Defrocking dualism: A new approach to defining industrial sectors

SOCIAL

SCIENCE

RESEARCH

10,

l-31 (1981)

Defrocking Dualism: A New Approach Defining Industrial Sectors

to

ROBERTL. KAUFMAN ANDRANDY HODSON University

of Texas-Austin

AND NEIL

D. FLIGSTEIN

University

of Arizona

In this paper we argue that a division of the economy into core and periphery sectors does not do justice to the complexity of the structure of the U.S. economy. The dualistic approach is inadequate both theoretically and empirically. While the dual economy literature has utilized multiple concepts it has conceived of them as forming a single dimension. We develop additional concepts from the complex organizations literature and utilize this enlarged set of concepts in a truly multidimensional framework. We also present a new technique of categorization based on a combination of factor and cluster analyses. The resulting categorization is highly interpretable, and it is superior to previous operationalizations in that it fully reflects the multidimensionality of economic segmentation.

In the not so distant past, stratification research focused mainly on the relationship between an individual’s social and educational characteristics and labor market outcomes such as income or status (Featherman and Hauser, 1978; Blau and Duncan, 1967; and Sewell and Hauser, 1975; are exemplars in this tradition). Recently, students of stratification have begun exploring structural characteristics of jobs, firms, and industries in order to gain a better understanding of how rewards become distributed (Stolzenberg, 1978; Hodson, 1978; Beck, Horan. and Tolbert 1978; Tolbert, Horan, and Beck, 1980; Bibb and Form, 1977; Wright and Perrone, 1977; Kluegel, 1978). The argument most of these writers make is that the We are indebted to Thomas N. Daymont, William Canak, Halliman H. Winsborough. and Robert M. Hauser for helpful comments and suggestions on this paper. Support for this research was provided by National Institute of Health, U.S. Public Health Service M-6275, the University of Wisconsin graduate fellowship program, Dissertation Grant 91-55-79-12 from the Employment and Training Administration, Department of Labor, and by the University of Wisconsin-Madison Center for Demography and Ecology which has core support from National Institute for Child Health and Human Development Grant HD-5876. 1

0049-089X/81/010001-31$02.00/0 Copyright @ 1981 by Academic press. Inc. AU rights of reproduction in any form reserved.

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KAUFMAN,

HODSON, AND FLIGSTEIN

social organization of labor preexists individuals and thus this organization, however it is defined, will affect the social and economic rewards individuals receive. The most salient of these arguments concerns what can be termed the “dual economy” perspective (Averitt, 1968; Beck et al., 1978; Tolbert et al., 1980; Hodson, 1978; O’Connor, 1973; Oster, 1979). This argument derives from Averitt (1968) and basically states that the economy is divided into two sectors-monopoly and competitive (and in some versions, the state)-and that the characteristics of these sectors imply different labor outcomes for persons in different sectors. In this paper, we call the “dualist” perspective into question on the grounds of both its theoretical clarity and empirical consistency. In the dualist perspective major dimensions which are theoretically relevant to the segmentation of industries have been either ignored or assumed to align in a consistently dichotomous pattern. In this paper we develop and utilize measures for a large set of theoretically relevant dimensions of industries. Through the use of factor analysis and cluster analysis, we demonstrate that a dualist version of the economy is inadequate for the analysis of the structure.of American industry. The implication of our results is that stratification researchers who wish to use the concept of segmented economies should move away from a simple dualistic perspective. Our discussion has the following organization. First, we review the dual economy literature. Second, we consider the relevance of work in organizational literature concerning the relation between growth, technology, and control of organizations. Based on the dualist and organizational accounts we suggest a number of dimensions which are theoretically relevant for the differentiation of industries into sectors. Finally, we develop measures of the various dimensions and offer a technique for assessing how these dimensions differentiate sectors. The technique is applied to an industrial data set which we have collected and the sectors that emerge are interpreted. In our conclusions, we note some implications of these findings for future research. THE DUAL ECONOMY PARADIGM The basic assertion of dual economy theorists is that the organization of private economic production and advanced capitalist nations results in two differentiated sectors: monopoly and competitive. Different authors have used different terms to describe these sectors. The two private capital sectors have been called monopoly and competitive (O’Connor, 1973), core and periphery (Averitt, 1968), the planning and market economies (Galbraith, 1973) and concentrated and unconcentrated industries (Bluestone, 1970). These various concepts all imply the same features for the two sectors. The core sector (however named) refers to firms with large numbers of employees, high capitalization, large profits, and

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large yearly sales. Most importantly, such firms control their markets and operate as price-setters because of the oligopolistic or monopolistic nature of their markets. These firms tend also to employ advanced technologies, have high productivity, and high rates of unionization. The periphery sector is characterized by small-scale capitalization, small size, regional or local dispersion, and single product lines. These firms operate in competitive markets which are unconcentrated. Further, they employ low levels of technology, tend to be labor intensive, and have low productivity and low rates of unionization. Based on the previous literature on dual economies, let us consider more precisely what the major criteria would be for discerning the difference between the core and periphery sectors. These criteria would include measures of size, concentration, geographic dispersion, technology, productivity, profit, unionization, state intervention, and state purchases. If one is to assign units to sectors, one must also decide what the relevant unit of analysis is. Most dual economy theorists believe that the ideal unit of analysis is the firm. However Spilerman (1977, p. 579) has argued that industries offer a better unit of analysis because firms in industries are “likely to have comparable technologies and organizational forms and would be subject to identical fluctuations in demand for their products.” Using a similar argument, Tolbert et al. (1980) and Bluestone et al. (1973) suggest that industries are the appropriate unit to discern economic structures. In choosing between firms and industries as the unit of analysis one should attempt to link concepts to the appropriate unit of measurement. Some concepts, such as organizational size, are clearly more appropriately measured at the firm level. Other concepts such as technology apply to an industry wide environment: all firms operating in the industry must attempt to match the “state of the art” technology in that industry. In choosing between these levels of analysis one inevitably sacrifices a certain amount of conceptual clarity in matching concepts with measures. Since all data that have been collected on a nationwide scale have been aggregated to the industry level, researchers have been forced to utilize this unit of analysis in their empirical work. The issue of firms versus industries as the unit of analysis in the study of economic segmentation remains an open question for future consideration and research. There have as yet been relatively few attempts to operationalize industrial segments of the American economy. Two of the earliest attempts (Bibb and Form, 1977; Beck et al., 1978) both suffer from a lack of empirical data. Bibb and Form rely on Averitt’s (1968) narrative description of major industrial divisions to define core and peripheral sectors. In a similar vein, Beck et al. base their assignment of major industrial divisions to a core and a periphery on the description of industries by Bluestone et al. (1973). The descriptive material on which these two

4

KAUFMAN,

HODSON,

AND

FLIGSTEIN

studies are based concern mainly manufacturing industries with little attention given to other industries. An early attempt to define industrial sectors using empirical data was made by Hodson (1978). He used measures of product and factor market concentration, size, unionization, degree of incorporation, and proportion of federal purchases to define whether an industry belonged in the core or periphery sector. The method employed by Hodson was to dichotomize each measure to indicate placement of an industry into core or periphery on the basis of that variable. Based on a perusal of these dichotomized indicators Hodson assigned industries to the core or periphery. In addition, he utilized several residual categories consisting of the state, construction, and farm production. But there are a number of problems with the data and method which Hodson employed. The scope of coverage of industries varied considerably for his different indicators with, overall, a good coverage of manufacturing industries but a limited coverage of other industries. Some of his measures with the best coverage of industries were available only for a fairly aggregated level of detail. Most importantly, there is the general problem of deciding how to group industries into sectors on the basis of multiple indicators of placement. Since a series of equally weighted dichotomous contrasts are used, Hodson’s method does not take into account the real size of the overall differences between industries. Oster (1979) attempts to test for the existence of a dual economy using a factor analytic approach. While Oster presents a number of wellconceived measures of industrial structure there are problems both with the industrial coverage of his data and with his interpretation of the results. Oster does not collect data for the retail, wholesale, service, and financial industries. One can question, then, whether or not the dualism which Oster finds represents the economy as a whole. One also wonders what part these excluded industries would play in a more inclusive classification scheme. His inclusion of measures of job stability and security also raises a question of circularity. If one were to attempt to use his results for the testing of hypotheses about these particular labor market outcomes, the analysis would be contaminated by the inclusion of these outcomes as defining characteristics.’ Oster presents results for only the first three factors extracted from a correlation matrix for 25 industrial characteristics. Since Oster does not present the full set of eigenvalues. it is not possible to determine if additional factors are significant and are needed to represent the data. We wonder what further insight could be gained into the strucute of the economy by an examination of a fuller set of factors. Examination of this ’ Oster educational especially

also includes in his analysis a number of variables describing the race, sex, and composition of industries. The wisdom of including such variables is debatable, if one wishes to study racial or sexual differences between sectors.

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fuller set might very well alter Oster’s conclusion that a dual economy scheme is consistent with his data. Oster identifies the first factor as a dual economy factor. He then tests whether or not two separate distributions of scores, one for the core and one for the periphery, are consistent with the overall distribution of scores on this single factor. While he finds that a two-sector scheme is consistent with the distribution of the scores for the first factor, this test is far from being conclusive. as Oster claims. Specific alternative hypotheses, such as a three-sector scheme, might very well also be consistent with this distribution. For the above reasons, we do not believe that Oster’s results provide strong evidence about the number and definition of economic sectors. Tolbert et al. (1980) also attempt to empirically define two sectors based on measures of potential for oligopolistic power (product market concentration and economic scale), oligopolistic behavior in product markets (mean profit, political contributions, and advertising expenditures), and oligopolistic behavior in labor markets (wages, job security/stability, and bureaucratic organization). Their data for 55 aggregated industrial categories cover all industries except government and professional services. They factor analyze these industrial characteristics and, after deleting several indicators due to multicollinearity, present a one-factor solution. Based on the factor scores, they assign each industry to the core or the periphery by dichotomizing the factor score distribution. Their choice of a cutting point was based on a break in the distribution near the mean. In a subsequent analysis of earnings they employ both the factor scores and the dichotomous measure of economic segmentation. There are, however, a number of serious flaws in the analysis of Tolbert et al. (see Hodson and Kaufman, 1980, for a more detailed critique). Most importantly, their conceptualization of economic segmentation is contaminated by a circularity between the defining characteristics of sectors and outcomes resulting from economic segmentation. That is, included in the indicators which they use to define sectors are measures of important labor market outcomes (e.g.. wages and job security/stability) which should be considered only as dependent variables. Such circularity invalidates the use of their measures of economic segmentation for testing hypotheses concerning labor market outcomes. Even if one were willing to ignore the circularity in the analysis of Tolbert et al., there are still problems concerning the data and methodology. The high degree of aggregation which they employ, which is not necessary for many of their indicators, reduces the real variation of industrial differences. Their choice of a cutting point to dichotomize the factor scores is arbitrary since there are four other breaks of comparable magnitude within 1.25 standard deviations of the mean which one could use to define from two to six sectors. Finally, a reanalysis of their data by

6

KAUFMAN,

HODSON,

AND

FLIGSTEIN

Hodson and Kaufman (1980) shows that a two factor solution is needed to adequately represent their limited set of industrial characteristics2 From this review of previous operationalizations it is clear that they all exhibit two kinds of problems: problems in the coverage of data for reasonably detailed industries and problems in the method of employing the data to define sectors. While it is apparent that economic segmentation exists, it is not so apparent that this segmentation can be adequately described by a dual solution. RETHINKING

ECONOMIC

SEGMENTATION

It may be of some value to consider what organizational theory can contribute to the discussion of the study of firms, industries, and economic sectors. Organizational theory suggests a set of concepts which interact to produce the form and substance of organizations. The major concepts of interest for organizations in general, and economic organizations in particular, are: (1) the environment of the organization, (2) the technology, (3) the size, (4) the control structures within the organization, and (5) the goals, performance, and policy-setting within the organization (see Azumi and Hage, 1972; Blau and Schoenherr, 1970; Hage and Aiken, 1970; Woodward, 1965; Hickson, Pugh, and Pheysey, 1969; and Chandler, 1962; for some representative studies). From an organizational point of view, one could construct the following argument. The key issue centers on the dynamics of the movement from small-scale to large-scale production. Both Marxist and non-Marxist students of the historical development of the growth of organizations have emphasized the causal role of profit-seeking firm behavior (Braverman, 1974; Chandler, 1962). The motivation for growth arises from the drive for profit but the strategy for growth and the resulting structure arise from the interaction of product, technology, and social control mechanisms. Beginning in the 1850s in the United States, new opportunities for profit were made possible by the shift from small-scale production to large-scale production and by the introduction of new technologies. This search for profits was actualized as two imperatives that have been identified as the profits/technology imperative and the profits/control imperative (Chandler, 1962): 1. Profits/technology imperative. The adoption of more complex technologies involving a greater utilization of machinery opened up new profit making opportunities. The dynamic in this imperative followed the kinds of goods that were produced and were most profitable. The effect of technology on the division of labor was twofold. First, it tended to break down tasks into component parts and thus deskill portions of the labor force. Second, it tended to create sets of industries which relied on highly ’ Two factors are needed both if one analyzes three circular variables are excluded.

their

final

nine-variable

data set or if the

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skilled and specialized labor. The overall result was a more complex division of labor. 2. Profits/control imperative. This imperative had two aspects. First, in order to use complex technologies and increase the scale of production it became necessary to develop more elaborate internal social control mechanisms. This involved creating layers of supervisory personnel. The result of this dynamic was the so-called “managerial revolufion.” Second, it became necessary to develop complex planning and control structures to deal with the firm’s external environment. These administrative structures were required to coordinate purchases, investment decisions, government regulation, and unionization and to maintain the overall level of profitability. This argument suggests that in order to secure profit and organizational survival, the firm must face two variables controllable in the short runtechnology and organizational structures-and one partially uncontrollable variable-the environment. As the economy expands, new control devices and structures will be developed. The uncertainty of the environment and the search for higher profits through growth will push the organization toward choosing one or more of the following strategies: guaranteeing its markets (increasing to national or international scope, expanding product lines), or its supplies (vertical integration), or its productivity (developing new technologies and modes of labor control). The strategy which any given firm or industry attempts to employ is dependent on the product it produces, its internal organization and its external constraints. If an organization is successful in the strategy of increasing its scale of activity, it must continue to develop new strategies and structures that will guarantee control of the labor force (cf. Edwards, 1979), promote the development and implementation of new technology (Chandler, 1962), and maximize control of the external environment. The issue of organizational survival in an insecure environment along with the profit motive help us to explain how technology and control mechanisms interact to produce larger and larger firms in some industries. In other industries the nature of the product or the available technology will limit the development of large firm or oligopolistic structure. In yet other industrial sectors the search for profits combined with the nature of the product and available technologies will have determined the presence or absence of multinational links, capital intensive production, high levels of unionization, high levels of profit, and so on. From this perspective, the development of economic segmentation is seen as the result of the working out of the dynamics of organizational imperatives over a long period of time. The perspective we have just presented would suggest that there indeed has been structural differentiation among firms and industries. But this differentiation does not imply that only two sectors should emerge. Given the multiplicity of strategies of growth and control available we suggest

8

KAUFMAN,

HODSON, AND FLIGSTEIN

that a great variety of differentiated structures and sectors should emerge. An example of such differentiation is provided by the contrast between the food-processing industries and large utilities both of which would be placed in the core sector under most dualistic schemes. Food-processing industries are heavily involved in foreign markets but are relatively labor intensive. Utilities, on the other hand, have minima1 foreign involvement but are extremely capital intensive. While a dual economy is a possible outcome of the organizational perspective we have just outlined it is not a necessary outcome. We believe the strategy, structure, and technology of firms interact to produce a much more differentiated economy. We also believe that the structure of the economy should be investigated empirically and not a priori forced into a dualistic mold. Based on the above discussion we suggest that the following concepts tap the multiple dimensions which are important in the differentiation of economic sectors. Concentration is the extent to which an industry is dominated by a small number of companies. Such concentration implies monopoly pricing and profits and greatly increases the range of options available to managers for dealing with their work forces and the external environment. Size measures the magnitude of economic activity. Size can be interpreted as share of total economic activity and as such offers a competing conceptualization of monopoly concentration-one based on the national market of total output rather than one based on industry or product lines. Size is crucial for such work place issues as span of control, economies of scale, and corporate power to adapt to changes in markets, technology, and the available work force. Capital intensity or labor intensity indicates the level of technology employed in an industry and influences such labor issues as pay, hiring practices, unemployment, and job satisfaction. Foreign involvement signifies the degree of involvement of American producers in foreign markets. Foreign involvement can occur both through the reliance of American industries on foreign markets as outlets for goods as well as through the expansion of American multinationals into foreign territories. Government intervention taps both direct government regulation of an industry and government purchases from an industry, the latter implying a degree of control and intervention similar to that involved in direct regulation. Government intervention is important for such issues as hiring practices (affirmative action) and unemployment. Profir is the rate of return achieved by a company and is important in allowing greater corporate options in dealing with problems and opportunities. Autonomy indicates the extent to which an industry operates as the

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dependent satellite of firms headquartered in other industries. In particular, this concept speaks to the issue of the horizontal and vertical integration of sets of industries. Productivity denotes the rate of economic output and the efficiency of production and by implication the level of technology employed. Unionization is the degree of worker organization and power in the work place. It is an essential concept in understanding rates of pay, job satisfaction, and unemployment. Growth taps both changes in the amount of economic activity in an industry and by implication changes in the nature of the organization of production in an industry. In the next section we describe the variables which we use to measure these concepts. Subsequently, we develop a method for operationalizing economic sectors which takes account of the multidimensional nature of economic segmentation. DATA We have collected a wide range of data which are available at a detailed level of industrial classification for the vast majority of our measures. Overall, our data sources provide a good coverage of the various industrial divisions. Using these data we developed a large number of measures of industrial structure. In selecting the measures to operationalize each concept group we chose all nonredundant indicators. For a detailed discussion of the operationalization of each of these measures see Hodson (1980) or Kaufman (1980). In Table 1 we present the empirical measures which we use to tap each concept group and the data sources from which they were extracted. These data were extracted from seven different sources. They apply to the early 1970s with a target date of 1972. The sources utilized are listed below, roughly as ordered by the amount of information we took from each. In parentheses we indicate the year to which the data apply. 1. Enterprise Statistics, 1972 (Table 1. I for 1967), 1977 (Tables I, 5,6,7 for 1972). 2. Internal Revenue Service, Corporate Income Tax Returns, 1977 (Tables 1, 2, 6 for 1972). 3. National Income and Product Accounts, 1976 (Tables 6.3, 6.5, 6.6, 6.7, 6.8 for 1972). 4. ZnputlOutpuf Study, 1967 (Machine Readable Data for 1967). 5. Census of Population Industry Characteristics, 1962 (Table 25 for 1960), 1972 (Table 37 for 1970). 6. Freeman-Medoff Unionization Data, 1978 (Machine Readable Data for 1970). 7. Scherer, 1970 (Data for 1970).

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KAUFMAN,

HODSON. AND FLIGSTEIN

TABLE I Industrial Structure Concepts and Variables Concentration Eight firm employment concentration (Enterprise, 1972) Eight firm sales concentration (Enterprise, 1972) Eight firm assets concentration (IRS, 1972) Percentage of industry sales in companies with over $250 million sales (Enterprise, 1972) Percentage of industry assets in companies with over $250 million assets (IRS, 1972) Advertising per company (IRS, 1972) Size Employment per company (Enrerprise, 1972) Sales per company (Enterprise, 1972) Assets per company (IRS, 1972) Net income per company (IRS, 1972) Value added per company (InpurJOurpur, l%7; Enterprise, 1%7) Percentage of companies which are corporations (Enrerprise, 1972) Establishments per company (Enterprise, 1972) Capital intensity or labor intensity Assets per employee (IRS, 1972; Enterprise, 1972) Payroll as a percentage of sales (IRS, 1972; Enterprise, 1972) Constant capital as a percentage of assets (IRS, 1972) Constant capital as a percentage of constant capital plus variable capital (InpuriOurpur, 1967; IRS, 1972; Enrerprise,

1972)

Percentage of employment which is part time (NIPA, Enterprise, 1972)

1972;

Foreign involvement Foreign dividends per company (IRS, 1972) Foreign tax credits per company (IRS, 1972) Exports per company (InpurlOurpur, 1967; Enterprise, 1%7) Exports as a percent of total output (Input/Output, 1967) Government intervention Government regulation (Scherer, 1970) Federal government purchases as a percentage of total output (InpurlOurpur, 1%7) Federal government purchases per firm (Input/Output, 1967; Enterprise, 1967) State and local government purchases as a percentage of total output (InpurlOurpur, 1%7) State and local goveriunent purchases per firm (InpurlOurpur, 1%7; Enterprise, 1967) Profit Net income per sales (IRS, 1972) Net income per assets (IRS, 1972)

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Table I-Continued Net income over constant capital plus variable capital (Input/Output, 1967; IRS, 1972) Conglomerate domination Percentage of industry work force employed by companies operating primarily in that industry (Enterprise, 1972) Productivity Value added per employee (InpuflOufpuf, 1967; Enterprise, 1967) Value added as a percentage of total output (Input/Output. 1967) Net national product per employee (NIPA, 1967) Unionization Percentage of all workers covered by collective bargaining agreements (Freeman & Medoff, 1970) Growth 1972 employment over 1967 employment (Enterprise. 1967, 1972) 1972 sales over I%7 sales (Enterprise, 1%7/1972) 1970 employment over 1960 employment (Census, 1960/1970) New capital expenditures per company (Enterprise, 1972) Employment per firm in 1972 over employment per ftrm in 1967 (Enterprise, 1967/ 1972) Source. Enterprise (1967/1972), U.S. Bureau of the Census (1972/1977); IRS (1972), U.S. Internal Revenue Service (1977); Input/Output (1%7), U.S. Department of Commerce, Interindustry Economics Division (1967); NIPA (1972). U.S. Bureau of Economic Analysis (1976); Census (1960/1970), U.S. Bureau of the Census (1962/1972).

The industry data from the various sources were reported in unique classification schemes adapted to each agency’s particular needs. In most cases the coding scheme employed was a variant of either the Standard Industry Classification (SIC) or the 1970 Census Industry Classification. The 1970 Census Industry Classification was chosen as a standard coding scheme because we anticipated using these data in conjunction with individual level data sets which employ this classification.3 3 Two sources allowed us to recode the different industry coding schemes into the Census Industry Classification. First, the Public Use Samples ofBasic Recodes for the 1970 Census (1972) reports the I%7 SIC equivalents of the 1970 Census Industry Classification. Second, the Standard Industrial Classification Manual (1972) describes the four-digit components of the 1967 and 1972 SIC coding schemes and records changes between these two classifications. By utilizing these two sources we were able to recode each coding scheme in a reasonably straightforward and satisfactory manner. Where problems arose because of changes in the allocation of detail components across coding schemes we relied on matching the names of categories or made a decision based on our examination of the industry descriptions in the SIC Manual.

12

KAUFMAN,

THE OPERATIONALIZATION

HODSON.

AND

FLIGSTEIN

OF INDUSTRIAL

STRUCTURE

The problem remains of how to best utilize the multiple characteristics of industrial structure developed above to define industrial sectors. The key question here is: How do you define the overall similarity of a pair of industries based on multiple nonindependent measure of similarity between the two industries? The issues involved will become clearer if we look at a simple two-dimensional picture of industries A and B plotted on variables X and Y (Fig. I). What we really wish to measure is the distance d between A and B as an indicator of the closeness or similarity of A and B. Since X and Y are nonorthogonal (correlated) we cannot define d2 as [X, - XrJ2 + [Y, - Y,]*. If we know the correlation between X and Y, which corresponds to cos 19in Fig. 1, then d* = [X,

- X,12 + [(Y,

- YB) - (X,

- X,) cos ~12csc2 8.

But the calculation of distance in nonorthogonal spaces for three or more dimensions quickly becomes prohibitively complex. On the other hand, the calculation of distance in n-dimensional orthogonal spaces is quite simple. This suggests that if we could transform our industrial characteristics into a set of orthogonal characteristics that it would be easy to calculate the similarity of any pair of industries. Such an orthogonalization of our original 40 industrial characteristics can be readily accomplished using a principal-components factor analysis. The principal components factor procedure differs from other types of factors analysis in that the extracted factors are exact mathematical transformations of the original variables and that no inferences are drawn concerning the structure of common

FIGURE

I

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versus unique variance among the variables. Using the orthogonal factors extracted from our 40 variables it is easy to calculate the distance between any pair of industries for any number of factors: d2 = ;

[FAj - FBj]2,

i=1

where F,i and F,i are the scores on factor i for industries A and B. These interindustry distances can then be used as indicators of dissimilarity in hierarchical clustering analysis to produce industrial sectors. The combination of a factor analysis to orthogonalize the original variable space with a cluster analysis to systematically group the industries together provides an elegant solution to the problem of multiple indicators which should prove useful in other similar situations. The key issue in performing the factor analysis concerns the number of factors which should be used for the computation of distances. If we were to use all of the possible factors (40) we would exactly replicate the original variable space. But it is likely that beyond some point the factors would only be picking up error variance (e.g., error due to measurement error or to differences in the level of detail), and, therefore, all 40 factors should not be used. While it is hard to determine at what point this would be true, it is instructive to compare the difference between an I l-factor solution and a 25-factor solution. In Table 2 we present the eigenvalues and the cumulative percentage of variance for the first 25 factors from our principal components factor analysis.4 The I l-factor solution accounts for 83% of the total variance of the original variables. However, this solution differentially accounts for the variance of variables from different concept groups. In particular, this solution best replicates the variables in the size concept group and most poorly replicates the variables in the concentration concept group.5 If we were to use the I l-factor solution, then, we would be reproducing the differences between industries in terms of size and concentration with differential accuracy. On the other hand, the 25factor solution accounts for 99% of the total variance, and it accounts for a minimum of 95% of the variance of any one variable. Using the 25-factor solution, then, we closely replicate the original variable space with variables from all concept groups being well reproduced. We chose to use the 25-factor solution since it has uniformly high accuracy for the different concept groups. For each industry we com4 Since we are using the principal components factor analytic technique the first I I eigenvalues presented in Table 2 are the exact eigenvalues for an 1 l-factor solution. 5 Based on the I l-factor solution the communalities for the variables in the size concept group (listed in the order in which they appear in Table 1) are .94, .98, .91, .88, .86. .90, and .8l. The communalities for the variables in the concentration concept group are .85, .82. .60. .6S. .88. and .78.

14

KAUFMAN,

HODSON.

AND

TABLE Eigenvalues

for

First

25 Factors

Factor

from

FLIGSTEIN

2 Principal

Components

15.737 3.127 2.260

2 3 4

Analysis

Cumulative percentage of variance

Eigenvalue

I

Factor

39.3 47.2 52.8

2. I87

58.3 63.1

5 6 7

1.936 I.742 1.593

8

1.416 I.087

75.0 77.7

I.072

80.4

9 IO II I2 13 I4 I5

67.5 71.5

,988 ,848 .783

82.9 85.0 86.9

,709

88.7 90.3

,630 ,557

I6 I7 I8

91.7

,489 ,430 ,410

92.9 94.0 95.0

,404

96.0

23

,315 .273 ,232

96.8 97.5 98. I

24 25

,205 ,172

98.6 99.0

I9 20 21 22

puted factor scores for each of the 25 factors6 Factor scores were not computed for any case for which one-half or more of the variables were missing. Factor scores could not be computed for only I I of our 213 industries: the 4 public administration industries and 7 of the “not specified” manufacturing industries.’ 6 The

weighting

procedure

used

to handle

FAJ = +

where N A

FAj hk xAK

= = = =

the the the the

missing

data

was:

x 2” fikx.uc. k=,

number of non-missing variables for case A, factor score for case A for factorj, factor score coefficient for factor j on variable standardized value of variable k for case A.

k,

’ The seven “not specified” industries for which factor scores cannot construction, metal manufacturing, machinery manufacturing, electrical ufacturing, professional equipment manufacturing. food manufacturing, “not specified” manufacturing industry.

be computed are machinery manand the general

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DUALISM

TABLE 3 Change in the Error Sum of Squares and a Test Statistic for the 14- to l&Cluster Solutions No. of clusters I8 I7 16 I5 I4

Change in ESS

Test statistic

P

70. I25 91.125 83.813 112.325 130.325

60.867 75.138 84.694 93.482 95.249

.OOl .OOl ,001 ,001 .oo I

Based on these factor scores we computed the inter-industry distances and used these distances as input to a hierarchical clustering procedure. The clustering method which we utilized is known as Ward’s method (1963) as implemented in the Clustan package (Wishart, 1968). This method of clustering is based on minimizing a total error sum of squares which is defined as the sum of the within-cluster error sum of squares. For each cluster the within-cluster error sum of squares is the sum of the squared distances of each cluster element from the centroid of the cluster. At the beginning of the cluster procedure each industry is treated as a separate cluster and the two closest clusters, in terms of a minimal increase in the error sum of squares, are fused. This step-by-step fusion process continues until a specified number of clusters has been achieved.a In Table 3 we present some statistics from the cluster analysis for 14 to 18 clusters. In deciding at what point to stop the fusion of clusters there are two criteria which should be considered: the statistical significance of the increase in the error sum of squares and the substantive meaning of the fusion. In Appendix A we show that a weighted calculation of the change in the error sum of squares, where the weights are the inverse of the variance of the factors, is distributed as x*(25). But this test statistic is not very useful in our case since every cluster fusion to less than 35 clusters is significant (p < .OOl). We chose to stop at the 16-cluster level for two reasons. First, the change in the error sum of squares appears to level off at 16 clusters before it sharply increases for 15 clusters. Second, as we discuss below, the 16-cluster solution has a conceptual appeal in terms of the differences between clusters on some key industrial characteristics. It should be noted that of these 16 clusters four represent single industry outliers. In empirical applications these four outliers could be B Initially we used this procedure to produce 24 clusters at which point we allowed a local optimization step to be added after each fusion of 2 clusters. The local optimization step was not added earlier in the clustering process due to the additional cost involved. The rationale for employing a local optimization is to take account of the fact that, after a new cluster has been defined by fusion, some of the elements of the new cluster may now be closer to the centroid of another cluster and, similarly, some elements of other clusters may now be closer to the centroid of the new cluster.

16

KAUFMAN,

HODSON. AND FLIGSTEIN

collapsed into the other clusters with minimal of the sectoral classification. INTERPRETATION

change in the interpretation

OF INDUSTRIAL CLUSTERS

The conceptual sense of the 16-cluster solution can be seen from an examination of Table 4 and Appendix B. Table 4 shows the cluster means of summary measures for each concept group. These summary measures are calculated as averages of the standardized variables within each concept group. Appendix B presents a listing of the industries in each of the 16 clusters.” The discussion of these results can be best organized around a series of profiles for each cluster.‘O Oligopoly

Sector

This sector has the highest values on almost every characteristic. In particular it has the highest values on size, concentration, capital intensity, foreign involvement. and profit. The seven industries in this cluster contain those firms which are among the very largest multinationals (e.g., IBM, GM, Kodak, Lilly, Exxon) and which are oligopolies in the American economy. Compared to the core sector, the oligopoly sector has considerably higher values on all the measures except unionization. Core Sector Excluding the oligopoly sector, the core sector has the highest values on profit and foreign involvement. On concentration, size, and unionization it also has high values being exceeded only by core utilities and transport in some cases. It is worth noting that the core sector has the least autonomy of any of the sectors. This sector is comprised solely of manufacturing industries. Contrasted to the wholesale, periphery, and small shop sectors, it is higher for almost every comparison. Wholesale Sector This sector has a low level of concentration and capital intensity. But it is roughly average on the size measures and has higher than average values for foreign involvement and profit. In addition to all the wholesale industries, this sector contains a few machinery manufacturing and R We changed the cluster placement of 3 of the 202 industries (crude petroleum extraction, ship and boat building, and miscellaneous petroleum products manufacturing). Each of these three industries was a large outlier in clusters where the other industries were tightly grouped, and each was almost as close to another cluster where it was conceptually more reasonable to place it. As discussed in Appendix A, a test statistic can be calculated for such changes in placement. This test statistic was not significant (p > .lO) for any of the three changes made. lo In verbalizing the rankings of the clusters on the various concept groups we exclude from consideration the four single industry outliers whose extreme values would distort the comparisons.

Oligopoly Core Wholesale Periphery Small shop Core utilities and finance Periphery utilities Core transport Periphery transport Local monopoly Education and nonprofit Agriculture Brokers Real estate Ordnance Tobacco

Sector

1.40 .I3 -.09 -.43 -.66 I .09

-.Ol

.99 -.03

-.70 -.84

-.73 -.35 -.67 1.03 1.74

.33

.53 .33

-.78 -.86

- 1.37 -.94 -1.13 .94 2.65

Size

1.22 .52 -.36 .oo -.55 .36

Concentration

-.I1 .48 .94 -.30 .63

-.74 -1.25

.41 .53

.86

1.28 .40 -.28 -.03 -.54 1.00

Capital intensity

-.58 -.66 -.8l .84 1.69

-.90 -1.00

.44 .3l

-.40

1.70 .84 .3l -.20 -1.06 -.I5

Foreign involvement

- .45 .4l -.28 4. I3 -.35

.67 -.07

.95 .I7

1.03

.97 -.20 -.22 -.I2 -.31 .66

Government intervention

-.34 5. I4 .47 - .03 2.83

-.63 - .25

- .63 -.29

.I2

I.59 .23 -.04 -.20 -.I8 .07

Profit

-2.84 I.12

1.09

.83

.26 -76 .27 .05 .76

Autonomy

TABLE 4 Means of Concept Group Standardized Summary Measures by Sector

-.53 -.87 4.28 -.08 I .09

.I5 -.41

.34 2.29

.29

.83 -.33 .39 -.24 - .05 -.08

Productivity

-1.12 -1.12 -.43 .87 1.24

-.I3 -1.00

-1.19 .27 .I9 -1.22 -.20

.08 1.34

-.3l -.44

-.94

1.07 1.50 .70

.20 .07 .08 -.04 -.I0 .I0

Growth

.I6 .74 -.34 -.I8 -.70 .oo

Unionization

18

KAUFMAN.

HODSON, AND FLIGSTEIN

professional service industries. Compared to the periphery, the wholesale sector is less concentrated but it has larger firms, more foreign involvement, and higher profits. Compared with the small shop sector, wholesale has higher values on all the major dimensions. Periphery Sector and Small Shop Sector The periphery sector, somewhat surprisingly, has an average level of concentration and capital intensity but is below average on all the other dimensions. This sector is comprised of a variety of industries: a large number of service industries, a few durable and nondurable manufacturing industries, most of mining, and those retail industries typified by chain stores. The small shop sector has extremely low values on almost all the dimensions. It is interesting to note the extremely high degree of autonomy of industries in this sector. The small shop sector is comprised primarily of retail industries, three manufacturing industries typified by small production, and offices of physicians and dentists. While both the periphery and small shop sectors have lower than average values on almost all dimensions of industrial structure, the periphery sector has higher values than the small shop sector on almost all the dimensions. For the most part, the differences between these sectors are ones of small differences along the various dimensions. But on the criteria of concentration and capital intensity, the sectors appear to be sharply differentiated. Many industries in the periphery sector contain some dominant firms of national scale, whereas few. if any, of the industries in the small shop sector contain firms which operate outside of local markets. Core Utilities and Finance Sector and Periphery Utilities Sector The core utilities and finance sector is typified by extremely high size and capital intensity. The industries comprising this sector are the electric and gas utilities, radio and TV broadcasting, and three finance industries. The periphery utilities sector, comprised of the miscellaneous utilities, is typified by high values on capital intensity, unionization, and government intervention. In comparing these two sectors, we see that both have above average values on concentration and profit. However, the core utilities sector is distinguished by its high value on size while the periphery utilities sector is distinguished by high values on unionization and government intervention. These two sectors produce very similar products and both utilize highly capital intensive modes of production, but their scale of operations is quite different. In differentiating the core utilities and finance sector from the oligopoly and core sectors, we see that the core utilities and finance sector has lower foreign involvement, a lower profit rate, and less concentration, but lies between the core and oligopoly sectors on the dimensions of size and capital intensity. These differences most likely result from greater government regulation of

DEFROCKING

DUALISM

19

utilities and finance and from differences in the nature of the products produced (e.g., the production of utilities is tied to a given geographic region, limiting the development of national and international ties). In contrasting the periphery utilities sector to the other sectors, we see that it is more similar to the core utilities sector than it is to the periphery or small shop sectors. This similarity reflects close government regulation, the high level of technology utilized. and the high skill requirements of production in the utilities sectors. Core Transport Sector and Periphery Transport Sector

The core transport sector is typified !by relatively high values on concentration, size, and capital intensity and a low value for profit rate. It has the highest value of any sector on unionization. This sector is comprised of railroad, bus, air, and water transport and telephone and telegraph services. The periphery transport sector is characterized by low values for concentration and profit, but high values for unionization and (somewhat surprisingly) for capital intensity. This sector is comprised of trucking and warehousing and pipeline transport industries. In contrasting these two sectors, we see that they are again typified by a “coreperiphery” relationship in terms of size., concentration, and unionization. But the periphery transport sector has a surprisingly high value for capital intensity. This, no doubt, partially results from the nature of the industrial product of this sector which requires large investments in buildings, equipment, and land. The comparison of the core transport sector to the core and oligopoly sectors and the periphery transport to the periphery and small shop sectors is similar to that discussed above for the core and periphery utilities sectors. That is, the periphery transport sector is more similar to the core transport sector than it is to the periphery or small shop sectors. In addition, the core and periphery transport sectors are differentiated from other sectors by extremely high rates of unionization, resulting from the historical importance of the Teamsters Union in these industries. Local Monopoly Sector, Agriculture Sector

Education and Nonprojit Sector, and

These three sectors are characterized by low values on almost all the major industrial characteristics. Within this group, the local monopoly sector is highest on unionization and government intervention.” The education and nonprofit sector has the lowest values for capital intensity and size. The agriculture sector has the lowest values for concentration ‘I The construction, taxi, and health services industries are strong monopolies in local markets, although they are not monopolies in the national market (Weiss. 1%6; Shepherd, 1970).

20

KAUFMAN,

HODSON,

AND

FLIGSTEIN

and unionization. In contrast to the other sectors these three residual sectors are negative outliers on almost all the dimensions. Brokers, Real Estate, Ordnance, and Tobacco

These four clusters are each comprised of a single industry outlier. The brokerage industry appears as an outlier due to its extremely low values on some dimensions and extremely high values on others. It has low values on concentration, size, foreign involvement, and unionization, but high values on capital intensity, profit; and government intervention. This industry consists of many competitive brokerage houses dealing with large volumes of financial capital. In contrast to brokers, the real estate sector has even lower values for concentration, size, and foreign involvement and has a low, rather than a high, value for government intervention. However, real estate has among the highest values of any sector for capital intensity due to high investment in land and buildings. The ordnance sector has among the highest values of any sector for concentration and size, and has especially high values for government intervention and unionization. However, it has among the lowest values for capital intensity because of its utilization of a large volume of skilled labor. The tobacco sector can be seen to be a large positive outlier on all the dimensions except government intervention and growth. Indeed, on some measures it has roughly equal values with the oligopoly sector, but on many measures it has considerably higher values. In an empirical application of these results tobacco could be merged into the oligopoly sector, ordnance could be merged into the core sector, and brokers and real estate could be merged into the periphery utilities sector. We believe this collapsing would result in little loss of interpretability. In reviewing the sector profiles and contrasts outlined above, we can see that there is some utility to a core versus periphery distinction. However, such a contrast does not hold across the entire industrial spectrum. Rather, it is a distinction which is reproduced within some of the broad industrial product types but which is unsuited to describing a large portion of the economy. We also find that many of the dimensions which theorists have relied upon to differentiate core and periphery sectors do not consistently demonstrate a pattern of high values grouping together and low values grouping together. For example, the wholesale sector is competitive but is based on production in average sized firms with high foreign involvement .12 Moreover, many of the outlying sectors demonstrate a pattern of extremely high values on some dimensions ‘* It is interesting to note that for the wholesale sector some of the industries are classified as core and some as periphery by both Hodson (1978) and Tolbert et al. (1980). But, they do not consistently agree as to which are to be included in the core and which are to be included in the periphery.

DEFROCKING

DUALISM

21

matched with extremely low values on others. The differentiation of a true oligopoly sector from a larger core sector highlights B final interesting point of contrast. Both the core and oligopoly sectors are typified by large-scale concentrated production, but the core sector is highly subordinated to outside ownership while the oligopoly sector is highly autonomous. It is interesting to note that the high autonomy of the oligopoly sector has a different meaning than in the case of the small shop sector. Oligopoly sector autonomy indicates corporate power while small shop sector autonomy indicates the secondary importance of these industries in the economy. CONCLUSIONS We have argued that a division of the economy into core and periphery sectors does not do justice to the complexity of the structure of the U.S. economy. The dualistic approach is inadequate both theoretically and empirically. We have argued that the single dynamic of increasing concentration and centralization does not offer a sufficient theoretical basis for comprehending economic segmentation. Rather, this is only one of several dynamics based on the interaction of profit seeking, technology, environment, union struggle. and government intervention which act to produce economic segmentation. We have also questioned the assumption that these multiple dimensions align in a consistent pattern with high values and low values grouping together. Our results demonstrate that the patterns of alignment which occur do not form a consistent dichotomy. While the dual economy literature has utilized multiple concepts it has conceived of them as forming a single dimension. In this paper we have both developed additional concepts from the complex organizations literature and utilized this enlarged set of concepts in a truly multidimensional framework. The resulting categorization embodies real differences among industries in economic structure. While the dual economy paradigm assumes a consistent alignment of the various dimensions of economic structure we have attempted to map out the empirical differences between industries which are extant in the economy. We offer this categorization as a fraimework for operationalizing key differences in industrial structure. We do not claim that it represents a definitive and final solution to the question of how to operationalize economic segmentation in the U.S. economy. However, we do believe that this categorization is superior to prior operationalizations in that it fully reflects the multidimensionality of economic segmentation. This classification also allows flexibility and choice for future research applications. In addition to being used at tlhe full level of detail, it can be collapsed across distinctions which researchers believe to be theoretically unimportant to their particular research problem. Indeed, in work

30

KAUFMAN,

HODSON, AND FLIGSTEIN

Blau, P., and Duncan, 0. D. (1967). The American Occupational Structure, Wiley, New York. Blau, P.. and Schoenherr, R. (1970). The Structure of Organizations, Basic Books, New York. Bluestone, B. (1970). “The tripartite economy: Labor markets and the working poor,” Poverty and Human Resources Abstracts 5, 15-35. Bluestone. B., Murphy, W., and Stevenson, M. (1973). Low Wages and the Working Poor, Institute of Labor and Industrial Relations, Ann Arbor. Braverman. H. (1974). Labor and Monopoly Capitalism, Monthly Review Press, New York. Chandler, A. (1962). Strategy and Structure, MIT Press, Cambridge, Mass. Edwards, R. C. (1979). Contested Terrain, Basic Books, New York. Featherman. D. L., and Hauser, R. M. (1978). Opportunity and Change, Academic Press, New York. Freeman, R. B.. and Medoff. J. L. (1979). “New estimates of private sector unionism in the United States,” Industrial and Labor Relations Review 32, 143-174. Galbraith, J. K. (1973). Economics and the Public Purpose, Houghton Mifflin, Boston. Hage, J., and Aiken. M. (1970). Social Change in Complex Organizations, Random House, New York. Hickson, D. J., Pugh, D. S., and Pheysey, D. (1969). “Operations technology and organization structure: An empirical reappraisal.” Administrative Science Quarterly 14, 378397. Hodson. R. (1978). “Labor in the monopoly. competitive, and state sectors of production,‘* Politics and Society 8, 429-480. Hodson, R. (1980). The Social Impact of Industrial Structure on Working Conditions, Ph.D. dissertation. Department of Sociology. University of Wisconsin-Madison. Hodson, R., and Kaufman, R. L. (1981). “Circularity in the dual economy: A comment on Tolbert. Horan, and Beck, 1980.” American Journal of Sociology, in press. Hogg, R. V., and Craig, A. T. (1970). Introduction to Mathematical Statistics. 3 ed., Macmillan, London. Kaufman, R. L. (1980). Racial Discrimination and Segmented Labor Markets, Ph.D. dissertation. Department of Sociology (forthcoming), University of Wisconsin-Madison. Kluegel, J. (1978). “The causes and costs of racial exclusion from job authority,” American Sociological Review 43, 285-301. O’Connor, J. (1973). The Fiscal Crisis of the State, St. Martin’s Press, New York. Oster. G. (1979). “A factor analytic test of the theory of the dual economy,” Review of Economics and Statistics 61, 33-39. Scherer, F. (1970). Industrial Market Structure and Economic Performance, Rand McNally, Chicago. Sewell, W., and Hauser, R. M. (1975). Education, Occupation. and Earnings, Academic Press, New York. Shepherd, W. G. (1970). Market Power and Economic Welfare, Random House. New York. Spilerman, S. (1977). “Careers, labor market structure, and socioeconomic achievement,” American Journal of Sociology 83, 551-593. Stolzenberg. R. (1978). “Bringing the boss back in.” American Sociological Review 43, 8 13-828. Tolbert, C., Horan, P.. and Beck, E. M. (1980). “The structure of economic segmentation: A dual economy approach,” American Journal of Sociology 85, lO95- I 116. U.S. Bureau of the Census (1962/1972). Census of Population. l%O/l970, Subject Reports: Occupation by Industry, U.S. Govt. Printing Office. Washington, D.C. U.S. Bureau of the Census (1972/1977). Enterprise Statistics, 1967/1972. Vol. I. General Report on Industrial Organization, U.S. Govt. Printing Office, Washington, D.C.

DEFROCKING

-

Hi-1

1

--

ni

1

-

1

---

Iii

ni

1

--

1

--

%

...

I-

--

Iii

ni- 1

ni

Ai =

--- 1

4

--

23

DUALISM

1 --nini

ni

4

..

’

1

-4

1

--

...

(3)

ni

..

1

-ni

--

1 ni

---

1 IZi

. .’

-

ni-1 4

Assuming that clusters K and K - 1 are fused, the change in the error sum of squares due to this fusion is ESS,,-,

Letting

= TSSKel - TSSK = ‘f

B = AcK-” -AcK’,

;Ei

x; [A (K-1)

-

A’K’]Xje

(4)

we have

(5)

where A g,K--I is a square matrix of order n,+n,-, defined analogously Ai in Eq. (3) with nK+nK-, substituted for ni. Letting

we have

to

24

KAUFMAN,

HODSON,

-1

nK

hi+nK-JnK., .

.

nK (nK+nxm,)nK., B*

AND FLIGSTEIN

Cn,+nnxl,)n,, nK+nK., -1 nh.+nK-,

nK h+n~-JnK-I

’ n,+nl,., -1 ’ ’ ‘nK+nK., (6)

zz

-1 nK+nK-,

.

-1

nK-] hl (nK+nKmI)nK. . (nK+nK-,)nA

nK+kI

.

-‘I nK+ib

-‘I nK+nKmI

.. nKmi h+n.+lh

.

4-, h

+ nK- I h

Now the rank of B* is 1 since the first nK-i rows are identical and the last nK rows are multiples of the first rows. Moreover, B* x B* = B* and, hence, B* is idempotent. Since B* is the only nonzero submatrix of B, this implies that the rank of B is 1 and that B is also idempotent. These properties of B will be important in determining the probability distribution of ESSK,K--I. However, we also need to know the distribution of the xJ’s in order to find the distribution of ESSK,K--I. Given that a factor analysis was used in our research to create the xj’s it is not unreasonable to assume that xj N(O, ,%I) forj = 1. . . ., J and that E(xixi) = 0 for i # j.13 The multinormality of thexi’s and the fact that B is idempotent with rank 1 implies that x;BxjIuf - x2(l) (see Hogg and Craig, 1970, pp. 384-387). Then, the moment generating function of x/Bxjlu~ is MT(t) = (1 - 2f)-1/2. Therefore the moment generating function ofxfBxj is M,(t) = (1 - 2fu5)- 1’2. Since ESSX,K--I is the sum of the xlBx,‘s and the xj’s are independent, the moment generating function of ESSK,K--I is M(r) = iiM,(r) j=l

(7)

= I?(1 - 2taf)-“2. J=1

Equation (7) is the moment generating function for a multivariate y distribution. Thus, ESS,,-, has a multivariate y distribution with parameters aj = l/2 and & = 2oj2, for j = 1, . . . , J. However, it is a difficult task, computationally not analytically, to calculate the percentage points of such a multivariate y distribution. If, I3 The creation of the E(xix;) = 0 for i # j. What

x,‘s by factor we are assuming

analysis implies that E(x,) is that the xr’s are multinormally

=

0 and that distributed.

DEFROCKING

25

DLfALlSM

instead, we define a different error stun of squares by weighting the components corresponding to each variable inversely to the variance of the variable, we obtain a test statistic that is x2. That is, let

The moment

generating function

of ESS&,-l

is

M*(t) = fi M,*(t) = fJ (I - 21)~“2 = (1 - 2r)-5’2 j=l

(9)

j=l

and ESSjjKpl is x2(./). While it is ESS,,..., that is actually minimized by Ward’s method of clustering, we can still use ESS,$K--I as a statistical test of the significance or nonsignificance of a given hierarchical fusion. Let us now turn to the situation involving the movement of one observation from a given cluster to a different cluster. For convenience, let us assume that we wish to move the first ekment of the second chrster into the first cluster. We can write the change in the error sum of squares which results from this relocation as ESS = 2 x;[A*‘~’

- A”O]xj,

(10)

i=l

where AcK’ is as defined in Eqs. (2) and (3) and

(11)

where A&

is a square matrix of order n, + n2 and is defined as -

n1 - n,+l -I n,fl-----

-I

n,flAT*

-1

".

-1 n,+l

0

0

n1 n,+l

...

-1 ff,+1

0

0

..

0

j

‘._

;

i

ii;

:

-1 n,+l

‘..

4 - n,+l

n,fl

0

0

0

0

=

(12) 0

0

0

0

o-.

o--

n,-I n,-2 -I n,-2

f 0

0

ifi

-1 n,-2 n,-I q-2

i 0

i -I n,-2-

-I n,-2

..’

- -I

‘.’

- -1 n,-2

‘.,

i

..’

n,-2

n,-I n,-2

26

KAUFMAN,

HODSON,

AND

FLIGSTEIN

The upper nonzero block of AF,2 represents a square symmetric submatrix of order n, + 1 while the lower nonzero block represents a square symmetric submatrix of order n2 - 1. Letting

C = A*‘K’ - AcK’ we have -

where I (n,+

-I

1 IIn,

0

0

- fl,+i

(n,+Ih,

:. :. :. 1 (n,+l)n, c*

=

I

-I

-I

-I

n,+l

n,+l

n,-n,+

I

I

(n,+l)n,

F

1

0

0

0

0

n,+l

(n,+lh

-I

(n,-

4

I 7;;-

“’

.(14)

-1

I)n*

(n,-

I)n,

.. . :::

-I

1 0

0

(n,-

4

-1 I)n*

(n*-

l)n*

Now the rank of C* is two since the first n, rows are identical, the last n2 1 rows are identical and the n + 1st row is the negative of the sum of the other rows. Moreover, it can be shown that the eigenvalues of C* areI n1

l/2

+nz

‘l = I (n, + l)n,

and AZ = -A,. 1

(13

Since C* is the only nonzero submatrix of C, C also has rank 2 and eigenvalues A, and AZ as given in Eq. (15). Thus, the moment generating function of x~Cx,/crjz is Mj(t) = [(l 2tAI)(l + 2tA2)]-“2 (see Hogg and Craig, 1970, pp. 384-387). Unfortunately, we have been unable to find any probability distribution with such a moment generating function. However, if we define a new test statistic based on C and the Xj’s as 14 Since the rank of C* is 2 we can write C* = PAP’ where A is a diagonal matrix with diagonal equal to (A,,h*,O,...,O). Now by computing (C*)*, we find that (C*)* = [(n, + n*)/ (n, + l)n*)] C*. This implies that A: = [(nl + n*)/{(n, + l)q}] Al and that A$ = [(n, + n*)/ = ~t[(n, +n*)/[{(n, + l)n*)]1/2andA* = ?A,.Now,ifA, =A* then(C*Y t (n, + l)n*)]A*.Thus,A, should be equal to +C*[(n, + n,)/{ (n, + l)n*}]ll*. By computing (C*p we find that this is not the case. Therefore A* = -A,.

DEFROCKING

27

DUALISM

G* = 2 x;C2xj/u;, j=l we can find the distribution of this function. The moment generating function of x~C2xj/u~ is M,(t) = (1 - 2th3-‘.15 Hence, the moment generating function of G* is M(t)

= fi

Mj(t)

j=l

= fi (1 - 2th:)-’ j=1

1 - 2t

n, + n*

--J

= (1 - 2tXf)-J (17)

(n, + IIn, 1 . Now Eq. (17) is the moment generating function for a-y distribution. Thus. G* has a y distribution with parameters (Y = --.I and p = 2 [(nl f n,)/{ (n, + 1)~) 1, and we can use G* to test the statistical significance of the relocation of an observation from one cluster to another. =t

APPENDIX 6: CLASSIFICATION Oligopoly Office and accounting machine mfg. Electronic computing equipment mfg. Motor vehicle and equipment mfg. Photographic equipment mfg. Drug and medicine mfg. Petroleum refining Misc. petro and coal products mfg. Core Crude petro and natural gas extraction Glass and glass products Cement and plaster products Structural clay products Pottery and related products Misc. stone products Blast furnaces, steel works, and mills Other primary iron and steel mfg. Primary aluminum mfg. Other primary nonferrous mfg. Cutlery and hardware metal mfg. Fabricated structural metal mfg. Metal stamping mfg. Misc. fabricated metal mfg. Engines and turbines mfg. Household appliance mfg. Electrical machinery mfg. n.e.c. Cycles and misc. transport equipment mfg.

OF INDUSTRIES INTO 16 SECTORS Meat products mfg. Dairy products mfg. Canning and preserving Grain mill products mfg. Bakery products mfg. Confectionary products mfg. Beverage mfg. Misc. food products mfg. Knitting mills Dyeing and finishing textile mfg. Floor covering, except hard surface, mfg. Yarn, thread, and fabric mills Apparel and accessory mfg. Pulp and paper mills Misc. paper and pulp products Paperboard containers mfg. Printing and publishing, except newspaw Industrial chemical mfg. Plastics, synthetics, and resin mfg. Synthetic fiber mfg. Soap and cosmetic mfg. Paints, varnishes, etc., mfg. Agricultural chemical mfg. Misc. chemical mfg. Not specified chemical mfg.

is The eigenvalues of Cz are the squared eigenvalues of C. Thus, the eigenvalues of C, are both equal to h: which gives the moment generatin function of x;C?r, as specified (see Hogg and Craig, 1970, pp. 384-387).

28

KAUFMAN,

HODSON. AND FLIGSTEIN

APPENDIX B-Continued Wholesale Farm machinery mfg. Construction equipment mfg. Metalworking machinery mfg. Railroad locomotive and equipment mfg. Mobile dwellings mfg. Legal services Engineering and architectural services Accounting and bookkeeping services Misc. professional and related services WHOLESALE Motor vehicle and equipment Drugs and chemicals Dry goods and apparel Food and related products Farm products-raw materials Electrical goods Hardware, plumbing, heating supplies Not specified electrical and hardware products Machinery equipment and supplies Metals and minerals, n.e.c. Petroleum products Scrap and waste materials Alcoholic beverages Paper and paper products Lumber and construction materials Wholesalers. n.e.c. Not specified wholesalers Periphery Metal mining Coal mining Nonmetallic mining Logging Sawmills Misc. wood products Screw machine products Radio, TV, communication equipment mfg. Aircraft and parts mfg. Ship and boat building Scientific instruments mfg. Optical and health service supplies mfg. Watches and clocks mfg. Misc. manufacturing Misc. textile products Misc. fabricated textile products

Rubber products Misc. plastic products Tanned and finished leather mfg. Leather products, except footwear Department stores Limited price variety stores Vending machine operators Direct selling stores Misc. general merchandise stores Dairy products retail Retail bakeries Food retailing, n.e.c. Advertising services Services to buildings Commercial R&D and testing services Employment agencies Business management and consulting services Computer programming services Detective and protective services Business services, n.e.c. Auto services, except repair Auto repair services Electrical repair services Misc. repair services Hotels and motels Other lodging places Laundering and garment services Beauty shops Barber shops Shoe repair shops Dressmaking shops Misc. personal services Theaters Bowling alleys and pool parlors Misc. entertainment services Small shop Furniture and fixture mfg. Newspaper printing and publishing Footwear, except rubber, mfg. RETAIL Lumber and building materials Hardware and farm equipment Grocery stores Motor vehicle dealers Tire, battery, and auto accessories Gas service stations Misc. vehicle dealers Apparel and accessories Shoe stores

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APPENDIX B-Continued Furniture and home furnishings Household appliances, TV. and radio Eating and drinking places Drug stores Liquor stores Farm and garden supplies Jewelry stores Fuel and ice dealers Retail florists Misc. retailing Not specified retail Offices of physicians Offices of dentists

Local monopoly General building contractors Other general contractors Special trade contractors Taxicab services Offices of chiropractors Hospitals Convalescent institutions Offices of health practioners, n.e.c. Health services, n.e.c. E’ducational and nonprofit services Private households Elementary and secondary schools Colleges and universities Libraries Educational services, n.e.c. Not specified educational services Museums, art galleries, and zoos Religious organizations Welfare services Residential welfare facilities Nonprofit membership organizations

Core utilities and finance Radio and TV broadcasting Electric light and power Electric and gas utilities Gas and steam supply systems Banking Credit agencies Insurance Periphery utilities Water supply Sanitary services Other and not specified utilities Core transport Railroads and railway express Street railways and bus lines Water transport Air transport Telephone services Telegraph and misc. communication services Periphery transport Trucking services Warehousing and storage services Pipe lines, except natural gas Services incidental to transport

Agriculture Agricultural production Agricultural services Horticultural services Forestry Fisheries Brokers Security, commodity brokerage, and investment companies Real estate Real estate Ordnance Ordnance Tobacco Tobacco mfg.

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Blau, P., and Duncan, 0. D. (1967). The American Occupational Structure, Wiley, New York. Blau, P.. and Schoenherr, R. (1970). The Structure of Organizations, Basic Books, New York. Bluestone, B. (1970). “The tripartite economy: Labor markets and the working poor,” Poverty and Human Resources Abstracts 5, 15-35. Bluestone. B., Murphy, W., and Stevenson, M. (1973). Low Wages and the Working Poor, Institute of Labor and Industrial Relations, Ann Arbor. Braverman. H. (1974). Labor and Monopoly Capitalism, Monthly Review Press, New York. Chandler, A. (1962). Strategy and Structure, MIT Press, Cambridge, Mass. Edwards, R. C. (1979). Contested Terrain, Basic Books, New York. Featherman. D. L., and Hauser, R. M. (1978). Opportunity and Change, Academic Press, New York. Freeman, R. B.. and Medoff. J. L. (1979). “New estimates of private sector unionism in the United States,” Industrial and Labor Relations Review 32, 143-174. Galbraith, J. K. (1973). Economics and the Public Purpose, Houghton Mifflin, Boston. Hage, J., and Aiken. M. (1970). Social Change in Complex Organizations, Random House, New York. Hickson, D. J., Pugh, D. S., and Pheysey, D. (1969). “Operations technology and organization structure: An empirical reappraisal.” Administrative Science Quarterly 14, 378397. Hodson. R. (1978). “Labor in the monopoly. competitive, and state sectors of production,‘* Politics and Society 8, 429-480. Hodson, R. (1980). The Social Impact of Industrial Structure on Working Conditions, Ph.D. dissertation. Department of Sociology. University of Wisconsin-Madison. Hodson, R., and Kaufman, R. L. (1981). “Circularity in the dual economy: A comment on Tolbert. Horan, and Beck, 1980.” American Journal of Sociology, in press. Hogg, R. V., and Craig, A. T. (1970). Introduction to Mathematical Statistics. 3 ed., Macmillan, London. Kaufman, R. L. (1980). Racial Discrimination and Segmented Labor Markets, Ph.D. dissertation. Department of Sociology (forthcoming), University of Wisconsin-Madison. Kluegel, J. (1978). “The causes and costs of racial exclusion from job authority,” American Sociological Review 43, 285-301. O’Connor, J. (1973). The Fiscal Crisis of the State, St. Martin’s Press, New York. Oster. G. (1979). “A factor analytic test of the theory of the dual economy,” Review of Economics and Statistics 61, 33-39. Scherer, F. (1970). Industrial Market Structure and Economic Performance, Rand McNally, Chicago. Sewell, W., and Hauser, R. M. (1975). Education, Occupation. and Earnings, Academic Press, New York. Shepherd, W. G. (1970). Market Power and Economic Welfare, Random House. New York. Spilerman, S. (1977). “Careers, labor market structure, and socioeconomic achievement,” American Journal of Sociology 83, 551-593. Stolzenberg. R. (1978). “Bringing the boss back in.” American Sociological Review 43, 8 13-828. Tolbert, C., Horan, P.. and Beck, E. M. (1980). “The structure of economic segmentation: A dual economy approach,” American Journal of Sociology 85, lO95- I 116. U.S. Bureau of the Census (1962/1972). Census of Population. l%O/l970, Subject Reports: Occupation by Industry, U.S. Govt. Printing Office. Washington, D.C. U.S. Bureau of the Census (1972/1977). Enterprise Statistics, 1967/1972. Vol. I. General Report on Industrial Organization, U.S. Govt. Printing Office, Washington, D.C.

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