Recursive system Assignment Help

Simultaneous equation models - Recursive system

Recursive system:

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:  

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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.

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