From several sites I found it says it does not have any affect; See below.
The hair shaft naturally tapers at the end, so what you typically see are the thinnest portions of your hair. When you shave, however, you are crossing the midshaft and exposing the thicker part of the hair, making it seem as if each individual strand is taking up a bit more space. Moreover, the stubble feels stiffer because it's shorter and cut straight across (body hair feels softer as it gets longer). Even the apparent darkening of the cut hair is an illusion — it appears darker because you are now seeing the hair dots directly against the backdrop of your normal skin color.
Scientists have actually conducted studies to test whether shaving affects hair growth. In a 1928 study published in the journal Anatomical Record, forensic anthropologist Mildred Trotter found that shaving has no effect on hair's color, texture or growth rate. More recently, research published in the Journal of Investigative Dermatology also looked at this tale. "No significant differences in total weight of hair produced in a measured area, or in width or rate of growth of individual hairs, could be ascribed to shaving," the researchers concluded in their 1970 study.
Does Shaving Really Cause Hair to Grow Back Thicker and Coarser? | Old Wives' Tales
Does shaving really make hair grow back thicker? - HowStuffWorks
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