Bayesian inference on time-varying proportions

Abstract

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.

Citation

McCausland, W.J. and Lgui, B. (2008), "Bayesian inference on time-varying proportions", Chib, S., Griffiths, W., Koop, G. and Terrell, D. (Ed.) Bayesian Econometrics (Advances in Econometrics, Vol. 23), Emerald Group Publishing Limited, Leeds, pp. 525-544. https://doi.org/10.1016/S0731-9053(08)23016-1