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Generalized instrumental variable models

Presentation

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) models 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 Generalised 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 nonseparably 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 realisations of outcomes. We use tools from random set theory to study identification in such models and provide a sharp characterisation 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.

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Cemmap Working Paper CWP63/15
This paper develops characterizations of identified sets of structures and structural features for complete and incomplete models involving continuous and/or discrete variables.
Cemmap Working Paper CWP04/14
In this paper the authors 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.
Cemmap Working Paper CWP43/13
The ability to allow for flexible forms of unobserved heterogeneity is an essential ingredient in modern microeconometrics. In this paper the authors extend the application of instrumental variable (IV) models to a wide class of problems in which multiple values of unobservable variables can be ...