The question regarding the relationship between money stock and GDP in the Euro Area is still under debate. In this paper we address the theme by resorting to Granger-causality spectral estimation and inference in the frequency domain  . We propose a new bootstrap test on unconditional and conditional Granger-causality  , as well as on their difference, to catch particularly prominent causality cycles . The null hypothesis is that each causality or causality difference is equal to the median across frequencies . In a dedicated simulation study, we prove that our tool is able to disambiguate causalities significantly larger than the median even in presence of a rich causality structure. Our results hold until the stationary bootstrap of Politis Romano (1994) is consistent on the underlying stochastic process . By this method, we point out that in the Euro Area money and output co-implied before the financial crisis of 2008, while after the crisis the only significant direction is from money to output with a shortened period .
 Granger-causality in the frequency domain is an emerging tool to analyze the causal relationship between two time series . We propose a bootstrap test on unconditional and conditional Granger-causality spectra , as well as on their difference, to catch particularly prominent causality cycles in relative terms. In particular, we consider a stochastic process derived applying independently the stationary bootstrap to the original series. Our null hypothesis is that each causality or causality difference is equal to the median across frequencies computed on that process. In this way, we are able to disambiguate causalities which depart significantly from the median one obtained ignoring the causality structure. Our test shows power one as the process tends to non-stationarity, thus being more conservative than parametric alternatives. As an example, we infer about the relationship between money stock and GDP in the Euro Area via our approach, considering inflation, unemployment and interest rates as conditioning variables. We point out that during the period 1999-2017 the money stock aggregate M1 had a significant impact on economic output at all frequencies, while the opposite relationship is significant only at high frequencies .
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The question regarding the relationship between money stock and GDP in the Euro Area is still under debate. In this paper we address the theme by resorting to
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spectral estimation and inference
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is an emerging tool to analyze the causal relationship between two time series
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new
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spectra
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. The
in relative terms. In particular, we consider a stochastic process derived applying independently the stationary bootstrap to the original series. Our
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. In a dedicated simulation study, we prove that our tool is
computed on that process. In this way, we are
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significantly larger than the median even in presence of a rich
which depart significantly from the median one obtained ignoring the
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results hold until the stationary bootstrap of Politis
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Romano (1994) is consistent on the underlying stochastic process . By this method, we point out that
test shows power one as the process tends to non-stationarity, thus being more conservative than parametric alternatives. As an example, we infer about the relationship between money stock and GDP
R
money and output co-implied before the financial crisis of 2008, while after the crisis the only significant direction is from money to output with a shortened period
via our approach, considering inflation, unemployment and interest rates as conditioning variables. We point out that during the period 1999-2017 the money stock aggregate M1 had a significant impact on economic output at all frequencies, while the opposite relationship is significant only at high frequencies