Estimating the Markov-switching almost ideal demand systems: a Bayesian approach

摘要

Allais and Nich`ele (2007) proposed a Markov-switching almostideal demand system (MS-AIDS) model by extending the idea ofHamilton (1989). This model enables us to determine when the regimeshifts occurred and to estimate parameters characterized across thedifferent regimes. Moreover, degree of belongingness to each of theregimes and transitions between regimes are quantified by the probabilities.In this paper, we propose a Bayesian estimation for MSAIDSmodel and illustrate applicability of our proposed method. TheBayesian estimation has some important advantages. First, it enablesus to avoid the singularity problem suggested by Hamilton (1990,1991). Second, our proposed Bayesian estimation ensures that transitionprobabilities lie between zero and one. Third, Bayesian estimationis able to avoid the messy calculations entailed in the scorefunctions of log-likelihood. We then run a simulation study to confirmthe validity of the proposed method. In the empirical study onthe Japanese meat market, we found that our Bayesian estimationimproves the mean squared errors for all meat products over the maximumlikelihood estimation, while successfully capturing the regimeshifts of meat demand coinciding with the timing of Bovine SpongiformEncephalopathy (BSE) cases in Japan and U.S.