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Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:

The concept of causality introduced by Wiener (1956) and Granger (1969) is defined in terms of
predictability one period ahead. This concept can be generalized by considering causality at a
given horizon h, and causality up to any given horizon h [Dufour andThe concept of causality introduced by Wiener (1956) and Granger (1969) is defined in terms of
predictability one period ahead. This concept can be generalized by considering causality at a
given horizon h, and causality up to any given horizon h [Dufour and Renault (1998)]. This
generalization is motivated by the fact that, in the presence of an auxiliary variable vector Z, it
is possible that a variable Y does not cause variable X at horizon 1, but causes it at horizon h >
1. In this case, there is an indirect causality transmitted by Z. Another related problem consists
in measuring the importance of causality between two variables. Existing causality measures
have been defined only for the horizon 1 and fail to capture indirect causal effects. This paper
proposes a generalization of such measures for any horizon h. We propose nonparametric and
parametric measures of unidirectional and instantaneous causality at any horizon h. Parametric
measures are defined in the context of autoregressive processes of unknown order and expressed
in terms of impulse response coefficients. On noting that causality measures typically involve
complex functions of model parameters in VAR and VARMA models, we propose a simple
method to evaluate these measures which is based on the simulation of a large sample from the
process of interest. We also describe asymptotically valid nonparametric confidence intervals,
using a bootstrap technique. Finally, the proposed measures are applied to study causality
relations at different horizons between macroeconomic, monetary and financial variables in the
U.S. These results show that there is a strong effect of nonborrowed reserves on federal funds
rate one month ahead, the effect of real gross domestic product on federal funds rate is
economically important for the first three months, the effect of federal funds rate on gross
domestic product deflator is economically weak one month ahead, and finally federal fundsrate
causes the real gross domestic product until 16 months.[+][-]