A simulation of social mobility in industrial societies

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  • A simulation of social mobility in industrial societies*

    LORNE TEPPERMAN I University of Toronto

    Une fois etablies Iuniversalite et la stabilite dun pour nos matrices de mobilite, il sera possible de developper de puissantes techniques de projection qui pourront predire des taux de mobilite sociale a partir de seulement quelques donnees eparses. Dans Iarticle en question, une telle technique est presentee tout en tenant compte du developpement extensif quexigeront des techniques similaires plus complexes. A la suite de cette illustration vient une analyse de donnees, de differentes societes industrielles, sur la mobilite sociale degeneration en generation. Lapproche est empruntee a Mosteller (1968) et Levine (1972) dans le but de construire une technique analytique basee sur Ihypothese suivante : les variations de valeurs culturelles jouent peu sur la mobilite sociale (Lipset et Bendix, 1959); le de la structure de professions sur la mobilite est enlevee.

    Enfin. un modele de simulation pour ordinateur est c o n p afin de mesurer Ieffet quauraient des changements dans la structure de professions sur la probabilite de mobilite sociale et de transmission hereditaire de professions. La these de Lipset et Bendix servant de presuppose, cent vingt simula- tions demontrent les effets de differents modeles de types-ideaux dindustrialisation sur la mobilite.

    Once the universality and stability of a basic nucleus of association in mobility matrices can be established, it will be possible to devise powerful techniques for projecting rates of social mobility with scant information. One such technique is illustrated, although it is acknowledged that more complex, related techniques will require considerable development. Using an approach developed by Mosteller (1968) and Levine (1972). this paper reanalyses data on intergenerational social mobility from various industrial societies following the assumption of Lipset and Bendix (1959) that social mobility is relatively uninfluenced by variation in cultural values. When the external constraint of occupational structure on mobility is removed, the basic nucleus of association is revealed. A computer simulation model is then used to examine the impact of change in the occupational structure on the probability of occupational inheritance and intergenerational mobility. One hundred and twenty simulations show the effects of different ideal-typical industrialization patterns upon mobility under the assumption that the Lipset and Bendix thesis is valid.

    Over a decade ago, Lipset and Bendix (1959) attempted to formulate a general theory of so- cia1 mobility in industrial societies. A major thrust of their argument was that intergenera- tional mobility across the manual-nonmanual line was relatively uniform across industrial societies for several reasons: ( I ) the aspiration

    to move upward into nonmanual occupations is universal; thus, (2) variation in rates of move- ment across this line is primarily determined by variation in the occupational structure; and (3) since there is a convergence of the forms of occupational organization in industrial soci- eties, there will be a convergence in the patterns

    * I am grateful for support provided by a Humanities and Social Sciences Grant from the Office of Research Administration, University of Toronto; and to my colleague Jeff Reitz for his comments and criticisms. Rev. canad. SOC. &Anth./Canad. Rev. SOC. &Anth. 13(1) 1976

  • Social mobility in industrial societies / 27

    of social mobility. The first premise. that there is a universal desire for upward mobility, was also enunciated in an earlier paper by Lipset and Zetterberg ( 1956). The second premise, that of structural primacy in the determination of social mobility, is more or less of a logical necessity, given the first premise. The third premise, that of the structural convergence of modern societies, had gained strong support among students of modernization in the 1950s and I ~ ~ O S , although it may currently enjoy less favour than it once did.

    One difficulty in the Lipset and Bendix argu- ment was the unavailability of adequate data to test these hypotheses. The data used by Lipset and Bendix were taken from many scattered sources and had obviously been collected and coded in different ways. The problem of com- parability among mobility surveys was reduced somewhat by confining attention t o only three gross occupational categories: to nonmanual (or white collar). manual (or blue collar), and farming. Even so. these data showed great vari- ation that is difficult to explain given the au- thors argument of essential uniformity among industrial nations. Further, as no data from nonindustrial societies were presented, it was impossible to judge whether the observed variation ctmong industrial nations was great or small relative to the variation b ~ t i ~ ~ v n indus- trial and nonindustrial nations.

    Despite increases in our data on mobility in both industrial and nonindustrial societies. the years since the publication ofthis study by Lip- set and Bendix have not brought another study of the same scope. excluding possibly the re- view of mobility studies by S.M. Miller (rg60) which appeared shortly after the Bendix and Lipset work. This can be explained by two re- cent developments, among others. First. there is the increased general sophistication of sociologists engaged in cross-national research: few are willing to make great generalizations about social structure on the basis of what we increasingly know to be wide cultural variations in the definition of social structure. A second related development derives from the paper by Duncan (1966) which enumerated the many dangers facing those who would compare mo- bility matrices from different countries. Of these, variations in sampling and coding proce- dures were not least important, according to Duncan. In effect, it became hard to see how an adequate cross-national study of mobility could be undertaken without prearranged uniform

    procedures of sampling, data collection. and coding, an unlikely and distant eventuality at best.

    It is the aim of this paper to return to the issues raised by Lipset and Bendix in cogniz- ance of the difficulties noted by Duncan and others. It was felt that such a study would need t o proceed by minimizing the error introduced by variations in study design in different indus- trial nations; this suggested a deductive rather than an inductive approach. in short. a simula- tion based upon as few empirical parameters as possible.

    Lipset and Bendix concluded. there is rela- tively little difference in rates ofsocial mobility. as measured by the shift across the manual- nonmanual line, in countries for which data exist ... Instead of supporting the assumption that value differences cause variations in mobil- ity rates, the data support the hypothesis that mobility patterns in Western industrialized societies are determined by the occupational structure (Lipset and Bendix. 1959:72-3). If Lipset and Bendix are correct. one should be able to find only one basic nucleus of associa- tion in all intergenerational mobility tables of industrialized societies, once the marginals in these tables - representing the relative sizes of occupational categories - have been equalized. That is, if occupational structures. the putative source of international variation among indus- trialized countries. are somehow made identi- cal, then given the (postulated) uniformity ofall other kinds. industrial mobility systems will be- come identical. The difficulty to this point has been in producing identical occupational struc- tures by statistical means; for although con- vergence theorists assume that such structures will naturally become identical in the course of time, this has not yet and may never happen.

    Mosteller (1968) and Levine (1972) may be primarily credited with having developed and publicized a technique for revealing the basic nucleus of association in a contingency table, through a process of iteration which standar- dizes table marginals to any desired size and normalizes the cell entries to the new row and column marginals while preserving the odds- ratios of intergenerational movement from one occupational category to another. Levine (1972) has used this method in the development of refined models of intergenerational mobility, working with the data originally collected by Glass (1954). Levine, however. dealt with only one national sample and used normalization as a

  • 28 / LorneTepperman

    preliminary to the elaboration of a mathemati- cal model of mobility. I shall deal with twenty- nine samples from various industrialized sys- tems, national and subnational, and seek to de- velop and evaluate a method for predicting in- tergenerational mobility in industrial societies.

    After revealing a common mobility matrix among industrial countries, I then combine the matrix with hypothetical rather than actual marginals. I f one wishes to know how mobility varies under different structural conditions. one can assume the existence of the invariant value structure such as that described above and confine further efforts to defining how an indus- trializing occupational structure will vary over time. The model of variation in the occupational structure will provide the hypothetical margi- nals which are combined with the model matrix to predict mobility rates under varying struc- tural conditions.

    F I N D I N G T H E B A S I C N U C L E U S O F

    A S S O C I A T I O N

    1 begin with twenty-nine 3x3 intergenerational mobility tables, including those used by Lipset and Bendix (1959) and others taken from pub- lished sources. These are mobility tables con- taining only three occupational categories: nonmanual (or white collar), manual (or blue collar), and farmer. The rows represent classes of origin (or fathers occupation) and the col- umns represent class of destination (or inter- view subjects occupation); the cell entries are c ~ ~ n t s of people. The table marginals are counts across rows and across columns; there are six marginals in each table, one marginal for each row and one marginal for each column. For simplicity, all marginals will be standar- dized to unity and therefore all cell entries will be reduced to fractions of one. After iteration has been completed, all cells in a given row and all cells in a given column will sum to one. The cell entries will then be regarded as normalized, and each transformed matrix will represent the basic nucleus of association of the original (raw count) mobility table.

    All twenty-nine transformed matrices should be identical if Lipset and Bendix are right. However for reasons of random error and varia- tions in sampling and coding, among others (cf. Duncan, I@), they willnot bequite identical. I

    therefore average the twenty-nine values for each cell, creating an average mobility matrix representative of all industrial societies. This average or model matrix contains nine cells which sum across rows and columns to unity.

    To assess the predictive value of this model matrix which stands as a proxy for the theoreti- cally invariant basic nucleus of association in industrial societies, the model matrix is recom- bined with each of the twenty-nine sets of origi- nal marginals. This process of destandardizing is quite similar to the process of standardizing in the sense that the computer carries out itera- tions of the cell entries until they sum across rows and columns to the desired marginal sizes. At this point, however, we are adjusting the cell entries to sum not to unity, but to the row and column marginals of each original data matrix. The resulting cell values in each matrix pro- duced by this method are compared with the original cell values and a rate of predictive error is computed for each matrix.

    This procedure requires between five and ten complete iterations of each matrix to bring the marginals to a value of I .o (plus or minus .OOI); while this can be done by hand, it is best done by computer. Matrices containing relatively small or zero cell values demand considerably more iterations to achieve standardization than do matrices without such cell values.

    Table I indicates that the main diagonal cell entries in each standardized matrix - the prob- abilities of inheriting a fathers occupation -are high, usually between .5 and .7, which implies that the probabilities of entering another occu- pational category are low. In this sense, there is little row and column independence in these matrices. To return to the argument with which this paper began, this evidence suggests that such independence or free movement into all occupations (including fathers) as may occur in industrial societies is a function of changes in the relative sizes of occupational categories be- tween the times fathers and sons enter the labour market. While there is a noticeable varia- tion in the average probabilities of inheriting each of the three occupational statuses, there is relatively little variation among the twenty-nine samples in the probabilities of inheriting a given occupational status.

    Table II displays the mean of twenty-nine transformed matrices. As suggested above, the

    I The main diagonal of this matrix runs from the upper left-hand comer to the lower right-hand comer of the matrix.

  • Social mobility in industrial societies / 29

    TABLE I

    STANDARDIZED PROBABILITY OF INHERITING A SPECIFIED OCCUPATIONAL STATUS, BY SAMPLE* AND OCCUPATIONAL STATUS

    Occupational status

    Sample White collar Blue Collar Farmer

    1 Aarhus 1949 2 Belgium 1953 3 Finland 4 France 1950 5 France 1964 6 Germany 7 Germany 8 Germ. Prot. 1953 9 Germ. Cath. 1953

    10 W. Germany 1955 11 Germany 1956 12 Indianapolis 1910 13 Indianapolis 1940 14 Japan 1956 15 Norway 1957 16 Puerto Rico 1960 17 Quebec Fr. Can. 1954 18 Quebec Fr. Can. 1964 19 Rome 1908 20 Russian emigrts 21 Sweden 22 Sweden 1957 23 Switzerland 24 USA 1947 (1)

    26 USA 1952 (1) 27 USA 1952 (2) 28 USA 1957 29 USA 1962

    25 USA 1947 (2)

    .50537

    .61866

    .71665

    .63413

    .61531

    .73505

    .67453

    .61478

    .63014

    .69999

    .59666

    .61602

    .67801

    .62617

    .61405

    .57275

    .65367

    .65129

    .75936

    .81686

    .46252 ,66302 .66569 . a 8 1 9 .60977 .62428 .64401 .60359 .61279

    .51305

    .69852 .57025 .62464 .62867 .61029 .60366 .S4792 .60107 .62693 .57307 .S7310 .45303 .59682 .54083 .SO594 .56426 .46505 .51372 .69469 .41106 .55185 .66162 .56743 .56981 .56218 .56535 .57493 .54745

    .54465

    .81589 .63762 .75846 .83579 .82186 .76708 .79896 .77812 .79564 .76730 .69711 .66886 .71027 .60244 .49586 .82463 .75298 .68808 .84125 .61900 .67143 .80068 .70868 .72016 .77521 .SO412 .70806 .73374

    * The source of each sample is given in Appendix A.

    TABLE I1

    MEAN* NORMALIZED PROBABILITY OF INTERGENERATIONAL MOBILITY, BY OCCUPATIONAL CATEGORY OF FATHER AND SON

    Fathers Sons occupational category

    category White Collar Blue Collar Farmer Total occupational

    White collar .63872 ,2601 2 .lo074 ,99958 Blue collar .26021 .56946 .I7016 .99983 Farmer .lo104 .17040 .72790 .99934 Total .99997 .99998 .99880 2.99875

    * Each cell entry is the mean of twenty-nine observations; each observation is produced by the normalization by iteration of a contingency table.

    variation of samples around the mean is rela- tively small; looking only at the main diagonal, the ratio of the standard deviation t o the mean cell value is between . rog and . I 19. However, because the standard deviations within each cell are similar in size, the ratio of standard deviation to mean cell value is much larger in cells off the main diagonal.

    Attention should also be called to the sym- metry of mean cell values around the main diagonal of the table. Controlling for differences in the relative sizes of classes of origin and destination (as we are doing through standardi- zation) and allowing for differences in the prob- ability of occupational inheritance in the three major classes, the chances of movement into

  • 30 I LorneTepperman

    and out of a class are about equal. For example, the probability ofa white-collar son moving into a blue-collarjob is the same as the probability of a blue-collar son moving into a white-collarjob.

    If these transition probabilities may be taken as measures of distance between occupational classes, farming is about two-and-a-half times as far from white-collar occupations as is a blue-collar job, in the sense that blue-collar sons are about two-and-a-half times as likely as farmers sons to enter a white-collar job, and, equally, white-collar sons are about two-and- a-half times as likely to enter blue-collar jobs as they are to enter farming. Whether this dis- tance reflects a difference ofjob situs, income, educational requirement, or socialization can- not be judged from these data.

    As indicated earlier, the mean matrix of trans- ition probabilities, or model mntrix, displayed in Table I I was next combined with the margi- nals of the original twenty-nine matrices to pro- duce twenty-nine predicted matrices. The cell entries in the original and predicted matrices were then compared; first the number of devia- tions of the predicted from the observed matrix were counted and then an index M was calcu- lated. following Taeuber and Taeuber (1965), to measure the percentage of respondents misclassified by the predictive technique in each of the twenty-nine matrices. Concretely, this index measured the percentage of persons in each sample who would have to move to another cell in order to make the predicted mat- rix identical to the observed matrix.

    Table 1 1 1 shows that the rate of error in classification by this technique is small. On average for all twenty-nine samples, the pcvwnragc. of cases misclassified is under 5 per cent (precisely 4.66 per cent) and is close to 4 per cent if we remove the two cases with misclassification errors of over 10 per cent. The ability of this technique to reconstitute the orig- inal matrices with such accuracy as this gives one reason to believe both that the Lipset- Bendix hypothesis of uniformity is valid and that this technique may prove valuable in pre- dictive situations where only the matrix margi- nals are known and a model matrix must be used in conjunction with these marginals to predict an otherwise unmeasured pattern of social mo- bility.

    The greatest misclassification was observed in respect to mobility in and out of farming

    occupations. This may have occurred because the definition of farmer varied from sample to sample or because there were true variations in mobility in and out of farming across nations. Where farming represented a relatively larger occupational category there was more mis- classification, which may account in part for the lower than average rate of misclassification in the United States samples examined here.

    S I M U L A T I N G V A R I A T I O N I N S T R U C T U R A L C O N D I T I O N S

    Having isolated the basic nucleus of association common to the mobility tables of industrial societies, I shall now try to develop sets of representative marginals for each stage of in- dustrialization. These marginals will then be combined with the model matrix to generate ideal-typical mobility rates for industrializing and industrialized societies.

    For the purpose of simulation, we must model plausible variations in occupational structure from fathers to sons generations. Let us begin by observing that at the beginning of industrialization very few people are em- ployed in white-collar occupations and many are farmers; at the end of industrialization the reverse is true. During the process of change, the proportion of the work force in blue-collar occupations increases considerably. For more exact measures of these changes in the occupa- tional structure, we may examine the data pre- sented by Kuznets (1966:106-7) for a large number of industrial countries. By plotting the proportion in farming against the proportion in industry at various dates and fitting a least squares line to these data, I estimated the aver- age proportions in agriculture and industry at early and late stages of industrialization; the proportion in white-collar occupations was ob- tained as a residual. We may conclude from these data that at the early stages of moderniza- tion about 70 per cent of the work force is em- ployed in farming, zz per cent in industry, and about 8 per cent in white collar occupations; in the later stages about 5 per cent are in farming, 55 per cent in industry, and 40 per cent in white-collar jobs.

    I shall make two working assumptions* about the transition to industrialized society: ( I ) it proceeds by smooth gradual changes in each of the three occupational categories, following an

    2 Some additional detail on the assumptions and procedure is provided in Appendix B.

  • Social mobility in industrial societies / 31

    TABLE III

    NUMBER AND PERCENTAGE OF RESPONDENTS MISCLASSIFIED, BY SAMPLE AND SAMPLE SIZE ( N )

    Misclassificat ions

    Percentage N = Sample Number of of cases

    Sample size deviaiions,* D misclassified,t M

    1 Aarhus 1949 26607 3130 5.88

    3 Finland 4760 955 10.03 4 France 1950 3023 175 2.89 5 France 1964 (1ooo)$ (74) 3.70 6 Germany 585 83 7.09 7 Germany 722 43 5.06 8 German Rot . 1953 635 60 4.72 9 German Cath. 1953 605 33 2.73

    10 W. Germany 1955 3156 306 4.85 11 Germany 1956 1108 93 4.20 12 Indianapolis 1910 10253 163 0.79 13 Indianapolis 1940 9890 528 2.67 14 Japan 1956 3364 262 3.89 15 Norway 1957 775 72 4.65 16 Puerto Rico 1960 3025 313 5.17 17 Quebec 1954 1234 129 5.23 18 Quebec 1964 1550 265 8.55 19 Rome 1908 3067 391 6.37 20 Russian emigrCs 1182 197 8.33 21 Sweden 23 1 51 11.04 22 Sweden 1957 871 59 3.39 23 Switzerland 1124 86 3.83 24 USA 1947 (unadj.) 1153 51 2.21 25 USA 1947 (adj.) 1153 49 2.12

    2 Belgium 1953 296 21 3.55

    26 USA 1952 794 38 2.39 27 USA 1952 747 39 2.61 28 USA 1957 1023 52 2.54 29 USA 1962 37677 3506 4.65

    * D, the number of deviations, is the absolute value of all differences between the actual and projected cell entries in the nine cells of a given matrix. t M is the proportion of respondents in a sample that would have to move to another cell to make the actual and projected matrices identical. M = lOO(D/2N). $ Only the proportional sizes of the row and column marginals were given in the source from which these data were taken. The matrix was treated as though all marginals summed to a total of 1OOO.

    exponential path: and (2) no more than 140 years are needed t o complete the transition, once begun. There is some evidence that indus- trial growth is exponential (cf. Meadows, Meadows et al.. 1972). although there is also evidence that it does not follow a smooth, gradual path. It is unlikely that modernization has ever taken more than 14oyears and, indeed, it has taken as long as 140 years only in the United Kingdom and France. Just as Kirk (1971) showed that the demographic transition is faster each successive time a new nation be- gins it, so Black (1966:90-1) provides data that indicate the progressive shortening of time re-

    quired for an 'economic and social transition' in modernizing societies.

    Table IV shows the resulting ' 15-stage' transi- tion, each stage comprising ten years ofchange; there is smooth exponential increase in the numbers of white- and blue-collar workers and exponential decrease in the number of farmers in the work force totalling 1000 persons. T h e numbers in Table IV will serve as the marginals in hypothetical mobility matrices to be com- puted below.

    T h e use of a ~ y s t a g e , 140-year model to this point is a purely arbitrary device, and now one must reckon with variation in the rates of

  • 32 I LorneTepperman

    TABLE IV

    NUMBERS OF PERSONS IN EACH OCCUPATIONAL CATEGORY, PER WORKERS, BY STAGE OF INDUSTRIALIZATION

    Occupational category Stage of

    industrialization White collar Blue collar Farmer

    1 80 220 700 2 99 259 642 3 121 301 578 4 145 342 513 5 171 381 448 6 196 421 383 7 223 455 322 8 249 485 266 9 275 509 216

    10 299 526 175 11 322 540 138 12 343 548 1 09 13 363 551 86 14 382 551 67 15 400 550 50

    change observed in industrializing countries. Industrialization in one country may take five generations, or roughly 140 years, implying that a fathers occupational distribution is three stages away from that that his son will en- counter. Industrialization in another country may take only three generations, implying that a fathers occupational distribution is five stages away from that of his sons. In order to create a general model that will reflect a variety of cross-national patterns, I shall simulate mobil- ity under oll rates of structural change possible within the present model: mobility where fathersstageis I andsonsstageis 1 , 2 , 3 ... 15, where fathers stage is 2 and sons stage is 2 , 3 , 4 ... 15, and so on until fathers stage is 15 and sons stage is 15. One hundred and twenty dis- tinct simulations are required to exhaust the possible combinations. They have been carried out and the results are reported below.

    To reiterate, I am simulating mobility by as- suming an invariant value system among indus- trializing countries (based on data from twenty-nine actual mobility surveys) and varia- tion in the occupational structure over time ac- cording to a 15-stage model which may be traversed quickly or slowly by any given soci- ety. I shall iterate a model matrix -representing the basic nucleus of association in mobility ma- trices ofindustrial and industrializing societies - to 120 different sets of marginals, exhausting the different combinations of occupational structuring in hypothetical fathers and sons

    generations. This iteration process, described by Mosteller, is accomplished painlessly by computer; about 5-10 complete iteration cycles are required to complete each simulation.

    4 E F F E C T S O F S I M U L A T E D S T R U C T U R A L C H A N G E

    1 shall first consider the effect ofstructural vari- ation upon intergenerational upward mobility from blue-collar origins to a white-collar desti- nation. Data in Table v shows that such upward mobility increases linearly with both ( I ) the proportion of all occupations that are non- manual (r = 357) and (2) the amount of change in the proportion of white-collar jobs from fathers to sons generation (r = .85 I). One finds stage 15 (fully industrialized) rates of upward mobility in a stage 8 society if there has been rapid change in the occupational structure (that is, six or seven stages moved) from fathers to sons generation. From this one may deduce that a society modernizing at the rate of 6 or 7 stages a generation, suggesting a total indus- trialization period of sixty to seventy-five years, can have as great upward mobility as a fully industrialized society. Indeed a society moder- nizing more rapidly than this will have higher mobility rates than a fully industrialized soci- ety, and full industrialization (the achievement and continuation of stage 15) will bring de- creased upward mobility to a society which has industrialized very quickly.

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  • 34 I LorneTepperman

    At the end ofindustrialization, the probabil- ity of mobility across the manual-nonmanual line is about 25 per cent, which is roughly twice what it was at the beginning of industrializa- tion (that is, at stage I).

    1 shall next consider changes in the probabil- ity of downward mobility, or intergenerational movement from white-collar to blue-collar oc- cupational status. Data in Table VI shows a weak decline in downward mobility with the increase of white-collar positions (r = -.694) and a strong decline with a high rate of change in the occupational structure from fathers to sons generation (r = -.892). A comparison of this table with the precedingone indicates there is always a higher probability ofdownward mo- bility out of the white-collar class than of up- ward mobility into the white-collar class. This presumably reflects the disparity in size of these two occupational categories. Accordingly, as the two categories become more similar in size (that is, towards the end of industrialization), the probabilities of upward and downward mo- bility become more similar. At the end of in- dustrialization, the probability of downward mobility out of the white-collar class into the blue-collar class is about 35 per cent, roughly the same as it was at the beginning of the industrialization process.

    Like upward mobility into the white-collar class, inheritance of a white-collar occupation increases with ( I ) the proportion ofwhite-collar occupations in the occupational structure ( r = ,877) and (2) the rate of change from fathers to sons generation ( r = .800). There is a zero- order correlation between white-collar inheri- tance and upward mobility of r = .989 which may be spurious and accounted for by the simi- lar conditions which produce each, notably, an increased availability of white-collar positions. However, it should be noted that although the same factors operate to increase both inheri- tance and upward mobility, upward mobility is increased proportionately more than white- collar inheritance, largely because there is more room for increase in the former than in the latter.

    At the end of the industrialization process, the probability of inheriting white-collar status is about 64 per cent, over one-half greater than at the beginning of industrialization. However white-collar inheritance has declined relative to upward mobility. At the beginning of indus- trialization, the probability of white-collar in- heritance is about three-and-a-half times as

    great as the probability of upward mobility into the white-collar class; but when industrializa- tion is completed, the probability of white- collar inheritance is only about two-and-a-half times as great as the probability of upward mo- bility. Thus, during the process of industrializa- tion upward mobility has gained at the expense of inheritance about ((3.5-2.5)/3.5) or, more precisely, 22 per cent. This provides some basis for asserting that the process of industrializa- tion reduces the influence of ascribed status on occupational attainment.

    As the preceding tables might have sug- gested, the probability of inheriting blue-collar status increases with the proportion of blue- collar jobs in the work force (r = .701). How- ever the amount of change in blue-collar occu- pations from fathers to sons generation pro- duces a curvilinear increase in blue-collar in- heritance. That is, blue-collar inheritance reaches a peak under conditions of moderately fast change and declines under conditions of extremely fast change, although never declining to a level as low as is found under conditions of little change from generation to generation. This curvilinearity presumably results from the very rapid emptying of farmers sons into the blue-collar category in the early stages of indus- trialization. From this blue-collar category there is slower progress into white-collar occu- pations.

    With the completion of industrialization, the probability of blue-collar inheritance is about 71 per cent, almost one-third higher than at the beginning of industrialization. However there is proportionally less increase in the in- heritance of blue-collar occupations than in the inheritance of white-collar occupations with in- dustrialization. This is in part because blue- collar inheritance is, at the beginning and in most cases throughout industrialization, great- er than white-collar inheritance. There is one exception to this rule: under conditions of rapid change, white-collar inheritance may become more probable than blue-collar inheritance.

    Net upward mobility was calculated for each of the 120 hypothetical societies by subtracting the number of downwardly mobile white-collar sons from the number of upwardly mobile blue-collar sons. These data are displayed in Table VII, where one finds, first, that under conditions of no change, net upward mobility is always zero: there is an exact balance main- tained in the number of movers up and down. Net upward mobility is strongly influenced by

  • TA

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  • Social mobility in industrial societies / 39

    the rate of industrialization and is virtually a linear function of the number of industrial stages traversed per generation. However, a change of one stage or n stages has a greater impact on net upward mobility in a more de- veloped than in a less developed society. For example. a move of one stage per generation produces over three times as much net upward mobility where fathers stage is 14 than where fathers stage is I .

    Net upward mobility is also a curvilinear function of the industrial stage in fathers gen- eration. For example. a move t o stage 15 from stage 6 produces more net upward mobility than a move to stage 15 from stage I , although such a move from stage I implies a faster rate of indus- trialization than the move from stage 6.

    Finally, the amount of net upward mobility produced by single-stage moves is always very little, although it increases over threefold as industrialization proceeds. Even in a highly in- dustrialized society near completion of the transition (for example, moving from stage 14 to stage 15 in one generation), only 12.1 members of the rooo-person work force are crossing the manual-nonmanual line upward (after subtrac- tion of the downward movers). Net upward mobility is over six times as great under condi- tions of rapid transition (such as transition to stage 15 from stages 5 . 6. or 7). This suggests that people are less likely to perceive their soci- ety as having great opportunity for upward mo- bility at late stages in industrialization where there is little possibility for further rapid change in the occupational structure than they are in earlier stages of industrialization where much higher rates of net upward mobility are pos- sible.

    D I S C lJ S S I 0 N

    Rapid growth contributes considerably to the probability and net amount of upward mobility in a society. independent of the stage of indus- trialization that society is at. This leads one t o think that as the possibility for continued rapid change diminishe5 - that is. as industrialization comes close to completion - rates of upward mobility will decline. The reader can verify this from the data presented in Table v by imagining those societies that are industrializing at rates of three or more stages per generation. thereafter levelling off at a probability of ,247 (the proba- bility of moving from a blue-collar into a white-

    collar occupation, where father is a stage 15). In every such instance, there will be a decline in the probability of upward mobility after stage 15 is reached. The extent of this decline is a func- tion of the number of industrial stages per gen- eration prior t o attainment of stage 15. For ex- ample, if a society has been industrializing at a rate of six stages per generation (i.e. an indus- trialization process requiring 70 to 75 years in toto), there is a predicted decline in the proba- bility of upward mobility of something in the order of 10 to 15 per cent when industrialization reaches completion.

    T h e data in Table v also imply that a society in which the rate of change from generation t o generation is not constant. as has been as- sumed, but rather declining, may show a declin- ing probability ofupward mobility although that society may have reached a high level of indus- trialization that is maintained or raised. If for example a society moves from stage I to stage 7 in one generation and then from stage 7 to stage 8 in the next generation, there will be a 17 per cent decline in upward mobility in the second generation as compared with the first genera- tion. This suggests a reason for the frustration associated with a revolution of rising expecta- tions. People are not dissatisfied with imagi- nary ills in a period of decreased change; they are experiencing a real decline in opportunity as compared with the opportunity available to their fathers.

    To turn this around, it is easy to understand the sense of optimism and buoyancy associated with rapid industrialization; such rapid change has the effect of real increases in opportunity. Although higher levels of opportunity are en- joyed after industrialization has been com- pleted than before it was begun. unless the transition has been exceptionally fast (15 stages in one or two generations) people will not adopt preindustrial mobility as their reference point. People rarely take great-great grandfathers as their reference group and thus may feel worse off after the rate of change begins to decline in late stages of industrialization than the objec- tive reality (that is. high rates of upward mobil- ity relative to preindustrial times) would justify.

    There are many obvious limitations to the present study. In the first place, the twenty-nine samples were selected to create the model ma- trix largely for reasons ofconvenience and they may or may not be representative of all con- ceivable samples. Indeed, United States sam- ples are overrepresented here. As such, the

  • 40 / LorneTepperman

    model matrix that will ultimnte/y come to be used in predictive studies may be somewhat different from the one discovered and used here as it will be based, one hopes, on a wider variety of samples than the present one. Second, the sense in which 1 have made or verified predic- tions in this study is limited despite a frequent use of the term prediction, since all of the expected values were generated by data from the same set of observed matrices. Given few samples to work with, I did not have the liberty, for example, to split the samples in half and use one half for construction of the model matrix and the other half for verification by comparing predictions from the model matrix with ob- served cell values. Such a research procedure will become feasible only as the number of available samples increases. Third, the samples used here varied widely in time, place, and qual- i ty as well as, one presumes, in the way they were drawn, the questions were asked, and the occupations were categorized. It is little short of miraculous that they displayed as much simi- larity and as little predictive misclassification as they did, considering the potential for extrane- ous error. The limitation of this study to 3x3 matrices purposely limited the amount of ex- traneous error due to variations in occupational classification. While a three-fold occupational classification is too gross to be of great utility in predictive studies of mobility, it should be realized that a method is best developed where extraneous error is minimal and then applied to matrices of larger size only afterwards.

    There is no way ofjudging whether 5 per cent error of misclassification by this method is ac- ceptable or not. This is indeed an individual judgment that the sociologist must make, just as he must decide on other occasions what is a satisfactory level of statistical significance to reject a hypothesis or a satisfactory proportion of variance to account for in a dependent vari- able. Given the many flaws and limitations in the present data, there is every reason to be- lieve that the rate of misclassification will ulti- mately be much lower when the model matrix is based on more samples of better quality. Addi- tional research with more samples may also reveal that there is not only one basic nucleus of association in mobility tables, as Lipset and Bendix have implied, but rather several some- what different ones which differ for reasons of national history, geography, or otherwise. Once we have empirically verified that there are several model matrices to choose from, and

    have explained the reasons for their differ- ences, a sociologist could then select the ap- propriate model matrix for prediction in a given case and achieve higher levels of predictive ac- curacy than would be possible with a single, universal model matrix.

    Yet whatever level of predictive accuracy may be achieved with this method, the subjec- tive assessment of its sufficiency will never be eliminated. Finally, it should be noted that there is not at present a more accurate predictor of mobility than the one discussed here.

    There is perhaps one more criticism, one that is especially difficult to meet, that may be level- led against the present approach to predicting mobility. This method assumes an accurate knowledge ofthe table marginals, or numbers of fathers and sons in the various occupational categories. Is it not unlikely, one might ask, that we would know the table marginals but not, by the same token, know the cell entries? After all, the method by which the table marginals are known is through interview with those persons who become represented as counts in the cells ofthe table. While this criticism is valid at pres- ent, one cannot rule out the possibility that fu- ture developments in accurately predicting the size of table marginals from, for example, cross tabulations of the actual (or predicted) work force by age will render the interview method of gathering such data unnecessary even where possible.

    There is good reason to believe that there is considerable uniformity among industrial na- tions in the basic nucleus of association in mobility tables and, since the samples used here cover a time span of over twenty-five years, some reason to believe that the basic nucleus of association is stable over time as well as space. However this assumption of stability over time is especially critical if we are to use thistech- nique in predicting future mobility. The collec- tion of additional samples to refine this method should not only attend to the similarity of ma- trices across space but also to the similarity across time. Ifwe discover that basic mobility patterns in industrialized societies change over time, we must hope that they change in an or- derly way so that by understanding that orderly change we will be able to predict future changes in the basic nucleus of association. Along with predictions of changes in the table marginals, we will then be able to predict the over-all future of mobility rates for specified times and places.

    My aim has been to suggest some of the inter-

  • Social mobility in industrial societies / 4 I

    nal dynamics of change in mobility, given as- sumptions based on the work of Lipset and Bendix. It is hoped that future work will both improve the parameters of such simulation and increase the complexity of the simulation model to a point that the model gives good prediction for specific societies a t specified points in the transition to industrial society. In this present

    A P P E N D I X A

    Sources q f d r i t r i irsrd in this paper3

    Strl?lple I Aarhus. Denmark 1949 2 Belgium 1953 3 Finland 4 France 1950 5 France 1964 6 Germany 7 Germany 8 Germany. Protestants 1953 9 Germany, Catholics 1953

    10 West Germany 1955 1 1 Germany 1956 12 Indianapolis 1910 13 Indianapolis 1940 14 Japan 1956 15 Norway 1957 16 Puerto Rico 1960 17 Quebec French Canadians 1954 18 Quebec French Canadians 1964 19 Rome 1908 20 Russian postwili' emigres 21 Sweden 22 Sweden 1957 23 Switzerland 24 USA 1947 (unadjusted) 25 USA 1947 (adjusted) 26 USA 1952 27 USA 1952 28 USA 1957 29 USA 1962

    paper I have attempted to minimize the com- plexity and hence the risk of being misunder- stood. Great simplification has also allowed me to minimize the number of empirically defined parameters in the model. a problem with which I expressed concern at the outset and one not readily remedied. Suggestions for further de- velopment of this model will be welcome.

    Source Lipset and Bendix, 1959:31 Goode, 1966;587 Lipset and Zetterberg, 1956:568 Lipset and Bendix, 1959: 19 Girod, 1971:82 Lipset and Bendix, 1959: 19 (Germany I I) Lipset and Bendix, 1959: 20 (Germany I I I) Lipset and Bendix, 1959:53 Lipset and Bendix, 1959:53 Goode, 1966: 589 Lipset and Bendix, 1959: 19 (Germany I) Lipset and Bendix. 1959:37 Lipset and Bendix, 1959:31 Lipset and Bendix, 1959: 20 Lipset and Bendix, 1959: 18 Tumin and Feldman, 1971:43o de Jocas and Rocher, 1968:714 Dofny and Garon-Audy , 1969: 283 Lipset and Bendix, 1959:37 Lipset and Bendix, 1959: 17 Lipset and Zetterberg, 1956:568 Lipset and Bendix, 1g59:zo Lipset and Bendix, 1959:20 Lipset and Bendix, 1959:21 Blau and Duncan, 1967: 102 Lipset and Bendix, 1959:21 (USA I I) Blau and Duncan, 1967: 102 Blau and Duncan, 1967: 102 Blau and Duncan, 1967:95

    A P P E N D I X I3

    I also assume. only to simplify the model and without any effect on its outcome, that the absolute number of farmers in the population never changes during the transition; the proportion of farmers declines because of population growth and an increase in the absolute number of non-farmers.

    3 In most cases 1 have used and cited data from secondary sources, for example, Lipset and Bendix, 1959. I did this for several reasons: ( I ) to work with the same data as Lipset and Bendix did; ( 2 ) to use data most accessible to myselfand to the reader who may wish to verify my findings; and (3) to retain the systems of classification used in the widely known secondary sources.

  • 42 / LorneTepperman

    Although this assumption is not critical, the reader can evaluate its plausibility in at least one case by examining a chart oflabour force trends in Canada, 1901-61 (Kalbach and McVey, 1971:240), which shows relative invariance in the absolute number of workers in primary industries over this period.

    I begin with a hypothetical work force of 1 0 0 people, of whom 70 are farmers, 22 are manual workers, and 8 are nonmanual workers. The number of blue-collar workers increases exponentially for 140 years at an annual rate of r = .0251049, and I record the hypothetical number of blue-collar workers at ten-year intervals; the number of white-collar workers increases exponentially at an annual rate ofr = .0300334, and I record the hypothetical number ofwhite-collar workers at ten-year intervals. Throughout the transition period of 140 years, there are only 70 farmers. By the end of the transition, the total work force has grown fourteen-fold, with increases in the proportions of white- and blue-collar workers and a decline in the proportion of farmers in the work force. The total work force size at each ten-year interval is calculated by adding the hypothetical numbers ofpeople in each of the three occupational categories. I now convert these work force totals to 1000 and compute the proportion of the work force in each category on a base of 1000. The result of these calculations is shown in Table I V .

    R E F E R E N C E S

    Black, C.E. 1966 The Dynamics of Modernization. New

    Blau, Peter M., and Otis Dudley Duncan 1967 The American Occupational Structure.

    Dofny, Jacques, and Muriel Garon-Audy 1969 Mobilites professionelles au Quebec.

    York: Harper and Row

    New York: Wiley

    Sociologie et Societes I (November): 277-301

    Duncan, O.D. 1966 Methodological issues in the analysis of

    social mobility. Pp. 51-97 in Neil J. Smelser and Seymour Martin Lipset (eds.), Social Structure and Mobility in Economic Development. Chicago: Al- dine

    Girod, Roger 1971 Mobilite Sociale. Geneva: Droz Glass, D.V. (ed.) 1954 Social Mobility in Britain. London: Rout-

    Goode, William J. 1966 Family and mobility. Pp. 582-601 in

    ledge and Kegan Paul

    Reinhard Bendix and Seymour Martin Lipset (eds.), Class, Status and Power. Second Edition. New York: Free Press

    de Jocas, Yves, and Guy Rocher 1968 Inter-generation occupational mobility in

    the province of Quebec. Pp. 71 1-23 in Bernard Blishen et al (eds.), Canadian Society. Third Edition. Toronto: Macmil- Ian of Canada

    Kalbach, Warren E., and Wayne McVey 1971 The Demographic Bases of Canadian So-

    ciety. Toronto: McGraw-Hill Ryerson Kirk, Dudley 1971 A new demographic transition. Pp.

    123-47 in National Academy of Sciences, Rapid Population Growth: Consequences and Policy Implications, Volume I I . Bal- timore: Johns Hopkins Press

    Kuznets, Simon 1966 Modern Economic Growth. New Haven:

    Levine, Joel 1972 A two-parameter model of interaction in

    Yale University Press

    father-son status mobility. Behavioral Science 17 (September): 455-65

    Lipset, Seymour Martin, and Reinhard Bendix 1959 Social Mobility in Industrial Society.

    Berkeley: University of California Press Lipset, Seymour Martin, and Hans Zetterberg 1956 A theory of social mobility. Transac-

    tions of the Third World Congress of Sociology 2: 155-77

    Meadows, Donella, and Dennis Meadows et al. 1972 The limits to Growth. New York: Uni-

    Miller, S.M. 1960 Comparative social mobility: a trend re-

    verse Books

    port and bibliography. Current Sociol- ogy 9: 1-89

    Mosteller, Frederick 1968 Association and estimation in contin-

    gency tables. Journal ofthe American Statistical Association 63 (March): 1-28

    Taeuber, Karl E., and Alma F. Taeuber 1965 Negroes in Cities. Chicago: Aldine Tumin, Melvin M., with Arnold Feldman 1971 Social Class and Social Change in Puerto

    Rico. Indianapolis: Bobbs Merrill

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