Not all simultaneous equation models give biased estimates when estimated by OLS. An important class of models for which OLS estimation is valid is that of recursive models. These are models in which the errors from the different equations are independent and the coefficients of the endogenous variables show a triangular pattern. For example, let us consider a model with three endogenous variables Y1, Y2 and Y3, and three exogenous variables, Z1, Z2 and Z3 which has the following structure:
which form a triangular structure. In such systems, each eqiihtion can be estimated by OLS. Suppose in the example above u2 and u3 are correlated but they are independent of u1; then the model is set to the block-recursive. The second and third equations have to be estimated jointly, hut the first equation can be estimated by OLS. Note that Y2 and Y3, depend on u2 and u1 only and hence are independent of the error term u1.