# On the Plausibility of the Latent Ignorability Assumption

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

## 2. IV Models with Nonresponse

**Assumption**

**1**(latent ignorability)

**.**

## 3. Empirical Illustration

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Angrist, Joshua D., Guido W. Imbens, and Donald B. Rubin. 1996. Identification of causal effects using instrumental variables. Journal of American Statistical Association 91: 444–72. [Google Scholar] [CrossRef]
- Barnard, John, Constantine E. Frangakis, Jennifer L. Hill, and Donald B. Rubin. 2003. A principal stratification approach to broken randomized experiments: A case study of school choice vouchers in new york city. Journal of the American Statistical Association 98: 299–323. [Google Scholar] [CrossRef]
- Chen, Y., Q. Zhang, Y. Wang, Y. Xiao, R. Fu, H. Bao, and M. Liu. 2015. Estimating the causal effect of milk powder supplementation on bone mineral density: A randomized controlled trial with both non-compliance and loss to follow-up. European Journal of Clinical Nutrition 69: 824–30. [Google Scholar] [CrossRef] [PubMed]
- Esterling, Kevin M., Michael A. Neblo, and David M. J. Lazer. 2011. Estimating treatment effects in the presence of noncompliance and nonresponse: The generalized endogenous treatment model. Political Analysis 19: 205–26. [Google Scholar] [CrossRef]
- Frangakis, Constantine E., and Donald B. Rubin. 1999. Addressing complications of intention-to-treat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes. Biometrika 86: 365–79. [Google Scholar] [CrossRef]
- Fricke, Hans, Markus Frölich, Martin Huber, and Michael Lechner. 2020. Endogeneity and non-response bias in treatment evaluation—Nonparametric identification of causal effects by instruments. Journal of Applied Econometrics 35: 481–504. [Google Scholar] [CrossRef][Green Version]
- Frölich, Markus, and Martin Huber. 2014. Treatment evaluation with multiple outcome periods under endogeneity and attrition. Journal of the American Statistical Association 109: 1697–711. [Google Scholar] [CrossRef][Green Version]
- Mattei, Alessandra, and Fabrizia Mealli. 2007. Application of the principal stratification approach to the faenza randomized experiment on breast self-examination. Biometrics 63: 437–46. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Mealli, Fabrizia, Guido W. Imbens, Salvatore Ferro, and Annibale Biggeri. 2004. Analyzing a randomized trial on breast self-examination with noncompliance and missing outcomes. Biostatistics 5: 207–22. [Google Scholar] [CrossRef] [PubMed][Green Version]
- O’Malley, A. James, and Sharon-Lise T. Normand. 2005. Likelihood methods for treatment noncompliance and subsequent nonresponse in randomized trials. Biometrics 61: 325–34. [Google Scholar] [CrossRef] [PubMed]
- Rubin, Donald B. 1976. Inference and missing data. Biometrika 63: 581–92. [Google Scholar] [CrossRef]
- Schochet, Peter Z., John Burghardt, and Steven Glazerman. 2001. National Job Corps Study: The Impacts of Job Corps on Participants’ Employment and Related Outcomes. Washington, DC: Mathematica Policy Research, Inc. [Google Scholar]
- Yamamoto, Teppei. 2013. Identification and Estimation of Causal Mediation Effects with Treatment Noncompliance. Working Paper, Cambridge: MIT Department of Political Science. [Google Scholar]

Total Sample | Working | Not Working | ||||
---|---|---|---|---|---|---|

Mean | Std.Dev | mean | Std.Dev | Mean | Std.Dev | |

education: 12 years | 0.23 | 0.42 | 0.25 | 0.44 | 0.17 | 0.37 |

education: 13 or more years | 0.03 | 0.18 | 0.04 | 0.19 | 0.01 | 0.10 |

race: black | 0.54 | 0.50 | 0.53 | 0.50 | 0.56 | 0.50 |

race: Hispanic | 0.19 | 0.39 | 0.18 | 0.38 | 0.21 | 0.40 |

age | 18.59 | 2.18 | 18.66 | 2.19 | 18.37 | 2.14 |

in school prior to randomization | 0.63 | 0.48 | 0.63 | 0.48 | 0.61 | 0.49 |

school information missing | 0.02 | 0.14 | 0.02 | 0.13 | 0.03 | 0.17 |

in job prior to randomization | 0.61 | 0.49 | 0.65 | 0.48 | 0.47 | 0.50 |

received AFDC | 0.41 | 0.49 | 0.40 | 0.49 | 0.45 | 0.50 |

received food stamps | 0.54 | 0.50 | 0.52 | 0.50 | 0.60 | 0.49 |

treatment: Job Corps participation | 0.45 | 0.50 | 0.46 | 0.50 | 0.41 | 0.49 |

instrument: randomization | 0.64 | 0.48 | 0.66 | 0.48 | 0.60 | 0.49 |

instrument: kids under 6 | 0.77 | 0.90 | 0.73 | 0.88 | 0.88 | 0.95 |

instrument kids under 15 | 1.15 | 1.26 | 1.12 | 1.23 | 1.25 | 1.34 |

LI + MAR | MAR | Wald | 2 IVs | |
---|---|---|---|---|

effect | 0.12 | 0.16 | 0.12 | 0.16 |

standard error | 0.06 | 0.06 | 0.05 | 0.33 |

bootstrap p-values (quantile-based) | 0.05 | 0.00 | 0.03 | 0.65 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huber, M. On the Plausibility of the Latent Ignorability Assumption. *Econometrics* **2021**, *9*, 47.
https://doi.org/10.3390/econometrics9040047

**AMA Style**

Huber M. On the Plausibility of the Latent Ignorability Assumption. *Econometrics*. 2021; 9(4):47.
https://doi.org/10.3390/econometrics9040047

**Chicago/Turabian Style**

Huber, Martin. 2021. "On the Plausibility of the Latent Ignorability Assumption" *Econometrics* 9, no. 4: 47.
https://doi.org/10.3390/econometrics9040047