Export taxes and import tariff have symmetric effects on trade.
International trade depends on relative price, p1/p2 = p*1/p*2, but trade restriction distorts domestic prices and creates a gap between the two relative prices. In the absence of tariffs or export taxes, p1/p2 = p*1/p*2,
The home country taxes export.
p*1 = p1(1 + x),
p*2 = p2.
The home country imposes a tariff on imports.
p1 = p*1,p2 = p*2(1 + t).
Thus, if t = x, then export taxes and import tariffs have the same effect on trade. However, export taxes are not used in the U.S; they are often used by infant governments or LDCs.
While the symmetry theorem is correct in the two-commodity world, countries trade innumerable commodities in the real world. If trade is balanced, the symmetry theorem can still work. A 10% export tax on all exportable goods has the same effect on trade as an equal (10%) tariff on all imports. However, this symmetry theorem is not practical, because trade is almost always not balanced.
The symmetry theorem also does not work in the presence of nontraded goods. A 10% tax on either exports or imports creates the same gap, (p*1/p*2)/(p1/p2).
In practice, nontraded goods account for a significant share of GDP, the Lerner symmetry theorem does not work. However, any export tax designed to raise the world price of the exportable necessarily raises the relative prices of the importables and has a protective effect on the import sectors.