What if the fundamental assumptions behind instrumental variables—like having a valid instrument that’s both relevant and exogenous—simply aren’t available? Is it still possible to estimate marginal treatment effects (MTEs) and understand how the impact of a treatment changes across individuals? This question gets at the heart of modern causal inference, especially when exploring policy effects, individual heterogeneity, and the real-world consequences of interventions. The short answer: Yes, marginal treatment effects can sometimes be estimated without instrumental variable (IV) assumptions, but doing so typically requires alternative strategies that lean on other identification approaches, richer data structures, or clever study designs. Let’s unpack how and when this is possible, drawing on insights from economics, econometrics, and the study of subjective well-being.
What Are Marginal Treatment Effects, and Why Are Instruments So Common? Marginal treatment effects represent the effect of a treatment (such as a policy, intervention, or change in environment) on individuals who are just indifferent, or marginal, to participating in the treatment. This concept is powerful because it helps policymakers and researchers understand not just the average effect of a policy, but how its impact might differ for people with varying propensities to receive the treatment. Traditionally, the estimation of MTEs relies on instrumental variables: variables that shift the probability of treatment but do not directly affect the outcome except through that treatment.
The reason for this reliance on IVs is straightforward. When treatment assignment is not random, simply comparing treated and untreated groups can be misleading: differences in outcomes might reflect pre-existing differences (selection bias) rather than the treatment itself. IVs, when valid, help break this confounding by providing exogenous variation in treatment assignment. However, finding a truly exogenous and relevant instrument is often a significant hurdle in empirical work.
Can We Estimate MTEs Without IVs? Exploring Alternative Strategies So, what can we do when there is no valid instrument? The short answer is that we can sometimes estimate marginal treatment effects by exploiting other forms of exogenous variation, richer data, or stronger modeling assumptions. Let’s explore several approaches, referencing research practices and methodological innovations.
Exploiting Natural Experiments and Policy Changes
One powerful alternative to standard IVs is to exploit natural experiments or large exogenous shocks—events that shift treatment status in ways that are plausibly unrelated to individual characteristics. For example, in the study by Helliwell, Bonikowska, and Shiplett (nber.org), immigration is used as a natural experiment to test the happiness set point hypothesis. Here, the researchers compare life satisfaction among immigrants to Canada from up to 100 source countries with the satisfaction levels in both their new and old countries. The key insight is that “the average levels and distributions of life satisfaction scores among immigrants mimic those of other Canadians rather than those in their source countries and regions” (nber.org). By leveraging the large, quasi-random shock of migration, the authors can estimate the impact of moving to Canada on subjective well-being—even in the absence of a traditional instrumental variable.
This kind of design works best when the external event or policy change is (at least approximately) random with respect to unobserved confounders, or when researchers can control for relevant observed characteristics. For example, if a new law changes eligibility for a benefit overnight, comparing those affected before and after the law can offer a credible estimate of the treatment effect for those at the margin.
Using Selection-on-Observables and Propensity Score Methods
Another approach, especially when instruments are lacking, is to assume that all confounding can be captured by observed variables—a “selection-on-observables” or “conditional independence” assumption. If, after controlling for a rich set of covariates, treatment assignment is as good as random, then researchers can use regression adjustment, matching, or weighting techniques to estimate treatment effects. Propensity score methods, for example, match treated and untreated individuals who have similar likelihoods of receiving treatment based on observable characteristics. While this approach does not directly identify the marginal treatment effect in the same way as IV methods, it can estimate “local” average treatment effects for those near the margin of treatment assignment in the observed data.
However, this approach is only as credible as the set of observed covariates: if important confounders remain unmeasured, the estimates can still be biased. The Helliwell et al. study, for instance, notes that “with or without various adjustments for selection effects,” their main findings persist, suggesting robustness to observable selection but not necessarily to unobserved factors (nber.org).
Exploiting Rich Panel Data and Fixed Effects
Panel data—repeated observations of the same individuals over time—can help address some forms of omitted variable bias without instruments. By comparing changes within individuals before and after a treatment or intervention, fixed effects models can control for all time-invariant unobserved heterogeneity. While this approach typically estimates average treatment effects rather than marginal ones, it can sometimes be extended to recover heterogeneous effects if the data allow for the modeling of how treatment effects vary with observed or time-varying characteristics.
For example, if we observe how immigrants’ life satisfaction changes before and after migration, and how those changes differ by factors like age, education, or prior happiness, we can begin to estimate how the effect of migration varies across subgroups. This isn’t a full identification of the marginal treatment effect curve, but it provides valuable information about heterogeneity in treatment response.
Regression Discontinuity Designs and Other Quasi-Experimental Methods
Regression discontinuity (RD) designs offer another path to causal identification without instruments. If treatment assignment is determined by a cutoff in an observed variable (such as an income threshold for a benefit), comparing individuals just above and below the threshold can yield credible estimates of the local average treatment effect—effectively for those “at the margin” of treatment. While not always labeled as MTEs, these estimates share a similar spirit: they reveal the effect for those whose treatment status was altered by a small, exogenous change in an assignment variable.
Recent lectures and methodological advances, such as those discussed by Raj Chetty and Kosuke Imai in the NBER’s Methods Lectures (nber.org), point to the growing use of mediation analysis and surrogate indices to uncover causal mechanisms. Mediation analysis does not rely on instrumental variables but instead leverages structural modeling and additional assumptions about the relationships between variables. By modeling the process through which a treatment affects an outcome—potentially through observed mediators—researchers can estimate direct and indirect effects, and sometimes even recover information about treatment effect heterogeneity.
For example, if we are interested in how education affects earnings, and we can model the pathway through skills acquisition (a mediator), mediation analysis can decompose the total effect and, under certain assumptions, illuminate variation in effects across individuals.
Limits, Caveats, and the Importance of Robustness
It’s crucial to recognize that all these alternatives come with their own assumptions and limitations. Selection-on-observables requires rich and accurate measurement of confounders. Natural experiments and RD designs depend on the plausibility of exogeneity and continuity assumptions. Mediation analysis hinges on correct model specification and the absence of unmeasured confounding between mediators and outcomes. No method is universally superior; the choice depends on the research context, data availability, and the plausibility of assumptions.
Moreover, as highlighted in the migration study, even when “the average levels and distributions of life satisfaction scores among immigrants mimic those of other Canadians rather than those in their source countries” (nber.org), it is essential to check robustness to selection effects and alternative explanations. This means conducting sensitivity analyses, exploring different subsamples, and, when possible, combining multiple identification strategies.
Summary: Beyond Instruments—Multiple Paths to Marginal Treatment Effects
In sum, while instrumental variables have been the traditional workhorse for estimating marginal treatment effects, they are not the only possible route. Researchers can sometimes estimate MTEs by leveraging natural experiments, selection-on-observables, panel data with fixed effects, regression discontinuity designs, or mediation analysis—each method relying on its own set of assumptions and data requirements. The credibility of any approach depends on the ability to rule out alternative explanations and to demonstrate that variation in treatment assignment is as good as random for the relevant comparison group.
The empirical literature, such as the work by Helliwell, Bonikowska, and Shiplett (nber.org), illustrates how creative use of natural experiments and robustness checks can provide credible estimates of treatment effects—sometimes even in the absence of a formal instrument. As new data sources and methodological advances emerge, the toolkit for estimating treatment effect heterogeneity continues to grow, offering researchers more flexibility to tackle complex causal questions, even when traditional IVs are out of reach.
