Doug Irwin estimates the Anderson-Neary trade restrictiveness index for a century of US trade policy to calculate the costs of historic protectionism:
As Paul Krugman (1997, 127) has written: “Just how expensive is protectionism? The answer is a little embarrassing, because standard estimates of the costs of protection are actually very low. America is a case in point… The combined costs of these major restrictions to the U.S. economy, however, are usually estimated at less than half of 1 percent of U.S. national income.”
However, what has been true for the past few decades has not always been true. In the heyday of America’s high tariff policy in the late nineteenth century, the static welfare cost was closer to one percent of GDP, although the associated redistribution of income was much higher, about eight percent of GDP according to estimates by Irwin (2007). This large redistribution and associated deadweight loss may be one reason why the political debate over trade policy was much more intense a century ago than today. By the mid-twentieth century, the deadweight loss was only about one-tenth of one percent of GDP, which not only makes the historical figures of one percent of GDP seem much larger, but partly explains why, after the early 1930s, trade policy was no longer a leading political issue in the country as it had been in the late nineteenth century…
A fundamental reason for the relatively low cost of protection in the United States is that it has always had a large domestic economy that was not very dependent upon international trade. Another reason is that for most of its history the United States used import tariffs as opposed to more distortionary trade policy instruments, such as import quotas and import licenses. For example, the cost of U.S. trade restrictions was much higher in the 1970s and 1980s than decades before or after because quantitative restrictions and voluntary export restraints were used to limit imports of automobiles, textiles and apparel, iron and steel, semiconductors, and other products (de Melo and Tarr 1992, Feenstra 1992). Foregone quota rents are generally orders of magnitude larger than the tariff-induced distortions to domestic resource allocation.
My guess would be this study probably ultimately underestimates the damage done by protectionism. Much of the damage is done to the country’s trade partners, and prevent our partners from developing stronger, modern economies, which would in turn benefit the US more than a developing country as a trade partner. Subsidies are a good example of this, as are the treaties that the US signed with Japan and China.