  Planck favours a negative running of the spectral index, with the likelihood
being dominated by low multipoles $l \lesssim 50$ and no preference for running
at higher $l$. A negative spectral index is also necessary for the 2-$\sigma$
Planck upper bound on the tensor-to-scalar ratio $r$ to be consistent with
values significantly larger than 0.1. Planck has also observed a hemispherical
asymmetry of the CMB power spectrum, again mostly at low multipoles. Here we
consider whether the physics responsible for the hemispherical asymmetry could
also account for the negative running of the spectral index and the consistency
of Planck with a large value of $r$. A negative running of the spectral index
can be generated if the hemispherical asymmetry is due to a scale- and
space-dependent modulation which suppresses the CMB power spectrum at low
multipoles. We show that the observed hemispherical asymmetry at low $l$ can be
generated while satisfying constraints on the asymmetry at higher $l$ and
generating a negative spectral index of the right magnitude to account for the
Planck observation and to allow Planck to be consistent with a large value of
$r$.
