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The cyclical sensitivity of white-collar skill margins.

I. Introduction

economists have been interested in the skill margin (SM), defined as the ratio of the earnings of workers in the highest skill level of an occupation to the earnings of workers in the lowest skill level, in part because of their concern over the distribution of income and its social welfare implications, but primarily because it reflects the extent to which wage rates respond to demand and supply conditions. All other things being equal, the more responsive wage rates are to market conditions the more likely prices are to remain stable over the business cycle [Hall, 1975].

The objective in this paper is to examine the sensitivity of white-collar SMs to the business cycle. The sensitivity of blue-collar SMs to business conditions has been examined previously [Reder, 1955; Gustman and Segal, 1974]. Similar studies of white-collar SMs have not been made, however, despite the large and rising proportion of this group of workers in the labor force.

The major finding of the study is that white-collar SMs vary with labor market conditions. In the professional occupations where fixed employment costs are substantial, the SM narrows during prosperity and widens during recession. In the clerical occupations where these costs are smaller, the SM behaves in the same manner but is less sensitive to the business cycle. White-collar SMs also vary with inflation, but inflation plays a smaller role compared to labor market conditions.

In the next section, theoretical considerations are discussed pertaining to the determinants of white-collar SMs. In Section III, a model is described for assessing the sensitivity of white-collar SMs. The data utilized, covering the period 1962-85, are also briefly described. The empirical results of the authors study are found in Section IV. A summary of the paper is provided in Section V.

II. Theoretical Considerations

(A) The Skill Margin and the Demand for Labor

The literature on SMs has at various times focused on the manual occupations, professional occupations, and the entire occupational structure [Ober, 1984; Keat, 1960; and Scitovsky, 1966]. While the long-term trend in SMs were examined in these early studies, the focus of the recent literature, as in this study, is the short-run. As indicated by Wals [1977], in the absence of adjustments in hiring standards and fixed employment costs for skilled labor, an increase in demand for goods and services can be expected to lead to a widening of the SM, provided that the short-run supply of skilled labor is less elastic than that of unskilled labor. In this case, short-falls of skilled labor relative to unskilled labor will arise, leading to a more rapid increase in the wage of the former than of the latter. (1)

But if firms ease hiring standards for skilled labor during business upturns, the upward pressure on skilled wage rates is moderated, and if sufficiently dampened, the SM can narrow. According to Reder, during extended periods of accelerated economic growth, hiring standards for skilled workers are relaxed in order to forestall rises in their wage rate. As less skilled workers are substituted for more skilled ones at each skill level, ultimately the supply of least skilled labor contracts when the labor reserves for this quality of labor are fully absorbed into the labor market. When this occurs, the SM between the most and least skilled may narrow. Supportive evidence for the view that the SM can decline during prosperity is found in data for the building trades during the expansions accompanying World War I and II.

A similar conclusion that the SM can fall during prosperity can be reached based on the model developed by Oil [1962]. His model is more directly applicable to inter-occupational comparisons, but it can also be applied to intra-occupational comparisons. In the Oi model, labor is treated as a quasifixed factor whose training costs are amortized over a worker's expected period of employment. During prosperity the demand for skilled workers increases only after the difference between their marginal revenue product and wage rate exceeds per period fixed employment costs, representing hiring costs and firm-specific investments in human capital. If these fixed employment costs are positively related to skill level within an occupation, workers with higher order skills should experience relatively smaller changes in demand than those with lower order skills. Hence, the SM may decrease when the demand for good and services expands.

Contrary movements in the short-run SM may be expected during periods of recession. Absent adjustments in hiring standards and fixed labor costs, the SM will narrow if, as is likely to be the case, the supply of skilled labor is less elastic than that of unskilled labor. But the SM can widen if hiring standards for skilled labor are tightened and/or if fixed employment costs are greater for skilled than for unskilled workers.

Considered by itself, an increase (decrease) in demand will widen (narrow) the SM; but when hiring standards and fixed employment costs are considered, the SM can move in the opposite direction. Hence, the direction of change in the SM cannot be ascertained a priori. One must rely on empirical data to determine those instances where the SM moves one way or the other, or remains stable. It is to be noted that in the standard approach to how SMs vary in response to cyclical changes in demand, the focus of the discussion is on the elasticity of supply of different grades of labor, abstracting from possibilities of substitution between one grade of labor for another, on the assumption that such possibilities are limited in the short-run. The Reder study examines epochal changes in demand following major wars; in this context the possibilities for factor substitution are more pronounced and, as Reder indicates, helps explain SM changes in the construction trades. Oi's analysis of fixed employment costs imply that labor is not a wholly variable factor. Oi shows how employment costs can influence SMs, all else being the same, even when there are no differences in the elasticity of supply between grades of labor and possibilities of substitution between grades of labor are absent. While both the Reder and Oi models yield the same conclusion regarding cyclical movements in SMs, the latter is more germane to the issues addressed below.

(B) The Skill Margin and Inflation

In addition to fluctuations in demand, the SM also may be affected by inflation. Ceteris paribus, during periods of rapidly rising prices the wage of unskilled workers may rise faster than that of skilled ones, thus narrowing the SM. This would occur if employers, because of equity considerations, give the same dollar increase in wages to all workers, or if employees at the lower end of the skill hierarchy obtain wage increases through collective bargaining that match the rise in the price of goods and services while higher skilled worker's wages rise more slowly than the price level. On the other hand, if highly skilled workers obtain wage increases that match changes in the cost of living while less skilled workers are unable to gain the same concession, the SM will increase in periods of inflation. What little evidence there is on this point suggests that inflation may act as an independent force narrowing the SM [Evans, 1963].

III. The Model and Data

(A) The Model

In an earlier study, Herbert Simon [1957] proposed that a manager's salary depends on the number of supervisory levels between the manager and the workers he or she supervises as well as the ratio of salaries in adjacent skill levels. If the annual salaries of workers in the highest and lowest skill levels of an occupation are [W.sub.h] and [W.sub.1], respectively, then [Mathematical Expression Omitted] where k is a constant; the parameter b is the ratio of salaries in adjacent skill levels (sometimes referred to as the scale ratio); j is the number of skill levels is an occupation and is analogous to the length of a job cluster; and e is an error term. As can be seen, the SM depends on the scale ratio and number of skill levels in an occupation.

The form of the model that is utilized below to determine the relationship between the SM, the demand for goods and services, and inflation is [Mathematical Expression Omitted] where and m are constants; [b.sub.c] and [b.sub.p] are the scale ratios for clerical and technical workers and for professional and administrative workers, respectively; (2) D is a dummy variable which equals zero for clerical workers and j-1 for professional workers; U, the unemployment rate, is a proxy for the demand for goods and services; and P is a measure of inflation, namely the percentage change in the Consumer Price Index.

From (2) it is seen that the SMs margins for clerical occupations (D=0) and for professional occupations (D=j-1) are [Mathematical Expression Omitted] and [Mathematical Expression Omitted] respectively. Letting J = j-1 and taking natural logarithms in (2) yields thel linear equation [Mathematical Expression Omitted]

Given this formulation, if the SM narrows (widens) when the unemployment rate falls (rises) as suggested by the Oi model, one would expect the coefficient of the unemployment rate variable, r, to be positive. And if inflation results in a reduction in the SM, the coefficient of the inflation rate variable, m, should be negative. Furthermore, it is to be expected that the SM is positively related to the number of skill levels in an occupation, i.e., that the coefficient of J is positive. As indicated elsewhere [Haber, 1983], it is also likely that the difference in salary needed to induce workers to seek a promotion is greater for professional than clerical workers because of the larger investment in human capital made by the former group; thus, the coefficient of D should be positive.

Besides the general issues relating to the affect on the SM of changes in the demand for goods and services and of inflation, two other questions of some interest are examined.

First, does [SM.sub.c] exhibit sensitivity to business conditions than [SM.sub.c]? The supply of professional workers is less elastic than the supply of clerical workers, but fixed employment costs are higher in the former occupations than in the latter. As indicated earlier, these factors tend to have offsetting effects, and it is not possible to say whether r is negative, zero, or positive for either occupational group. (3)

To determine which of the aforementioned possibilities is the case, [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are estimated for clerical and professional workers, respectively. The variable D is dropped from these equations, since the clerical and professional occupations are examined separately and within each group the scale ratios are assumed to be the same. If [SM.sub.p] fluctuates more than [SM.sub.c] because of the greater fixed employment costs associated with professional occupations; r in (7) should be larger than in (6).

Second, how does the SM of workers with lower-order skills behave over the business cycle compared to that of workers with higher-order skills? To answer this question, the SM can be decomposed as shown below. Denoting the skill levels in an occupation by 1, 2,...,h, [Mathematical Expression Omitted]

Letting [W.sub.h/W.sub.2] = [SM.sub.h] i.e., the skill margin for workers with higher-order skills, and [W.sub.2/W.sub.1] = [SM.sub.1], i.e., the skill margin for workers with lower-order skills, [SM=SM.sub.h . SM.sub.1]. Likewise, [SM.sub.c] and [SM.sub.p] can be decomposed in a similar manner.

If hiring and training costs increase substantially with skill level, the Oi model suggests that [SM.sub.1] and [SM.sub.h], like SM, should narrow during economic expansions and widen during economic contractions. This expectation is strengthened if factor substituion occurs. Not so clear, however, is how [SM.sub.1] changes relative to [SM.sub.h].

To determine whether [SM.sub.1] or [SM.sub.h] fluctuates more when demand and conditions change, equations similar to (5), (6) and (7) were estimated. For workers with lower-order skills the analogue of (6) is [Mathematical Expression Omitted]

Similarly, for workers with higher-order skills the analogue of (7) is [Mathematical Expression Omitted]

Note, in estimating (9),J=j-1=1 so that (lnbJ) is a constant is subsumed into lnk. In estimating (10), J = j-2, since the lowest skill level is omitted in the skill margin calculation and the number of skill levels can vary among occupations. Also, for example, if [SM.sub.h] fluctuates more than [SM.sub.1], r in (10) should be larger than in (9). (4)

(B) The Data

In studying skill margins, investigators have been limited by data availability. The data of this study are from the Bureau of Labor Statistics National Survey of Professional, Administrative, Technical, and Clerical occupations (known as the PATC survey). These data show mean full-time full-year earnings by skill level for a number of private sector white-collar occupations. (5) In each occupation, workers are classified by skill level defined independently of earnings. Twenty-seven occupations with data for five or more consecutive years were identified. (6)

In all occupations except three, the lowest skill level is the entry level. Typically, at this level the work is routine, specific instructions are provided regarding the tasks to be performed, and the work is done under close supervision regardless of the formal training brought to the job. At higher skill levels, the work is less routine and there is more discretion in planning and performing work.

The number of skill levels varies among occupations. The greatest number of skill levels, e.g., eight for engineers, is in the professional occupations. Only two levels are found for most clerical occupations. In general, the greater the amount of training and the wider the range of tasks and responsibilities, the greater the number of skill levels.

The period covered by the data includes a period of relatively mild inflation, 1962-72, during which the unemployment rate fell as low as 3.5 percent, and a period marked by substantial inflation, 1973-82, during which the umemployment rate rose as high as 9.7 percent. The diversity of economic conditions and the uniqueness of the data permit assessment of the issues raised above.

IV. Empirical Results

As indicated, the PATC data enable one to examine a number of different issues relating to white-collar SMs. From a policy perspective, the most important issue is how white-collar SMs change over the business cycle. In particular, it makes a difference whether SMs widen (contract) during expansion (recession) or more in the opposite direction. A widening of SMs during the expansionary phase of the business cycle is indicative of bottlenecks for skilled workers and is more likely to result in rising prices than if SMs narrow. If this is the case, the coefficient of the unemployment rate would be negative. Analogously, bottlenecks will have a more adverse impact on prices if the skill margin for workers with higher-order skills increases more rapidly than the corresponding skill margin for workers with lower-order skills.

In applying the model developed, in the preceding section, to address these issues, we have lagged the unemployment rate and rate of change in the CPI by one year to account for the fact that it takes time for wages to respond to changes in the level of unemployment and the rate of inflation. Separate regressions were run for all occupations, the clerical occupations, and the professional occupations. Within each category, equations were also estimated for workers in the lowest two skill levels and workers in the second to highest skill levels. The results of the analysis are shown in Tables 1 and 2.

Looking at line 1 of Table 1, one notes from the coefficient of J that the white-collar SM is highly correlated with the number of skill levels in an occupation. It is also seem from the coefficient of D that the SM for professional workers is significantly higher than that for clerical workers as might be expected, based on differences in human capital between the two groups.

Of importance for the major question raised in this paper, the white-collar SM is found to be positively related to the level of the unemployment rate. Taking the antilog of the coefficient of U(line 1, Table 1), it is found that the white-collar SM increases by 7.4 percent, $Iceteris paribus,$N when the unemployment rate increases by one percentage point. Thus, for a decrease in the unemployment rate of 3.2 percentage points (the decline is the unemployment rate between 1962-69), the SM would fall by 22.2 percent, all else [TABLE DATA OMITTED] being the same. This result is the opposite of what one would expect if only elasticities of supply were considered. It suggests that employment growth in the professional occupations expands rapidly when aggregate demand increases (as it did in the 1960s), but moderates when aggregate demand slackens (as it did in the early 1970s).

Evidence of a positive relationship between white-collar SMs and the unemployment rate is also seen from the regressions in Table 2 where skill levels are disaggregated. In all but one of the regressions the coefficient of the unemployment rate variable is positive and significantly different from zero; in the one regression where it is negative, statistical significance is absent. The results suggest that white-collar SMs vary with demand conditions, decreasing durig expansions (and, alternatively, increasing during recessions), thereby dampening inflationary pressures.

The finding are also in conformance with the hypothesis implicit to the Oi model, namely, that during recessions SMs are likely to rise most in those occupations with the highest fixed employment costs. Comparing the coefficients of the [TABLE DATA OMITTED] unemployment rate variable for the professional occupations with those for the clerical occupations, it is found that the former are larger than the latter, as suggested above in the discussion of equations (6) and (7).

A related hypothesis implicit to the Oi model is that as the distance between skill levels increases, the amplitude of fluctuation in the skill margin also increases. This proposition follows from the plausible assumption that there is a positive relationship between fixed employment costs and the length of a job cluster. In terms of the earlier illustration of the academic labor market, the Oi model implies that when the demand for academics increases, the wage of full professors relative to assistant professors will fall more than the wage of associate professors relative to assistant professors. In the context of this study, r, the coefficient of the unemployment rate variable, should therefore be larger in the [SM.sub.h] equations than in the [SM.sub.1] equations. This is the case as can be seen from Table 2 by comparing the [SM.sub.h] and [SM.sub.1] equations. The unemployment rate coefficients for the higher-order skill levels are larger than the corresponding coefficients for the lower-order skill-levels. (7) Over all of the white-collar occupations in the sample, [SM.sub.h] changes by 6.6 percent when the unemployment rate changes by one percentage point; the corresponding figure for [SM.sub.1] is 3.5 percent. Thust the greater responsiveness of the SM of workers with higher-order skills coupled with the narrowing of the overall SM provides further evidence that the movement of white-collar wages dampens the rise in prices associated with economic expansion.

Besides being affected by demand conditions, it may be that the white-collar SM is related to changes in consumer prices. Equity considerations suggest that social welfare might be enhanced if the SM were to decline during periods of rapidly rising prices. To the extent that employers consider social equity in their pay decisions, the earnings of workers with lower-order skills would be eroded less by inflation than the earnings of workers with higher-order skills.

If equity considerations during inflation have a moderating influence on SMs, i.e., tend to reduce SMs, one would expect this influence to be strongest where wage rates are the lowest. In this study, the lowest wage rates are found in the low-order skill levels of the clerical occupations. As can be seen from Table 2, the coefficient of P in the [SM.sub.c1] regression for clerical workers is negative and significant, indicating a reduction in the SM for this group during periods of rising prices, all else being the same; but this is the only instance where this occurs.

In contrast, the SM for workers with higher-order skills in both the professional and clerical occupations, i.e., [] and [], widened when inflation accelerated. Although the most highly skilled workers typically do not belong to a union, losses in real earnings could impel them to seek new employment if their wages do not keep pace with inflation. The bargaining leverage possessed by this group may be absent however for workers in lower-order skills in professional jobs. Because of the more elastic supply of workers in these jobs, they are likely to be less successful in finding alternative employment and hence more reluctant to press for higher wages.

These results suggest that inflation does impact on white-collar SMs but not in a uniform way. However, this should not obscure the fact that for each of the occupational groupings examined, with the possible exception of workers with lower-order skills in the clerical occupations, inflation exerts a much smaller influence on white-collar SMs than unemployment rates.

V. Summary

In this paper the authors assess the extent to which white-collar skill margins (SMs) fluctuate over the business cycle. Whether the SM increases (decreases) during economic expansion (recession) or moves in an opposite direction depends on the elasticity of supply of highly skilled and entry level workers and, according to Oi's model of labor as a quasi-fixed factor, the fixed employment costs incurred by firms in hiring each of these categories of labor. Since the effects of supply elasticity and fixed employment costs tend to offset each other, the cyclical sensitivity of the white-collar SM can only be ascertained by recourse to empirical data. Bureau of Labor Statistics data from the Professional, Administrative, Technical, and Clerical Survey covering the period 1962-85 are used for this purpose.

The major finding of the paper is that white-collar SMs narrow during the expansionary phase of the business cycle and widen during periods of recession. In accordance with implications that can be drawn from the Oi model, it is also found that over the business cycle the SM of professional workers varies more than the SM of clerical workers; likewise the SM of workers with higher-order skills varies more than the SM of workers with lower-order skills. The primary policy implication of the findings is that, during the period covered by the data, white-collar SMs have moved in such a manner as to dampen price increases during the expansionary phase of the business cycle.

Skill margins are found to narrow when the rate of inflation is high among workers with lower-order skills in the clerical occupations, but to widen among workers in the higher-order skills in the professional and clerical occupations. Overall, however, inflation appears to exert a much smaller influence on white-collar SMs than the unemployment rate.

(1) This may be particularly true of the construction industry where union wages are interdependent, e.g., between unionized electricians and unionized plumbers, and the degree of interdependence lessens during periods of expansion [Gustman and Segal, 1974]. As a result, equal dollar amount increases in earnings are less common during prosperity and SMs may rise faster than otherwise.

(2) For ease of exposition these occupational groups are hereafter referred to as the clerical occupations and professional occupations.

(3) The same indeterminacy exists in companing, say, the SM of engineers vs. engineering technicians or the SM of accountants vs. accounting clerks.

(4) In the academic labor market, casual observation suggests that during periods of prosperity the wage of full professors relative to associate professors declines more than the wage of associate professors relative to assistant professors. During recessionary periods, the reverse may occur. If the same pattern occurs in other white-collar labor markets, [SM.sub.l] and [SM.sub.h] would both be positively related to the level of the unemployment rate and, as indicated, r in (10) should be greater than in (9).

(5) PATC salary data by skill level for private sector white-collar occupations have been collected annually since 1960 by the Bureau of Labor Statistics to facilitate comparisons of earnings between private sector and federal government employees. Since in almost all cases, the salary data are available beginning in 1962 only, the data prior to this date were excluded from the study. Occupations with fewer than 5 years of data were, likewise, excluded. The data are further restricted to metropolitan areas to extend the period over which comparable figures can be obtained.

(6) The series with a different number of skill levels are used for six occupations. For example, the series for secretaries has four levels between 1967-73 and five levels between 1976-85. The six occupations are counted twice in the total of 27 occupations.

The occupations included in the sample, number of levels, and the time periods for which the data were available, respectively, are as follows: Clerical workers--Switchboard Operators, 2, (1962-70), Accounting Clerks, 2, (1962-83), and 4, (1970-85), Keypunch Operators, 2 (1962-85), Stenographers, 2, (1962-85), Typists, 2, (1962-85), Tabulating Machine Operators, 3, (1962-70), File Clerks, 3, (1962-85), and Secretaries, 4, (1967-73), and 5, (1976-85); Technical workers--Draftsmen, 4, (1965-78), and 5, (1979-85), Engineering Technicians, 5, (1962-85); Administrative--Office Services Managers, 4, (1962-68), Job Analysts, 4, (1962-74), Buyers, 4, (1966-85), and Directors of Personnel, 4, (1962-85); Professional workers--Auditors, 4, (1962-85), Accountants, 5, (1962-79), and 6, (1980-85), Public Accountants, 4, (1979-85), Chief Accountants, 4, (1962-85), Attorneys, 7, (1962-66), and 6 (1969-85), Chemists, 8, (1962-79), and 7, (1980-85), and Engineers, 8, (1962-85).

(7) Only occupations with three or more skill levels are included in Table 2, since it is not possible to compare SM and [SM.sub.l] or [SM.sub.h] and [SM.sub.l] for occupations with only two skill levels.


Robert Evans, "Wage Differentials, Excess Demand for Labor, and Inflation," Review of Economics and Statistics, February 1963, pp. 95-8.

Richard Freeman, The Over-Educated American, Academic Press, 1976.

Alan L. Gustman and Martin Segal, "The Skilled-Unskilled Wage Differential in Construction," Industrial and Labor 1974, pp. 261-75.

Sheldon E. Haber, "Wage Structure in Internal Labor Markets and Marginal Productivity Theory," Atlantic Economic Journal, December 1983, pp. 66-70.

Robert E. Hall, "The Rigidity of Wages and the Persistence of Unemployment," Brookings Papers on Economic Activity, No. 2, 1975, pp. 301-35.

Paul G. Keat, "Long-Run Changes in Occupational Wage Structure, 1900-1956," Journal of Political Economy, December 1960, pp. 584-600.

Harry Ober, "Occupational Wage Differentials, 1907-1947," Monthly Labor Review, August 1948, pp. 127-34.

Walter Oi, "Labor as a Quasi-Fixed Factor," Journal of Political Economy, December 1962, pp. 538-55.

M. W. Reder, "The Theory of Occupational Wage Differentials," American Economic Review, December 1955, pp. 833-52.

Tibor Scitovsky, "An International Comparison of the Trend of Professional Earnings," American Economic Review, March 1966, pp. 25-42.

Herbert Simon, "The Compensation of Executives," Sociometry, March 1957, pp. 32-5.

William D. Walsh, "The Short-Run Behavior of Skilled Wage Differentials," Industrial and Labor Relations Review, April 1977, pp. 302-13.
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Title Annotation:sensitivity of white-collar skill margin to the business cycle
Author:Haber, Sheldon E.
Publication:Atlantic Economic Journal
Date:Jun 1, 1991
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