Partial identification of discrete counterfactual distributions with sequential update of information

The credibility of standard instrumental variables assumptions is often under dispute. This paper imposes weak monotonicity in order to gain information on counterfactual outcomes, but avoids independence or exclusion restrictions. The outcome process is assumed to be sequentially ordered, building up and depending on the information level of agents. The potential outcome distribution is assumed to weakly increase (or decrease) with the instrument, conditional on the continuation up to a certain stage. As a general result, the counterfactual distributions can only be bounded, but the derived bounds are informative compared to the no-assumptions bounds thus justifying the instrumental variables terminology. The construction of bounds is illustrated in two data examples.