Joint distributions and multiple inequalities

Joint distributions and multiple inequalities

Social and economic disadvantage takes many different forms, and can be measured in many different ways: by education, income, disability, race/ethnicity, gender, sexual orientation, and other factors.

Individual policies are increasingly aiming to tackle multiple types of disadvantage, and this approach is useful and important. A recent example was the introduction of targeted energy bill support measures in 2022-23 by the UK government, which encompassed households receiving means-tested benefits, older individuals, disabled people, and other vulnerable households.

Mitigating multiple types of inequalities within the same policy can be practical and beneficial. Specific organisations or government entities may have limited policy levers at their disposal to address a wide range of barriers. Combining multiple objectives into one policy may reduce the costs of introducing and administering interventions, the costs of coordinating distinct policies, and the costs to individuals or businesses of navigating multiple programmes.

Simultaneously, there are risks of unintended consequences. The Tinbergen Rule, an oft-cited policy principle, advises a government or organisation to introduce multiple policy instruments if the organisation has multiple policy objectives. Attempting to bundle many aims into a single instrument may lead to inefficient policies, because of the design compromises required.

Intersectionality provides one lens through which to examine this issue.

Intersectionality is a conceptual framework that examines how, why, and to what extent multiple aspects of identity (e.g. race, gender, education, class, nationality) interact, and how these interactions contribute to structures of advantage and disadvantage. To use an illustrative example: households that receive means-tested benefits are at higher risk of energy insecurity, and also disabled people are at higher risk of energy insecurity, but households that both receive means tested benefits and also include a disabled person may experience a level of risk that is more than the sum of the effects of the two risk factors.

In cases of market failure that involve intersectional distributional effects, there are risks of different adverse outcomes:   

  1. Gaps in support due to incomplete information about the market failure. For example, a bibliometric analysis of the relationship between scientific researcher characteristics and publication topics highlighted how supply-side interventions (ie reducing barriers to entry for minority researchers) can be complemented by demand-side interventions (ie grant funding to topics disproportionately by minorities).
  2. Intersectional disadvantage arising from policy simplification. Policies can inadvertently undersupply or oversupply support to different groups due to a lack of consideration for varying levels or types of interventions needed to achieve equitable outcomes. One example was the increased mortality rates of minority medical staff during the COVID-19 pandemic, which highlighted the intersectional effects of race/ethnicity and occupational risk.
  3. Intersectional disadvantage due to a misalignment between policy intent and implementation. In cases where an organisation must choose who the beneficiaries of a policy are (e.g. education admissions, grant programmes, policies with quotas), intersectional issues may lead to unintended consequences. To take a hypothetical example, a university could institute an objective to increase the enrolment of BAME students. Individual departments could follow this objective by admitting BAME students from private schools, or from overseas, rather than increasing enrolment of domestic BAME students from state schools.

Traditional distributional analyses in policy appraisal and evaluation often sequentially analyse individual characteristics like income quintiles, regions, or gender. For example:

  • HM Treasury’s distributional analysis of Budgets is based solely on impacts by income decile (see e.g. Budget 2023 analysis).
  • Equalities Impact Assessments are often carried out for policies and programmes in the UK in service of the Public Sector Equality Duty. They help ensure that equalities issues are considered against the full range of protected characteristics, but guidance rarely explores intersectionality see e.g. Equality impact assessment guidance and template (

The Poverty and Inequality Commission in Scotland has highlighted that "siloed" approaches to addressing distributional outcomes overlook the complex interaction between different aspects of inequality. By conducting analyses along joint distributional dimensions, policymakers can better understand the relative value of the policy to different groups, understand the (distinct) barriers and enablers that contribute to the policy efficacy in different groups, and better understand unintended consequences.

While an intersectional approach has been widely adopted in qualitative research, quantitative intersectional research faces practical challenges. Data availability is often a barrier:

  • Surveys need larger sample sizes or boosted samples to draw robust conclusions about specific subpopulations
  • Public statistics need to be reported at lower levels of aggregation
  • Some intersectional questions may require microdata analysis

Currently there is not a standardised approach to assessing risks of intersectional outcomes, that can inform policy design and monitoring (Scottish Government has published a synthesis of evidence). The lack of evidence about compounding effects of multiple types of disadvantage leads to uncertainty in appraisal estimates, and requires additional assumptions.

Simple cross tabulations do not borrow statistical power across observations, which may lead to noisy estimates for small subgroups. To reduce noise, assumptions may be required to borrow statistical power (over time, across survey items, across individuals, etc). Archetypes are another approach, which can be identified based on expert input or through a data-driven approach. In regressions, it is standard to explore interaction effects between risk factors, and decision trees can also be used to identify the combination of beneficiary characteristics that best predicts outcomes.

Tackling inequality is an urgent political and economic task. The factors that contribute to inequality are complex and, importantly, intertwined. An intersectional approach to policy appraisal and evaluation, investing in primary data collection and analysing distributional outcomes holistically,  has the potential to produce more effective, targeted and equitable policy.