Hypothesis Testing and the Search for Global Theories

An important objective of science is to find global theories, those that ex-plain/predict what happens in a wide variety of circumstances. Along the way, scientists usually encounter local theories which are either discarded or embedded in a more general theory. Statistical hypothesis tests provide two tools for this scientific method: (a) Tests for theory significance, regardless of local/global distinction, and (b) Tests for global-ness versus local-ness. The present work takes pieces of information from each method and builds some new tests, with power focused on global theories. The tests answer the ques-tion: “Is the theory valid and global?”, rather than a subordinate question: “Is it valid? ” or “Is it global?”. The statistics are asymptotically equivalent to quadratic forms in statistics obtained from standard methods (a) and (b), and under simplifying assumptions these forms coincide with out-of-sample and nested-sample model validation statistics. We examine test performance in simulation, and illustrate with an economic example