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Journal ArticleDOI

Intergenerational Persistence in Income and Social Class: The Impact of Within-Group Inequality

TL;DR: In this article, the authors derive a formal framework which relates mobility as measured by family income or earnings to mobility as defined by social class and test several alternative hypotheses to explain the difference between the trends.
Abstract: Family income is found to be more closely related to sons' earnings for a cohort born in 1970 compared with a cohort born in 1958. This result is in stark contrast with the finding on the basis of social class; intergenerational mobility for this outcome is found to be unchanged. Our aim here is to explore the reason for this divergence. We derive a formal framework which relates mobility as measured by family income or earnings to mobility as measured by social class. Building on this framework we then test several alternative hypotheses to explain the difference between the trends. We find evidence of an increase in the intergenerational persistence of the permanent component of income that is unrelated to social class. We reject the hypothesis that the observed decline in income mobility is a consequence of the poor measurement of permanent family income in the 1958 cohort.

Summary (4 min read)

1. Introduction

  • For both of these comparisons the findings of economists and sociologists contrast sharply for the UK.
  • The view the authors adopt here is that both approaches are trying to assess long-term or permanent socio-economic status but measure it in different ways.

2.1 The components of income

  • Here the authors set out a framework which demonstrates the relationships between permanent family income, income at a point in time and fathers' social class.
  • Note that the authors are considering an asymmetric relationship, relating combined parental income to the sons' own earnings.
  • The correlation between the error and permanent income would lead to downward bias in the estimate of intergenerational income mobility (  ).
  • In their data this downward bias is more likely to be greater in the later cohort (BCS) than the earlier cohort (NCDS) as earnings are measured in the BCS at age 30, compared to age 33 in the earlier cohort.
  • In the lifetime mobility context, where this type of error appears on both sides of the equation, a consequence of this mean reversion is that mobility is understated due to the correlation in errors within individuals.

2.2 Applying the framework to the BHPS

  • The cohort datasets only have comparable information on current parental income at age 16 meaning that the authors cannot directly measure permanent parental income in this data.
  • The authors can, however, estimate permanent income in the British Household Panel Study (BHPS).
  • Alongside income, the BHPS includes information on fathers' social class and so the authors are able to predict the relationship between social class and income ( ˆpf SC  ) from both (3) and (5) using both permanent childhood income and current income.
  • The authors aim is to assess the difference in the share of the variance of permanent and current income that these measures capture to see if the components of current income are good proxies for permanent childhood income and its components.
  • There remains a large residual permanent component of income which forms a substantial part of residual current income (that is, income which is orthogonal to social class and their other explanatory variables).

3.1 Data

  • For the headline results on intergenerational mobility, both sociologists and economists have utilised the two publicly accessible mature British cohort studies: the British Cohort Study (BCS) of those born in 1970 and the National Child Development Study (NCDS) of those born in 1958.
  • In the NCDS parents were asked to place the father's earnings, the mother's earnings and other income into one of twelve categories.
  • The authors continue with the measures used in the original papers to keep the analysis consistent with Goldthorpe and Jackson (2007) .
  • The authors use these to address the issue of measurement error directly.

3.2 Measures of Intergenerational Mobility using Income and Class

  • Table 2 provides the headline results from the examination of intergenerational income mobility using the regression approach.
  • Likewise, relative social class mobility can also be summarised from transition matrices (see working paper, Blanden et al. (2011) : tables 3 and 4 for full transition matrices and a discussion of absolute mobility.
  • In Erikson and Goldthorpe (2010) much is made of the stronger association across generations in social class compared to income.
  • Their method for a direct comparison between the two is based on comparing income quintiles to a collapsed five rather than seven social class schema.
  • This still does not provide the relevant comparison.

3.3 Samples

  • Before digging deeper the authors must first check if differences in samples can explain the divergent results.
  • The cross-tabulations for income and social class the authors have seen so far are not based on the same sample, and this alone could generate differences in the estimated trends.
  • There is no evidence, however, that restricting the sample has affected the trend in intergenerational mobility by social class.
  • As has already been mentioned in section 3.1, the samples available for both analyses are substantially smaller than the initial samples of around 9,000 male cohort members.
  • Even though the authors have shown that the difference in samples is not responsible for the different trends in mobility, attrition and item non-response could nonetheless be leading to a misleading perception of the change in mobility.

3.4 Data Quality

  • As shown above in Section 2.1 classical measurement error in parental income will lead to attenuation in their parameters of interest.
  • The structure of the parental income questions is different between the cohorts; this could be a source of differential error.
  • In the BCS just one total band is provided.
  • Further investigation of the data, its original form and quality, is included in the corresponding discussion paper (Blanden, Gregg and Macmillan, 2011) , but is omitted here for reasons of brevity.
  • This is in line with Grawe's (2004) study who finds no evidence of income misreporting in the NCDS due to the reduced working week.

4. Alternative Hypotheses

  • The authors return to the income components identified in Section 2 and show that the intergenerational income relationship can be decomposed into the intergenerational relationships between these components.
  • This framework enables us to generate a number of hypotheses which could explain the difference between the trends in income and social class mobility.
  • The estimated decompositions reported in Sections 4.2 and 4.3 will enable us to comment on the plausibility of the different hypotheses.

4.1 Expanding the Framework: A Decomposition Approach

  • The measure of income mobility the authors use in the cohorts is the association between the current earnings of sons in their thirties and their parental income at age 16.
  • By expanding the co-variances as suggested in equation ( 12) and scaling them by the denominator of equation ( 11) the authors can decompose r into four components: the intergenerational correlation of incomes associated with social class, the intergenerational association of residual incomes and their cross-correlations.
  • What is important is that predicted income will be uncorrelated with random error, implying that if the elements in the middle row of equation ( 15) are higher in the BCS, the divergence in the income and social class is not driven by pure measurement error in parental income.
  • To test this hypothesis, the authors can expand their residual income term further to incorporate the transitory element of income.
  • There is a greater degree of measurement error in the first cohort, the NCDS, which leads to larger attenuation bias understating intergenerational persistence in the cohort.

4.2 Decomposing Persistence by the Components of Income

  • The first explanation for the differences in results for trends in social class and income mobility is that the association between p fi SC Table 4 also allows us to explore the relationship between fathers' income associated with social class and sons' residual earnings.
  • Combined, the results show that the larger part of the difference in the results between income and social class must be generated by the relationship between sons' earnings and the other elements of parental income.
  • Table 5 summarises the relationship between current income and the available Xs in the BHPS and in the cohorts.
  • This contradicts the hypothesis of differential data quality.

4.3 The Role of Transitory Income

  • There are three points that need to be made about this evidence.
  • To assess this, the authors divide their predicting characteristics into two groups.
  • The authors also include in the permanent group any timevarying factors which are measured in the cohorts before age 16 when income is measured, as their predictive power must come from their correlation with long-term differences in living standards.
  • Table 8 repeats the decomposition, separating out the influence of predicted transitory income as described by equation ( 18).
  • The results from this exercise indicate that transitory income is unlikely to be driving the difference in results, although as expected the transitory component is correlated with sons' earnings, and this association increases slightly across the cohorts.

5. Discussion and Conclusion

  • This paper extends a framework first set out by Björklund and Jäntti (2000) to model the link between social class and income measures of intergenerational mobility.
  • Hence the hypothesis of differential measurement error is rejected.
  • It is possible that the relationship between fathers' social class and family income has changed, perhaps owing to changes in the importance of mothers' earnings for family income.
  • It seems plausible that the divergence of trends in intergenerational mobility for income and social class in the UK is related to the growth in within-class income inequality over the same period.
  • Share of increase in persistence across cohorts from increased persistence in part of income associated with other income components = 0.126-0.074 = 0.052 (46% of total 0.114 increase) 34 3. Transitory income is calculated as the deviation of current income in the last observed period from average income across all observed periods.

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1
Intergenerational Persistence in Income and Social Class:
The Impact of Within-Group Inequality
Jo Blanden*, Paul Gregg** and Lindsey Macmillan**
March 2012
* Department of Economics, University of Surrey and Centre for Economic
Performance, London School of Economics
** Department of Economics, University of Bristol and Centre for Market and
Public Organisation, University of Bristol
Abstract
Family income is found to be more closely related to sons’ earnings for a cohort born in 1970
compared to one born in 1958. This result is in stark contrast to the finding on the basis of
social class; intergenerational mobility for this outcome is found to be unchanged. Our aim
here is to explore the reason for this divergence. We derive a formal framework which relates
mobility as measured by family income/earnings to mobility as measured by social class.
Building on this framework we then test a number of alternative hypotheses to explain the
difference between the trends. We find evidence of an increase in the intergenerational
persistence of the permanent component of income that is unrelated to social class. We reject
the hypothesis that the observed decline in income mobility is a consequence of the poor
measurement of permanent family income in the 1958 cohort.
JEL codes: J13, J31, Z13
Keywords: Intergenerational income mobility, social class fluidity, income inequality.
Acknowledgements:
We would like to thank Anders Björklund, Stephen Machin, Sandra McNally, Elizabeth
Washbrook, Christian Dustmann, Patrick Sturgis, Robert Erikson and John Goldthorpe for
their helpful comments. We also appreciate the comments of the editors and referees who
have helped to substantially improve the paper.

2
1. Introduction
Both economists and sociologists measure the intergenerational persistence of socio-
economic status, with economists tending to use income or earnings as the measure of status
(for surveys see Solon, 1999, Black and Devereux, 2010) while sociologists use fathers’
social class (Erikson and Goldthorpe, 1992) or an index of occupational status (Blau and
Duncan, 1967). To ascertain whether the measured extent of mobility is high or low, both
literatures have asked: i) how does mobility compare across nations? ii) has mobility
increased or decreased across time? For both of these comparisons the findings of economists
and sociologists contrast sharply for the UK.
International comparisons of income mobility place the UK as a country with low
mobility (Corak, 2006) whereas those using the measure of social class/occupational status
tend to rank it closer to the middle (Erikson and Goldthorpe 1992, Breen, 2004). Cross-
country rankings across the two approaches are very weakly correlated with each other
(Blanden, 2011). Similar ambiguity exists when comparing trends in intergenerational
mobility across time. Blanden, Goodman, Gregg and Machin (2004) find that
intergenerational income mobility decreases for a cohort born in 1970 (British Cohort Study)
compared to a cohort born in 1958 (National Child Development Study) while Goldthorpe
and Jackson (2007) find no change in social class mobility for the same datasets. Our aim in
this research is to analyse the factors responsible for the difference in the measured trends in
mobility. Our interest in trends is driven, in part, by wide acceptance of the finding of falling
mobility among politicians and commentators and its contribution to the sense that Britain
has a ‘mobility problem’ (Goldthorpe and Jackson, 2007, Blanden, 2010 and Saunders,
2010). It is therefore crucial to examine the robustness of this result given the contrary results
emanating from the literature that uses social class as the relevant measure.
In addition, we aim to draw out the conceptual links between mobility as measured by
economists and sociologists and therefore offer a fresh perspective on both literatures. The
divergent results may simply reflect underlying conceptual differences. Economists are
aiming to measure economic resources whereas class reflects workplace autonomy and
broader social capital (Goldthorpe, 2000). However, the view we adopt here is that both
approaches are trying to assess long-term or permanent socio-economic status but measure it
in different ways. In principle there are advantages and disadvantages to both measurement
approaches. Erikson and Goldthorpe use a seven-category class schema, and might therefore
only capture a limited amount of the potential variation in permanent economic status
between families (see critiques by Grusky and Weeden 2001 and McIntosh and Munk 2009).

3
In addition, mobility measures based on fathers’ social class or fathers’ earnings will ignore
the contribution of mothers. Recently economists have moved to using measures of parental
income in the first generation to account for this increasingly important contribution (Lee and
Solon, 2009, Aaronson and Mazumder, 2008). However, social class measures are sometimes
argued to be better at measuring the most important aspects of the permanent status of the
family (see Goldthorpe and McKnight, 2006). A particular difficulty with the income data
that we use from the cohort studies is that it is measured based on a single interview where
families are asked about their current income. Erikson and Goldthorpe (2010) and Saunders
(2010) suggest that social class is a more reliable measure than current income and that the
differing results between the two approaches are explicable by the poor measurement of
family income in the 1958 cohort.
We begin our analysis by formulating a framework to examine the relationship
between permanent income, social class and current income. This framework is then explored
empirically using the British Household Panel Survey (BHPS). We find that there is a
substantial portion of permanent income which is unrelated to social class. Conceptually, this
component can account for the divergent results. Section 3 of the paper outlines the main
results concerning the trend in mobility over the British cohorts using both economic and
sociological methodologies and addresses the main issues concerning data and measurement.
We focus on a number of specific measurement issues in the National Child Development
Study (NCDS) which might explain our result that income mobility is greater in the earlier
cohort compared with the later British Cohort Study (BCS). We find no evidence to support
the hypothesis that data quality or differential measurement is generating the observed
decline in mobility.
In Section 4 we detail other potential mechanisms that could generate different trends
in measured income and social class mobility. To do this we show that current income can be
decomposed into a number of different components. As mentioned above, the permanent
component can be split into the part associated with social class, and the residual part, which
we refer to as within-class permanent income. In addition current measured income will
include transitory error (the difference between current and permanent income) and finally
any mismeasurement. We then establish four alternative testable hypotheses that could
account for the diverging trends in mobility. In brief they are as follows: (1) the link between
fathers social class and family income within generations has changed, perhaps due to the
increasing role of women in accounting for family socio-economic position; (2) the

4
divergence is due to differential measurement error across the cohorts; (3) within-class
permanent income has become more important in determining children’s outcomes; and (4)
differences can be explained by a decline in the transitory component of parental income.
We find no evidence that a change in the mapping from father’s social class to income
affects our results; instead we find that a substantial part of the increased persistence across
generations can be predicted by observable short and long-run income proxies. Indeed, it is
possible to plausibly account for the full rise in income persistence through the increased
persistence of within-class permanent income. This is fully consistent with the data
examination which finds no evidence that the differential results could be explained by
measurement problems. In summary, it appears that explanation (3) above, is the most likely.
2. Measuring permanent income
2.1 The components of income
Here we set out a framework which demonstrates the relationships between permanent family
income, income at a point in time and fathers’ social class. This provides clear foundations
for our examination of the reasons behind the divergent results regarding intergenerational
mobility as measured by income or social class.
For economists, the intergenerational relationship of interest is the relationship
between parents’ permanent income and the child’s permanent income. y* represents the log
of permanent income with subscripts p and s referring to the parents and child
(son).Intergenerational mobility can be summarised by
ˆ
,
the estimate of the coefficient
from the following equation:
**
si pi i
y y u

(1)
The focus on sons here simplifies the analysis so that we are focusing on male social class in
both generations and to reduce the issues resulting from endogenous labour market
participation (a lot more important for women). Note that we are considering an asymmetric
relationship, relating combined parental income to the sons’ own earnings. We take care to
reflect this asymmetry in the rest of the paper and we explicitly consider the role of mothers
earnings as part of our first hypothesis in Section 4 below.
The intergenerational correlation, r, is also of interest in cross-cohort studies as this
adjusts
for any changes in variance that occur across cohorts.
ˆ
r
is calculated by adjusting
ˆ
by the sample standard deviations of parental income and child’s income. Björklund and

5
Jäntti (2009) urge the more widespread use of this statistic when making international
comparisons of mobility and the same arguments apply when considering trends over time.
)
ˆ
(
)
ˆ
(
ˆ
ˆ
*
*
s
p
y
y
r
(2)
Following Björklund and Jäntti (2000), permanent parental income can be
decomposed into the part that is associated with fathers social class (in our exposition social
class is denoted by a continuous variable
fi
SC
, but categorical variables are used in our
analysis; the subscript f represents father) and
.
p
v
is the parentspermanent income that is
uncorrelated with fathers’ social class.
*
pi p fi pi
y SC v

(3)
p
will reflect the relationships with fatherssocial class and of all the different components
which make up total income: fathers and mothers earnings and unearned income. This is a
point we shall return to later. The child’s permanent income can also be split into similar
components: the part that is related to the child’s own class and the part that is independent of
this.
*
si s si si
y SC v

(4)
Unfortunately, permanent income is generally not available for intergenerational research
(see Solon, 1992 for the first discussion of resulting biases) and the British cohort studies
suffer from this limitation. Measured current parental income is permanent income plus the
deviation between current measured income and permanent income (
pi
e
). Later in the
analysis we will explore the components that make up this term, but for now we consider it to
be anything which leads to a difference between measured and permanent income. Measures
of current income are related to these components as follows:
pipifippi
evSCy
(5)
sisisissi
evSCy
(6)
Under classical measurement error assumptions that the level of measured
i
y
is uncorrelated
with the size of the total error and that errors are uncorrelated across generations it is
straightforward to show that any error in measuring parental permanent income will lead to a

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References
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TL;DR: The American Occupational Structure is renowned for its pioneering methods of statistical analysis as well as for its far-reaching conclusions about social stratification and occupational mobility in the United States.

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"Intergenerational Persistence in In..." refers background in this paper

  • ...…of socio-economic status, with economists tending to use income or earnings as the measure of status (for surveys see Solon (1999) and Black and Devereux (2011)) whereas sociologists use fathers’ social class (Erikson and Goldthorpe, 1992) or an index of occupational status (Blau and Duncan, 1967)....

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TL;DR: A study of social mobility within the developing class structures of modern industrial societies based on a unique data-set constructed by John Goldthorpe and Robert Erikson is presented in this paper.
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"Intergenerational Persistence in In..." refers background in this paper

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    [...]

  • ...…and the part that is independent of this, yÅsi = δs SCsi +vsi: .4/ Unfortunately, permanent income is generally not available for intergenerational research (see Solon (1992) for the first discussion of resulting biases) and the cohort studies carried out in Britain suffer from this limitation....

    [...]

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TL;DR: While standard methods will not eliminate the bias when measurement errors are not classical, one can often use them to obtain bounds on this bias, and it is argued that validation studies allow us to assess the magnitude of measurement errors in survey data, and the validity of the classical assumption.
Abstract: Economists have devoted increasing attention to the magnitude and consequences of measurement error in their data. Most discussions of measurement error are based on the “classical” assumption that errors in measuring a particular variable are uncorrelated with the true value of that variable, the true values of other variables in the model, and any errors in measuring those variables. In this survey, we focus on both the importance of measurement error in standard survey-based economic variables and on the validity of the classical assumption. We begin by summarizing the literature on biases due to measurement error, contrasting the classical assumption and the more general case. We then argue that, while standard methods will not eliminate the bias when measurement errors are not classical, one can often use them to obtain bounds on this bias. Validation studies allow us to assess the magnitude of measurement errors in survey data, and the validity of the classical assumption. In principle, they provide an alternative strategy for reducing or eliminating the bias due to measurement error. We then turn to the work of social psychologists and survey methodologists which identifies the conditions under which measurement error is likely to be important. While there are some important general findings on errors in measuring recall of discrete events, there is less direct guidance on continuous variables such as hourly wages or annual earnings. Finally, we attempt to summarize the validation literature on specific variables: annual earnings, hourly wages, transfer income, assets, hours worked, unemployment, job characteristics like industry, occupation, and union status, health status, health expenditures, and education. In addition to the magnitude of the errors, we also focus on the validity of the classical assumption. Quite often, we find evidence that errors are negatively correlated with true values. The usefulness of validation data in telling us about errors in survey measures can be enhanced if validation data is collected for a random portion of major surveys (rather than, as is usually the case, for a separate convenience sample for which validation data could be obtained relatively easily); if users are more actively involved in the design of validation studies; and if micro data from validation studies can be shared with researchers not involved in the original data collection.

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"Intergenerational Persistence in In..." refers background in this paper

  • ...As found by Bound et al. (2001) mean reversion is common when reporting income, with those of higher income tending to under-report (negative errors) and with positive errors showing up among those with lower incomes....

    [...]

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    [...]