D:\my documents\my papers\joe\mobility aer new v4c.wpd
“Intergenerational Occupational Mobilityin Britain and the U.S. Since 1850” Abstract
The U.S. both tolerates more inequality than Europe and believes its economicmobility is greater than Europe’s. These attitudes and beliefs help account fordifferences in the magnitude of redistribution through taxation and social welfarespending. In fact, the U.S. and Europe had roughly equal rates of inter-generationaloccupational mobility in the late twentieth century. We extend this comparison intothe late nineteenth century using longitudinal data on 23,000 nationally-representative British and U.S. fathers and sons. The U.S. was substantially moremobile than Britain through 1900, so in the experience of those who created the U.S. welfare state in the 1930s, the U.S. had indeed been “exceptional.” The margin bywhich U.S. mobility exceeded British mobility was erased by the 1950s, as U.S. mobility fell compared to its nineteenth century levels.
Extremely useful comments were provided on previous drafts by Robert Moffitt and three
anonymous referees, Robert Margo and Enrico Moretti and by participants at Northwestern University’sEconomic History Workshop and Institute for Policy Research Faculty Seminar, the Harvard EconomicHistory Workshop, the 2002 meeting of the National Bureau of Economic Research Program in CohortStudies, the 2002 Congress of the International Economic History Association, the 2003 Economic HistorySociety Meetings, the 2004 ASSA Meetings, the 2004 European Social Science History Conference, and the2004 All-UC Economic History Conference.
[W]e have really everything in common with America nowadays, except, of course,language. Oscar Wilde, The Canterville Ghost (1887).
The economies of Britain and the U.S. have had much in common over the two centuries
since the American Revolution: their legal traditions and property rights systems, sources of labor,
capital, and technology, political ties and alliances in two world wars, and – Wilde’s quip
notwithstanding – language and culture are the most obvious. One significant respect in which they
have differed, however, is the progressivity of their taxation and the scale of their social welfare
spending, at least through the late 1970s. Policies in the U.S. reflect a belief that high rates of
economic mobility leave little need for substantial redistribution by the state. Public opinion surveys
are consistent with these priorities and a belief in high rates of mobility: Americans are less
concerned by inequality and are less willing to support redistribution than Europeans regardless of
their position in the income distribution. (Alesina, Di Tella, and MacCulloch, 2001)
Since the 1970s, new large, nationally-representative longitudinal datasets for a variety of
industrialized countries have made possible systematic cross-country mobility comparisons that call
into question the assumptions regarding mobility that seem to underlie U.S. redistributive policies.
The U.S. today exhibits no more income mobility or occupational mobility across generations than
similarly developed countries (Solon, 2002; Solon, 1999; Erickson and Goldthorpe, 1992), though
U.S. policies for the last 75 years have been predicated on American “exceptionalism” to the
mobility patterns seen across a broad set of nations. Piketty (1995) provides a model of “dynastic
learning” in which two economies can, as a result of differences in mobility in the past, settle upon
and retain very different redistributive regimes even after their mobility patterns have converged.2
2 Piketty contends that “The multiplicity of steady states explains at the same time why different
countries can remain in different redistributive equilibria, although the underlying structural parameters ofmobility are essentially the same. This is particularly likely if a country exhibited for some time in the past asignificantly different experience of social mobility before joining the ‘common’ pattern. The ‘canonical’
The question we address is whether we can identify, for Britain and the U.S., those historical
differences in mobility, particularly intergenerational occupational mobility.
Commentators throughout the nineteenth century suggested that the U.S. was indeed
“exceptional” in the occupational mobility experienced by its population (as well as in its geographic
mobility). Using nationally-representative data for Britain and the U.S. that follows 23,000 pairs of
fathers and sons from the beginning of the 1850s to the beginning of the 1880s, we offer the first
detailed comparisons of the mobility regimes experienced by these two countries in the three
generations before they constructed their respective welfare states. In the process, we also offer a
new perspective on the very different histories of labor relations and political activity by workers in
Britain and the U.S. that past scholars (e.g. Turner in the 1890s; Sombart in the early 1900s;
Thernstrom in the 1970s) have attributed to different amounts of economic opportunity and
mobility by individual workers. Can we actually observe sufficiently large differences to explain these
Britain was chosen as the country to which to compare the U.S. experience because of the
availability of comparable data (described below). But this is also a particularly illuminating
comparison because of the large number of characteristics these two economies have shared since
the middle of the nineteenth century when U.S. industrialization got underway. Intergenerational
occupational change was adopted as the metric for mobility for reasons of convenience as well: it is
the only economic outcome that can be examined throughout the period since 1850. It is in some
application is the United States, whose nineteenth century mobility and class structure differed significantlyfrom that of Europe before the two countries [sic] converged in the twentieth century.” (p. 554) As we shallsee below, the extent of the difference in mobility between the nineteenth century U.S. and the twentiethcentury U.S. is itself a subject of some controversy and one upon which we offer new evidence below.
ways superior to income as a measure of mobility, and in some ways inferior.3 But it is what we have,
and has already been the object of a great deal of research in sociology where methods to analyze
mobility have evolved substantially since the 1960s.
I. Previous Research on Mobility in Britain and the U.S.
Our primary interest is in (1) assessing the differences in mobility between Britain and the
U.S. in the second half of the nineteenth century; (2) comparing that difference to the difference
observed by the 1970s; and (3) explicitly evaluating the change in mobility within the U.S. from the
second half of the nineteenth century to the second half of the twentieth.4 There has been until now
a lack of appropriate data to undertake any of these tasks (though there has been considerable work
comparing twentieth century mobility rates across a set of developed countries, including Britain and
the U.S., in the absence of data adequate to task (1), it has not been possible to say how mobility
differences among countries have changed over long periods of time). We briefly survey the existing
literatures in these areas before proceeding to our own contribution.
The comparison between Britain and the U.S. in the nineteenth century has been marked by
the boldest pronouncements and the weakest empirical evidence. Britain has been viewed, since the
time of de Tocqueville and Marx, as a considerably more rigid system in which family background
plays a much more significant role is determining current prospects than in the U.S.5 These
3 Björklund and Jäntti (1999, pp. 15-19) summarize some of the relative merits of income and
occupation for the measurement of intergenerational mobility, and discuss scenarios in which they providevery different results. McMurrer et al. (1997) offer a similar discussion of the relative advantages of differentmeasures of intergenerational mobility.
4 No explicit comparison for Britain between mobility in the second half of the nineteenth century
and in the second half of the twentieth century is made because of data comparability issues discussed below.
5 In the 1830s, de Tocqueville noted, “Among aristocratic peoples, families remain for centuries in
the same condition and often in the same place. . . . Among democratic peoples [e.g. in the U.S.], new families
differences have been attributed to a number of factors – the frontier and the rapid growth of
completely new cities in the U.S., the feudal tradition and guild and apprenticeship systems in
Britain, and the wide availability of free, public education in the U.S. But there has been no
consistent data with which these assertions could be directly tested. There are several studies that
have looked at both British nineteenth century mobility and U.S. nineteenth century mobility in
For nineteenth century Britain, Miles (1993 and 1999) and Mitch (1993) have each used
samples of marriage registrations from 1839 to 1914 to measure intergenerational occupational
mobility.6 At the time of registration, both bride and groom as well as bride’s father and groom’s
father were required to list their occupation. From this information, Miles calculates that between 60
and 68 percent of grooms married between 1839 and 1894 were in the same occupational class as
their fathers when the grooms married. (Miles, 1999, p. 29). Though his finding are in general quite
similar, Mitch finds evidence for slightly more mobility – 61 percent of grooms married between
1869 and 1873 were in the same class as their father, 20 percent were higher, and 19 percent lower.
The data used in both studies, however, are less than ideal.7
continually spring from nowhere while others disappear to nowhere and all the rest change their complexion.”Three decades later in the 1860s, Marx saw the U.S. as more open and fluid than the older European societies,with their “developed formation of classes.” American classes, on the other hand, “have not yet become fixedbut continually change and interchange their elements in constant flux.” He related “this situation to theimmature character of the American working-class movement.” He characterized the U.S. as having “acontinuous conversion of wage laborers into independent self-sustaining peasants. The position of wageslaborer is for a very large part of the American people but a probational state, which they are sure to leavewithin a longer or a shorter term.”
6 Their samples were somewhat different. They both used marriage registries, but they used different
(possibly overlapping) samples of registries.
7 The marriage registry data include only couples married in Anglican churches, so toward the end of
the nineteenth century, these samples are increasingly unrepresentative. By 1914, 42 percent of all marriagestook place outside the Anglican church (Vincent, 1989, p. 281). Also, the occupations of the groom and hisfather are recorded at the time of the groom’s marriage, so the father’s and son’s occupations are observed at
For the nineteenth century U.S., a large number of studies have been completed for specific
communities in the U.S. that give us a rough sense of occupational mobility in the past. For
example, among males who remained in Boston, from 37 to 40 percent of sons ended up in the
same occupational categories as their fathers over the period 1840-89. (Thernstrom, 1973, p. 83)
Though this might in itself seem a sufficient basis on which to conclude that the nineteenth century
U.S. had greater intergenerational occupational mobility than nineteenth century Britain (total
mobility – the fraction of sons found outside their fathers’ occupational categories – was twice as
great in Boston as in Britain), the data for Boston suffers, like that from Britain, from a number of
shortcomings that prevent such simple comparisons.
The principal difficulty with historical estimates for the U.S. is that they were most often
constructed by observing a single community over a period of decades. The only individuals whose
occupational mobility could be observed were those who remained in the community. It would be
surprising if the movers and stayers did not have systematically different patterns of occupational
mobility, given the positive and often substantial costs of migration. Occupational mobility
measured using marriage records suffers from the same shortcoming as the British data: sons’
occupations are examined at different points in their careers than fathers’ occupations. The new
nineteenth century data used below for the U.S. (like that for Britain) is not limited to individuals
who remained in a place for a decade or more and examines sons’ and fathers’ occupations at similar
ages, presenting a more representative picture of mobility than has previously been available. Two
additional difficulties apart from the inconsistencies in the collection of the data and biases
different points in their life cycles, with the son being considerably younger than the father. If it were possibleto observe the father’s and son’s occupations holding age constant, a different picture of intergenerationalmobility might emerge. Specifically, we might expect to observe a greater likelihood of mobility as the songained years and experience in the labor market.
introduced by the source materials are: (1) the possibility that differences between the British and
U.S. occupational structures account for much of the difference in total mobility; and (2) the
possibility that even in the absence of these differences in occupational distributions, the imprecision
of the mobility measure employed would obscure more fundamental differences or similarities in
mobility. The measures of mobility provided in our analysis overcome these difficulties.
One study offers a long-run perspective on intergenerational occupational mobility within
Britain: Miles (1999) attempts to reconcile his findings of increasing fluidity over the nineteenth and
early twentieth centuries with work by Erickson and Goldthorpe (1992), among others, who discern
no trend in intergenerational mobility from the 1940s to the 1970s. Differences in the data for the
two eras (Miles used marriage registers and Erickson and Goldthorpe relied on survey data with a
retrospective question on the occupation of the respondent’s father when the respondent was 14
years of age) diminish the reliability of this comparison.
Only two studies have attempted to assess how intergenerational mobility changed between
the nineteenth and twentieth centuries in the U.S. In a re-analysis of several city-specific studies
from the nineteenth century and together with the Occupational Change in a Generation (OCG)
cohorts for the twentieth, Grusky (1987) concluded that there was significant immobility in the
nineteenth century, with the non-manual/manual divide particularly difficult to cross, and an
increase in intergenerational mobility from the nineteenth century to the twentieth century.
The work by Guest et al. (1989) is closest to the comparison between U.S. mobility in the
nineteenth century and twentieth centuries carried out below. Comparing a sample of young males
linked from the 1880 U.S. census to the 1900 U.S. census, they find little change from the last two
decades of the nineteenth century to the end of the period covered by the second OCG cohort
(1973). Their comparison is less than entirely apt, however. Their nineteenth century data excluded
most interstate migrants, and the time between the observation of the fathers’ and sons’ occupations
was in all cases greater (by as much as a factor of two) in the nineteenth century data than in the
The literature comparing twentieth century intergenerational mobility across developed
countries is now voluminous.9 The comparison between Britain and the U.S. undertaken by
Kerckhoff et al. (1985), like almost all international comparisons involving these two countries, uses
the Oxford Social Mobility Study (1972) for Britain and the second cohort of the OCG (1973) for
the U.S. They find “considerably more overall inter-generational and career mobility in the United
States, but . . . the major differences between the two societies are due to shifts in the distributions
of kinds of occupations.” (1985, p. 281). Erickson and Goldthorpe (1992) examine a broader set of
countries, and likewise find the U.S. and Britain roughly similar in intergenerational mobility, after
accounting for differences in the distributions of occupations across the two countries, as did
Grusky and Hauser (1984) in analyzing a set of 16 countries including Britain and the U.S.10 In
income terms, Solon (2002) and Björklund and Jäntti (1999) find similarly high rates of income
immobility across generations in Britain and the U.S., with both exhibiting considerably less mobility
from fathers to sons than Canada, Finland, and Sweden.
8 In their nineteenth century data, the individual’s father’s occupation was observed in 1880, and the
individual’s own occupation was observed in 1900, twenty years later. In the two OCG cohorts, theindividual’s own occupation was observed in the survey year (1962 or 1973), but the father’s occupationreported was that for the father when the respondent was 16 years of age. Guest et al. (1989) used males fromthe OCG who were 25-34 in the survey year, so they have between 9 (for 25 year olds) and 18 years (for 34year olds) between the report of their father’s occupation and the report of their own.
9 Treiman and Ganzenboom (2000) provide a useful survey of the entire history of comparative
research on occupational mobility, both within and across generations.
10 Contrasting views are found in Wong (1990) who finds greater mobility in Britain than in the U.S.,
and Yamaguchi (1987) who finds mobility greater in the U.S. than in Britain. II. The Data
We use a common methodology in constructing nineteenth century data to compare
mobility between the U.S. and Britain. For both countries we link a sample of males from the
1850/1851 census to the census taken thirty years later in 1880/1881. Our choice of Britain as a
comparison was dictated by the availability of sources making it possible to construct longitudinal
data in exactly the same manner as for the U.S. For Britain we use information on approximately
13,000 males linked from the 1851 British census to the 1881 British census, and for the U.S. on
nearly 10,000 males linked from the 1850 to the 1880 U.S. Federal Censuses. Details on the
matching procedure, representativeness, and sensitivity tests are described in Appendix 1.
The only economic outcome available in the longitudinal data used here is self-reported
occupation. We observe the father’s occupation in 1850 (U.S.) or 1851 (Britain) and the son’s
occupation thirty years later. After collapsing hundreds of occupational titles into a reasonable set of
categories it becomes possible to construct tables that describe the transitions from fathers’
occupational categories to sons’ occupational categories. We have used four categories (white collar,
farmer, skilled and semi-skilled, and unskilled) to reduce the sparseness of the mobility tables, but
where it has been possible to use a larger number of categories, the basic qualitative results reported
11 “White Collar” is comprised of professional, technical, and kindred; managers, officials, and
proprietors; clerical; and sales. “Farmer” is comprised of only farm owners and farm managers. “Skilled/Semiskilled” is comprised of craftsmen and operatives. “Unskilled” is comprised of service workersand laborers, including farm laborers. These categories are sufficiently broad and the boundaries betweenthem are sufficiently well understood that we believe that movement among them represents a goodapproximation to the conventional understanding of “intergenerational mobility.” Nonetheless, in comparingmobility across countries or over time, a reasonable concern is that these categories are not consistent, andthat as important sub-divisions arise within them, ignoring those sub-divisions will lead to an understatementof mobility for the period or country where such distinct, new groupings have become prominent. Forexample, over the century and a half spanned by our inquiry, the white collar category has changedsubstantially in the U.S. as the fraction of the labor force in clerical and sales positions has grown. To account
For the twentieth century, we have employed the same data as others who have worked in
this area: the Oxford Mobility Study for Britain and the OCG (1973 cohort) for the U.S.12 In each
the respondent’s occupation at the time of the survey is taken as the son’s occupation, and the
occupation that the respondent reported his father to have had when the respondent was age 14
(Britain) or 16 (U.S.) is taken as the father’s. To prevent differences in the impact of World War
Two and the Great Depression from influencing the results, males age 31-37 (whose fathers’
reported occupations would have been in 1949-1955) were used from the British data and males age
33-39 (whose fathers’ reported occupations would have been in 1950-1956) were used from the U.S.
data.13 This yields a range of years between fathers’ and sons’ occupations of 17 to 23 years, and an
average of roughly 20. This was done to ensure comparability with the U.S. data from the nineteenth
century: though the direct nineteenth century comparison between Britain and the U.S. will use a
thirty-year interval between fathers’ and sons’ occupations (a restriction dictated by the sources
available for Britain), the U.S. sources also allowed the creation of two twenty-year samples (one
for such changes (as well as the greater fraction of factory operatives in nineteenth century Britain and in themodern U.S. compared to the nineteenth century U.S.), we will employ up to six occupational groups wherethe data make this possible (separating high and low white collar workers, and splitting skilled and semiskilledblue collar workers).
12 The Oxford Mobility Study (University of Oxford, 1978) for Britain is available at the U.K. Data
Archive at the University of Essex as study number 1097. See http://www.dataarchive.ac.uk/. The original1962 Occupational Change in a Generation study (Blau and Duncan, 1967) and its 1973 replication(Featherman and Hauser, 1975 and 1978) are available from the Inter-University Consortium for Political andSocial Research as study number 6162. See http://www.icpsr.umich.edu/.
13 In the 1973 OCG, sons who were 31-39 (41-49) in the survey year who reported their fathers’
occupations when they themselves were 16 years of age would have been referring to the calendar years 1950-56 (1940-46). Similarly, in the 1972 Oxford Mobility Study, sons who were 31-37 (41-47) in the survey yearwho reported their fathers’ occupations when they themselves were 14 years of age would have been referringto the calendar years 1949-55 (1939-55). Comparisons between the samples using males 43-49 (OCG) and 41-47 (Oxford Mobility Study) will be provided, but readers are cautioned against drawing strong conclusionsfrom them as they may reflect differences in the experience of U.S. and British fathers during World WarTwo more than underlying differences in “normal” levels of intergenerational mobility.
with fathers observed in 1860 and sons in 1880, and one with fathers observed in 1880 and sons in
1900). These will be used for assessing change in mobility over time within the U.S.14
III. Measuring and Modeling Intergenerational Occupational Mobility
Intergenerational occupational mobility can be assessed through the analysis of simple two
dimensional matrices, with categories for fathers’ occupations arrayed across one dimension and
categories for sons’ occupations arrayed across the other. Comparing mobility across two places or
times requires comparison of two matrices. Suppose fathers and sons can be found in either of two
jobs.15 A matrix that summarizes intergenerational mobility in location P has the form P =
with numbers of fathers in the two occupations (1 or 2) in columns and numbers of sons in these
occupations in rows. The entry in the power left (p ) is the number of sons of job 1 fathers who
themselves obtained job 2. One simple measure of the overall mobility in P is the fraction of sons
who end up in jobs different from those of their fathers: M =(p +p )/ (p +p +p +p ).
Though this measure has the virtue of simplicity as a benchmark, it also has a shortcoming
when mobility is compared across two matrices P and Q: it does not distinguish between differences
in mobility (1) arising from differences across the matrices in the distributions of fathers’ and sons’
occupations (differences in what Hauser, 1980, labels “prevalence”) and (2) arising from differences
14 Two additional British sample with twenty year intervals (1861-1881 and 1881-1901) are compared
both to U.S. data for 1860-80 and 1880-1900 and to the Oxford Mobility Study in Long and Ferrie (2006). The results presented there support the conclusions below: that in the nineteenth century, intergenerationaloccupational mobility was considerably more pronounced in the U.S. than in Britain, but that this gap waslargely eliminated by the second half of the twentieth century.
15 No ordering can be imposed on the occupations. When we turn to analysis of the nineteenth
century data with four categories (white collar, farmer, skilled/semi-skilled, and unskilled), it is possible torank unskilled last unambiguously, but it is not clear how to rank the others relative to unskilled. There are nogood sources that would allow us to calculate average incomes by occupation. We thus require analysistechniques that rely not on the ordering of occupational categories but only on their labeling.
across the matrices in the association between father’s and sons’ jobs that may occur even if the
distributions of fathers’ and sons’ occupations were identical in P and Q (differences in what
Hauser, 1980, calls “interaction”). Consider and
M =7/10. The marginal frequencies differ, so it is not clear whether the difference in observed
mobility M results from this difference or from something more fundamental such as differences
between P and Q in the amount of human capital necessary to achieve job 1.
One way to proceed is to adjust one of the matrices so it has the same marginal frequencies
as the other. Such a transformation, if achieved by multiplication of rows and columns by arbitrary
constants, does not alter the underlying mobility embodied in the matrix. (Mosteller, 1968; Altham
and Ferrie, 2007) If we multiply the first row of Q by 2 and then multiply the first column of the
resulting matrix by ½, we produce a new matrix with the same marginal frequencies as
in matrix P, with an associated total mobility measure MQN=5/8. We could then calculate the
QN and be confident that the difference in mobility does not result from differences
in the distributions of occupations between the two locations.
There still may be differences in mobility between P and Q, even after adjusting the marginal
QN = 0, however. The fundamental measure of association
between rows and columns in a mobility table is the cross-product ratio, which for P is p p /p p
and can be rearranged to give (p /p )/(p /p ), the ratio of (1) the odds that sons of job 1 fathers
get job 1 rather than job 2 to (2) the odds that sons of job 2 fathers get job 1 rather than job 2. If
there is perfect mobility, the cross-product ratio would be one: sons of job 1 fathers would have no
advantage in getting job1 relative to sons of job 2 fathers. The more the cross-product ratio exceeds
one, the greater the relative advantage of having a job 1 father in getting job 1. The cross-product
ratio for P is 3 and for Q is 1/3 (as it is for QN), so there is more underlying mobility in Q than in P.
For a table with more than two rows or columns, there are several cross-products ratios, so a
summary measure of association should take account of the full set of them. One such measure has
been suggested by Altham (1970): the sum of the squares of the differences between the logs of the
cross-product ratios in tables P and Q. For two tables which each have r rows and s columns, it
measures how far the association between rows and columns in table P departs from the association
The metric d(P,Q) tells us the distance between the row-column associations in tables P and Q.16 A
simple likelihood-ratio P2 statistic G2 (Agresti, 2002, p. 140) with (r-1)(s-1) degrees of freedom can
then be used to test whether the matrix 1 with elements 2 =log(p /q ) is independent; if we can
reject the null hypothesis that 1 is independent, we essentially accept the hypothesis that d(P,Q)…0
so the degree of association between rows and columns differs between table P and table Q.
The statistic does not tell us which table has the stronger association, but that can be
determined by calculating d(P,I) and d(Q,I), which use the same formula as d(P,Q) but replace one
table with a matrix of ones. If d(P,Q)>0 and d(P,I)>d(Q,I), we conclude that mobility is greater in
16 See Altham and Ferrie (2007) for a discussion of the distance measure and test statistic. As it obeys
the triangle inequality, so d(P,Q) + d(Q,I) $ d(P,I), the metric d(P,Q) can be thought of as the distancebetween the row-column association in table P and the row-column association in table Q, while d(P,I) andd(Q,I) are the distances, respectively, between the row-column associations in tables P and Q and the row-column association in a table in which rows and columns are independent. This property of the Althamstatistic – its interpretation as a distance measure – makes it possible to visualize how the row-columnassociations differ across various tables. For a set of N tables, the pair-wise distances among all the tables andthe distance from each to a table with independent rows and columns are sufficient to allow us to display thepositions of these tables relative to independence in a multidimensional space. The idea is the same asgenerating a map of cities in the U.S. knowing only the distances between each pair of cities and selecting anarbitrary point of reference.
table Q (i.e. mobility is closer in Q than in P to what we would observe under independence of rows
and columns, in which the occupation of a father provides no information in predicting the
occupation of his son). It is, of course, possible that in some circumstances d(P,Q) > 0 but
d(P,I).d(Q,I), in which case we will say that tables P and Q have row-column associations that are
equally distant from the row-column association observed under independence, but that tables P and
Q differ in how they differ from independence (i.e. the odds ratios in table P that depart the most
from independence are different from those that depart the most from independence in table Q).
Contingency tables are often dominated by elements along the main diagonal (which in the
case of mobility captures immobility or occupational inheritance). It will prove useful to calculate an
additional version of d(P,Q) that examines only the off-diagonal cells to see whether, conditional on
occupational mobility occurring between fathers and sons, the resulting patterns of mobility are
similar in P and Q. This new statistic will then test whether P and Q differ in their proximity to
“quasi-independence.” (Agresti, 2002, p. 426) For square contingency tables with r rows and
columns, this additional statistic d i(P,Q) will have the same properties as d(P,Q), but the likelihood
ratio P2 statistic G2 will have [(r-1)2-r] degrees of freedom.
Because it is a pure function of the odds ratios in tables P and Q, d(P,Q) is invariant to the
multiplication of rows or columns in either table by arbitrary constants. As a result, d(P,Q) provides
a measure of the difference in row-column association between two tables that abstracts from
differences in marginal frequencies. Because [d(P,Q)]2 is a simple sum of the squares of log odds
ratio contrasts, it can be conveniently decomposed into its constituent elements: for an r × s table,
there will be [r(r-1)/2][s(s-1)/2] odds ratios in d(P,Q) and it will be possible to calculate how much
each contributes to [d(P,Q)]2, in the process identifying the locations in P and Q where the
differences between them are greatest.
In analyzing how mobility differs between two tables, we will then proceed in three steps:
1. calculate total mobility for each table as the ratio of the sum of the off-diagonal elements to thetotal number of observations in the table, and find the difference in total mobility between P and Q;
2. adjust one of the tables to have the same marginal frequencies as the other and re-calculate thedifference in total mobility to eliminate the influence of differences in the distribution ofoccupations;
3. calculate d(P,Q), d i(P,Q), d(P,I), and d(Q,I) and the likelihood ratio P2 statistics G2; if d(P,Q)…0,calculate the full set of log odds ratio contrasts and identify those making the greatest contributionto [d(P,Q)]2.
This differs from common practice in sociology, where the estimation of log-linear models
has dominated the empirical analysis of mobility since the 1960s.17 Log-linear analysis decomposes
the influences on the log of each entry in a contingency table into a sum of effects for its row and
column and an interaction between the row and column. Controlling for row and column effects
eliminates the effect of the distribution of fathers’ and sons’ occupations on mobility. The remaining
interaction between rows and columns captures the strength of the association between rows and
columns which in turn measures mobility, though the coefficient on the interaction term has no
meaning in itself as it is a component of a highly non-linear system.18 In comparing mobility in two
tables, the underlying question addressed is how well a particular pattern of mobility fits the different
layers of the table, through comparisons of likelihood ratios. Attention is generally focused on the
statistical significance of the difference in the fit of particular models across layers rather than on the
magnitude of differences in row-column association. Simple comparisons of differences in the
strength of the row-column association are not generally performed without the imposition of
17 See Hauser (1980) and Hout (1983).
18 Goodman (1970) suggests using the standard deviations of the log-linear model parameters in
additive form as a measure of the strength of the row-column association in each layer. The approach adoptedhere instead has some advantages, described below, over this approach.
additional structure. For example, an analysis may have as its maintained hypothesis that all of the
odds ratios in P differ in exactly the same degree from all of the odds ratios in Q, or that the odds
ratios can be partitioned into sets that differ uniformly across the tables.
The measure of underlying mobility adopted here has several advantages over the more
commonly employed measures of mobility derived from log-linear analysis: the measure used here
(1) generates a simple, meaningful measure of the distance between the row and column association
in P and the row and column association in Q that is conceptually straightforward and easy to
visualize (see Figure 1 below);19 (2) can be easily decomposed, allowing us to isolate the specific odds
ratios that account for the largest part of difference between the association in P and the association
in Q; (3) has a simple associated one-parameter test statistic that allows us to say whether the
difference between the row-column association in P and the row-column association in Q is non-
zero; and (4) answers a question (“does the row-column association in P differ from that in Q, and if
so by how much and in which odds ratios?”) that should be methodologically prior to the question
addressed by more commonly employed measures of differences in row-column association based
on log-linear analysis (“can we find a particular pattern of row-column association that is common
to tables P and Q?”). For purposes of comparison, we will nonetheless provide measures based on
log-linear analysis for the historical data. IV. Britain vs. the U.S. in the Twentieth Century
Before turning to the nineteenth century, we assess the difference in mobility between
Britain and the U.S. using the tools described in the previous section and males age 31-37 in 1972
19 Goodman and Hout (1998) provide a method to visualize differences in row-column association
across tables for each log-odds ratio, but do not offer a summary measure for the entire table.
from the Oxford Mobility Study and white, native-born males age 33-39 in 1973 from the
Occupational Change in a Generation survey. All cases in which the respondent reported a non-
civilian occupation for himself or his father were excluded. Table 1 provides a cross-classification of
son’s occupation by father’s occupation, and Table 2 provides summary measures of mobility for
each panel in Table 1 and for differences in mobility between the panels.
According to the simple measure of total mobility M (Table 2, panel 1, column 1), young
men in their thirties in 1972-73 were less likely in the U.S. than in Britain to find themselves in the
occupations their fathers had in 1949-55. But this difference was largely a result of differences in the
occupational structures of the two economies. If total mobility is measured for both countries using
either the British (45.3 vs. 48.3) or U.S. (53.7 vs. 56.7) distributions of occupations, the gap in total
mobility falls from 11.4 percentage points to 3 percentage points.20 If Britain had the U.S.
occupational distribution but the underlying association between rows and columns actually seen in
Britain (panel 1, column 2, row 1), and the U.S. had the British occupational distribution but the
underlying association between rows and columns actually seen in the U.S. (panel 1, column 2, row
2), the British (53.7 percent) would have actually had more total mobility than the U.S. (48.3
In both Britain and the U.S., an underlying association between fathers’ and sons’
occupations apart from that induced by differences in occupational distributions was present (for
both, we can reject the null hypothesis that their association between rows and columns was the
20 All of the underlying five-way mobility tables employed in the following analyses are contained in
Appendix 3. To illustrate, Table A2-5 in Appendix 3 shows the British and U.S. mobility tables from Table 1that result from applying the other country’s marginal frequencies to each country’s mobility table, usingiterative proportional fitting. The MN entries in Column (2) of Table 2 were generated by calculating thepercentage who end up off the main diagonal (i.e. in occupations different than their fathers) in Table A2-5 . For example, when the U.S. marginal frequencies are imposed on the British mobility table, 53.7 percent ofBritish sons are off the main diagonal; when the British marginal frequencies are imposed on the U.S. mobilitytable, 48.3 percent of U.S. sons are off the main diagonal.
same as we would observe under independence). The difference between them in their degrees of
association (Table 2, panel 1, column 7) is small in magnitude (7.9), and we cannot reject at any
conventional significance level the null hypothesis that their associations are identical.21 This is not
solely the result of strong similarities in the tendency of sons to inherit their fathers’ occupations, as
we cannot reject the null hypothesis that association is identical even if we focus only on the off-
diagonal elements in each table (panel 1, column 9). These results confirm the findings of Erickson
and Goldthorpe (1992) and Kerckhoff et al. (1985) that, after accounting for differences in their
occupational distributions, Britain and the U.S. exhibited similar intergenerational occupational
mobility in the third quarter of the twentieth century.
The white collar category is quite broad in both countries in the twentieth century, spanning
professionals and managers as well as clerical and sales workers. If substantially more mobility
occurs within this category in one country than in another, mobility comparisons based on only four
categories may be misleading. To remedy this, we divided “white collar” into “high white collar”
(professional, technical, and kindred; managers, officials, and proprietors) and “low white collar”
(clerical and sales) and calculated new Altham statistics for Britain (P) and the U.S. (Q). The
magnitudes of the Altham statistics rose somewhat for both countries (d(P,I)=37.50, d(Q,I)=31.06),
as did the magnitude of the difference between them in row-column association (d(P,Q)=17.81), but
21 The comparison between Britain and the U.S. is substantially different if males age 41-47 (Britain)
and 43-49 (U.S.) whose fathers’ occupations are reported during World War Two are used instead of 31-37and 33-39 year old males: the Altham statistics for Britain (d(P,I)=30.02), for the U.S. (d(Q,I)=17.98), and forthe difference in row-column association (d(P,Q)=15.18, G2=41.89, p<0.001) reveal a great deal moremobility in the U.S., and a large difference between the row-column associations in the two countries that isnot apparent when younger males whose father were observed after World War Two are used. This couldreflect either the influence of differences between the two countries in fathers’ occupations during the waryears (a cohort effect) or greater occupational mobility in the U.S. than in Britain during the additional tenyears between fathers’ and sons’ occupations (a time effect) that the 41-47 & 43-49 year olds’ data captures.
it was again not possible to reject the null hypothesis that the true difference was zero
V. Britain vs. the U.S. in the Nineteenth Century
How different were Britain and the U.S. in intergenerational occupational mobility a century
earlier? Table 3 presents the cross-classification of sons’ and father’s occupations using our new data
linking fathers in 1850 (U.S.) or 1851 (Britain) and sons in 1880 (U.S.) or 1881 (Britain). Summary
mobility measures again appear in Table 2. The simplest measure of mobility shows the U.S. with a
slight advantage (inheritance of the father’s occupation was 2.8 percentage points less likely in the
U.S.), but substantial differences in occupational distributions obscure much larger differences. If
the U.S. had Britain’s occupational distribution, the U.S. advantage in total mobility would have been
5.3 percentage points; if Britain had the U.S. distribution, the U.S. advantage would have been 9.9
percentage points. Finally, if Britain and the U.S. had swapped occupational distributions and
retained their underlying association between fathers’ and sons’ occupations, the U.S. advantage
would have been 12.4 percentage points.
These simple comparisons suggest that more fundamental measures of association between
fathers’ and sons’ occupations would reveal a weaker association (and greater mobility) in the U.S.
The second set of summary mobility measures in Table 2 shows that this was indeed the case:
though the association between fathers’ and sons’ occupations differed from independence in
Britain and the U.S., the magnitude of the association was twice as great in Britain (22.7) as in the
U.S. (11.9) (compare Table 2, panel 2, columns 3 and 5). We can safely reject the null hypothesis that
the difference between them in their associations was actually zero. The point estimate for d(P,Q)
was 13.2, indicating a difference in mobility after controlling for occupational distributions that was
not only statistically significant but also large in magnitude, compared to d(P,I) and d(Q,I).22
Table 4 disaggregates [d(P,Q)]2 into its components, and calculates the contribution of each
of the [d (P,Q)]2 that account for three quarters of [d(P,Q)]2 to the total. G2 is also reported for each
contrast, as well as the underlying odds ratios from P and Q. For example, the first entry is the
relative advantage in entering farming rather than unskilled work from having a farmer father rather
than an unskilled father. In Britain, sons of farmers were 49 times more likely to enter farming rather
than unskilled work than were the sons of unskilled workers. In the U.S., the ratio was only 4.5 to
one, so the advantage of having a farm father rather than an unskilled father in making this move
(into farming rather than unskilled work) was 11 times greater in Britain than in the U.S. This odds
ratio contrast alone accounts for nearly 13 percent of the difference between the association in P and
the association in Q. Of the nine odds ratios that account for 75 percent of the difference in
association between P and Q, six display a smaller disadvantage in the U.S. in entering farming
rather than another occupation for the sons of non-farmers, indicating that an important source of
greater intergenerational mobility in the U.S. than in Britain was an easier path to farm operation
from outside agriculture, regardless of the distribution of occupations for fathers and sons. But the
importance of farming by no means exhausts the sources of higher mobility in the U.S. For example,
in Britain, white collar sons had a 20 to one advantage in entering white collar rather than unskilled
jobs compared to the sons of unskilled workers; in the U.S., their advantage was only 4 to one, a
fifth of the advantage in making this transition conveyed in Britain by having a white collar father.
22 If we split white collar into high and low white collar groups, the Altham statistics reveal the same
stark differences between Britain (P) and the U.S. (Q): d(P,I)=41.17, d(Q,I)=16.98, d(P,Q)=29.58,G2=136.98, p<0.001. If we use six categories (splitting both high and low white collar and skilled andsemiskilled), the difference between Britain (P) and the U.S. (Q) remains: d(P,I)=59.18, d(Q,I)=28.40,d(P,Q)=43.90, G2=185.85, p<0.001.
Not only is overall mobility greater in the U.S., but upward mobility also exceeds that in
Britain. Without a comparable scheme of fully ranked occupational categories for both countries, a
complete analysis of upward and downward mobility is impossible. However, some conclusions
follow from innocuous assumptions. Assuming that unskilled occupations are less desirable than all
others, Table 3 indicates that in the U.S. 81.4 percent of all sons of unskilled laborers moved up into
other occupations, while only 54.3 percent of unskilled British sons experienced upward mobility; if
the British marginal distribution of occupations is imposed on the U.S. mobility table, the U.S.
advantage is narrowed but not eliminated (upward mobility in the U.S. falls to 61.8 percent,
compared to 53.3 percent in Britain), while if the U.S. marginal distribution of occupations is
imposed on the British mobility table, the British disadvantage is narrowed slightly but remains large
(upward mobility in Britain rises to 61.2 percent, compared to 81.4 percent in the U.S.). Downward
mobility in the U.S. was lower than in Britain: 8.7 percent moved into unskilled labor in the U.S.
versus 14.0 percent in Britain, though this difference is reversed if either the British or U.S. marginal
distributions are used for both countries. Thus, the U.S. was not only a less static labor market than
Britain (as the Altham statistics reveal), but also a labor market with (1) better prospects for upward
movement even after accounting for differences between its occupational structure and Britain’s,
and (2) less downward mobility than in Britain, though downward mobility would have been slightly
greater in the U.S. than in Britain if the two countries had the same occupational distributions.
VI. Nineteenth Century vs. Twentieth Century Mobility in the U.S.
The difference in mobility between Britain and the U.S. in the nineteenth century was
substantial, both before and after taking account of differences in their distributions of occupations.
We have already seen that Britain and the U.S. were indistinguishable in terms of intergenerational
occupational mobility in the third quarter of the twentieth century, after taking account of their
occupational distributions. How was this convergence in underlying mobility achieved? Did U.S.
mobility fall or did British mobility rise to U.S. levels? We cannot directly assess the change over
time in British mobility in the absence of nineteenth century longitudinal data that span twenty years,
unless we were to include the Great Depression. For the U.S. however, we have samples that span
1860-80 and 1880-1900 that are identical in their construction to the 1850-80 sample we used in the
comparison to Britain 1851-81. Males age 33-39 at the end of the 1860-80 and 1880-1900 U.S.
samples can be compared to males age 33-39 in the 1973 cohort of the OCG. These samples then
both span either exactly 20 years between fathers’ and sons occupations (1860 to 1880 and 1880 to
1900) or an average of 20 years between fathers’ and sons’ occupations (1949-55 to 1973). Table 5
presents the cross-classification of fathers’ and sons’ occupations for the 1860-80 data, which are
compared to the OCG data from the lower panel of Table 1. Summaries of the comparison between
them appear in the third set of contrasts in Table 2.
Total mobility shows a 6.1 percentage point advantage for the modern data, but when it is
calculated for both tables using common marginal frequencies, the nineteenth century table has
higher total mobility, by from one (using the 1860-80 frequencies) to 6.9 percentage points (using
the 1973 frequencies). If the marginal frequencies are swapped but the underlying associations are
left unchanged, the nineteenth century U.S. had a total mobility rate 1.3 times greater than that in the
1949-73 period. The more fundamental measure of mobility, d(P,Q), also shows greater mobility (i.e.
a weaker association between fathers’ and sons’ occupations) in the nineteenth century than in the
twentieth: we can safely reject the null hypothesis that the associations are equal (G2=46.7 on 9
degrees of freedom, probability(H : same association)< 0.0001), and the difference d(P,Q) is large in
magnitude.23 We cannot, however, reject the hypothesis that the associations are identical when the
diagonal elements in P and Q are excluded, suggesting that change in the likelihood of direct
inheritance of the father’s occupational status by the son was the greatest difference between these
eras, rather than more subtle change in the structure of association between one generation’s
Table 6 decomposes the elements of d(P,Q) into those that account for three quarters of the
difference between mobility in the nineteenth century and mobility in the twentieth. The single
greatest difference – making up nearly 15 percent of the difference between the association in the
nineteenth century and the association in the twentieth – is in the upper left four cells of the
contingency table. In the nineteenth century, getting a white collar job rather than a farm job was 11
times more likely for the son of a white collar worker than for the son of a farmer; by the twentieth
century, the advantage of white collar sons had grown nearly eight-fold relative to farm sons in
getting white collar jobs rather than farm jobs. The second and third contrasts in Table 6 show
swings in the odds ratios of similar magnitude from the nineteenth to the twentieth centuries (the
advantage of farm sons relative to skilled and semiskilled sons in getting (1) white collar rather than
farm jobs, and (2) farm jobs rather than unskilled jobs). Of the seven substantial differences between
the nineteenth and twentieth centuries, three provide evidence of greater difficulty entering white
collar jobs (for the sons of farmers relative to sons of white collar workers, for the sons of skilled
workers relative to sons of farmers, and for sons of unskilled workers relative to sons of farmers).
23 This is in marked contrast to the findings of Hauser et al. (1975) who found no trend toward an
increase in the association between fathers’ and sons’ occupations in the U.S. over the twentieth century. Though part of this difference may result from different methodologies, we suspect that most is the result offundamental changes in the U.S. economy explored in the next section.
24 When five occupational categories are used rather than four, the greater mobility for the nineteenth
century (P) compared to the twentieth (Q) persists: d(P,I)=21.90, d(Q,I)=31.06, d(P,Q)=16.71,probability(H : d(P,Q)=0)<0.001.
The difference between nineteenth and twentieth century mobility persists into the last two
decades of the nineteenth century. If the 1880-1900 sample is used (P) and compared to the 1973
OCG cohort (Q), substantially more mobility is again observed in the historical data than in the
more recent past. Contrast 4 in Table 2 shows these results: total mobility was greater in the past if
the nineteenth century occupational distributions are used or if the occupational distributions are
swapped and each period retains its actual association between fathers’ and sons’ occupations. The
unadjusted total mobility and total mobility using the twentieth century frequencies, however, favor
the more recent data. But the underlying association measured by d(P,I), d(Q,I), and d(P,Q) was
substantially greater in the past than more recently. We can safely reject the hypothesis that the
association was identical (G2=36.7 on 9 degrees of freedom, probability(H : same association)<
0.0001). Even in the last two decades of the nineteenth century, mobility was greater than in the
1949-73 period, a difference that was both large in substance and statistically significant.25 Ferrie
(2005, pp. 206-208) reports Altham statistics comparing mobility from three intervals in the
nineteenth and early twentieth centuries (1860-80, 1880-1900, and 1900-20) to mobility from three
intervals in the second half of the twentieth century (the 1973 OCG, the General Social Survey for
1977-90 , and the National Longitudinal Survey of Youth 1979 cohort). All six samples span roughly
twenty years from the report of the father’s occupation to the report of the son’s occupation. After
calculating d(P,I) for each table and calculating d(P,Q) for each pair of tables, multidimensional
scaling (Davison, 1983) can be employed to locate each table’s mobility in a two-dimensional space
relative to an arbitrarily located origin representing independence, as in Figure 1.
25 When five occupational categories are used rather than four, the greater mobility for the nineteenth
century (P) compared to the twentieth (Q) again persists: d(P,I)=26.41, d(Q,I)=31.06, d(P,Q)=18.10,probability(H : d(P,Q)=0)<0.001.
High mobility in the nineteenth century U.S. was thus not principally a consequence of the
enormous turnover in the U.S. labor force occasioned by the death of a substantial fraction of the
working-age male population in the Civil War, or of the presence of an expanding agricultural
frontier – the frontier was already “closed” by 1890, according to the U.S. Census Office.26 It is also
not the result of some peculiarity of the OCG data used for the twentieth century, as similar results
are obtained when other modern surveys are employed.27
VII. Economic Sources of Higher 19th Century Mobility in the U.S. Than in Britain and of Declining Mobility in the U.S. During the Twentieth Century
The U.S. was considerably more mobile than Britain in the nineteenth century and roughly
similar in mobility in the twentieth. At least some of this convergence occurred because of declining
mobility in the U.S. (as opposed to improved mobility in Britain). Unfortunately, the foregoing
analysis sheds little light on the sources of either the U.S. advantage in the nineteenth century or its
relative decline in mobility from the nineteenth century to the twentieth. Because the metric for the
distance in association used here focuses on odds ratios, it is not even possible to say for certain
whether the observed differences result from differences in the numerators, in the denominators, or
26 The Superintendent of the Census reported in 1890 that “Up to and including 1880 the country
had a frontier of settlement, but at present the unsettled area has been so broken into by isolated bodies ofsettlement that there can hardly be said to be a frontier line. In the discussion of its extent, its westwardmovement, etc., it can not, therefore, any longer have a place in the census reports.” (U.S. Census Office,1891).
27 In each case, the late nineteenth and early twentieth century displays mobility that is greater in
magnitude than the late twentieth century, differences that are in every case highly statistically significant. Bycontrast, differences within the twentieth century are small in magnitude and not statistically significant.
28 For example, the third contrast in Table 4 and the first in Table 6 – [(WW)/(WF)]/[(FW)/(FF)] –
is the ratio of the odds of white collar sons entering white collar jobs rather than farming to the odds of farmsons entering white collar jobs rather than farming. It is greater in nineteenth century Britain and the
Are the differences we have observed (between the mid-nineteenth century U.S. and either
mid-nineteenth century Britain or the mid-twentieth century U.S.) simply a reflection of differences
in the size of the farm sector, i.e. so many more farmers in the mid-nineteenth century U.S. and as a
result much movement out of farming and more “mobility?” The measure of mobility we have used
already adjusts for differences in the size of the occupation groups, however. If the mid-nineteenth
century U.S. farm sector is driving the results, it must be more than the difference in the sector’s
sheer size generating differences with Britain at the same time or the U.S. 100 years later. There must
Consider nineteenth century Britain versus the nineteenth century U.S.: Britain has already
seen almost all of its flight from agriculture by 1851 (Figure 2), so the sons of farmer fathers are
already selected for remaining in farming (all the sons who were more loosely attached to the sector
have already left by 1851). At the same time, the sons of non-farm fathers are already selected for
remaining outside farming (all the sons eager to enter farming have already done so). In the U.S.,
this weeding out process has not taken place in the nineteenth century, so the U.S. has more
mobility both out of and into farming that gets added onto whatever the underlying amount of
mobility would be otherwise.29 At least some of the high mobility in the nineteenth century U.S. may
then result from it being at an earlier stage of development than nineteenth century Britain or the
twentieth century U.S. than in the nineteenth century U.S. But is this because the nineteenth century U.S. has(1) greater ease for farm sons in attaining white collar jobs in the nineteenth century U.S. (FW 8) , (2) aweaker attachment to farming among farm sons (FF 9), (3) easier entry by white collar sons into farming (WF8), or (4) a weaker attachment to white collar jobs among sons of white collar workers (WW 9)? Or does itresult from some combination of these?
29 Alternatively, as a referee has pointed out, we can think not of the survival of sons as farmers but
rather of the survival of farms as the mechanism leading to some change in the “quality” of movers out offarming over time: as more farms fail or are sold off in a process of consolidation, more of the less-able farmsons are entering non-farm occupations. Of course, for the story to work for the nineteenth century versustwentieth century U.S. case, there must be no increase in the selectivity of movement out of or into farmingeven as late as 1900 when farmers as a fraction of the labor force had fallen to 20% from 45% in 1850.
twentieth century U.S., so its farm sector was relatively larger and selective exit from farming and
entry into farming were less apparent than in Britain at the same time or in the U.S. a century later.
As late as 1850, 45 percent of U.S. workers were still in farming, compared to 4 percent in Britain in
1880 and 7 percent in the U.S. in 1950.
To get at the amount of mobility after taking out the effect of selective mobility out of or
into farming, we re-ran the analyses after removing the cell Farm [father]-Farm [son] and the cells
White Collar-Farm, Skilled/Semiskilled-Farm, and Unskilled-Farm. This is preferable to leaving out
the farm sector altogether, as it still allows us to include the mobility of sons of farmers conditional
on their departure from farming. The results are
d(P,I)=12.79 (prob < 0.0001)d(Q,I)= 8.81 (prob < 0.0001)d(P,Q)=7.42 (prob < 0.009).
Even if we ignore the Farm-Farm immobility difference and ignore differences in entry into farming,
then, the differences in mobility still go in the same direction (the nineteenth century U.S. is
markedly more mobile than nineteenth century Britain). For the U.S. over time, the same is true as
well, though the remaining magnitudes are smaller:30
d(P,I)=8.00 (prob < 0.0001)d(Q,I)=8.15 (prob < 0.0001)d(P,Q)=3.35 (prob < 0.078).
30 When five occupational categories are used rather than four, the nineteenth century results for
Britain (P) and the U.S. (Q) are: d(P,I)=29.95, d(Q,I)=13.09, d(P,Q)=23.10, probability(H : d(P,Q)=0)<0.001.
For the comparison between the 1860-80 U.S. (P) and the 1973 OCG, the results are: d(P,I)=16.97,d(Q,I)=14.41, d(P,Q)=9.26, probability(H : d(P,Q)=0)<0.03.
Simple differences in the selectivity of exit from or entry into farming, in any case, cannot
explain the majority of the contrasts in Tables 4 and 6.31 Other features of the nineteenth century
U.S. economy may help explain its uniquely high rates of mobility. A useful starting point for
analyzing the economic causes of differences in mobility across times or places is the formulation of
Becker and Tomes (1986) who model intergenerational mobility as an outcome generated by the
endowments transmitted directly from parents to children, and by investments made by parents
faced with several investment opportunities and possibly constrained by the operation of capital
markets from making the efficient level of investment in their children.
As Grawe and Mulligan (2002) demonstrate, this simple model provides some testable
implications regarding spatial or temporal differences in earnings mobility.32 Ignoring capital
constraints (generated by the inability of parents to borrow against the future labor earnings of
children), intergenerational earnings mobility will be higher when the ease with which ability is
transferred to children is reduced. Han and Mulligan (2001, p. 225) show that earnings mobility is
also greater when ability displays less variance. Finally, if parents are constrained in the credit market,
they will invest less in their children, whose earnings will more closely reflect ability, reducing
31 For example, the third contrast in Table 4 does not involve farmers. The fifth contrast in Table 4
(which is also the seventh in Table 6) – [(WF)/(WS)]/[(FF)/(FS)] – can be higher in nineteenth centuryBritain and the twentieth century U.S. than in the nineteenth century U.S. because of selectivity only if exitfrom farming by farm sons exceeded entry by white collar sons into farming by a greater margin in thenineteenth century U.S. than in either nineteenth century Britain or the twentieth century U.S. If this was notthe case, differential entry into skilled and semi-skilled jobs by white collar and farm sons must also accountfor some of the greater size of this contrast for the nineteenth century U.S. To see this, re-write the contrastas [(WF)/(FF)]/[(WS)/(FS)].
32 Though these implications relate to earnings mobility, it is straightforward to map them into
occupational mobility. If there are two possible jobs and investment (by parents or the state) both raises (1)the odds that sons of job 1 fathers will get job 1 rather than job 2 and (2) the odds that sons of job 2 fatherswill get job 1 rather than job 2, but (2) rises by more than (1), the odds ratio will fall, indicating greatermobility. The only additional assumption necessary for the implications discussed by Grawe and Mulligan(2002) to apply to occupational mobility as well is that all workers qualified for job 1 can obtain job 1.
mobility. Where credit markets function well, or where wealth is greater so fewer parents find the
capital constraint binding, mobility will be greater than where credit markets do not function well, or
where most parents find themselves constrained by low wealth.
We have no direct evidence on how easily abilities were transmitted from parents to children
in the nineteenth century in Britain and the U.S. or in the twentieth century U.S. But we can suppose
that the greater heterogeneity in the origins of the U.S. population compared to the British
population in the nineteenth century corresponded to greater variance in abilities in the U.S., a force
working to undermine the U.S. advantage in occupational mobility relative to Britain at this time.
Though we cannot test directly for the role of credit market constraints in generating the advantage
enjoyed by the U.S. relative to Britain in the nineteenth century and the decline in relative mobility
by the twentieth century, it is possible to see how important such impediments to investment may
have been in generating the level of mobility seen within the nineteenth century U.S.
The 1860-80 sample provides information from the 1860 population census on the total
wealth owned by the household (the sum of real estate and personal estate). This makes is possible
to assess the role of credit constraints by examining whether mobility differs systematically by
household wealth, an indicator of the probability that a household is credit constrained. Following
Mazumder (2001), the 1860-80 sample was divided in half: high total wealth families (wealth $
median wealth=$1,400) and low total wealth families (wealth < median). Intergenerational
occupational mobility matrices were then constructed (P=high wealth, Q=low wealth), and the
underlying association between fathers’ and sons’ occupations was calculated along with the
difference in association between P and Q. For both types of households, mobility was different
from that expected under independence though slightly greater in high wealth households
(d(P,I)=12.65, d(Q,I)=13.25, while the G2 statistics for both are significant at 0.01. Of greater
interest is the difference in association between P and Q: d(P,Q)=6.14 (G2=21.2, prob=0.01),
confirming that mobility in the 1860s and 1870s was in fact greater among high wealth households
Grawe and Mulligan (2002, p. 51) suggest that “one way to investigate [the role of credit
market imperfections] is through analysis of cross-country evidence on whether countries with
greater public provision of human capital experience greater intergenerational mobility.” The U.S.
provided considerably more public education than Britain in the middle of the nineteenth century:
68.1 percent of 5-14 year olds were enrolled in primary school in the U.S. in 1850 compared to only
49.8 percent in England and Wales (Lindert, 2004, p. 92). The U.S. educational system in the second
half of the nineteenth century, though less extensive at the secondary and post-secondary levels than
European systems was considerably more egalitarian (Goldin, 1999, p. 2). To the extent that
intergenerational mobility is greater where fewer parents are constrained, superior mobility in the
U.S. may well have been a consequence of its educational system, which provided a public
alternative to a private education that was outside the reach of many families.
The importance of free, public education provides a less satisfactory explanation for the
trend in mobility over time within the U.S., though: while enrollment rates, graduation rates, and
spending have increased dramatically since the nineteenth century (Goldin, 1999, pp. 52-68),
intergenerational occupational mobility has nonetheless fallen. Though the educational requirements
to advance in occupational status (or to avoid a decline in occupational status) may have risen more
rapidly than the aggregate statistics on the provision of education, there is no evidence with which to
33 Becker and Tomes (1986, p. S31) suggest with some justification that capital constraints construed
more generally fell from the nineteenth century to the twentieth in the U.S. But this, too, runs counter to thetrend of decreasing mobility from the nineteenth century to the twentieth. The model’s prediction that larger
A potentially more promising avenue for explaining both the U.S. advantage in mobility
compared to Britain within the nineteenth century and the decline in relative U.S. mobility since the
nineteenth century is to consider characteristics of the U.S. economy that correspond to both of
these contrasts. The most obvious candidate is residential mobility. Migration can be seen as an
investment (Schultz 1961, Becker 1964). These investments made by families can then improve a
child’s chances for occupational mobility in the same way as a family’s investment in the human
capital of its children can promote mobility in the Becker and Tomes (1986) model. If a family is
credit-constrained and unable to undertake such investments, or unaware of such investment
opportunities either because of poor information or because some opportunities did not yet exist
when the child was young, the child may be able to make the investment instead, by migrating later
In Britain, 27 percent of sons were observed in different counties in 1851 and 1881, while in
the U.S. 62 percent of sons were in different counties in 1850 and 1880. Sons in the U.S. were also
more likely to cross a state boundary over these three decades than British sons were to cross a
county boundary.34 Though we lack comparable data on mobility over a span of thirty years for the
twentieth century U.S., the National Longitudinal Survey (NLS) cohorts of Older Men and Young
Men provide a comparison over ten years, the shortest span we can observe in the nineteenth
century linked files. Between 1870 and 1880, 55 percent of young (20-29 years) white, native-born
males changed county and 30 percent changed state; between 1971 and 1981, only 42 percent of
family size will be associated with lower investment per child and lower mobility (if fertility is exogenous) isanother force working against the finding of relatively greater mobility in the nineteenth century U.S. than inthe twentieth: the total fertility rate in the U.S. fell from 5.42 in 1850 to 2.98 in 1950.
34 The 52 traditional counties of England and Wales are 1,123 mi.2 in area on average; the 3,112
county units in the continental U.S. are 1,003 mi.2 in area on average.
otherwise identical males changed county, while only 22 percent changed state. Among older men
(45-59 years) the declines in both inter-county mobility (from 35 percent 1870-80 to 16 percent
1966-76) and inter-state mobility (from 22 percent 1870-80 to 8 percent 1966-76) were even more
Though mid-nineteenth century Britain was a considerably more compact economy with an
extensive transportation network, residential mobility was greater in the mid-nineteenth century U.S.
Though transportation costs fell dramatically over the century from 1870 to 1970 within in the U.S.,
residential mobility at the county and state levels fell from the 1870s to the 1970s in the U.S. These
comparisons imply that the rate of return on geographic mobility must have been greater in the U.S.
in the second half of the nineteenth century than in either late nineteenth century Britain or the late
The late nineteenth century U.S. was remarkable in an additional respect: it also probably had
a greater distribution in the returns to migration across its physical geography. One force promoting
differences in the rate of return to migration across locations was differences in the economic
activities being undertaken in different places. Using data on employment by one-digit SIC code
sectors, Kim finds that “Regional specialization in the overall economy rose through the early
nineteenth century, leveled off between the late nineteenth and the early twentieth centuries, and
then fell precipitously through most of the twentieth century.” (Kim 1998, p. 667).
These differences in the geographic concentration helped generate large differences in the
rates of growth of urban places across the country, as cities and towns arose to meet region-specific
35 The high rates of return to geographic mobility in the late nineteenth century was not a direct
result of the existence of large, internal frontier; however: (1) both intergenerational occupational mobility andgeographic mobility were as high through 1910, twenty years after the frontier’s demise; and (2) the vastmajority of internal migrants never went to the western frontier.
demand. Figure 3 shows the standard deviation in population growth rates for the largest 100 urban
places in the U.S. since 1840, with separate tabulations for all places ever in the top 100, places that
were in the top 100 for at least 5 decades, and places that were in the top 100 for at least 10 decades.
This simple measure of how differently cities were growing falls through the second half of the
nineteenth century and remains low through the end of the twentieth century.36
At the regional level, the absence of large differences in wages indicates that the U.S. labor
market, at least within the North, was well-integrated by the middle of the nineteenth century.
(Margo, 2000; Rosenbloom, 1996). There remains the possibility, however, that differences across
smaller units of geography than regions may have continued to present opportunities for “locational
arbitrage” – migrating from a place with poor prospects for occupational mobility to one with better
prospects – that could be exploited as avenues to occupational mobility through the 1930s. Higher
levels of regional specialization and the presence of more urban places growing at widely divergent
rates in the late nineteenth century U.S. may have provided greater opportunities for such locational
arbitrage than in late nineteenth century Britain or the late twentieth century U.S.37
36 Late nineteenth century Chicago is an example of an urban place that arose to provide services to
the Midwest’s growing farm sector, grew more rapidly than other U.S. cities, and emerged as a site ofextraordinary economic opportunity. From 1850 to 1870, its population grew by a factor of ten, and thengrew by nearly a factor of three from 1870 to 1890. Galenson (1991, p. 597) characterized late nineteenthcentury Chicago as “a place of unusually great economic opportunity.”
37 Though Blau and Duncan (1967, pp. 252-253) find no link between geographic mobility and
intergenerational occupational mobility other than that arising from differences in the marginal distributionsof occupations across locations, their data (from the original Occupational Changes in a Generation 1962survey), as well as that from the OCG 1973 replication, come predominantly from a period well after thedecline in regional specialization and the homogenization in urban growth rates that are suggested here tounderlie a link between geographic and occupational mobility in the late nineteenth and early twentiethcentury U.S.
Though the U.S. exhibited no more intergenerational occupational mobility in the late
twentieth century than similarly developed countries, a widely-shared belief that the U.S. is a place of
unusually easy mobility has consistently guided public policy and shaped debate regarding the
appropriate functions of the government in promoting social welfare from the 1930s to the present.
Using new longitudinal data for the nineteenth century, we have identified an era when the U.S.
mobility experience was indeed exceptional: even after controlling for differences in their
occupational structures, the U.S. had substantially more occupational mobility across generations
than either Britain in the three decades after 1850 or the modern U.S. Though it remains to be seen
exactly why nineteenth century U.S. mobility exceeded that in both nineteenth century Britain and
the twentieth century U.S., and when the transition to a lower mobility regime in the U.S. took place,
high U.S. intergenerational occupational mobility corresponded to high rates of residential mobility.
A fall in U.S. residential mobility after 1910 as economic activity across locations became more
homogenous may have reduced the ability of families and individuals to “invest through migration”
and foster occupational mobility across generations.
Appendix 1: Linked Census Data
The population censuses of Britain and the U.S. are generally regarded to be the best sources
of individual-level, nationally representative data from the nineteenth century for those countries.
However, the cross-sectional censuses do not provide the continuity over time needed to study
issues of mobility at the level of the individual. Two new sources have made it possible to create the
necessary continuity from the British and U.S. historical census records. The Genealogical Society of
Utah in conjunction with the Federation of Family History Societies has computerized the
individual-level records from the enumerators’ books of the 1881 Census of the Population of
England, Wales, and Scotland and from the 1880 U.S. Federal Population Census. These data make
it possible to search for specific individuals in the 1881 British or 1880 U.S. census. To construct the
data for this study, we searched for individuals from two other censuses: the 1851 British and the
For Britain, we attempted to match all the English and Welsh born males age 25 and below
from the computerized two percent sample of the 1851 census compiled principally by Anderson,
Collins, and Stott. For the U.S. we attempted to match white males age 25 and below from the 1850
Federal Census one percent public use sample.38 We employed a common matching technique for
the British and U.S. data. Both countries’ censuses provide information that either remains
consistent between enumerations (name and birthplace) or changes predictably (age) that can be
used to identify a given individual in more than one census. The British census has more specific
38 The 1851 data for Britain are from a 2% Public Use Sample available as Study No. 1316 from the
U.K. Data Archive at the University of Essex (http://www.dataarchive.ac.uk). It is a stratified two percentsystematic cluster sample from the enumerators’ books. For a full description see Anderson (1987). Thecomplete 1881 census for Britain was obtained as Study No. 3643 from the U.K. Data Archive. The 1880U.S. file was obtained from the North American Population Project (http://www.nappdata.org) and the 1850U.S. 1% Public Use Sample was obtained from the Integrated Public Use Microdata Series available from theMinnesota Population Center (http://www.ipums.org).
information than the U.S. census on each individual’s birthplace (parish in Britain, state in the U.S.).
In the 1880 U.S. census, respondents were asked to give the place of birth of their parents as well
(state for those whose parents were born in the U.S. and country for those whose parents were born
abroad). This question was missing entirely from the nineteenth century British census.
For Britain, in order to be considered a true match for an individual from 1851, an individual
from 1881 had to have either the same name or a close phonetic variation thereof (for example,
Aitken and Aitkin were considered to be equivalent), a year of birth different by no more than five
years, and the same county and parish of birth. For the U.S., the individual must provide the same
state of birth for himself (and his parents if they were present in 1850) in 1850 and 1880, and the
year of birth could differ by no more than three years. The variation in birth year was allowed in
order to account for age misreporting, a fairly common phenomenon in nineteenth century societies
which lacked the systematic record keeping and where individuals often had only an approximate
idea of their age.39 None of the matching information could be missing from an individual’s record.
Also, only unique matches were considered: if an individual from the 1850/51 sample had more
than one match in the 1880/81 census, then that individual was dropped.40
Applying this matching process to 69,785 English and Welsh males age 25 and under from
the 1851 two percent sample yielded 14,191 men observed in Britain both in 1851 and 1881, a
success rate of 20%. From a pool of 43,438 U.S. white males age 25 and under in 1850, 9,497 were
found in the 1880 U.S. census, a 22 percent success rate. The inability to link every observation from
the initial public use sample (1850 for the U.S. and 1851 for Britain) is a function of mortality (and
39 The smaller margin of age reporting error for the U.S. matching process is in response to the less
specific birthplace information. For a discussion of age enumeration in the Victorian census, see Higgs (1986).
40 The same procedure created the 1860-80, 1880-1900, and 1870-80 linked U.S. samples.
out-migration from Britain) over the following thirty years, under-enumeration in the terminal
census (1880 for the U.S. and 1881 for Britain), and the inaccurate recording in either the initial or
terminal year by the census takers or by those who performed the census transcriptions of the
characteristics on which the linkage is based: name, year of birth, and birthplace (for the individual
as well as his parents in the U.S. and for the individual only in Britain).41
For the U.S., 69 percent of white, native-born males under age 25 survived from 1850 to
1880 (based on the survival of five-year age cohorts in the IPUMS 1850 and 1880 samples); for
Britain, 67 percent of males both survived from 1851 to 1881 and remained in Britain (based on
published population-by-age tables in Mitchell, 1962, p. 12). Estimates of under-enumeration for the
nineteenth century U.S. range from as high as 22% (Adams and Kasakoff, 1991) to as low as 9%
(Hacker, 2000). Though we lack estimates of the extent of mis-reporting for names, birth years, and
birth places, if we take the error in each of these to be 5 to 10 percent and assume for simplicity that
all of the factors preventing linkage occur independently, we can calculate a set of projected linkage
rates ranging from optimistic to pessimistic.42 For the U.S., the anticipated linkage rate ranges from
(0.69)(0.91)(0.95)10=37.6% (“optimistic) to (0.69)(0.78)(0.90)10=18.8% (“pessimistic”).43
The actual linkage rate for the U.S. is safely within this range, even without taking account of
the fraction of individuals who could not be uniquely matched (e.g. they were matched to more than
41 Steckel (1991) surveys research on the accuracy of nineteenth century U.S. population censuses.
42 One of the few studies to report an estimate of mis-reporting for a characteristic contained in the
U.S. population census for the nineteenth century is Knights (1971): he reports that 11 percent of thoselocated in Boston in both 1850 and 1860 reported a year of birth (inferred from age at the census) thatdiffered by five or more years between the two censuses. Steckel (1988) found that literacy was inconsistentlyclassified for seven percent of household heads located in both 1850 and 1860.
43 There are five characteristics that must be reported correctly (name, birth year, own birth place,
father’s birth place, and mother’s birthplace) in each of two censuses, so the proportion with correctlyreported characteristics is between (0.95)10 (if each is reported with error 5% of the time) and (0.90)10 (if eachis reported with error 10% of the time).
one individual in the 1880 census, and it was not possible to identify the best match). In 1880, 1.5
percent of white, native-born males shared the same name, birth year, birth place, and parents’
birthplaces with at least one other individual, while 80.5% were uniquely identified by this set of
characteristics. For the remaining 18%, there were several individuals who had names that were
phonetically close and birth years that were within three years, but when an individual from the 1850
pubic use sample was matched to one of these individuals, it was possible in these cases to rank the
matches by the proximity of the name and birth year, and choose the “best” match.
We lack estimates of under-enumeration and mis-reporting in the nineteenth century British
censuses, though we know that the combined effects of mortality and net migration were slightly
higher over the 1851-81 period than in Britain (only 67 percent of males age 25 and under present in
1851 would have still been present in Britain in 1881). At the same time, there was less variety in the
distribution of surnames in Britain than in the U.S., so a larger fraction of potential matches (six
percent) had to be discarded because a unique match could not be made. Using plausible
assumptions for the under-enumeration and mis-reporting and for the probability of multiple
matches, the British linkage rate can be shown to lie within the range of expected linkage rates.
The linkage for both the U.S. and Britain excluded those individuals who were linked from
the initial census to more than one individual in the terminal census. In some cases, this discards
potentially useful information. For example, if an individual whose father’s occupation was observed
in the 1850 U.S. public use sample was then linked to two individuals in the 1880 census, but both
of those individuals had the same 1880 occupation, inclusion of either potential match, or a linear
combination of them, would add the same information to a mobility table comparing the
occupations of father and sons. We nonetheless excluded such individuals for two reasons: (1) their
inclusion would induce a bias in favor of more common father-son occupation pairs; and (2) in
some parts of the analysis (e.g. residential mobility, occupational mobility related to family wealth),
the particular linkage made is more consequential than in the simple mobility calculations.
For each country, the data come from two nationally representative sources, so as long as the
matching process does not skew the sample, the set of matched individuals should also be
representative of the two national populations that survived 1850-80 and 1851-81. In order to assess
the representativeness of the linked samples, we compared their characteristics to those in the public
use samples for the initial year (1850 or 1851) and terminal year (1880 or 1881). Tables A-1 and A-2
present marginal effects from probit regressions in which the dependent variable is 1 for
observations from the linked sample and 0 for observations from the public use sample.44
In general, the matched samples represent the overall population quite well. Though several
characteristics exert a statistically significant influence on the probability of linkage, compared to the
predicted probability the magnitude is small in each case.45 In order to reduce the impact of these
already small differences between the linked samples and the general population, we constructed
weights to produce linked samples that would duplicate the marginal frequencies of the
characteristics in the general population. (Deming and Stephan, 1940) Two sets of weights were
generated, one for the initial year and one for the terminal year. In Columns (2) and (4) of Tables
A1-1 and A1-2, the weights are imposed on the linked individuals, leaving them statistically
44 Each linked individual thus enters the regression twice: once in the linked sample and once in the
public use sample. This is done to facilitate comparison with the regressions in Columns (2) and (4) of eachtable in which weights are imposed to make the linked individuals nationally-representative (rather thanmerely indistinguishable from the unlinked). For the British, 8,655 individuals in the public use sample for1851 were missing one or more of the characteristics used in the probit analysis and were dropped from theregressions in Columns (1) and (2) of Table A-2. For the comparisons with 1880 and 1881, 25 percentrandom samples of the complete files for those years were used rather than the complete files.
45 The large coefficients on the migration history variables in Column (3) of Table A-2 result from
the inability to identify the year of arrival in the U.S. for immigrants present in the U.S. in 1880 (the excludedcategory in the regression).
indistinguishable from the general population. Though we have used the unweighted data
throughout this paper, the results are insensitive to the imposition of these weights. The weighting
can eliminate the impact of linkage selectivity on observable characteristics; it cannot, however,
eliminate the impact of unobservables on the linkage probability.
A final concern is whether the linkage process has resulted in too many “false positives”
(individuals who are not in fact the same person in both the initial and terminal years). For the
comparison between the U.S. and Britain in the nineteenth century, this is a difficulty if the sample
for one country has more false positives than the sample for the other. For example, more false
positives in the U.S. than in Britain will generate more “noise” in comparing the occupations of
fathers and sons, and lead to a spurious finding of greater occupational mobility in the U.S. than in
Britain. For the comparison over time within the U.S., it is also a problem, because the data for the
twentieth century were constructed in a way that prevented such incorrect matches (the respondent
in the OCG was asked himself to state the occupation of his father when the respondent was 16
years of age). Greater “noise” in the nineteenth century U.S. data would also produce a spurious
finding of greater mobility in the nineteenth century U.S. than in the twentieth.
The comparison between mobility in Britain 1851-81 and in the U.S. 1850-80 was performed
again, but this time with the samples restricted to those whose surnames matched exactly and whose
age was off by no more than one year. Though this will not entirely eliminate false positives, it will
reduce their prevalence, so if the difference between Britain and the U.S. in the nineteenth century
persists, we can have greater confidence that this finding is not being driven by differences in the
prevalence of false positives. The results were quite similar to those shown in the second panel of
d(P,I)=24.50 (prob < 0.0001)d(Q,I)= 14.22 (prob < 0.0001)d(P,Q)=15.22 (prob < 0.0001)
Though mobility in the U.S. with the more restricted sample is slightly farther from what we would
observe if the occupations of fathers and sons were independent, the difference between mobility in
the U.S. and in Britain is actually slightly greater. When the 1880-1900 U.S. sample is restricted to
those whose surname matched exactly and whose age was off by no more than a year, the nineteenth
century U.S. remained substantially more mobile than the twentieth century though the magnitude
of the difference is reduced. We again can reject the null hypothesis that the association between the
occupations of fathers and sons was identical in these two eras:
d(P,I)=15.90 (prob < 0.0001)d(Q,I)=20.76 (prob < 0.0001)d(P,Q)=6.94 (prob < 0.005). Appendix 2: Log-Linear Analysis
Xie (1992) is the standard reference for differences in mobility across tables calculated using
conventional log-linear analysis. The “log-multiplicative layer effect” is an estimate, for each “layer”
in a contingency table (in the present context, a table is comprised of rows for sons’ occupations,
columns for fathers’ occupations, and layers for countries or time periods), of the amount by which
the row-column association in a layer must be multiplied to obtain the average row-column
association across the entire table.
In order to test the robustness of our comparative mobility results to alternative log-linear
analytical methods, we calculate and compare “Xie statistics” for four of our main mobility
Xie (1992, pp. 384-387), using the OCG data for the U.S. and the Oxford Mobility Study
multiplicative layer effects for the off-diagonal cells) if no ordering is imposed on the occupational
categories, so the row-column association is similar in the U.S. and Britain, but 20 to 23 percent
lower in Japan. In a comparison of mobility for Britain, France and Sweden (p. 389), he finds NBritain
=0.4676. If we use the four-way classification of occupations in
Table 1, impose no ordering on the categories, and calculate Xie’s N using all the cells in P and Q,
=0.7783 and N =0.6279. Xie provides no test for the statistical significance of the
, but bootstrapped standard errors yield probability (H : N
0.001. For the five-way occupational breakdown (which splits white collar into high and low subgroups), the
=0.8937 and N =0.4487, a difference that is statistically significant at
any conventional level (bootstrapped standard errors with 1,000 replications). The magnitude of the
difference is three times greater in absolute terms than that in the twentieth century (0.4450 compared to
0.1504) and four times greater as a percentage of the U.S. figure (100% compared to 24%). If we split white
collar into high and low white collar groups, the N for this comparison are N
which is again substantially greater than the corresponding N with five categories for the twentieth century.
The log-multiplicative layer effect model confirms greater mobility in the 1860-80 period than in the 1973
OCG, whether four or five categories are used. For four categories: N
Again, the log-multiplicative layer effect model confirms greater mobility in the 1880-1900 period than in the
1973 OCG, whether four or five categories are used. For four categories: N
Appendix 3: Expanded Occupational Categories For online publication only
The following tables provide the raw frequency counts for all of the 5 × 5 and 6 × 6 contingency
tables, which can be collapsed down to 4 × 4 tables like those shown in the text by combining high
and low white collar or skilled and semi-skilled. The Xie statistic was calculated using the “unidiff”
macro in STATA, with a modification to return the N , N , and N -N as scalars that could then be
bootstrapped (the modified “unidiff” macro is available on request, together with the short program
that does the bootstrapping, again using the frequencies in Table 3 that generated the results
reported in footnote 27). The entries in Tables 4 and 6 were generated by repeated calculation of the
Altham statistic for each odds ratio in Tables P and Q. Finally, this appendix provides a version of
Table 1 from the text which imposes each country’s marginal frequencies on the other country.
1. Raw 5 × 5 and 6 × 6 contingency tables:
2. British and U.S. Mobility in the Twentieth Century With Each Country’s Marginal FrequenciesReplaced By Those From the Other Country
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FOREST LAKE AREA SCHOOLS Superintendent.Dr. Linda M. Madsen September 1, 2009 To District Families: The following important information regarding the upcoming flu season, including issues related to the H1N1 virus, is from the Minnesota Department of Health (MDH): During the coming school year, more people than usual in our schools and communities are likely to be getting sick