When the # of endogenous variables and the # of instrumental variables are the same, we cannot test the exogeneity of IVs(k=l). But if the Conditional moment condition holds, we can generate infinitely many moment conditions by tranforming the IVs. For example Z, Z^2, Z^3, ...
The issues that arise here are :
- How to optimally choose the moment conditions?
- Is there any optimality condtion?
- Algorithm for choosing moment coditions?
- Theoretical results for the choice of ""?