In econometrics and related empirical fields, the local average treatment effect (LATE), also known as the complier average causal effect (CACE), is the effect of a treatment for subjects who comply with the experimental treatment assigned to their sample group. It is not to be confused with the average treatment effect (ATE), which includes compliers and non-compliers together. Compliance refers to the human-subject response to a proposed experimental treatment condition. Similar to the ATE, the LATE is calculated but does not include non-compliant parties. 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 can be estimated by a ratio of the estimated intent-to-treat effect and the estimated proportion of compliers, or alternatively through an instrumental variable estimator. 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. 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. At the core, the LATE interpretation clarifies what can and cannot be learned from such experiments." The phenomenon of non-compliant subjects (patients) is also known in medical research. 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. Baker, Kramer, Lindeman (2016) summarized the history of its development. Various papers called both Imbens and Angrist (1994) and Baker and Lindeman (1994) seminal. An early version of LATE involved one-sided noncompliance (and hence no monotonicity assumption). In 1983 Baker wrote a technical report describing LATE for one-sided noncompliance that was published in 2016 in a supplement. In 1984, Bloom published a paper on LATE with one-sided compliance. For a history of multiple discoveries involving LATE see Baker and Lindeman (2024).
General definition The typical terminology of the Rubin causal model is used to measure the LATE, with units indexed i = 1 , … , N {\displaystyle i=1,\ldots ,N} and a binary treatment indicator, z i {\displaystyle z_{i}} for unit i {\displaystyle i} . The term Y i ( z i ) {\displaystyle Y_{i}(z_{i})} is used to denote the potential outcome of unit i {\displaystyle i} under treatment z i {\displaystyle z_{i}} . In an ideal experiment, all subjects assigned to the treatment will comply with the treatment, while those that are assigned to control will remain untreated. In reality, however, the compliance rate is often imperfect, which prevents researchers from identifying the ATE. In such cases, estimating the LATE becomes the more feasible option. The LATE is the average treatment effect among a specific subset of the subjects, who in this case would be the compliers.
Potential outcome framework The LATE is defined within the potential outcomes framework of causal inference. The treatment effect for subject i {\displaystyle i} is Y i ( 1 ) − Y i ( 0 ) {\displaystyle Y_{i}(1)-Y_{i}(0)} . It is impossible to simultaneously observe Y i ( 1 ) {\displaystyle Y_{i}(1)} and Y i ( 0 ) {\displaystyle Y_{i}(0)} for the same subject. At any given time, only a subject in its treated Y i ( 1 ) {\displaystyle Y_{i}(1)} or untreated Y i ( 0 ) {\displaystyle Y_{i}(0)} state can be observed. Through random assignment, the expected untreated potential outcome of the control group is the same as that of the treatment group, and the expected treated potential outcome of the treatment group is the same as that of the control group. The random assignment assumption thus allows one to take the difference between the average outcome in the treatment group and the average outcome in the control group as the overall average treatment effect, such that:
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