Specification Testing in Nonparametric Instrumental Quantile Regression

Abstract

There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This paper develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.

Specification testing in random coefficient models

“…It remains to show that j Q nj d → N (0 1), which follows by Lemma A.3 of Breunig (2016) by using the following computations. To show ∞ j=1 E|Q nj | 2 ≤ 1, observe that j =j δ I l (V j t)δ R l (V j t) − δ R l (V j t)δ I l (V j t) (t) dt = 0…”

“…In this paper, we use sieve estimators for the unknown distributional elements. In the econometrics literature, sieve methodology was recently used to construct Wald statistics (see Chen and Pouzo () and Chen and Pouzo () for sieve minimum distance estimation) or nonparametric specification tests (see Breunig ()), and, in nonparametric instrumental regression, tests based on series estimators have been proposed by Horowitz () and Breunig (). Moreover, in the nonparametric IV model, tests for parametric specification have been proposed by Horowitz () and Horowitz and Lee (), while Blundell and Horowitz () proposed a test of exogeneity.…”

Testing exogeneity in nonparametric instrumental variables models identified by conditional quantile restrictions

“…However, the model and hypothesis in this paper are different from those in Horowitz (2006) and Horowitz and Lee (2009) and require a separate treatment. Breunig (2018) presents a test of exogeneity in nonparametric quantile IV models and derives its asymptotic distribution under the null hypothesis of exogeneity and under local alternatives. The test presented here is more powerful than that of Breunig (2018) against a large class of alternatives.…”

“…Breunig (2018) presents a test of exogeneity in nonparametric quantile IV models and derives its asymptotic distribution under the null hypothesis of exogeneity and under local alternatives. The test presented here is more powerful than that of Breunig (2018) against a large class of alternatives. The theoretical reason for the power difference is explained in Section 3.5 of this paper.…”

“…The theoretical reason for the power difference is explained in Section 3.5 of this paper. There are, however, certain types of alternatives against which Breunig's (2018) test has greater power. These are described in Section 3.5.…”