Invariance, observational equivalence, and identification: Some implications for the empirical performance of affine term structure models

Scholars working on the class of affine term structure models (ATSM) use econometric theory to postulate that any two ATSMs can be connected through any combination of affine transformations (AT), leaving their implied bond prices and distributions identical. Our results, which are obtained through the derivation and testing of two hypotheses, show that, first, the application of AT introduces a lack of precision in the parameters resulting from their not being identified, and, this leads to very statistically distinct model performance. Secondly, we also demonstrate that, owing to the property of observational equivalence, AT neither improves nor worsens the empirical performance of ATSM. Results are robust to a Monte Carlo simulation experiment. Taken together, our findings show that the usage of invariant transformations introduces statistically significant differences in empirical performance that are economically unimportant. The fundamental lack of identification of the parameters introduces imprecision in ATSM when applying affine transformations, which affects the structure of the yield pricing errors and this causes statistical differences in empirical performance, while not causing substantive economic changes to it.