observational equivalence

{{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 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.{{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}}{{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}}{{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 }} This term often arises in relation to the 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."{{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 }}

In the formal semantics of programming languages, 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,{{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 }} who called it "extensional equivalence."{{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 }}