Alex Tabarrok runs through the basic microeconomics of export restrictions and says that while there may be particular cases where sound arguments about spillovers or some such exist, "the basic analysis suggest we should be wary of such arguments."
I tend to agree. But he brings this up in the specific case of natural gas exports where I don't think the generic analysis is the best one. Not because there's anything wrong with trade theory but because natural resources are different from manufactured goods. Natural gas wealth is essentially a form of land wealth and taxes on land are the most efficient kind of taxes. So an export restriction that redistributes wealth from owners of gas-rich land to consumers of energy (which is to say basically everyone) is much more benign than trying to help domestic consumers of airplanes by restricting exports of made-in-America planes.
Another way of putting it is that the total quantity of natural gas located in North America is not impacted by American public policy. If restrict airplane exports, fewer planes will be manufactured. If we restrict gas exports, gas will be extracted at a slower rate but the gas still exists.
That said, natural gas export restrictions clearly aren't optimal public policy. What you ought to do is explicitly tax gas production (rather than subsidizing it through the tax code as we currently do)_and then let gas extractors sell it to wherever market conditions take the gas. But holding the rest of the policy options constant, I think there's a decent case for the export restrictions option. If at some point export restrictions cause the U.S. gas extraction rate to fall precipitously, I would want to revisit that policy. But as long as domestic demand alone is sufficient to drive rising levels of extraction, blocking exports seems like a reasonably sound quasi-Georgist measure.