This paper studies the identifying content of the instrument monotonicity assumption of Imbens and Angrist (1994) on the distribution of potential outcomes in a model with a binary outcome, a binary treatment and an exogenous binary instrument. In the context of this setup, conclusions from previous results can be generally summarized as follows: (i) imposing instrument monotonicity can misspecify the model; and (ii) when the model is not misspecified, instrument monotonicity does not have any identifying content on the marginal distributions of the potential outcomes. In this paper, I demonstrate that instrument monotonicity can however have identifying content on features of the joint distribution of the potential outcomes when the model is not misspecified. I illustrate how this identifying content can lead to additional informative conclusions with respect to the proportion who benefit, a specific feature of the joint distribution of the potential outcomes .
This paper studies the identifying content of the instrument monotonicity assumption of Imbens and Angrist (1994) on the distribution of potential outcomes in a model with a binary outcome, a binary treatment and an exogenous binary instrument. Specifically, I derive necessary and sufficient conditions on the distribution of the data under which the identified set for the distribution of potential outcomes when the instrument monotonicity assumption is imposed can be a strict subset of that when it is not imposed .
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In the context of this setup, conclusions from previous results can be generally summarized as follows: (i) imposing instrument monotonicity can misspecify the model; and (ii) when the model is not misspecified, instrument monotonicity does not have any identifying content on the marginal distributions of the potential outcomes. In this paper, I demonstrate that instrument monotonicity can however have identifying content on features of the joint distribution of the
Specifically, I derive necessary and sufficient conditions on the distribution of the data under which the identified set for the distribution of
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model is not misspecified. I illustrate how this identifying content can lead to additional informative conclusions with respect to the proportion who benefit, a specific feature of the joint distribution of the potential outcomes
instrument monotonicity assumption is imposed can be a strict subset of that when it is not imposed