I believe this should be scripted, it is not standard two-stage least squares. Regress X1 on Z1 and Z2 and obtain the fitted values, say X1_f Regress X2 on Z3 and Z4 and obtain the fitted values, X2_f Regress Y on a constant and  X1_f, X2_f, Ψ1,Ψ2. Alecos Papadopoulos PhD Affiliate Researcher Dpt of Economics, Athens University of Economics and Business Foundation for Economic and Industrial Research (IOBE) web: alecospapadopoulos.wordpress.com/ ORCID:0000-0003-2441-4550 On 10/8/2023 20:21, elfsog(a)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? > _______________________________________________ > Gretl-users mailing list -- gretl-users(a)gretlml.univpm.it > To unsubscribe send an email to gretl-users-leave(a)gretlml.univpm.it > Website: https://gretlml.univpm.it/postorius/lists/gretl-users.gretlml.univpm.it/

I should have written: How Gretl understands which instrument stands for which endogenous variable when using standard IV/2SLS menu? I mean, how, using the above menu, could I match variables Z1 and Z2 to X1 and Z3 and Z4 to X2? Is it a matter of input sequence?

On 10/08/2023 20:21, Alecos Papadopoulos wrote: From an econometric point of view, there is an ambiguity in the original post that must be resolved before explaining how to do things in gretl, as Alecos rightly pointed out. A common misconception in IV estimation is that a given instrument is related to a given endogenous variable. This is by no means true in general. Generally speaking, ALL instruments are used for ALL endogenous variables. Having said this, it is perfectly possible to impose constraints in the "first-stage" regression, for example by stipulating that some of the instruments don't enter some of the equations. But in order to do so, you can't rely on the plain IV estimator and you have to use a different estimator (maximum likelihood, or possibly GMM). Here is an example on artificial data that highlights the differences between the two approaches; for the constrained estimator, FIML is used: <hansl> nulldata 256 scalar a = 0.75 # amount of endogeneity loop i = 1 .. 4 series z$i = normal() endloop series u1 = normal() series u2 = normal() series x1 = 1 + z1 + z2 + u1 series x2 = 2 + z3 + z4 + u2 series y = 3 + x1 + x2 + normal() + a * (u1 + u2) list X = const x1 x2 list Z1 = const z1 z2 list Z2 = const z3 z4 list Z = Z1 || Z2 ### ordinary IV estimation tsls y X ; Z ### restricted IV estimation system method=fiml equation y X equation x1 Z1 equation x2 Z2 endog y x1 x2 end system </hansl> ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------

On 11/08/2023 14:45, Sven Schreiber wrote: If one had strong reasons (possibly, from some a-priori reasoning) to put some zero constraints on the first-stage regressions, then in theory you'd get some efficiency gain by using the ad-hoc procedure. But then, (a) your a-priori could be wrong and (b) the efficiency gain would be unlikely to be dramatic anyway. Therefore, I agree with Sven's bottom line: in a real-world scenario you'll probably want to use plain-vanilla 2-stage LS. ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------

I should have written: How Gretl understands which instrument stands for which endogenous variable when using standard IV/2SLS menu? I mean, how, using the above menu, could I match variables Z1 and Z2 to X1 and Z3 and Z4 to X2? Is it a matter of input sequence?