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http://hdl.handle.net/10419/64756
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| Title: | | Sharp identified sets for discrete variable IV models  |
| Authors: | | Chesher, Andrew Smolinski, Konrad |
| Issue Date: | | 2010 |
| Series/Report no.: | | cemmap working paper CWP11/10 |
| Abstract: | | Instrumental variable models for discrete outcomes are set, not point, identifying. The paper characterises identi.ed sets of structural functions when endogenous variables are discrete. Identi.ed sets are unions of large numbers of convex sets and may not be convex nor even connected. Each of the component sets is a projection of a convex set that resides in a much higher dimensional space onto the space in which a structural function resides. The paper develops a symbolic expression for this projection and gives a constructive demonstration that it is indeed the identi.ed set. We provide a MathematicaTM notebook which computes the set symbolically. We derive properties of the set, suggest how the set can be used in practical econometric analysis when outcomes and endogenous variables are discrete and propose a method for estimating identified sets under parametric or shape restrictions. We develop an expression for a set of structural functions for the case in which endogenous variables are continuous or mixed discrete-continuous and show that this set contains all structural functions in the identified set in the non-discrete case. |
| Subjects: | | Discrete endogenous variables Discrete outcomes Endogeneity Fourier-Motzkin Elimination Incomplete models Instrumental variables Set idenfication Threshold Crossing Models |
| JEL: | | C10 C14 C50 C51 |
| Persistent Identifier of the first edition: | | doi:10.1920/wp.cem.2010.1110 |
| Document Type: | | Working Paper |
| Appears in Collections: | | cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)
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