In the case of non-stochastic explanatory variables, the adding up constraint on the dependent variables was shown to imply that the error terms and the coefficients of different explanatory variables sum to zero over the M equtions. When consideration is expanded to simultaneous equation systems, this issue is more complex and is related to whether or not the equations are identified. One way to describe an underidentified equation is that the set of coefficients for which it is linear in the explanatory variables and has a random error term with zero mean, is not unique. In the case where all M equations are identified, the coefficient constraints which apply to the case of non-stochastic explanatory variables also apply to simultaneous equations. One of the standard methods for estimating a system of simultaneous equations is three-stage least squares (3SLS) and the investigation of constraint item estimation procedures will be based on this approach.