lfe (version 2.0-1570)

condfstat: Compute conditional F statistic for weak instruments in an IV-estimation with multiple endogenous variables.

Description

When using multiple instruments for multiple endogenous variables, the ordinary individual t-tests for the instruments in the first stage do not always reveal a weak set of instruments. Conditional F statistics can be used for such testing.

Usage

condfstat(object, type='default')

Arguments

object

object of class "felm", a result of a call to felm.

type

character. Error structure. Passed to waldtest. If NULL, both iid and robust Fs are returned.

Value

• A p x k matrix, where k is the number of endogenous variables. Each row are the conditional F statistics on a residual equation as described in Sanderson and Windmeijer (2014), for a certain error structure. The default is to use iid, or cluster if a cluster was specified to felm. The third choice is 'robust', for heteroskedastic errors. If type=NULL, iid and robust Fs are returned, and cluster, if that was specified to felm.

  Note that for these F statistics it is not the p-value that matters, it is the F statistic itself which (coincidentally) pops up in the denominator for the asymptotic bias of the IV estimates, and thus a large F is beneficial. This F statistic is not known to have the same interpretation for heteroskedastic and clustered errors.

References

Sanderson, E. and F. Windmeijer (2014) A weak instrument F-test in linear IV models with multiple endogenous variables, Disc. Paper 14/644, Univ of Bristol. http://www.efm.bris.ac.uk/economics/working_papers/pdffiles/dp14644.pdf

Examples

set.seed(43)
z1 <- rnorm(4000)
z2 <- rnorm(length(z1))
u <- rnorm(length(z1))
# make x1, x2 correlated with errors u

x1 <- z1 + z2 + 0.2*u + rnorm(length(z1))
x2 <- z1 + 0.95*z2 - 0.3*u + rnorm(length(z1))
y <- x1 + x2 + u
est <- felm(y ~ 1 | 0 | (x1 | x2 ~ z1 + z2))
summary(est$stage1, lhs='x1')
summary(est$stage1, lhs='x2')
summary(est)
# everything above looks fine, t-tests for instruments, 
# as well as F-tests for excluded instruments in the 1st stages.
# The standard errors are large, though
# However, the conditional F-test reveals that the instruments are weak
# (it's close to being only one instrument, z1+z2, for both x1 and x2)
condfstat(est,type=NULL)