Published online by Cambridge University Press: 11 April 2017
We propose a characteristic function based test for conditional independence, applicable to both cross-sectional and time series data. We also derive a class of derivative tests, which deliver model-free tests for such important hypotheses as omitted variables, Granger causality in various moments and conditional uncorrelatedness. The proposed tests have a convenient asymptotic null N (0, 1) distribution, and are asymptotically locally more powerful than a variety of related smoothed nonparametric tests in the literature. Unlike other smoothed nonparametric tests for conditional independence, we allow nonparametric estimators for both conditional joint and marginal characteristic functions to jointly determine the asymptotic distributions of the test statistics. Monte Carlo studies demonstrate excellent power of the tests against various alternatives. In an application to testing Granger causality, we document the existence of nonlinear relationships between money and output, which are missed by some existing tests.
Wang acknowledges financial supports from the National Science Foundation of China (No. 71401160), the Ministry of Education of Humanities and Social Sciences Project of China (No. 14YJC790120), Fujian Provincial Key Laboratory of Statistics (Xiamen University, No. 2016003). We thank the editor Peter C. B. Phillips, the co-editor Liangjun Su, two referees, and seminar participants at Chinese Academy of Sciences, Kansas Econometrics Workshop, New York Econometrics Camp, Singapore Management University, and UC Riverside for their comments and suggestions. We are most grateful to Peter C. B. Phillips, who has gone beyond the call of duty for an editor in carefully correcting our English. We also thank Liangjun Su for providing us the computer codes to implement his tests. All remaining errors are solely our own.