Instrumental Variable (IV) VAR IDENTIFICATION

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joe_p
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Joined: Fri Mar 25, 2022 2:01 pm

Instrumental Variable (IV) VAR IDENTIFICATION

Postby joe_p » Tue Mar 29, 2022 2:03 pm

Hi everyone,
I'm trying to identify the VAR as proposed by Shapiro and Watson (1988) by the means of an instrumental variable approach.
The results should match the classical estimation of VARs by OLS.
My system is made up of 3 variables, and the identification is placed on the long-run effect matrix, i.e. C(1). It has a recursive structure, that is, a shock in the 2nd or 3rd equation does not have long-run effects on the first variable; a shock in the 1st equation does have long-run effects on the second variable but a shock in the third equation does not have LR-effects on the 2nd variable, and a shock in the 1st or 2nd equation does have LR-effects on the third variable.
These long-run restrictions result in parametric restrictions between the A0, A1, ..., Ap matrices. In particular, if I want to estimate the system equation-by-equation OLS, I cannot, since, because of the restrictions placed in C(1), I have the second difference of the contemporaneous value of the 2nd and 3rd variable entering in the first equation, and so such regressors are correlated with the error term and this makes OLS unfeasible. A solution is 2SLS. That's what I've done, and I have estimated the first equation with the following instruments: lag from 1 to p for all three variables. Then, the second equation was estimated by using the same instruments as the first plus the residual of the first equation.
In the third and last equation, since there are no regressors correlated with the residual, it was estimated by OLS, by using as additional regressors the residuals of the first and second equation.
Once I've done it, what should I do next to estimate the VAR?
Thanks in advance

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