Thus, the "average treatment effect" is a weighted average of the individual treatment effects, where the weight is proportional to the variance of the explanatory variable within the group. Numerical Example
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What is the average treatment effect?
Jump to navigation Jump to search. The average treatment effect ( ATE) is a measure used to compare treatments (or interventions) in randomized experiments, evaluation of policy interventions, and medical trials. The ATE measures the difference in mean (average) outcomes between units assigned to the treatment and units assigned to the control.
Can we use the SDO to estimate average treatment effects?
When using the SDO to estimate average treatment effects, we must be cautious of differing responses to treatment between treated individuals and untreated individuals, as it incurs bias which obscures our estimate of the average treatment effect of an entire sample population.
What is the local average treatment effect (late)?
The local average treatment effect (LATE), also known as the complier average causal effect (CACE), was first introduced into the econometrics literature by Guido W. Imbens and Joshua D. Angrist in 1994.
What is the individual-level treatment effect?
General definition. However, this individual-level treatment effect is unobservable because individual units can only receive the treatment or the control, but not both. Random assignment to treatment ensures that units assigned to the treatment and units assigned to the control are identical (over a large number of iterations of the experiment).
What is the local average treatment effect?
Angrist in 1994. It is the treatment effect for the subset of the sample that takes the treatment if and only if they were assigned to the treatment, otherwise known as the compliers. It is not to be confused with the average treatment effect (ATE), which is the average subject-level treatment effect; the LATE is only the ATE among the compliers. 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.
What would be expected potential outcomes if all subjects were assigned to treatment?
If all subjects were assigned to treatment, the expected potential outcomes would be a weighted average of the treated potential outcomes among compliers, and the untreated potential outcomes among never-takers, such that
How to extrapolate the untreated compliers?
Given this, extrapolation is possible by projecting the untreated potential outcomes of the compliers to the always-takers, and the treated potential outcomes of the compliers to the never-takers. In other words, if it is assumed that the untreated compliers are informative about always-takers, and the treated compliers are informative about never-takers, then comparison is now possible among the treated always-takers to their “as-if” untreated always-takers, and the untreated never-takers can be compared to their “as-if” treated counterparts. This will then allow the calculation of the overall treatment effect. Extrapolation under the weak monotonicity assumption will provide a bound, rather than a point-estimate.
What would happen if all subjects were assigned to control?
If all subjects were assigned to control, however, the expected potential outcomes would be a weighted average of the untreated potential outcomes among compliers and never-takers , such that
Why is it important to generalize from the late to the ate?
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. In these cases, the LATE may not be the parameter of interest, and researchers have questioned its utility. Other researchers, however, have countered this criticism by proposing new methods to generalize from the LATE to the ATE. Most of these involve some form of reweighting from the LATE, under certain key assumptions that allow for extrapolation from the compliers.
What is the expected untreated potential outcome of the control group?
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 treatment group is the same as that of the control group . The random assignment assumption thus allows us 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:
Is the compliance rate imperfect?
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.
Why do analysts randomly assign treatment?
In experimental studies, or studies where an analyst has control over treatment assignment, analysts can randomly assign treatment to individuals to ensure that the treatment and the potential outcomes of observed individuals are drawn from independent probability distributions. For example, if I were to assign email alerts with images to my email subscribers randomly, their potential outcomes from receiving emails with and without images, would be statistically independent from the event that they were chosen for treatment. While randomizing treatment enables the SDO to be an unbiased estimate of ATE, in order to minimize the variance of the estimate practitioners must also ensure they are calculating an SDO from a sufficiently large sample population.
Can we measure average treatment effects?
Unfortunately, as a result of the fundamental problem of causal inference, we cannot directly measure average treatment effects. This is because we cannot witness more than one potential outcome, as we cannot set an explanatory variable to more than one value.
Overview
The local average treatment effect (LATE), also known as the complier average causal effect (CACE), was first introduced into the econometrics literature by Guido W. Imbens and Joshua D. Angrist in 1994. It is the treatment effect for the subset of the sample that takes the treatment if and only if they were assigned to the treatment, otherwise known as the compliers. It is not to be confused with the average treatment effect (ATE), which is the average subject-level treatment e…
General definition
The typical terminology of the Rubin causal model with units indexed and binary treatment indicator for unit i, is used. Potential outcomes denote the potential outcome of unit i under treatment .
In an ideal experiment, all subjects assigned to treatment are treated, while those that are assigned to control will remain untreated. In reality, however, the compliance rate is often imperf…
Potential outcome framework
The treatment effect for subject is . Both and for the same subject can never be observed simultaneously. At any given time, only a subject in its treated or untreated 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 treatment group is the same as that of the control group. The random assignment assumption thus allow…
Identification
The , whereby
The measures the average effect of experimental assignment on outcomes without accounting for the proportion of the group that was actually treated (i.e. an average of those assigned to treatment minus the average of those assigned to control). In experiments with full compliance, the .
Others: LATE in instrumental variable framework
LATE can be thought of through an IV framework. Treatment assignment is the instrument that drives the causal effect on outcome through the variable of interest , such that only influences through the endogenous variable , and through no other path. This would produce the treatment effect for compliers.
In addition to the potential outcomes framework mentioned above, LATE can also be estimated …
Generalizing LATE
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 an experiment with perfect compliance, the average treatment effect can be obtained easily. However, many experiments are likely to experience either one-sided or two-sided non-compliance. In the presence of non-compliance, the ATE can no longer be recovered. Instead, w…
Further reading
• Angrist, Joshua D.; Fernández-Val, Iván (2013). Advances in Economics and Econometrics. Cambridge University Press. pp. 401–434. doi:10.1017/cbo9781139060035.012. ISBN 9781139060035.