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I am working on a referee report for a field experiment focused on the employment process. The experiment investigates if including a video in job applications can reduce employment disadvantages for individuals with disabilities (specifically, those who use wheelchairs). Each application is randomly assigned to either include or exclude a video. Furthermore, the videos are randomly assigned to either disclose the applicant's disability or not. However, not all employers viewed the videos when included, leading to a scenario of one-sided noncompliance with compliers and "never-takers".

The researchers have utilized a linear probability model in their analysis, incorporating the "video inclusion" as a variable in their regressions. My understanding is that the coefficient of the "video" variable could represent the intent-to-treat effect (ITT).

I am now interested in estimating the Complier Average Causal Effect (CACE). I would like to know if the random assignment of the video can be used as an instrument in a two-stage least squares (2SLS) regression. Is there anyone with experience in this type of analysis who can provide insights or suggest methodologies for accurately estimating CACE in this context?

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Yes, you can use random assignment as an instrument to estimate the average treatment effect on the compliers. In fact, when there are only compliers and never takers, this is the same as the average treatment effect on the treated. You get your point estimate by dividing the ITT by the first stage (=the effect of random assignment on the probability of watching the video) and 2SLS would be the most straightforward approach to hypothesis testing.

The original references would be:

  • Imbens , G. W. and Angrist , J. 1994 . “Identification and Estimation of Local Average Treatment Effects,” . Econometrica , 62 : 467 – 476. https://doi.org/10.2307/2951620

  • Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996). Identification of causal effects using instrumental variables. Journal of the American statistical Association, 91(434), 444-455. https://doi.org/10.1080/01621459.1996.10476902

But I think this might be more suitable, since it is practical application that deals specifically with one-sided non-compliance and it includes multiple treatment groups, which is also similar to your case:

However, consider whether the ITT might not be what is actually intersting? Is it the effect of an employer watching a video or the effect of making an applicant provide a video that is relevant for policy?

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