  A Bayesian method of moments/instrumental variable (BMOM/IV) approach is
developed and applied in the analysis of the important mean and multiple
regression models. Given a single set of data, it is shown how to obtain
posterior and predictive moments without the use of likelihood functions, prior
densities and Bayes' Theorem. The posterior and predictive moments, based on a
few relatively weak assumptions, are then used to obtain maximum entropy
densities for parameters, realized error terms and future values of variables.
Posterior means for parameters and realized error terms are shown to be equal
to certain well known estimates and rationalized in terms of quadratic loss
functions. Conditional maxent posterior densities for means and regression
coefficients given scale parameters are in the normal form while scale
parameters' maxent densities are in the exponential form. Marginal densities
for individual regression coefficients, realized error terms and future values
are in the Laplace or double-exponential form with heavier tails than normal
densities with the same means and variances. It is concluded that these results
will be very useful, particularly when there is difficulty in formulating
appropriate likelihood functions and prior densities needed in traditional
maximum likelihood and Bayesian approaches.
