Bayesian Analysis of Haavelmo's Models

Abstract

In this paper, the exact posterior distributions of the parameters of Haavelmo's model I is derived for locally uniform prior distributions. Marginal distributions of the parameters have been obtained for Haavelmo's data. Then the predictive probability density of the model is derived for given values of the exogenous variable, investment. In order to check some of the specifying assumptions, the model is expanded and analyzed under the assumption that the error terms are generated by a first order autoregressive scheme. Exact finite sample results are obtained and the posterior distributions are computed for Haavelmo's data. Conditional distributions of the parameters of the model are computed for given values of the autocorrelation parameter, p, in order to assess the effects of departures from our specifying assumptions. Another specifying assumption that is examined concerns the exogenous nature of investment. For this. Haavelmo's model II, in which investment is assumed to be endogenous, is used. Posterior distributions of the parameters of the model are computed for this model. The sensitiveness of the inference about the parameters of the model to the assumption that investment is exogeneous is studied by computing various conditional distributions for model II. It is seen that this assumption is very crucial for Haavelmo's data. Finally, tvAo different pr-ior distribLutions reflecting two different views about investmeint are introduced. The posterior distributions of the same parameter are then used to determille how one's prior belief is modified by the sample information.