The nice thing about retaliatory tariffs, is that if they succeed, China will stop subsidizing industries. This is not good because the US will export more; it's good because it decreases price distortions. Wealth (on a global scale) increases. But such tariffs can back-fire if China doesn't back down. Instead of having one problem, you have two.
Suppose China will remove subsidies at a probability of x. If W is world wealth, S is the effect subsidies have on world wealth, and T is the effect tariffs have on world wealth, the US (assume the US cares about the world's wealth, not just American wealth) should not threaten a tariff if:
W - S > W - (1 - x)(S + T)
S < (1 - x)(S + T)
If that equation looks familiar to you, then bravo to you! It's the Learned Hand Rule. To quote the Wikipedia entry,
an act is in breach of the duty of care if:In other words, you're held liable for something if it was cheaper to remove the possibility of the bad thing from happening than it was to suffer the bad thing, weighted by the probability that the bad thing would happen. For example, it's easy to install a guardrail, likely someone will fall and very harmful if the person falls. So if you don't install a guardrail and someone falls, you're held liable.
B < PL
where B is the cost (burden) of taking precautions, and P is the probability of loss (L). L is the gravity of loss. The product of P x L must be a greater amount than B to create a duty of due care for the defendant.
My equation runs a similar vein, though you tolerate a subsidy instead of put up a guardrail. If the cost of suffering the subsidy is less than cost of the subsidy and tariff, adjusted for probability, you shouldn't threaten a tariff. Not tolerating the subsidy is negligent as threatening the tariff exposes the world economy to an inefficient level of risk.
Let's rewrite the equation:
S/T < (1-x)/x
If the above inequality holds, then threatening a tariff would be negligent. Let's summarize the right handed side with a graph. If S/T is above the line, you should threaten the tariff; if below, you should not.
Suppose we agree that subsidies and tariffs have an equally negative impact on wealth, or S/T is one. That means if x < 0.5 (Chinese have less than even odds at backing down), don't threaten. If x > 0.5, then you should threaten. Yes, you can get into a lot about reputation building, threatening (and following through) even if x is low in an attempt to increase x. But this post is already quite long and would make this model very complex.
It's politically harder to get rid of subsidies than tariffs, I'd wager, since tariffs are a tax and people love seeing their taxes fall. Therefore, S > T because the long term damage is higher. But it also means x is lower than we thought since it's harder for the government to give up something that is so popular. Assume S is twice as bad as T (S/T = 2) because it is twice as hard as we thought to get rid of (x is 0.5x). Because of the curve of the graph, x would have to be 0.67 (before adjusting for the change due to political viability) before you get the same payoff threatening a tariff as you do letting the subsidy stand. That's higher than the even odds I mentioned earlier.
The point of this post is to get us to think more about retaliatory tariffs as an efficiency goal, not a justice goal. Lots of people point to "leveling the playing field" and "fairness" when they advocate retaliatory tariffs, as if the aim is to punish people for wrong doing. But that's a means to an end, which is to stop subsidies. Recognizing that some subsidies aren't worth the risk of retaliation is the first step to being smarter about trade policy.