Becker and Heckman write in the WSJ?
We should cut federal government activities that can be performed at least as well by the private sector, and maintain, or even increase, productive federal activities that the private sector alone cannot handle effectively. There is legitimate disagreement about which activities belong in which category, but the great majority of economists have long agreed that the federal government should have an important role in the sponsorship of basic research. For-profit companies have weak incentives to invest in basic research partly because the results are not patentable, and partly because the culture of basic researchers, and the journals they publish in, makes the results of basic research available to all.
For these reasons the U.S. government has long played a leading role in supporting research in physics, chemistry, biology and medicine, and to a smaller extent in economics and other social sciences. It has also played a leading role in creating objective databases on which to make wise policy. This research and data have paid great dividends in helping to provide a better understanding of DNA, genetics and the human genome, and many other phenomena crucial to the modern world.HT: @MargRev.
Tyler Cowen's opinion is here.
How about developing countries? What the priority should be? Although there are unique characteristics in every country that could justify specific research, there is a lot of research done in the North America and Europe that could be applied or replicated in developing countries. In economics in particular, take for example the literature on RCTs. It will probably be cost effective to replicate private or public interventions that can have high impact. Some examples are here.