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st: Re: Simultaneous equations in panel data

From   Kit Baum <[email protected]>
To   Fardad Zand <[email protected]>
Subject   st: Re: Simultaneous equations in panel data
Date   Wed, 11 Feb 2009 09:20:30 -0500

Per the Statalist FAQ, questions from Statalist should lead to responses on Statalist.

(1) In a simultaneous equations model, this is obviously true; the whole point is that y1 may be the LHS of one equation and on the RHS of others. That by itself does not require systems estimation techniques.

(2) To apply cross-equation constraints you need a systems estimator, and the whole point is that a systems estimator for simultaneous equations of panel data may be hard to find.

(3) This is a FAQ; see various postings by Mark Schaffer and myself. There is nothing wrong with estimating an equation using IV techniques where one of the RHS endogenous variables is a dummy. IV yields consistent estimates.

(4) Yes, limited info techniques are single-equation estimation methods.

(5)You obviously have instruments if you have simultaneous equations. By definition, if you write down the whole system, all the variables that do not appear on the LHS of any equation are instruments for each equation in the system. Some will be included instruments, some will be excluded instruments. But if you cannot identify an equation via the order condition for single-equation estimation, you cannot solve the problem with a systems estimator.

(6) sureg is not a solution for simultaneous equations problems. It presumes that each equation is a proper OLS equation.

(7) No. If you have a set of linear simultaneous equations, each of which contains panel data with the potential for unobserved heterogeneity, the right way to approach estimation IMHO is with xtivreg2, fe or xtivreg2, fd. You could use xtivreg, re if it passed a Hausman test, but that is often problematic.

I don't think looking at the specifics would matter; if the setup is as stated in my (7) then no matter what the equations/variables are, that is likely to be the best way to go.

Kit Baum, Boston College Economics and DIW Berlin
An Introduction to Modern Econometrics Using Stata:

On Feb 10, 2009, at 10:00 , Fardad Zand wrote:

Dear Kit,

Thank you very much for your kind support through replying to my question posted on Statalist.

To further clarify the issue, I would like to ask you a few follow- up questions to find out the best approach to be followed:

1- You are referring to cross-equation correlations; I believe such correlations do exist as the endogenous variables are scattered among the different equations, sometimes as a dependent and sometimes as an independent. Yet, I don't know really how the correlations are or will be developed over time. Is there any way I can measure or estimate these correlations?

2- In case I want to define the cross-equation constraints in Stata how should I proceed?

3- Some of my dependent variables are contentious while others dummy. Does this fact pose any additional constrained on the method to use? The equations can have one or more endogenous variables.

4- You are referring to limited info techniques. If I understood it well, you mean estimating the equations separately using panel data techniques such as -xtreg. Right?

5- You are referring to -xtivreg(2). The problem is that I don't have access to reliable and good exogenous instruments. Is there any remedy to this?

6- You are also referring to -sureg. Is it a solution to my problem if I rely on limited info. do I still need to know the cross- equation correlations? What is the difference between using -sureg and 9 times (due to 9 equations) -xtreg or -xtprobit?

7- Do you think something like -gllamm will work for me at all?

I can send you the exact specification of my simultaneous equations set, if that will help you to advice and guide me.

I really appreciate your time and support in advance.

My best wishes from Holland,

ir. Fardad Zand
Researcher & PhD Candidate
MSc Management of Technology

Department of Economics & Management of Innovation
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Delft University of Technology

Kruisstraat 30
2611 MJ Delft
the Netherlands

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