Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series


Inferences for a Partially Varying Coefficient Model With Endogenous Regressors

Zongwu Cai
Ying Fang
Ming Lin
Jia Su

In this article, we propose a new class of semiparametric instrumental variable models with partially varying
coefficients, in which the structural function has a partially linear form and the impact of endogenous
structural variables can vary over different levels of some exogenous variables. We propose a three-step
estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic
normality of these proposed estimators are established. Moreover, a generalized F-test is developed to
test whether the functional coefficients are of particular parametric forms with some underlying economic
intuitions, and furthermore, the limiting distribution of the proposed generalized F-test statistic under the
null hypothesis is established. Finally, we illustrate the finite sample performance of our approach with
simulations and two real data examples in economics.

Endogeneity; Functional coefficients; Generalized F-test; Instrumental variables models;
Nonparametric test; Profile least squares

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