The Bayesian method of moments (BMOM) in some aggregation problems in econometrics

Abstract

The BMOM is particularly useful for obtaining post-data moments and densities for parameters and future observations when the form of the likelihood function is unknown and thus a traditional Bayesian approach cannot be used. Also, even when the form of the likelihood is assumed known, in time series problems it is sometimes difficult to formulate an appropriate prior density. Here, we show how the BMOM approach can be used in two, nontraditional problems. The first one is conditional forecasting in regression and time series autoregressive models. Specifically, it is shown that when forecasting disaggregated data (say quarterly data) and given aggregate constraints (say in terms of annual data) it is possible to apply a Bayesian approach to derive conditional forecasts in the multiple regression model. The types of constraints (conditioning) usually considered are that the sum, or the average, of the forecasts equals a given value. This kind of condition can be applied to forecasting quarterly values whose sum must be equal to a given annual value. Analogous results are obtained for AR(p) models. The second problem we analyse is the issue of aggregation and disaggregation of data in relation to predictive precision and modelling. Predictive densities are derived for future aggregate values by means of the BMOM based on a model for disaggregated data. They are then compared with those derived based on aggregated data.