“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the proofs presented in the accompanying paper by Sennewald (2006). Additional examples are given which highlight the correct use of the Hamilton-Jacobi-Bellman equation and the change-of-variables formula (sometimes referred to as ``Itô's Lemma'') under Poisson uncertainty.     

Reputation and Perfection in Repeated Common Interest Games

We consider a wide class of repeated common interest games perturbed with one-sided incomplete information: one player (the informed player) might be a commitment type playing the Pareto dominant action. As discounting, which is assumed to be symmetric, and the prior probability of the commitment type go to zero, it is shown that the informed player can be held close to her minmax payoff even when perfection is imposed on the equilibrium.Journal of Economic LiteratureClassification Numbers: C73, D83.     

The measurement and decomposition of nonuse values: A critical review

We critically review the literature that claims that existence values, or nonuse values in general, are a large and measurable component of total value for certain environmental resources. Our concern is not with the question “do nonuse values exist?” For some individuals they surely do. Rather, our concern is with two interrelated questions: are there operationally meaningful theorems which might lead to the specific measurement of nonuse values, and do we in fact have a body of credible evidence which shows that nonuse values, particularly components of any nonuse value, are “large”? We find nothing in the way of operationally meaningful hypotheses which would permit the estimation of values attributable to specific motives of individuals. We find no credible basis for claims related to either the measurement of existence and other motive-related values or claims for the “large” relative size of such values. In short, we question the conventional wisdom that such values are measurable and that they are significant as a component of total value.     

A child health production function estimated from longitudinal data. Cebu Study Team

Collaborating researchers used a multi equation model to analyze 3080 mother-infant pairs living on the island of Cebu in the central Philippines and to estimate a child health production function. The econometric methods used eliminated obstacles such as heterogeneity and endogeneity of significant explanatory factors. They also maximized the longitudinal quality of the data. The results showed that morbidity in 1 period reduced infant weight in following periods. For example, diarrhea and febrile respiratory infection reduced growth in the time period following the illnesses. Further effects of some contributing factors were great near birth not diminished with age. For example, breast feeding promoted growth and protected against infection, especially diarrhea and febrile respiratory infection, more substantially near birth than it did later. Further, in urban areas, preventive health care positively affected growth independently of its indirect influence on reducing respiratory infection. Yet it had little effect on diarrhea. Diarrhea had a strong adverse effect on growth. Exposure of the infant to enteric pathogens had the greatest influence on production of diarrhea. In urban areas, exposure included water supply contamination, exposure to feces, a more pathogenic diet, and community crowding. In rural areas, however, exposure included community crowding and increased rainfall which presumably washed feces into the water supply. Household crowding in both urban and rural areas and irritation from smoke in urban areas only tended to bring about febrile respiratory infection.