J. Angrist, G. Imbens, and D. Rubin, Identification of causal effects using instrumental variables, Journal of the American Statistical Association, vol.91, pp.444-455, 1996.

C. Behaghel and G. , Private and public provision of counseling to jobseekers : Evidence from a large controlled experiment, 2012.
URL : https://hal.archives-ouvertes.fr/halshs-01067926

J. Behrman, P. S. Todd, and P. , Medium term impacts of the oportunidades conditional cash transfer program on rural youth in mexico, Poverty, Inequality and Policy in Latin America, 2009.

D. Campbell, Reforms as experiments, American Psychologist, vol.24, pp.409-438, 1969.

C. Card and W. , The spike at benefit exhaustion : Leaving the unemployment system or starting a new job ?, American Economic Review, vol.97, issue.2, pp.113-118, 2008.

M. Das, W. K. Newey, and F. Vella, Nonparametric estimation of sample selection models, Review of Economic Studies, vol.70, issue.1, pp.33-58, 2003.

J. Fitzgerald, P. Gottschalk, and R. Moffitt, An analysis of sample attrition in panel data: The michigan panel study of income dynamics, Journal of Human Resources, vol.33, issue.2, pp.251-299, 1998.

J. J. Heckman, The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models, The Annals of Economic and Social Measurement, vol.5, pp.475-492, 1976.

J. J. Heckman, Sample selection bias as a specification error, Econometrica, vol.47, issue.1, pp.153-61, 1979.

J. L. Horowitz and C. F. Manski, Identification and robustness with contaminated and corrupted data, Econometrica, vol.63, issue.2, pp.281-302, 1995.

J. L. Horowitz and C. F. Manski, Censoring of outcomes and regressors due to survey nonresponse: Identification and estimation using weights and imputations, Journal of Econometrics, vol.84, issue.1, pp.37-58, 1998.

J. Horowitz and C. Manski, Nonparametric analysis of randomized experiments with missing covariate and outcome data, Journal of the American Statistical Association, vol.95, issue.449, pp.77-84, 2000.

M. Kremer, E. Miguel, and R. Thornton, Incentives to learn, The Review of Economics and Statistics, vol.91, issue.3, pp.437-456, 2009.

A. B. Krueger, Experimental estimates of education production functions, The Quarterly Journal of Economics, vol.114, issue.2, pp.497-532, 1999.

R. J. Lalonde, Evaluating the econometric evaluations of training programs with experimental data, American Economic Review, vol.76, issue.4, pp.604-624, 1986.

D. Lee, Training, wages, and sample selection: Estimating sharp bounds on treatment effects, Review of Economic Studies, vol.76, pp.1071-1102, 2009.

C. Manski, Anatomy of the selection problem, Journal of Human Resources, vol.24, issue.3, pp.343-60, 1989.

W. K. Newey and D. Mcfadden, Large sample estimation and hypothesis testing, of Handbook of Econometrics, vol.4, pp.2111-2245, 1986.

E. Vytlacil, Independence, monotonicity, and latent index models: An equivalence result, Econometrica, vol.70, issue.1, pp.331-341, 2002.

, Potential outcomes are y(t, z), with t ? {0, 1} and z ? {0, 1}. We consider the usual set of assumptions of the Angrist, Imbens and Rubin model: Assumption 5 1

, Z)) ??(Z

. Z-?-y,

, Note that we changed notation for the sake of readability: y(0) and y(1) now denote potential outcome under the different treatment statuses;?(0) and?(1) correspond to potential outcomes under the different assignment statuses that were noted y(0) and y(1) above.) It is well known that under this set of assumptions

, We now consider non response. We extend assumption ??

, Latent variable threshold-crossing response model

W. and Z. ??,

. Z-?-w,