A Note on Algebraic Solutions to Identification

Algebraic methods to establish the identification of structural equation models remains a viable option. However, sometimes it is unclear whether the algebraic solution establishes identification. One example is when there is more than one way to solve for the parameter, but one way leads to a single value and a second way leads to a function with more than one value. This note proves that one explicit and unique solution is sufficient for model identification even when other explicit solutions permit more than one solution. The results are illustrated with an example. The results are useful to attempts to use algebraic means to address model identification.