Output gaps and inflation: an approach using a multivariable Beveridge-Nelson decomposition

This paper uses state-space techniques to derive a Moving Average representation of an error correction model of the time series yt ~I(1). This can be seen as a proof by construction of the Granger Representation Theorem in the reverse direction. The paper then shows how this state-space representation can be used to explicitly compute the Beveridge-Nelson Decomposition of the time series and hence their trends and the spectra and co-spectra of the cyclical components. These techniques are then applied to the analysis of the business cycle in France, Germany, the United Kingdom and the United States. Particular attention is paid to estimating the output gap and both the long and short-run relationships between output and inflation.

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