Description: This figure shows the GMM objective functions for GMM estimation of the coefficient of relative risk aversion (a) and the GMM-rank test (b).

Interpretation:Kleibergen and Zhan (2020) use ill-conditioned GMM objective functions that are always arbitrarily rounded to zero by the statistical software package for large enough absolute values of (“GMM trap”). For the GMM-rank test, the problem is particularly severe because the only local minima are on the far left and the far right in the “GMM trap.” The implication is that it is impossible to conclude that factor correlation is sufficient when this test is used. This problem is a numerical issue unrelated to the actual factor correlation. For estimation of the coefficient of relative risk aversion, there is a third local minimum around zero, and the result is up to luck. The GMM objective functions in Kroencke (2017) and the modified GMM-rank test proposed in this paper are not subject to this numerical issue.