Reparameterization strategies for hidden Markov models and Bayesian approaches to maximum likelihood estimation

This paper synthesizes a global approach to both Bayesian and likelihood treatments of the estimation of the parameters of a hidden Markov model in the cases of normal and Poisson distributions. The first step of this global method is to construct a non-informative prior based on a reparameterization of the model; this prior is to be considered as a penalizing and bounding factor from a likelihood point of view. The second step takes advantage of the special structure of the posterior distribution to build up a simple Gibbs algorithm. The maximum likelihood estimator is then obtained by an iterative procedure replicating the original sample until the corresponding Bayes posterior expectation stabilizes on a local maximum of the original likelihood function.     

CONSUMPTION SPENDING AND THE PAPER-BILL SPREAD: THEORY AND EVIDENCE

This paper explains recent findings that the paper-bill spread helps forecast consumption spending using an intertemporal optimizing model of consumption and portfolio allocation. The spread is simply the opportunity cost in terms of foregone future consumption of holding government debt rather than higher yielding private debt. Thus, if government debt appears along with consumption in the single period utility function, the spread appears in one of the Euler equations for consumption and asset accumulation. Empirical tests strongly support the model. Finally, including the spread in a rule of thumb model of consumption reduces the importance of non-optimizing behavior. ( JEL E21, E43, C22, C32)     

Tracking Edges, Corners and Vertices in an Image

Abstract.  In a range of imaging problems, particularly those where the images are of man-made objects, edges join at points which comprise three or more distinct boundaries between textures. In such cases the set of edges in the plane forms what a mathematician would call a planar graph. Smooth edges in the graph meet one another at junctions, called 'vertices', the 'degrees' of which denote the respective numbers of edges that join there. Conventional image reconstruction methods do not always draw clear distinctions among different degrees of junction, however. In such cases the algorithm is, in a sense, too locally adaptive; it inserts junctions without checking more globally to determine whether another configuration might be more suitable. In this paper we suggest an alternative approach to edge reconstruction, which combines a junction classification step with an edge-tracking routine. The algorithm still makes its decisions locally, so that the method retains an adaptive character. However, the fact that it focuses specifically on estimating the degree of a junction means that it is relatively unlikely to insert multiple low-degree junctions when evidence in the data supports the existence of a single high-degree junction. Numerical and theoretical properties of the method are explored, and theoretical optimality is discussed. The technique is based on local least-squares, or local likelihood in the case of Gaussian data. This feature, and the fact that the algorithm takes a tracking approach which does not require analysis of the full spatial data set, mean that it is relatively simple to implement.     

APRIL 15 SYNDROME

In tax year 1988, delaying filing income tax returns cost the 73.2 million taxpayers claiming refunds nearly one billion dollars of interest. "Impatient" tax filers, who mail in their tax payments before the filing deadline, passed up $46 million in interest.
We develop a model of tax filing based on stochastic opportunity cost, and then investigate whether filing times are consistent with that model. We find some evidence for this because, ceteris paribus, higher refunds are associated with earlier filing and complex returns are associated with later filing, as are higher incomes (as a proxy for higher costs of time).