Editing Simultaneous equations model (section)

=== Three-stage least squares (3SLS) ===
The three-stage least squares estimator was introduced by {{harvtxt|Zellner|Theil|1962}}.<ref>{{cite journal
  | last1 = Zellner | first1 = Arnold |author-link1=Arnold Zellner
  | last2 = Theil   | first2 = Henri |author-link2=Henri Theil
  | title = Three-stage least squares: simultaneous estimation of simultaneous equations
  | year = 1962
  | journal = Econometrica
  | volume = 30 | issue = 1
  | pages = 54–78
  | jstor = 1911287
  | doi=10.2307/1911287
  }}</ref><ref>{{cite book |first=Jan |last=Kmenta |chapter=System Methods of Estimation |title=Elements of Econometrics |location=New York |publisher=Macmillan |edition=Second |year=1986 |pages=695–701 |isbn=9780023650703 |chapter-url=https://books.google.com/books?id=Bxq7AAAAIAAJ&pg=PA695 }}</ref>  It can be seen as a special case of multi-equation [[Generalized method of moments|GMM]] where the set of [[instrumental variable]]s is common to all equations.<ref>{{cite book |first=Fumio |last=Hayashi |chapter=Multiple-Equation GMM |title=Econometrics |publisher=Princeton University Press |year=2000 |pages=276–279 |isbn=1400823838 |chapter-url=https://books.google.com/books?id=QyIW8WUIyzcC&pg=PA276 }}</ref> If all regressors are in fact predetermined, then 3SLS reduces to [[seemingly unrelated regressions]] (SUR). Thus it may also be seen as a combination of [[2SLS|two-stage least squares]] (2SLS) with SUR.