  Tensions in cosmological parameters measurement motivate a revisit of the
effects of instrumental systematics. In this article, we focus on the Pearson's
correlation coefficient of the cosmic microwave background temperature and
polarization E modes $\mathcal{R}_\ell^{\rm TE}$ which has the property of not
being biased by multiplicative instrumental systematics. We build a
$\mathcal{R}_\ell^{\rm TE}$-based likelihood for the Planck data, and present
the first constraints on $\Lambda$CDM parameters from the correlation
coefficient. Our results are compatible with parameters derived from a power
spectra based likelihood. In particular the value of the Hubble parameter $H_0$
characterizing the expansion of the Universe today, 67.5 $\pm$ 1.3 km/s/Mpc, is
consistent with the ones inferred from standard CMB analysis. We also discuss
the consistency of the Planck correlation coefficient with the one computed
from the most recent ACTPol power spectra.
