Very useful. Running bright lights in the daytime significantly reduces accidents*. The brighter the light, the better. Planet Bike lights are not bright enough for daytime (or even night time, really) use. Look into a light with a minimum of 300 lumens (Cygolite, Nite Rider, etc) with 700+ being ideal.

*Madsen, J. C., Andersen, T., & Lahrmann, H. S. (January 01, 2013). Safety effects of permanent running lights for bicycles: A controlled experiment. Accident; Analysis and Prevention, 50, 820-9.