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December 06, 2005
Simultaneity
If the regressors are not exogenous, we need to worry about simultaneity bias. That is, the parameters estimates are inconsistent, which means that they are biased and the bias does not go away in large samples.
A basic supply and demand model nicely illustrates the main concepts. There are two curves in the model, and a regression tries to fit one line to the data.
Details:
Here is how both curves shifting generates the data. Shifts in either curves change both price and quantity.
Exclusion restrictions that cause a given variable to shift just one curve help to identify the other curve.
Indirect least squares shows how we can recover estimates of the structural parameters from the reduced form parameters if exogenous variables are excluded from some equations.
If an equation is identified, we can calculate consistent parameter estimates using two-stage least squares.
Posted by bparke at December 6, 2005 11:20 PM