Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/97370 
Year of Publication: 
2014
Series/Report no.: 
cemmap working paper No. CWP04/14
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
The ability to allow for flexible forms of unobserved heterogeneity is an essential ingredient in modern microeconometrics. In this paper we extend the application of instrumental variable (IV) methods to a wide class of problems in which multiple values of unobservable variables can be associated with particular combinations of observed endogenous and exogenous variables. In our Generalized Instrumental Variable (GIV) models, in contrast to traditional IV models, the mapping from unobserved heterogeneity to endogenous variables need not admit a unique inverse. The class of GIV models allows unobservables to be multivariate and to enter non-separably into the determination of endogenous variables, thereby removing strong practical limitations on the role of unobserved heterogeneity. Important examples include models with discrete or mixed continuous/discrete outcomes and continuous unobservables, and models with excess heterogeneity where many combinations of different values of multiple unobserved variables, such as random coefficients, can deliver the same realizations of outcomes. We use tools from random set theory to study identification in such models and provide a sharp characterization of the identified set of structures admitted. We demonstrate the application of our analysis to a continuous outcome model with an interval-censored endogenous explanatory variable.
Subjects: 
instrumental variables
endogeneity
excess heterogeneity
limited information
set identification
partial identification
random sets
incomplete models
JEL: 
C10
C14
C24
C26
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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