Observational equivalence is the property of two or more underlying entities being indistinguishable on the basis of their
observable
In physics, an observable is a physical property or physical quantity that can be measured. In classical mechanics, an observable is a real-valued "function" on the set of all possible system states, e.g., position and momentum. In quantum ...
implications. Thus, for example, two
scientific theories are observationally equivalent if all of their
empirical
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.
There is no general agreement on how t ...
ly
testable
Testability is a primary aspect of science and the scientific method. There are two components to testability:
#Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible.
#The practical feasibilit ...
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
Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
, 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
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...
of observable data.
This term often arises in relation to the
identification problem.
In
macroeconomics
Macroeconomics is a branch of economics that deals with the performance, structure, behavior, and decision-making of an economy as a whole. This includes regional, national, and global economies. Macroeconomists study topics such as output (econ ...
, 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."
In the
formal semantics of programming languages
In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid string (computer science), strings in a programming language syntax. It is cl ...
, two
terms ''M'' and ''N'' are observationally equivalent if and only if, in all contexts ''C''
..where ''C''
'M''is a valid term, it is the case that ''C''
'N''is also a valid term with the same value. Thus it is not possible, within the system, to distinguish between the two terms. This definition can be made precise only with respect to a particular calculus, one that comes with its own specific definitions of ''term'', ''context'', and the ''value of a term''. The notion is due to
James H. Morris, who called it "extensional equivalence."
See also
*
Underdetermination
In the philosophy of science, underdetermination or the underdetermination of theory by data (sometimes abbreviated UTD) is the idea that evidence available to us at a given time may be insufficient to determine what beliefs we should hold in re ...
References
Statistical theory
Econometric modeling
Programming language semantics
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