Since Paul Samuelson's text in mathematical economics, economists have studied and applied mathematical tools for making predictions. They accomplish it by deriving comparative statics predictions in optimization problems and in equilibrium problems. Recently, this topic has received renewed attention. The first goal of this project is to develop and apply new methods for deriving comparative statics predictions in formal economic models of stochastic problems and games of incomplete information. The second goal of the project is to develop a framework for empirical testing of the theoretical predictions about comparative statics, focusing on problems with multiple endogenous variables. The theoretical part of the project concerns monotone comparative statics in stochastic optimization problems and equilibrium problems. Theorems are introduced which can be used in conjunction with the new methods on comparative statics, or with traditional methods of analysis in stochastic problems. A number of potential economic applications are explored, some of which require further theoretical research. In addition a monograph is developed, providing a systematic approach to the analysis of comparative statics based on the new literature. It advances a particular set of themes which is to some extent implicit, but far from fully articulated, in the published research to date, and also included some new results, particularly in the area of equilibrium analysis. The empirical component is motivated by a growing theoretical and empirical literature which studies complementarities in a wide variety of economic problems (two variables are complementary if increasing one variable increases the returns to increasing the other.) An econometric strategy is developed to test theories about complementarities, evaluate the properties of these tests using Monte Carlo experiments, and finally, to apply this strategy to an economic problem.
