You are stating that X = {X1, X2, Z1,Z2, Z3, Z4} are uncorrelated with e.  Out of all possible linear combinations of the variables in X that can be used as an instrument for  Ψ1,Ψ2 You should choose the ones that is most highly correlated with the endogenous variables.  Thus you should use the entire set for each variable.  See for example section 5.2.3 - Asymptotic Efficiency of Two-Stage Least Squares in Wooldridge (2012), Econometric Analysis of Cross Section and Panel Data, MIT.   I would presume that this correct approach is taken by Gretl.



On Thu, 10 Aug 2023 at 18:21, <elfsog@yahoo.gr> wrote:
Consider the following 2SLS model:

Y= b0 +b1X1+b2X2+θ1Ψ1+θ2Ψ2+e
Where:
Y  represents the dependent variable,
X1, X2  denote the endogenous variables,
Ψ1,Ψ2  represent the exogenous variables.

To address endogeneity in the model, a set of four instruments, is introduced. Two instruments (Z1 and Z2) are employed to instrument for X1, while two other instruments (Z3 and Z4) are used to instrument for X2.
My question is: How Gretl understand which instrument stands for which endogenous variable?
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