We argue that the Bayesian approach is appealing to parameter estimation for multi-sector economic models, in that it (i) handles problems with many parameters and little data, (ii) allows for explicit and flexible formulation of prior knowledge on parameter values, and parameter constraints, (iii) provides full account of uncertainty of the estimates, (iv) is based on a single estimation strategy for a wide variety of models. It is an alternative to the more common maximum entropy (minimum cross entropy) techniques. We specify a Bayesian model for the linear expenditure system, and estimate it based on data for Poland, using the open source Stan package. We then extend the basic formulation to allow for changes in tastes, represented by time-varying marginal budget shares
