Observational equivalence

In econometrics, two parameter values (sometimes called structures, from among a class of statistical models) are considered observationally equivalent if they both result in the same probability distribution of observable data.^[1][2][3] This term often arises in relation to the identification problem.

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.

References

1. ^ Dufour, Jean-Marie; Hsiao, Cheng (2008). "Identification". In Durlauf, Steven N.; Blume, Lawrence E.. The New Palgrave Dictionary of Economics (Second ed.). http://www.dictionaryofeconomics.com/article?id=pde2008_I000004. 
2. ^ Stock, James H. (July 14, 2008). "Weak Instruments, Weak Identification, and Many Instruments, Part I". National Bureau of Economic Research. http://www.nber.org/WNE/slides7-14-08/Lecture3.pdf. 
3. ^ Koopmans, Tjalling C. (1949). "Identification problems in economic model construction". Econometrica 17 (2): 125–144. doi:10.2307/1905689. 

This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.