Hair does not grow any faster and does not get any thicker if you shave. As hair grows out, however, the blunt tip of the hair may cause the area to feel coarse or "stubbly" for a short period of time. A hair fiber is made of a protein called keratin. The visible portion of the hair that is cut by shaving has no biological activity. Since this "dead" hair shaft cannot send information about being cut to the hair follicle (the site of hair growth), growth continues as usual. Similarly, clipping a fingernail, also made of keratin, does not cause the fingernail to grow any slower or faster because it was trimmed.
Early research done in 1928 by forensic anthropologist Mildred Trotter, published in the journal, Anatomical Record, found that shaving had no effect on hair color, texture or growth rate. More recently, a study in the Journal of Investigative Dermatology also concluded, "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."
False: Shaving does NOT cause hair to grow back thicker.