantly related to salary- the j2 coefficients are all significant at the 5 per cent level. (The formula to calculate the F statistic to determine the significance of each of the /2 coefficients is given in [1]).

The model was estimated with the dependent variable entering both linearly and in logs. Three separate factors were considered in an attempt to determine which formulation was superior.

(1) Sargan [13] provides a criterion to determine the superior formulation: residual -sum of squares (linear)/residual sum of squares (log) x geometric mean = 1. If 1> 1 the log formulation is preferred and if 1< 1 the linear formulation is preferred. In our case 1 = 011 leading us to prefer the linear formulation.

(2) Our sample consists of individuals on the university lecturer pay scale. The range between the highest and lowest salaries in our sample is ?2945-?1240 = ?1705. This results, not surprisingly, in a problem of heteroscedasticity, but on a relatively minor scale. When the model is estimated with the dependent variable in logs the extent of heteroscedasticity appears, on a visual test, to be approximately the same as when the dependent variable enters linearly.

(3) The R2's are almost identical. R2 (linear) = 0 744, R2 (log) = 0-746. Therefore only criterion (1) aids in the choice of the form of the model, and this

indicates the linear formulation which is therefore used in this paper. Results using the log formulations (the corrections corresponding to Table II being made multiplicatively) are available in manuscript to anyone interested.



Documents

Pay Dispersion, Information, and Returns to Search in a Professional Labour Market