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...nal on the inequality index employed for the calculations. It is also well-known that inequality indices differ in the sensitivity to income differences in different parts of the income distribution (=-=Atkinson, 1970-=-). So, it is important to know how estimates of rigidity and mobility relate to choice of inequality index, and how differences in inequality index sensitivity translate into mobility index sensitivit...

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...s of parental income can be motivated by theoretical concerns. A commonly cited concern is the potential presence of borrowing constraints with respect to parental investments in child human capital (=-=Becker and Tomes, 1986-=-; Grawe, 2004b; Bratsberg et al., 2007). Bratsberg et al. (2007) fit a polynomial in parental income to the data for the US drawn from the NLSY to allow for a flexible shape between offspring and pare...

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... comparable points in the lifecycle and preferably multiple such measurements to allow for the effect of measurement errors. 66Intergenerational persistence can be estimated using two-sample methods (=-=Björklund and Jäntti, 1997-=-), which we discuss below. 148 There are three main types of data that are used. Many studies rely on longitudinal household surveys that have been running long enough to allow for the offspring to be...

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...and residual variances. Other approaches, such as non-parametric bivariate density estimates, similar to Figure 4 in the intragenerational case in Section 3, would in principle be available (see e.g. =-=Bowles and Gintis, 2002-=-). Very few studies take that route, however. Quantile regression (Koenker, 2005) can also be used to examine the conditional distribution of offspring income, conditioned on parental income. While th...

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...out that in the case of homothetic preferences, ‘the signs of higher derivatives depend on the relation between the degree of “inequalityaversion” ... and the degree of substitution’ between periods (=-=Atkinson and Bourguignon, 1982-=-, 18), i.e. the relation between parameters ε and ρ discussed earlier, they do not elaborate. It is difficult to understand what the sign conditions mean in everyday language. Third, analysts may be i...

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...led generalized-errors-in-variables (GEIV) model calls into question the assumption that transitory income variations have the same properties as classical measurement errors (Haider and Solon, 2006; =-=Böhlmark and Lindquist, 2006-=-). The GEIV model for the annual income process of an individual in family i in generation j(= Offspring,Parent) at age t relates permanent income y and transitory errors v to annual or current income...

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...Section 3. The main result about trends is that mobility declined between 1981 and 1991, regardless of which inequality index M is calculated with and using window lengths of one, four, or six years (=-=Buchinsky and Hunt, 1999-=-, Table 2). Positional mobility also declined: the chances of remaining in the same quintile group, and the average jump and normalized trace indices also fell. The decline in mobility as equalisation...

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...ctual Swedish father-son pairs are almost exactly the same as the two-sample IV estimate. There have been a large number of studies subsequently that use two-sample IV estimators including for Italy (=-=Checchi et al., 1999-=-), Brazil (Dunn, 2007), Australia (Leigh, 2007) and France (Lefranc et al., 2009). 153 Mazumder (2005b), using earnings information from the US Social Security Administration (SSA), examines intergene...

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... different countries on the vertical axis and estimated income inequality, often in the parental generation, on the horizontal, adding a linear bivariate regression line (Corak, 2013a; Blanden, 2013; =-=Björklund and Jäntti, 2009-=-). Labelled the ‘Great Gatsby’ curve by the then Chairman of the US Council of Economic Advisors (Krueger, 2012), such plots are interpreted to suggest countries with higher persistence are also count...

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...egression of child height on parent height also used mid-parent height on the right hand side, see Galton (1886) and Goldberger (1989). 139 by labour market earnings. It has long been recognized (see =-=Atkinson, 1981-=-b) that short-run income measures are different from longer-run measures because of transitory fluctuations, and that the association sought were those of the more stable or permanent measures of livi...

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...egression of child height on parent height also used mid-parent height on the right hand side, see Galton (1886) and Goldberger (1989). 139 by labour market earnings. It has long been recognized (see =-=Atkinson, 1981-=-b) that short-run income measures are different from longer-run measures because of transitory fluctuations, and that the association sought were those of the more stable or permanent measures of livi...

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...n their analysis using more conventional definitions (but excluding Sweden), mobility levels change for all countries but ‘the mobility ordering of countries is unaffected by this sensitivity check’ (=-=Aaberge et al., 2002-=-, 457). The Aaberge et al. (2002) study provides analysis for 1986–91 and 1990– 91, with the end chosen because a major Swedish tax reform in 1991 made later income data non-comparable (the registers ...

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...thers, which has not been much explored in the literature. The Beta for Swedish father-son pairs is around 0.25 (see e.g. Björklund and Chadwick, 2003) but much higher at the top of the distribution (=-=Björklund et al., 2012-=-). Estimates from Denmark suggest quite low levels of persistence (e.g. Bonke et al., 2005) Lefranc et al. (2013) estimate Betas for Japanese sons and daughters using two-step sample methods. The esti...

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... persistence in different countries on the vertical axis and estimated income inequality, often in the parental generation, on the horizontal, adding a linear bivariate regression line (Corak, 2013a; =-=Blanden, 2013-=-; Björklund and Jäntti, 2009). Labelled the ‘Great Gatsby’ curve by the then Chairman of the US Council of Economic Advisors (Krueger, 2012), such plots are interpreted to suggest countries with highe...

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...es for the 1955–70 cohorts. This difference suggests an increasing role for mothers, which has not been much explored in the literature. The Beta for Swedish father-son pairs is around 0.25 (see e.g. =-=Björklund and Chadwick, 2003-=-) but much higher at the top of the distribution (Björklund et al., 2012). Estimates from Denmark suggest quite low levels of persistence (e.g. Bonke et al., 2005) Lefranc et al. (2013) estimate Betas...

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... mobility is relatively large. It is unclear what lies behind the secular decline in mobility, but we note that it was at the end of the 1970s that US family income inequality also began to increase (=-=Burkhauser et al., 2011-=-), suggesting that inequality and positional mobility share some common drivers. There is no very obvious association between series’ turning points and the business cycle (there were recessions at th...

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...ile transition matrices, not R. Again, the conclusions point more to cross-national similarities rather than differences: ‘[i]ndividual mobility patterns in the two countries are remarkably similar’ (=-=Burkhauser et al., 1998-=-, 143–4). For example, the proportion of individuals in the same quintile group of post-tax post-transfer household income in 1983 and 1988 is 44.7 per cent in the USA compared to 41.4 per cent in WG;...

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..., and that SWF is homothetic, then the mobility measure ‘has a natural interpretation; it is the percentage change in equality of the aggregate distribution compared with the first-period benchmark’ (=-=Chakravarty et al., 1985-=-, 6). Although the authors go on to state that appear to no convincing ethical argument for applying the same welfare function to both distributions, all empirical applications that we are aware of ha...

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... the estimated persistence in different countries on the vertical axis and estimated income inequality, often in the parental generation, on the horizontal, adding a linear bivariate regression line (=-=Corak, 2013a-=-; Blanden, 2013; Björklund and Jäntti, 2009). Labelled the ‘Great Gatsby’ curve by the then Chairman of the US Council of Economic Advisors (Krueger, 2012), such plots are interpreted to suggest count...

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... also provided for the very top income groups. The authors report that there is a large amount of turnover at the top and that ‘the incomes of many taxpayers at the highest levels are very volatile’ (=-=Auten and Gee, 2009-=-, 311). For example, among the richest 0.01% in 1996 only 23 per cent remained in the group in 2005. Although over 80 per cent were still in the top 1%, 6 per cent dropped out of the richest fifth (Au...

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...and Heisz (1999) rely on tax records for of only the earnings information, but also the father-son link. In the Nordic countries, parent-child links are from either Census data or from birth records (=-=Bratsberg et al., 2007-=-). 68Two-sample methods were independently developed by Angrist and Krueger (1992) and Arellano and Meghir (1992). Methods to estimate the variance of such estimators were derived by (see Inoue and So...

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...ining in the same decile group falling to between 25 per cent and 30 per cent for all the countries. Chen’s summary refers to ‘a high degree of similarity in relative income mobility across nations’ (=-=Chen, 2009-=-, 81) rather than to differences. Chen (2009, Table 1) presents estimates of the Fields and Ok (1999b) index of income flux, the average absolute log-income change calculated over five-year intervals ...

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...me equivalized by the modified-OECD scale, and mobility is examined for all individuals using a balanced five-wave panel for each country. According to the Fields and Ok (1999b) index of income flux (=-=Ayala and Sastre, 2008-=-, Table 2), the average absolute log-income change, and looking at income changes between 1993 and 1997, Spain, Great Britain, and Italy have relatively high income flux (index values of 0.390, 0.373,...

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...port finding mean reversion and serial correlation.) There is also a more fundamental question of whether administrative record data can be assumed to provide error-free representations of the truth (=-=Abowd and Stinson, 2013-=-).39 A rather different sort of measurement error arises in the case of outlier observations, for example very high or very low observations. These may be genuine but may also represent errors of e.g....

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...tant for this group. Overall, the authors conclude from their analysis that ‘redistribution and risk insurance provided by the welfare state is more pronounced in Germany than in the United Kingdom’ (=-=Bartels and Bönke, 2013-=-, 250). Whether this also applies to other groups beyond prime-aged men requires examination. Mobility in top incomes in Germany over the period 2001–6 is studied by Jenderny (2013) using tax administ...

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...ome mobility is greater in WG than the USA in each year. The profile of R (and for the other measure) for the USA lies above that for WG thoughout, though the gap between them gets smaller over time (=-=Bayaz-Ozturk et al., 2013-=-, Figure 1). In this sense, the results are consistent with the Burkhauser and Poupore (1997) finding (see also Figure 8). However, when the indices are calculated using a moving five-year window (and...

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...t is perhaps the similarities of the ‘end results’ of the two labor markets, despite substantial differences in their institutions, that highlight our multiperiod look at these two industrial giants (=-=Burkhauser et al., 1997-=-, 793). Burkhauser et al. (1998) supplement the two earlier studies from the Burkhauser team. As in the first study they use multiple measures of income (and associated samples), but analyze individua...

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...r annual labour earnings is 88 per cent for the USA and 79 per cent for WG. For the subset of men, the corresponding estimates are 86 per cent and 78 per cent; for women, 87 per cent and 66 per cent (=-=Burkhauser and Poupore, 1997-=-, Table 4). The mobility of labour earnings over the same period is analyzed in greater detail by Burkhauser et al. (1997) using different summary methods: statistics based on quintile transition matr...

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... Social Mobility stated that ‘Social mobility matters because . . . equality of opportunity is an aspiration across the political spectrum. Lack of social mobility implies inequality of opportunity’ (=-=Aldridge, 2001-=-). For more about equality of opportunity, see Chapter 5 in this volume by Roemer and Trannoy. From this perspective, greater mobility is socially desirable since equality of opportunity is a principl...

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...rs is around 0.25 (see e.g. Björklund and Chadwick, 2003) but much higher at the top of the distribution (Björklund et al., 2012). Estimates from Denmark suggest quite low levels of persistence (e.g. =-=Bonke et al., 2005-=-) Lefranc et al. (2013) estimate Betas for Japanese sons and daughters using two-step sample methods. The estimates for men are all quite close to 0.35. For daughters, estimates vary between 0.182 and...