When grouping university majors changes what a causal estimate means

Broad labels, hidden switches

Physics and engineering both belong to STEM, but they are not interchangeable educational experiences. If an admission offer moves a student between them, the student’s outcome could change even though their STEM status stays the same.

That is the problem examined by Didier Nibbering, Matthijs Oosterveen and Pedro Luis Silva in Instrumental variables with treatment clusters. Their arXiv preprint, first submitted on November 9, 2026, develops conditions under which grouping distinct choices still permits a meaningful causal estimate. Preprint status means the supplied source does not establish peer-reviewed publication.

Researchers have practical reasons to group treatments—the alternatives whose effects they want to compare. Small categories can raise privacy concerns, detailed comparisons can be imprecise, and policymakers may care about broad groups. But aggregation does not remove the underlying choices.

What the statistical method identifies

Students choose fields partly because of preferences and circumstances that may also influence academic performance. Comparing their outcomes directly therefore need not reveal what studying a field causes.

Instrumental-variable methods instead use an outside encouragement that changes enrollment. For two clusters, the estimate divides the encouragement’s effect on the outcome by its effect on enrollment in the target cluster. A causal interpretation requires that the encouragement affect outcomes only through treatment, alongside other identifying assumptions.

The authors show that, under their conditions, the clustered estimate is a positively weighted average of local average treatment effects. These are effects for people whose choices change in response to particular encouragements, not effects for everyone. The average combines comparisons between individual treatments across clusters; its weights depend on how people respond and which encouragements occur.

Crucially, the restrictions concern individual treatments, not merely broad labels. For a target cluster, an encouragement cannot move someone out of a particular treatment they would otherwise choose within that cluster. If someone stays outside the target cluster under either encouragement, their specific treatment must remain unchanged. With more than two clusters, an additional restriction prevents certain switches involving a third cluster.

These conditions eliminate within-cluster switches that could change outcomes without changing the recorded cluster. They are less restrictive than the assumptions needed to identify all the individual treatment effects separately. Nevertheless, identifying the weighted average does not generally identify each component effect.

Testing the categories in Portugal

The empirical illustration uses administrative records for 49,272 applicants across four Portuguese higher-education cohorts, from 2013–14 through 2016–17. The authors classify 22 fields into either STEM and non-STEM or eight broader academic groups.

Portugal’s centralized admission system creates score cutoffs for courses. Applicants just above a relevant cutoff receive an offer from their locally preferred field; those just below receive an offer from a next-best alternative. Those alternatives are constructed from submitted rankings and feasible admission options, rather than necessarily being the first two listed choices.

The authors use a fuzzy regression discontinuity design: crossing a cutoff changes the probability of enrollment, but does not determine enrollment perfectly. The outcome is second-year credits under the European Credit Transfer and Accumulation System, or ECTS.

For students preferring STEM over non-STEM, the estimated enrollment effect is a reduction of 3.15 second-year credits. For students preferring non-STEM over STEM, the estimated effect of non-STEM enrollment is an increase of 1.33 credits. These are different groups with different underlying comparisons, so the estimates need not be mirror images.

The interpretation is academic progress, not educational value. Credits measure completed intended workload; fewer credits do not establish less learning, lower future earnings or worse welfare.

A diagnostic, not a guarantee

Detailed field-level data allow the researchers to test necessary implications of their assumptions. After correction for multiple testing, they find no statistically significant violations for the STEM classification. For the eight-group classification, they reject necessary conditions in comparisons involving Health and Personal services as next-best fields, undermining the proposed causal interpretation in those cases.

Passing these tests does not prove the assumptions. Different underlying responses can offset one another, concealing violations. The implemented tests also approximate conditional relationships linearly and evaluate credits between the 20th and 80th percentiles, rather than checking every possible outcome value.

Other limitations remain. The analysis includes students with observed second-year enrollment, so offer-induced selection could matter. Offers may change institutions or first-year experiences in ways not captured by second-year field. Strategic preference reporting could also threaten the design. Balance and density checks are reassuring, but do not eliminate these concerns.

The main lesson is methodological: broad categories can support causal analysis, but only when researchers explain—and, where possible, challenge—the detailed behavioral assumptions hidden beneath them.