Common trends models provide a useful tool for studying growth and business cycle phenomena in a joint framework. In this paper we study the problem of how to estimate and analyse a common stochastic trends model for an n dimensional time series which is cointegrated of order (1,1) with r<n cointegration vectors. Identification of k=n-r permanent (trend) and r transitory innovations is discussed in terms of impulse responses and variance decompositions. Finally, we derive analytical expressions of the asymptotic distributions for estimates of these functions, thereby making formal hypothesis testing and inference possible within this framework.

KEYWORDS: Cointegration, common trends, impulse response function, permanent and transitory shocks, variance decomposition.
JEL CLASSIFICATION NUMBERS: C32, C51.

We report evidence that the relation between the financial sector share, private savings and growth in the United States 1948-1996 is characterized by several regime shifts. The finding is based on vector autoregressions on quarterly data that allow for Markov switching regimes. The evidence may be interpreted as support for a hypothesis that the relation between financial development and growth evolves in a stepwise fashion. Theoretical models where financial market extensions entail fixed costs imply such stepwise patterns. The estimated variable relations are roughly consistent with the patterns to be expected from such models, although our data do not admit definite conclusions. The timing of the shifts coincide with changes in regulation and in the financial market structure.

KEYWORDS: Financial markets extensions, growth, Markov switching, saving, vector autoregression.
JEL CLASSIFICATION NUMBERS: C32, E44, O16, O51.

In this paper we study 2-state Markov switching VAR models of monthly unemployment and inflation for three countries: Sweden, United Kingdom, and the United States. The primary purpose is to examine if periods of low inflation are associated with high or low unemployment volatility. We find that MS-VAR models seem to provide a better description of the data than single regime VARs and need fewer lags to account for serial correlation. To interpret the regimes the empirical results are compared with the predictions from a version of Rogoff's (1985) model of monetary policy. We find that both the theoretical and the empirical results suggest that an increase in central bank "conservativeness" can be associated with either a higher or a lower variance in unemployment. In the U.S. case we find that the variance of unemployment is lower in the low inflation regime than in the high inflation regime, while the Swedish and the U.K. cases suggest that unemployment variability is higher in the low inflation regime.

KEYWORDS: Cointegration, monetary policy, Phillips curve, regime switching.
JEL CLASSIFICATION NUMBERS: C32, E31, E52.

This paper analyses three Granger noncausality hypotheses within a conditionally Gaussian MS-VAR model. Noncausality in mean is based on Granger's original concept for linear predictors by defining noncausality from the 1-step ahead forecast error variance for the conditional expectation. Noncausality in mean-variance concerns the conditional forecast error variance, while noncausality in distribution refers to the conditional distribution of the forecast errors. Necessary and sufficient parametric conditions for noncausality are presented for all hypotheses. As an illustration, the hypotheses are tested using monthly postwar U.S. data on money and income. We find that money is not Granger causal in mean for income, but Granger causal in mean-variance, i.e. there is unique information in money for predicting the next period regime and the regime affects the uncertainty about the income forecast.

KEYWORDS: Granger causality, Markov process, regime switching, vector autoregression.
JEL CLASSIFICATION NUMBERS: C32.

This paper presents estimates of the effects of monetary policy shocks on the Swedish economy. A theoretical model of an open economy is used to identify a structural VAR model. The empirical results from the identified VAR model are compared with two less structural approaches for identification of monetary policy shocks. The first assumes that shocks can be measured as deviations from a forward looking interest rate rule, estimated using Sveriges Riksbank's (Swedish central bank) own forecasts. The second approach focuses on the effects of "narrative" monetary policy shocks as given by devaluations of the Swedish currency. We find that plausible theoretical restrictions often result in price puzzles. Although conventional results obtain with certain theoretical restrictions imposed on the VAR, another way to achieve this is by using external information about large policy shocks. Thus, we find that the effects of some devaluations are consistent with the conventional wisdom about the effects of monetary policy shock.

KEYWORDS: Common trends, devaluations, identification, inflation, monetary policy shocks, open economy, structural vector autoregression.
JEL CLASSIFICATION NUMBERS: C32, E31, E52.

This paper re-examines two data issues concerning euro area money demand: aggregation of national data and measurement of the own rate. The main purpose is to study if euro area money demand is subject to parameter non-constancies using formal tests rather than informal diagnostics. As a complement to inference based on asymptotics we perform small-scale bootstraps. The empirical evidence supports the existence of a stable long-run relationship between money and output and that the cointegration space is constant over time. However, the interest rate semi-elasticities are imprecisely estimated. Conditional on the cointegration relations the remaining parameters of the system appear to be constant. We also examine the relevance of stock prices for money demand and find that our measure does not not matter for the long-run relations, but may be useful in forecasting exercises. Finally, the conclusions are robust for the aggregation method and the choice of sample.

KEYWORDS: Aggregation, Bootstrap, Money Demand, Own Rate of Money, Parameter Constancy.
JEL CLASSIFICATION NUMBERS: C22, C32, E41.

Structural VARs have been extensively used in empirical macroeconomics during the last two decades, particularly in analyses of monetary policy. Existing Bayesian procedures for structural VARs are at best confined to a severely limited handling of cointegration restrictions. This paper extends the Bayesian analysis of structural VARs to cover cointegrated processes with an arbitrary number of cointegrating relations and general linear restrictions on the cointegration space. A reference prior distribution with an optional small open economy effect is proposed and a Gibbs sampler is derived for a straightforward evaluation of the posterior distribution. The methods are used to analyze the effects of monetary policy in Sweden.

KEYWORDS: Structural, Vector Autoregression, Monetary Policy, Impulse Responses, Counterfactual Experiments.
JEL CLASSIFICATION NUMBERS: C11, C32, E52.

The paper considers a Bayesian approach to the cointegrated VAR model with a uniform prior on the cointegration space. Building on earlier work by Villani (2005), where the posterior probability of the cointegration rank can be calculated conditional on the lag order, the current paper also makes it possible to compute the joint posterior probability of these two parameters as well as the marginal posterior probabilities under the assumption of a known upper bound for the lag order. When the marginal likelihood identity is used for calculating these probabilities, a point estimator of the cointegration space and the weights is required. Analytical expressions are therefore derived of the mode of the joint posterior of these parameter matrices. The procedure is applied to a money demand system for the euro area and the results are compared to those obtained from a maximum likelihood analysis.

KEYWORDS: Bayesian inference, cointegration, lag order, money demand, vector autoregression.
JEL CLASSIFICATION NUMBERS: C11, C15, C32, E41.