Bayesian inference on time-varying proportions

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Bayesian Econometrics (Advances in Econometrics Vol 23), 2009, 1, pp. 525 - 544
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Time-varying proportions arise frequently in economics. Market shares show the relative importance of firms in a market. Labor economists divide populations into different labor market segments. Expenditure shares describe how consumers and firms allocate total expenditure to various categories. We introduce a state space model where unobserved states are Gaussian and observations are conditionally Dirichlet. Markov chain Monte Carlo techniques allow inference for unknown parameters and states. We draw states as a block using a multivariate Gaussian proposal distribution based on a quadratic approximation of the log conditional density of states given parameters and data. Repeated draws from the proposal distribution are particularly efficient. We illustrate using automobile production data.
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