Intergenerational Persistence in Income and Social Class: The Impact of Within-Group Inequality. Jo Blanden, Paul Gregg and Lindsey Macmillan

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1 THE CENTRE FOR MARKET AND PUBLIC ORGANISATION Intergenerational Persistence in Income and Social Class: The Imact of Within-Grou Inequality Jo Blanden, Paul Gregg and Lindsey Macmillan March 2010 Working Paer No. 10/230 (Udate of Working Paer No. 08/195) Centre for Market and Public Organisation Bristol Institute of Public Affairs University of Bristol 2 Priory Road Bristol BS8 1TX htt:// Tel: (0117) Fax: (0117) cmo-office@bristol.ac.uk The Centre for Market and Public Organisation (CMPO) is a leading research centre, combining exertise in economics, geograhy and law. Our objective is to study the intersection between the ublic and rivate sectors of the economy, and in articular to understand the right way to organise and deliver ublic services. The Centre aims to develo research, contribute to the ublic debate and inform olicy-making. CMPO, now an ESRC Research Centre was established in 1998 with two large grants from The Leverhulme Trust. In 2004 we were awarded ESRC Research Centre status, and CMPO now combines core funding from both the ESRC and the Trust. ISSN X

2 CMPO Working Paer Series No. 10/230 Intergenerational Persistence in Income and Social Class: The Imact of Within-Grou Inequality Jo Blanden 1, 2, Paul Gregg 3, 4 and Lindsey Macmillan 3, 4, 5 1 Deartment of Economics, University of Surrey 2 Centre for Economic Performance, London School of Economics 3 Deartment of Economics, University of Bristol 4 Centre for Market and Public Organisation, University of Bristol 5 Kennedy School of Government, Harvard University March 2010 (Udated Version of Working Paer 08/195) Abstract Family income is found to be more closely related to sons earnings for a cohort born in 1970 comared to one born in 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. We set u a formal framework which relates mobility in measured family income/earnings to mobility in social class. Building on this framework we then test a number of hyotheses to exlain the difference between the trends. We reject Erikson and Goldthore s (2009) assertion that the divergent results are driven by the oorer measure of ermanent family income in the 1958 cohort. Instead we find evidence of an increase in the intergenerational ersistence of the ermanent comonent of income that is unrelated to social class. Keywords: Intergenerational mobility, Earnings, social class JEL Classification: J62, I2, D31 Electronic version: Acknowledgements We would like to thank Anders Björklund, Stehen Machin, Sandra McNally, Elizabeth Washbrook, Christian Dustmann, Patrick Sturgis, Robert Erikson and John Goldthore for helful comments. Address for Corresondence CMPO, Bristol Institute of Public Affairs University of Bristol 2 Priory Road Bristol BS8 1TX P.gregg@bristol.ac.uk CMPO is jointly funded by the Leverhulme Trust and the ESRC

3 1. Introduction Intergenerational ersistence is the link between arents socio-economic status and their children s socio-economic osition in adulthood. Both economists and sociologists measure intergenerational links, with the first grou of researchers tending to use income or earnings as the main measure of status (Solon, 1999) while the second use social class (Erikson and Goldthore, 1992) or an index of occuational status (Blau and Duncan, 1967). Both literatures face a roblem of interretation; it is imlicit that the intergenerational association should not be too strong, but how strong is too strong? To cast light on this roblem researchers make comarisons and ask the following questions: i) how does mobility comare across nations; ii) whether mobility is increasing or decreasing with time? For both of these comarisons the findings of economists and sociologists are sharly contrasting for the UK. International comarisons of income mobility lace the UK as country with low mobility (Blanden, 2009a, Corak, 2006) but sociologists tend to rank it closer to the middle (Erikson and Goldthore 1992, Breen, 2004). Cross-country rankings across the two aroaches are barely correlated with each other (Blanden, 2009a). Likewise on trends, Blanden, Goodman, Gregg and Machin (2004) find that intergenerational mobility decreases for a cohort born in 1970 comared to a cohort born in 1958 while Goldthore and Jackson (2007) find no change in social class mobility for the same datasets. 1 Of course the divergent results may simly reflect underlying concetual differences. Economists are aiming to measure economic resources whereas class reflects worklace autonomy and broader social caital. An alternative exlanation is that the differences are driven by measurement roblems in arental status. Information on arental income in the cohorts is taken on a one-shot basis, and reliable measures of ermanent income are not available. Fathers social class has only seven categories, this will fail to cature much of the variation in ermanent income between families. In addition, the imortance of fathers social class in determining the outcomes of the next generation is inherently connected to the male breadwinner model of the family, a aradigm which is becoming less and less aroriate as 1 Nicoletti and Ermisch (2007) use data from the British Household Panel Survey to consider trends in intergenerational earnings mobility. Their results oint to no substantial trend in mobility for cohorts born from 1950 to From 1961 to 1972 there is a decline in mobility as measured by the elasticity of earnings across generations, but no change in the artial correlation (our referred measure). It should be noted that due to the use of fathers earnings redicted from social class and education Ermisch and Nicoletti s methodology lies somewhere between the ure income and ure social class aroaches. 2

4 women contribute more to family income, both in coules and by heading single-arent families. One motivation for the reconciliation of these results is the wide accetance of the findings on trends in income mobility (Blanden et al 2004 and subsequent aers) among oliticians and commentators. The icture of falling mobility resented has contributed to the sense that Britain has a mobility roblem (Goldthore and Jackson, 2007, and Blanden, 2009b). It is therefore crucial to examine the robustness of this result. Furthermore, by drawing out the concetual links between mobility as measured by economists and sociologists we hoe to be able to offer a fresh ersective on both literatures, outlining clearly what is measured in each case and the advantages and disadvantages of each aroach. Our aer offers an alternative argument from the one resented in Erikson and Goldthore (2009) who roose that the differing results are exlicable by the oor measurement of ermanent family income in the 1958 cohort. If measurement error is more substantial in the first cohort this could lead to a downward bias on the estimate of ersistence and the misleading imlication that mobility has declined. The aim in our aer is to exand on the measurement error story by considering in detail all the ossible mechanisms that could generate different trends in measured income and social class mobility. We then formulate a number of hyotheses and test them using the British cohort data. Our starting oint is the assumtion that the objective is to measure the intergenerational link between the ermanent income of arents and their children. Therefore both current income and social class are incomlete roxies for ermanent income. The question is: why do they differ, and further, which is referable? Our concetual framework owes much to Björklund and Jäntti (2000) who attemt to reconcile results on economic and social mobility across countries. Björklund and Jäntti (2000) divide ermanent income in each generation into the art that is associated with social class (of fathers and sons, resectively) and the art that is orthogonal to this (the residual). Intergenerational ersistence can then be decomosed by studying the intergenerational correlations and cross-correlations of these comonents. We show that residual income can be further decomosed into three arts. First, ermanent income that is uncorrelated with social class, this can be thought of as within-class ermanent income differences, second, transitory error (the difference between current and ermanent income) and finally any ure measurement error. As noted above, larger errors of either tye (transitory variation or measurement error) in the first cohort could be resonsible 3

5 for the increase in measured ersistence. In order to differentiate within-class differences in ermanent income from error we add another comonent to our framework; the art of income in each generation which is uncorrelated with social class but is correlated with other characteristics (education, housing tenure, etc). This rovides an estimate of the within-class comonent of ermanent income. An examination of data from the British Household Panel Survey (BHPS) reveals that current income is a good redictor of ermanent income (as measured by a long-run average); whereas father s social class erforms relatively oorly. We find that there is a substantial comonent of ermanent income which is unrelated to social class. Concetually, this can account for the divergent results. We can then decomose the change in ersistence across the cohorts by the different comonents of income. We find that a substantial art of the increased ersistence is due to an increased imact of arental within-class ermanent income (uncorrelated with social class but correlated with family characteristics) on the earnings of the next generation. We conclude our analysis by bringing together some additional evidence which casts doubt on Erikson and Goldthore s concerns over measurement error. Our findings suggest that there is little evidence of differential measurement error and that evidence for changes in transitory income cannot overturn the main result of rising income ersistence. In the next section we build u a framework which relates social class mobility to our measure of mobility based on family income and sons earnings. This enables us to demonstrate clearly the reasons why results based on the two aroaches might differ. In Section 3 we outline the data and in Section 4 we test each hyothesis in turn. Section 5 concludes by discussing the imlications of our results for the study of mobility. 2. Framework 2.1 The Comonents of Income Here we set out a framework which demonstrates the relationshis between ermanent income, income at a oint in time and fathers social class. This rovides clear foundations for our examination of the reasons behind the divergent results for income and social class. For economists, the intergenerational relationshi of interest is the relationshi between arents ermanent income and the child s ermanent income. As is common we shall denote ermanent variables by * and logs by lower case variables. Intergenerational mobility can be summarised by β from the following regression: 4

6 * * ysi yi i = α + β + ε (1) The intergenerational correlation, r, is also of interest in cross-cohort studies as this adjusts β for any changes in variance that occur across cohorts. 2 * * Cov( yi, ysi ) r = or * * ( Var( y i ) Var( ysi ) * y ( σ ) r = β * ys ( σ ) (2) Following Björklund and Jäntti (2000), ermanent arental income can be decomosed into the art that is associated with father s social class (in our exosition social class is denoted by a continuous variable, but categorical variables are used in our analysis) and, this is ermanent income which is uncorrelated to fathers social class. At this stage we assume no measurement error. * y = δ SC +v (3) i fi i The δ will reflect the relationshi with social class of all the different comonents which make u total income. This is a oint we shall return to in later analysis. The child s ermanent earnings can also be slit into similar comonents, the art that is related to the child s own class and the art that is indeendent of this. In our alication the child s income measure is son s earnings, so we use the subscrit s 3. * y = δ SC + v (4) si s si si Unfortunately ermanent income is generally not available to researchers (see Solon, 1992 for the first discussion of the biases that result) and the British cohort studies suffer from this limitation. Measured current arental income is ermanent income lus two additional comonents, the transitory element of income ( u ) and the ure error comonent ( e ) which means that measured income deviates from true income even at a oint in time. y = δ SC + v + u + e (5) i fi i i i y = δ SC + v + u + e (6) si s si si si si v 2 Björklund and Jäntti (2009) urge the more widesread use of this statistic when making international comarisons of mobility and the same arguments aly when considering trends over time. 3 We follow Blanden, Gregg and Macmillan (2007) in focusing on sons. This is done to simlify the analysis so that we are focusing on male social class in both generations and to reduce the issues resulting from endogenous labour market articiation. In general, it is surrising how little focus there is on the consequences of gender for the social class analysis, this is an area where further research is clearly needed. 5

7 Under classical measurement error assumtions 4 it is straightforward to show that the error in measuring arental ermanent income will lead to a downward bias in the estimate of β and that this bias will be contingent on the amount of variance in the transitory and error comonents. σ lim ˆ β = β σ σ + 2 * y 2 2 * + y u e Notice that the artial correlation, r, is affected by measurement error in a different way (see equation 2), because r is β multilied by the ratio of the standard deviations of arents to sons income. As classical measurement error will tend to increase the estimated variance, this means that any error in sons earnings will downward bias ˆr (it has no effect on ˆ β ) while the error in arental income will have less of an imact on this measure relative to β. We shall take u these oints again in section 4.4. (7) 2.2 Alying the framework to the BHPS The cohort data has information on father s social class and current arental income at age 16, meaning that we cannot directly measure ermanent arental income in this data. He can however, estimate ermanent income in the BHPS, and we can use this to understand more about how the comonents of current income in the cohorts might be related to ermanent income as described in equations (3) and (5). Solon (1992) oints out that time averaging over many years of income observations allows us to get closer to a ermanent income measure. The British Household Panel Study (BHPS) began in 1991 and now rovides a long enough series of income data to allow us to aroximate ermanent income in childhood for the youngest samle members. We select 1206 two-arent families with children under 16 who have more than 7 income reorts available. 17% of these have reorted income in the full 15 years of the study while 65% have income reorts for 10 years or more; these are averaged to create a ermanent childhood income measure. This can be comared with current income measured when the child is aged 16 or in the latest swee. 4 These assumtions are that the level of y i is uncorrelated with the size of the total error, and that errors are uncorrelated across generations. Under these assumtions, errors in the deendent variable will have no imact on estimates of β. 6

8 Alongside income, the BHPS includes information on father s social class, and by regressing average income on social class we are able to redict δˆsc f. 5 We also have information on other household characteristics that will be related to ermanent income and using these we can slit v into the art that can be redicted ( γ X ˆ ), with the remainder forming a ermanent unmeasured residual caturing any variance in ermanent income not catured by social class and our observable household characteristics, we denote this element as ˆi ε. * y = ˆ δ SC + ˆ γ X + ˆ ε (8) i fi i i Note that this two ste aroach means that fathers class is not cometing in the regression with other family characteristics but is given its maximum exlanatory ower. The characteristics X in the BHPS are arental education, emloyment status, age, housing tenure and self-reorted financial difficulties. The same aroach can also be used to decomose current income. ˆ ˆ 6 y ( ˆ ) ( ˆ ) ˆ ˆ i = λsc fi + π ˆ i + φ X i + τ i + ε i + u i + e (9) i Current income and ermanent income can then be analysed searately to assess the size the comonents and measure their correlation with ermanent income. If useful, we can aly this aroach in the cohorts because although we do not have access to ermanent income we do have information on characteristics that will be correlated with it. This will enable us to searate out measurement error from ermanent income which is uncorrelated from social class, to the extent that this is correlated with other variables. The first column of Table 1 decomoses the variances of ermanent and current income into the comonents described in the equations above. The first asect to notice is that the social class comonent is a fairly small minority (16%) of the variance of average childhood income whereas rather more (23%) is accounted for by the alternative income roxies. 7 The majority of the variance in average (ermanent) childhood income is, however, unexlained; ε i is substantial. The second art of the table considers the decomosition of 5 Here social class is reresented as a continuous variable, but in our analysis it is always estimated as a set of categorical dummies. 6 Note that ˆ λ ˆ SC fi + π i = ˆSC δ f and ˆ φ ˆ X i + τ i= ˆ γ X. ˆ π i therefore, measures the discreancy between the redicted social class comonents of current and ermanent income while ˆi τ fulfils the same function for that art of income redicted by the other ermanent family characteristics. 7 This is articularly surrising in the context of the two-ste aroach we adot, which means that the roxies are only icking u variation in income within social class grous. 7

9 current income as reresented in equation (12). What we find is that a very small art of the variance is related to social class (7.5%) but more than half (60%) of the variation in current income is actually due to the ermanent comonents, with the residual ermanent comonent forming the largest element of this. The lesson here is that the majority of ermanent income cannot be redicted by social class, and that current income will have a substantial ermanent comonent, even after the arts correlated with observed characteristics are accounted for. The second column shows the correlation between these comonents and ermanent income, this once again emhasises the imortance of residual ermanent income ( ε i ) as this has the strongest correlation with our measure of ermanent income. What is also aarent is that the correlation between current income and ermanent income is very strong, at 0.74; this is much stronger than the association between ermanent income and income as redicted by fathers social class (0.4). Our results suggest that the relationshi between current income and ermanent income is strong, and that current income is a better roxy for ermanent income than fathers social class is. It is also imortant to note that the residual ermanent comonent of income forms a large art of residual current income (that is, income that is orthogonal to social class and our other exlanatory variables). The imlication of this is that it is not correct to assume that all current income which is unrelated to social class is simly error of one tye or another. 2.3 Exlaining differences in mobility trends Returning to our relationshi of interest, the link between ermanent incomes across generations, we can rewrite r in terms of variances and covariances. r = Cov y Var y * * ( i, ysi ) * * ( i ). Var( ysi ) (10) The numerator can be decomosed into the elements described above in equations (3) and (4). * * ( i, si ) = ( δ i, δs si ) + ( i, δs si ) + ( si, δ i Cov y y Cov SC SC Cov v SC Cov v SC + Cov( v, v ) i si ) (11) The first reason why results based on social class and income might vary is because the covariance between those arts of income exlained by social class differs from the direct 8

10 association in social class across generations. One of the reasons why this might occur is due to the changing role of mothers earnings. To see this, think of ermanent arental income as having three comonents, the ermanent elements of each of fathers earnings, mothers earnings and other income. y = y + y + y * * * * i fi mi oi Each of these three elements can be decomosed into the art which is associated with father s social class and the ermanent comonent which is uncorrelated with this. The overall δ SC iwill be a weighted average of these comonents with the weights deendent on the comonent s share in total income. δ SC i = S fδ fsc i + SmδmSC i + (1 S f Sm) δosc i (13) (12) where S ( f S m ) is the share of fathers (mothers ) ermanent earnings in ermanent arental income. The overall Cov( δ SC, δ SC ) will be influenced by changes in any of the i s si following asects; the shares, the δ s on the comonents and the intergenerational relationshi between the arts associated with social class. In the NCDS arental income is recorded by comonent, and in this cohort the correlation between sons earnings as redicted by his social class and the art of father s earnings redicted by fathers social class is.288, for mothers earnings it is.253 and for other income it is The association with father s social class is weaker for mothers earnings than for father s own earnings (the r-squared for the mothers earnings regression is just 0.01 comared with 0.16 for fathers). Taking one examle if everything else is constant, a shift in the share of family income contributed by mothers rather than fathers will lead to decline in Cov( δ SC, δ SC ) i s si across the cohorts. 8 However, if changing atterns of women s articiation mean that either the link between mother s earnings and sons earnings or the association between mother s earnings and father s social class increase then this could imly a increase in Cov( δ SC, δ SC ) that is not resent for Cov( SC, SC ) i s si As with the BHPS data, we can regress current income on social class in each birth cohort and for each generation j to identify ˆj λ SC ji i si. The residual from the regression of income on social class is the sum of the estimated v u and e. By exanding the coi i i 8 The share of mothers earnings in total income in the GHS for 1974/5 and 1986/7 rises slightly from 21 ercent to 24 ercent in the coule-headed households with children. 9

11 variances as suggested in equation (11) and scaling them by the denominator of equation (10) we can formulate a 2x2 matrix for each cohort of the comonents of ˆr. ˆs λ SC si vˆ ˆ ˆ si + us i + e si λˆ ˆ ˆ SC fi Cov( λsc i, λsscsi) Cov( ˆ λ, ˆ SC i vˆs + ˆ i usi + esi) Var( y ) Var( y ) i si Var( y ) Var( y ) vˆ + uˆ + eˆ Cov( vˆ + uˆ + eˆ, ˆ λ SC ) Cov( vˆ + uˆ + eˆ, vˆ + uˆ + eˆ ) i i i i i i s si Var( y ) Var( y ) i si i i i i si si si si Var( y ) Var( y ) i si (14) We start by exloring the element in the to-left hand corner of matrix (14). If this art shows a different attern across cohorts from the trend in social class mobility then the social class redictions of income have changed their role across the cohorts, erhas owing to changes in mothers earnings as just described. The uer right quadrant shows the contribution of the relationshi between fathers social class variation in income and within-class variation in sons earnings. The lower half shows the relationshis between within-class family income and sons outcomes. In order to begin to distinguish the role of unexlained ermanent variation from the other residual elements we again follow the BHPS analysis and estimate φ X by regressing the residual from the revious regression on a set of Xs. υ = ˆ φ X + ε + u + e (15) ji j ji ji ji ji Exanding the covariance matrix gives ˆj j i λˆ SC fi ε + u + e Cov( ˆ λ SC, ˆ λ SC ) Cov( ˆ λ SC, ˆ φ X ) Cov( ˆ λ SC, ˆ ε + uˆ + eˆ ) ˆs λ SC si ˆs φ X s s s s i s si i s si Var( y i) Var( ysi) Var( yi) Var( ysi) ˆ φ X Cov( ˆ φ, ˆ ) X i λ sscsi Cov( ˆ ˆ X i, sx si) Var( y i) Var( ysi) Var( y i ) Var( ysi ) ε + u + e Cov( ˆ ε ˆ ˆ, ˆ ) i + u i + ei λsscsi Cov( ˆ ε ˆ ˆ ˆ i + u i + ei, φsx si) Var( y ) Var( y ) Var( y ) Var( y ) i si i si si si Var( y ) Var( y ) φ φ Cov( ˆ φ X, ˆ ε + uˆ + eˆ ) i si i si i si si si Var( y ) Var( y ) i Cov( ˆ ε + uˆ + eˆ, ˆ ε + uˆ + eˆ i i i si si si si Var( y ) Var( y ) i si (16) The intergenerational ersistence of income can therefore be decomosed into the relationshis between the ˆj λ SC ji, the ˆj φ X ji and the residual comonent ε ji + uji + eji. This gets us close to analysing the comonents of the covariance as described in equation (11) 10

12 above and enables us to begin to differentiate the ersistence in the ermanent element of income which is not related to social class from the imact of transitory variation in income and measurement error. Decomosing the artial correlation will enable us to get a good indication as to whether differences in results across discilines are driven by the within-class redicted ermanent income factors, ˆj φ X ji. If the terms of the middle row of equation (19) are higher in the BCS this suggests that within class ermanent income is becoming more ersistent across the cohorts and contributing to the divergent results. However we must remember that φ X ˆj ji is not equivalent to v ji, a substantial element of which will remain in the estimated residual. As shown above in equation (7) transitory income and measurement error will lead to attenuation in our arameters of interest. The degree of attenuation will be deendent uon the share of the variance of y which is comrised of variation in u and e. So, if Erikson and Goldthore (2009) are correct and the share of non-ermanent variance in arental income is larger in the first cohort than the second, this too could exlain the differences in the results obtained by income and social class. The measurement error will inflate the variance of arental income relative to the covariance between income and earnings. In this case the results obtained by Blanden et al (2004) would not be a correct reflection of the changing influence of arental income on later earnings. It is necessary for us to confront the ossibility that our results are driven by measurement error and we do this in Section 4.4. To summarise; the differences in the reorted results for trends in income and social class mobility could be generated in the following ways: 1. The maing from social class to income/earnings changed between the cohorts. This might occur if the share of fathers earnings in total income was changing as a result of increased emloyment among mothers or increased worklessness among fathers. 2. The ermanent income of arents that is unrelated to social class but redicted by other characteristics ( ˆ φ X cohort (the BCS) comared with the first (the NCDS). ) has a larger influence on sons income in the second 3. Parental residual ermanent income ( ε ) has a larger influence on sons income in the second cohort comared with the first. 4. Results are based on measured current income rather than ermanent income. If transitory income and/or measurement error in arental income are larger in the first 11

13 cohort than the second cohort this leads to greater attenuation bias in measuring β and r in the first cohort and the misleading imression of a rise in intergenerational ersistence. Our aim in the remainder of this aer is to distinguish between these hyotheses and then draw out the imlications of our findings for the study of intergenerational ersistence. 3. Data Both sociologists and economists have utilised the two ublicly accessible mature British cohort studies, the British Cohort Study of those born in 1970 and the National Child Develoment Study of those born in Both cohorts began with around 9000 baby boys included, although as we shall see the samles used are considerably smaller than this. The NCDS contains all children born in the UK in a week in 1958 and obtains data at birth and ages 7, 11, 16, 23, 33, 42 and most recently 46. The BCS included all those born in Great Britain in a week in Information was obtained about the samle members and their families at birth and at age 5, 10, 16, 30 and 34. In the childhood surveys of both cohorts, information was obtained from arents on many toics including information on the child s birth weight and height, the child s behaviour and ersonality and the material circumstances of the family. The adult surveys have continued to be very detailed and have gathered information on (amongst other things) relationshis, children and jobs. Fathers social class is measured at various ages in childhood but for consistency with the sociologists we will use measures at age 11 in the NCDS and 10 in the BCS. The social class measure is created from coding the father s Socio-Economic Grou (SEG), into a seven-oint Goldthore social class scheme (see Heath and McDonald, 1987). Details are rovided in Goldthore and Jackson s Table 1. The arental income information is taken from the age 16 survey for both cohorts. In the NCDS arents were asked to lace father s earnings, mother s earnings and other income into a category. Family income is obtained by taking the midoints of the three measures within their category and summing. In the BCS arents are only asked about their total family income, and are asked to give one of eleven categories. We generate a continuous income variable for the BCS by fitting a Singh-Maddala distribution to the data using maximum 12

14 likelihood estimation 9. We also adjust the BCS to a net of tax variable and imute child benefit. This must be done to overcome differences in the way income is measured across the cohorts (see Blanden, Chater 4 for full details). Adult earnings and destination social class information is obtained at age 33 (NCDS) and 30 (BCS), where individuals are asked to rovide information on their usual ay. A limitation of the data is that information on self-emloyment income is oor. Consequently, self-emloyed cohort members are droed from our analysis. Destination social class in the NCDS is measured at 33 and is already available as a Goldthore schema. In the BCS there is no measure of the Goldthore schema at aged 30 so the individuals SOC90 occuational codes and emloyment status are recoded to the same schema used in the NCDS, we follow Goldthore and Jackson (2007) in the way we do this. Additional arental background variables are obtained at various oints during the cohort member s childhood; this enables us to generate a matrix of X variables. These are arental age, arental education reorted at age 16 in both cohorts, mother s and father s emloyment at 16 and mother s emloyment at birth and 7 (5 in the BCS), lone arenthood at age 7 (5 in the BCS) and 16, housing tenure at age 16, whether the child received free school meals at age 11 (10 in the BCS) and arent-reorted financial difficulties at Similarly the surveys in the cohort members early 30s are used to derive comarable X s variables for sons, we use detailed education measures, a measure of early labour market attachment, and information on housing tenure, car ownershi and ension contribution. 4. Results 4.1 Intergenerational mobility in income and social class Table 2 rovides the headline results from the examination of intergenerational income mobility using the regression aroach. 11 The first anel rovides results for the full samle, while the second includes only those cohort members living with their fathers at age 11(NCDS) or 10 (BCS). Through the rest of our analysis we concentrate on this no lonearent samle. Because fathers social class is so crucial to what follows it makes little sense 9 Singh and Madalla (1976). Many thanks to Christoher Crowe for roviding his stata rogram smint.ado which fits Singh-Maddala distributions to interval data. 10 The characteristics we observe are likely to do a better job at redicting low income as oosed to high income. 11 These differ very slightly from those reorted in Blanden, Gregg and Macmillan (2007) as age controls are not included. This is because age is more aroriately included as one of the Xs used to redict arental income. 13

15 to include those without co-resident fathers in our analysis. It is clear from Table 2 that this restriction has little imact on measured intergenerational income mobility; however, it does raise questions about the legitimacy of measures of mobility based on fathers social class which exclude this oulation by design, an issue which becomes increasingly ertinent as more children are brought u in non-nuclear families. For both income based measures of ersistence, β and r, the association of arental income at age 16 and sons earnings in his early 30s has increased substantially and statistically significantly. The strengthened intergenerational association can also be demonstrated by using the transition matrix aroach. We grou incomes in each generation into equal-sized categories (in this case quintiles) and document the roortion of the total samle of families who make each ossible move. In a world of erfect mobility each cell would contain 4% of the samle. Table 3 reveals the change in the extent of income ersistence across generations using this aroach. A larger roortion of cases are clustered near to the diagonal and there is less evidence of long-range movement. The results for absolute social class mobility can also be easily summarised by transition matrices, and these are reorted for the two cohorts in Table 4. The scales have been reversed from the usual reading of social class; one is now the bottom social class and seven the to social class. This is for ease of comarison with income and earnings measures. As with Goldthore and Jackson s (2007) results, there is no evidence of a change in absolute mobility across the cohorts. The unadjusted roortions rovide information on absolute mobility, but in contrast to income grouings, social classes are not a constant fraction of the oulation; they can, and do, change size across the cohorts. This structural change means that a full consideration of trends in mobility also needs to look at relative fluidity which measures the extent of mobility abstracting from overall shifts in the roortions in each social class. It is easy to consider this in a very simle way; Table 5 shows that for both cohorts just over 30% of children born into the two lowest social classes migrate to the to two as adults and likewise a constant 65% of those born with fathers in the to two social classes remain in these classes as adults. A near constant 2:1 ratio of chances of entering the to two classes is revealed. Notice that the results resented here do not allow for a direct comarison of the strength of the association in social class and income. We concentrate on trends only. In Erikson and Goldthore (2009) much is made of the stronger association across generations in social class comared to income. However this result comares the association in 7 14

16 category social class with the association in 5 category income quintile. The use of income quintile disregards the majority of the variation in family income; we do not regard this as a legitimate comarison. This reliminary exloration of income and class mobility suggests that simle crosstabulations reveal a growth in the association of income across the two cohorts while the strength of links in social class between generations remain quantitatively similar. This confirms the findings of Blanden, Goodman, Gregg and Machin (2004) and Goldthore and Jackson (2007). 4.2 Samles Before beginning our analysis of the role of the different income comonents we must first check if differences in samles can exlain the divergent results. The cross-tabulations for income and social class we have seen so far are not based on the same samle, and this alone could generate differences in the estimated trends. Table 5 reorts simle summary statistics for relative mobility. When the social class results are recomuted for the income samle there is evidence of relatively more long-range mobility from the bottom two into the to two social classes and relatively less mobility from the to into the bottom. There is no evidence, however, that restricting the samle has affected the trend in intergenerational mobility by social class. 4.3 Decomosing ersistence by the comonents of income Recalling the framework in Section 2 the first substantive reason for the differences in results for trends in social class and income mobility is because the relationshi between δ SC and δ SC increases across cohorts even though the relationshi between social classes is s s constant. To test for this we use our decomosition aroach to assess the relationshis between ˆSC λ and λ SC in each cohort. In our concetual discussion we ointed to the role ˆs s of mothers earnings as a ossible source of any discreancy. Table 6 estimates matrix (14) for the two cohorts and decomoses r into four arts, the correlation across individuals of ermanent income/earnings redicted by social class, the correlation of residual income (residual ermanent and transitory income/earnings and measurement error) and the cross-correlations. The cells sum to the total artial correlation. There is very little change in the correlation of incomes/earnings associated with social class as shown in the to left-hand corner of the matrix for each cohort. Indeed this element of 15

17 ersistence has reduced slightly. This suggests that changes in mothers emloyment atterns are not behind the differences. Table 6 also allows us to exlore the relationshi between fathers income associated with social class and sons residual earnings. This element of ersistence has increased from 0.01 to In total the elements associated with father s social class account for 13% (1.5) of the 11.4 ercentage oint change across the cohorts. Hence there is a contribution to the difference in mobility from an increased relationshi between income associated with fathers social class and the sons earnings, but it does not come through sons social class. This shows that the larger art of the difference in the results between income and social class must be generated by the relationshi between sons earnings and the other elements of income, either through ˆ φ X, ˆ ˆ ε, u or e. ˆ Following equation (16) we can further decomose measured income/earnings, icking out the art of income that is associated with ermanent characteristics other than social class in each generation. The X s used have been discussed in the Data section and the full regression results are reorted in Aendix Table A1. The fitted R-squared including class is around 0.4 in both the NCDS and the BCS. Table 7 reorts the full three by three matrix. This allows us to exlore how much of the rise in the artial correlation is associated with redicted ermanent income. The results show that all of the elements of sons income are more strongly correlated with ˆ φ X in the second cohort comared with the first. Overall the increase in the artial correlation associated with this redicted art of ermanent income rovides 0.04 oints or 30 ercent of the total rise. In total, oints or 45 ercent of the change in income ersistence can be accounted for as due to income associated with father s social class or other arental characteristics. We can think of this as a lower bound on the true change in beta, it is obtained by assuming that the change ersistence associated with the residual ermanent income ˆ ε is zero. This assumtion imlies that the relationshi between ermanent income which is uncorrelated with social class and our observed Xs (which we know to be a large art) and sons earnings has quite a different ersistence trend than the other comonents of ermanent income. An alternative aroach is to aly some of our knowledge gained about residual ermanent income in the BHPS to the cohorts. Table 8 comares the shares of the variance in current arental income that are attributable to social class, other characteristics and the residual. Broadly, the cohorts seem quite similar to the BHPS. Based on these results we can 16

18 make the alternative assumtion that in the cohorts, as in the BHPS, the variance of the ermanent residual comonent is twice the magnitude of the ˆ φ X art. 12 Using an Oaxaca-style decomosition, where accounted for by ε in cohort c and correlation (see Table 2) we can show that: Cov( ε, y ) Cov( ε, y ) = Var( ) ( ) i si 70 i si 58 Sε70R70 Sε58R58 ε i 70 Var ε i 58 Cov( ε, y ) Cov( ε, y ) Cov( ε, y ) ( ) ( Var( ) Var( ) Var( ) S ε c is the share of ermanent income Rc is the ratio which transforms the beta into the artial i si 70 i si 58 i si 70 Sε58R58 + Sε 70R70 Sε58R58 ) ε i 70 ε i 58 ε i 70 (17) We assume that the shares of ermanent income from ε i ( S ε 70 and S ε 58 ) do not change and are set to the level in the BHPS, and that the multilying ratios are constant across the cohorts so the second term dros out. Setting the change in the ersistence of ε i across the cohorts equal to that of ˆ φ X means that the 0.04 change is doubled to make (because the share of ermanent income associated with ε i is twice that associated with φ X ˆ ). If this is added to our lower band of the exected change is This is actually larger than the real change and suggests that in reality either the share of residual ermanent income in the 1958 cohort is lower than in the BHPS, and/or ersistence in this comonent has risen less strongly than ersistence in redicted ermanent income. However, this thought exeriment shows that it would be easy to exlain the changes we do find using this aroach. These uer and lower bound estimates based on assessments of ermanent income straddle the observed rise in intergenerational ersistence and clearly show that the rise is non-zero (even father s social class makes a contribution). Next we must address the evidence on measurement error. If this is greater in the 1958 cohort then we might seculate that the true change in intergenerational ersistence is towards the lower bound. 4.4 Measurement Error and Transitory Income 12 Table 8 is based on banded income data for the cohorts but continuous income information in the BHPS. We have exlored converting the BHPS into comarable bands and find that this does not influence the broad conclusion that the BHPS and cohort data are similar on the exlored dimensions. 13 In fact R > R so the second term will also add a (likely) small amount to the estimate of

19 Erikson and Goldthore (2009) assert that much, if not all, of the.114 rise in the intergenerational artial correlation is a consequence of greater error in the arental income measure in the NCDS. Our decomosition aroach allows us to state that at the minimum.055 of the.114 is not due to measurement error, while our uer bound indicates that (under lausible assumtions) all the change in ersistence is genuine. Our aim in this section is to collect together a number of ieces of evidence to enable us to assess directly the extent of measurement error in the 1958 cohort comared with measurement error in the 1970 cohort. If we return to equation (7), the effect of measurement error on the intergenerational elasticity, we see that in the resence of classical measurement error the arental income variable will have increased variance. Table 8 indicates that the attern in the cohorts is the reverse of what we would anticiate in the resent of differential measurement error in the first cohort. The total variance of log income in the NCDS is.138 comared with.225 in the BCS. This attern is relicated for residual income, where measurement error would be concentrated. Another feature of measurement error is its imact on the two measures of intergenerational ersistence β and r. With classical measurement error in the exlanatory variable β will be downward biased, however as r is β scaled by the relative variance of arental to sons income larger variance in arental income will lead to a larger estimate of r relative to ˆ β. In this case differential measurement error would manifest itself in a smaller rise in ˆr across the cohorts comared to the rise in ˆ β. Our results in Table 2 show a clear rise in both measures, with the artial correlation increasing slightly more than the elasticity. The arental income question in the NCDS was asked, in art, during the eriod of the three-day working week which occurred at the start of 1974 as a result of industrial action in the coal industry. It is ossible that the reorted income is that of the three-day week rather than usual weekly income, if this was the case it could lead to unusually high measurement error in the first cohort and bias results towards finding a fall in mobility. We check this articular issue by estimating the intergenerational coefficient and artial correlation for those families interviewed in January and February 1974 (definitely within the three-dayweek eriod). We find that if anything intergenerational ersistence is stronger for these families. This is in line with Grawe s (2004) study who finds no evidence of income misreorting in the NCDS due to the reduced working week. As noted in the Data Section the structure of the arental income questions is different between the cohorts; this could be another source of differential error. The arents of the 18

20 NCDS cohort members rovide banded information on three sources of income, fathers earnings, mothers earnings and other income; the mid oints are then added. In the BCS just one total band is rovided. We might think that this would lead to more accurate income information in the NCDS and certainly a single banded total income will reduce the measured variance of income by more than one derived from three comonent sources of income. We have modelled the imlications of both banding aroaches in the continuous BHPS data and find that neither has an areciable imact on total variance or the decomosition of current income into the different ermanent income comonents. Overall, it seems that there is nothing in the data construction that will lead to greater measurement error in the NCDS. We confirm this by comaring the income reorts from the cohorts with incomes given in a nationally reresentative survey over the same eriod. Figure 1 mas the cumulative distribution functions of log arental income in the cohorts alongside those for families with similar-aged children in the Family Exenditure Survey (FES) in the same years. It aears that in both datasets cohort arents tend to reort lower incomes than arents in the FES. This is not surrising as questioning in the FES is a good deal more thorough so is likely to uncover more income sources. The categorical nature of the income data in the cohorts tends to lead to a more lumy distribution (articularly in the BCS) and a truncated uer tail. For our uroses the most notable feature is that these asects are certainly no more ronounced in the NCDS than in the BCS. Erikson and Goldthore (2009) exress concern about the arental income data in the NCDS because of the weaker link between social class and arental income in the NCDS comared with the BCS. Social class can exlain 9% of the variance of arental income in the NCDS and 23% in the BCS. Erikson and Goldthore infer from this that the income variable in the NCDS is a oorer measure of arental income than for the BCS. This could be due to more transitory income or more measurement error. 14 They, however, resent no suorting evidence for this assertion. We can examine this finding by comaring the redictive ower of father s social class in the cohorts with the same eriods in the GHS data. Table 9 shows that fathers social class exlains more of the variance in family earnings in the second eriod in the GHS, mirroring the attern found in the cohorts. This finding is not sensitive to selecting the samle based on the emloyment status of arents. 14 Erikson and Goldthore (2009) note in articular that the association between arental income in the NCDS is lower than the corresonding association in the BCS and the association between the offsring s own earnings and own social class in both cohorts. However, the comarison across generations is invalid because the income measures are different, we would exect the correlation between own earnings and own social class to differ from the association between arental income and father s class. 19

21 So far our discussion of measurement error has been more concerned with ure reorting error than error in ermanent income due to transitory variation. In Blanden et al (2004) the New Earnings Survey (NES) is used to calculate the roortion of variance in earnings over a five year eriod that could be regarded as ermanent for men in the years around the age 16 income measures. We find that in the years around 1986 men s transitory fluctuations account for 21 ercent of the variance in any year, around 1974 this was 32 ercent. It aears that there is some evidence to oint towards greater transitory error in the first cohort. Erikson and Goldthore (2009) note that if allowance were made for this roblem, the fall in mobility would no longer aear as dramatic as it does when the data are taken at face value. Alying the same figures to arental income, transitory error of this magnitude would imly a true β of.321 in the NCDS and.366 in the BCS, reducing the change in beta to.045, comared to the 0.07 found in Table 2. There are three oints that need to be made about this evidence. First, that this reduced figure is still a statistically significant rise and, at about 60% of the observed figure, is broadly in line with the lower bound estimate given before. Secondly, the NES calculations are for individual earnings, whereas we need to know about transitory error in family income, including the imact of mothers earnings and other income. Furthermore using social class as the measure of economic status will not resolve this roblem. As we have seen reviously, social class redicts a minority of the variance of ermanent income. Further investigation using the NES reveals that current earnings uncorrelated to social class (residual income, in our terms) also has an increasing ermanent comonent. The average residual of income from a social class regression redicts 62 ercent of income variation in 1974 and 73 ercent of income variation in This asect of ermanent income will not be included in the social class analysis. 5. Discussion and Conclusion The aer extends a framework first set out by Björklund and Jäntti (2000) to model the link between social class and income measures of intergenerational mobility. We take as our baseline model the relationshi between the ermanent income of arents and the ermanent income of sons. Using a framework which relates ermanent income to social class and current income we are able to offer four ossible exlanations for the divergence between trends in intergenerational mobility in income and social class in the UK. Here we will 20