Measuring Dynamics of Respondents' Opinions by Means of Nonhomogeneous Markov Chain
This paper is focused on a new approach to analyze changes of qualitative characteristic of economic process by means of a special kind of nonhomogeneous Markov chain related to the concept of switching models. Qualitative feature of economic process (such as evaluation of economic situation) may be in natural way modeled by multinomial distribution. While observing time series of such variables it is appealing to let that the parameters of multinomial distribution be time-varying. In the paper I propose to model the qualitative variable by means of fitting the probability distribution which is a mixture (or Markov mixture) of multinomial probability distributions with parameters depending on transition probabilities of a Markov chain. Such approach lets treat the observed data as an outcome of a nonhomogeneous Markov chain with transition matrix in each period belonging to a finite set of possible matrices. The choice of the matrix describing the process in each moment of observation is governed by an unobserved regime variable and so the nonhomogeneity of the chain results from switches between different regime transition matrices. This paper presents the maximum likelihood estimators of the model parameters developed for micro data (i.e. when the whole history of responses of each individual respondent is available) and macro data (only the structures of responses are available). It also includes the analysis of the results of business tendency survey in Polish industry. The proposed model has been applied to analyze the dynamics of respondents' opinions concerning volume of production and financial situation under two possible regimes. (original abstract)
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