Paul Bingley

Research

A recurring lesson in this work is that the obvious comparison often points the wrong way. What looks harmful can be beneficial, and inequality that looks modest can be large.

A tutoring trial that randomises pupils inside a school nets out any gain to their classmates, and across 81 Danish schools the untutored pupils gained as well. Children whose parent was a victim of crime do worse at school, but so do children whose parent was victimised only after they left it, so most of the gap is not the crime. The gap in lifespan between the top and bottom of Danish society is 9 years by education alone and 24 when five measures of status are combined.

The seven areas below are the themes the work runs through.

By Life Course

Infancy and Early Childhood

School

Leaving School

Working Life

Retirement and Later Life

The Whole Life, and the Next

Education and Early Skills

Early literacy instruction, the returns to schooling and skills, and how children's family circumstances show up in what they learn.

Standard trials understate the gains from tutoring The lower bound on the social multiplier is 3.2 at the observed tutoring share of 0.171, 2.0 to 3.7 across shares 0.15 to 0.25, and falls to 1 at a share of 0.40. Plausible range No gain to classmates At least 3× at the share schools tutored 1× 2× 3× 4× 5× 15% 20% 25% 30% 35% 40% Share of pupils a school would tutor True gain vs. what a standard trial sees

Tutoring a few kindergartners raised reading for the whole school.

Tutoring trials usually randomise pupils within schools, which nets out any benefit to classmates. We randomised 81 Danish schools and 2,583 kindergartners, tutored a few in each and tested all of them. Decoding rose 0.38 standard deviations in the pre-registered target group and 0.27 school-wide. Bounds needing only random assignment and the test's range put the gain to never-tutored peers at 0.19 SD or more, so evaluating tutoring within schools understates its value two- to threefold.

The line is a lower bound, built only from random assignment and the test's score range.

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Family Background and the Transmission of Advantage

What passes from parents to children and between siblings: earnings, schooling, employers, and the shocks that reach a child through a parent.

Effect of parental job loss on grade 9 maths by the child's age at the job loss Job loss when the child is 0 to 1 lowers grade 9 maths by 0.041 SD (95% interval -0.071 to -0.010). Effects at later ages are smaller and their intervals include zero. Ages 17 to 22, after school, are the reference group. After school −0.04 SD +0.02 0 −0.02 −0.04 −0.06 0–1 Infancy 2–5 6–11 12–16 17–22 Child's age when parent lost job Effect on grade 9 maths (SD)

Parental job loss hurts children most when it hits in infancy.

Earlier work shows that losing a job harms the children of the worker, without saying whether the child's age matters. We use Danish plant closures, match exposed children to similar peers, and difference out the selection that does not vary with the child's age by using parents displaced after school has ended. A job loss in a child's first two years lowers ninth-grade maths by 0.04 SD, and the families who cannot borrow their way through the shock drive the result. Job losses later in childhood do much less harm.

Dots are effects by the child's age when the parent lost their job, with 95% intervals. The grey dot is the after-school group everything is compared against.

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Effect of a parent's criminal victimization on grade 9 maths, by crime type and child's age Violent victimization of a parent when the child is 0 to 5 lowers grade 9 maths by 0.048 SD (95% interval -0.087 to -0.009). Later ages show smaller effects with intervals including zero. Theft effects are close to zero at every age. Ages 17 to 21 are the reference group. After school −0.05 SD +0.02 0 −0.02 −0.04 −0.06 −0.08 0–5 6–11 12–16 17–21 Child's age when parent was victimized Effect on grade 9 maths (SD) Violent crime Theft

When a parent is attacked, their young children do worse at school years later.

We link Danish police records to children's exam results and compare children whose parent was a victim of crime with closely matched children whose parent was not. Much of the raw gap is selection, because children whose parents are victimized only after they leave school already score 0.10 SD lower. Subtracting that, violent crime against a parent lowers a child's maths score by 0.05 SD when it happens before age six, while property crime has none. Treating the family rather than the individual victim is what the paper argues for.

Dots are effects by the child's age when the parent was victimized, with 95% intervals. Blue shows violent crime, grey shows theft. Victimization after school ends is the comparison group.

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Share of the variance explained by heritability, under the classic twin design and after relaxing its equal-environments assumption Heritability falls from 34 to 9 percent for schooling, 60 to 16 for earnings, 56 to 14 for disposable income and 42 to 14 for wealth, once the degree of environmental sharing is allowed to differ between identical and fraternal twin pairs. 0 20 40 60 Schooling 9 34 Earnings 16 60 Disposable income 14 56 Wealth 14 42 Heritability, % of the variance Twin-family model Classic twin design

Testing the twin model's equal-environments assumption cuts the heritability of schooling from 34 to 9 percent.

The classic twin design reads any excess similarity between identical pairs as genetic, which holds only if identical and fraternal pairs share their environments to the same degree. Linking the Danish Twin Registry to the twins' spouses and children identifies the model without assuming it, and the assumption is rejected. Heritability falls from 34 to 9 percent of the variance in schooling and from 60 to 16 percent in earnings. Shared family environment accounts for 42 and 26 percent.

Not every relaxation of the model lowers heritability: allowing assortative mating on genes raises the schooling estimate to 45 percent, and the data show no genetic dominance. At 9 percent, schooling sits nearer the 4 to 5 percent that direct genetic effects in genome-wide studies imply than the 40 percent twin designs usually return. Danish twin families, twins born around 1950.

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Composition of the intergenerational transmission of education for two parental cohorts For parents born in the early 1920s, 93 percent of the transmission of education came from factors both parents shared and 7 percent from each parent separately. For parents born in the early 1950s the parent-specific share is 27 percent. Total persistence is unchanged. 93% 7% Parents born early 1920s 73% 27% Parents born early 1950s Shared by both parents From each parent separately

Three quarters of what parents transmit comes from both of them at once.

Educated people marry each other, so a child's schooling cannot easily be credited to one parent or the other. We model education within more than 400,000 Danish families of two parents and two children. About 75 percent of the intergenerational correlation in education comes from what the parents share, and what each transmits on their own is a sixth the size. Sorting into couples by education fell 38 percent across parents born from the early 1920s to the early 1950s.

Bars split the transmission of education into what both parents share and what each passes on independently. Total persistence is the same in both cohorts, because the parent-specific share grew as the shared share fell.

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Share of the correlation between brothers' earnings that comes from transmission from the father Earlier studies, which assume transmission works the same way in every family, put the share of the sibling earnings correlation due to intergenerational transmission at 6 percent. Allowing transmission to differ between families raises it to 72 percent. Earlier studies 6% Allowing families to differ 72% 0 20 40 60 80 Share of the sibling correlation (%) The brothers' earnings correlate 0.22 over the life cycle.

Transmission from the father accounts for 72 percent of how alike brothers earn.

Brothers' earnings resemble each other, and the standard reading is that parents account for little of it, with shared schools, neighbourhoods and friends doing the work. Those shares came from calibrations that assume transmission works the same way in every family. Using Danish father and two-son triads we measure it directly and let families differ. The sibling correlation averages 0.22 over the life cycle, and 72 percent of it is intergenerational.

Bars are the share of the brothers' earnings correlation that comes from transmission from the father. The correlation itself is U-shaped over the life cycle, which no earlier study could see.

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Pensions, Retirement and Later Life

Retirement behaviour and pension reform, the capacity to work at older ages, and how reforms fall on people who entered old age with different resources.

Mechanical effect of two waves of Danish pension reform on expected lifetime benefits The 1990 to 2008 reforms raised expected lifetime benefits by 30 percent for the lowest socioeconomic group and about 18 percent for the highest. The 2008 to 2022 reforms cut them by 4 percent for the lowest group and raised them 14 percent for the highest. -10% 0 +10% +20% +30% +30% +18% 1990–2008 -4% +14% 2008–2022 Reform period Lowest fifth by affluence Highest fifth Change in expected lifetime benefits

Denmark's pension reforms first favoured the poorest, then reversed.

Whether a pension reform helps or hurts depends on who you are and how long you live. We model Danish retirement decisions by affluence group from 1990 to 2022, allowing for the fact that poorer Danes collect their pension for fewer years. Lowering the state pension age from 67 to 65 raised expected lifetime benefits by 30 percent for the poorest fifth and about 18 percent for everyone else. Raising it back cut the poorest fifth by 4 percent while the richest fifth gained 14.

Bars are the mechanical effect of each reform period, holding retirement ages fixed. Behavioural responses are far smaller, zero to 2 percent in the first period and between 3 and 6 percent lower in the second.

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Effect of job displacement on employment and retirement, all ages against displacement at 55 to 59 One year after displacement, employment is 5 percentage points lower on average and 10 points lower for those displaced in their late fifties. Four years after, retirement is 1 point higher on average and 6 points higher for the late fifties group. no change Employment, one year after -10 -5 Retired, four years after +6 +1 -10 -5 0 +5 Percentage points All ages Displaced at 55–59

Earnings do not recover for workers displaced in their late fifties.

We follow Danish workers displaced by workplace closures for ten years, against matched workers whose employers stayed open. On average employment is 5 percentage points lower the year after and back to 2 points by year ten, while earnings fall 10 percent and recover to 5. Workers displaced in their late fifties take twice the immediate employment penalty, and their earnings do not recover, and keep falling for seven more years. Four years on, 6 percent more of them have retired.

Dots are the gap between displaced workers and their matched controls. The hollow dot is the average over all ages at displacement, the blue dot those displaced at 55 to 59.

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Years worked by Danish men aged 55 to 69 in 2010, and the additional years their health could have supported Men aged 55 to 69 worked 7.8 years on average in 2010. At the employment rates that prevailed in 1977 for the same level of mortality, they could have worked 4.7 years more, 60 percent above the actual figure. Ages 55 to 69, Danish men, 2010 7.8 4.7 Years actually worked Additional capacity at 1977 mortality The unused capacity is 60 percent of the years actually worked.

Danish men in their late fifties and sixties could work years longer than they do.

Mortality is a crude measure of health but a comparable one over long periods, so we ask how much men used to work at the mortality rates men have now. In 2010, men aged 55 to 69 worked 7.8 years on average. At 60 their mortality was 1.0 percent and 67 percent of them were employed; in 1977, at that same mortality, 86 percent were. Repeating the comparison at every age gives 4.7 further years of capacity.

The bar splits the 12.5 years that 1977 employment implies into the 7.8 actually worked and the 4.7 unused. Capacity is an upper bound, counting health alone and not preferences, demand for older workers or pension rules.

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Health, Longevity and Inequality

How long people live and in what health, set against the whole of their socioeconomic position and not one proxy for it.

Gap in life expectancy at 40 between lowest and highest socioeconomic status, Danish men and women born 1942 to 1944 Education: men 78 to 87, women 83 to 92; IQ at the draft board: men 76 to 85; Income: men 68 to 85, women 80 to 88; Wealth: men 69 to 86, women 80 to 92; Occupation: men 67 to 86, women 83 to 92; All combined: men 65 to 89, women 74 to 97. Education 9 / 9 yrs IQ at the draft board 9 yrs / n.a. (men only) Income 17 / 8 yrs Wealth 17 / 12 yrs Occupation 19 / 9 yrs All combined 24 / 23 yrs 65 89 74 97 60 70 80 90 100 Expected age at death, lowest to highest status Men Women

The socioeconomic gap in lifespan is far bigger than education or income alone suggest.

Studies of inequality in lifespan usually rank people by one measure, such as schooling or income, missing anyone high on one and low on another. We follow every Dane born in 1942 to 1944 from age 40 to 78 and use machine learning to combine education, income, wealth, occupation and IQ into one ranking. The highest-status men can expect to live 24 years longer than the lowest, and women 23 years, compared with only 9 years for either sex when ranked by education alone. Wealth is the most informative measure.

Each bar runs from the life expectancy at 40 of the lowest-ranked group to that of the highest, for each measure alone and for all combined. Right-hand numbers give the gap for men, then women.

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Years of ageing equivalent to the income gap in health among Danish retirees, by health domain Among Danes aged 65 to 89, the health gap between income deciles is equivalent to 19 years of ageing for mental health, 12 years for functional health, 8 years for comprehensive health and 5 years for cognitive health. Mental health, 2017 9th against 5th income decile 19 yrs Functional health, 2006 9th against 2nd income decile 12 yrs Comprehensive health, 2017 9th against 5th income decile 8 yrs Cognitive health, 2015 5th against 2nd income decile 5 yrs 0 5 10 15 20 Catch-up time (years of ageing)

Among Danish retirees, the income gap in mental health is worth 19 years of ageing.

Denmark now indexes its pension age to life expectancy, which assumes the extra years are healthy and that they are healthy for everyone. Following Danes aged 65 to 89 from 2004 to 2022, we convert each income gap in health into the years of ageing it is equivalent to. Mental health gives the longest gap at 19 years and functional health 12. Both have narrowed since, largely because lower-income retirees got healthier.

Catch-up time is how much longer a lower-income retiree would have to live to reach the health of the higher-income group. Each bar names the income deciles compared, which differ by domain and year.

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Association between schooling and health outcomes, before and after comparing identical twins with each other Across six outcomes, an extra standard deviation of schooling is associated with 7 to 21 percent less hospitalization and mortality. Comparing identical twins within a pair removes the association in every case, and three of the six estimates change sign. Days in hospital, to 2003 Days in hospital, to two years before death Died by 2003, men born 1921–35 Died by 2003, men born 1936–50 Died by 2003, women born 1921–35 Died by 2003, women born 1936–50 -20% -10% 0 +10% All individuals Within twin pairs

Between identical twins, more schooling does not predict better health.

People with more schooling spend fewer days in hospital and die later, and the association is often read as a return to education. Schooling also stands in for what is inherited and raises both. Using the Danish Twin Registry linked to population registers, we compare identical twins with each other, which holds genes and family fixed. An extra standard deviation of schooling is associated with 7 to 21 percent less hospitalization and mortality. Within twin pairs it disappears.

Each pair of dots is one outcome. The blue dot is the association across individuals, the hollow dot the same estimate within identical twin pairs. Three of the six change sign.

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Labour Supply, Taxes and Transfers

How taxes and transfer programmes change how much people work, including the in-work transfer programmes that lone mothers in Britain faced, and the elasticity of taxable income in Denmark.

Elasticity of taxable income in Denmark, employees against the self-employed Employees bunch at tax kinks with an elasticity of about 0.01 in every one of six tax regimes between 1980 and 2022. The self-employed show elasticities between 0.05 and 0.45, tracking the opportunities each regime left for shifting income. Employees, every regime 1980–2022 0.01 Self-employed, across six regimes 0.05–0.45 0 0.1 0.2 0.3 0.4 0.5 Elasticity of taxable income

Danish employees barely respond to income tax rates. The self-employed respond a great deal.

How much taxable income moves when tax rates change decides what a tax costs in efficiency, and published estimates differ by more than an order of magnitude. We apply one bunching design to six Danish tax regimes between 1980 and 2022. Employees bunch at kinks with an elasticity near 0.01 in every regime. The self-employed range from 0.05 to 0.45, rising and falling with the scope each regime left for shifting income between bases.

The bar spans the elasticities estimated across the six regimes. Employees are held still by third-party reporting. Those changing jobs, who are adjusting their income anyway, respond no more.

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Elasticities of gross wages, gross earnings and labour supply with respect to the marginal income tax rate A higher marginal tax rate raises gross wages with an elasticity of 0.44 and gross earnings with an elasticity of 0.36, so part of the burden shifts to the employer. The labour supply elasticity with respect to the wage is 0.14. Gross wage, to the marginal tax rate 0.44 Gross earnings, to the marginal tax rate 0.36 Labour supply, to the wage 0.14 0 0.1 0.2 0.3 0.4 0.5 Elasticity

Part of a rise in income tax lands on the employer.

Studies of how income tax changes work usually hold the gross wage fixed, so the whole of a tax change reaches the worker by construction. Using matched Danish establishment and worker records we let the wage adjust instead. A higher marginal rate raises gross wages with an elasticity of 0.44 and gross earnings with an elasticity of 0.36, so employers carry part of the burden though not all of it. Assuming no shifting overstates the incentive effect by about a factor of two.

All three elasticities come from one model estimated on establishment and worker panel data, and all are precisely measured.

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Firms, Wages and Careers

Earnings dynamics over a career, the part of wage inequality that belongs to firms rather than workers, and the returns to staying put.

Share of earnings inequality explained by firms and by workers, early and late in a career Firm heterogeneity explains about a quarter of earnings dispersion at age 30 and 8 percent by the mid-fifties, by which point permanent differences between workers explain about 70 percent. Firms, at age 30 25% Firms, mid-fifties 8% Workers, mid-fifties 70% 0 20 40 60 80 Share of earnings inequality (%)

The firm explains a quarter of the earnings gap at 30, and 8 percent by the mid-fifties.

Work on earnings dynamics usually leaves firms out, and work on firm pay premiums usually leaves the life cycle out. We identify both together from the covariance of co-workers' earnings in the Italian private sector. At 30, firms account for about a quarter of earnings dispersion and worker-firm sorting for a fifth. By the mid-fifties firms account for 8 percent and permanent differences between workers for about 70 percent.

Each bar is a share of the total variance of earnings at the age shown. Ignoring the tendency of similar workers to end up together overstates sorting by a factor of two.

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Military Service and the Draft

Denmark assigned conscription by lottery and tested every recruit first, which is how the cost of a year of service, and the pull of one brother on another, can be measured at all.

Qualification test scores of deployed Danish soldiers by local unemployment and route into service Deployed soldiers who volunteered score 18 percent of a standard deviation below deployed conscripts. Conscripts' scores fall by 13 percent of a standard deviation for each point of local unemployment, volunteers' by 8 percent, so the two converge when unemployment is high. -0.6 -0.4 -0.2 0 +0.2 Conscripts Volunteers 2% 4% 6% 8% Local unemployment at deployment Test score, SD from a conscript at 4% The gap closes as unemployment rises.

A draft lottery brought in sharper soldiers than volunteering did.

Denmark recruits conscripts and volunteers at the same time and assigns the conscripts by lottery, which makes the two routes comparable. Among soldiers deployed to peacekeeping and peace-enforcing missions, those who had volunteered score 18 percent of a standard deviation below those who were drafted. Conscripts' scores also track the economy more closely, falling 13 percent of a standard deviation per point of local unemployment against 8 percent for volunteers.

Lines are fitted from the estimated coefficients, measured against a conscript deployed when local unemployment is 4 percent. On every other deployment outcome measured, the two routes are alike.

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Effect of military service on adult numeracy and literacy by position in the forces' qualification test Among men in the lowest third of the Armed Forces Qualification Test, service raises numeracy by 22 percent of a standard deviation and literacy by 16 percent. In the middle third numeracy rises 24 percent. In the highest third neither effect is statistically significant. 0 10 20 22 16 Lowest third 24 n.s. Middle third n.s. n.s. Highest third Armed Forces Qualification Test at 18 Numeracy Literacy Effect, % of a standard deviation

Conscription raised the literacy only of the men who tested worst.

Conscription is usually judged by what it costs in earnings and schooling, seldom by what it teaches. We match the Danish draft lottery to adult skills measured about ten years after service. Service raises numeracy and literacy by 7 to 10 percent of a standard deviation. The literacy gain belongs entirely to men who scored in the lowest third of the forces' own test at 18, and the numeracy gain to the lowest and middle thirds. For the lowest third it offsets 45 percent of their literacy shortfall.

Bars are instrumental variable estimates of the effect of serving, by third of the Armed Forces Qualification Test. Men in the lowest and middle thirds are also more likely to complete vocational training after service.

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Effect of an elder brother's military service on a younger brother's service A younger brother's service has no effect on his elder brother. An elder brother's service raises a younger brother's chance of serving by about 3 percentage points on average, rising to 26 points for three closely spaced brothers with no sisters, with a wide interval. Placebo: younger brother → elder 0 Elder → younger, all pairs +3 pts …born within 3 years +5 pts …with a third brother +8 pts …three close brothers, no sisters +26 pts 0 10 20 30 40 50 Change in chance of serving (percentage points)

An elder brother sent to serve makes his younger brother more likely to serve.

Brothers often make similar choices, but it is hard to tell whether they influence each other or just share a background. Denmark draws lottery numbers for each brother separately, so an elder brother sent to serve by chance lets us measure his pull on the younger one. It raises the younger brother's chance of serving by 7 percent on average, and by 55 percent among three closely spaced brothers with no sisters. A younger brother's service does nothing to his elder brother, so the influence runs one way.

Dots are IV estimates with 95% intervals. The top row is a placebo test of the reverse direction. Each lower row narrows the sample to closer brothers.

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Effect of military service on earnings at ages 25 to 35, by quartile of the forces' qualification test Serving changes earnings by +1.3 percent in the lowest quartile and -1.4 in the second, neither significantly different from zero, by -2.9 in the third and by -7.1 percent in the highest. -10% -5% 0 +5% Lowest 2nd 3rd Highest −7% Cognitive ability at the draft board (quartile) Not significant Significant Effect of serving on earnings (%)

Among the men Denmark drafted, the ones with the best prospects paid the highest price.

Economists have long argued that conscription is a hidden tax, but not who pays it. Between 1994 and 2007, Denmark assigned military service by lottery after testing every recruit, so we can estimate the cost of serving separately by ability. Among men in the lowest quarter of the forces' test, serving leaves earnings at 25 to 35 unchanged. Among the highest quarter it lowers them 7 percent, a lifetime penalty of about $23,000, and part of it runs through schooling the service delayed.

Instrumental variable estimates of the effect of serving on log earnings at ages 25 to 35, by quartile of the Armed Forces Qualification Test, with 95% intervals. The two lower quartiles are not significantly different from zero.

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Data and Identification

Nearly all of the work runs on Danish administrative registers held by Statistics Denmark and reached through VIVE. They follow the whole resident population year by year rather than a sample, they go back decades, and they link people to their parents, siblings and children, to their workplaces, to their schooling and to their contacts with the health system. That is what makes it possible to ask how a child's education stands fifteen years after a parent lost their job.

The registers do not settle what causes what. The work therefore rests on situations where something was allocated by chance: the conscription lottery, workplace closures that hit some employees and not others, and trials designed from scratch, such as the reading experiments run in Danish classrooms. Where no such situation exists, affected families are compared with closely matched families that were not affected.