Simultaneous equations bias?

Question

What is it? I don't really understand what is meant by this, in econometric terms. Also, what methods can be used to solve it? I think Instrumental variables is one way, as this reduces the variables in equations. Thanks,

Answer 1

I take this class next semester, might I recommend looking at the MIT open courseware as they do offer this course as a full download. Maybe if you looked at it being taught in a different perspective it would click!

Sorry I couldn't been of more help, give me 6 months!

Answer 2

When the OLS estimation is biased, then you can assume that you have an endogeneity bias (in other words, a simultaneous equations bias).

For example:

Let us assume the following framework (omitting the i subscripts on the variables):

    * qd = α0 + α1p + u

    * qs = β0 + β1p + v

    * qd = qs

If we regress qd on a constant and p in order to try to estimate the demand equation for some good, the OLS estimate of α1 is given by the formula α1OLS =Cov(p,q)/Var(p).

Let's  solve Cov(p,q) below:

    * Cov(p,q)=Cov(p, α0 + α1p + u)

    * = E(α0p + α1p2 + pu) - E(p)*E[α0 + α1p + u]

    * = α1Var(p) + Cov(p,u) [1]

To find Cov(p,u) we can solve the first system of equations above.

    * p= [(α0 - β0) + (u - v)]/(β1 - α1)

    * Cov(p,u)= Var(u)/(β1 - α1) [2]

So, substituting [2] into [1], we have:

    * Cov(p,q)= α1Var(p) + Var(u)/(β1 - α1)

Thus, our bias term for the OLS regression is:

    * Cov(p,q)/Var(p) - α1 = Cov(p,u)/Var(p) [3]

Since we see in equation [2] that Cov(p,u) is not equal to 0 unless Var(u) = 0—which is unlikely—we know the OLS estimate is biased.

What we have here is a simultaneous equations bias. The problem is that the error term (u) is correlated with the independent variable (p). The main way to solve this problem is to use an instrumental variables methodology.

Thus, RTFM

http://en.wikipedia.org/wiki/Instrumenta...

I hope this helps