Editing Observational equivalence (section)

{{Short description|Semantic property}}
{{Unfocused|date=October 2024}}
'''Observational equivalence''' is the property of two or more underlying entities being indistinguishable on the basis of their [[observable]] implications. Thus, for example, two [[scientific theory|scientific theories]] are observationally equivalent if all of their [[empirical]]ly [[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.<ref name="palgrave">{{cite encyclopedia |last1=Dufour |first1=Jean-Marie |last2=Hsiao |first2=Cheng |editor1-last=Durlauf |editor1-first=Steven N. |editor2-last=Blume |editor2-first=Lawrence E. |title=Identification |encyclopedia=The New Palgrave Dictionary of Economics |edition=Second |year=2008 |url=http://www.dictionaryofeconomics.com/article?id=pde2008_I000004}}</ref><ref name="nber">{{cite web |last=Stock |first=James H. |publisher=National Bureau of Economic Research  |date=July 14, 2008 |title=Weak Instruments, Weak Identification, and Many Instruments, Part I |url=http://www.nber.org/WNE/slides7-14-08/Lecture3.pdf}}</ref><ref name="koopmans">{{cite journal |last=Koopmans |first=Tjalling C. |title=Identification problems in economic model construction |journal=Econometrica |volume=17 |issue=2 |year=1949 |pages=125–144 | doi=10.2307/1905689 |jstor=1905689 }}</ref>  This term often arises in relation to the [[Parameter identification problem|identification problem]].

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."<ref name="science direct">{{cite journal |last1=Canova |first1=Fabio |last2=Sala |first2=Luca |journal=Journal of Monetary Economics  |date=May 2009|title=Back to square one: Identification issues in DSGE models |volume=56 |issue=4 |pages=431–449 |doi=10.1016/j.jmoneco.2009.03.014 |url=https://www.sciencedirect.com/science/article/abs/pii/S0304393209000439|hdl=10230/308 |hdl-access=free }}</ref>

In the [[formal semantics of programming languages]], two [[term (logic)|term]]s ''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]],<ref>{{cite arXiv |title=Local Reasoning for Robust Observational Equivalence|first1=Dan R.|last1=Ghica|first2=Koko|last2=Muroya|first3=Todd Waugh|last3=Ambridge|year=2019 |page=2|class=cs.PL |eprint=1907.01257 }}</ref> who called it "extensional equivalence."<ref>{{cite thesis|url=https://dspace.mit.edu/handle/1721.1/64850|title=Programming languages and lambda calculus|first=James|last=Morris|publisher=Massachusetts Institute of Technology|date=1969|pages=49–53|hdl=1721.1/64850 }}</ref>