Bayesian Analysis of Haavelmo's Models

In this paper, the exact posterior distributions of the parameters of Haavelmo's model I
is derived for locally uniform prior distributions. Marginal distrlbutions 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 finlte
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
in~estment.For this. Haavelmo's model 11. in Ivhich investment is assumed to be endogenous.
is used. Posterlor d~strlbutionso f the parameters of the model are computed for this model.
The ~ensiti\enesosf the inference about the parameters of the model to the assumption that
investment is exogeneous is studied by computing various conditional distributions for
model 11. It is seen that this assumption IS very crucial for Haavelmo's data.
F111all).t i$(-d, iffcrcnt prior distrlbutions reflect~ng1.0 different \ i t a s about In\estlncnt
are introduced. The posterlor distributions of the same parameter are then used to determ~ne
how one's prior belief is modified by the sample information.
1. INTRODUCTION
IN RECENT YEARS. the Bayesian approach has been used to analyze the robustness
of specifying assumptions in stochastic models. Box and Tiao [3] used this approach
to assess the effects of a departure from normality in the comparison of variances.
Zellner and Tiao [18]. using the Bayesian approach, analyzed the effects of
departures from serial independence of the error terms in a multiple regression
model on inferences about the model's parameters.