The Son Also Rises Read online

  FIGURE 11.5. Earnings variation by birth decade by surname type, later social elites, 1920–79.

  Thus the case of Chile seems to underscore a theme of earlier chapters: social and political movements have a surprisingly modest effect on the rate of social mobility. Events that at the time seem crucial, powerful, and critical determinants of the fate of societies leave astonishingly little imprint in the objective records of social mobility rates. Allende tried to remake Chilean society and died bravely when the military intervened to destroy his dream. Thousands were imprisoned, tortured, and murdered under Pinochet’s brutal military regime. But if social mobility rates were the only record of the history of Chile in the past hundred years, we would detect no trace of these events. Despite the cries, the suffering, the outrage, and the struggle, social mobility continued its slow shuffle toward the mean, indifferent to the events that so profoundly affected the lives of individual Chileans.

  1 There is debate about how social mobility in Chile compares with that of other South American countries, but no question that it is lower than in the Nordic countries.

  2 Students, retirees, and housewives are excluded. Chile, Ministerio del Trabajo y Prevision Social 2008.

  3 Chile, Ministry of Planning and Cooperation 2006. HDI is a measure that includes life expectancy, education, and income.

  4 Cruz-Coke and Moreno 1994, table 2.

  5 Galdames (2008) uses phonetic transcription to generate a compilation of Mapuche surnames that is used here.

  6 González Pomes 1966.

  7 The encomendero surnames were derived from Amunátegui Solar 1932 and Góngora 1970.

  8 Basque surnames were identified from Irigoyen 1881 and Narbarte 1992.

  9 Chile, Estado que manifiesta la renta agrícola 1855.

  10 Valenzuela O. 1923.

  11 Villalobos 1990; Nazer Ahumada 1993, 2000.

  12 Chile, Oficina del Censo 1866.

  13 Pellegrino 1927.

  14 Valenzuela O. 1920.

  15 Sloan, n.d.

  16 Núñez and Miranda 2007. These are high for conventional estimates compared to those for Nordic countries, or even Canada, the United Kingdom, and the United States.

  17 Technically the figure shows average log income for each surname group minus the Chilean average log income.

  TWELVE

  The Law of Social Mobility and Family Dynamics

  CHAPTER 6 CONJECTURES that all social mobility is governed by a simple underlying law, independent of social structure and government policy:

  xt + 1 = bxt + et

  where xt is the underlying social status of a family in generation t, et is a random component, and b is in the region 0.7–0.8.1 This simple law of mobility makes surprising predictions about the earlier history of social elites and underclasses observed at any point in time.

  The social status of any individual family can follow any possible path over many generations. But when we observe that a family has high or low status in some earlier period, such as 1800–1829, this law of mobility implies that on average, the status of the descendants will move toward the mean for the society generation by generation. When the persistence rate, b, is as high as 0.8, this is a slow process, taking many hundreds of years for families who are initially far above or below the mean. Once we look at large groups of families of high or low status, the movement on average to the mean becomes deterministic and predictable.

  This law of motion has, however, a counterintuitive implication about the history of current elites and underclasses. For it predicts that on average, a family’s path as it diverges from and regresses toward the mean will be symmetrical. The law of motion implies that we can infer the average history of the rich and poor families of any generation as reliably as we can predict their future.

  We have a fascination with rags-to-riches stories. Biographies of Charles Dickens, for example, rarely neglect to mention that he came from a childhood where he was removed from school at age 9 and set to work in a blacking factory before he rose to become the richest and most celebrated writer of nineteenth-century England.2 Similarly, biographers of Andrew Carnegie tend to dwell on his birth in a one-room cottage in Dunfermline, Scotland, as the son of an impoverished handloom weaver.3

  But the law of mobility tells us that the rags-to-riches path is the anomaly and the exception. The elite of any generation typically come from families only modestly less elite. On average, the fabulously rich and the extravagantly talented are the offspring of the moderately rich and moderately talented. The truly poor and completely talentless are the children of the modestly poor and somewhat untalented.

  This law can be demonstrated empirically. Figure 12.1 shows the average path of a random group of families toward and away from the upper and lower tails of social status, using the above equation and assuming b is 0.8.4 This figure shows simulations for five hundred families over fifty generations. For any family that achieves either high or low status in any generation, the figure shows its average status for the ten generations preceding and following. Even with random errors included, there is an elegant symmetry in the rise and decline of social status. The persistence rate estimated for the high-status group in the ten generations preceding is 0.81, and for subsequent generations it is 0.85. For the low-status group, the respective persistence rates are 0.81 and 0.77.

  The paths for individual families vary widely. Figure 12.2 shows the paths of six randomly chosen individual families underlying the averages for the elite group in figure 12.1. Even with extensive individual variation, the figure shows that for the preceding and following four generations, these families consistently have above-average status.

  FIGURE 12.1. The implied path through twenty-one generations for elite and underclass families of the base generation.

  FIGURE 12.2. Paths of six elite families compared to the average.

  The empirical result shown in figure 12.1 can be shown mathematically in a few lines.5 The law of motion implies that for any social group, where the indicates average status, on average

  But it also implies, paradoxically, that on average

  That is, if we observe any group of families that now deviate from average social status, then they will have deviated on average by a lesser amount, determined by b, in the previous generation. For these groups, expected future and past trajectories are precisely symmetrical.

  This symmetry implies that if a group deviates in the current generation from the mean social status, set at zero, then on average it will have deviated by a smaller amount, determined by b, in the previous generation. A group of families now of high social status will have arrived at this status over many generations by a series of upward steps from the mean. And the length and speed of that ascent, paradoxically, are determined by the rate of persistence, b. The greater this persistence rate, the longer the implied path to the elite, or indeed to the lower class.

  Social mobility rates can be measured equivalently by how long it takes an existing elite to regress to the mean and by how long it took them to depart from the mean and attain their current position.

  To grasp intuitively why the dynamics of social position must ever be thus, note that the fundamental equation of social mobility posits a deterministic component, bxt, and a random component, et, to any family’s underlying social position. The bigger is b, the smaller is the typical random component. When b is large, to move from a social position at or below the mean to the top in one generation would require an enormous positive random shock. It would require winning an El Gordo of a lottery in the random components of status.

  Thus if the intergenerational correlation is 0.75, the equation predicts that the chance of a family going from the mean of the status distribution to the top 0.5 percent in one generation is roughly one in five hundred million. It is quite likely that it has never happened in England. The chance of going from the bottom 0.5 percent to the top 0.5 percent in one generation is essentially zero. It has never happened in the history of a
ny society.

  In contrast, although high-status families are being constantly pulled back to the middle by the forces of regression to the mean, they are also subject to the same random shocks, and for them even a relatively modest shock can overcome the force of regression to the mean and move them higher in the social ranks. Thus the typical family found in an elite in any generation was recruited from a cadet elite of somewhat lower status in the previous generation. Since this is true across all generations, the typical path of a family to its current elite status involves a series of modest positive shocks over many generations.

  This implies that if the rate of persistence is indeed 0.75 or higher, families observed at any time in the elite spend twenty or more generations (six hundred years) at above-average status. The same holds for families observed at low status: they typically linger at below-average status for twenty generations or more. A high persistence rate implies very slow regression back to the mean; it also implies the persistence of some families above or below the social mean for astonishingly long periods.

  It may appear that some strange causal mechanism is consistently propelling some families toward the upper reaches of social status. It may also seem that as soon as we observe an elite, we ensure its destruction, its decline toward the mean. As in quantum mechanics, we somehow influence the outcome just by making an observation. But both of these impressions are incorrect. We are simply observing the patterns predicted by the random processes of the fundamental equation. Although we may be able to infer that the elite families of 1850 have been on an upward social path since 1550, we cannot predict which of the average families of 1550 will join the 1850 elite.

  The empirical strength of this result can be demonstrated for England using two rich sets of surname observations introduced in chapter 4 above. The first is the set of people whose wills were proved in the probate courts of England from 1384 to 2012, indicating greater wealth. The second is the set of people attending Oxford and Cambridge from 1500 to 2012, indicating greater educational attainment.

  One elite group we can observe all the way from 1384 to 1858, for example, is the people whose wills were proved in the highest probate court in the land, the Prerogatory Court of the Archbishop of Canterbury (PCC). The share of men dying in England with wills proved in the PCC was fairly stable over the years 1680–1858, averaging 5 percent of all adult male deaths. Thus we can take the testators proved in this court after 1680 as representing the wealthiest 5 percent in English society. Not all were men: by 1680 a quarter of the wills probated in this court were from women, typically widows or spinsters. Thus this measure of status indicates the general inheritance of wealth within families, not only through the male line.

  TABLE 12.1. Representation of rare surnames in PCC probates

  Table 12.1 shows the numbers of estates probated in the PCC by generation of death, 1680–1858, and the sizes of the rich and poor rare-surname groups of 1858–87 discussed in chapter 5. By dividing the share of probates from the rich-surname group by the share of population represented by that group in each generation, we obtain the relative representation of these surnames among the probates.6

  The rich surnames of 1858–87 are always overrepresented in the earlier probates. But as we go back in time, that relative representation declines from 7.2 to 2.6. Conversely, the poor surnames are always underrepresented, but as we go back in time, their relative representation rises from 0.2 to 0.8.

  Figure 12.3 shows the pattern of relative representation for these groups. Also shown is the relative representation predicted by the persistence rate that best fits the pattern. For the rich rare surnames, that rate is 0.85. Again wealth is predicted to regress very slowly to the mean in the years 1680–1858, this time measured by the rate of increase in wealth for later elite families. For these same surname groups in the period 1858–2012, the best-fitting intergenerational correlation is 0.82. These numbers are not identical, as the theory would predict, but they are close.

  FIGURE 12.3. Relative representation in PCC probates for rich and poor surname groups of 1858–87.

  For the poor rare surnames, the best-fitting implied persistence is 0.71. The estimate of persistence rates for the poor for the period 1858–2012 is 0.64, but this later estimate has a great deal of imprecision. Thus downward mobility is close to symmetrical with upward mobility. Families who end up at the bottom of the status distribution follow a trajectory that looks very similar in shape to that followed by families who end up at the top.

  Using the PCC records, we can also systematically measure upward and downward mobility at the time of the Industrial Revolution, 1680–1860. Were they equal, as the law of mobility predicts? For each thirty-year period, starting in 1680–1709 and ending in 1830–58, a set of rare surnames was identified that were associated with estates probated in the PCC. The bearers of these surnames were typically four to six times as likely to be probated in the PCC than the average surname, represented here by Clark(e), in periods immediately before and after they were identified.7

  Figure 12.4 shows the regression of these surname groupings toward average representation in the PCC in later generations. As before, these patterns can be used to estimate social mobility rates in each of these generations, and these estimates are shown in table 12.2. They confirm what is by now a familiar story. The average persistence rate for downward mobility during the entire Industrial Revolution period is 0.82, despite the huge structural transformation of the economy in this period. The rise of new industries, and new wealth, from 1760 onward makes no impression on these measured mobility rates. The decline of the old landed aristocracy has no effect either. Intergenerational wealth mobility was extremely slow in Industrial Revolution England (1710–1858), just as it was in modern England (1858–2012). Consequently the high-status surnames of preindustrial England (1710–39) retain relatively high status in the period 1830–58, four generations later, and well after the Industrial Revolution effected major changes in economy and society. You can transform a society, but you do not change the slow march of social mobility.

  FIGURE 12.4. Relative representation in PCC probates for elite-surname cohorts, 1710–1858.

  TABLE 12.2. Implied persistence rate for downward mobility for PCC elite, 1710–1858

  We can use the same PCC data to measure rates of upward mobility for the years 1680–1829 by looking at the rate of rise in relative representation of the surnames that formed elites in later periods. Figure 12.5 shows these patterns. If upward social mobility rates are the same as downward, then the slopes of the upward and downward curves showing relative representation for the same surnames across multiple generations should be the same. The symmetry between figure 12.5 and figure 12.4 is very clear. Upward and downward mobility are symmetrical processes. Table 12.3 summarizes the implied persistence rates from the rate of rise of later elites. The overall average estimate of persistence for upward mobility is 0.77, close to the 0.82 calculated for downward mobility. Allowing for the random fluctuations inherent in any measure that involves sampling, rates of upward and downward mobility are indeed similar. The laws of social mobility show remarkably stable and predictable patterns over very different epochs and social regimes in England.

  FIGURE 12.5. Relative representation, elite-surname cohorts, PCC probates, 1680–1829.

  TABLE 12.3. Implied persistence rate of upward wealth mobility for PCC elite, 1710–1858

  Educational Mobility

  We can show the same symmetrical rise and fall of families in educational mobility over the period 1530–2012 (seventeen generations). The source is the rare surnames of students at Oxford and Cambridge.

  The first elite set of rare surnames is those of the rich who died in the years 1858–87. Figure 5.8 shows the slow downward mobility of these surname groups as measured by their relative representation at the universities from 1830 to 2012, with an intergenerational correlation of 0.82. Figure 12.6 shows their relative representation at Oxford and Cambridge from 1
530 to 2012. The start date of 1530 was chosen because measures of the relative population shares of surnames are possible only from 1538 on, with the beginning of parish registers of baptisms, marriages, and burials. This surname group shows the expected symmetrical rise from 1530 to 1799, with a persistence rate of 0.83.

  The second set of elite rare surnames consists of those that just happen to appear at Oxford and Cambridge in the years 1800–1829.8 Figure 12.6 shows the relative representation of these surnames. Again the pattern is as predicted. The persistence parameter implied by the relative representations for 1830–2012 is 0.77, exactly the same as that estimated for 1530–1799.9 Thus, again, the law of mobility for status holds good over a period of five hundred years during which England underwent profound social changes: the reformation of the Church of England, the Scientific Revolution, the Civil War, the Glorious Revolution, the Industrial Revolution, the move to universal male suffrage and mass public education, and the rise of the welfare state.

  FIGURE 12.6. Relative representation and implied persistence of wealthy and rare surnames at Oxford and Cambridge, 1530–2012.

  FIGURE 12.7. Relative representation for rare-surname cohorts at Oxford and Cambridge, 1680–2012.

  For both these groups, the persistence rates are the same for education as for wealth. For 1680–1858, the persistence rate for wealth was estimated above as being in the range 0.71–0.85. The persistence rate for education is in the range 0.77–0.82.