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This study provides a basis for super exogeneity possessing further valuable implications which have not been clarified yet in preceding research. The relevance of super exogeneity to  S -ancillary statistics is reexamined from a theoretical viewpoint, and it is then argued that the small-sample precision of statistical inference for cointegrating parameters can be improved by conditioning on a class of super exogenous variables. Monte Carlo experiments are conducted to verify the theoretical argument. An empirical analysis is also performed as a demonstration of the practicality of the argument.

Revealing unnoticed properties of super exogeneity in a cointegrated vector autoregression