Local Identification of Nonparametric and Semiparametric Models

By Xiaohong Chen, Victor Chernozhukov, S. Lee, Whitney K. Newey. 2011

123 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/252834e3913b5e35bdaf9da44502b40a799c29ec

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. David M. Blei
2. Yixin Wang
3. Timothy M. Christensen

In Finance

1. David M. Blei
2. Yixin Wang
3. Timothy M. Christensen

Citations in the corpus

• Nonparametric stochastic discount factor decomposition (2014, methodology): “In particular, the long-term pricing implications of many models with habit persistence and models with a limiting type of recursive preferences are identical to the long-term pricing implications the C-CAPM.”
• Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2015, unknown): “See Florens, Johannes, and Van Bellegem (2012), Chen et al. (2014) for identification of (β0 h0) in this model.”
• Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models (2014, unknown): “Theorem B of Chen et al. (2003) establish the consistency of nonparametric bootstrap for a general class of semiparametric two step GMM estimators θ̂gmm of root-n estimable Euclidean parameter θ0: ∣∣∣LV∞|Z∞ (√n(θ̂B gmm − θ̂gmm) | Zn)− L(√n(θ̂gmm − θ0))∣∣∣ = oPZ∞ (1).”
• Multiple Causes: A Causal Graphical View (2019, background): “See Chen et al. (2014) for a detailed discussion of completeness.”