Long‐run Causality, with an Application to International Links Between Long‐term Interest Rates

Abstract

In this paper we give a precise definition of long‐run causality in a multivariate non‐stationary, possibly cointegrated, framework. A variable is said to be causal for another in the long‐run if knowledge of the past of the former improves long‐run predictions of the latter. In a VAR framework, we show that long‐run non‐causality can be easily tested with a Wald statistics, conditionally on the cointegration rank. The methodology is used to study long‐run causal links between US, German, and French long‐term interest rates from January 1990 to June 1997.

Speed of adjustment in cointegrated systems

“…Then a 0 1 X t is said not to Granger cause b 0 1 X t in the long run if b 0 1 X 1jt does not depend on (X 0 t a 1 : X 0 t 1 a 1 : ::: : X 0 t k+1 a 1 ) 0 , which contains a 0 1 X t and its lags. Bruneau and Jondeau (1999) show that this corresponds to the conditions …”

“…In this Appendix we describe how the conditions for long-run noncausality for I(1) systems as de…ned in Bruneau and Jondeau (1999) and Yamamoto and Kurozumi (2006) can be expressed as hypothesis on the IF F . Hence tests of long-run noncausality or neutrality can be considered as special cases of tests on the impact factors F .…”

“…Tests of (16), (17) are also considered in Bruneau and Jondeau (1999) and Yamamoto and Kurozumi (2006). These tests are relevant in the setup of this paper in order to empirically distinguish between Case 1 and Case 2.…”

Market Performance of Potato Auctions in Bhutan

“…The price of market x drives the price of market y in the long run if the price of market x does not respond to the lagged values of the price of market y nor to the price of any other market whose price does respond to lagged values of the price of market y, whereas the price of market y does respond to lagged values of the price of market x and/or lagged values of prices of markets other than market x but responsive to lagged values of the price of market x (cf. Bruneau and Jondeau, 1999 First of all, we select the order k of the tri-variate VAR model in (1a) - (1c), where each equation includes a constant as the only deterministic term. Given the small number of observations in each of the five seasonal subsamples that consitute our sample, we fixed the maximum number of lags to 2.…”

Geometric and long run aspects of Granger causality

“…To motivate the second extension, frequency-domain results are available for checking long run GNC (Hosoya, 1991(Hosoya, , 2001). There are also time-domain results for cointegrated VAR models (Granger & Lin, 1995;Bruneau & Jondeau, 1999;Yamamoto & Kurozumi, 2006). It would be useful to obtain time-domain criteria for long run GNC for a wider class of processes.…”