As US power plants increasingly switch from coal to natural gas for purely economic reasons (see, e.g., here), we should not be quick to conclude that this is good news for the climate. For one thing, as many others have pointed out (see, e.g., here), incompletely combusted natural gas emits methane, which is a more powerful greenhouse gas (GHG) than carbon dioxide, the main GHG emitted from burning coal. However, methane remains in the atmosphere only about 10% as long as carbon dioxide, so the switch to natural gas is probably a net gain for the climate.
What many commentators fail to note, however, is that while the switch to natural gas has reduced overall US emissions of GHGs (see, e.g., here), we are still digging just as much coal out of the ground as we always have done, only instead of burning it ourselves we are exporting it to other countries to burn. See the chart below from Reuters.
Of course, coal exports are subject to fluctuation (just like many other goods) based on season or supply gluts. Just yesterday the Wall Street Journal reported (here) that exports of coal dropped 31% from March to April this year (which is less than the heating bill for my own house dropped during the same period). But the overall trend is clear: the coal we are not burning ourselves, we are exporting to fast-developing countries in Asia and elsewhere, for which coal still remains the cheapest, and dirtiest, source of energy.
We are not reducing the climate costs of coal by switching to natural gas; we are simply exporting them. The only way to fix that problem is to increase the price of coal as it comes out of the ground, e.g., via a tax on the carbon content of coal at the point of extraction. Of course, if other big coal using/exporting countries do not impose a similar tax, we would simply be shooting our economy in the foot, with no net effect on climate change, which remains very much a collective-action problem - a problem that cannot be resolved by one country acting alone.