Nonparametric Tests for Conditional Independence Using Conditional Distribution

Abstract

The concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works in this literature focus on the causality in the mean. This paper aims to propose a different nonparametric statistic to test the conditional independence and Granger non-causality between two random variables conditional on another one. The test statistic is based on the comparison of conditional distribution functions using the L² metric. We use the Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. The power of the proposed conditional distribution-based test is better than that of Su and White (2008)’s test. Further, our test has the same power compared to the characteristic function-based test of Su and White (2007) and it is very simple to implement. We run a simulation study to investigate the finite sample properties of the tests and we illustrate their practical relevance by considering many empirical applications where we examine the Granger non-causality between financial variables.