Introduction

Virtually without exception, inference in dynamic econometric models of aggregate economic time series data is based on the asymptotic sampling–theoretic distribution of estimators, often maximum–likelihood estimators. There is no population for which sets of observations of aggregate economic time series can be drawn repeatedly, as may be the case with longitudinal or panel data. Sampling–theoretic results for independent populations have been extended to inference from a single realization of a time series, but the length of periods for which parametric models of economic time series may reasonably be regarded as stable usually limit attention to modest departures from the linear model. There is no way to incorporate carefully the inequality restrictions that often emerge from economic theory. Improvements on asymptotic theory, especially for highly nonlinear estimators, are arduous theoretical tasks whose occasional completion seems to have had little effect on the way applied work is carried out.

This situation and recent drastic reductions in computing costs suggest that alternatives to this standard approach to inference for economic time series be contemplated. This chapter explores a formal numerical Bayesian approach with diffuse priors, relying on cheap computing to disregard the analytical intractability of useful priors and functions of the parameters of interest. The ability to select diffuse priors arbitrarily means that inequality restrictions can be imposed, and the power to choose functions of interest for their bearing on empirical questions means that issues relegated to equivocal discussions can be treated formally.