Nonparametric methods for inference in the presence of instrumental variables

By Peter Hall, Joel L. Horowitz. 2003

448 citations recorded by the source corpus.

We suggest two nonparametric approaches, based on kernel methods and orthogonal series, respectively, to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the "difficulty" of which depends on eigenvalues of a certain integral operator which is determined by the joint density of endogenous and instrumental variables. We delineate the role played by problem difficulty in determining both the optimal convergence rate and the appropriate choice of smoothing parameter.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

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Citations in the corpus

Instrumental variable methods for recovering continuous linear functionals (2011, background): “K µ x i i xj h ¶ ( 11 ) In certain cases it will necessary to resort to higher order kernels in order to attain the appropriate rates of convergence.”
Instrumental regression in partially linear models (2012, unknown): “This condition is weaker than to require the strong identification of X,Z by W (as used, e.g., in Darolles, Florens, and Renault (2002) or Hall and Horowitz (2005)).”
Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models (2007, background): “Although there are a few results on convergence rates of purely nonparametric sieve MD estimation of h o in specific models; see e.g. Blundell et al. (2001) and Hall and Horowitz (2005) for the model E[Y1 − ho(Y2)”
Identification in Nonparametric Simultaneous Equations Models (2008, background): “variables. For nontriangular systems, Newey and Powell (1989, 2003), Darolles, Florens, and Renault (2003), and Hall and Horowitz (2005) considered estimation using conditional moment conditions between additive unobservables and instruments.”
Nonparametric Instrumental Variables Estimation of a Quantile Regression Model (2006, background): “2) is related to Hall’s and Horowitz’s (2005) estimator of g in (1.”
Applied Nonparametric Instrumental Variables Estimation (2011, methodology): “The available estimators include kernel-based estimators (Darolles, Florens and Renault 2006; Hall and Horowitz 2005) and series or sieve estimators (Newey and Powell 2003; Blundell, Chen, and Kristensen 2007).”
Examples of L2-Complete and Boundedly-Complete Distributions (2011, unknown): “These models include: (i) the nonparametric IV regression model, see Newey and Powell (2003), Darolles, Florens, and Renault (2000), Hall and Horowitz (2005), and references in Horowitz (2010), (ii) semiparametric IV models, see Ai and Chen (2003), Blundell, Chen, and Kristensen (2007), and Chen…”
Control functions in nonseparable simultaneous equations models (2014, background): “Newey and Powell (2003), Darolles, Florens, and Renault (2002), Ai and Chen (2003), Hall and Horowitz (2003), Chernozhukov and Hansen (2005), Chernozhukov, Imbens, and Newey (2007), and Chen and Pouzo (2012) followed this instrumental variable approach.”
Identification and Estimation of Triangular Simultaneous Equations Models without Additivity (2002, background): “Powell (2003), Das (2004), Darrolles, Florens, and Renault (2003), Hall and Horowitz (2005) ,”
Threshold Regression with Endogeneity (2017, unknown): “Most of the existing literature such as Newey et al. (1999), Ai and Chen (2003), Newey and Powell (2003), Hall and Horowitz (2005) and Darolles et al. (2011) use a nonparametric IV approach to help resolve this problem but with deleterious effects on the convergence rate; see Florens (2003) and…”
NONPARAMETRIC IDENTIFICATION USING INSTRUMENTAL VARIABLES: SUFFICIENT CONDITIONS FOR COMPLETENESS (2011, methodology): “…in a variety of models including the nonparametric IV regression model (see Newey and Powell (2003), Darolles, Fan, Florens, and Renault (2011), Hall and Horowitz (2005), and Horowitz (2011)), semiparametric IV models (see Ai and Chen (2003) and Blundell, Chen, and Kristensen (2007)),…”
Nonparametric identification and estimation of transformation models (2015, methodology): “In this case, we can now in principle employ any existing nonparametric IV estimator proposed in literature such as the kernel estimator of Hall and Horowitz (2005) or the sieve estimator of Blundell, Chen, and Kristensen (2007).”