We experimentally study the coherence time of a below-threshold Raman laser in which the gain medium is a gas of magneto-optically trapped atoms. The second-order optical coherence exhibits photon bunching with a correlation time which is varied by two orders of magnitude by controlling the gain. Results are in good agreement with a simple analytic model which suggests the effect is dominated by gain, rather than dispersion, in this system. Cavity ring-down measurements show the photon lifetime, related to the first-order coherence time, is also increased.