Using the standard linear model as a base, a unified theory of Bayesian Analyses of Cointegration Models is constructed. This is achieved by defining (natural conjugate) priors in the linear model and using the implied priors for the cointegration model. Using these priors, posterior results for...

Cointegration occurs when the long run multiplier of a vector autoregressive model exhibits rank reduction. Priors and posteriors of the parameters of the cointegration model are therefore proportional to priors and posteriors of the long run multiplier given that it has reduced rank. Rank...

We propose a novel Bayesian test under a (noninformative) Jeffreys’ prior specifica- tion. We check whether the fixed scalar value of the so-called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standard- ized distribution under the...

We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: necessity of a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson (1951), sensitivity to the ordering of the variables for the...

We propose a natural conjugate prior for the instrumental variables regression model. The prior is a natural conjugate one since the marginal prior and posterior of the structural parameter have the same functional expressions which directly reveal the update from prior to posterior. The...

Statistical inference in nested linear models that result from linear restrictions on the parameters of encompassing linear models can be considered to result from the conditional distribution under the encompassing model. We extend this reasoning to nested models that result from general...

We consider representation, estimation and inference on cointegration in a (PVAR). We show that cointegration amounts to a restriction on a product of parameter matrices. We therefore use GMM to construct estimators of the long-run (cointegration) parameters and to obtain test statistics for...

Diffuse priors lead to pathological posterior behavior when used in Bayesian analyses of Simultaneous Equation Models (SEMs). This results from the local nonidentification of certain parameters in SEMs. When this, a priori known, feature is not captured appropriately, an a posteriori favor for...

Many common statistical models can be specified as linear models with restrictions imposed on the parameters. A large amount of these models impose restrictions which do not allow for the analytical construction of the probability density function (pdf) of the parameters given the restrictions....

Generalized Method of Moments (GMM) Estimators are derived for Reduced Rank Regression Models, the Error Correction Cointegration Model (ECCM) and the Incomplete Simultaneous Equations Model (INSEM). The GMM (2SLS) estimators of the cointegrating vector in the ECCM are shown to have normal...