  We investigate the Lagrange multiplier formulation of teleparallel theories,
including f(T) gravity, in which the connection is not set to zero a priori and
compare it with the pure frame theory. We show explicitly that the two
formulations are equivalent, in the sense that the dynamical equations have the
same content. One consequence is that the manifestly local Lorentz invariant
f(T) theory cannot be expected to be free of pathologies, which were previously
found to plague f(T) gravity formulated in the usual pure frame approach.
