We study general dynamic programming problems with continuous and discrete choices and general constraints. The value functions may have kinks arising (1) at indifference points between discrete choices and (2) at constraint boundaries. Nevertheless, we establish a general envelope theorem:...

A key open question in economics is the practical, portable modeling of bounded rationality. In this short note, I report ongoing progress that is more fully developed elsewhere. I present some results from a new model in which the decision-maker builds a simplified representation of the world....

Though the envelope theorem is a widely used tool of applied economic analysis, the standard version of the theorem can only be used if all of the choice variables are assumed to be continuous. This limitation is significant because the natural description of many economic choice variables is as...

First order conditions from the dynamic optimization problems of consumers and firms are important tools in empirical macroeconomics. When estimated on micro-data these equations are typically linearized so standard IV or GMM methods can be employed to deal with the measurement error that is...