This paper studies the effects of different types of research policy on economic growth. We find that while tax incentives to private research, public funding of private projects, and basic research performed at public institutions have unambiguously positive effects on economic growth, performing applied research at public institutions could have negative growth effects. This is due to the large crowding out of private research caused by public R\&D when it competes with private firms in the "patent race". Concerning the effects of these policies on welfare, it is found that research policy can either improve or reduce consumer welfare depending on the characteristics of the policy and that an excessively high research subsidy will reduce it.