maylsm 发表于 2009-8-17 22:59
Testing for instruments exogeneity

To test for the instruments exogeneity we must have more
instruments than endogenous explanatory variables, i.e. the model
should be overidentified .

The “ test for overidentifying restrictions” can be used to check
for IV exogeneity.

The null hypothesis of the test is “ All instruments are valid”

If the null hypothesis is true, the test statistic will have a chisquared
distribution with degrees of freedom equal to the number
of surplus instruments (overidentifying restrictions).

If the null hypothesis is rejected, it means that at least one of the
instruments is not exogenous or valid.

Unfortunately, the test cannot tell which of the instruments
are not valid.


This is the minimum requirement: we need to have at least as
many instruments as endogenous explanatory variables.

When there are just as many instruments as endogenous
variables, the model is said to be just identified.

If we have more instruments than is strictly necessary, we say
that the model is overidentified.

The number of surplus instruments is sometimes called the
number of overidentifying restrictions.

A model can have a mixture of endogenous and exogenous
explanatory variables.