**<Source Information**> Jin Seo Cho and Peter C.B. Phillips (2018): *Journal of Econometrics*, 202, 45--56.

**<Abstract> ** We provide a new test for equality of two symmetric
positive-definite matrices that leads to a convenient mechanism for testing
specification using the information matrix equality and the sandwich
asymptotic covariance matrix of the GMM estimator. The test relies on a new
characterization of equality between two *k* dimensional symmetric
positive-definite matrices *A* and *B*: the traces of *AB*^{-1} and
*BA*^{-1}
are equal to *k* if and only if *A=B*. Using this criterion, we introduce a
class of omnibus test statistics for equality and examine their null and
local alternative approximations under some mild regularity conditions. A
preferred test in the class with good omni-directional power is recommended
for practical work. Monte Carlo experiments are conducted to explore
performance characteristics under the null and local as well as fixed
alternatives. The test is applicable in many settings, including GMM
estimation, SVAR models and high dimensional variance matrix settings.