Does inflation asymmetrically affect relative price variability?

The U-shaped relationship between inflation and price dispersion around nonzero inflation rate is due to the use of aggregate measure of relative price variability (RPV), which amounts to specification errors in a piecewise linear regression models. However, the true underlying relationship between inflation and inflation-induced RPV is found to be U-shaped around zero inflation and inflation seems to have asymmetric impact on price dispersion as predicted by menu cost models.