I picked up a copy of it today from a library. It essentially makes three points.
First - they argue that the south recognized how a rudimentary concept of the Laffer curve worked when it came to taxation. They argue that the concept was at least known prior to the war, and that it made its way into confederate policy, confederate tariffs, and the confederate constitution. Their evidence is mostly a matter of referenced fact.
Second - they argue the theory of the laffer curve and how it would apply in the case of the tariff issue. This part is economic theory.
Third - they argue that the tariff issue was more prominent in secession's causes than many historians hold and point to various events demonstrating this. Among the items they point to are historical tariff rates spiking upward after the Morrill bill, the actuality of the Morrill bill's pre-war introduction and the clear sectional split over it in the House before the election, the GOP and northern endorsement of the tariff, and the tariff issue's prominence during the drafting of the confederate constitution. This last part is based heavily on notes and letters about the drafting by one of the delegates.
The article does not conclusively declare the tariff to be the sole issue nor did it ever intend to. It does demonstrate that it was an issue, some of the economic implications of it as an issue, and reason for its greater consideration as a cause in secession than has been afforded in recent years.
The "upward spike" in tariff rates is due first to the withdrawal of Southern Senators and Representatives from Congress and secondly to the necessity of financing the war. Higher taxes, North and South, were the rule during the war.
Do they mention the support of James Buchanan and other Democrats for an upward revision of tariffs to pay for the deficit? Regardless of what we think about the economic wisdom of this, a modest increase in tariff rates was apparently a relatively uncontroversial proposal in the early Buchanan administration.
Do they mention sugar tariffs? It's been alleged that the Confederacy retained the protective sugar tariff to please Louisiana. If true, it's a blow to the views attributed to the article's authors and to their whole reading of the Confederate Constitution.
And of course, an area under blockade was not likely to get much from import tariffs. One would have to consider other taxes as well, such as the income tax, capital levies, labor requisitions, excise taxes, the export tax, and the "hidden tax" of inflation. Military needs led the Confederate government to establish a highly centralized and bureaucratized comparatively high-tax wartime regime. There may be some truth in a snapshot view of Confederate attitudes towards tariffs in 1861, but since we don't know what tax policies the Confederacy would eventually have pursued, it's hard to make a comparison to subsequent US tax history.
Given that a revolt against higher taxes led to the nation's founding, it would be surprising if no one in 19th century America argued that lower taxes would stimulate economic activity. But what distinguished Jefferson Davis's South from Ronald Reagan's America is the largely colonial character of region. Lower import duties might bring some economic stimulation, but would not necessarily promote the development of industry or economic independence. Low tariffs promoted an agrarian economy that was dependent on foreign markets for its raw materials. It was natural that those who weren't a part of this colonial arrangement would be economically marginalized and wish for industrial stimulation.
Ronald Reagan's America already had a highly trained workforce, a comprehensive transportation network, and a developed industrial and commercial infrastructure. The fear in the mid-nineteenth century was that an America which devoted itself to providing raw materials for foreign manufacturers would never have developed such institutions. To some degree this became a North vs. South issue, but the development of industry clearly would have benefited poor Southern Whites and however many or few free Blacks as lived there. It would also have had national or regional defense benefits. But it conflicted with the slave-based, export crop economy and the power of the dominant class.
That's not to say that the low tariff side was wrong or that industrial development was a wholly good thing. Many of us would have preferred an agrarian country, if that option hadn't been bundled with slavery. I just point out that 1861 was not 1981, and the context surrounding tax and tariff questions was very different for Davis and Reagan. To ignore the colonial elements in the Southern economy of the day is to leave something very important out of the picture.