Maximum likelihood estimation and inference on cointegration — with applications to the demand for money
Søren Johansen,Katarina Juselius +1 more
TLDR
In this paper, the estimation and testing of long-run relations in economic modeling are addressed, starting with a vector autoregressive (VAR) model, the hypothesis of cointegration is formulated as a hypothesis of reduced rank of the long run impact matrix.Abstract:
The estimation and testing of long-run relations in economic modeling are addressed. Starting with a vector autoregressive (VAR) model, the hypothesis of cointegration is formulated as the hypothesis of reduced rank of the long-run impact matrix. This is given in a simple parametric form that allows the application of the method of maximum likelihood and likelihood ratio tests. In this way, one can derive estimates and test statistics for the hypothesis of a given number of cointegration vectors, as well as estimates and tests for linear hypotheses about the cointegration vectors and their weights. The asymptotic inferences concerning the number of cointegrating vectors involve nonstandard distributions. Inference concerning linear restrictions on the cointegration vectors and their weights can be performed using the usual chi squared methods. In the case of linear restrictions on beta, a Wald test procedure is suggested. The proposed methods are illustrated by money demand data from the Danish and Finnish economies.read more
Citations
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Journal ArticleDOI
Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models
TL;DR: In this article, the authors derived the likelihood analysis of vector autoregressive models allowing for cointegration and showed that the asymptotic distribution of the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations.
Journal ArticleDOI
A simple estimator of cointegrating vectors in higher order integrated systems
James H. Stock,Mark W. Watson +1 more
TL;DR: In this paper, an efficient estimator of cointegrating vectors is presented for systems involving deterministic components and variables of differing, higher orders of integration. But the estimators are computed using GLS or OLS, and Wald Statistics constructed from these estimators have asymptotic x 2 distributions.
Journal ArticleDOI
Numerical distribution functions of likelihood ratio tests for cointegration
TL;DR: In this article, the authors employ response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration.
Journal ArticleDOI
Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK
S∅ren Johansen,Katarina Juselius +1 more
TL;DR: In this paper, the authors developed some new tests for structural hypotheses in the framework of a multivariate error correction model with Gaussian errors, based on an analysis of the likelihood function and motivated by an empirical investigation of the PPP relation and the UIP relation for the United Kingdom.
Journal ArticleDOI
Does financial development cause economic growth? Time-series evidence from 16 countries
TL;DR: This article conducted causality tests between financial development and real GDP using recently developed time series techniques and found little support to the view that finance is a leading sector in the process of economic development.
References
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Journal ArticleDOI
Co-integration and Error Correction: Representation, Estimation and Testing
TL;DR: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples.
Journal ArticleDOI
Statistical analysis of cointegration vectors
TL;DR: In this paper, the authors consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors, and derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions.
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Journal ArticleDOI
Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models
TL;DR: In this article, the authors derived the likelihood analysis of vector autoregressive models allowing for cointegration and showed that the asymptotic distribution of the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations.
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