Detection of Spurious Maxima through Random Draw Tests and Specification Tests

Consistent estimation requires finding the global maximum of some specified objective function. Local maxima are often easy to find, but do not necessarily yield consistent estimates. In many nonlinear applications, the researcher can rarely be certain that a found local maximum is global. This paper examines the ability of random draw tests and specification tests to detect spurious maxima. For random draw tests we analyze Veall (1990) and a test introduced here based on a generalized beta distribution. Specification tests routinely used by researchers are also examined as methods for detecting spurious maxima. Monte Carlo results are reported on various test functions. The results suggest that specification testa are more useful than the random draw tests for detecting spurious maxima.