{"title":"Interacting Treatments With Endogenous Takeup","authors":"Máté Kormos, Robert P. Lieli, Martin Huber","doi":"10.1002/jae.3120","DOIUrl":null,"url":null,"abstract":"<p>We study causal inference in randomized experiments (or quasi-experiments) following a \n<span></span><math>\n <semantics>\n <mrow>\n <mn>2</mn>\n <mo>×</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$$ 2\\times 2 $$</annotation>\n </semantics></math> factorial design. There are two treatments, denoted \n<span></span><math>\n <semantics>\n <mrow>\n <mi>A</mi>\n </mrow>\n <annotation>$$ A $$</annotation>\n </semantics></math> and \n<span></span><math>\n <semantics>\n <mrow>\n <mi>B</mi>\n </mrow>\n <annotation>$$ B $$</annotation>\n </semantics></math>, and units are randomly assigned to one of four categories: treatment \n<span></span><math>\n <semantics>\n <mrow>\n <mi>A</mi>\n </mrow>\n <annotation>$$ A $$</annotation>\n </semantics></math> alone, treatment \n<span></span><math>\n <semantics>\n <mrow>\n <mi>B</mi>\n </mrow>\n <annotation>$$ B $$</annotation>\n </semantics></math> alone, joint treatment, or none. Allowing for endogenous non-compliance with the two binary instruments representing the intended assignment, as well as unrestricted interference across the two treatments, we derive the causal interpretation of various instrumental variable estimands under more general compliance conditions than in the literature. In general, if treatment takeup is driven by both instruments for some units, it becomes difficult to separate treatment interaction from treatment effect heterogeneity. We provide auxiliary conditions and various bounding strategies that may help zero in on causally interesting parameters. We apply our results to a program randomly offering two different treatments to first-year college students, namely, tutoring and financial incentives, in order to assess the effect of the treatments on academic performance.</p>","PeriodicalId":48363,"journal":{"name":"Journal of Applied Econometrics","volume":"40 4","pages":"424-437"},"PeriodicalIF":2.3000,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jae.3120","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Econometrics","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jae.3120","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study causal inference in randomized experiments (or quasi-experiments) following a
factorial design. There are two treatments, denoted
and
, and units are randomly assigned to one of four categories: treatment
alone, treatment
alone, joint treatment, or none. Allowing for endogenous non-compliance with the two binary instruments representing the intended assignment, as well as unrestricted interference across the two treatments, we derive the causal interpretation of various instrumental variable estimands under more general compliance conditions than in the literature. In general, if treatment takeup is driven by both instruments for some units, it becomes difficult to separate treatment interaction from treatment effect heterogeneity. We provide auxiliary conditions and various bounding strategies that may help zero in on causally interesting parameters. We apply our results to a program randomly offering two different treatments to first-year college students, namely, tutoring and financial incentives, in order to assess the effect of the treatments on academic performance.
我们在遵循2 × 2 $$ 2\times 2 $$析因设计的随机实验（或准实验）中研究因果推理。有两种处理，分别表示为A $$ A $$和B $$ B $$，单位随机分配到以下四类之一：单独治疗A $$ A $$，单独治疗B $$ B $$，联合治疗，或不治疗。考虑到代表预期分配的两种二元工具的内生不依从性，以及两种治疗之间的无限制干扰，我们在比文献中更一般的依从性条件下推导出各种工具变量估计的因果解释。一般来说，如果某些单位的治疗使用是由两种工具驱动的，则很难将治疗相互作用与治疗效果异质性分开。我们提供了辅助条件和各种边界策略，可以帮助将因果关系中有趣的参数归零。我们将我们的结果应用于一个项目，随机为一年级大学生提供两种不同的治疗方法，即辅导和经济激励，以评估治疗对学习成绩的影响。
期刊介绍：
The Journal of Applied Econometrics is an international journal published bi-monthly, plus 1 additional issue (total 7 issues). It aims to publish articles of high quality dealing with the application of existing as well as new econometric techniques to a wide variety of problems in economics and related subjects, covering topics in measurement, estimation, testing, forecasting, and policy analysis. The emphasis is on the careful and rigorous application of econometric techniques and the appropriate interpretation of the results. The economic content of the articles is stressed. A special feature of the Journal is its emphasis on the replicability of results by other researchers. To achieve this aim, authors are expected to make available a complete set of the data used as well as any specialised computer programs employed through a readily accessible medium, preferably in a machine-readable form. The use of microcomputers in applied research and transferability of data is emphasised. The Journal also features occasional sections of short papers re-evaluating previously published papers. The intention of the Journal of Applied Econometrics is to provide an outlet for innovative, quantitative research in economics which cuts across areas of specialisation, involves transferable techniques, and is easily replicable by other researchers. Contributions that introduce statistical methods that are applicable to a variety of economic problems are actively encouraged. The Journal also aims to publish review and survey articles that make recent developments in the field of theoretical and applied econometrics more readily accessible to applied economists in general.
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