In combining theory and experiments, we should have two objectives in mind. The first objective is to confront the theory with some data to see whether the theory is at all consistent with the behavior exhibited in the laboratory. Clearly, there is much that can be learned about the theory from the data, quite apart from any notion of "testing" the theory. We hope to learn whether the theory is useful in interpreting the data, of course, but we also expect to find out what extensions of the theory are required to make it compatible with the data. The second objective is to confront the data with the theory. A theoretical framework is needed for two reasons. First, the data set generated by experiments can be extremely rich and the behavior predicted by the theory is sometimes complex and subtle. Any attempt to explain rich datasets in purely "behavioral" terms would require a large number ad hoc assumptions, which would render the "explanation" rather uninformative. The second reason is that, without a theoretical framework, it is impossible to draw general conclusions that go beyond the particular setting of the experiment.
For example, the standard model of decisions under uncertainty is based on von Neumann and Morgenstern (1947) Expected Utility Theory (EUT), so it is natural that experimentalists should want to test the empirical validity of the Savage (1954) axioms on which EUT is based. Empirical violations of EUT provoke intriguing questions about the rationality of individual behavior and, at the same time, raise criticisms about the status of the Savage axioms as the touchstone of rationality. These criticisms have resulted in the development of various theoretical alternatives to EUT, and the investigation of these theories has led to new empirical regularities in the laboratory. Developing appropriate methods for appropriately confronting the theory of choice under risk with experimental evidence has implications in many areas of economic theory and policy. And the same is true for attitudes toward time, ambiguity and inequality, which are important inputs into any broader measure of social welfare and enter virtually every realm of individual decision-making.