Journal of Econometrics 97 (2000) 293 } 343 Structural analysis of vector error correction models with exogenous I(1) variables M. Hashem Pesaran*, Yongcheol Shin, Richard J. Smith Faculty of Economics and Politics, Austin Robinson Building, University of Cambridge, Sidgwick Avenue, Cambridge CB3 9DD, UK Department of Economics, University of Edinburgh, UK Department of Economics, University of Bristol, UK Received 1 April 1997; received in revised form 1 October 1999; accepted 1 October 1999 Abstract This paper generalizes the existing cointegration analysis literature in two respects. Firstly, the problem of e$cient estimation of vector error correction models containing exogenous I(1) variables is examined. The asymptotic distributions of the (log-)likelihood ratio statistics for testing cointegrating rank are derived under di!erent intercept and trend speci"cations and their respective critical values are tabulated. Tests for the presence of an intercept or linear trend in the cointegrating relations are also developed together with model misspeci"cation tests. Secondly, e$cient estimation of vector error correction models when the short-run dynamics may di!er within and between equations is considered. A re-examination of the purchasing power parity and the uncovered interest rate parity hypotheses is conducted using U.K. data under the maintained assumption of exogenously given foreign and oil prices.  2000 Elsevier Science S.A. All rights reserved. JEL classixcation: C12; C13; C32 Keywords: Structural vector error correction model; Cointegration; Unit roots; Likeli- hood ratio statistics; Critical values; Seemingly unrelated regression; Monte Carlo simulations; Purchasing power parity; Uncovered interest rate parity * Corresponding author. Tel.: #44 1223 335216; fax: #44 1223 335471. E-mail address: hashem.pesaran@econ.cam.ac.uk (M.H. Pesaran). 0304-4076/00/$ - see front matter  2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 - 4 0 7 6 ( 9 9 ) 0 0 0 7 3 - 1