An electron carries an electric charge. A stationary electron creates no magnetic field. (Like a wire with no current). An electron moving at constant velocity generates a steady magnetic field, but (like a stationary magnet in a coil of wire) a constant magnetic field won't result in another electric field. An electron moving with a CHANGING velocity (ie. accelerating), however, generates a CHANGING magnetic field, which WILL produce a changing electric field, which produces a changing magnetic field, etc. In other words, it generates an electromagnetic wave.