How Mobility Is Actually Measured

The last lesson established what mobility is. This one is about the fact that measuring it is genuinely difficult, and that getting it wrong produced, for two decades, a national self-understanding that was substantially false.

This is 7.2.2's measurement-error problem with the largest political consequences of any example in this course.

How a country discovered it was half as mobile as it thought.

Through the 1970s and 1980s, the standard estimates of intergenerational income mobility in the United States told a reassuring story. The association between fathers' and sons' earnings appeared to be weak — around 0.2 on the standard measure. On that figure, any advantage or disadvantage would wash out almost entirely within three generations. A family at the very top would be close to average by the time of the grandchildren.

This was cited widely, and it fitted a national self-image.

Then in 1992 two economists, working independently, showed that the estimates were badly biased downwards, and why.

The problem was that the studies used a single year's earnings as a measure of a parent's economic position.

A single year is a noisy measure of what you actually want, which is the parent's permanent or lifetime economic position. Any given year contains a bonus, an unemployment spell, a strike, an illness, a one-off sale, a bad harvest — transitory variation that has nothing to do with the family's standing.

And 7.2.2 tells you exactly what noise in a predictor does: it attenuates the coefficient towards zero. The measurement error was making the association look weaker than it was.

The correction was to use averages of earnings over several years, and to use samples that followed families properly. The estimated association roughly doubled, to around 0.4 or higher.

Nothing about American society had changed. The measurement had. And the difference between 0.2 and 0.4 is the difference between advantage disappearing in three generations and persisting well beyond five — which is the difference between two entirely different countries.

The lesson generalises beyond this case, and it is the reason for the lesson. Every quantity in this field — origins, destinations, permanent income, class position — is a latent variable measured through a noisy proxy (see 7.2.2). The estimates are only as good as the proxies, and the direction of the bias is usually knowable.

What, exactly, are you correlating?

Mobility of what? Class position, earnings, total income, wealth, education, occupational status. These give systematically different answers, in a consistent order.

Educational mobility is highest — the association between parents' and children's education is real and weaker than the others, partly because education is capped at the top and mass expansion compressed it.

Income mobility is intermediate.

Wealth mobility is lowest of all. Wealth transmits directly through gifts and inheritance, compounds by earning returns, and is not capped (see 8.1.2). Studies that measure only earnings systematically understate how much advantage is transmitted, because they omit the component that transmits most reliably.

And whose position? Fathers and sons, historically — because early data linked men to men, and because women's own earnings were shaped by labour supply decisions the model had no way to handle. Including daughters requires a choice: use their own earnings, which are affected by whether and how much they work, or family income, which imports a partner's position and turns the study partly into one of marriage matching. Both are defensible and they answer different questions, and studies that quietly pick one should say so.

The measures

Four, each answering a different question.

One — the intergenerational elasticity. Regress the logarithm of the child's income on the logarithm of the parent's. The coefficient says: a one per cent difference in parental income is associated with X per cent difference in the child's. Zero means origins predict nothing; one means complete persistence.

Its known weakness matters and is often ignored. The elasticity conflates persistence with the spread of the distribution. If inequality widens, the same underlying degree of persistence produces a larger elasticity, because the same rank position now corresponds to a bigger income gap. Comparing elasticities across countries with different inequality — which is precisely what cross-country mobility comparisons do — is therefore comparing two things at once.

Two — the rank-rank slope. Convert everyone to a percentile rank within their own generation, and regress the child's rank on the parent's. The coefficient says: moving up ten percentiles in the parental distribution is associated with moving up X percentiles in the child's.

This is the modern workhorse, because it is unaffected by how unequal either generation's distribution is, it handles zero and negative incomes that logs cannot, and it is stable across specifications. When you see a modern mobility figure from administrative data, it is usually this.

Three — the transition matrix. Divide each generation into fifths (or tenths) and tabulate origin against destination. The most legible measure in the field, and the one that reveals what the single-number measures hide: movement is not uniform across the distribution.

Four — absolute income mobility. The proportion of children earning more than their parents did at the same age. This is the "am I doing better than my parents" question from 8.3.1, in income rather than class terms.

And the American finding on this measure is one of the most striking numbers in the field. For children born around 1940, roughly 90 per cent out-earned their parents at the same age. For those born around 1980, roughly half. Decomposition attributes the great majority of the decline not to slower growth but to the distribution of that growth — the gains going disproportionately to the top, so that a given amount of growth lifted far fewer people past their parents' position.

Four measurement problems that change estimates substantially.

Attenuation from transitory income. The story above. The remedy is multi-year averages — several years at minimum, and the correction is large.

Lifecycle bias, which is subtler and equally important. Earnings profiles diverge over a career: people with more education start lower and rise more steeply. So the age at which you measure changes the answer. Measuring parents or children too young or too near retirement biases the estimate of persistence, and the least-biased point is somewhere around mid-career. Studies measuring children in their twenties systematically understate persistence, and there have been a lot of them.

Linkage and selection. Connecting children to parents requires observing both, which in survey data means the family stayed traceable. Families that split, moved, migrated or dropped out are under-represented — and they are not randomly distributed with respect to the outcome (see 7.3.2).

And what administrative data fixes and does not. Tax records linking parents to children (see 7.4.4) transformed the field: enormous samples, minimal measurement error, and enough precision to estimate mobility for small geographic areas. What they cannot see is untaxed income, wealth transfers, informal work, and anyone outside the tax system — which is a specific and patterned blindness at both ends of the distribution.

What the better data showed

Three findings that single numbers concealed.

One — the extremes are sticky, at both ends.

Transition matrices consistently show that mobility out of the bottom fifth and out of the top fifth is much lower than mobility within the middle. The middle of the distribution churns; the ends do not.

And the top-end version has a name worth knowing: the glass floor. Studies in several countries have found that children from advantaged families who perform poorly are more likely to end up as high earners than children from disadvantaged families who perform well. Low attainment does not produce downward mobility for the advantaged at anything like the rate high attainment produces upward mobility for the disadvantaged.

Read that carefully, because it is 8.3.1's zero-sum problem made visible. The glass floor is what prevents downward mobility — and without downward mobility there is no room for upward mobility in a static structure. The glass ceiling and the glass floor are the same phenomenon observed from two sides.

Two — mobility varies enormously within countries.

Administrative data made it possible to estimate mobility at the level of small areas, and the variation is very large — in the United States, differences between local areas in the chances of a child from the bottom fifth reaching the top fifth are comparable in magnitude to differences between countries.

The correlates of high-mobility places are consistent: less residential segregation, lower local income inequality, better schools, more two-parent households, and higher measured social capital.

And the causal question was addressed properly, which is why this evidence is worth more than the correlations. A design based on families who moved — comparing children who moved to a better area at different ages — found that outcomes improved roughly in proportion to the number of childhood years spent in the better area, with the gains concentrated among those who moved young. That exposure pattern is very hard to explain by selection, and it is the same finding as Moving to Opportunity's (see 7.4.2), arriving from a completely different design. Two designs with different weaknesses converging is what 7.8.3 says to look for.

Three — the cross-national relationship between inequality and mobility.

Plotting countries' income inequality against their intergenerational persistence produces a clear positive association: more unequal countries tend to be less mobile.

The relationship is real and the inference from it needs care, and this course applies its own standards here.

The sample is around a dozen to twenty countries, with mobility measured by different studies using different data and different age windows. The countries are not independent observations (see 7.5.4 on Galton's problem). The elasticity measure used on one axis is itself sensitive to the inequality on the other, which builds in part of the relationship mechanically — the rank-based measures reduce but do not eliminate this.

And a cross-sectional association between countries cannot establish the mechanism. The plausible story — that greater distance between rungs means larger differences in what parents can invest, and stronger incentives to hoard — is consistent with the data and not demonstrated by it.

So: a real and suggestive pattern, consistent with within-country evidence and with a plausible mechanism, resting on a small number of non-independent observations and a measure with a built-in dependency. Worth citing; not worth citing as settled.

And the multigenerational claim, which is the most contested thing in the field.

Two-generation studies may understate persistence, because they miss anything transmitted by grandparents, extended family, or lineage-level resources that skip a generation.

The most striking attempt to measure this used surnames. Tracking rare surnames through elite institutions — universities, professional registers, probate records — across many generations and several societies, it reported an underlying rate of persistence far higher than conventional estimates, of the order of 0.7 to 0.8, and remarkably similar across societies and centuries, implying that status regresses to the mean very slowly indeed and that policy has done little to change it.

The criticisms are serious and largely persuasive.

Rare surnames are not a random sample of families. They select on groups with unusual histories — regional, religious, ethnic or dynastic — whose persistence may exceed that of ordinary families.

Group-level persistence is not individual persistence. A surname group's average status can persist while individuals within it move a great deal; the method estimates the former and the conclusion is drawn about the latter.

And the method assumes surnames track lineages in a way that intermarriage, name changes and migration all disrupt.

What survives. The general point that two-generation studies probably understate long-run persistence is well taken and supported by other evidence. The specific claim of a near-universal high constant of social persistence is not established, and the direct evidence on grandparent effects — using proper multigenerational data — is mixed, with some studies finding a real net grandparent association and others finding it disappears once parental position is measured well.

Because "mobility is falling" is asserted constantly and is four different claims.

Five questions for any mobility figure.

Mobility of what — class, earnings, income, wealth, education? Wealth is where the transmission is strongest, and it is measured least.

Which measure — elasticity (sensitive to the inequality of both distributions), rank-rank, a transition matrix, or the proportion out-earning their parents? These answer different questions and can move in different directions.

Measured at what age, and averaged over how many years? A single year in the twenties is the combination that produces the most optimistic and least reliable answer.

Absolute or relative (see 8.3.1)? The most-quoted recent finding — the fall from around 90 per cent to around half out-earning their parents — is an absolute measure, and most of it is attributed to how growth was distributed rather than to the fairness of the competition.

And whose parents, whose children? Fathers and sons only, or including daughters, and by own earnings or family income?

Two things are solidly established across all of this. The extremes are sticky at both ends, and the glass floor is as real as the glass ceiling. And place matters causally, on the strength of two designs with different weaknesses reaching the same exposure-graded conclusion.

Everything else in this lesson deserves a magnitude and a method attached to it — which is the discipline 7.9.1 asked for, applied to the field where the numbers get quoted most and checked least.

American intergenerational income persistence was estimated at around 0.2 until 1992, when two studies showed that using a single year of parental earnings attenuated the coefficient towards zero. With multi-year averages it roughly doubled, to around 0.4 or above. Nothing about the society changed — and the difference is between advantage vanishing in three generations and persisting well beyond five.

Mobility of what matters: educational mobility is highest, income intermediate, wealth lowest of all — and studies measuring only earnings omit the component that transmits most reliably. And whose position: including daughters requires choosing between own earnings and family income, which answer different questions.

Four measures. The elasticity, which conflates persistence with the spread of the distribution and therefore cannot be compared cleanly across countries with different inequality. The rank-rank slope, the modern workhorse, unaffected by either distribution's spread. The transition matrix, the most legible, which reveals what single numbers hide. And absolute income mobility — where the proportion of Americans out-earning their parents fell from about 90 per cent for the 1940 cohort to about half for the 1980 cohort, most of it attributed to the distribution of growth rather than its rate.

Four measurement problems: transitory-income attenuation; lifecycle bias, where measuring children in their twenties systematically understates persistence; linkage and selection in survey data; and administrative data's specific blindness to untaxed income, wealth transfers and anyone outside the tax system.

Three findings the better data revealed. The extremes are sticky at both ends — and the glass floor, where low-attaining advantaged children out-earn high-attaining disadvantaged ones, is 8.3.1's zero-sum problem made visible: the glass ceiling and the glass floor are one phenomenon seen from two sides. Place matters causally, on the strength of a movers design showing gains proportional to childhood years of exposure, converging with the Moving to Opportunity evidence from a different design. And the cross-national inequality–immobility association is real, suggestive, and resting on a dozen or so non-independent observations with a measure that has part of the relationship built in.

The surname studies' claim of a near-universal high persistence constant does not survive — rare surnames select on unusual groups, and group-level persistence is not individual persistence — but the underlying point that two-generation studies understate long-run persistence is well taken.

Permanent income — a family's lifetime economic position; the latent quantity a single year proxies badly.

Attenuation bias — the pull of a noisy predictor's coefficient towards zero.

Intergenerational elasticity — the log-log association; conflates persistence with distributional spread.

Rank-rank slope — the association between percentile ranks across generations; robust to changing inequality.

Transition matrix — origin quintile against destination quintile.

Absolute income mobility — the share of children out-earning their parents at the same age.

Lifecycle bias — distortion from measuring earnings at an age where profiles have not converged.

Stickiness at the extremes — much lower mobility out of the top and bottom than through the middle.

Glass floor — the protection of low-attaining advantaged children from downward mobility.

Exposure effect — outcomes improving in proportion to childhood years spent in a better environment.

Great Gatsby curve — the cross-national association between inequality and intergenerational persistence.

Multigenerational persistence — transmission beyond two generations; surname methods and their selection problem.

One — check the age. Find any mobility study and locate the ages at which parents' and children's incomes were measured. If the children are under thirty, expect the persistence to be understated.

Two — find the wealth version. For any country whose income mobility you know, look for an estimate of wealth mobility. The difference between the two figures is the part of transmission that earnings studies miss.

Three — read a transition matrix. Find one for your country and compare the diagonal cells at the top and bottom with those in the middle. The stickiness will be visible without any statistics.

Four — test the elasticity problem. Take two countries with different inequality and the same rank-rank slope. Work out why their elasticities would differ, and then check how the comparison is usually reported.

Five — apply 7.9.1 to the Gatsby curve. Find the chart, count the countries, and ask: are these independent observations, and is the measure on one axis affected by the variable on the other? Then decide how much weight it can carry — which is not zero.