Is there a symmetric nonlinear causal relationship between large and small firms?

This paper uses both linear and nonlinear causality tests to reexamine the causal relationship between the returns on large and small firms. Consistent with previous results, we find that large firms linearly lead small firms. We also find a significant linear causality in the direction from small firms to large firms, particularly in the more recent time period where the impact from small firms to large firms is greater than from large to small. More important, in contrast to the received literature, we find significant nonlinear causality that is bi-directional and of the same duration in either direction. Using the BEKK asymmetric GARCH model we are able to capture most of the detected nonlinear relationship. This indicates that volatility spillovers are largely responsible for the observed nonlinear Granger causality.