Christophe Planas

The production function methodology for calculating potential growth rates and output gaps

This paper provides a detailed description of the current version of the Ecofin Council approved production function (PF) methodology which is used for assessing both the productive capacity (i.e. potential output) and cyclical position (i.e. output gaps) of EU economies. Compared with the previous 2010 paper on the same topic, there have been two significant changes to the PF methodology, namely an overhaul of the NAWRU methodology & the introduction of a new T+10 methodology.

Bayesian Analysis of the Output Gap

Our objective is to build output gap estimates that benefit from information provided by Phillips curve theory and business cycle studies. For this, we develop a Bayesian analysis of the bivariate Phillips curve model proposed by Kuttner for estimating potential output. Given our priors, we obtain samples from parameters and state variables joint posterior distribution following a Gibbs sampling strategy. We sample the state variables given parameters using the Carter–Kohn procedure, and we exploit a likelihood factorization to draw parameters given the state. A Metropolis–Hastings step is used to remove the conditioning on starting values. To accommodate the variance moderation that has been observed on U.S. gross domestic product, Kuttners model is extended for a change in variance parameters. We apply this methodology to the analysis of the output gap in the United States and in the European Monetary Union. Finally, some important extensions to the original Kuttner model are discussed.

Does capacity utilisation help estimating the TFP cycle

In the production function approach, accurate output gap assessment requires a careful evaluation of the TFP cycle. In this paper we propose a bivariate model that links TFP to capacity utilization and we show that this model improves the TFP trend-cycle decomposition upon univariate and Hodrick-Prescott filtering. In particular, we show that estimates of the TFP cycle that load information about capacity utilization are less revised than univariate and HP estimates, both with 2009 and real-time TFPdata vintages. We obtain this evidence for twelve pre-enlargement EU countries.

Overcoming Nonadmissibility in ARIMA-Model-Based Signal Extraction

We analyze the situation in which the decomposition of a time series into orthogonal balanced components as performed by the AR IMA-model-based (AMB) method is nonadmissible. We show that considering top-heavy models for the components can solve the problem. The top-heavy decomposition is derived and the improvement achieved is illustrated by an application to a class of models often encountered in practice. Two empirical applications allow us to draw a comparison with the results yielded by the AMB decomposition of an approximated model by using an ad hoc filter such as X11-ARIMA and by direct specification of the structural time series models.

Efficient MCMC sampling in dynamic mixture models

We show how to improve the efficiency of Markov Chain Monte Carlo (MCMC) simulations in dynamic mixture models by block-sampling the discrete latent variables. Two algorithms are proposed: the first is a multi-move extension of the single-move Gibbs sampler devised by Gerlach, Carter and Kohn (in J. Am. Stat. Assoc. 95, 819–828, 2000); the second is an adaptive Metropolis-Hastings scheme that performs well even when the number of discrete states is large. Three empirical examples illustrate the gain in efficiency achieved. We also show that visual inspection of sample partial autocorrelations of the discrete latent variables helps anticipating whether blocking can be effective.

Marginal distribution of Markov-switching VAR processes

ABSTRACT We make available simple and accurate closed-form approximations to the marginal distribution of Markov-switching vector auto-regressive (MS VAR) processes. The approximation is built upon the property of MS VAR processes of being Gaussian conditionally on any semi-infinite sequence of the latent state. Truncating the semi-infinite sequence and averaging over all possible sequences of that finite length yields a mixture of normals that converges to the unknown marginal distribution as the sequence length increases. Numerical experiments confirm the viability of the approach which extends to the closely related class of MS state space models. Several applications are discussed.

Skewness and kurtosis of multivariate Markov-switching processes

Exact formulae are provided for the calculation of multivariate skewness and kurtosis of Markov-switching Vector Auto-Regressive (MS VAR) processes as well as for the general class of MS state space (MS SS) models. The use of the higher-order moments in non-linear modeling is illustrated with two examples. A Matlab code that implements the results is available from the authors.

The marginal likelihood of dynamic mixture models

Analytical results for reducing the parameter space dimension when computing the marginal likelihood are given for the broad class of dynamic mixture models. These results allow the integration of scale parameters out of the likelihood by Kalman filtering and Gaussian quadrature. The method is simple and improves the accuracy of four marginal likelihood estimators, namely, the Laplace method, the Chib estimator, reciprocal importance sampling, and bridge sampling. For some empirically relevant cases like the local level and the local linear models, the marginal likelihood can be obtained directly without any posterior sampling. Implementation details are given in some examples. Two empirical applications illustrate the gain in accuracy achieved.