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.