Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/309995 
Year of Publication: 
2025
Series/Report no.: 
cemmap working paper No. CWP06/24
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
Abstract: 
Multidimensional heterogeneity and endogeneity are important features of a wide class of econometric models. With control variables to correct for endogeneity, nonparametric identification of treatment effects requires strong support conditions. To alleviate this requirement, we consider varying coefficients specifications for the conditional expectation function of the outcome given a treatment and control variables. This function is expressed as a linear combination of either known functions of the treatment, with unknown coefficients varying with the controls, or known functions of the controls, with unknown coefficients varying with the treatment. We use this modeling approach to give necessary and sufficient conditions for identification of average treatment effects. A sufficient condition for identification is conditional nonsingularity, that the second moment matrix of the known functions given the variable in the varying coefficients is nonsingular with probability one. For known treatment functions with sufficient variation, we find that triangular models with discrete instrument cannot identify average treatment effects when the number of support points for the instrument is less than the number of coefficients. For known functions of the controls, we find that average treatment effects can be identified in general nonseparable triangular models with binary or discrete instruments. We extend our analysis to flexible models of increasing dimension and relate conditional nonsingularity to the full support condition of Imbens and Newey (2009), thereby embedding semi- and non-parametric identification into a common framework.
Subjects: 
Identification
Conditional nonsingularity
Limited exogenous variation
Treatment effects
Heterogeneous coefficients
Control variable
Discrete instruments
Testability
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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