Characterizing the Instrumental Variable Identifying Assumption as Sample Selection Conditions

Christian Belzil and Jorgen Hansen

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Abstract: We build on Rosenzweig and Wolpin (2000) and Keane (2010) and show that in order to ful ll the Instrumental variable (IV) identifying moment condition, a policy must be designed so that compliers and non-compliers either have the same average error term, or have an error term ratio equal to their relative share of the population. The former condition (labeled Choice Orthogonality) is essentially a no-selection condition. The latter one, referred to as Weighted Opposite Choices, may be viewed as a distributional (functional form) assumption necessary to match the degree of selectivity between compliers and noncompliers to their relative population proportions. Those conditions form a core of implicit IV assumptions that are present in any empirical applications. They allow the econometrician to gain substantial insight about the validity of a speci c instrument, and they illustrate the link between identi cation and the statistical strength of an instrument. Finally, our characterization may also help designing a policy generating a valid instrument.

Keywords: Treatment E ects; Instrumental Variable methods; Implicit Assumptions; Treatment E ects. (search for similar items in EconPapers)
Date: 2012-11-19
Note: View the original document on HAL open archive server: https://hal.science/hal-00753539v1
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Working Paper: Characterizing the Instrumental Variable Identifying Assumption as Sample Selection Conditions (2012)
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