Topic: Title: Causality tests and delay measures in a frequency band Authors:  Sven Schreiber - Macroeconomic Policy Institute IMK and Free U Berlin (Germany) [presenting]
Joerg Breitung - University of Cologne (Germany)
Abstract: We first extend the frequency-specific Granger causality test from the literature to a more general null hypothesis that allows non-causality at unknown frequencies within an interval, instead of having to prespecify a single frequency. This setup corresponds better to most hypotheses that are typically analyzed in applied research and is easy to implement within a linear VAR framework, while still being statistically rigorous. The resulting test is shown to be somewhat conservative (hence not exceeding its nominal size) but with generally good power. In an empirical application dealing with the dynamics of US temperatures and CO2 emissions we find that emissions cause temperature changes only at very low frequencies with more than 30 years of oscillation. Secondly we analyze the frequency-specific time shift of a target variable with respect to the Granger-causal input variable. In order to assess the corresponding estimation uncertainty of this lead/delay measure we make use of the fact that the time shift in the frequency domain is a function of the impulse response coefficients via the phase shift, after applying appropriate adjustments to the phase shift for this particular case of a causal (one-sided) filter. Hence standard errors are provided by applying the analytical delta approximation and through simulation-based techniques.