Here's an excerpt from a very interesting new paper by Doug Irwin and Anson Soderbery:
What objective is a government trying to achieve in setting import tariffs? ... what factors would drive government behavior in the absence of such agreements when countries have complete autonomy in setting tariff rates? It could be for purely domestic reasons, partly based on social welfare and partly based on industry influence, as in the Grossman and Helpman (1994) "protection for sale" model. Or it could be the desire to impose optimal tariffs that maximize the national advantage through terms-of-trade manipulation. It is difficult to answer this question because the existence of cooperative trade agreements in recent decades does not allow us to observe unconstrained, non-cooperative trade policies by major countries such as the United States that might have both a terms-of-trade motive for tariffs and also be susceptible to producer and consumer interests. ...
This paper seeks to shed light on non-cooperative tariff setting in a large country by looking at the United States in a unique historical period when its tariff policy was unconstrained by international agreements and was therefore set purely for domestic reasons, not in multilateral negotiations. We focus on the late 1920s and early 1930s, around the time of the Smoot-Hawley tariff of 1930, a period when tariffs were the only major instrument of trade policy (import quotas were not yet employed) and industry lobbying was fairly transparent as revealed in the Congressional hearings on the tariff schedule. At the same time, as the world’s largest economy, the United States was likely to have had market power vis-a-vis imports and therefore may have benefited from an optimal tariff in the absence of retaliation. The availability of highly detailed import data allows us to estimate trade elasticities at what today would be considered the 4-digit level. Thus, in this historical period when the U.S. policymakers (members of Congress) had complete discretion in setting tariffs, we can examine whether tariffs were set on the basis of market power (trade elasticities) or domestic political factors (industry lobbying) and to determine the relative weights placed on both.
... We find that the median (inverse) export supply elasticity implies a median optimal tariff of 14 percent and that there is a weak but positive relationship between the implied optimal and actual applied tariff. In Section 4 we introduce lobbying and find that these political-economy determinants of tariffs slightly dominate the terms of trade factors in explaining the pattern of tariffs across goods. We also decompose the applied tariffs into lobbying and terms of trade components, suggesting that about half of the tariff level is due to firm lobbying with the remainder split between worker lobbies and terms-of-trade factors.
Over on Twitter, I asked Doug this question: "In cases where the tariff was an optimal one, do you think that was more a result of skilled calculation or dumb luck?" His response was: "Knowing what I know about the political process, luck! US didn't impose tariffs on coffee, silk, etc where arguably there would have been a terms of trade gain because there was no industry lobbying for tariffs."