Estimating Non Accelerating Inflation Rate of Unemployment (NAIRU)

Phillips (1958) in his study on England, showed the existence of a relationship between the unemployment rate and inflation, and the potential existence of an arbitrage between those two aggregates. Indeed, when the unemployment rate decreases, the costs of production of firms tend to increase, which results in an increase of prices. Yet, a good economic health requires a decrease in unem-ployment and a bearable inflation rate. Thus, it is necessary to determine the unemployment rate that allows a stable inflation, so called NAIRU (Non Accelerating Inflation Rate of Unemployment). Since the NAIRU cannot actually be observed (Blanchard (2003)), it is difficult to measure it. Several unclear estimates have been made on the american NAIRU . Thus, the present study aims to contribute to this literature by a rigorous estimation of the American NAIRU with Bayesian estimation methods including MCMC (Markov Chain Monte Carlo) in a state space univariate gaussian model. In our strategy, the latent variable (NAIRU) is obtained using a Kalman filter and a backward smoothing algorithm as introduced by de Jong et Shephard(1995) ; the draw of parameters is performed through a Gibbs sampling. All those steps are realized many times by MCMC simulations for convergence requirement.