MOBILITY CONCEPTS

Writers on income mobility have long emphasized that mobility has multiple dimen­sions. For example, a leading survey from a decade ago commented that:

the mobility literature does not provide a unified discourse of analysis.

Fields and Ok (1999a, p. 557)

The systematic reviews by Fields and Ok and others have done much to reduce the potential confusion. But they cannot banish mobility’s multiple facets, and so newcomers continue to require guided tours of the concepts and literature. This section explains what the multiple dimensions of mobility are. We address the question of whether more mobility is socially desirable in each case, arguing that the answer depends on which mobility concept is the focus. A review of the implications of mobility’s various facets for social welfare is used to illustrate trade-offs between different types of mobility. We also point out how different concepts have received different emphasis in studies of mobility within or between generations.

10.2.1 Mobility's Multiple Dimensions

Consider first the case in which there are observations on income for N individuals for two periods. In the first period, the income distribution is x, in the second period, the distribution is y; there is a bivariate joint density f(x, y). Overall mobility for the popu­lation can be thought of as the transformation linking marginal distribution x with mar­ginal distribution y.

In this section, we distinguish four concepts (Jenkins, 2011a): positional change (which comes in two flavors), individual income growth, reduction of longer-term inequality, and income risk.^[574] The different concepts “standardize” the marginal distribu­tions x and y in different ways to focus attention on the nature of the link x #8594; y.

Positional change refers to mobility that arises separately from any changes in the shapes of the marginal distributions in each period, for example, a rise in average income or in income inequality or, more generally, a change in the concentration of individuals at dif­ferent points along the income range in y compared to in x. Standardization for such changes is most easily accomplished by summarizing each person’s position not in terms of their income per se but in terms of their rank in the population normalized by the population size. (The marginal distribution of these “fractional” (or “normalized”) ranks is a standard uniform distribution for both x and y.) Thus positional change mobility refers to the pattern of exchange of individuals between positions, while abstracting from any change in the concentration of people in a particular slot in each year. The latter change is “structural mobility,” whereas the former is “exchange mobility”: see, for example, Markandya (1984). Changes in income affect positional mobility only insofar as these changes alter each person’s position relative to the position of others. Equipro­portionate income growth or equal absolute additions to income for everyone raise incomes, but there is immobility in the positional sense.

There are some distinctive characteristics of the concept of mobility as positional change. Mobility for any specific individual necessarily depends on other people’s positions as well, which is not true for every mobility concept, as we shall see. The def­inition of each person’s origin and destination position depends on the positions of every­one else in the society: It is these taken altogether that define a hierarchy of positions. Second, and related, if one person changes position, then so too must at least one other person. It is not possible for everyone to be upwardly mobile or, indeed, downwardly mobile. Third, the situation corresponding to “no mobility” is straightforwardly defined: Maximum immobility occurs when every person has the same position in x and in y.

One situation is when one’s destination is completely unrelated to one’s income ori­gin (“origin independence”). For example, the chances of being found in the richest 10th in period 2 are exactly the same for people who were in the poorest 10th in period 1 as for the people who were in the richest 10th in period 1. In transition matrix terms, this is the case in which #945;_jk = a_mk for all origin classes j or m (each row of the transition matrix has identical entries). Another view is that the reference case when there is mobility is if des­tination positions are a complete reversal of origin positions (“rank reversal”), emphasiz­ing positional movement per se. For example, the poorest person in period 1 is the richest person in period 2, and the richest person in period 1 is the poorest person in period 2, and so on. All entries in the transition matrix lie on the diagonal going from bottom left (richest origin class and poorest destination class) to top right (poorest origin class and richest destination class).^[575]

Mobility as individual income growth refers to an aggregate measure of the changes in income experienced by each individual within the society between two points in time, where the individual-level changes might be gains or losses. Income growth is defined for each individual separately, and income mobility for society overall is derived by aggre­gating the mobility experienced by each and every individual.^[576] This mobility concept contrasts sharply with the positional change one in several ways.

In the individual economic growth case, it is natural to define mobility for each indi­vidual in terms of “distance” between origin and destination income and to think of the maximum immobility case for the population as being when the measure of distance equals zero for every individual (x_i = y_i for all i). Mobility is greater if the distance between origin and destination is greater for any individual, other things being equal. This is similar to the idea of greater movement, meaning more mobility according to the “reversals” version ofpositional mobility. Again, there is no natural maximum mobil­ity reference point as distance has no obvious upper bound.^[577] Defining the metric for “distance” in terms of the income change for each individual is, of course, vitally impor­tant for the concept, and the main distinctions have been measures of “directional” and “nondirectional” growth. In the first case, income increases over time are treated differ­ently from income decreases; in the second, an income increase and an income decrease of equal magnitude are attributed the same distance and the measure summarizes income “flux” (more on this shortly). For more precise definitions, see Fields and Ok (1999a).

The third mobility concept defines income mobility with reference to its impact on inequality in longer-term incomes. The longer-term income for each individual is defined as the longitudinal average of incomes in each period (variations on this are considered later). In the two-period case, longer-term income equals ¹ /2(x_i + y_i) for each i.

The fourth concept of mobility, as income risk, is related to the third. The previous paragraph expressed each person’s period-specific income as the sum of a “permanent” component (the longer-term average) and a “transitory” component (the period-specific deviations from the average). Suppose now that the longer-term average is given a behav­ioral interpretation: It is the expected future income per period given information in the first period about future incomes. From this ex ante perspective, the transitory compo­nents represent unexpected idiosyncratic shocks to income, and the greater their disper­sion across individuals each period, the greater is income risk for this population.

10.2.2 Is Income Mobility Socially Desirable?

In what ways are these various mobility concepts of public interest over and above providing useful descriptive content? Does having more mobility represent a social improvement, or is it undesirable? The answers depend on the mobility concept employed, and the support for the different concepts has depended on whether one is assessing within- or between-generation mobility.

Greater mobility in the sense of less association between origins and destinations has long been linked with having a more open society; if where you end up does not depend on where you started from, there is greater equality of opportunity. For example, a classic statement by R. H. Tawney, originally from 1931, is that equality of opportunity

obtains in so far as, and only in so far as, each member of a community, whatever his birth, or occupation, or social position, possesses in fact, and not merely in form, equal chances of using to the full his natural endowments of physique, of character, and of intelligence.

Tawney (1964, pp. 103-105)

More recently, a UK government advisor’s report on 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, p. 1). For more about equality of opportunity, see Chapter 5.

From this perspective, greater mobility is socially desirable because equality of oppor­tunity is a principle that is widely supported, regardless of attitudes to inequality of out­comes. This is relevant because independence of origins and destinations is consistent with inequality of outcomes being relatively equal or unequal. The argument just rehearsed is, however, typically made in the context of intergenerational mobility rather than intragenerational mobility, and origins refer to parental circumstances, such as “birth, or occupation, or social position” referred to by Tawney. The appeal to fairness in this context is based on the meritocratic idea that someone’s life chances should depend on their own abilities and efforts rather than on who their parents were. At the same time, it is important to appreciate that the degree of intergenerational association is an imperfect indicator of the degree of inequality of opportunity.

The degree of origin independence is a direct measure of inequality of opportunity only if two rather special conditions apply (Roemer, 2004). First, the advantages associ­ated with parental background (over which it is assumed that an individual had no choice) are entirely summarized by parental income. Second, the concept of equality of oppor­tunity that is employed views as unacceptable any income differences in the children’s generation that are attributable to differences in innate talents (which might be partly genetically inherited). This is what Swift (2006) described as a “radical” interpretation of the equality of opportunity principle and likely to command much less widespread assent than what he refers to as the “minimal” and “conventional” definitions (respec­tively, access and recruitment processes to life chances are free of prejudice and discrim­ination; and outcomes achieved depend on “ability” and “effort” but not on family background).

The social desirability of mobility as independence of origins has less force in the intragenerational context. The reason is that incomes are measured at a point within the life course. By that stage, period-1 incomes are likely to reflect differences in peoples’ abilities and efforts (in addition to family background and other factors), and period-2 incomes to reflect the persisting effects of these factors. To the extent that abilities and efforts do play this role (or are seen to) and also viewed as fair on the grounds of merit or desert, the reduction of dependence between origins and destination has less appeal as a principle of social justice.

More common in the within-generation context are statements that income mobility is desirable because it is a force for reduction in the inequality of longer-term incomes. The most famous statement in this connection was by Milton Friedman six decades ago in his Capitalism and Freedom (though observe that he also refers to equality of opportunity in this context):

A major problem in interpreting evidence on the distribution of income is the need to distinguish two basically different kinds of inequality; temporary, short-run differences in income, and differences in long-run income status. Consider two societies that have the same annual distribution of income. In one there is great mobility and change so that the position of particular families in the income hierarchy varies widely from year to year. In the other there is great rigidity so that each family stays in the same position year after year. The one kind of inequality is a sign of dynamic change, social mobility, equality of opportunity; the other, of a status society.

Friedman (1962, p. 171)

Similar views are apparent across the political spectrum in the United States. The chair­man of President Obama’s Council of Economic Advisors recently stated,

Higher income inequality would be less of a concern if low-income earners became high-income earners at some point in their career, or if children of low-income parents had a good chance of climbing up the income scales when they grow up. In other words, if we had a high degree of income mobility we would be less concerned about the degree of inequality in any given year.

Krueger (2012, p. 3)

Although both authors are referring to the distributions of incomes within generations, one could extend the same inequality-reduction idea to the intergenerational context, by summarizing mobility in terms of the extent to which dynastic inequality (referring to incomes averaged over generations of the same family) is less than the inequality in any given generation. But this is rarely done, perhaps because the normative appeal of the dynastic average income is much less than that of a multiperiod average within generations, and data for more than two generations are rarely available.

According to the arguments about longer-term inequality reduction, income mobil­ity is socially desirable for instrumental reasons rather than for its own sake. That is, soci­ety is assumed to care about income inequality (less is better, other things being equal), but inequality is assessed using longer-term incomes, and year-to-year mobility means that the inequality of this distribution is less than the inequality of incomes in any par­ticular year. The normative content of the mobility principle therefore hinges on views concerning the nature and validity of the benchmark that is provided by the distribution of longer-term incomes. As Shorrocks points out,^[578] there is

the presumption that individuals are indifferent between two income streams offering the same real present value. This might be true if capital markets were perfect (or if there was perfect substitutability of income between periods), but it seems likely that individuals are concerned with both the average rate of income receipts and the pattern of receipts over time. We may go further and suggest that individuals tend to prefer a constant income stream, or one which is growing steadily, to one which continually fluctuates.

Shorrocks (1978a, p. 392)

Thus, the argument is not only about the feasibility of smoothing incomes to achieve the longer-term average, but also the undesirability of the uncertainty associated with a fluc­tuating income stream.

This brings us to the fourth concept of income mobility, as income risk. To illustrate this, Shorrocks defines for each individual a “constant income flow rate generating receipts which gives the same level of welfare as the income stream he currently faces” (Shorrocks, 1978a, p. 392), and he argues that

[r]eplacing actual recorded incomes with this alternative income concept in the computation of inequality values introduces a new dimension into the discussion of mobility. No longer is mobility necessarily desirable. Changes in relative incomes still tend over time to equalise the distribution of total income receipts, and to this extent welfare is improved. But greater variability of incomes about the same average level is disliked by individuals who prefer a stable flow. So to the extent that mobility leads to more pronounced fluctuations and more uncertainty, it is not regarded as socially desirable. A more detailed examination of these two facets of mobility will provide a better understanding of the impact of income variability and the implications for social welfare.

Shorrocks (1978a, pp. 392-393)

Thus, even though income mobility has an inequality-reducing impact, mobility is not necessarily socially desirable if mobility represents transitory shocks. In this case, mobility is a synonym for not only income fluctuation but also unpredictability and economic insecurity. Fluctuating incomes are undesirable because most people prefer greater sta­bility in income flows to less, other things being equal, if only because it facilitates easier and better planning for the future. But, more than this, by definition, transitory income variation is an idiosyncratic shock that cannot be predicted at the individual level; greater transitory variation corresponds to greater income risk, and greater risk is undesirable for risk-averse individuals. The definition of the “alternative income concept” from which transitory shocks deviate is, of course, crucial, and we return to this.

What about the social desirability of individual income growth (the second mobility concept)? The answer is not clear cut because it depends on the nature of the income growth and who receives it. An increase in income for any given individual is a social improvement, and an income fall is socially undesirable. The main issue, then, is how to aggregate gains and losses in the social calculus. Evaluation of the impact of individual income growth on the welfare of society as a whole requires a weighing up of the gains and losses for different people, and opinions are likely to differ about how to do this. An egalitarian may weight income gains for the initially poor greater than income gains for the initially rich because this will contribute to reducing income differences between them over time. (On the progressivity of income growth, see, e.g., Benabou and Ok, 2000 and Jenkins and van Kerm, 2006.)

Arguments to the contrary appealing to principles of desert or incentives might also be made. It might be argued, for instance, that differential income growth rates are of less concern if income gains among the rich reflect appropriate returns to entrepreneurial activity or to widely acclaimed talents. The rise in bankers’ bonuses in the manner observed in many Anglophone countries in recent years may not count as an example of the former. But as an example of the latter, we note the views of the UK’s former Prime Minister Tony Blair expressed in an interview asking him whether it was accept­able for the gap between rich and poor to get bigger. His response referred instead to individual income growth:

[T]he justice for me is concentrated on lifting incomes of those that don't have a decent income. It's not a burning ambition for me to make sure that David Beckham earns less money,... [T]he issue isn't in fact whether the very richest person ends up becoming richer... the most important thing is to level up, not level down.

Interview on BBC Newsnight (5 June 2001)^[579]

Another concept of desert may also be relevant when assessing mobility. This is the argu­ment concerning “distressed gentlefolk”—people who were previously well-off, but experience a significant fall in resources through no fault of their own. Thus income gains and income losses for an individual may not be assessed symmetrically but, again, relate to why income changed (see also the discussion of “loss aversion” below).

We end this section with two observations. First, our discussion of the social desir­ability or otherwise of income mobility has referred to income movement from through­out the range of base-period income origins to all potential final-period income destinations. There has been no particular focus on persistence at the bottom or at the top. In part, this is because such a focus arguably does not raise additional conceptual issues, except where to draw the cutoffs demarcating the poor and nonpoor, or rich and nonrich. Indeed if the bivariate joint distribution is summarized using a transition matrix, then suitable definition of the income groups reveals the movement at the top and the bottom. However, we do discuss selected aspects of the measurement of high- and low-income persistence in the next two sections.

Second, our discussion of the social desirability of mobility has focused on its norma­tive aspects. We ignore the positive political economy arguments about public support for mobility. On this, see, e.g., the analysis by Benabou and Ok (2001) of the “prospect of upward mobility” (POUM) hypothesis, which is that individuals who currently have low income may not support high levels of redistribution because of their aspiration that they or their children will become rich in the future.

10.2.3 Income Mobility and Social Welfare

The discussion so far demonstrates that the impact on social welfare of greater income mobility is not clear cut and depends on the mobility concept that is emphasized. A natural question for an economist to ask is whether there are explicit welfare foundations for the various mobility concepts that have been discussed so far. For inequality measurement, the use of an explicit model of social welfare is known to yield dividends; see, notably, Atkinson’s (1970) demonstration of how the “cost” of income inequality can be summarized in social welfare terms and how inequality comparisons based on Lorenz curves are intimately linked to orderings by social welfare functions (SWFs) that are additive, increasing, and concave functions of individuals’ incomes. The corresponding literature on the social welfare foundations of mobility measure­ment is small, with contributions including Atkinson (1981a), reprinted as Atkinson (1983), Atkinson and Bourguignon (1982), Markandya (1984), and Gottschalk and Spolaore (2002). In this section, we focus on the nature of the SWFs employed in the mobility context; how these functions relate to mobility dominance results is dis­cussed later.

The SWF used in the multiperiod context is a straightforward generalization of the one-period case discussed by Atkinson (1970). Overall social welfare, W, is the expected value (average) of the utility-of-income functions of individuals. In the two-period case, the utility-of-income function is U(x,y) and weighted by the joint probability density fx,y). That is,

G(x, y)f (x, y)dxdy,

0

(10.1)

where U(x,y) is differentiable and a_x and a_y are the maximum incomes in periods 1 and 2. It is assumed that increases in income in either period are desirable, other things being equal (so positive income growth raises utility): U₁ #8805;0 and U₂ #8805; 0.

Research in this tradition concentrates on the case in which the marginal distributions x and y are identical. In other words, the economic context is the same as the one used earlier to characterize positional mobility. All relevant mobility is encapsulated by the changes in individuals’ ranks or by the transition matrix when individual incomes are classified into discrete classes. Atkinson and Bourguignon (1982) show that if the SWF is additively separable across time periods (so that U₁₂ = 0, then income mobility is irrelevant for social welfare; only the marginal distributions matter.^[580] If, instead, U(x,y) is a concave transformation of the sum of the per-period utilities, then U₁₂ lt; 0.

How does one interpret this sign? Atkinson and Bourguignon (1982) discussed the class of least concave functions associated with a particular preference ordering and the special case in which preferences are homothetic. In this situation, the utility function U(.) is neatly characterized by two parameters: #949; gt; 0 summarizing aversion to inequality of multiperiod utility, and #961; gt; 0 summarizing the inverse of the elasticity of substitution between income in each period (i.e., the degree of aversion to intertemporal fluctuations in income; Gottschalk and Spolaore, 2002, p. 195). The case U₁₂ lt; 0 corresponds to the situation in which #949; gt;#961;, i.e., in the social welfare assessment, multiperiod inequality aversion offsets aversion to intertemporal fluctuations (which are of course reducing mul­tiperiod inequality). When #961; = 0, an increase in income mobility must increase social welfare. With perfect substitution of income between periods, one is only interested in the reduction of multiperiod inequality.

Gottschalk and Spolaore (2002) pointed out that origin dependence has no role in the Atkinson-Bourguignon model.^[581] In transition matrix terms, if there is any preference at all for income reversals (#949; gt; #961;), not only does an increase in mobility represent a social wel­fare gain, but also the complete reversal scenario is preferred to the origin independence one. This feature has relevance to the application of the social welfare framework to mobility measurement using stochastic dominance checks (discussed in the next section). The irrelevance of origin dependence suggests that the approach is less applicable to inter- generational mobility comparisons because origin independence is the principle most commonly espoused in that context (see earlier discussion).

However, an important contribution of Gottschalk and Spolaore (2002) was to show that greater origin independence can be social welfare improving if the SWF is gener­alized to take account of aversion to future income risk. In the two-period context, they drop Atkinson and Bourguignon’s assumption that period-2 income is known with cer­tainty in period 1. Individuals take conditional expectations of period-2 incomes based on observed period-1 incomes and the joint density of outcomes. With homothetic preferences, the utility function is now characterized by a third parameter, #947;, summa­rizing the degree of aversion to second-period risk. As Gottschalk and Spolaore demonstrated,

Origin independence reduces both multi-period inequality and intertemporal fluctuations, but increases future risk. Individuals will positively value origin independence as long as aversion to multi-period inequality and aversion to fluctuations dominate aversion to future risk (e and p are not smaller than g, and at least one of them is larger).

Gottschalk and Spolaore (2002, p. 204)

In summary, evaluation of income mobility in terms of social welfare has payoffs. There is a single unifying framework. Within this, whether an increase in income mobility is social welfare improving depends on the priority given to different mobility concepts. For instance, reversals are less likely to be valued the greater the aversion to intertemporal fluctuations and to future income risk, but more likely to be valued the greater the aver­sion to multiperiod inequality. Nonetheless one limitation of the SWF framework dis­cussed so far is that it does not incorporate evaluations of mobility in the form of individual income growth—apart from aspects of this that overlap with the other con­cepts. One leading exception is the research by Bourguignon (2011), who shows that the Atkinson and Bourguignon results can be applied to comparisons of alternative “growth processes” in the case in which the pair of marginal distributions relating to the first period are identical. However, this is a severe constraint on the applicability of the results.

An alternative strategy is to define SWFs explicitly in terms of income mobility— income changes rather than income levels. For example, one may assume that individual-level mobilities are represented by some measure of “distance” between first­and second-period incomes for each individual i, d(x_i,y_i), where the distance function is common to all individuals, and a social weight. Overall social welfare is the weighted sum over individuals of the d_i. King (1983) and Chakravarty (1984) assume that d_i is a function ofperiod-1 and period-2 income ranks (the positional mobility case), and that reranking is desirable (#8706; W#8725;#8706;d_i gt; 0) and the social weight is increasing in period-2 income. By con­trast, for Van Kerm (2006, 2009) and Jenkins and van Kerm (2011), d_i is a directional measure of individual income growth, and the social weight depends on base-year income ranks. For a more general discussion, see Bourguignon (2011), who discussed how the Atkinson-Bourguignon utility-of-income function, U(x,y), can be rewritten as V(x,y — x) with the same properties on the differentials of the second (income change) argument. This framework would lead one to question, for example, the approach of Fields et al. (2002), whose SWF is the simple average of the d_i (equality of social weights), and so #8706;V#8725;#8706;x = 0: mobility evaluations do not depend on initial income at all.

The main advantage of defining SWFs in terms of mobility directly is that there is great flexibility in the specification of the distance function d_i. The disadvantage of the approach is that it runs the risk of being ad hoc rather than a general unifying frame­work like the Atkinson and Bourguignon (1982) one. In particular, how should the social weights be specified? Unfortunately, the Bourguignon (2011) framework provides no simple answers.

The social welfare approaches described so far assume that W is a form of expected utility evaluation, though modified to context: Atkinson and Bourguignon (1982) incor­porated preferences that were not time-additive, and in addition, Gottschalk and Spolaore (2002) abandoned complete predictability of income. A different approach alto­gether is to suppose that evaluations are based not on expected utility but prospect theory. Jantti et al. (2014) explored this idea, utilizing a utility function that incorporates reference-income dependence and loss aversion. The latter feature means that, over and above any preference for smooth rather than fluctuating incomes over time, fluctu­ations lower individuals’ welfare directly because losses outweigh gains of equal size. There is therefore an asymmetric treatment of income decreases and decreases, as for the “distressed gentlefolk” argument cited earlier but rather differently motivated. This approach is a promising area of research and chimes with more popular expressions of the problem of growing income risk. Hacker and Jacobs (2008), for instance, specif­ically cited loss aversion as one of the factors related to the growth of income risk in the United States.

10.3.