After months or years under development and implementation, navigating the practical, theoretical and inferential pitfalls of experimental social science research, your experiment has finally been completed. Comparing the treatment and control groups, you find a substantively and statistically significant result on an outcome of theoretical interest. Before you can pop the champagne in celebration of an intervention well evaluated, a friendly colleague asks: “But what does this tell us about the world?”

1. What is external validity?

External validity is another name for the generalizability of results, asking “whether a causal relationship holds over variation in persons, settings, treatments and outcomes.”1 A classic example of an external validity concern is whether traditional economics or psychology lab experiments carried out on college students produce results that are generalizable to the broader public. In the political economy of development, we might consider how a community-driven development program in India might apply (or not) in West Africa, or Central America.

External validity becomes particularly important when making policy recommendations that come from research. Extrapolating causal effects from one or more studies to a given policy context requires careful consideration of both theory and empirical evidence. This methods guide discusses some key concepts, pitfalls to avoid, and useful references to consider when going from a Local Average Treatment Effect to the larger world.

2. How is this different than internal validity?

Internal validity refers to the quality of causal inferences being made for a given subject pool. As originally posited by Campbell,2 internal validity asks, “did in fact the experimental stimulus make some significant difference in this specific instance.” This concept dovetails with the counterfactual approach to causality that experimentalists typically use, which asks whether outcomes change depending on the presence or absence of a treatment.3

Before you can extrapolate a causal effect to a distinct population, it is vital that the original Average Treatment Effect be based on a well-identified result. For most experimentalists, random assignment provides the requisite identifying variation, provided no attrition, interference, spillovers, or other threats to inference. For observational studies, additional identifying assumptions are needed, such as conditional independence of the treatment from potential outcomes.

4. Theory and generalization

Extrapolating a result to a distinct context, outcome, population or treatment is not a mechanical process. As discussed by Samii6 and Rosenbaum,7 relevant theory should be used to guide generalization, taking the relevant existing evidence and making predictions for other contexts in a principled fashion. Theories boil down complex problems into more parsimonious representations, and help to elucidate what factors matter. Just as theory guides the content of interventions and research designs, theoretical propositions can tell you which scope conditions are relevant for extrapolating a result. What covariates matter? What contextual information matters?

5. How can I determine where my results apply?

There are two primary means of generalizing results, one based on the covariates of units in the study and the other based on actual experimental manipulation of moderating variables. Observing how a treatment effect varies over a non-randomized pre-treatment variable can describe treatment effect heterogeneity, which can be highly suggestive about where or for whom the intervention is likely to be most effective, beyond the original sample. Note, however, that this type of analysis cannot pin down whether the treatment-effect heterogeneity is caused by that pre-treatment variable. The concern—endemic to observational research—is that the non-randomized covariate may be correlated with an unobserved variable, and it is this “unseen” factor that in fact is responsible for the heterogeneous impacts of the treatment.8 Ideally, therefore, we want to leverage exogenous variation in the moderator of interest, thereby ruling out the possibility of such confounding. A factorial experimental design in which the researcher assigns the moderator independently of the main treatment of interest can generate especially compelling evidence about a moderator’s role. Though, of course, considerations of cost and statistical power may preclude this approach in practice.

Because generalization is primarily a prediction exercise, asking where we can expect a causal relationship similar to one observed locally, extrapolating heterogeneous effects based on similar covariates is often reasonable, provided theory does not indicate sources of confounding.9 Nonetheless, the strongest evidence for the generalizability of a result comes from a well-identified interaction between an exogenous moderator and the treatment, then projected across the covariate profile of a target population. Indeed, with some strong assumptions extrapolation can provide as good or better results than carrying out a second experiment in situ.10 The calculation of an extrapolated estimate can often be best performed using machine learning, although linear regression also performs reasonably well.11

6. Strategic behavior can scuttle your extrapolations

Extrapolating a local result to a different context can prove challenging even with a compelling covariate profile to which you want to generalize effects. A randomized experimental manipulation in a local area generates a “partial equilibrium effect.” Strategic dynamics, including compensatory behavior or backlashes, outside the local context of an experimental intervention can complicate efforts to generalize a result. Suppose, for example, that an unconditional cash transfer intervention is shown to increase welfare, entrepreneurship, and employment in a sample of 200 villages. What would happen if the intervention were extended to encompass 1000 villages? At this point, one could imagine that regions excluded from the program are more likely to learn about it. Untreated units may start to demand other types of transfers from the government, giving rise to effects similar to those produced by the direct cash transfer. In a similar vein, sometimes causal relationships only work when they are applied to some people. For example, imagine a job skills program that functions very well (as compared to those who did not receive it), what would happen if it were extended to all workers? Even if there are positive effects across all participants, there could be reduced or no average effects as higher skilled jobs are already filled by the first batch and the second batch is forced to remain in their previous jobs, now overqualified. In short, under general equilibrium conditions we might expect different results even where the covariate profile matches.

7. Don’t confuse external validity with construct validity or ecological validity

Internal and external validity are not the only ‘validity’ concerns that can be leveled at experimental work, and though relevant, they are also distinct. Ecological validity, as defined by Shadish, Cook and Campbell12 concerns whether an intervention appears artificial or out of place when deployed in a new context. For example, does an information workshop in a rural town carried out by experimenters resemble the kinds of information sharing that the population may experience in regular life? Similarly, if the same workshop were held in a large city, would it appear out of place?

Construct validity considers whether a theoretical concept being tested in a study is appropriately operationalized by the treatment(s). If your experiment is testing the effect of anger on political reciprocity and you are in fact manipulating fear or trust in your treatment, construct validity may be violated. Both construct and ecological validity are relevant for generalizations, and thus useful for making claims about external validity.

8. Extrapolation across treatments and outcomes

While much of this guide has implicitly focused on porting a given treatment to a new place or time, external validity also considers variations in treatments and outcomes. That is, imagine we did the same experiment on the same sample, but with a variation on the treatment, would we predict the local causal effect to be similar? Similarly, can we predict if a given treatment will produce the same or different causal effects on a different outcome? Sometimes we can address these concerns by conducting experiments that assess alternative treatments and outcomes. When follow-up experiments are in short supply, such issues have to be settled analytically. Rather than considering the features of subjects, extrapolation in this case requires thinking through, aided by theory, the characteristics of the treatments or outcomes and making reasonable predictions.

9. Replication is important

No single study represents the final word on a scholarly question. Following the logic of Bayesian updating, additional evidence in favor of or against a given theory allows the scientific and policy community to update their beliefs about the strength and validity of a causal relationship.

Replication of studies is an important part of this: scholars should replicate studies in contexts that look very different, but also in some contexts that look very similar. The former allows us to identify local causal relationships that can be triangulated with existing evidence and generalized as appropriate. At the same time, it is important to directly replicate existing studies under conditions that are as close as possible to the original in order to verify that local effects one may be interested in extrapolating are indeed reliable. The Open Science Collaboration13 found, for example, that when reproducing 100 major psychology experiments, just 47% of the original reported effect sizes fell within the 95% confidence interval of the effect size shown in the replication.

10. Don’t forget time

When thinking about causal relationships of interest, it is important also to consider time: do things we learn about the past extend to the future? How do an individual’s potential outcomes change over time? Immutable laws govern the physical and chemical worlds; hence what we learn about these laws today will always remain true. By contrast, we understand far less about the underlying drivers of social behavior and whether they hold constant in the same way. The answer may well be no. When making decisions about the policy relevance and generalizability of results, these considerations can help scholars determine a reasonable level of uncertainty and help policy makers adjust accordingly.

  1. Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Houghton, Mifflin and Company.

  2. Campbell, D. T. (1957). Factors relevant to the validity of experiments in social settings. Psychological bulletin, 54(4), 297.

  3. More details can be found in the causal inference methods guide: http://egap.org/methods-guides/10-things-you-need-know-about-causal-inference

  4. Imbens, G. (2013). Book Review Feature: Public Policy in an Uncertain World: By Charles F. Manski. The Economic Journal,123(570), F401-F411.

  5. Manski, C. F. (2013). Response to the review of ‘public policy in an uncertain world’. The Economic Journal 123: F412–F415.

  6. Samii, Cyrus. (2016). “Causal Empiricism in Quantitative Research.” Journal of Politics 78(3):941–955.

  7. Rosenbaum, Paul R. (1999). “Choice as an Alternative to Control in Observational Studies” (with discussion). Statistical Science 14(3): 259–304.

  8. Gerber, A. S., & Green, D. P. (2012). Field experiments: Design, analysis, and interpretation. WW Norton.

  9. Bisbee, James; Rajeev Dehejia; Cristian Pop-Eleches & Cyrus Samii. (2016). “Local Instruments, Global Extrapolation: External Validity of the Labor Supply-Fertility Local Average Treatment Effect.” Journal of Labor Economics

  10. Bisbee, James; Rajeev Dehejia; Cristian Pop-Eleches & Cyrus Samii. (2016). “Local Instruments, Global Extrapolation: External Validity of the Labor Supply-Fertility Local Average Treatment Effect.” Journal of Labor Economics

  11. Kern, H. L., Stuart, E. A., Hill, J., & Green, D. P. (2016). Assessing methods for generalizing experimental impact estimates to target populations. Journal of Research on Educational Effectiveness, 9(1), 103-127.

  12. Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Houghton, Mifflin and Company.

  13. Open Science Collaboration. (2015). Estimating the reproducibility of psychological science. Science, 349(6251), aac4716.