Assessing Causal Effects in a Longitudinal Observational Study With “Truncated” Outcomes Due to Unemployment and Nonignorable Missing Data

Abstract

Important statistical issues pervade the evaluation of training programs’ effects for unemployed people. In particular, the fact that offered wages are observed and well-defined only for subjects who are employed (truncation by death), and the problem that information on the individuals’ employment status and wage can be lost over time (attrition) raise methodological challenges for causal inference. We present an extended framework for simultaneously addressing the aforementioned problems, and thus answering important substantive research questions, in training evaluation observational studies with covariates, a binary treatment and longitudinal information on employment status and wage, which may be missing due to the lost to follow-up. There are two key features of this framework: we use principal stratification to properly define the causal effects of interest and to deal with nonignorable missingness, and we adopt a Bayesian approach for inference. The proposed framework allows us to answer an open issue in economics: the assessment of the trend of reservation wage over the duration of unemployment. We apply our framework to evaluate causal effects of foreign language training programs in Luxembourg, using administrative data on the labor force (IGSS-ADEM dataset). Our findings might be an incentive for the employment agencies to better design and implement future language training programs.

Keywords:

• Bayesian inference
• Defiers
• Principal stratification
• Reservation wage
• Training programs
• Unconfoundedness

Supplementary Materials

The online supplementary materials provide details on (1) the Bayesian approach to inference and the MCMC algorithm with Data Augmentation we use to derive the posterior distributions of the causal estimands of interest (Sections 1–5); (2) the observed groups with associated data pattern and possible latent principal strata (Section 6); (3) the design phase of the study (Section 7); and (4) results from the complete-case analysis (Section 8).

Additional information

Funding

Michela Bia, Alessandra Mattei, and Andrea Mercatanti acknowledge financial support from the European Social Fund Project: “Evaluation of Active Labor Market Policies in Luxembourg”—EvaLab4Lux, cofunded by the Ministry of Labor, Employment and the Social and Solidarity Economy of Luxembourg and LISER. The views expressed herein are those of the authors and do not necessarily reflect those of the corresponding institutions.