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On the Testability of Identification in Some Nonparametric Models with Endogeneity
, 2013
"... This paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity. The first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogenei ..."
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Cited by 11 (1 self)
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This paper examines three distinct hypothesis testing problems that arise in the context of identification of some nonparametric models with endogeneity. The first hypothesis testing problem we study concerns testing necessary conditions for identification in some nonparametric models with endogeneity involving mean independence restrictions. These conditions are typically referred to as completeness conditions. The second and third hypothesis testing problems we examine concern testing for identification directly in some nonparametric models with endogeneity involving quantile independence restrictions. For each of these hypothesis testing problems, we provide conditions under which any test will have power no greater than size against any alternative. In this sense, we conclude that no nontrivial tests for these hypothesis testing problems exist.
Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models1
, 2013
"... This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is often difficult to verify wheth ..."
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Cited by 6 (1 self)
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This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is often difficult to verify whether a functional is regular (i.e., rootn estimable) or irregular (i.e., slower than rootn estimable). We provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is regular or not. We establish the following new useful results: (1) the asymptotic normality of a plugin penalized sieve minimum distance (PSMD) estimator of a (possibly irregular) functional; (2) the consistency of simple sieve variance estimators of the plugin PSMD estimator, and hence the asymptotic chisquare distribution of the sieve Wald statistic; (3) the asymptotic chisquare distribution of an optimally weighted sieve quasi likelihood ratio (QLR) test under the null hypothesis; (4) the asymptotic tight distribution of a nonoptimally weighted sieve QLR statistic under the null; (5) the consistency of generalized residual bootstrap sieve Wald and QLR tests; (6) local power properties of sieve Wald and QLR tests and of their bootstrap versions; (7) Wilks phenomenon of the sieve QLR test of hypothesis with increasing di
Stochastic Compounding and Uncertain Valuation
, 2013
"... Exploring longterm implications of valuation leads us to recover and use a distorted probability measure that reflects the longterm implications for risk pricing. Formally, we apply a generalized version of PerronFrobenius theory to construct this probability measure. We discuss methods for recov ..."
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Cited by 2 (0 self)
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Exploring longterm implications of valuation leads us to recover and use a distorted probability measure that reflects the longterm implications for risk pricing. Formally, we apply a generalized version of PerronFrobenius theory to construct this probability measure. We discuss methods for recovering this distribution from financial market data; we apply this distribution to characterize the impact of model misspecification; and we apply it to study KrepsPorteus style utility recursions for infinite horizon economies. 1
Sieve Quasi Likelihood . . . Conditional Moment Models
, 2013
"... This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals. These models belong to the difficult (nonlinear) illposed inverse problems with unknown operators, and include all of the (nonlinear) nonparametric inst ..."
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This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals. These models belong to the difficult (nonlinear) illposed inverse problems with unknown operators, and include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is generally difficult to verify whether a functional is regular (i.e., rootn estimable) or irregular (i.e., slower than rootn estimable). In this paper we provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is regular or irregular. We establish the following new results: (1) the asymptotic normality of the plugin penalized sieve minimum distance (PSMD) estimators of the (possibly iregular) functionals; (2) the consistency of sieve variance estimators of the plugin PSMD estimators; (3) the asymptotic chisquare distribution of an optimally weighted sieve quasi likelihood ratio (SQLR) statistic; (4) the asymptotic tight distribution of a possibly nonoptimally weighted SQLR statistic; (5) the consistency of the nonparametric bootstrap and the weighted bootstrap (possibly nonoptimally weighted) SQLR and sieve Wald statistics, which are proved under virtually the same conditions as those for the originalsample statistics. Small simulation studies and an empirical illustration of a nonparametric quantile IV regression are presented.
On completeness and consistency in nonparametric instrumental variable models∗
, 2015
"... This paper provides a first test for the identification condition in a nonparametric instrumental variable model, known as completeness, by linking the outcome of the test to consistency of an estimator. In particular, I show that uniformly over all distributions for which the test rejects with pro ..."
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This paper provides a first test for the identification condition in a nonparametric instrumental variable model, known as completeness, by linking the outcome of the test to consistency of an estimator. In particular, I show that uniformly over all distributions for which the test rejects with probability bounded away from 0, an estimator of the structural function is consistent. This is the case for a large class of complete distributions as well as certain sequences of incomplete distributions. As a byproduct of this result, the paper makes two additional contributions. First, I present a definition of weak instruments in the nonparametric instrumental variable model, which is equivalent to the failure of a restricted version of completeness. Second, I show that the null hypothesis of weak instruments, and thus failure of a restricted version of completeness, is testable and I provide a test statistic and a bootstrap procedure to obtain the critical values. Finally, I demonstrate the finite sample properties of the tests and the estimator in Monte Carlo simulations.
cemmap working paper CWP59/15 Constrained Conditional Moment Restriction Models
, 2015
"... This paper examines a general class of inferential problems in semiparametric and nonparametric models defined by conditional moment restrictions. We construct tests for the hypothesis that at least one element of the identified set satisfies a conjectured (Banach space) “equality ” and/or (a Banac ..."
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This paper examines a general class of inferential problems in semiparametric and nonparametric models defined by conditional moment restrictions. We construct tests for the hypothesis that at least one element of the identified set satisfies a conjectured (Banach space) “equality ” and/or (a Banach lattice) “inequality ” constraint. Our procedure is applicable to identified and partially identified models, and is shown to control the level, and under some conditions the size, asymptotically uniformly in an appropriate class of distributions. The critical values are obtained by building a strong approximation to the statistic and then bootstrapping a (conservatively) relaxed form of the statistic. Sufficient conditions are provided, including strong approximations using Koltchinskii’s coupling. Leading important special cases encompassed by the framework we study include: (i) Tests of shape restrictions for infinite dimensional parameters; (ii) Confidence regions for functionals that impose shape restrictions on the underlying parameter; (iii) Inference for functionals in semiparametric and nonparametric models defined by conditional moment (in)equalities; and (iv) Uniform inference in possibly nonlinear and severely illposed problems.
Iterative Estimation of Solutions to Noisy Nonlinear Operator Equations in Nonparametric Instrumental Regression Fabian DUNKER∗†, JeanPierre FLORENS‡,
, 2013
"... Abstract: This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newtontype iteration and establish convergence and convergence rate results. A particular emphasis is on instrume ..."
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Abstract: This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newtontype iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data.
Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models1
, 2013
"... This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals. These models belong to the difficult (nonlinear) illposed inverse problems with unknown operators, and include all of the (nonlinear) nonparametric ins ..."
Abstract
 Add to MetaCart
This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals. These models belong to the difficult (nonlinear) illposed inverse problems with unknown operators, and include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is generally difficult to verify whether a functional is regular (i.e., rootn estimable) or irregular (i.e., slower than rootn estimable). In this paper we provide computationally simple, unified inference procedures that are asymptotically valid regardless of whether a functional is regular or irregular. We establish the following new results: (1) the asymptotic normality of the plugin penalized sieve minimum distance (PSMD) estimators of the (possibly iregular) functionals; (2) the consistency of sieve variance estimators of the plugin PSMD estimators; (3) the asymptotic chisquare distribution of an optimally weighted sieve quasi likelihood ratio (SQLR) statistic; (4) the asymptotic tight distribution of a possibly nonoptimally weighted SQLR statistic; (5) the consistency of the nonparametric bootstrap and the weighted bootstrap (possibly nonoptimally weighted) SQLR and sieve Wald statistics, which are proved under virtually the same conditions as those for the originalsample