This paper identifies the probability of causation when there is sample selection. We show that the probability of causation is partially identified for individuals who are always observed regardless of treatment status and derive sharp bounds under three increasingly restrictive sets of assumptions. The first set imposes an exogenous treatment and a monotone sample selection mechanism. To tighten these bounds, the second set also imposes the monotone treatment response assumption, while the third set additionally imposes a stochastic dominance assumption. Finally, we use experimental data from the Colombian job training program \J\'ovenes en Acci\'on to empirically illustrate our approach's usefulness. We find that, among women who are always employed regardless of treatment, at least 12 and at most 19 transition to the formal labor market because of this training program.
翻译:本文确定了在抽样选择时因果关系的概率。 我们显示,在三种日益限制性的假设下,对无论治疗状况如何总是观察到的个人,因果关系的概率是部分确定的。 第一套规定了一种外源治疗和单质抽样选择机制。为了收紧这些界限,第二套也规定了单质治疗反应假设,而第三套又规定了一种随机主控假设。最后,我们用哥伦比亚职业培训方案(Colombia Particle Programme en Acquines en Acquinis en Acticle)的实验数据来从经验上说明我们的方法的效用。我们发现,在无论治疗方式如何总是被雇用的妇女中,至少有12人,最多19人因为这一培训方案而过渡到正规劳动力市场。