Economics Letters 58 (1998) 1–5 Testing cointegrating coefficients in vector autoregressive error correction models * Gerd Hansen, Jeong-Ryeol Kim, Stefan Mittnik Institute of Statistics and Econometrics, Christian Albrechts University at Kiel, Olshausenstr. 40, D-24098 Kiel, Germany Received 7 November 1996; accepted 19 June 1997 Abstract Tests of cointegrating coefficients in vector autoregressive error correction models ignore the Cauchy-like behavior of the 2 estimator’s finite-sample distribution. This causes excessive rejections of the null in standard x tests. We propose a 2 Cauchy-based x test, and show, via simulation, that it yields adequate rejection rates.  1998 Elsevier Science S.A. Keywords: Cointegration; Error correction model; Granger causality; Chi-square test; Cauchy distribution JEL classification: C12; C22; C32 1. Introduction Testing for causality is a central issue in macroeconometrics. Since Granger (1969) introduced an operational concept of causality, the Wald test has been widely used for testing zero restrictions implying Granger-noncausality. It is especially important to find causal structures in vector autoregressive (VAR) analyses, because all variables are – in the sense of Sims (1980) – assumed to be endogenous. In view of the fact that most macroeconomic variables are nonstationary, Engle and Granger (1987) introduced the concepts of cointegration and error correction. Johansen (1988) proposed a vector autoregressive error correction model (VEC) based on canonical correlation and full information maximum likelihood (FIML) estimation. Ahn and Reinsel (1990) investigated the asymptotic distribution of the FIML estimator of VEC coefficients when variables are nonstationary. The efficiency of this estimator was analyzed in Saikkonen (1991). Toda and Phillips (1994) considered causality testing in a VEC and showed that both the Wald statistic for long-run and that for 2 short-run Granger-noncausality are asymptotically x distributed. Johansen and Juselius (1994) found that this also holds for the likelihood-ratio test statistic when testing overidentifying zero restrictions on cointegrating coefficients. Investigating the finite-sample distribution of the FIML estimator of cointegrating coefficients in a VEC Phillips (1994) found that the reduced rank regression estimator has a heavy-tailed distribution * Corresponding author. Tel.: 149 431 8802166; fax: 149 431 8802673; e-mail: mittnik@stat-econ.uni-kiel.de 0165-1765 / 98 / $19.00  1998 Elsevier Science S.A. All rights reserved. PII S0165-1765(97)00199-7