Classical Estimation of Multivariate Markov-Switching Models using MSVARlib

This paper introduces an upgraded version of MSVARlib, a Gauss and Ox- Gauss compliant library, focusing on Multivariate Markov Switching Regressions in their most general specification. This new set of procedures allows to estimate, through classical optimization methods, models belonging to the MSI(M)(AH)-VARX ``intercept regime dependent'' family. This research enhances the first package MSVARlib 1.1, which has been deeply inspired by the works of Hamilton and Krolzig. Not to mention the extension to a generalized multivariate regression framework, it notably augments the range of models with a possibly unlimited finite number of Markov states, offers automatic or manual intialization procedures and adds new statistical tests. The first part of this article provides the basic theoretical grounds of the related Markov-switching models. Following sections give some illustrations of the programs through univariate and multivariate examples. One is based on a non-linear reading of the american unemployment rate. A second study is focused on coincident stochastic models of US recessions and slowdowns. The paper concludes on possible extensions and new applications. Detailed guidelines in appendices and tutorial programs are provided to help the reader handling the Gauss package and the joined replication files.Multivariate Markov-Switching Regressions, Hidden markov Models, Non linear regressions, Open source Gauss library, Business cycle, EM algorithm, Kittagawa-Hamilton Filtering, Recession Detection Models, MSVAR, MS-VAR, Hamilton's Model, Krolzig MSVAR library,Filtered probabilities, Smoothed probabilities.

Detecting Turning Points with Many Predictors through Hidden Markov Models

This paper explores the American business cycle with the Hidden Markov Model (HMM) as a monitoring tool using monthly data. It exhibits ten US time series which offer reliable information to detect recessions in real time. It also proposes and assesses the performances of different and complementary “recession models” based on Markovian processes, discusses the most efficient and easiest way of encompassing information through these models and draws three main conclusions: simple HMM are decisive to monitor the business cycle and some series are proved highly reliable; more sophisticated models such as the Dynamic Factor with Markov Switching (DFMS) model or Stock and Watson’s Experimental Recession Index seem not to be more powerful than simple (univariate or pseudo-multivariate) Hidden Markov Models, which remain far more parsimonious; combining information in temporal space seems to work marginally better than in probability space for high frequency data. We conclude about leading and “real time detection” properties related to HMM and give some hints for further research.Business Cycle, Markov Switching, Dynamic Factor, Coincident Indicators

Une lecture probabiliste du cycle d’affaires américain

This paper explores 35 years of the American business cycle with the Hidden Markov Model (HMM) as a monitoring tool using monthly data. It exhibits ten US time series, which offer reliable information to detect recessions in real time. It also assesses the performances of different and complementary “recession models” based on Markovian processes : the “Pooled data model” and a multivariate HMM, and draws two main conclusions: simple HMM are decisive to monitor the business cycle providing that the series are proved highly reliable; models adding a multivariate dimension are useful but work marginally better than a simple summary : the inner quality of series seem to dominate their modeling. This paper introduces a new reading of the business cycle through, a favored recession model and concludes about leading and “real time detection” limitations. This paper is written in French.Business Cycle, Markov Switching, MSVAR, Real time data vintage, Coincident Indicators, Recession, NBER dating

MSVARlib: a new Gauss library to estimate multivariate Hidden Markov Models

This paper introduces a new open source Gauss library to estimate Multivariate Hidden Markov Models (HMM) in their simpler specification. These new programs are based upon the works of Hamilton (1994) and Krolzig (1998) and allow assessment of models with 2, 3 or 4 states through classical optimization of the maximum likelihood method. The modular architecture of the program is presented in a first part. It has been designed to allow new improvements (generalized non linear MS models or enhancement to a Bayesian framework). A second part, gives some illustration through a three state model based on the American Industrial production and a new stochastic coincident indicator of a recession for the US economy, following the papers of Ferrara (2003), Bellone and Saint-Martin (2003) and Bellone (2004).

Présentation de la Maquette Retraites MARS-2003

This paper describes the model MARS, which is the shared property of the DP and the DSS. Currently, MARS aims at planning the general evolution of the first pillar pension scheme for private sector wage-earners, based on macroeconomic and demographic data. It allows to evaluate the impact of changing the parameters used when calculating one’s annuities, or changing general hypotheses. The model provides results which deal with the dynamics of the average annuity and the financial sustainability of the pension scheme. MARS relies on a macroeconomic approach and aims at forecasting the life cycle of average individuals representing their generation. In concrete terms, each generation is represented by two agents (a man and a woman), whose behaviour is supposed to match the average economic and demographic characteristics of their peers (as far as fertility, activity and employment are concerned). In addition, another source of heterogeneity is acknowledged in the model concerning the retirement age, the distribution of which is determined endogenously. Then the evolution of the representative annuity, calculated on the basis of these data, is considered to reflect the dynamics of the average annuity – and at this stage, sustainability indicators for the pension scheme can be inferred. First, the document introduces the demographic and macroeconomic framework of the model, which basically relies on the population and labour force projections of the INSEE, and takes the Conseil d’Orientation des Retraites scenario as a benchmark for the evolution of real wages and unemployment. The making of the retirement decision is a key feature of the model : it is assumed that men will retire when reaching entitlement to the full rate, and that the male and female distributions of retirement ages will match from the 1970 generation onwards. On the basis of these hypotheses, the average pension and the financing requirement of the pension scheme can be evaluated. As an illustration, the results of two variants are displayed: one deals with the impact of the lengthening of the contribution period which results from the August 2003 Act, the other one shows the sensitiveness of the results to alternative demographic scenarios. We conclude about the weaknesses of the model, which is based on the lifecycle of average individuals, and the flaws associated to a macroeconomic approach, versus a dynamic microsimulation one. Besides, MARS should encounter new limits, due to non-linear effects and deeper uncertainty associated to changes in the method used to calculate pensions after the 2003 reform. This paper is written in French.long term forecast, modeling of pay as you go pension schemes