New Distribution-Sensitive Measure Tracks UK Wellbeing Shifts in COVID-19 Second Wave

When the second wave of the COVID-19 pandemic swept across Britain in the winter of 2020–21, the damage was not distributed evenly, and a new study has now measured precisely who lost the most happiness and why. Writing in Social Indicators Research, economist Paul Allanson of the University of Dundee School of Business introduces a distributionally sensitive framework for evaluating what he terms wellbeing mobility and applies it to the pandemic’s deadliest months. The results show that women in every age group saw their happiness decline more sharply than men, that the burden fell unevenly depending on where people started on the wellbeing ladder, and that older men who slid into low happiness found it unusually hard to climb back out. Beyond the headline findings, the study offers a new statistical toolkit that could reshape how governments judge whether a crisis has made a population better or worse off.

The empirical engine behind the analysis is the UCL COVID-19 Social Study, the largest panel survey in the UK tracking the psychological and social consequences of the pandemic, in which more than 70,000 adults participated between March 2020 and November 2021. From this resource Allanson assembled a balanced panel of 25,511 individuals, each observed once in a four-week window covering the onset of the second wave, from late August to mid-September 2020, and once in a matching window at its peak, from early January to early February 2021, by which time the UK COVID-19 death rate stood at an all-time high and stay-at-home orders had been reimposed nationwide. Respondents answered the Office for National Statistics question “In the past week, how happy did you feel?” on an 11-point scale running from “not at all” to “completely”. For the mobility analysis this scale was collapsed into four tested bands — low, medium, high and very high — and the sample was reweighted using an entropy balancing algorithm so that every gender-by-age subgroup matched official UK population controls for gender, age, ethnicity, education and nation of residence.

The heart of the method is the mobility matrix. Each individual’s initial and final happiness category are cross-tabulated into a grid whose cells record the proportion of the population making every possible journey between states, so that the matrix jointly captures the first-wave wellbeing profile and the transition process linking the two waves. From it comes the paper’s baseline gauge, popNAM, the population-level measure of net absolute mobility: the share of people moving up the happiness scale minus the share moving down. The approach borrows its evaluative logic from prospect theory, judging each person’s second-wave wellbeing against their own first-wave position rather than against a population average. Because it relies purely on counted movements rather than on the size of those movements, the measure also sidesteps a notorious pitfall in happiness research — numerical responses on wellbeing scales cannot be meaningfully compared in magnitude across individuals, a problem highlighted by economists Bond and Lang that undermines any analysis treating the scores as cardinal numbers. A positive popNAM means a randomly chosen adult was more likely to improve than to decline; a negative value means the opposite.

The verdict for the second wave was unambiguous. Between the two windows, 12.4 percent of British adults reported being happier while 35.8 percent reported being unhappier, leaving popNAM at minus 23.3 percentage points: a randomly chosen adult faced a 23.3-point smaller chance of becoming happier rather than unhappier. A counterfactual version of the measure that assumes outcomes are independent of starting positions still registered a 17.4-point deterioration, and both estimates were statistically significant under bootstrap resampling designed to respect the survey’s sociodemographic weighting. The underlying transition matrix was strictly monotone, meaning happiness prospects rose steadily with starting position: someone who began in the low band faced a 48.8-point smaller chance of improving than the average adult, while someone starting very high enjoyed a 49.9-point larger one. Movement was overwhelmingly between adjacent categories, and low happiness proved sticky. Only those who started in the lowest state had net positive prospects, with 27.5 percent of them climbing higher, while 54.5 percent of those who began very high slid downwards.

Yet popNAM carries a blind spot that sits at the heart of the paper: it counts every gained and lost place on the happiness ladder identically, whoever experiences it. Because wellbeing prospects are systematically worse for those lower down — a property known as a monotone transition process — any given aggregate change is more socially damaging when it concentrates among people who started out poor, a case made in the mobility literature by economist Valentino Dardanoni and one that argues for placing greater weight on their fates. Allanson confronts this with two novel devices. The first is a hierarchy of nonparametric mobility preference conditions built on the statistical preference criterion, a probability-based dominance rule that asks whether a randomly drawn individual is more likely to do better rather than worse. First-order preference demands that every initial wellbeing state enjoy at least as good a net chance of improvement as before, with a strict gain in at least one state; second-order preference demands this only for the pooled chances of the bottom states cumulated together; higher orders relax the requirement further. The conditions parallel established mobility dominance tests in the welfare literature but are deliberately weaker, and they proved decisive precisely where the stricter tests fell silent.

The second device is a parametric family of mobility evaluation indices, denoted m(σ), drawn from the extended Gini class introduced by Donaldson and Weymark. The parameter σ encodes society’s aversion to inequality in wellbeing prospects across ranks. At σ equal to one the weights are uniform and the index collapses to popNAM; at σ equal to two the weights fall linearly with rank, as in the familiar Gini coefficient; at three they fall at a decreasing rate; and as σ grows without bound only the prospects of the unhappiest state matter. In the British data, weighting the initially low happiness group 9.4 times more heavily than the very high group softened the measured decline, while at σ equal to three — a weight ratio of 67.2 — the index for happiness just barely turned positive. The framework then supplies a decomposition that splits any subgroup’s mobility gap into an initial-profile component, reflecting who was happy to begin with, and a transition-process component, reflecting how events actually moved people between states.

Applied across eight gender-by-age groups, the decomposition delivered its most striking results. Overall mobility differences were negative for women and positive for men in every age band, and the transition-process component followed the same gendered pattern, providing evidence that women’s happiness declined more than men’s even after controlling for differences in starting positions. For women aged 18 to 29 and 60 and over, the transition process was unambiguously worse than the national one under the first-order preference condition, a verdict the conventional first-order dominance criterion could not deliver for any subgroup at all. The deterioration among young women was not primarily a starting-point story: relatively few of them began very happy, which should have cushioned their group average, but their net prospects conditional on initial happiness were poor enough to swamp that advantage. For women over 60, adverse starting profiles — above-average numbers beginning at the top of the scale, from whom the only direction was down — combined with adverse transitions to produce the largest happiness declines of any group. Comparative happiness rose with age in both sexes, and the spread between the best- and worst-placed groups, some 11.1 percentage points, barely budged between windows.

The study also uncovers a quieter anomaly. Men aged 60 and over enjoyed the highest comparative happiness of any group in both windows, yet those among them who fell into low happiness were significantly less likely than the population at large to escape it, a pattern echoed, though less sharply, among men aged 46 to 59. Their above-average prospects when starting from high or very high positions masked this trapped minority in the headline numbers, with the gains of one set of starting states more than offsetting the losses of another. Allanson singles out the unusual persistence of low wellbeing among older men as a possible cause for concern that averages alone would have buried entirely. The same accounting explains why the over-60s of both sexes declined faster than everyone else: they had further to fall, having entered the second wave with unusually large numbers reporting the highest happiness categories.

Where does that leave society’s verdict on the second wave? Allanson argues that the degree of inequality aversion needed to declare the episode acceptable is implausibly extreme. For the happiness index to turn positive, σ must reach three, a value implying indifference between giving one more person an escape route out of the lowest happiness state and allowing 48 to 75 additional people, depending on the measure, to slide down from the top. Results for life satisfaction and worthwhileness, reported alongside the main analysis, tell the same story: both fell significantly between the windows, their transition matrices were monotone, and only the aggressive three-rank weighting turned their indices positive. Women again fared worse than men of the same age on both measures, women aged 18 to 29 ended the period with the poorest wellbeing of any subgroup on all three indicators, and parallel checks using data from the Understanding Society COVID-19 study broadly corroborated the pattern. The conclusion is stark: between the onset and the peak of the second wave, the change in UK wellbeing was, in the paper’s terms, socially undesirable.

The framework’s reach extends well beyond a single pandemic. Because it needs only discrete responses across two waves of panel data, it can be pointed at income, social status or health wherever such data exist, and its decomposition tells policymakers not merely that a crisis hurt some groups more, but why: whether a disadvantaged group suffered because it began behind, or because events dragged it down faster from the same starting line. That distinction matters for intervention design. Allanson notes that the acute vulnerability of young women is consistent with evidence on mental health during the pandemic’s first wave and might justify targeted support in any future lockdown, while the stubbornness of low happiness among older men argues for monitoring mobility rather than means. As the paper’s deeper point makes clear, wellbeing prospects are best judged relative to each person’s own past — a standard that averages, however convenient, can never meet.