  A recent article by Wojtak {\it et al} (arXiv:1504.00718) pointed out that
the local gravitational redshift, despite its smallness ($\sim 10^{-5}$), can
have a noticeable ($\sim 1\%$) systematic effect on our cosmological parameter
measurements. The authors studied a few extended cosmological models (nonflat
$\Lambda$CDM, $w$CDM, and $w_0$-$w_a$CDM) with a mock supernova data set. We
repeat this calculation and find that the $\sim 1\%$ biases are due to strong
degeneracy between cosmological parameters. When cosmic microwave background
(CMB) data are added to break the degeneracy, the biases due to local
gravitational redshift are negligible ($\lesssim 0.1 \sigma$).

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory