If the goal is to evaluate the effect of a treatment in ideal, compliant subjects, the LATE value will give a more precise estimate.
However, it may lack external validity by ignoring the effect of non-compliance that is likely to occur in the real-world deployment of a treatment method.
The LATE was first introduced in the econometrics literature by Guido W. Imbens and Joshua D. Angrist in 1994, who shared one half of the 2021 Nobel Memorial Prize in Economic Sciences.
[1][2] As summarized by the Nobel Committee, the LATE framework "significantly altered how researchers approach empirical questions using data generated from either natural experiments or randomized experiments with incomplete compliance to the assigned treatment.
[3] In the biostatistics literature, Baker and Lindeman (1994) independently developed the LATE method for a binary outcome with the paired availability design and the key monotonicity assumption.
In 1983 Baker wrote a technical report describing LATE for one-sided noncompliance that was published in 2016 in a supplement.
[11] The typical terminology of the Rubin causal model is used to measure the LATE, with units indexed
The LATE is the average treatment effect among a specific subset of the subjects, who in this case would be the compliers.
Researchers frequently encounter non-compliance problems in their experiments, whereby subjects fail to comply with their experimental assignments.
In an experiment with non-compliance, the subjects can be divided into four subgroups: compliers, always-takers, never-takers and defiers.
In the case of one-sided non-compliance, a number of the subjects who were assigned to the treatment group remain untreated.
Under one-sided noncompliance, all subjects assigned to control group will not take the treatment, therefore:[13]
The table below lays out the hypothetical schedule of potential outcomes under two-sided noncompliance.
However, because of SEM’s strict assumption of constant effect on every individual, the potential outcomes framework is in more prevalent use today.
The primary goal of running an experiment is to obtain causal leverage, and it does so by randomly assigning subjects to experimental conditions, which sets it apart from observational studies.
In one example, Angrist (1989)[16] attempts to estimate the causal effect of serving in the military on earnings, using the draft lottery as an instrument.
However, if researchers are concerned about a more universal draft for future interpretation, then the ATE would be more important (Imbens 2009).
[1] Generalizing from the LATE to the ATE thus becomes an important issue when the research interest lies with the causal treatment effect on a broader population, not just the compliers.
[19][20][21] Most of these involve some form of reweighting from the LATE, under certain key assumptions that allow for extrapolation from the compliers.
By leveraging instrumental variables, Aronow and Carnegie (2013)[19] propose a new reweighting method called Inverse Compliance Score weighting (ICSW), with a similar intuition behind IPW.
This method assumes compliance propensity is a pre-treatment covariate and compliers would have the same average treatment effect within their strata.
ICSW first estimates the conditional probability of being a complier (Compliance Score) for each subject by Maximum Likelihood estimator given covariates control, then reweights each unit by its inverse of compliance score, so that compliers would have covariate distribution that matches the full population.
The compliance score is treated as a latent pretreatment covariate, which is independent of treatment assignment
is the cumulative distribution function for a probit model By the LATE theorem,[1] average treatment effect for compliers can be estimated with equation:
[22] In another approach, one might assume that an underlying utility model links the never-takers, compliers, and always-takers.
The ATE can be estimated by reweighting based on an extrapolation of the complier treated and untreated potential outcomes to the never-takers and always-takers.
The estimation of the extrapolation to ATE from the LATE requires certain key assumptions, which may vary from one approach to another.
It is not a design-based approach per se, and the field of experiments is not usually in the habit of comparing groups unless they are randomly assigned.
Even in case when assumptions are difficult to verify, researchers can incorporate through the foundation of experiment design.
If the compliance rate remains stable under different intensity, if could be a signal of homogeneity across groups.