Abstract :
We consider estimation of parameters in a regression model with endogenous regressors.
The endogenous regressors along with a large number of other endogenous
variables are driven by a small number of unobservable exogenous common factors.
We show that the estimated common factors can be used as instrumental variables
and they are more efficient than the observed variables in our framework. Whereas
standard optimal generalized method of moments estimator using a large number of
instruments is biased and can be inconsistent, the factor instrumental variable estimator
(FIV) is shown to be consistent and asymptotically normal, even if the number
of instruments exceeds the sample size. Furthermore, FIV remains consistent even
if the observed variables are invalid instruments as long as the unobserved common
components are valid instruments.We also consider estimating panel data models in
which all regressors are endogenous but share exogenous common factors.We show
that valid instruments can be constructed from the endogenous regressors. Although
single equation FIV requires no bias correction, the faster convergence rate of the
panel estimator is such that a bias correction is necessary to obtain a zero-centered
normal distribution.
