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 ${\mathcal{R}}_{\ell }^{\mathrm{TE}}$, which has the property of not being biased by multiplicative instrumental systematics. We build a ${\mathcal{R}}_{\ell }^{\mathrm{TE}}$-based likelihood for the Planck data and present the first constraints on $\mathrm{\Lambda }\mathrm{CDM}$ (Lambda cold dark matter) 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, $67.5\pm 1.3\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$, is consistent with the ones inferred from standard cosmic microwave background analysis. We also discuss the consistency of the Planck correlation coefficient with the one computed from the most recent ACTPol power spectra.