Peter Boswijk and Jean-Pierre Urbain for several useful comments. This paper is a revised version of Dufour and Renault (1995). Canada Research Chair Holder (Econometrics). Centre interuniversitaire de recherche en analyse des organisations (CIRANO), Centre interuniversitaire de recherche en économie quantitative (CIREQ), and Département de sciences

The impact of the choice of the lag length on tests for the number of cointegration relations in a vector autoregressive (VAR) process is investigated. It is shown that the asymptotic distribution of likelihood ratio (LR) tests for the cointegrating rank remains unchanged if the true data generation process (DGP) is of finite order and a consistent model selection criterion is used for choosing the lag length. A similar result also holds if the true DGP is an infinite order VAR. In a simulation study we find that small sample power and size of LR cointegration tests strongly depend on the choice of the lag order.

this paper was carried out within Sonderforschungsbereich 373 at the Humboldt University Berlin and was printed using funds made available by the Deutsche Forschungsgemeinschaft. 1 Introduction

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Vector autoregression (VAR) models have become widely used in applied economic research since Sims (1980) pioneered this approach. In a VAR each variable is regressed against the same number of lags of every variable. In other words, VAR lag specifications are symmetrical. Unfortunately, VARs often estimate a large number of statistically insignificant coefficients, and therefore the impulse responses and

We consider Johansen’s (1988, 1991) cointegration tests when a Vector AutoRegressive (VAR) process of order k is used to approximate a more general linear process with a possibly infinite VAR representation. Traditional methods to select the lag order, such as Akaike’s (AIC) or the Bayesian information criteria, often lead to too parsimonious a model with the implication that the cointegration tests suffer from substantial size distortions in finite samples. We extend the analysis of Ng and Perron (2001) to derive a Modified Akaike’s Information Criterion (MAIC) in this multivariate setting. The idea is to use the information specified by the null hypothesis as it relates to restrictions on the parameters of the model to keep an extra term in the penalty function of the AIC. This MAIC takes a very simple form for which this extra term is simply the likelihood ratio test for testing the null hypothesis of r against more than r cointegrating vectors. We provide theoretical analyses of its validity and of the fact that cointegration tests constructed from a VAR whose lag order is selected using the MAIC have the same limit distribution as when the order is finite and known. We also provide theoretical and simulation analyses to show how the MAIC leads to VAR approximations that yield tests with drastically improved size properties with little loss of power.

In cointegrated vector autoregressive (VAR) analyses various nonlinear functions of the coefficients are of interest. Notable examples are impulse responses. A general theory for asymptotic inference on such functions is developed under the assumption that the actual data generation process (DGP) is of potentially infinite VAR order although finite order VAR models are fitted to the data and are used for computing the quantities of interest. In the asymptotic theory the VAR order is assumed to grow with the sample size albeit at a smaller rate. Both authors gratefully acknowledge financial support by the DFG, Sonderforschungsbereich 373. This research was partly carried out while the first author was visiting the Institute of Statistics and Econometrics at the Humboldt University and partly while the second author was a Visiting Research Fellow at the Australian National University in Canberra. We thank Kirstin Hubrich for comments. The paper was printed using funds made available b...

* The corresponding author. The authors are grateful to Anita Akkaş and the members of the Pazar11 discussion group for their valuable suggestions. All the views expressed in this paper are of the authors and do not necessarily represent those of the Central

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A fishing expedition in the Mekong Delta: market volatility and price substitutes for Vietnamese fresh water fish