Thus, for example, two scientific theories are observationally equivalent if all of their empirically testable predictions are identical, in which case empirical evidence cannot be used to distinguish which is closer to being correct; indeed, it may be that they are actually two different perspectives on one underlying theory.
In econometrics, two parameter values (or two structures, from among a class of statistical models) are considered observationally equivalent if they both result in the same probability distribution of observable data.
In macroeconomics, it happens when you have multiple structural models, with different interpretation, but indistinguishable empirically.
"the mapping between structural parameters and the objective function may not display a unique minimum.
The notion is due to James H. Morris,[5] who called it "extensional equivalence.