In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that there are corresponding sufficient conditions for nonparametric models. A nonparametric rank condition and differentiability of the moment conditions with respect to a certain norm imply local identification. It turns out these conditions are slightly stronger than needed and are hard to check, so we provide weaker and more primitive conditions. We extend the results to semiparametric models. We illustrate the sufficient conditions with endogenous quantile and single index examples. We also consider a semiparametric habit-based, consumption capital asset pricing model. There we find the rank condition is implied by an integral equation of the second kind having a one-dimensional null space.
Authors
Research Fellow Columbia University
Sokbae is an IFS Research Fellow and a Professor at Columbia University, with an interest in Econometrics, Applied Microeconomics and Statistics.
Whitney K. Newey
Yale University
Working Paper details
- DOI
- 10.1920/wp.cem.2011.1711
- Publisher
- IFS
Suggested citation
Chen, X et al. (2011). Local identification of nonparametric and semiparametric models. London: IFS. Available at: https://ifs.org.uk/publications/local-identification-nonparametric-and-semiparametric-models (accessed: 19 May 2024).
Related documents
More from IFS
Understand this issue
Where next for the state pension?
13 December 2023
Social mobility and wealth
12 December 2023
Autumn Statement 2023: IFS analysis
23 November 2023
Policy analysis
The past and future of UK health spending
14 May 2024
Recent trends in and the outlook for health-related benefits
19 April 2024
Progression of nurses within the NHS
12 April 2024
Academic research
Keeping the peace whilst getting your way: Information, persuasion and intimate partner violence
17 May 2024
The role of hospital networks in individual mortality
13 May 2024
Forced displacement, mental health, and child development: Evidence from Rohingya refugees
10 May 2024